Finite Group Databasebeta

← #7715641

Subgroups — #7715641

Order 512.

8436 conjugacy classes of subgroups.

The subgroup lattice has 1921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3546C211yesmaximal, characteristic, complemented
2C2×#3449C211yesmaximal, characteristic, complemented
3#49566C214yesmaximal, complemented
4#49547C212yesmaximal, complemented
5#49546C212yesmaximal, complemented
6#47853C214yesmaximal, complemented
7#47831C212yesmaximal, complemented
8#47830C212yesmaximal, complemented
9#47797C214yesmaximal, complemented
10#47794C214yesmaximal, complemented
11#47760C214yesmaximal, complemented
12#47689C214yesmaximal, complemented
13#37846C212yesmaximal, complemented
14#37844C212yesmaximal, complemented
15#37839C212yesmaximal, complemented
16#37836C212yesmaximal, complemented
17#37658C212yesmaximal, complemented
18#37657C212yesmaximal, complemented
19#37650C212yesmaximal, complemented
20#37648C212yesmaximal, complemented
21#37639C211yesmaximal, characteristic, complemented
22#37550C211yesmaximal, characteristic, complemented
23#37273C212yesmaximal, complemented
24#37272C212yesmaximal, complemented
25#35302C211yesmaximal, characteristic, complemented
26#35301C211yesmaximal, characteristic, complemented
27#35251C212yesmaximal, complemented
28#35250C212yesmaximal, complemented
29#34367C211yesmaximal, characteristic, complemented
30C23×#41C2212yescomplemented
31#3546—216no—
32C2×#560C2214yescomplemented
33C2×#556C2211yescharacteristic, complemented
34C2×#553C2212yescomplemented
35C2×#550C2211yescharacteristic, complemented
36C2×#550C2212yescomplemented
37C2×#547C2211yescharacteristic, complemented
38C2×#546C2212yescomplemented
39C2×#546C2212yescomplemented
40C2×D42C2211yescharacteristic, complemented
41C2×#542C2212yescomplemented
42C2×#538C2214yescomplemented
43#3449—216no—
44C2×#537C2211yescharacteristic
45C2×#537C2212yescomplemented
46C2×#537C2211yescharacteristic, complemented
47C2×#537C2212yescomplemented
48C2×#537C2212yescomplemented
49C2×#536C2212yescomplemented
50C2×#536C2212yescomplemented
51C2×#535C2212yes—
52C2×#535C2212yes—
53C2×#535C2212yescomplemented
54C2×#535C2212yescomplemented
55C2×#535C2212yescomplemented
56C2×#534C2211yescharacteristic
57C2×#534C2211yescharacteristic, complemented
58C2×#534C2212yescomplemented
59C2×#532C2211yescharacteristic
60C2×#532C2211yescharacteristic, complemented
61C2×#532C2211yescharacteristic, complemented
62C2×#532C2212yescomplemented
63C2×#529C2211yescharacteristic, complemented
64C2×#525C2212yes—
65C2×#525C2212yescomplemented
66C2×#525C2212yescomplemented
67C2×#525C2212yescomplemented
68C2×#525C2212yescomplemented
69C22×#121C2212yescomplemented
70C22×#117C2211yescharacteristic, complemented
71#2855C2211yescharacteristic, complemented
72#2854C2212yescomplemented
73#2854C2211yescharacteristic, complemented
74#2848C2212yescomplemented
75#2848C2211yescharacteristic, complemented
76#2847C2211yescharacteristic
77#2847C2212yescomplemented
78#2847C2212yescomplemented
79#2847C2212yescomplemented
80#2847C2212yescomplemented
81#2821C2212yescomplemented
82#2819C2214yescomplemented
83#2818C2212yescomplemented
84#2733C2214yescomplemented
85#2731C2214yescomplemented
86#2730C2214yescomplemented
87#2729C2214yescomplemented
88#2706C2214yescomplemented
89#2705C2214yescomplemented
90#2703C2214yescomplemented
91#2702C2214yescomplemented
92#2699C2214yescomplemented
93#2699C2214yescomplemented
94#2698C2214yescomplemented
95#2696C2214yescomplemented
96#2693C2214yescomplemented
97#2692C2214yescomplemented
98#2688C2214yescomplemented
99#2687C2214yescomplemented
100#2686C2214yescomplemented
101#2686C2214yescomplemented
102#2685C2214yescomplemented
103#2684C2214yescomplemented
104#2684C2214yescomplemented
105#2682C2214yescomplemented
106#2682C2214yescomplemented
107#2681C2214yescomplemented
108#2681C2214yescomplemented
109#2679C2214yescomplemented
110#2678C2214yescomplemented
111#2678C2214yescomplemented
112#2678C2214yescomplemented
113#2678C2214yescomplemented
114#2678C2214yescomplemented
115#2678C2214yescomplemented
116#2676C2214yescomplemented
117#2675C2214yescomplemented
118#2673C2214yescomplemented
119#2673C2214yescomplemented
120#2673C2214yescomplemented
121#2673C2214yescomplemented
122#2673C2214yescomplemented
123#2672C2214yescomplemented
124#2671C2214yescomplemented
125#2671C2214yescomplemented
126#2671C2214yescomplemented
127#2669C2214yescomplemented
128#2669C2214yescomplemented
129#2669C2214yescomplemented
130#2669C2214yescomplemented
131#2669C2214yescomplemented
132#2661C2214yescomplemented
133#2635C2212yescomplemented
134#2635C2212yescomplemented
135#2629C2212yescomplemented
136#2628C2212yescomplemented
137#2620C2212yescomplemented
138#2619C2214yescomplemented
139#2619C2212yescomplemented
140#2616C2212yescomplemented
141#2616C2212yescomplemented
142#2615C2212yes—
143#2615C2212yes—
144#2615C2212yescomplemented
145#2615C2212yescomplemented
146#2615C2212yescomplemented
147#2615C2212yescomplemented
148#2615C2212yescomplemented
149#2615C2212yescomplemented
150#2610C2214yescomplemented
151#2610C2214yescomplemented
152#2609C2214yescomplemented
153#2601C2214yescomplemented
154#2598C2214yescomplemented
155#2591C2212yescomplemented
156#2579C2212yescomplemented
157#2563C2212yescomplemented
158#2563C2212yescomplemented
159#2562C2211yescharacteristic, complemented
160#2562C2211yescharacteristic, complemented
161#2560C2214yescomplemented
162#2559C2214yescomplemented
163#2554C2214yescomplemented
164#2553C2214yescomplemented
165#2543C2214yescomplemented
166#2541C2212yescomplemented
167#2541C2212yescomplemented
168#2540C2211yescharacteristic, complemented
169#2540C2211yescharacteristic, complemented
170#2539C2214yescomplemented
171#2539C2212yescomplemented
172#2537C2212yescomplemented
173#2537C2212yescomplemented
174#2536C2212yescomplemented
175#2535C2212yescomplemented
176#2534C2212yescomplemented
177#2488C2214yescomplemented
178#2487C2212yescomplemented
179#2486C2212yescomplemented
180#2485C2212yescomplemented
181#2485C2212yescomplemented
182#2472C2214yescomplemented
183#2465C2214yescomplemented
184#2464C2214yescomplemented
185#2464C2214yescomplemented
186#2463C2214yescomplemented
187#2461C2214yescomplemented
188#2458C2214yescomplemented
189#2457C2214yescomplemented
190#2456C2214yescomplemented
191#2450C2214yescomplemented
192#2445C2214yescomplemented
193#2437C2214yescomplemented
194#2436C2214yescomplemented
195#2433C2214yescomplemented
196#2433C2214yescomplemented
197#2431C2214yescomplemented
198#2431C2214yescomplemented
199#2430C2214yescomplemented
200#2430C2214yescomplemented
201#2430C2214yescomplemented
202#2428C2214yescomplemented
203#2424C2214yescomplemented
204#2424C2214yescomplemented
205#2424C2214yescomplemented
206#2424C2214yescomplemented
207#2418C2214yescomplemented
208#2417C2212yescomplemented
209#2416C2212yescomplemented
210#2416C2212yescomplemented
211#2416C2212yescomplemented
212#2415C2212yescomplemented
213#2414C2212yescomplemented
214#2414C2212yescomplemented
215#2414C2212yescomplemented
216#2413C2212yescomplemented
217#2411C2212yescomplemented
218#2410C2214yescomplemented
219#2410C2214yescomplemented
220#2410C2214yescomplemented
221#2410C2214yescomplemented
222#2409C2214yescomplemented
223#2408C2212yescomplemented
224#2408C2214yescomplemented
225#2408C2212yescomplemented
226#2408C2214yescomplemented
227#2407C2212yescomplemented
228#2407C2212yescomplemented
229#2407C2214yescomplemented
230#2407C2214yescomplemented
231#2406C2212yescomplemented
232#2404C2214yescomplemented
233#2404C2214yescomplemented
234#2404C2214yescomplemented
235#2404C2212yescomplemented
236#2403C2214yescomplemented
237#2403C2214yescomplemented
238#2403C2214yescomplemented
239#2377C2212yescomplemented
240#2377C2212yescomplemented
241#2363C2214yescomplemented
242#2354C2212yescomplemented
243#2352C2212yescomplemented
244#2352C2212yescomplemented
245D4×C4⋊C4C2212yescomplemented
246#2337C2214yescomplemented
247#2331C2212yescomplemented
248#2328C2212yescomplemented
249#2324C2212yescomplemented
250#2324C2212yescomplemented
251#2324C2212yescomplemented
252#2323C2212yescomplemented
253#2311C2212yescomplemented
254#2311C2212yescomplemented
255#2311C2212yescomplemented
256#2311C2212yescomplemented
257#2285C2211yescharacteristic, complemented
258#2283C2211yescharacteristic, complemented
259#2280C2212yescomplemented
260C2×#380C2212yescomplemented
261C22×#41—216no—
262C22×#41—48no—
263C22×#41—48no—
264C22×#41C2312yes—
265C22×#41C2312yes—
266C22×#41C2312yes—
267C22×#41C2312yes—
268C22×#41C2312yes—
269C22×#41C2312yes—
270C22×#41C2312yes—
271C22×#41C2312yes—
272C22×#41C2312yes—
273C22×#41C2312yes—
274C22×#41C2312yes—
275C23×Q8C2312yes—
276C23×D4C2312yes—
277C23×D4C2312yes—
278C23×D4C2312yes—
279C23×D4C2312yes—
280C23×D4C2312yes—
281C23×D4C2314yes—
282C24×C4C2311yescharacteristic
283C24×C4C2312yes—
284C24×C4C2312yes—
285#560—232no—
286#556—28no—
287#553—216no—
288#550—216no—
289#550—28no—
290#547—28no—
291#546—216no—
292#546—216no—
293D42—28no—
294#542—216no—
295#538—232no—
296#537—216no—
297#537—28no—
298#537—28no—
299#537—216no—
300#537—48no—
301#536—216no—
302#536—216no—
303#535—216no—
304#535—216no—
305#535—216no—
306#535—216no—
307#535—48no—
308#534—28no—
309#534—28no—
310#534—216no—
311#532—216no—
312#532—28no—
313#532—28no—
314#532D4116yescomplemented
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×#127C2311yescharacteristic
320C2×#127C2311yescharacteristic
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2314yes—
324C2×#127C2314yes—
325C2×#127C2314yes—
326C2×#127C2311yescharacteristic
327#529—28no—
328C2×#126C2314yes—
329C2×#126C2312yes—
330C2×#126C2314yes—
331C2×#125C2311yescharacteristic
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2311yescharacteristic
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2312yes—
339C2×#124C2314yes—
340C2×#124C2312yes—
341#525—216no—
342#525—216no—
343#525—216no—
344#525—216no—
345#525—48no—
346C2×#123C2312yes—
347C2×#123C2312yes—
348C2×#123C2312yes—
349C2×#123C2312yes—
350C2×#123C2312yes—
351C2×#123C2312yes—
352C2×#123C2312yes—
353C2×#123C2312yes—
354C2×#123C2312yes—
355C2×#123C2314yes—
356C2×#123C2314yes—
357C2×#123C2314yes—
358C2×#123C2314yes—
359C2×#123C2314yes—
360C2×#123C2312yes—
361C2×#123C2314yes—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2312yes—
364C2×C22⋊Q8C2311yescharacteristic
365C2×C22⋊Q8C2312yes—
366C2×C22⋊Q8C2314yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2312yes—
369C2×C22⋊Q8C2312yes—
370C2×C22⋊Q8C2312yes—
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2312yes—
374C2×C22⋊Q8C2312yes—
375C2×C22⋊Q8C2312yes—
376C2×C22⋊Q8C2312yes—
377C2×C22⋊Q8C2314yes—
378C2×#121—48no—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2312yes—
383C2×#121C2311yescharacteristic
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2312yes—
387C2×#121C2312yes—
388C2×#121C2311yescharacteristic
389C2×#121C2311yescharacteristic
390C2×#121C2312yes—
391C2×#121C2314yes—
392C2×#121C2312yes—
393C2×#121C2314yes—
394C2×#121C2314yes—
395C2×#121C2312yes—
396C2×#121C2312yes—
397C2×#121C2312yes—
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2312yes—
401C2×#121C2312yes—
402C2×#121C2314yes—
403C2×#121C2314yes—
404C2×#121C2312yes—
405C2×#121C2312yes—
406C2×#121C2312yes—
407C2×#121C2312yes—
408C2×#121C2312yes—
409C2×#121C2314yes—
410C2×#121C2312yes—
411C2×#121C2312yes—
412C2×#121C2312yes—
413C2×#121C2312yes—
414C2×#121C2312yes—
415C2×#121C2312yes—
416C2×#121C2314yes—
417C2×#121C2314yes—
418C2×#121C2314yes—
419C2×#121C2314yes—
420C2×#121C2314yes—
421C2×#121C2314yes—
422C2×#121C2314yes—
423C2×#121C2314yes—
424C2×#121C2314yes—
425C2×#121C2314yes—
426C2×#121C2311yescharacteristic
427C2×#121C2312yes—
428C2×#121C2311yescharacteristic
429C2×#120C2312yes—
430C2×#120C2314yes—
431C2×#120C2314yes—
432C2×#120C2312yes—
433C2×#120C2312yes—
434C2×#120C2314yes—
435C2×#120C2312yes—
436C2×#120C2312yes—
437C2×#120C2312yes—
438C2×#120C2312yes—
439C2×#120C2312yes—
440C2×#120C2314yes—
441C2×#120C2314yes—
442C2×#120C2314yes—
443C2×#120C2314yes—
444C2×#120C2312yes—
445C2×#120C2314yes—
446C2×#120C2314yes—
447C2×#120C2314yes—
448C2×#120C2314yes—
449C2×#120C2314yes—
450C2×#120C2314yes—
451C2×C4×Q8C2311yescharacteristic
452C2×C4×Q8C2312yes—
453C2×C4×D4C2311yescharacteristic
454C2×C4×D4C2311yescharacteristic
455C2×C4×D4C2312yes—
456C2×C4×D4C2312yes—
457C2×C4×D4C2312yes—
458C2×C4×D4C2311yescharacteristic
459C2×C4×D4C2312yes—
460C2×C4×D4C2312yes—
461C2×C4×D4C2312yes—
462C2×C4×D4C2312yes—
463C2×C4×D4C2312yes—
464C2×C4×D4C2314yes—
465C2×C4×D4C2312yes—
466C2×C4×D4C2314yes—
467C2×C4×D4C2314yes—
468C2×C4×D4C2314yes—
469C2×C4×D4C2311yescharacteristic
470C2×C4×D4C2312yes—
471C2×C4×D4C2311yescharacteristic
472C2×#117—28no—
473C2×#117C2312yes—
474C2×#117C2312yes—
475C2×#117C2312yes—
476C2×#117C2312yes—
477C2×#117C2312yes—
478C2×#117C2312yes—
479C2×#117C2312yes—
480C2×#117C2312yes—
481C2×#117C2312yes—
482C22×C4⋊C4C2312yes—
483C22×C4⋊C4C2311yescharacteristic
484C22×C4⋊C4C2311yescharacteristic
485C22×C4⋊C4C2312yes—
486C22×C4⋊C4C2312yes—
487C22×C22⋊C4C2311yescharacteristic
488C22×C22⋊C4C2311yescharacteristic
489C22×C22⋊C4C2314yes—
490C22×C22⋊C4C2314yes—
491C22×C22⋊C4C2314yes—
492C22×C42C2311yescharacteristic
493C22×C42C2311yescharacteristic
494#400C2312yes—
495#400C2312yes—
496#400C2314yes—
497#400C2314yes—
498#399C2312yes—
499#399C2312yes—
500#399C2314yes—
501#399C2314yes—
502#398C2314yes—
503#398C2314yes—
504#398C2314yes—
505#398C2314yes—
506#398C2314yes—
507#397C2314yes—
508#397C2314yes—
509#397C2314yes—
510#397C2314yes—
511#397C2314yes—
512#396C2314yes—
513#396C2314yes—
514#396C2314yes—
515#396C2314yes—
516#396C2314yes—
517#396C2314yes—
518#396C2314yes—
519#396C2314yes—
520#395C2314yes—
521#395C2314yes—
522#395C2314yes—
523#394C2314yes—
524#394C2312yes—
525#394C2312yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2314yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2314yes—
542#394C2314yes—
543#394C2314yes—
544#394C2314yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#393C2314yes—
554#393C2314yes—
555#393C2314yes—
556#393C2314yes—
557#393C2314yes—
558#393C2314yes—
559#393C2314yes—
560#393C2314yes—
561#393C2314yes—
562#392C2314yes—
563#392C2312yes—
564#392C2312yes—
565#392C2314yes—
566#392C2314yes—
567#392C2314yes—
568#392C2314yes—
569#392C2314yes—
570#392C2314yes—
571#392C2314yes—
572#392C2314yes—
573#392C2314yes—
574#392C2314yes—
575#392C2314yes—
576#392C2314yes—
577#392C2314yes—
578#392C2314yes—
579#392C2314yes—
580#392C2314yes—
581#392C2314yes—
582#392C2314yes—
583#392C2314yes—
584#392C2314yes—
585#392C2314yes—
586#392C2314yes—
587#392C2314yes—
588#392C2314yes—
589#392C2314yes—
590#392C2314yes—
591#392C2314yes—
592#392C2314yes—
593#392C2314yes—
594#391C2314yes—
595#391C2314yes—
596#391C2314yes—
597#391C2314yes—
598#391C2312yes—
599#390C2314yes—
600#390C2314yes—
601#390C2314yes—
602#390C2314yes—
603#390C2314yes—
604#390C2314yes—
605#390C2314yes—
606#390C2312yes—
607#390C2312yes—
608#390C2312yes—
609#390C2314yes—
610#390C2314yes—
611#390C2314yes—
612#390C2314yes—
613#390C2314yes—
614#390C2314yes—
615#390C2314yes—
616#390C2314yes—
617#389C2312yes—
618#389C2314yes—
619#389C2312yes—
620#389C2312yes—
621#389C2312yes—
622#389C2314yes—
623#389C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2312yes—
662#386C2312yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2312yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#384C2312yes—
705#383C2312yes—
706#382C2314yes—
707#382C2312yes—
708#382C2312yes—
709#381C2312yes—
710#381C2312yes—
711#381C2314yes—
712#381C2314yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2314yes—
722#380C2314yes—
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2311yescharacteristic
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2314yes—
736#380C2314yes—
737#380C2314yes—
738#379C2312yes—
739#379C2314yes—
740#379C2314yes—
741#379C2314yes—
742#379C2314yes—
743C4×C4⋊C4C2314yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C22⋊C4C2314yes—
749C4×C22⋊C4C2312yes—
750C4×C22⋊C4C2314yes—
751C4×C22⋊C4C2314yes—
752C4×C22⋊C4C2314yes—
753#376C2312yes—
754C2×#95C2314yes—
755C25C2411yescharacteristic
756C25C2412yes—
757C25C2412yes—
758C25C2414yes—
759C2×#41—28no—
760C2×#41—28no—
761C2×#41—28no—
762C2×#41—28no—
763C2×#41—28no—
764C2×#41—28no—
765C2×#41—28no—
766C2×#41—28no—
767C2×#41—28no—
768C2×#41—28no—
769C2×#41—28no—
770C2×#41—28no—
771C2×#41—44no—
772C2×#41—44no—
773C2×#41—44no—
774C2×#41—44no—
775C2×#41—44no—
776C2×#41—44no—
777C2×#41—44no—
778C2×#41—44no—
779C2×#41—44no—
780C2×#41—44no—
781C2×#41—44no—
782C2×#41—44no—
783C2×#41—44no—
784C2×#41—44no—
785C2×#41—44no—
786C2×#41—44no—
787C2×#41—4128no—
788C2×#41—84no—
789C2×#41—84no—
790C2×#41C2×D4116yescomplemented
791C22×Q8—28no—
792C22×Q8—44no—
793C22×Q8—44no—
794C22×Q8C2411yescharacteristic
795C22×Q8C2412yes—
796C22×Q8C2412yes—
797C22×Q8C2412yes—
798C22×Q8C2412yes—
799C22×Q8C2412yes—
800C22×D4—28no—
801C22×D4—28no—
802C22×D4—28no—
803C22×D4—28no—
804C22×D4—28no—
805C22×D4—44no—
806C22×D4—44no—
807C22×D4—44no—
808C22×D4—44no—
809C22×D4—44no—
810C22×D4—44no—
811C22×D4—44no—
812C22×D4—44no—
813C22×D4—48no—
814C22×D4—84no—
815C22×D4—84no—
816C22×D4—84no—
817C22×D4C2411yescharacteristic
818C22×D4C2412yes—
819C22×D4C2412yes—
820C22×D4C2412yes—
821C22×D4C2412yes—
822C22×D4C2412yes—
823C22×D4C2412yes—
824C22×D4C2412yes—
825C22×D4C2412yes—
826C22×D4C2412yes—
827C22×D4C2414yes—
828C22×D4C2412yes—
829C22×D4C2411yescharacteristic
830C22×D4C2411yescharacteristic
831C22×D4C2412yes—
832C22×D4C2412yes—
833C22×D4C2414yes—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2414yes—
838C22×D4C2414yes—
839C22×D4C2414yes—
840C22×D4C2414yes—
841C22×D4C2414yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2412yes—
854C22×D4C2411yescharacteristic
855C22×D4C2411yescharacteristic
856C22×D4C2412yes—
857C22×D4C2412yes—
858C22×D4C2412yes—
859C23×C4—24no—
860C23×C4—28no—
861C23×C4—28no—
862C23×C4—28no—
863C23×C4—28no—
864C23×C4—28no—
865C23×C4—44no—
866C23×C4—44no—
867C23×C4C2411yescharacteristic
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2412yes—
874C23×C4C2412yes—
875C23×C4C2412yes—
876C23×C4C2412yes—
877C23×C4C2412yes—
878C23×C4C2412yes—
879C23×C4C2411yescharacteristic
880C23×C4C2412yes—
881C23×C4C2414yes—
882C23×C4C2411yescharacteristic
883C23×C4C2411yescharacteristic
884C23×C4C2414yes—
885C23×C4C2414yes—
886C23×C4C2412yes—
887C23×C4C2414yes—
888C23×C4C2414yes—
889C23×C4C2411yescharacteristic
890C23×C4C2411yescharacteristic
891C4⋊Q8—28no—
892C4⋊Q8—24no—
893C4⋊Q8—24no—
894C4⋊Q8C2×D418yescomplemented
895#127—28no—
896#127—28no—
897#127—216no—
898#127—24no—
899#127—24no—
900#127—48no—
901#127—84no—
902#127C2×D418yes—
903#126—216no—
904#126—216no—
905#126—28no—
906#125—24no—
907#124—28no—
908#124—216no—
909#124—28no—
910#124—28no—
911#124—24no—
912#124—28no—
913#124—28no—
914#124—48no—
915#124C2×D4116yescomplemented
916#123—28no—
917#123—28no—
918#123—28no—
919#123—28no—
920#123—28no—
921#123—216no—
922#123—28no—
923#123—28no—
924#123—28no—
925#123—28no—
926#123—216no—
927#123—216no—
928#123—48no—
929#123—82no—
930#123—84no—
931#123—84no—
932C22⋊Q8—216no—
933C22⋊Q8—24no—
934C22⋊Q8—28no—
935C22⋊Q8—28no—
936C22⋊Q8—28no—
937C22⋊Q8—28no—
938C22⋊Q8—28no—
939C22⋊Q8—28no—
940C22⋊Q8—28no—
941C22⋊Q8—28no—
942C22⋊Q8—28no—
943C22⋊Q8—28no—
944C22⋊Q8—28no—
945C22⋊Q8—48no—
946C22⋊Q8—44no—
947C22⋊Q8—44no—
948#121—28no—
949#121—28no—
950#121—28no—
951#121—28no—
952#121—28no—
953#121—28no—
954#121—28no—
955#121—28no—
956#121—216no—
957#121—216no—
958#121—216no—
959#121—216no—
960#121—24no—
961#121—24no—
962#121—24no—
963#121—28no—
964#121—28no—
965#121—28no—
966#121—28no—
967#121—28no—
968#121—28no—
969#121—28no—
970#121—28no—
971#121—28no—
972#121—28no—
973#121—28no—
974#121—28no—
975#121—28no—
976#121—28no—
977#121—216no—
978#121—216no—
979#121—48no—
980#121—48no—
981#121—48no—
982#121—48no—
983#121—44no—
984#121—44no—
985#121—44no—
986#121—44no—
987#121—44no—
988#121—44no—
989#121—48no—
990#121—84no—
991#121—84no—
992#121—84no—
993#121—84no—
994#121—84no—
995#121C2×D418yes—
996#121C2×D418yescomplemented
997#121C2×D4116yescomplemented
998#120—28no—
999#120—28no—
1000#120—28no—
1001#120—28no—
1002#120—216no—
1003#120—216no—
1004#120—216no—
1005#120—28no—
1006#120—28no—
1007#120—28no—
1008#120—28no—
1009#120—216no—
1010#120—48no—
1011#120—48no—
1012#120—48no—
1013#120—84no—
1014#120—84no—
1015#120—82no—
1016#120—84no—
1017#120—84no—
1018#120—84no—
1019#120—84no—
1020C4×Q8—28no—
1021C4×Q8—24no—
1022C4×D4—28no—
1023C4×D4—28no—
1024C4×D4—28no—
1025C4×D4—28no—
1026C4×D4—28no—
1027C4×D4—28no—
1028C4×D4—216no—
1029C4×D4—24no—
1030C4×D4—24no—
1031C4×D4—28no—
1032C4×D4—24no—
1033C4×D4—28no—
1034C4×D4—28no—
1035C4×D4—48no—
1036C4×D4—48no—
1037C4×D4—84no—
1038C4×D4C2×D418yes—
1039C4×D4C2×D4116yescomplemented
1040C4×D4C2×D418yescomplemented
1041#117—28no—
1042#117—28no—
1043#117—28no—
1044#117—28no—
1045#117—28no—
1046#117—28no—
1047#117—44no—
1048#117—44no—
1049#117—82no—
1050C2×C4⋊C4—24no—
1051C2×C4⋊C4—24no—
1052C2×C4⋊C4—28no—
1053C2×C4⋊C4—44no—
1054C2×C4⋊C4—44no—
1055C2×C4⋊C4C2411yescharacteristic
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2411yescharacteristic
1066C2×C4⋊C4C2412yes—
1067C2×C4⋊C4C2412yes—
1068C2×C4⋊C4C2412yes—
1069C2×C4⋊C4C2412yes—
1070C2×C4⋊C4C2411yescharacteristic
1071C2×C4⋊C4C2411yescharacteristic
1072C2×C4⋊C4C2412yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2412yes—
1075C2×C4⋊C4C2412yes—
1076C2×C4⋊C4C2412yes—
1077C2×C4⋊C4C2414yes—
1078C2×C4⋊C4C2412yes—
1079C2×C4⋊C4C2414yes—
1080C2×C4⋊C4C2412yes—
1081C2×C4⋊C4C2414yes—
1082C2×C4⋊C4C2414yes—
1083C2×C4⋊C4C2414yes—
1084C2×C4⋊C4C2414yes—
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2414yes—
1087C2×C4⋊C4C2414yes—
1088C2×C4⋊C4C2414yes—
1089C2×C4⋊C4C2414yes—
1090C2×C4⋊C4C2414yes—
1091C2×C4⋊C4C2411yescharacteristic
1092C2×C4⋊C4C2411yescharacteristic
1093C2×C4⋊C4C2412yes—
1094C2×C22⋊C4—24no—
1095C2×C22⋊C4—24no—
1096C2×C22⋊C4—216no—
1097C2×C22⋊C4—48no—
1098C2×C22⋊C4—84no—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2412yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2412yes—
1123C2×C22⋊C4C2412yes—
1124C2×C22⋊C4C2412yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2412yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2412yes—
1140C2×C22⋊C4C2412yes—
1141C2×C22⋊C4C2414yes—
1142C2×C22⋊C4C2414yes—
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2414yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2414yes—
1149C2×C22⋊C4C2414yes—
1150C2×C22⋊C4C2414yes—
1151C2×C22⋊C4C2414yes—
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2414yes—
1154C2×C22⋊C4C2414yes—
1155C2×C22⋊C4C2414yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2414yes—
1158C2×C22⋊C4C2414yes—
1159C2×C22⋊C4C2414yes—
1160C2×C22⋊C4C2414yes—
1161C2×C22⋊C4C2414yes—
1162C2×C22⋊C4C2414yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2414yes—
1165C2×C22⋊C4C2414yes—
1166C2×C22⋊C4C2412yes—
1167C2×C22⋊C4C2412yes—
1168C2×C22⋊C4C2412yes—
1169C2×C22⋊C4C2412yes—
1170C2×C42—24no—
1171C2×C42C2×D418yescomplemented
1172C2×C42C2412yes—
1173C2×C42C2412yes—
1174C2×C42C2412yes—
1175C2×C42C2414yes—
1176C2×C42C2414yes—
1177C2×C42C2414yes—
1178C2×C42C2414yes—
1179C2×C42C2412yes—
1180C2×C42C2412yes—
1181C2×C42C2411yescharacteristic
1182C2×C42C2411yescharacteristic
1183C2×C42C2411yescharacteristic
1184C2×C42C2411yescharacteristic
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2412yes—
1199#95C2414yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215C24—22no—
1216C24—24no—
1217C24—24no—
1218C24—24no—
1219C24—24no—
1220C24—24no—
1221C24—28no—
1222C24—42no—
1223C24—42no—
1224C24—42no—
1225C24—42no—
1226C24—42no—
1227C24—42no—
1228C24—44no—
1229C24—41no—
1230C24—42no—
1231C24—42no—
1232C24—42no—
1233C24—42no—
1234C24—41no—
1235C24—42no—
1236C24—44no—
1237C24—44no—
1238C24—44no—
1239C24—44no—
1240C24—44no—
1241C24C2512yes—
1242C24C2514yes—
1243C24C2512yes—
1244C24C2512yes—
1245C24C2512yes—
1246C24C2512yes—
1247C24C2511yescharacteristic
1248C24C2512yes—
1249#41—432no—
1250#41—432no—
1251#41—432no—
1252#41—432no—
1253#41—432no—
1254#41—432no—
1255#41—432no—
1256#41—432no—
1257#41—816no—
1258#41—816no—
1259#41—816no—
1260C2×Q8—22no—
1261C2×Q8—24no—
1262C2×Q8—24no—
1263C2×Q8—24no—
1264C2×Q8—24no—
1265C2×Q8—24no—
1266C2×Q8—24no—
1267C2×Q8—24no—
1268C2×Q8—42no—
1269C2×Q8—42no—
1270C2×Q8—42no—
1271C2×Q8—42no—
1272C2×Q8—42no—
1273C2×Q8—42no—
1274C2×Q8—44no—
1275C2×Q8—432no—
1276C2×Q8C22×D418yes—
1277C2×D4—24no—
1278C2×D4—24no—
1279C2×D4—24no—
1280C2×D4—24no—
1281C2×D4—24no—
1282C2×D4—24no—
1283C2×D4—24no—
1284C2×D4—24no—
1285C2×D4—24no—
1286C2×D4—24no—
1287C2×D4—24no—
1288C2×D4—24no—
1289C2×D4—24no—
1290C2×D4—24no—
1291C2×D4—24no—
1292C2×D4—28no—
1293C2×D4—28no—
1294C2×D4—28no—
1295C2×D4—28no—
1296C2×D4—28no—
1297C2×D4—28no—
1298C2×D4—28no—
1299C2×D4—28no—
1300C2×D4—22no—
1301C2×D4—24no—
1302C2×D4—24no—
1303C2×D4—24no—
1304C2×D4—24no—
1305C2×D4—24no—
1306C2×D4—24no—
1307C2×D4—24no—
1308C2×D4—22no—
1309C2×D4—22no—
1310C2×D4—28no—
1311C2×D4—24no—
1312C2×D4—24no—
1313C2×D4—24no—
1314C2×D4—24no—
1315C2×D4—24no—
1316C2×D4—42no—
1317C2×D4—42no—
1318C2×D4—42no—
1319C2×D4—42no—
1320C2×D4—42no—
1321C2×D4—42no—
1322C2×D4—42no—
1323C2×D4—42no—
1324C2×D4—42no—
1325C2×D4—42no—
1326C2×D4—42no—
1327C2×D4—42no—
1328C2×D4—42no—
1329C2×D4—42no—
1330C2×D4—42no—
1331C2×D4—42no—
1332C2×D4—42no—
1333C2×D4—42no—
1334C2×D4—42no—
1335C2×D4—42no—
1336C2×D4—44no—
1337C2×D4—42no—
1338C2×D4—42no—
1339C2×D4—432no—
1340C2×D4—44no—
1341C2×D4—44no—
1342C2×D4—44no—
1343C2×D4—42no—
1344C2×D4—42no—
1345C2×D4—44no—
1346C2×D4—44no—
1347C2×D4—42no—
1348C2×D4—44no—
1349C2×D4—44no—
1350C2×D4—44no—
1351C2×D4—44no—
1352C2×D4—44no—
1353C2×D4—44no—
1354C2×D4—44no—
1355C2×D4—44no—
1356C2×D4—44no—
1357C2×D4—44no—
1358C2×D4—44no—
1359C2×D4—44no—
1360C2×D4—42no—
1361C2×D4—42no—
1362C2×D4—42no—
1363C2×D4—42no—
1364C2×D4—42no—
1365C2×D4—44no—
1366C2×D4—44no—
1367C2×D4—44no—
1368C2×D4—44no—
1369C2×D4—44no—
1370C2×D4—42no—
1371C2×D4—44no—
1372C2×D4—44no—
1373C2×D4—42no—
1374C2×D4—42no—
1375C2×D4—44no—
1376C2×D4—42no—
1377C2×D4—42no—
1378C2×D4—44no—
1379C2×D4—42no—
1380C2×D4—42no—
1381C2×D4—42no—
1382C2×D4—44no—
1383C2×D4—44no—
1384C2×D4—44no—
1385C2×D4—44no—
1386C2×D4—44no—
1387C2×D4—44no—
1388C2×D4—44no—
1389C2×D4—44no—
1390C2×D4—44no—
1391C2×D4—44no—
1392C2×D4—432no—
1393C2×D4—432no—
1394C2×D4—816no—
1395C2×D4—816no—
1396C2×D4—832no—
1397C2×D4C22×D414yes—
1398C2×D4C22×D418yes—
1399C2×D4C22×D414yes—
1400C2×D4C22×D418yes—
1401C2×D4C22×D418yes—
1402C2×D4C22×D418yes—
1403C22×C4—232no—
1404C22×C4—22no—
1405C22×C4—24no—
1406C22×C4—24no—
1407C22×C4—24no—
1408C22×C4—24no—
1409C22×C4—24no—
1410C22×C4—24no—
1411C22×C4—24no—
1412C22×C4—24no—
1413C22×C4—24no—
1414C22×C4—24no—
1415C22×C4—24no—
1416C22×C4—24no—
1417C22×C4—24no—
1418C22×C4—24no—
1419C22×C4—24no—
1420C22×C4—22no—
1421C22×C4—22no—
1422C22×C4—28no—
1423C22×C4—24no—
1424C22×C4—24no—
1425C22×C4—24no—
1426C22×C4—24no—
1427C22×C4—24no—
1428C22×C4—24no—
1429C22×C4—24no—
1430C22×C4—24no—
1431C22×C4—24no—
1432C22×C4—24no—
1433C22×C4—24no—
1434C22×C4—24no—
1435C22×C4—24no—
1436C22×C4—24no—
1437C22×C4—24no—
1438C22×C4—28no—
1439C22×C4—28no—
1440C22×C4—41no—
1441C22×C4—42no—
1442C22×C4—42no—
1443C22×C4—42no—
1444C22×C4—42no—
1445C22×C4—42no—
1446C22×C4—42no—
1447C22×C4—41no—
1448C22×C4—44no—
1449C22×C4—42no—
1450C22×C4—432no—
1451C22×C4—432no—
1452C22×C4—44no—
1453C22×C4—44no—
1454C22×C4—44no—
1455C22×C4—44no—
1456C22×C4—44no—
1457C22×C4—44no—
1458C22×C4—44no—
1459C22×C4—44no—
1460C22×C4—41no—
1461C22×C4—42no—
1462C22×C4—44no—
1463C22×C4—41no—
1464C22×C4—44no—
1465C22×C4—44no—
1466C22×C4—44no—
1467C22×C4C22×D414yes—
1468C22×C4C22×D418yes—
1469C22×C4C22×D418yes—
1470C22×C4C22×D414yes—
1471C22×C4C22×D414yes—
1472C22×C4H(5,𝔽2)18yes—
1473C22×C4C2514yes—
1474C22×C4C2514yes—
1475C22×C4C2514yes—
1476C22×C4C2512yes—
1477C22×C4C2512yes—
1478C22×C4C2514yes—
1479C22×C4C2514yes—
1480C22×C4C2512yes—
1481C22×C4C2512yes—
1482C22×C4C2512yes—
1483C22×C4C2512yes—
1484C22×C4C2512yes—
1485C22×C4C2511yescharacteristic
1486C22×C4C2511yescharacteristic
1487C22×C4C2511yescharacteristic
1488C22×C4C2512yes—
1489C22×C4C2511yescharacteristic
1490C22×C4C2512yes—
1491C22×C4C2511yescharacteristic
1492C22×C4C2512yes—
1493C22×C4C2511yescharacteristic
1494C4⋊C4—22no—
1495C4⋊C4—24no—
1496C4⋊C4—24no—
1497C4⋊C4—24no—
1498C4⋊C4—24no—
1499C4⋊C4—24no—
1500C4⋊C4—28no—
1501C4⋊C4—22no—
1502C4⋊C4—24no—
1503C4⋊C4—24no—
1504C4⋊C4—24no—
1505C4⋊C4—24no—
1506C4⋊C4—24no—
1507C4⋊C4—24no—
1508C4⋊C4—24no—
1509C4⋊C4—24no—
1510C4⋊C4—22no—
1511C4⋊C4—22no—
1512C4⋊C4—24no—
1513C4⋊C4—28no—
1514C4⋊C4—24no—
1515C4⋊C4—24no—
1516C4⋊C4—24no—
1517C4⋊C4—24no—
1518C4⋊C4—24no—
1519C4⋊C4—28no—
1520C4⋊C4—44no—
1521C4⋊C4—44no—
1522C4⋊C4—44no—
1523C4⋊C4—44no—
1524C4⋊C4—44no—
1525C4⋊C4—44no—
1526C4⋊C4—44no—
1527C4⋊C4—44no—
1528C4⋊C4—44no—
1529C4⋊C4—44no—
1530C4⋊C4C22×D414yes—
1531C4⋊C4C22×D414yes—
1532C4⋊C4C22×D418yes—
1533C22⋊C4—28no—
1534C22⋊C4—28no—
1535C22⋊C4—24no—
1536C22⋊C4—24no—
1537C22⋊C4—24no—
1538C22⋊C4—24no—
1539C22⋊C4—24no—
1540C22⋊C4—28no—
1541C22⋊C4—24no—
1542C22⋊C4—24no—
1543C22⋊C4—24no—
1544C22⋊C4—24no—
1545C22⋊C4—24no—
1546C22⋊C4—28no—
1547C22⋊C4—24no—
1548C22⋊C4—24no—
1549C22⋊C4—24no—
1550C22⋊C4—28no—
1551C22⋊C4—24no—
1552C22⋊C4—24no—
1553C22⋊C4—24no—
1554C22⋊C4—24no—
1555C22⋊C4—24no—
1556C22⋊C4—24no—
1557C22⋊C4—24no—
1558C22⋊C4—24no—
1559C22⋊C4—28no—
1560C22⋊C4—28no—
1561C22⋊C4—28no—
1562C22⋊C4—28no—
1563C22⋊C4—28no—
1564C22⋊C4—28no—
1565C22⋊C4—44no—
1566C22⋊C4—44no—
1567C22⋊C4—44no—
1568C22⋊C4—44no—
1569C22⋊C4—44no—
1570C22⋊C4—44no—
1571C22⋊C4—44no—
1572C22⋊C4—44no—
1573C22⋊C4—44no—
1574C22⋊C4—44no—
1575C22⋊C4—42no—
1576C22⋊C4—42no—
1577C22⋊C4—44no—
1578C22⋊C4—44no—
1579C22⋊C4—44no—
1580C22⋊C4—44no—
1581C22⋊C4—44no—
1582C22⋊C4—44no—
1583C22⋊C4—44no—
1584C22⋊C4—44no—
1585C22⋊C4—44no—
1586C22⋊C4—44no—
1587C22⋊C4—44no—
1588C22⋊C4—44no—
1589C22⋊C4—44no—
1590C22⋊C4—44no—
1591C22⋊C4—44no—
1592C22⋊C4—44no—
1593C22⋊C4—44no—
1594C22⋊C4—44no—
1595C22⋊C4—44no—
1596C22⋊C4—44no—
1597C22⋊C4—44no—
1598C22⋊C4—44no—
1599C22⋊C4—44no—
1600C22⋊C4C22×D418yes—
1601C22⋊C4C22×D418yes—
1602C22⋊C4C22×D418yes—
1603C22⋊C4C22×D418yes—
1604C42—24no—
1605C42—24no—
1606C42—24no—
1607C42—28no—
1608C42—42no—
1609C42—44no—
1610C42—44no—
1611C42—44no—
1612C42—42no—
1613C42C22×D414yes—
1614C42C22×D414yes—
1615C42C22×D414yes—
1616C42C22×D414yes—
1617C23—28no—
1618C23—22no—
1619C23—22no—
1620C23—22no—
1621C23—22no—
1622C23—22no—
1623C23—22no—
1624C23—22no—
1625C23—21no—
1626C23—22no—
1627C23—22no—
1628C23—22no—
1629C23—22no—
1630C23—22no—
1631C23—22no—
1632C23—22no—
1633C23—22no—
1634C23—22no—
1635C23—22no—
1636C23—21no—
1637C23—22no—
1638C23—22no—
1639C23—22no—
1640C23—22no—
1641C23—22no—
1642C23—22no—
1643C23—24no—
1644C23—24no—
1645C23—24no—
1646C23—24no—
1647C23—22no—
1648C23—22no—
1649C23—22no—
1650C23—22no—
1651C23—22no—
1652C23—22no—
1653C23—24no—
1654C23—22no—
1655C23—22no—
1656C23—22no—
1657C23—22no—
1658C23—24no—
1659C23—24no—
1660C23—24no—
1661C23—22no—
1662C23—22no—
1663C23—24no—
1664C23—22no—
1665C23—22no—
1666C23—48no—
1667C23—48no—
1668C23—48no—
1669C23—48no—
1670C23—82no—
1671C23—84no—
1672C23—84no—
1673C23—82no—
1674C23—84no—
1675C23—84no—
1676C23—84no—
1677C23—84no—
1678C23—84no—
1679C23—84no—
1680C23—88no—
1681C23—88no—
1682C23—88no—
1683C23—84no—
1684C23—84no—
1685C23—84no—
1686C23—84no—
1687C23—88no—
1688C23—88no—
1689C23—164no—
1690C23—164no—
1691C23C23×D414yes—
1692C23C23×D414yes—
1693C23C23×D412yes—
1694C23C2×H(5,𝔽2)14yes—
1695C23C2611yescharacteristic
1696Q8—48no—
1697Q8—48no—
1698Q8—48no—
1699Q8—48no—
1700Q8—48no—
1701Q8—44no—
1702D4—48no—
1703D4—48no—
1704D4—48no—
1705D4—44no—
1706D4—48no—
1707D4—44no—
1708D4—48no—
1709D4—48no—
1710D4—48no—
1711D4—48no—
1712D4—48no—
1713D4—48no—
1714D4—48no—
1715D4—48no—
1716D4—48no—
1717D4—48no—
1718D4—44no—
1719D4—48no—
1720D4—82no—
1721D4—82no—
1722D4—84no—
1723D4—84no—
1724D4—88no—
1725D4—84no—
1726D4—84no—
1727D4—84no—
1728D4—84no—
1729D4—84no—
1730D4—88no—
1731D4—88no—
1732D4—88no—
1733D4—88no—
1734D4—88no—
1735D4—88no—
1736D4—88no—
1737D4—88no—
1738D4—88no—
1739D4—88no—
1740D4—88no—
1741D4—164no—
1742D4—164no—
1743D4—164no—
1744C2×C4—216no—
1745C2×C4—28no—
1746C2×C4—22no—
1747C2×C4—22no—
1748C2×C4—22no—
1749C2×C4—22no—
1750C2×C4—22no—
1751C2×C4—22no—
1752C2×C4—22no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—22no—
1756C2×C4—22no—
1757C2×C4—21no—
1758C2×C4—21no—
1759C2×C4—216no—
1760C2×C4—28no—
1761C2×C4—216no—
1762C2×C4—216no—
1763C2×C4—22no—
1764C2×C4—22no—
1765C2×C4—22no—
1766C2×C4—22no—
1767C2×C4—24no—
1768C2×C4—22no—
1769C2×C4—22no—
1770C2×C4—22no—
1771C2×C4—24no—
1772C2×C4—24no—
1773C2×C4—24no—
1774C2×C4—24no—
1775C2×C4—24no—
1776C2×C4—22no—
1777C2×C4—22no—
1778C2×C4—22no—
1779C2×C4—22no—
1780C2×C4—24no—
1781C2×C4—24no—
1782C2×C4—24no—
1783C2×C4—24no—
1784C2×C4—24no—
1785C2×C4—22no—
1786C2×C4—22no—
1787C2×C4—22no—
1788C2×C4—24no—
1789C2×C4—24no—
1790C2×C4—24no—
1791C2×C4—24no—
1792C2×C4—22no—
1793C2×C4—24no—
1794C2×C4—24no—
1795C2×C4—22no—
1796C2×C4—22no—
1797C2×C4—44no—
1798C2×C4—44no—
1799C2×C4—48no—
1800C2×C4—48no—
1801C2×C4—48no—
1802C2×C4—48no—
1803C2×C4—48no—
1804C2×C4—48no—
1805C2×C4—48no—
1806C2×C4—48no—
1807C2×C4—48no—
1808C2×C4—88no—
1809C2×C4—88no—
1810C2×C4—82no—
1811C2×C4—82no—
1812C2×C4—88no—
1813C2×C4—88no—
1814C2×C4—164no—
1815C2×C4C23×D412yes—
1816C2×C4C23×D412yes—
1817C2×C4C23×D414yes—
1818C2×C4C23×D412yes—
1819C2×C4C23×D412yes—
1820C2×C4C23×D412yes—
1821C2×C4C23×D414yes—
1822C2×C4C23×D412yes—
1823C2×C4C2×H(5,𝔽2)14yes—
1824C2×C4C2×H(5,𝔽2)14yes—
1825C22—24no—
1826C22—22no—
1827C22—24no—
1828C22—24no—
1829C22—22no—
1830C22—24no—
1831C22—24no—
1832C22—22no—
1833C22—24no—
1834C22—24no—
1835C22—24no—
1836C22—24no—
1837C22—42no—
1838C22—42no—
1839C22—42no—
1840C22—42no—
1841C22—42no—
1842C22—42no—
1843C22—42no—
1844C22—42no—
1845C22—42no—
1846C22—42no—
1847C22—42no—
1848C22—42no—
1849C22—42no—
1850C22—42no—
1851C22—42no—
1852C22—42no—
1853C22—44no—
1854C22—42no—
1855C22—42no—
1856C22—44no—
1857C22—42no—
1858C22—42no—
1859C22—42no—
1860C22—42no—
1861C22—44no—
1862C22—42no—
1863C22—42no—
1864C22—44no—
1865C22—42no—
1866C22—44no—
1867C22—44no—
1868C22—42no—
1869C22—42no—
1870C22—44no—
1871C22—42no—
1872C22—44no—
1873C22—42no—
1874C22—42no—
1875C22—42no—
1876C22—44no—
1877C22—88no—
1878C22—816no—
1879C22—816no—
1880C22—1616no—
1881C22C24×D411yescharacteristic
1882C22C22×H(5,𝔽2)12yes—
1883C22H(7,𝔽2)12yes—
1884C22H(7,𝔽2)11yescharacteristic
1885C222−1+611yescharacteristic
1886C4—24no—
1887C4—22no—
1888C4—24no—
1889C4—24no—
1890C4—22no—
1891C4—22no—
1892C4—22no—
1893C4—22no—
1894C4—42no—
1895C4—42no—
1896C4—42no—
1897C4—42no—
1898C4—44no—
1899C4—42no—
1900C4—42no—
1901C4—42no—
1902C4—44no—
1903C4—44no—
1904C4—44no—
1905C4—44no—
1906C4#348414yes—
1907C2—42no—
1908C2—44no—
1909C2—44no—
1910C2—44no—
1911C2—82no—
1912C2—82no—
1913C2—84no—
1914C2—82no—
1915C2C2×#348411yescharacteristic
1916C2#6285211yescharacteristic
1917C2#6285311yescharacteristic
1918C2#6287412yes—
1919C2#6287512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3546C2semidirect
2. C2×#3449C2semidirect
3. #49566C2semidirect
4. #49547C2semidirect
5. #49546C2semidirect
6. #47853C2semidirect
7. #47831C2semidirect
8. #47830C2semidirect
9. #47797C2semidirect
10. #47794C2semidirect
11. #47760C2semidirect
12. #47689C2semidirect
13. #37846C2semidirect
14. #37844C2semidirect
15. #37839C2semidirect
16. #37836C2semidirect
17. #37658C2semidirect
18. #37657C2semidirect
19. #37650C2semidirect
20. #37648C2semidirect
21. #37639C2semidirect
22. #37550C2semidirect
23. #37273C2semidirect
24. #37272C2semidirect
25. #35302C2semidirect
26. #35301C2semidirect
27. #35251C2semidirect
28. #35250C2semidirect
29. #34367C2semidirect
30. C23×#41C22semidirect
32. C2×#560C22semidirect
33. C2×#556C22semidirect
34. C2×#553C22semidirect
35. C2×#550C22semidirect
36. C2×#550C22semidirect
37. C2×#547C22semidirect
38. C2×#546C22semidirect
39. C2×#546C22semidirect
40. C2×D42C22semidirect
41. C2×#542C22semidirect
42. C2×#538C22semidirect
45. C2×#537C22semidirect
46. C2×#537C22semidirect
47. C2×#537C22semidirect
48. C2×#537C22semidirect
49. C2×#536C22semidirect
50. C2×#536C22semidirect
53. C2×#535C22semidirect
54. C2×#535C22semidirect
55. C2×#535C22semidirect
57. C2×#534C22semidirect
58. C2×#534C22semidirect
60. C2×#532C22semidirect
61. C2×#532C22semidirect
62. C2×#532C22semidirect
63. C2×#529C22semidirect
65. C2×#525C22semidirect
66. C2×#525C22semidirect
67. C2×#525C22semidirect
68. C2×#525C22semidirect
69. C22×#121C22semidirect
70. C22×#117C22semidirect
71. #2855C22semidirect
72. #2854C22semidirect
73. #2854C22semidirect
74. #2848C22semidirect
75. #2848C22semidirect
77. #2847C22semidirect
78. #2847C22semidirect
79. #2847C22semidirect
80. #2847C22semidirect
81. #2821C22semidirect
82. #2819C22semidirect
83. #2818C22semidirect
84. #2733C22semidirect
85. #2731C22semidirect
86. #2730C22semidirect
87. #2729C22semidirect
88. #2706C22semidirect
89. #2705C22semidirect
90. #2703C22semidirect
91. #2702C22semidirect
92. #2699C22semidirect
93. #2699C22semidirect
94. #2698C22semidirect
95. #2696C22semidirect
96. #2693C22semidirect
97. #2692C22semidirect
98. #2688C22semidirect
99. #2687C22semidirect
100. #2686C22semidirect
101. #2686C22semidirect
102. #2685C22semidirect
103. #2684C22semidirect
104. #2684C22semidirect
105. #2682C22semidirect
106. #2682C22semidirect
107. #2681C22semidirect
108. #2681C22semidirect
109. #2679C22semidirect
110. #2678C22semidirect
111. #2678C22semidirect
112. #2678C22semidirect
113. #2678C22semidirect
114. #2678C22semidirect
115. #2678C22semidirect
116. #2676C22semidirect
117. #2675C22semidirect
118. #2673C22semidirect
119. #2673C22semidirect
120. #2673C22semidirect
121. #2673C22semidirect
122. #2673C22semidirect
123. #2672C22semidirect
124. #2671C22semidirect
125. #2671C22semidirect
126. #2671C22semidirect
127. #2669C22semidirect
128. #2669C22semidirect
129. #2669C22semidirect
130. #2669C22semidirect
131. #2669C22semidirect
132. #2661C22semidirect
133. #2635C22semidirect
134. #2635C22semidirect
135. #2629C22semidirect
136. #2628C22semidirect
137. #2620C22semidirect
138. #2619C22semidirect
139. #2619C22semidirect
140. #2616C22semidirect
141. #2616C22semidirect
144. #2615C22semidirect
145. #2615C22semidirect
146. #2615C22semidirect
147. #2615C22semidirect
148. #2615C22semidirect
149. #2615C22semidirect
150. #2610C22semidirect
151. #2610C22semidirect
152. #2609C22semidirect
153. #2601C22semidirect
154. #2598C22semidirect
155. #2591C22semidirect
156. #2579C22semidirect
157. #2563C22semidirect
158. #2563C22semidirect
159. #2562C22semidirect
160. #2562C22semidirect
161. #2560C22semidirect
162. #2559C22semidirect
163. #2554C22semidirect
164. #2553C22semidirect
165. #2543C22semidirect
166. #2541C22semidirect
167. #2541C22semidirect
168. #2540C22semidirect
169. #2540C22semidirect
170. #2539C22semidirect
171. #2539C22semidirect
172. #2537C22semidirect
173. #2537C22semidirect
174. #2536C22semidirect
175. #2535C22semidirect
176. #2534C22semidirect
177. #2488C22semidirect
178. #2487C22semidirect
179. #2486C22semidirect
180. #2485C22semidirect
181. #2485C22semidirect
182. #2472C22semidirect
183. #2465C22semidirect
184. #2464C22semidirect
185. #2464C22semidirect
186. #2463C22semidirect
187. #2461C22semidirect
188. #2458C22semidirect
189. #2457C22semidirect
190. #2456C22semidirect
191. #2450C22semidirect
192. #2445C22semidirect
193. #2437C22semidirect
194. #2436C22semidirect
195. #2433C22semidirect
196. #2433C22semidirect
197. #2431C22semidirect
198. #2431C22semidirect
199. #2430C22semidirect
200. #2430C22semidirect
201. #2430C22semidirect
202. #2428C22semidirect
203. #2424C22semidirect
204. #2424C22semidirect
205. #2424C22semidirect
206. #2424C22semidirect
207. #2418C22semidirect
208. #2417C22semidirect
209. #2416C22semidirect
210. #2416C22semidirect
211. #2416C22semidirect
212. #2415C22semidirect
213. #2414C22semidirect
214. #2414C22semidirect
215. #2414C22semidirect
216. #2413C22semidirect
217. #2411C22semidirect
218. #2410C22semidirect
219. #2410C22semidirect
220. #2410C22semidirect
221. #2410C22semidirect
222. #2409C22semidirect
223. #2408C22semidirect
224. #2408C22semidirect
225. #2408C22semidirect
226. #2408C22semidirect
227. #2407C22semidirect
228. #2407C22semidirect
229. #2407C22semidirect
230. #2407C22semidirect
231. #2406C22semidirect
232. #2404C22semidirect
233. #2404C22semidirect
234. #2404C22semidirect
235. #2404C22semidirect
236. #2403C22semidirect
237. #2403C22semidirect
238. #2403C22semidirect
239. #2377C22semidirect
240. #2377C22semidirect
241. #2363C22semidirect
242. #2354C22semidirect
243. #2352C22semidirect
244. #2352C22semidirect
245. D4×C4⋊C4C22semidirect
246. #2337C22semidirect
247. #2331C22semidirect
248. #2328C22semidirect
249. #2324C22semidirect
250. #2324C22semidirect
251. #2324C22semidirect
252. #2323C22semidirect
253. #2311C22semidirect
254. #2311C22semidirect
255. #2311C22semidirect
256. #2311C22semidirect
257. #2285C22semidirect
258. #2283C22semidirect
259. #2280C22semidirect
260. C2×#380C22semidirect
314. #532D4semidirect
790. C2×#41C2×D4semidirect
894. C4⋊Q8C2×D4semidirect
915. #124C2×D4semidirect
996. #121C2×D4semidirect
997. #121C2×D4semidirect
1039. C4×D4C2×D4semidirect
1040. C4×D4C2×D4semidirect
1171. C2×C42C2×D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35462
C2×#34492
#495662
#495472
#495462
#478532
#478312
#478302
#477972
#477942
#477602
#476892
#378462
#378442
#378392
#378362
#376582
#376572
#376502
#376482
#376392
#375502
#372732
#372722
#353022
#353012
#352512
#352502
#343672