Finite Group Databasebeta

← #7732042

Subgroups — #7732042

Order 512.

7392 conjugacy classes of subgroups.

The subgroup lattice has 1867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3536C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic, complemented
3#49587C214yesmaximal, complemented
4#49584C214yesmaximal, complemented
5#47453C214yesmaximal, complemented
6#46375C214yesmaximal, complemented
7#43887C214yesmaximal, complemented
8#42999C214yesmaximal, complemented
9#39471C212yesmaximal, complemented
10#39420C212yesmaximal, complemented
11#39415C212yesmaximal, complemented
12#39375C212yesmaximal, complemented
13#39364C212yesmaximal, complemented
14#39335C212yesmaximal, complemented
15#38041C212yesmaximal, complemented
16#38035C212yesmaximal, complemented
17#37838C212yesmaximal, complemented
18#37648C212yesmaximal, complemented
19#37439C211yesmaximal, characteristic, complemented
20#37280C212yesmaximal, complemented
21#37272C212yesmaximal, complemented
22#36360C212yesmaximal, complemented
23#36275C212yesmaximal, complemented
24#35569C212yesmaximal, complemented
25#35564C212yesmaximal, complemented
26#35306C211yesmaximal, characteristic, complemented
27#35010C211yesmaximal, characteristic, complemented
28C2×#2414C211yesmaximal, characteristic, complemented
29#34202C211yesmaximal, characteristic, complemented
30#3536—216no—
31C2×#562C2214yescomplemented
32C2×#554C2212yes—
33C2×#548C2212yescomplemented
34C2×#547C2212yescomplemented
35C2×#546C2212yes—
36C2×#546C2214yes—
37#3460—216no—
38C2×#544C2211yescharacteristic
39C2×#543C2212yes—
40C2×#542C2212yescomplemented
41C2×#542C2212yescomplemented
42C2×#542C2212yescomplemented
43C2×#540C2212yescomplemented
44C2×#540C2212yescomplemented
45C2×#539C2212yescomplemented
46C2×#538C2212yes—
47C2×#538C2211yescharacteristic
48C2×#538C2212yes—
49C2×#538C2211yescharacteristic
50C2×#537C2211yescharacteristic
51C2×#537C2212yescomplemented
52C2×#537C2212yescomplemented
53C2×#537C2212yescomplemented
54C2×#536C2211yescharacteristic, complemented
55C2×#535C2212yes—
56C2×#532C2212yescomplemented
57C2×#532C2212yescomplemented
58C2×#529C2212yescomplemented
59C2×#529C2212yescomplemented
60C2×#525C2212yes—
61C2×#525C2211yescharacteristic
62C2×#525C2211yescharacteristic
63C22×C22⋊Q8C2211yescharacteristic
64C22×#121C2211yescharacteristic
65C22×#121C2211yescharacteristic
66C2×#520C2211yescharacteristic, complemented
67C2×C4×#41C2212yes—
68C22×C4×D4C2211yescharacteristic
69C22×#117C2211yescharacteristic
70#2857C2212yes—
71#2857C2212yescomplemented
72#2855C2212yes—
73#2855C2212yescomplemented
74#2854C2212yescomplemented
75#2850C2212yes—
76#2850C2212yescomplemented
77#2848C2212yes—
78#2813C2214yescomplemented
79#2730C2214yescomplemented
80#2729C2214yescomplemented
81#2727C2214yescomplemented
82#2723C2214yescomplemented
83#2720C2214yescomplemented
84#2718C2214yescomplemented
85#2712C2214yescomplemented
86#2710C2214yescomplemented
87#2710C2214yescomplemented
88#2710C2214yescomplemented
89#2710C2214yescomplemented
90#2704C2214yescomplemented
91#2703C2214yescomplemented
92#2703C2214yescomplemented
93#2702C2214yescomplemented
94#2701C2214yescomplemented
95#2700C2214yescomplemented
96#2699C2214yescomplemented
97#2699C2214yescomplemented
98#2695C2214yescomplemented
99#2694C2214yescomplemented
100#2690C2214yescomplemented
101#2688C2214yescomplemented
102#2687C2214yescomplemented
103#2686C2214yescomplemented
104#2682C2214yescomplemented
105#2682C2214yescomplemented
106#2681C2214yescomplemented
107#2681C2214yescomplemented
108#2677C2214yescomplemented
109#2676C2214yescomplemented
110#2675C2214yescomplemented
111#2673C2214yescomplemented
112#2673C2214yescomplemented
113#2672C2214yescomplemented
114#2672C2214yescomplemented
115#2671C2214yescomplemented
116#2671C2214yescomplemented
117#2671C2214yescomplemented
118#2671C2214yescomplemented
119#2656C2212yescomplemented
120#2639C2212yescomplemented
121#2628C2212yescomplemented
122#2627C2212yes—
123#2626C2212yes—
124#2626C2212yes—
125#2624C2212yescomplemented
126#2621C2212yescomplemented
127#2620C2212yescomplemented
128#2620C2212yescomplemented
129#2617C2212yes—
130#2616C2212yescomplemented
131#2615C2212yescomplemented
132#2615C2212yescomplemented
133#2592C2212yescomplemented
134#2582C2212yescomplemented
135#2580C2212yescomplemented
136#2579C2214yescomplemented
137#2567C2212yescomplemented
138#2564C2214yescomplemented
139#2560C2214yescomplemented
140#2560C2214yescomplemented
141#2557C2214yescomplemented
142#2556C2214yescomplemented
143#2556C2214yescomplemented
144#2555C2214yescomplemented
145#2555C2214yescomplemented
146#2549C2214yes—
147#2547C2212yescomplemented
148#2543C2214yescomplemented
149#2543C2214yescomplemented
150#2540C2212yescomplemented
151#2540C2214yescomplemented
152#2537C2212yescomplemented
153#2536C2212yescomplemented
154#2521C2214yescomplemented
155#2512C2214yescomplemented
156#2501C2214yescomplemented
157#2492C2214yescomplemented
158#2491C2214yescomplemented
159#2488C2214yescomplemented
160#2487C2212yes—
161#2487C2212yescomplemented
162#2487C2212yescomplemented
163#2486C2212yescomplemented
164#2476C2214yescomplemented
165#2472C2214yes—
166#2471C2214yescomplemented
167#2466C2214yescomplemented
168#2464C2214yescomplemented
169#2461C2214yescomplemented
170#2461C2214yescomplemented
171#2459C2214yescomplemented
172#2458C2214yescomplemented
173#2456C2214yescomplemented
174#2453C2214yescomplemented
175#2449C2214yes—
176#2449C2214yescomplemented
177#2444C2214yes—
178#2441C2214yescomplemented
179#2438C2214yes—
180#2438C2214yescomplemented
181#2437C2214yes—
182#2431C2214yescomplemented
183#2430C2214yescomplemented
184#2429C2214yescomplemented
185#2428C2214yescomplemented
186#2427C2214yescomplemented
187#2426C2214yescomplemented
188#2424C2214yes—
189#2422C2214yescomplemented
190#2418C2214yes—
191#2418C2214yes—
192#2417C2212yes—
193#2417C2212yes—
194#2417C2212yescomplemented
195#2417C2212yescomplemented
196#2417C2212yescomplemented
197#2416C2212yescomplemented
198#2416C2212yescomplemented
199#2416C2212yescomplemented
200#2416C2214yescomplemented
201#2416C2214yescomplemented
202#2415C2212yescomplemented
203#2415C2212yescomplemented
204#2415C2212yescomplemented
205#2414C2214yes—
206#2414C2212yes—
207#2414C2212yes—
208#2414C2212yes—
209#2414C2214yes—
210#2414C2212yes—
211#2414C2212yescomplemented
212#2413C2214yescomplemented
213#2412C2214yes—
214#2410C2214yes—
215#2410C2214yes—
216#2409C2212yescomplemented
217#2408C2212yes—
218#2408C2214yes—
219#2407C2212yescomplemented
220#2407C2212yescomplemented
221#2407C2214yescomplemented
222#2406C2214yescomplemented
223#2404C2214yes—
224C2×#394C2212yes—
225C2×#392C2212yes—
226#2359C2214yescomplemented
227#2358C2214yes—
228#2358C2214yes—
229#2354C2212yescomplemented
230#2352C2212yes—
231#2352C2212yescomplemented
232D4×C4⋊C4C2212yes—
233D4×C4⋊C4C2214yes—
234#2342C2214yes—
235#2339C2214yes—
236#2324C2212yescomplemented
237#2324C2212yescomplemented
238#2323C2212yescomplemented
239#2323C2212yescomplemented
240#2317C2211yescharacteristic, complemented
241#2317C2211yescharacteristic, complemented
242#2315C2212yes—
243#2311C2211yescharacteristic, complemented
244#2311C2212yescomplemented
245#2311C2211yescharacteristic, complemented
246#2310C2211yescharacteristic, complemented
247#2308C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yescomplemented
250C4×#121C2212yes—
251C4×#121C2212yescomplemented
252#2297C2212yescomplemented
253C2×#390C2211yescharacteristic
254C2×#390C2212yes—
255C2×#389C2211yescharacteristic
256C2×#389C2212yescomplemented
257C2×#388C2212yes—
258C2×#380C2211yescharacteristic
259C2×#380C2211yescharacteristic
260#2274C2211yescharacteristic, complemented
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2312yes—
264C22×#41C2312yes—
265C22×#41C2314yes—
266C22×#41C2311yescharacteristic
267C23×Q8C2311yescharacteristic
268C23×D4C2311yescharacteristic
269C23×D4C2311yescharacteristic
270C23×D4C2312yes—
271C23×D4C2312yes—
272C24×C4C2311yescharacteristic
273C24×C4C2311yescharacteristic
274#562—232no—
275#554—216no—
276#548—216no—
277#547—216no—
278#546—232no—
279#546—216no—
280#544—28no—
281#543—216no—
282#542—216no—
283#542—216no—
284#542—216no—
285#540—216no—
286#540—216no—
287#539—216no—
288#538—28no—
289#538—28no—
290#538—216no—
291#538—216no—
292#537—216no—
293#537—28no—
294#537—216no—
295#537—48no—
296#536—44no—
297#535—216no—
298#532—216no—
299#532—216no—
300C2×C4⋊Q8C2312yes—
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×#127C2312yes—
305C2×#127C2312yes—
306#529—216no—
307#529—216no—
308C2×#126C2312yes—
309C2×#126C2314yes—
310C2×#126C2312yes—
311C2×#126C2312yes—
312C2×#126C2312yes—
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2314yes—
316C2×#124C2312yes—
317C2×#124C2312yes—
318C2×#124C2312yes—
319C2×#124C2314yes—
320C2×#124C2312yes—
321C2×#124C2312yes—
322C2×#124C2312yes—
323C2×#124C2312yes—
324C2×#124C2314yes—
325C2×#124C2312yes—
326C2×#124C2314yes—
327#525—28no—
328#525—216no—
329#525D4116yescomplemented
330C2×#123C2312yes—
331C2×#123C2312yes—
332C2×#123C2312yes—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2312yes—
336C2×#123C2312yes—
337C2×#123C2312yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×#123C2312yes—
345C2×C22⋊Q8—28no—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2314yes—
360C2×C22⋊Q8C2314yes—
361C2×C22⋊Q8C2314yes—
362C2×C22⋊Q8C2314yes—
363C2×C22⋊Q8C2314yes—
364C2×C22⋊Q8C2312yes—
365C2×C22⋊Q8C2312yes—
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2314yes—
368C2×C22⋊Q8C2314yes—
369C2×C22⋊Q8C2311yescharacteristic
370C2×C22⋊Q8C2311yescharacteristic
371C2×#121—28no—
372C2×#121—44no—
373C2×#121C2312yes—
374C2×#121C2311yescharacteristic
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2311yescharacteristic
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2312yes—
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2314yes—
387C2×#121C2314yes—
388C2×#121C2314yes—
389C2×#121C2312yes—
390C2×#121C2312yes—
391C2×#121C2314yes—
392C2×#121C2314yes—
393C2×#121C2312yes—
394C2×#121C2312yes—
395C2×#121C2312yes—
396C2×#121C2312yes—
397C2×#121C2312yes—
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2312yes—
401C2×#121C2314yes—
402C2×#121C2314yes—
403C2×#121C2314yes—
404C2×#121C2314yes—
405C2×#121C2314yes—
406C2×#121C2314yes—
407C2×#121C2314yes—
408C2×#121C2314yes—
409C2×#121C2311yescharacteristic
410C2×#121C2311yescharacteristic
411C2×#120C2314yes—
412C2×#120C2312yes—
413C2×#120C2312yes—
414C2×#120C2312yes—
415C2×#120C2314yes—
416C2×#120C2312yes—
417#520—44no—
418C4×#41—216no—
419C2×C4×Q8C2312yes—
420C2×C4×Q8C2312yes—
421C2×C4×Q8C2312yes—
422C2×C4×Q8C2312yes—
423C2×C4×D4—28no—
424C2×C4×D4C2312yes—
425C2×C4×D4C2312yes—
426C2×C4×D4C2312yes—
427C2×C4×D4C2314yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2312yes—
430C2×C4×D4C2312yes—
431C2×C4×D4C2312yes—
432C2×C4×D4C2312yes—
433C2×C4×D4C2312yes—
434C2×C4×D4C2312yes—
435C2×C4×D4C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2312yes—
438C2×C4×D4C2314yes—
439C2×C4×D4C2312yes—
440C2×C4×D4C2314yes—
441C2×C4×D4C2314yes—
442C2×C4×D4C2314yes—
443C2×C4×D4C2312yes—
444C2×C4×D4C2312yes—
445C2×#117—44no—
446C2×#117C2311yescharacteristic
447C2×#117C2311yescharacteristic
448C2×#117C2312yes—
449C2×#117C2312yes—
450C2×#117C2311yescharacteristic
451C2×#117C2312yes—
452C2×#117C2312yes—
453C2×#117C2311yescharacteristic
454C2×#117C2311yescharacteristic
455C2×#117C2312yes—
456C2×#117C2312yes—
457C2×#117C2312yes—
458C2×#117C2311yescharacteristic
459C22×C4⋊C4C2311yescharacteristic
460C22×C4⋊C4C2312yes—
461C22×C4⋊C4C2312yes—
462C22×C4⋊C4C2311yescharacteristic
463C22×C4⋊C4C2312yes—
464C22×C4⋊C4C2311yescharacteristic
465C22×C4⋊C4C2311yescharacteristic
466C22×C4⋊C4C2311yescharacteristic
467C22×C4⋊C4C2311yescharacteristic
468C22×C4⋊C4C2311yescharacteristic
469C22×C4⋊C4C2312yes—
470C22×C4⋊C4C2314yes—
471C22×C22⋊C4C2312yes—
472C22×C22⋊C4C2311yescharacteristic
473C22×C22⋊C4C2312yes—
474C22×C22⋊C4C2314yes—
475C22×C22⋊C4C2312yes—
476C22×C22⋊C4C2311yescharacteristic
477C22×C22⋊C4C2312yes—
478C22×C22⋊C4C2312yes—
479C22×C22⋊C4C2312yes—
480C22×C22⋊C4C2312yes—
481C22×C22⋊C4C2312yes—
482C22×C42C2312yes—
483C22×C42C2312yes—
484C22×C42C2311yescharacteristic
485C22×C42C2312yes—
486#400C2314yes—
487#400C2314yes—
488#400C2314yes—
489#400C2314yes—
490#399C2314yes—
491#399C2314yes—
492#399C2314yes—
493#399C2314yes—
494#399C2314yes—
495#399C2314yes—
496#399C2314yes—
497#398C2314yes—
498#398C2314yes—
499#398C2314yes—
500#398C2314yes—
501#398C2314yes—
502#398C2314yes—
503#398C2314yes—
504#398C2314yes—
505#398C2314yes—
506#397C2314yes—
507#397C2314yes—
508#397C2314yes—
509#397C2314yes—
510#397C2314yes—
511#397C2314yes—
512#397C2314yes—
513#397C2314yes—
514#396C2314yes—
515#396C2314yes—
516#396C2314yes—
517#396C2314yes—
518#396C2314yes—
519#396C2314yes—
520#396C2314yes—
521#396C2314yes—
522#396C2314yes—
523#396C2314yes—
524#395C2314yes—
525#395C2314yes—
526#395C2314yes—
527#395C2314yes—
528#395C2314yes—
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#392C2314yes—
560#392C2314yes—
561#392C2314yes—
562#392C2314yes—
563#392C2314yes—
564#392C2314yes—
565#392C2314yes—
566#392C2314yes—
567#392C2314yes—
568#392C2314yes—
569#392C2314yes—
570#392C2314yes—
571#392C2314yes—
572#392C2314yes—
573#392C2314yes—
574#391C2312yes—
575#391C2314yes—
576#391C2312yes—
577#391C2312yes—
578#391C2312yes—
579#391C2312yes—
580#391C2312yes—
581#391C2314yes—
582#391C2312yes—
583#391C2314yes—
584#391C2312yes—
585#391C2314yes—
586#391C2314yes—
587#390C2314yes—
588#390C2314yes—
589#390C2312yes—
590#390C2312yes—
591#390C2314yes—
592#390C2312yes—
593#390C2314yes—
594#390C2314yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2314yes—
599#390C2314yes—
600#390C2314yes—
601#390C2314yes—
602#390C2314yes—
603#390C2314yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2314yes—
612#389C2314yes—
613#389C2312yes—
614#389C2312yes—
615#389C2314yes—
616#389C2312yes—
617#389C2314yes—
618#389C2314yes—
619#389C2314yes—
620#389C2314yes—
621#389C2314yes—
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#388C2314yes—
647#388C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
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#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#384C2314yes—
703#384C2312yes—
704#384C2312yes—
705#382C2312yes—
706#382C2312yes—
707#381C2314yes—
708#381C2314yes—
709#381C2314yes—
710#381C2314yes—
711#380C2314yes—
712#380C2314yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2312yes—
722#380C2312yes—
723#380C2314yes—
724#380C2314yes—
725#380C2314yes—
726#380C2314yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2314yes—
733#379C2314yes—
734#379C2314yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2314yes—
741C4×C22⋊C4C2314yes—
742C4×C22⋊C4C2314yes—
743C4×C22⋊C4C2314yes—
744C4×C22⋊C4C2314yes—
745C4×C22⋊C4C2314yes—
746C4×C22⋊C4C2314yes—
747C4×C22⋊C4C2314yes—
748C2×#95C2312yes—
749C2×#95C2312yes—
750C2×#95C2314yes—
751C2×#95C2312yes—
752C25C2412yes—
753C25C2411yescharacteristic
754C25C2411yescharacteristic
755C2×#41—28no—
756C2×#41—216no—
757C2×#41—24no—
758C2×#41—28no—
759C2×#41—28no—
760C2×#41—28no—
761C2×#41—42no—
762C2×#41—42no—
763C2×#41—42no—
764C2×#41—44no—
765C2×#41—42no—
766C2×#41—44no—
767C2×#41—44no—
768C2×#41—44no—
769C2×#41—44no—
770C2×#41—84no—
771C2×#41—84no—
772C2×#41C2×D418yescomplemented
773C22×Q8—24no—
774C22×Q8—42no—
775C22×Q8—42no—
776C22×Q8C2412yes—
777C22×Q8C2412yes—
778C22×Q8C2414yes—
779C22×Q8C2412yes—
780C22×Q8C2412yes—
781C22×Q8C2411yescharacteristic
782C22×Q8C2411yescharacteristic
783C22×D4—24no—
784C22×D4—28no—
785C22×D4—24no—
786C22×D4—24no—
787C22×D4—42no—
788C22×D4—44no—
789C22×D4—42no—
790C22×D4—42no—
791C22×D4—44no—
792C22×D4—82no—
793C22×D4—82no—
794C22×D4—82no—
795C22×D4C2412yes—
796C22×D4C2412yes—
797C22×D4C2412yes—
798C22×D4C2412yes—
799C22×D4C2412yes—
800C22×D4C2412yes—
801C22×D4C2412yes—
802C22×D4C2412yes—
803C22×D4C2412yes—
804C22×D4C2414yes—
805C22×D4C2414yes—
806C22×D4C2414yes—
807C22×D4C2412yes—
808C22×D4C2412yes—
809C22×D4C2412yes—
810C22×D4C2412yes—
811C22×D4C2412yes—
812C22×D4C2414yes—
813C22×D4C2411yescharacteristic
814C22×D4C2414yes—
815C22×D4C2414yes—
816C22×D4C2414yes—
817C22×D4C2414yes—
818C22×D4C2412yes—
819C22×D4C2411yescharacteristic
820C22×D4C2412yes—
821C23×C4—24no—
822C23×C4—42no—
823C23×C4—42no—
824C23×C4—42no—
825C23×C4—42no—
826C23×C4C2×D418yes—
827C23×C4C2412yes—
828C23×C4C2412yes—
829C23×C4C2412yes—
830C23×C4C2412yes—
831C23×C4C2412yes—
832C23×C4C2411yescharacteristic
833C23×C4C2411yescharacteristic
834C23×C4C2412yes—
835C23×C4C2411yescharacteristic
836C23×C4C2411yescharacteristic
837C23×C4C2411yescharacteristic
838C23×C4C2412yes—
839C23×C4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2414yes—
844C23×C4C2414yes—
845C23×C4C2414yes—
846C23×C4C2412yes—
847C23×C4C2414yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C4⋊Q8—28no—
856C4⋊Q8—28no—
857C4⋊Q8—28no—
858C4⋊Q8—44no—
859#127—28no—
860#127—28no—
861#126—28no—
862#126—28no—
863#126—216no—
864#126—28no—
865#126—28no—
866#125—28no—
867#125—28no—
868#125—216no—
869#124—28no—
870#124—28no—
871#124—28no—
872#124—28no—
873#124—28no—
874#124—28no—
875#124—216no—
876#124—216no—
877#124—28no—
878#124—44no—
879#124—84no—
880#123—28no—
881#123—28no—
882#123—28no—
883#123—28no—
884#123—216no—
885#123—28no—
886#123—28no—
887#123—28no—
888#123—216no—
889#123—216no—
890#123—216no—
891#123—48no—
892#123—84no—
893#123—84no—
894#123C2×D4116yescomplemented
895C22⋊Q8—216no—
896C22⋊Q8—28no—
897C22⋊Q8—28no—
898C22⋊Q8—28no—
899C22⋊Q8—28no—
900C22⋊Q8—24no—
901C22⋊Q8—24no—
902C22⋊Q8—28no—
903C22⋊Q8—28no—
904C22⋊Q8—28no—
905C22⋊Q8—216no—
906C22⋊Q8—216no—
907C22⋊Q8—216no—
908C22⋊Q8—28no—
909C22⋊Q8—28no—
910C22⋊Q8—28no—
911C22⋊Q8—216no—
912C22⋊Q8—216no—
913C22⋊Q8—48no—
914C22⋊Q8—44no—
915C22⋊Q8—44no—
916C22⋊Q8—44no—
917C22⋊Q8—84no—
918C22⋊Q8C2×D418yes—
919C22⋊Q8C2×D418yescomplemented
920#121—28no—
921#121—28no—
922#121—28no—
923#121—28no—
924#121—28no—
925#121—28no—
926#121—28no—
927#121—216no—
928#121—216no—
929#121—216no—
930#121—216no—
931#121—28no—
932#121—28no—
933#121—28no—
934#121—28no—
935#121—24no—
936#121—24no—
937#121—28no—
938#121—28no—
939#121—28no—
940#121—28no—
941#121—28no—
942#121—28no—
943#121—28no—
944#121—216no—
945#121—48no—
946#121—48no—
947#121—48no—
948#121—44no—
949#121—44no—
950#121—44no—
951#121—48no—
952#121—84no—
953#121—84no—
954#121—84no—
955#121—84no—
956#121C2×D418yes—
957#121C2×D418yescomplemented
958#120—28no—
959#120—28no—
960#120—216no—
961#120—28no—
962#120—48no—
963#120C2×D4116yes—
964C4×Q8—28no—
965C4×Q8—28no—
966C4×Q8—28no—
967C4×Q8—44no—
968C4×D4—28no—
969C4×D4—216no—
970C4×D4—28no—
971C4×D4—28no—
972C4×D4—28no—
973C4×D4—28no—
974C4×D4—28no—
975C4×D4—28no—
976C4×D4—28no—
977C4×D4—28no—
978C4×D4—28no—
979C4×D4—28no—
980C4×D4—216no—
981C4×D4—28no—
982C4×D4—28no—
983C4×D4—44no—
984C4×D4—48no—
985C4×D4—48no—
986C4×D4—84no—
987C4×D4C2×D4116yes—
988C4×D4C2×D4116yescomplemented
989#117—24no—
990#117—28no—
991#117—24no—
992#117—24no—
993#117—28no—
994#117—28no—
995#117—28no—
996#117—44no—
997#117—44no—
998#117—42no—
999#117—42no—
1000#117—44no—
1001#117C2×D418yescomplemented
1002C2×C4⋊C4—24no—
1003C2×C4⋊C4—24no—
1004C2×C4⋊C4—28no—
1005C2×C4⋊C4—24no—
1006C2×C4⋊C4—28no—
1007C2×C4⋊C4—24no—
1008C2×C4⋊C4—28no—
1009C2×C4⋊C4—42no—
1010C2×C4⋊C4—42no—
1011C2×C4⋊C4—42no—
1012C2×C4⋊C4—82no—
1013C2×C4⋊C4—84no—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2411yescharacteristic
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2411yescharacteristic
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2414yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2411yescharacteristic
1064C2×C4⋊C4C2411yescharacteristic
1065C2×C4⋊C4C2412yes—
1066C2×C4⋊C4C2411yescharacteristic
1067C2×C22⋊C4—24no—
1068C2×C22⋊C4—28no—
1069C2×C22⋊C4—24no—
1070C2×C22⋊C4—28no—
1071C2×C22⋊C4—28no—
1072C2×C22⋊C4—216no—
1073C2×C22⋊C4—44no—
1074C2×C22⋊C4—44no—
1075C2×C22⋊C4—44no—
1076C2×C22⋊C4—82no—
1077C2×C22⋊C4—82no—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2412yes—
1138C2×C22⋊C4C2412yes—
1139C2×C22⋊C4C2412yes—
1140C2×C22⋊C4C2412yes—
1141C2×C22⋊C4C2412yes—
1142C2×C42—24no—
1143C2×C42—28no—
1144C2×C42—28no—
1145C2×C42—44no—
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2412yes—
1149C2×C42C2412yes—
1150C2×C42C2412yes—
1151C2×C42C2412yes—
1152C2×C42C2412yes—
1153C2×C42C2414yes—
1154C2×C42C2412yes—
1155C2×C42C2412yes—
1156C2×C42C2412yes—
1157C2×C42C2412yes—
1158C2×C42C2414yes—
1159C2×C42C2414yes—
1160C2×C42C2414yes—
1161C2×C42C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194C24—22no—
1195C24—22no—
1196C24—22no—
1197C24—24no—
1198C24—22no—
1199C24—24no—
1200C24—22no—
1201C24—24no—
1202C24—41no—
1203C24—41no—
1204C24—41no—
1205C24—41no—
1206C24—41no—
1207C24—41no—
1208C24—41no—
1209C24—41no—
1210C24—42no—
1211C24—42no—
1212C24—42no—
1213C24—42no—
1214C24C22×D414yes—
1215C24C2514yes—
1216C24C2512yes—
1217C24C2512yes—
1218C24C2511yescharacteristic
1219C24C2511yescharacteristic
1220C24C2512yes—
1221C24C2511yescharacteristic
1222#41—416no—
1223#41—432no—
1224#41—88no—
1225#41—816no—
1226#41—816no—
1227#41—832no—
1228C2×Q8—24no—
1229C2×Q8—24no—
1230C2×Q8—24no—
1231C2×Q8—28no—
1232C2×Q8—22no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—24no—
1236C2×Q8—24no—
1237C2×Q8—41no—
1238C2×Q8—42no—
1239C2×Q8—41no—
1240C2×Q8—42no—
1241C2×Q8—44no—
1242C2×Q8—42no—
1243C2×Q8—44no—
1244C2×Q8—41no—
1245C2×Q8—42no—
1246C2×Q8—42no—
1247C2×Q8—41no—
1248C2×Q8—88no—
1249C2×Q8C22×D414yes—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—28no—
1257C2×D4—24no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—28no—
1262C2×D4—28no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—28no—
1267C2×D4—24no—
1268C2×D4—24no—
1269C2×D4—24no—
1270C2×D4—22no—
1271C2×D4—24no—
1272C2×D4—24no—
1273C2×D4—28no—
1274C2×D4—24no—
1275C2×D4—24no—
1276C2×D4—24no—
1277C2×D4—24no—
1278C2×D4—41no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—41no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—416no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—42no—
1293C2×D4—44no—
1294C2×D4—42no—
1295C2×D4—42no—
1296C2×D4—44no—
1297C2×D4—42no—
1298C2×D4—44no—
1299C2×D4—42no—
1300C2×D4—42no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—44no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—42no—
1309C2×D4—42no—
1310C2×D4—44no—
1311C2×D4—41no—
1312C2×D4—42no—
1313C2×D4—44no—
1314C2×D4—42no—
1315C2×D4—44no—
1316C2×D4—42no—
1317C2×D4—41no—
1318C2×D4—42no—
1319C2×D4—42no—
1320C2×D4—44no—
1321C2×D4—42no—
1322C2×D4—44no—
1323C2×D4—44no—
1324C2×D4—44no—
1325C2×D4—88no—
1326C2×D4—816no—
1327C2×D4—816no—
1328C2×D4C22×D418yes—
1329C2×D4C22×D418yes—
1330C2×D4C22×D418yes—
1331C2×D4C22×D414yes—
1332C22×C4—22no—
1333C22×C4—22no—
1334C22×C4—22no—
1335C22×C4—24no—
1336C22×C4—22no—
1337C22×C4—22no—
1338C22×C4—22no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—24no—
1342C22×C4—24no—
1343C22×C4—24no—
1344C22×C4—24no—
1345C22×C4—22no—
1346C22×C4—24no—
1347C22×C4—24no—
1348C22×C4—24no—
1349C22×C4—22no—
1350C22×C4—28no—
1351C22×C4—24no—
1352C22×C4—24no—
1353C22×C4—24no—
1354C22×C4—24no—
1355C22×C4—24no—
1356C22×C4—24no—
1357C22×C4—24no—
1358C22×C4—24no—
1359C22×C4—24no—
1360C22×C4—24no—
1361C22×C4—24no—
1362C22×C4—24no—
1363C22×C4—28no—
1364C22×C4—28no—
1365C22×C4—24no—
1366C22×C4—28no—
1367C22×C4—416no—
1368C22×C4—41no—
1369C22×C4—42no—
1370C22×C4—41no—
1371C22×C4—41no—
1372C22×C4—41no—
1373C22×C4—41no—
1374C22×C4—41no—
1375C22×C4—42no—
1376C22×C4—42no—
1377C22×C4—42no—
1378C22×C4—42no—
1379C22×C4—42no—
1380C22×C4—41no—
1381C22×C4—42no—
1382C22×C4—41no—
1383C22×C4—42no—
1384C22×C4—42no—
1385C22×C4—41no—
1386C22×C4—44no—
1387C22×C4—42no—
1388C22×C4—44no—
1389C22×C4—44no—
1390C22×C4—42no—
1391C22×C4—44no—
1392C22×C4—42no—
1393C22×C4—44no—
1394C22×C4—44no—
1395C22×C4—42no—
1396C22×C4—42no—
1397C22×C4—42no—
1398C22×C4—44no—
1399C22×C4—42no—
1400C22×C4—41no—
1401C22×C4—42no—
1402C22×C4—44no—
1403C22×C4—42no—
1404C22×C4—42no—
1405C22×C4—42no—
1406C22×C4—42no—
1407C22×C4—42no—
1408C22×C4—42no—
1409C22×C4—88no—
1410C22×C4C22×D414yes—
1411C22×C4C22×D418yes—
1412C22×C4C22×D414yes—
1413C22×C4C22×D414yes—
1414C22×C4C22×D414yes—
1415C22×C4C22×D414yes—
1416C22×C4C22×D414yes—
1417C22×C42−1+414yes—
1418C22×C4C2514yes—
1419C22×C4C2512yes—
1420C22×C4C2512yes—
1421C22×C4C2512yes—
1422C22×C4C2512yes—
1423C22×C4C2514yes—
1424C22×C4C2512yes—
1425C22×C4C2514yes—
1426C22×C4C2514yes—
1427C22×C4C2512yes—
1428C22×C4C2514yes—
1429C22×C4C2512yes—
1430C22×C4C2512yes—
1431C22×C4C2512yes—
1432C22×C4C2511yescharacteristic
1433C22×C4C2512yes—
1434C22×C4C2512yes—
1435C22×C4C2511yescharacteristic
1436C22×C4C2511yescharacteristic
1437C22×C4C2512yes—
1438C22×C4C2512yes—
1439C22×C4C2511yescharacteristic
1440C4⋊C4—24no—
1441C4⋊C4—24no—
1442C4⋊C4—24no—
1443C4⋊C4—24no—
1444C4⋊C4—24no—
1445C4⋊C4—28no—
1446C4⋊C4—28no—
1447C4⋊C4—28no—
1448C4⋊C4—24no—
1449C4⋊C4—24no—
1450C4⋊C4—24no—
1451C4⋊C4—24no—
1452C4⋊C4—24no—
1453C4⋊C4—24no—
1454C4⋊C4—22no—
1455C4⋊C4—24no—
1456C4⋊C4—22no—
1457C4⋊C4—24no—
1458C4⋊C4—28no—
1459C4⋊C4—24no—
1460C4⋊C4—24no—
1461C4⋊C4—24no—
1462C4⋊C4—28no—
1463C4⋊C4—28no—
1464C4⋊C4—24no—
1465C4⋊C4—24no—
1466C4⋊C4—22no—
1467C4⋊C4—28no—
1468C4⋊C4—22no—
1469C4⋊C4—22no—
1470C4⋊C4—28no—
1471C4⋊C4—24no—
1472C4⋊C4—42no—
1473C4⋊C4—42no—
1474C4⋊C4—42no—
1475C4⋊C4—44no—
1476C4⋊C4—44no—
1477C4⋊C4—44no—
1478C4⋊C4—44no—
1479C4⋊C4—44no—
1480C4⋊C4—44no—
1481C4⋊C4—44no—
1482C4⋊C4—44no—
1483C4⋊C4—44no—
1484C4⋊C4—44no—
1485C4⋊C4—44no—
1486C4⋊C4—44no—
1487C4⋊C4—44no—
1488C4⋊C4C22×D418yes—
1489C4⋊C4C22×D414yes—
1490C4⋊C4C22×D414yes—
1491C4⋊C4C22×D418yes—
1492C4⋊C4H(5,𝔽2)14yes—
1493C22⋊C4—28no—
1494C22⋊C4—24no—
1495C22⋊C4—24no—
1496C22⋊C4—28no—
1497C22⋊C4—24no—
1498C22⋊C4—24no—
1499C22⋊C4—24no—
1500C22⋊C4—24no—
1501C22⋊C4—28no—
1502C22⋊C4—24no—
1503C22⋊C4—28no—
1504C22⋊C4—24no—
1505C22⋊C4—24no—
1506C22⋊C4—28no—
1507C22⋊C4—28no—
1508C22⋊C4—28no—
1509C22⋊C4—28no—
1510C22⋊C4—24no—
1511C22⋊C4—24no—
1512C22⋊C4—24no—
1513C22⋊C4—24no—
1514C22⋊C4—24no—
1515C22⋊C4—24no—
1516C22⋊C4—28no—
1517C22⋊C4—28no—
1518C22⋊C4—24no—
1519C22⋊C4—24no—
1520C22⋊C4—24no—
1521C22⋊C4—24no—
1522C22⋊C4—28no—
1523C22⋊C4—28no—
1524C22⋊C4—28no—
1525C22⋊C4—28no—
1526C22⋊C4—44no—
1527C22⋊C4—42no—
1528C22⋊C4—42no—
1529C22⋊C4—44no—
1530C22⋊C4—44no—
1531C22⋊C4—44no—
1532C22⋊C4—44no—
1533C22⋊C4—44no—
1534C22⋊C4—44no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—44no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C22⋊C4—44no—
1543C22⋊C4—44no—
1544C22⋊C4—44no—
1545C22⋊C4—44no—
1546C22⋊C4—44no—
1547C22⋊C4—44no—
1548C22⋊C4—44no—
1549C22⋊C4—44no—
1550C22⋊C4—44no—
1551C22⋊C4—44no—
1552C22⋊C4C22×D418yes—
1553C22⋊C4C22×D418yes—
1554C22⋊C4C22×D418yes—
1555C22⋊C4C22×D418yes—
1556C22⋊C4C22×D418yes—
1557C42—24no—
1558C42—24no—
1559C42—24no—
1560C42—24no—
1561C42—24no—
1562C42—24no—
1563C42—24no—
1564C42—28no—
1565C42—24no—
1566C42—24no—
1567C42—42no—
1568C42—42no—
1569C42—44no—
1570C42—44no—
1571C42—44no—
1572C42C22×D418yes—
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23—21no—
1577C23—21no—
1578C23—21no—
1579C23—22no—
1580C23—22no—
1581C23—21no—
1582C23—21no—
1583C23—21no—
1584C23—22no—
1585C23—21no—
1586C23—21no—
1587C23—22no—
1588C23—21no—
1589C23—22no—
1590C23—22no—
1591C23—21no—
1592C23—21no—
1593C23—21no—
1594C23—21no—
1595C23—28no—
1596C23—22no—
1597C23—24no—
1598C23—22no—
1599C23—22no—
1600C23—24no—
1601C23—22no—
1602C23—24no—
1603C23—22no—
1604C23—22no—
1605C23—22no—
1606C23—24no—
1607C23—24no—
1608C23—22no—
1609C23—22no—
1610C23—22no—
1611C23—22no—
1612C23—22no—
1613C23—22no—
1614C23—24no—
1615C23—22no—
1616C23—24no—
1617C23—44no—
1618C23—44no—
1619C23—44no—
1620C23—44no—
1621C23—44no—
1622C23—48no—
1623C23—82no—
1624C23—82no—
1625C23—82no—
1626C23—82no—
1627C23—82no—
1628C23—82no—
1629C23—82no—
1630C23—82no—
1631C23—84no—
1632C23—84no—
1633C23—84no—
1634C23—84no—
1635C23—84no—
1636C23—84no—
1637C23C23×D412yes—
1638C23C23×D412yes—
1639C23C23×D414yes—
1640C23C23×D412yes—
1641C23C2×2−1+412yes—
1642C23#58512yes—
1643C23C2611yescharacteristic
1644Q8—44no—
1645Q8—48no—
1646Q8—48no—
1647Q8—84no—
1648Q8—82no—
1649Q8—84no—
1650Q8—88no—
1651D4—216no—
1652D4—44no—
1653D4—48no—
1654D4—48no—
1655D4—48no—
1656D4—48no—
1657D4—48no—
1658D4—416no—
1659D4—48no—
1660D4—48no—
1661D4—84no—
1662D4—84no—
1663D4—88no—
1664D4—82no—
1665D4—84no—
1666D4—84no—
1667D4—84no—
1668D4—88no—
1669D4—84no—
1670D4—84no—
1671D4—84no—
1672D4—88no—
1673D4—88no—
1674D4—88no—
1675D4—88no—
1676D4—164no—
1677C2×C4—22no—
1678C2×C4—21no—
1679C2×C4—21no—
1680C2×C4—22no—
1681C2×C4—21no—
1682C2×C4—22no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—21no—
1686C2×C4—21no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—21no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—28no—
1694C2×C4—28no—
1695C2×C4—28no—
1696C2×C4—28no—
1697C2×C4—216no—
1698C2×C4—22no—
1699C2×C4—22no—
1700C2×C4—22no—
1701C2×C4—22no—
1702C2×C4—24no—
1703C2×C4—24no—
1704C2×C4—22no—
1705C2×C4—24no—
1706C2×C4—22no—
1707C2×C4—22no—
1708C2×C4—22no—
1709C2×C4—24no—
1710C2×C4—22no—
1711C2×C4—24no—
1712C2×C4—22no—
1713C2×C4—22no—
1714C2×C4—22no—
1715C2×C4—22no—
1716C2×C4—24no—
1717C2×C4—24no—
1718C2×C4—22no—
1719C2×C4—24no—
1720C2×C4—22no—
1721C2×C4—22no—
1722C2×C4—24no—
1723C2×C4—22no—
1724C2×C4—22no—
1725C2×C4—24no—
1726C2×C4—22no—
1727C2×C4—22no—
1728C2×C4—24no—
1729C2×C4—24no—
1730C2×C4—22no—
1731C2×C4—22no—
1732C2×C4—22no—
1733C2×C4—24no—
1734C2×C4—24no—
1735C2×C4—24no—
1736C2×C4—22no—
1737C2×C4—44no—
1738C2×C4—44no—
1739C2×C4—44no—
1740C2×C4—48no—
1741C2×C4—48no—
1742C2×C4—48no—
1743C2×C4—48no—
1744C2×C4—48no—
1745C2×C4—48no—
1746C2×C4—84no—
1747C2×C4—88no—
1748C2×C4—84no—
1749C2×C4—88no—
1750C2×C4—88no—
1751C2×C4—82no—
1752C2×C4—84no—
1753C2×C4—84no—
1754C2×C4—82no—
1755C2×C4—84no—
1756C2×C4—84no—
1757C2×C4—88no—
1758C2×C4—162no—
1759C2×C4—162no—
1760C2×C4C23×D414yes—
1761C2×C4C23×D414yes—
1762C2×C4C23×D412yes—
1763C2×C4C23×D414yes—
1764C2×C4C23×D412yes—
1765C2×C4C23×D412yes—
1766C2×C4C23×D412yes—
1767C2×C4C2×H(5,𝔽2)14yes—
1768C2×C4C2×H(5,𝔽2)12yes—
1769C2×C4C2×2−1+414yes—
1770C2×C4#58512yes—
1771C22—22no—
1772C22—22no—
1773C22—22no—
1774C22—22no—
1775C22—22no—
1776C22—22no—
1777C22—22no—
1778C22—22no—
1779C22—24no—
1780C22—24no—
1781C22—22no—
1782C22—22no—
1783C22—22no—
1784C22—24no—
1785C22—22no—
1786C22—42no—
1787C22—41no—
1788C22—41no—
1789C22—42no—
1790C22—41no—
1791C22—41no—
1792C22—42no—
1793C22—41no—
1794C22—41no—
1795C22—41no—
1796C22—42no—
1797C22—41no—
1798C22—42no—
1799C22—42no—
1800C22—44no—
1801C22—42no—
1802C22—42no—
1803C22—44no—
1804C22—44no—
1805C22—42no—
1806C22—42no—
1807C22—42no—
1808C22—42no—
1809C22—44no—
1810C22—42no—
1811C22—44no—
1812C22—42no—
1813C22—42no—
1814C22—42no—
1815C22—44no—
1816C22—42no—
1817C22—44no—
1818C22—42no—
1819C22—88no—
1820C22—88no—
1821C22—168no—
1822C22#348914yes—
1823C22C24×D411yescharacteristic
1824C22C22×H(5,𝔽2)11yescharacteristic
1825C22C22×2−1+411yescharacteristic
1826C22C2×#58511yescharacteristic
1827C22C2×#58511yescharacteristic
1828C22H(7,𝔽2)11yescharacteristic
1829C22H(7,𝔽2)11yescharacteristic
1830C4—22no—
1831C4—22no—
1832C4—22no—
1833C4—24no—
1834C4—24no—
1835C4—24no—
1836C4—24no—
1837C4—24no—
1838C4—42no—
1839C4—42no—
1840C4—44no—
1841C4—42no—
1842C4—44no—
1843C4—42no—
1844C4—44no—
1845C4—42no—
1846C4—42no—
1847C4—42no—
1848C4—42no—
1849C4—44no—
1850C4—44no—
1851C4#349614yes—
1852C2—24no—
1853C2—44no—
1854C2—42no—
1855C2—42no—
1856C2—82no—
1857C2—82no—
1858C2—84no—
1859C2C2×#349611yescharacteristic
1860C2C2×#348911yescharacteristic
1861C2#6285211yescharacteristic
1862C2#6291711yescharacteristic
1863C2#6291811yescharacteristic
1864C2#6292911yescharacteristic
1865C2#6293511yescharacteristic
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×#3536C2semidirect
2. C2×#3460C2semidirect
3. #49587C2semidirect
4. #49584C2semidirect
5. #47453C2semidirect
6. #46375C2semidirect
7. #43887C2semidirect
8. #42999C2semidirect
9. #39471C2semidirect
10. #39420C2semidirect
11. #39415C2semidirect
12. #39375C2semidirect
13. #39364C2semidirect
14. #39335C2semidirect
15. #38041C2semidirect
16. #38035C2semidirect
17. #37838C2semidirect
18. #37648C2semidirect
19. #37439C2semidirect
20. #37280C2semidirect
21. #37272C2semidirect
22. #36360C2semidirect
23. #36275C2semidirect
24. #35569C2semidirect
25. #35564C2semidirect
26. #35306C2semidirect
27. #35010C2semidirect
28. C2×#2414C2semidirect
29. #34202C2semidirect
31. C2×#562C22semidirect
33. C2×#548C22semidirect
34. C2×#547C22semidirect
40. C2×#542C22semidirect
41. C2×#542C22semidirect
42. C2×#542C22semidirect
43. C2×#540C22semidirect
44. C2×#540C22semidirect
45. C2×#539C22semidirect
51. C2×#537C22semidirect
52. C2×#537C22semidirect
53. C2×#537C22semidirect
54. C2×#536C22semidirect
56. C2×#532C22semidirect
57. C2×#532C22semidirect
58. C2×#529C22semidirect
59. C2×#529C22semidirect
66. C2×#520C22semidirect
71. #2857C22semidirect
73. #2855C22semidirect
74. #2854C22semidirect
76. #2850C22semidirect
78. #2813C22semidirect
79. #2730C22semidirect
80. #2729C22semidirect
81. #2727C22semidirect
82. #2723C22semidirect
83. #2720C22semidirect
84. #2718C22semidirect
85. #2712C22semidirect
86. #2710C22semidirect
87. #2710C22semidirect
88. #2710C22semidirect
89. #2710C22semidirect
90. #2704C22semidirect
91. #2703C22semidirect
92. #2703C22semidirect
93. #2702C22semidirect
94. #2701C22semidirect
95. #2700C22semidirect
96. #2699C22semidirect
97. #2699C22semidirect
98. #2695C22semidirect
99. #2694C22semidirect
100. #2690C22semidirect
101. #2688C22semidirect
102. #2687C22semidirect
103. #2686C22semidirect
104. #2682C22semidirect
105. #2682C22semidirect
106. #2681C22semidirect
107. #2681C22semidirect
108. #2677C22semidirect
109. #2676C22semidirect
110. #2675C22semidirect
111. #2673C22semidirect
112. #2673C22semidirect
113. #2672C22semidirect
114. #2672C22semidirect
115. #2671C22semidirect
116. #2671C22semidirect
117. #2671C22semidirect
118. #2671C22semidirect
119. #2656C22semidirect
120. #2639C22semidirect
121. #2628C22semidirect
125. #2624C22semidirect
126. #2621C22semidirect
127. #2620C22semidirect
128. #2620C22semidirect
130. #2616C22semidirect
131. #2615C22semidirect
132. #2615C22semidirect
133. #2592C22semidirect
134. #2582C22semidirect
135. #2580C22semidirect
136. #2579C22semidirect
137. #2567C22semidirect
138. #2564C22semidirect
139. #2560C22semidirect
140. #2560C22semidirect
141. #2557C22semidirect
142. #2556C22semidirect
143. #2556C22semidirect
144. #2555C22semidirect
145. #2555C22semidirect
147. #2547C22semidirect
148. #2543C22semidirect
149. #2543C22semidirect
150. #2540C22semidirect
151. #2540C22semidirect
152. #2537C22semidirect
153. #2536C22semidirect
154. #2521C22semidirect
155. #2512C22semidirect
156. #2501C22semidirect
157. #2492C22semidirect
158. #2491C22semidirect
159. #2488C22semidirect
161. #2487C22semidirect
162. #2487C22semidirect
163. #2486C22semidirect
164. #2476C22semidirect
166. #2471C22semidirect
167. #2466C22semidirect
168. #2464C22semidirect
169. #2461C22semidirect
170. #2461C22semidirect
171. #2459C22semidirect
172. #2458C22semidirect
173. #2456C22semidirect
174. #2453C22semidirect
176. #2449C22semidirect
178. #2441C22semidirect
180. #2438C22semidirect
182. #2431C22semidirect
183. #2430C22semidirect
184. #2429C22semidirect
185. #2428C22semidirect
186. #2427C22semidirect
187. #2426C22semidirect
189. #2422C22semidirect
194. #2417C22semidirect
195. #2417C22semidirect
196. #2417C22semidirect
197. #2416C22semidirect
198. #2416C22semidirect
199. #2416C22semidirect
200. #2416C22semidirect
201. #2416C22semidirect
202. #2415C22semidirect
203. #2415C22semidirect
204. #2415C22semidirect
211. #2414C22semidirect
212. #2413C22semidirect
216. #2409C22semidirect
219. #2407C22semidirect
220. #2407C22semidirect
221. #2407C22semidirect
222. #2406C22semidirect
226. #2359C22semidirect
229. #2354C22semidirect
231. #2352C22semidirect
236. #2324C22semidirect
237. #2324C22semidirect
238. #2323C22semidirect
239. #2323C22semidirect
240. #2317C22semidirect
241. #2317C22semidirect
243. #2311C22semidirect
244. #2311C22semidirect
245. #2311C22semidirect
246. #2310C22semidirect
249. C4×C22⋊Q8C22semidirect
251. C4×#121C22semidirect
252. #2297C22semidirect
256. C2×#389C22semidirect
260. #2274C22semidirect
329. #525D4semidirect
772. C2×#41C2×D4semidirect
894. #123C2×D4semidirect
919. C22⋊Q8C2×D4semidirect
957. #121C2×D4semidirect
988. C4×D4C2×D4semidirect
1001. #117C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35362
C2×#34602
#495872
#495842
#474532
#463752
#438872
#429992
#394712
#394202
#394152
#393752
#393642
#393352
#380412
#380352
#378382
#376482
#374392
#372802
#372722
#363602
#362752
#355692
#355642
#353062
#350102
C2×#24142
#342022