Finite Group Databasebeta

← #7732314

Subgroups — #7732314

Order 512.

7508 conjugacy classes of subgroups.

The subgroup lattice has 1870 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#49588C214yesmaximal, complemented
4#49583C214yesmaximal, complemented
5#47455C214yesmaximal, complemented
6#46373C214yesmaximal, complemented
7#43904C214yesmaximal, complemented
8#43489C214yesmaximal, complemented
9#39470C212yesmaximal, complemented
10#39421C212yesmaximal, complemented
11#39415C212yesmaximal, complemented
12#39380C212yesmaximal, complemented
13#39359C212yesmaximal, complemented
14#39334C212yesmaximal, complemented
15#38040C212yesmaximal, complemented
16#38034C212yesmaximal, complemented
17#37839C212yesmaximal, complemented
18#37649C212yesmaximal, complemented
19#37442C211yesmaximal, characteristic, complemented
20#37277C212yesmaximal, complemented
21#37272C212yesmaximal, complemented
22#36374C212yesmaximal, complemented
23#36259C212yesmaximal, complemented
24#35568C212yesmaximal, complemented
25#35564C212yesmaximal, complemented
26#35252C211yesmaximal, characteristic, complemented
27#35000C211yesmaximal, characteristic, complemented
28C2×#2415C211yesmaximal, characteristic, complemented
29#34202C211yesmaximal, characteristic, complemented
30#3536—216no—
31C2×#562C2214yescomplemented
32C2×#554C2212yescomplemented
33C2×#548C2212yes—
34C2×#547C2212yes—
35C2×#547C2214yescomplemented
36C2×#546C2214yes—
37C2×#546C2212yescomplemented
38#3460—216no—
39C2×#544C2211yescharacteristic, complemented
40C2×#543C2212yescomplemented
41C2×#542C2212yes—
42C2×#542C2212yescomplemented
43C2×#542C2212yescomplemented
44C2×#540C2212yes—
45C2×#540C2212yescomplemented
46C2×#539C2212yes—
47C2×#538C2212yes—
48C2×#538C2212yescomplemented
49C2×#538C2211yescharacteristic, complemented
50C2×#538C2211yescharacteristic, complemented
51C2×#537C2212yes—
52C2×#537C2212yescomplemented
53C2×#537C2211yescharacteristic, complemented
54C2×#537C2212yescomplemented
55C2×#535C2212yes—
56C2×#535C2211yescharacteristic, complemented
57C2×#534C2212yes—
58C2×#532C2212yes—
59C2×#532C2212yescomplemented
60C2×#529C2212yes—
61C2×#529C2212yescomplemented
62C2×#525C2211yescharacteristic
63C2×#525C2211yescharacteristic
64C2×#525C2212yescomplemented
65C22×C22⋊Q8C2211yescharacteristic
66C22×C22⋊Q8C2211yescharacteristic, complemented
67C22×#121C2211yescharacteristic
68C2×#520C2211yescharacteristic, complemented
69C2×C4×#41C2212yescomplemented
70C22×C4×D4C2211yescharacteristic
71C22×#117C2211yescharacteristic
72#2857C2212yescomplemented
73#2856C2212yes—
74#2855C2212yescomplemented
75#2854C2212yes—
76#2854C2212yescomplemented
77#2850C2212yes—
78#2850C2212yescomplemented
79#2847C2212yes—
80#2814C2214yescomplemented
81#2730C2214yescomplemented
82#2729C2214yescomplemented
83#2725C2214yescomplemented
84#2721C2214yescomplemented
85#2719C2214yescomplemented
86#2715C2214yescomplemented
87#2706C2214yescomplemented
88#2705C2214yescomplemented
89#2703C2214yescomplemented
90#2703C2214yescomplemented
91#2702C2214yescomplemented
92#2700C2214yescomplemented
93#2700C2214yescomplemented
94#2699C2214yescomplemented
95#2697C2214yescomplemented
96#2696C2214yescomplemented
97#2693C2214yescomplemented
98#2692C2214yescomplemented
99#2689C2214yescomplemented
100#2688C2214yescomplemented
101#2686C2214yescomplemented
102#2683C2214yescomplemented
103#2683C2214yescomplemented
104#2682C2214yescomplemented
105#2681C2214yes—
106#2681C2214yescomplemented
107#2681C2214yescomplemented
108#2681C2214yescomplemented
109#2678C2214yes—
110#2676C2214yescomplemented
111#2676C2214yescomplemented
112#2674C2214yes—
113#2674C2214yescomplemented
114#2673C2214yescomplemented
115#2673C2214yescomplemented
116#2672C2214yescomplemented
117#2672C2214yescomplemented
118#2671C2214yescomplemented
119#2669C2214yes—
120#2668C2214yescomplemented
121#2659C2212yescomplemented
122#2639C2212yescomplemented
123#2628C2212yescomplemented
124#2627C2212yescomplemented
125#2625C2212yescomplemented
126#2620C2212yescomplemented
127#2620C2212yescomplemented
128#2619C2212yescomplemented
129#2618C2212yes—
130#2618C2212yescomplemented
131#2617C2212yes—
132#2616C2212yescomplemented
133#2616C2212yescomplemented
134#2615C2212yescomplemented
135#2592C2212yescomplemented
136#2581C2212yescomplemented
137#2563C2212yescomplemented
138#2560C2214yescomplemented
139#2558C2214yescomplemented
140#2557C2214yescomplemented
141#2555C2214yescomplemented
142#2554C2214yescomplemented
143#2554C2214yescomplemented
144#2553C2214yescomplemented
145#2550C2214yescomplemented
146#2546C2212yescomplemented
147#2543C2214yes—
148#2543C2214yescomplemented
149#2543C2214yescomplemented
150#2540C2212yescomplemented
151#2539C2214yescomplemented
152#2538C2212yescomplemented
153#2538C2212yescomplemented
154#2535C2212yescomplemented
155#2534C2214yes—
156#2519C2214yescomplemented
157#2491C2214yescomplemented
158#2490C2214yescomplemented
159#2488C2214yescomplemented
160#2488C2214yescomplemented
161#2487C2212yescomplemented
162#2486C2212yes—
163#2486C2212yescomplemented
164#2486C2212yescomplemented
165#2480C2214yescomplemented
166#2477C2214yescomplemented
167#2474C2214yescomplemented
168#2472C2214yes—
169#2472C2214yescomplemented
170#2465C2214yescomplemented
171#2464C2214yescomplemented
172#2459C2214yescomplemented
173#2452C2214yescomplemented
174#2449C2214yescomplemented
175#2445C2214yes—
176#2444C2214yescomplemented
177#2443C2214yes—
178#2440C2214yescomplemented
179#2430C2214yescomplemented
180#2430C2214yescomplemented
181#2429C2214yescomplemented
182#2429C2214yescomplemented
183#2428C2214yescomplemented
184#2428C2214yescomplemented
185#2427C2214yescomplemented
186#2426C2214yescomplemented
187#2425C2214yescomplemented
188#2425C2214yescomplemented
189#2424C2214yes—
190#2424C2214yescomplemented
191#2424C2214yescomplemented
192#2420C2214yescomplemented
193#2419C2214yescomplemented
194#2417C2212yescomplemented
195#2417C2212yescomplemented
196#2417C2212yescomplemented
197#2416C2212yes—
198#2416C2212yes—
199#2416C2212yes—
200#2416C2212yes—
201#2416C2214yescomplemented
202#2416C2214yescomplemented
203#2416C2214yescomplemented
204#2416C2212yescomplemented
205#2415C2214yes—
206#2415C2212yes—
207#2415C2212yes—
208#2415C2212yescomplemented
209#2415C2214yescomplemented
210#2415C2212yescomplemented
211#2415C2214yescomplemented
212#2415C2212yescomplemented
213#2414C2212yescomplemented
214#2414C2212yescomplemented
215#2414C2212yescomplemented
216#2413C2214yescomplemented
217#2413C2214yescomplemented
218#2412C2214yes—
219#2411C2214yescomplemented
220#2410C2214yes—
221#2409C2212yescomplemented
222#2408C2212yes—
223#2407C2212yescomplemented
224#2407C2212yescomplemented
225#2404C2214yescomplemented
226C2×#397C2212yes—
227C2×#394C2212yes—
228#2364C2214yescomplemented
229#2359C2214yescomplemented
230#2359C2214yescomplemented
231#2358C2214yes—
232#2354C2212yescomplemented
233#2352C2212yescomplemented
234#2352C2212yescomplemented
235D4×C4⋊C4C2212yescomplemented
236#2339C2214yescomplemented
237#2324C2212yescomplemented
238#2324C2212yescomplemented
239#2323C2212yescomplemented
240#2323C2212yescomplemented
241#2317C2211yescharacteristic, complemented
242#2317C2211yescharacteristic, complemented
243#2311C2211yescharacteristic, complemented
244#2311C2212yescomplemented
245#2311C2211yescharacteristic, complemented
246#2309C2211yescharacteristic, complemented
247#2308C2212yes—
248C4×C22⋊Q8C2212yescomplemented
249C4×C22⋊Q8C2212yescomplemented
250C4×#121C2212yescomplemented
251C4×#121C2212yescomplemented
252#2297C2212yescomplemented
253C2×#391C2211yescharacteristic, complemented
254C2×#389C2212yescomplemented
255C2×#389C2211yescharacteristic, complemented
256C2×#389C2212yescomplemented
257C2×#388C2212yescomplemented
258C2×#380C2211yescharacteristic
259C2×#380C2211yescharacteristic, complemented
260#2274C2211yescharacteristic, complemented
261C22×#41C2312yes—
262C22×#41C2312yes—
263C22×#41C2311yescharacteristic
264C22×#41C2314yes—
265C22×#41C2312yes—
266C22×#41C2311yescharacteristic
267C23×Q8C2311yescharacteristic
268C23×D4C2311yescharacteristic
269C23×D4C2312yes—
270C23×D4C2311yescharacteristic
271C24×C4C2311yescharacteristic
272C24×C4C2311yescharacteristic
273#562—232no—
274#554—216no—
275#548—216no—
276#547—216no—
277#547—416no—
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—216no—
294#537—28no—
295#537—48no—
296#535—216no—
297#535—44no—
298#534—48no—
299#532—216no—
300#532—216no—
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2312yes—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2314yes—
305C2×#127C2312yes—
306C2×#127C2312yes—
307C2×#127C2312yes—
308#529—216no—
309#529—216no—
310C2×#126C2312yes—
311C2×#126C2312yes—
312C2×#126C2312yes—
313C2×#126C2312yes—
314C2×#126C2314yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#124C2312yes—
319C2×#124C2312yes—
320C2×#124C2312yes—
321C2×#124C2314yes—
322C2×#124C2312yes—
323C2×#124C2312yes—
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2314yes—
327C2×#124C2312yes—
328#525—28no—
329#525—216no—
330#525D4116yescomplemented
331C2×#123C2314yes—
332C2×#123C2312yes—
333C2×#123C2312yes—
334C2×#123C2312yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2312yes—
338C2×#123C2312yes—
339C2×#123C2312yes—
340C2×#123C2312yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2312yes—
348C2×C22⋊Q8—28no—
349C2×C22⋊Q8—44no—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2314yes—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2312yes—
364C2×C22⋊Q8C2314yes—
365C2×C22⋊Q8C2314yes—
366C2×C22⋊Q8C2314yes—
367C2×C22⋊Q8C2314yes—
368C2×C22⋊Q8C2312yes—
369C2×C22⋊Q8C2314yes—
370C2×C22⋊Q8C2312yes—
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2314yes—
373C2×C22⋊Q8C2314yes—
374C2×C22⋊Q8C2314yes—
375C2×C22⋊Q8C2311yescharacteristic
376C2×C22⋊Q8C2311yescharacteristic
377C2×#121—28no—
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2311yescharacteristic
382C2×#121C2311yescharacteristic
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2312yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2312yes—
390C2×#121C2314yes—
391C2×#121C2312yes—
392C2×#121C2312yes—
393C2×#121C2312yes—
394C2×#121C2314yes—
395C2×#121C2314yes—
396C2×#121C2314yes—
397C2×#121C2312yes—
398C2×#121C2312yes—
399C2×#121C2312yes—
400C2×#121C2312yes—
401C2×#121C2312yes—
402C2×#121C2314yes—
403C2×#121C2312yes—
404C2×#121C2312yes—
405C2×#121C2312yes—
406C2×#121C2314yes—
407C2×#121C2314yes—
408C2×#121C2314yes—
409C2×#121C2314yes—
410C2×#121C2314yes—
411C2×#121C2314yes—
412C2×#121C2314yes—
413C2×#121C2314yes—
414C2×#121C2311yescharacteristic
415C2×#121C2311yescharacteristic
416C2×#120C2312yes—
417C2×#120C2312yes—
418C2×#120C2312yes—
419C2×#120C2314yes—
420C2×#120C2314yes—
421C2×#120C2314yes—
422C2×#120C2314yes—
423C2×#120C2312yes—
424#520—44no—
425C4×#41—216no—
426C2×C4×Q8C2312yes—
427C2×C4×Q8C2312yes—
428C2×C4×Q8C2312yes—
429C2×C4×Q8C2312yes—
430C2×C4×D4—28no—
431C2×C4×D4C2312yes—
432C2×C4×D4C2312yes—
433C2×C4×D4C2312yes—
434C2×C4×D4C2314yes—
435C2×C4×D4C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2312yes—
438C2×C4×D4C2312yes—
439C2×C4×D4C2312yes—
440C2×C4×D4C2312yes—
441C2×C4×D4C2312yes—
442C2×C4×D4C2312yes—
443C2×C4×D4C2312yes—
444C2×C4×D4C2312yes—
445C2×C4×D4C2314yes—
446C2×C4×D4C2312yes—
447C2×C4×D4C2314yes—
448C2×C4×D4C2314yes—
449C2×C4×D4C2314yes—
450C2×C4×D4C2312yes—
451C2×C4×D4C2312yes—
452C2×#117—44no—
453C2×#117C2311yescharacteristic
454C2×#117C2311yescharacteristic
455C2×#117C2312yes—
456C2×#117C2312yes—
457C2×#117C2311yescharacteristic
458C2×#117C2312yes—
459C2×#117C2312yes—
460C2×#117C2311yescharacteristic
461C2×#117C2311yescharacteristic
462C2×#117C2312yes—
463C2×#117C2312yes—
464C2×#117C2312yes—
465C2×#117C2311yescharacteristic
466C22×C4⋊C4C2311yescharacteristic
467C22×C4⋊C4C2312yes—
468C22×C4⋊C4C2311yescharacteristic
469C22×C4⋊C4C2312yes—
470C22×C4⋊C4C2311yescharacteristic
471C22×C4⋊C4C2312yes—
472C22×C4⋊C4C2312yes—
473C22×C4⋊C4C2311yescharacteristic
474C22×C4⋊C4C2311yescharacteristic
475C22×C4⋊C4C2311yescharacteristic
476C22×C4⋊C4C2311yescharacteristic
477C22×C4⋊C4C2312yes—
478C22×C4⋊C4C2314yes—
479C22×C22⋊C4C2311yescharacteristic
480C22×C22⋊C4C2311yescharacteristic
481C22×C22⋊C4C2312yes—
482C22×C22⋊C4C2312yes—
483C22×C22⋊C4C2314yes—
484C22×C22⋊C4C2312yes—
485C22×C22⋊C4C2312yes—
486C22×C22⋊C4C2312yes—
487C22×C22⋊C4C2312yes—
488C22×C42C2312yes—
489C22×C42C2311yescharacteristic
490C22×C42C2312yes—
491C22×C42C2312yes—
492#400C2314yes—
493#400C2314yes—
494#400C2314yes—
495#400C2314yes—
496#399C2314yes—
497#399C2314yes—
498#399C2314yes—
499#398C2314yes—
500#398C2314yes—
501#398C2314yes—
502#398C2314yes—
503#398C2314yes—
504#398C2314yes—
505#398C2314yes—
506#398C2314yes—
507#398C2314yes—
508#397C2314yes—
509#397C2314yes—
510#397C2314yes—
511#397C2314yes—
512#397C2314yes—
513#397C2314yes—
514#397C2314yes—
515#397C2314yes—
516#397C2314yes—
517#397C2314yes—
518#397C2314yes—
519#397C2314yes—
520#396C2314yes—
521#396C2314yes—
522#396C2314yes—
523#396C2314yes—
524#396C2314yes—
525#396C2314yes—
526#396C2314yes—
527#396C2314yes—
528#396C2314yes—
529#396C2314yes—
530#396C2314yes—
531#396C2314yes—
532#396C2314yes—
533#396C2314yes—
534#395C2314yes—
535#395C2314yes—
536#395C2314yes—
537#395C2314yes—
538#395C2314yes—
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#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2314yes—
558#394C2314yes—
559#394C2314yes—
560#394C2314yes—
561#394C2314yes—
562#394C2314yes—
563#393C2314yes—
564#393C2314yes—
565#393C2314yes—
566#393C2314yes—
567#393C2314yes—
568#393C2314yes—
569#392C2314yes—
570#392C2314yes—
571#392C2314yes—
572#392C2314yes—
573#392C2314yes—
574#392C2314yes—
575#392C2314yes—
576#392C2314yes—
577#392C2314yes—
578#392C2314yes—
579#392C2314yes—
580#391C2314yes—
581#391C2312yes—
582#391C2312yes—
583#391C2314yes—
584#391C2312yes—
585#391C2312yes—
586#391C2312yes—
587#391C2312yes—
588#391C2314yes—
589#391C2314yes—
590#390C2314yes—
591#390C2314yes—
592#390C2312yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2314yes—
599#390C2314yes—
600#390C2314yes—
601#390C2312yes—
602#390C2312yes—
603#390C2314yes—
604#390C2314yes—
605#390C2314yes—
606#390C2314yes—
607#390C2314yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2314yes—
613#389C2314yes—
614#389C2312yes—
615#389C2312yes—
616#389C2312yes—
617#389C2312yes—
618#389C2314yes—
619#389C2314yes—
620#389C2312yes—
621#389C2314yes—
622#389C2314yes—
623#389C2314yes—
624#389C2312yes—
625#389C2314yes—
626#389C2314yes—
627#389C2314yes—
628#389C2314yes—
629#389C2314yes—
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#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
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#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
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#384C2312yes—
706#382C2314yes—
707#382C2312yes—
708#382C2312yes—
709#381C2314yes—
710#381C2314yes—
711#381C2314yes—
712#381C2314yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2314yes—
725#380C2314yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2314yes—
731#380C2314yes—
732#380C2314yes—
733#379C2314yes—
734#379C2314yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2314yes—
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×#95C2314yes—
750C2×#95C2312yes—
751C2×#95C2312yes—
752C2×#95C2312yes—
753C2×#95C2312yes—
754C25C2411yescharacteristic
755C25C2411yescharacteristic
756C25C2412yes—
757C2×#41—28no—
758C2×#41—216no—
759C2×#41—24no—
760C2×#41—28no—
761C2×#41—28no—
762C2×#41—28no—
763C2×#41—42no—
764C2×#41—42no—
765C2×#41—42no—
766C2×#41—44no—
767C2×#41—42no—
768C2×#41—44no—
769C2×#41—44no—
770C2×#41—48no—
771C2×#41—48no—
772C2×#41—44no—
773C2×#41—44no—
774C2×#41C2×D418yes—
775C22×Q8—24no—
776C22×Q8—42no—
777C22×Q8—42no—
778C22×Q8C2412yes—
779C22×Q8C2412yes—
780C22×Q8C2412yes—
781C22×Q8C2414yes—
782C22×Q8C2412yes—
783C22×Q8C2411yescharacteristic
784C22×Q8C2411yescharacteristic
785C22×D4—24no—
786C22×D4—28no—
787C22×D4—24no—
788C22×D4—24no—
789C22×D4—42no—
790C22×D4—42no—
791C22×D4—42no—
792C22×D4—44no—
793C22×D4—44no—
794C22×D4C2412yes—
795C22×D4C2414yes—
796C22×D4C2412yes—
797C22×D4C2412yes—
798C22×D4C2412yes—
799C22×D4C2412yes—
800C22×D4C2412yes—
801C22×D4C2414yes—
802C22×D4C2412yes—
803C22×D4C2412yes—
804C22×D4C2412yes—
805C22×D4C2412yes—
806C22×D4C2414yes—
807C22×D4C2414yes—
808C22×D4C2412yes—
809C22×D4C2412yes—
810C22×D4C2412yes—
811C22×D4C2414yes—
812C22×D4C2411yescharacteristic
813C22×D4C2412yes—
814C22×D4C2414yes—
815C22×D4C2414yes—
816C22×D4C2414yes—
817C22×D4C2412yes—
818C22×D4C2412yes—
819C22×D4C2411yescharacteristic
820C23×C4—24no—
821C23×C4—42no—
822C23×C4—42no—
823C23×C4—42no—
824C23×C4—42no—
825C23×C4C2×D418yes—
826C23×C4C2412yes—
827C23×C4C2412yes—
828C23×C4C2412yes—
829C23×C4C2412yes—
830C23×C4C2412yes—
831C23×C4C2412yes—
832C23×C4C2411yescharacteristic
833C23×C4C2411yescharacteristic
834C23×C4C2412yes—
835C23×C4C2411yescharacteristic
836C23×C4C2411yescharacteristic
837C23×C4C2412yes—
838C23×C4C2412yes—
839C23×C4C2411yescharacteristic
840C23×C4C2411yescharacteristic
841C23×C4C2412yes—
842C23×C4C2414yes—
843C23×C4C2414yes—
844C23×C4C2414yes—
845C23×C4C2414yes—
846C23×C4C2412yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C4⋊Q8—28no—
855C4⋊Q8—28no—
856C4⋊Q8—28no—
857C4⋊Q8—48no—
858#127—28no—
859#127—28no—
860#127—44no—
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#123—28no—
880#123—28no—
881#123—216no—
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—48no—
893#123—48no—
894#123—48no—
895#123C2×D4116yes—
896C22⋊Q8—216no—
897C22⋊Q8—28no—
898C22⋊Q8—28no—
899C22⋊Q8—28no—
900C22⋊Q8—28no—
901C22⋊Q8—24no—
902C22⋊Q8—24no—
903C22⋊Q8—28no—
904C22⋊Q8—28no—
905C22⋊Q8—28no—
906C22⋊Q8—216no—
907C22⋊Q8—216no—
908C22⋊Q8—216no—
909C22⋊Q8—28no—
910C22⋊Q8—28no—
911C22⋊Q8—28no—
912C22⋊Q8—216no—
913C22⋊Q8—216no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—48no—
917C22⋊Q8—48no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8C2×D418yes—
922C22⋊Q8C2×D418yes—
923#121—28no—
924#121—28no—
925#121—28no—
926#121—28no—
927#121—28no—
928#121—28no—
929#121—28no—
930#121—216no—
931#121—216no—
932#121—216no—
933#121—216no—
934#121—28no—
935#121—28no—
936#121—28no—
937#121—28no—
938#121—24no—
939#121—24no—
940#121—28no—
941#121—28no—
942#121—28no—
943#121—28no—
944#121—28no—
945#121—28no—
946#121—28no—
947#121—216no—
948#121—48no—
949#121—48no—
950#121—48no—
951#121—48no—
952#121—48no—
953#121—44no—
954#121—44no—
955#121—44no—
956#121—48no—
957#121—48no—
958#121—48no—
959#121C2×D418yes—
960#121C2×D418yes—
961#120—28no—
962#120—28no—
963#120—216no—
964#120—28no—
965#120—48no—
966#120—48no—
967#120—48no—
968#120C2×D4116yes—
969C4×Q8—28no—
970C4×Q8—28no—
971C4×Q8—28no—
972C4×Q8—44no—
973C4×D4—28no—
974C4×D4—216no—
975C4×D4—28no—
976C4×D4—28no—
977C4×D4—28no—
978C4×D4—28no—
979C4×D4—28no—
980C4×D4—28no—
981C4×D4—28no—
982C4×D4—28no—
983C4×D4—28no—
984C4×D4—28no—
985C4×D4—216no—
986C4×D4—28no—
987C4×D4—28no—
988C4×D4—44no—
989C4×D4—48no—
990C4×D4—48no—
991C4×D4—48no—
992C4×D4C2×D4116yes—
993C4×D4C2×D4116yes—
994#117—24no—
995#117—28no—
996#117—24no—
997#117—24no—
998#117—28no—
999#117—28no—
1000#117—28no—
1001#117—44no—
1002#117—44no—
1003#117—42no—
1004#117—42no—
1005#117—44no—
1006#117C2×D418yes—
1007C2×C4⋊C4—24no—
1008C2×C4⋊C4—24no—
1009C2×C4⋊C4—28no—
1010C2×C4⋊C4—24no—
1011C2×C4⋊C4—28no—
1012C2×C4⋊C4—28no—
1013C2×C4⋊C4—24no—
1014C2×C4⋊C4—28no—
1015C2×C4⋊C4—42no—
1016C2×C4⋊C4—42no—
1017C2×C4⋊C4—42no—
1018C2×C4⋊C4—44no—
1019C2×C4⋊C4—48no—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2411yescharacteristic
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2411yescharacteristic
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2414yes—
1063C2×C4⋊C4C2414yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2414yes—
1067C2×C4⋊C4C2414yes—
1068C2×C4⋊C4C2412yes—
1069C2×C4⋊C4C2411yescharacteristic
1070C2×C4⋊C4C2411yescharacteristic
1071C2×C4⋊C4C2412yes—
1072C2×C4⋊C4C2411yescharacteristic
1073C2×C22⋊C4—24no—
1074C2×C22⋊C4—28no—
1075C2×C22⋊C4—24no—
1076C2×C22⋊C4—28no—
1077C2×C22⋊C4—216no—
1078C2×C22⋊C4—44no—
1079C2×C22⋊C4—44no—
1080C2×C22⋊C4—44no—
1081C2×C22⋊C4—44no—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2412yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2412yes—
1144C2×C22⋊C4C2412yes—
1145C2×C22⋊C4C2412yes—
1146C2×C42—24no—
1147C2×C42—28no—
1148C2×C42—28no—
1149C2×C42—44no—
1150C2×C42C2412yes—
1151C2×C42C2412yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2412yes—
1155C2×C42C2412yes—
1156C2×C42C2412yes—
1157C2×C42C2414yes—
1158C2×C42C2412yes—
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2412yes—
1162C2×C42C2414yes—
1163C2×C42C2414yes—
1164C2×C42C2414yes—
1165C2×C42C2412yes—
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—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198C24—22no—
1199C24—22no—
1200C24—22no—
1201C24—24no—
1202C24—22no—
1203C24—22no—
1204C24—41no—
1205C24—41no—
1206C24—41no—
1207C24—41no—
1208C24—41no—
1209C24—41no—
1210C24—41no—
1211C24—41no—
1212C24—42no—
1213C24—42no—
1214C24—42no—
1215C24—42no—
1216C24—42no—
1217C24—42no—
1218C24C22×D414yes—
1219C24C2512yes—
1220C24C2514yes—
1221C24C2512yes—
1222C24C2511yescharacteristic
1223C24C2511yescharacteristic
1224C24C2512yes—
1225C24C2511yescharacteristic
1226#41—416no—
1227#41—432no—
1228#41—88no—
1229#41—816no—
1230#41—816no—
1231#41—832no—
1232C2×Q8—24no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—28no—
1236C2×Q8—22no—
1237C2×Q8—24no—
1238C2×Q8—24no—
1239C2×Q8—24no—
1240C2×Q8—24no—
1241C2×Q8—41no—
1242C2×Q8—41no—
1243C2×Q8—42no—
1244C2×Q8—42no—
1245C2×Q8—42no—
1246C2×Q8—44no—
1247C2×Q8—41no—
1248C2×Q8—42no—
1249C2×Q8—41no—
1250C2×Q8—42no—
1251C2×Q8—44no—
1252C2×Q8—88no—
1253C2×Q8C22×D414yes—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—24no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—28no—
1261C2×D4—28no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—28no—
1265C2×D4—24no—
1266C2×D4—24no—
1267C2×D4—28no—
1268C2×D4—28no—
1269C2×D4—24no—
1270C2×D4—24no—
1271C2×D4—24no—
1272C2×D4—28no—
1273C2×D4—24no—
1274C2×D4—24no—
1275C2×D4—24no—
1276C2×D4—22no—
1277C2×D4—24no—
1278C2×D4—24no—
1279C2×D4—24no—
1280C2×D4—24no—
1281C2×D4—24no—
1282C2×D4—28no—
1283C2×D4—24no—
1284C2×D4—41no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—41no—
1291C2×D4—42no—
1292C2×D4—42no—
1293C2×D4—416no—
1294C2×D4—44no—
1295C2×D4—42no—
1296C2×D4—44no—
1297C2×D4—42no—
1298C2×D4—42no—
1299C2×D4—44no—
1300C2×D4—42no—
1301C2×D4—44no—
1302C2×D4—42no—
1303C2×D4—41no—
1304C2×D4—42no—
1305C2×D4—44no—
1306C2×D4—42no—
1307C2×D4—42no—
1308C2×D4—44no—
1309C2×D4—42no—
1310C2×D4—42no—
1311C2×D4—42no—
1312C2×D4—42no—
1313C2×D4—41no—
1314C2×D4—42no—
1315C2×D4—42no—
1316C2×D4—44no—
1317C2×D4—44no—
1318C2×D4—42no—
1319C2×D4—42no—
1320C2×D4—44no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—44no—
1324C2×D4—44no—
1325C2×D4—44no—
1326C2×D4—44no—
1327C2×D4—44no—
1328C2×D4—44no—
1329C2×D4—88no—
1330C2×D4—816no—
1331C2×D4C22×D418yes—
1332C2×D4C22×D418yes—
1333C2×D4C22×D418yes—
1334C2×D4C22×D414yes—
1335C22×C4—22no—
1336C22×C4—22no—
1337C22×C4—22no—
1338C22×C4—24no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—24no—
1345C22×C4—24no—
1346C22×C4—24no—
1347C22×C4—24no—
1348C22×C4—24no—
1349C22×C4—24no—
1350C22×C4—22no—
1351C22×C4—24no—
1352C22×C4—24no—
1353C22×C4—24no—
1354C22×C4—22no—
1355C22×C4—28no—
1356C22×C4—24no—
1357C22×C4—24no—
1358C22×C4—24no—
1359C22×C4—24no—
1360C22×C4—24no—
1361C22×C4—24no—
1362C22×C4—24no—
1363C22×C4—24no—
1364C22×C4—24no—
1365C22×C4—24no—
1366C22×C4—24no—
1367C22×C4—24no—
1368C22×C4—28no—
1369C22×C4—28no—
1370C22×C4—24no—
1371C22×C4—28no—
1372C22×C4—416no—
1373C22×C4—41no—
1374C22×C4—41no—
1375C22×C4—41no—
1376C22×C4—41no—
1377C22×C4—41no—
1378C22×C4—41no—
1379C22×C4—42no—
1380C22×C4—42no—
1381C22×C4—42no—
1382C22×C4—42no—
1383C22×C4—42no—
1384C22×C4—41no—
1385C22×C4—44no—
1386C22×C4—44no—
1387C22×C4—44no—
1388C22×C4—44no—
1389C22×C4—42no—
1390C22×C4—42no—
1391C22×C4—42no—
1392C22×C4—41no—
1393C22×C4—42no—
1394C22×C4—42no—
1395C22×C4—44no—
1396C22×C4—42no—
1397C22×C4—41no—
1398C22×C4—41no—
1399C22×C4—42no—
1400C22×C4—42no—
1401C22×C4—42no—
1402C22×C4—42no—
1403C22×C4—44no—
1404C22×C4—44no—
1405C22×C4—44no—
1406C22×C4—42no—
1407C22×C4—42no—
1408C22×C4—42no—
1409C22×C4—42no—
1410C22×C4—42no—
1411C22×C4—42no—
1412C22×C4—88no—
1413C22×C4C22×D414yes—
1414C22×C4C22×D418yes—
1415C22×C4C22×D414yes—
1416C22×C4C22×D414yes—
1417C22×C4C22×D414yes—
1418C22×C4C22×D414yes—
1419C22×C4C22×D414yes—
1420C22×C4H(5,𝔽2)14yes—
1421C22×C4C2512yes—
1422C22×C4C2512yes—
1423C22×C4C2514yes—
1424C22×C4C2512yes—
1425C22×C4C2512yes—
1426C22×C4C2514yes—
1427C22×C4C2512yes—
1428C22×C4C2514yes—
1429C22×C4C2514yes—
1430C22×C4C2514yes—
1431C22×C4C2512yes—
1432C22×C4C2512yes—
1433C22×C4C2512yes—
1434C22×C4C2512yes—
1435C22×C4C2512yes—
1436C22×C4C2512yes—
1437C22×C4C2511yescharacteristic
1438C22×C4C2511yescharacteristic
1439C22×C4C2511yescharacteristic
1440C22×C4C2512yes—
1441C22×C4C2512yes—
1442C22×C4C2511yescharacteristic
1443C4⋊C4—24no—
1444C4⋊C4—24no—
1445C4⋊C4—24no—
1446C4⋊C4—24no—
1447C4⋊C4—24no—
1448C4⋊C4—28no—
1449C4⋊C4—28no—
1450C4⋊C4—28no—
1451C4⋊C4—24no—
1452C4⋊C4—24no—
1453C4⋊C4—24no—
1454C4⋊C4—24no—
1455C4⋊C4—24no—
1456C4⋊C4—24no—
1457C4⋊C4—22no—
1458C4⋊C4—24no—
1459C4⋊C4—22no—
1460C4⋊C4—24no—
1461C4⋊C4—28no—
1462C4⋊C4—24no—
1463C4⋊C4—24no—
1464C4⋊C4—24no—
1465C4⋊C4—28no—
1466C4⋊C4—28no—
1467C4⋊C4—24no—
1468C4⋊C4—28no—
1469C4⋊C4—24no—
1470C4⋊C4—22no—
1471C4⋊C4—28no—
1472C4⋊C4—28no—
1473C4⋊C4—22no—
1474C4⋊C4—22no—
1475C4⋊C4—28no—
1476C4⋊C4—28no—
1477C4⋊C4—28no—
1478C4⋊C4—24no—
1479C4⋊C4—42no—
1480C4⋊C4—42no—
1481C4⋊C4—42no—
1482C4⋊C4—44no—
1483C4⋊C4—44no—
1484C4⋊C4—44no—
1485C4⋊C4—44no—
1486C4⋊C4—44no—
1487C4⋊C4—44no—
1488C4⋊C4—44no—
1489C4⋊C4—44no—
1490C4⋊C4—44no—
1491C4⋊C4C22×D418yes—
1492C4⋊C4C22×D414yes—
1493C4⋊C4C22×D414yes—
1494C4⋊C4C22×D418yes—
1495C4⋊C4H(5,𝔽2)14yes—
1496C22⋊C4—28no—
1497C22⋊C4—24no—
1498C22⋊C4—24no—
1499C22⋊C4—28no—
1500C22⋊C4—24no—
1501C22⋊C4—24no—
1502C22⋊C4—24no—
1503C22⋊C4—24no—
1504C22⋊C4—28no—
1505C22⋊C4—24no—
1506C22⋊C4—28no—
1507C22⋊C4—24no—
1508C22⋊C4—24no—
1509C22⋊C4—28no—
1510C22⋊C4—28no—
1511C22⋊C4—28no—
1512C22⋊C4—28no—
1513C22⋊C4—24no—
1514C22⋊C4—24no—
1515C22⋊C4—24no—
1516C22⋊C4—24no—
1517C22⋊C4—24no—
1518C22⋊C4—24no—
1519C22⋊C4—28no—
1520C22⋊C4—28no—
1521C22⋊C4—24no—
1522C22⋊C4—24no—
1523C22⋊C4—24no—
1524C22⋊C4—24no—
1525C22⋊C4—28no—
1526C22⋊C4—28no—
1527C22⋊C4—28no—
1528C22⋊C4—28no—
1529C22⋊C4—44no—
1530C22⋊C4—44no—
1531C22⋊C4—42no—
1532C22⋊C4—42no—
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⋊C4—44no—
1553C22⋊C4—44no—
1554C22⋊C4—44no—
1555C22⋊C4C22×D418yes—
1556C22⋊C4C22×D418yes—
1557C22⋊C4C22×D418yes—
1558C22⋊C4C22×D418yes—
1559C22⋊C4C22×D418yes—
1560C42—24no—
1561C42—24no—
1562C42—24no—
1563C42—24no—
1564C42—24no—
1565C42—24no—
1566C42—24no—
1567C42—28no—
1568C42—24no—
1569C42—24no—
1570C42—42no—
1571C42—42no—
1572C42—44no—
1573C42—44no—
1574C42—44no—
1575C42C22×D418yes—
1576C23—21no—
1577C23—21no—
1578C23—21no—
1579C23—21no—
1580C23—21no—
1581C23—21no—
1582C23—21no—
1583C23—22no—
1584C23—22no—
1585C23—21no—
1586C23—21no—
1587C23—21no—
1588C23—22no—
1589C23—22no—
1590C23—21no—
1591C23—21no—
1592C23—22no—
1593C23—22no—
1594C23—21no—
1595C23—21no—
1596C23—21no—
1597C23—21no—
1598C23—28no—
1599C23—22no—
1600C23—24no—
1601C23—22no—
1602C23—22no—
1603C23—24no—
1604C23—24no—
1605C23—22no—
1606C23—22no—
1607C23—22no—
1608C23—22no—
1609C23—22no—
1610C23—22no—
1611C23—24no—
1612C23—24no—
1613C23—22no—
1614C23—24no—
1615C23—24no—
1616C23—22no—
1617C23—22no—
1618C23—22no—
1619C23—22no—
1620C23—44no—
1621C23—44no—
1622C23—44no—
1623C23—44no—
1624C23—48no—
1625C23—44no—
1626C23—82no—
1627C23—82no—
1628C23—82no—
1629C23—82no—
1630C23—82no—
1631C23—82no—
1632C23—82no—
1633C23—82no—
1634C23—84no—
1635C23—84no—
1636C23—162no—
1637C23—162no—
1638C23—162no—
1639C23—162no—
1640C23C23×D412yes—
1641C23C23×D412yes—
1642C23C23×D414yes—
1643C23C23×D412yes—
1644C23C2×H(5,𝔽2)12yes—
1645C23#58512yes—
1646C23C2611yescharacteristic
1647Q8—44no—
1648Q8—48no—
1649Q8—48no—
1650Q8—84no—
1651Q8—82no—
1652Q8—84no—
1653Q8—88no—
1654D4—216no—
1655D4—48no—
1656D4—44no—
1657D4—48no—
1658D4—48no—
1659D4—48no—
1660D4—48no—
1661D4—416no—
1662D4—48no—
1663D4—48no—
1664D4—84no—
1665D4—88no—
1666D4—84no—
1667D4—82no—
1668D4—84no—
1669D4—84no—
1670D4—84no—
1671D4—88no—
1672D4—84no—
1673D4—84no—
1674D4—84no—
1675D4—88no—
1676D4—88no—
1677D4—164no—
1678D4—164no—
1679D4—164no—
1680C2×C4—22no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—21no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—21no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—22no—
1694C2×C4—22no—
1695C2×C4—22no—
1696C2×C4—28no—
1697C2×C4—28no—
1698C2×C4—28no—
1699C2×C4—28no—
1700C2×C4—216no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—22no—
1705C2×C4—24no—
1706C2×C4—24no—
1707C2×C4—22no—
1708C2×C4—24no—
1709C2×C4—22no—
1710C2×C4—22no—
1711C2×C4—22no—
1712C2×C4—24no—
1713C2×C4—24no—
1714C2×C4—24no—
1715C2×C4—22no—
1716C2×C4—24no—
1717C2×C4—22no—
1718C2×C4—24no—
1719C2×C4—22no—
1720C2×C4—24no—
1721C2×C4—22no—
1722C2×C4—22no—
1723C2×C4—24no—
1724C2×C4—22no—
1725C2×C4—22no—
1726C2×C4—22no—
1727C2×C4—24no—
1728C2×C4—24no—
1729C2×C4—24no—
1730C2×C4—22no—
1731C2×C4—22no—
1732C2×C4—24no—
1733C2×C4—22no—
1734C2×C4—22no—
1735C2×C4—22no—
1736C2×C4—22no—
1737C2×C4—22no—
1738C2×C4—22no—
1739C2×C4—24no—
1740C2×C4—44no—
1741C2×C4—44no—
1742C2×C4—44no—
1743C2×C4—48no—
1744C2×C4—48no—
1745C2×C4—48no—
1746C2×C4—48no—
1747C2×C4—48no—
1748C2×C4—48no—
1749C2×C4—84no—
1750C2×C4—88no—
1751C2×C4—84no—
1752C2×C4—88no—
1753C2×C4—88no—
1754C2×C4—82no—
1755C2×C4—84no—
1756C2×C4—84no—
1757C2×C4—82no—
1758C2×C4—84no—
1759C2×C4—84no—
1760C2×C4—88no—
1761C2×C4—162no—
1762C2×C4—162no—
1763C2×C4C23×D414yes—
1764C2×C4C23×D412yes—
1765C2×C4C23×D414yes—
1766C2×C4C23×D414yes—
1767C2×C4C23×D412yes—
1768C2×C4C23×D412yes—
1769C2×C4C23×D412yes—
1770C2×C4C2×H(5,𝔽2)14yes—
1771C2×C4C2×H(5,𝔽2)14yes—
1772C2×C4C2×H(5,𝔽2)12yes—
1773C2×C4#58512yes—
1774C22—22no—
1775C22—22no—
1776C22—22no—
1777C22—22no—
1778C22—22no—
1779C22—22no—
1780C22—22no—
1781C22—22no—
1782C22—24no—
1783C22—24no—
1784C22—22no—
1785C22—22no—
1786C22—24no—
1787C22—22no—
1788C22—22no—
1789C22—42no—
1790C22—41no—
1791C22—41no—
1792C22—42no—
1793C22—41no—
1794C22—41no—
1795C22—41no—
1796C22—42no—
1797C22—41no—
1798C22—42no—
1799C22—41no—
1800C22—41no—
1801C22—42no—
1802C22—42no—
1803C22—44no—
1804C22—42no—
1805C22—44no—
1806C22—42no—
1807C22—42no—
1808C22—42no—
1809C22—44no—
1810C22—42no—
1811C22—44no—
1812C22—42no—
1813C22—42no—
1814C22—44no—
1815C22—42no—
1816C22—42no—
1817C22—44no—
1818C22—42no—
1819C22—42no—
1820C22—42no—
1821C22—44no—
1822C22—88no—
1823C22—88no—
1824C22—168no—
1825C22#348814yes—
1826C22C24×D411yescharacteristic
1827C22C22×H(5,𝔽2)11yescharacteristic
1828C22C22×H(5,𝔽2)11yescharacteristic
1829C22C2×#58511yescharacteristic
1830C22C2×#58511yescharacteristic
1831C222−1+611yescharacteristic
1832C222−1+611yescharacteristic
1833C4—22no—
1834C4—22no—
1835C4—22no—
1836C4—24no—
1837C4—24no—
1838C4—24no—
1839C4—24no—
1840C4—24no—
1841C4—42no—
1842C4—42no—
1843C4—44no—
1844C4—44no—
1845C4—42no—
1846C4—44no—
1847C4—42no—
1848C4—42no—
1849C4—42no—
1850C4—44no—
1851C4—42no—
1852C4—42no—
1853C4—44no—
1854C4#349614yes—
1855C2—24no—
1856C2—44no—
1857C2—42no—
1858C2—42no—
1859C2—82no—
1860C2—82no—
1861C2—84no—
1862C2C2×#349611yescharacteristic
1863C2C2×#348811yescharacteristic
1864C2#6285911yescharacteristic
1865C2#6291411yescharacteristic
1866C2#6291911yescharacteristic
1867C2#6293111yescharacteristic
1868C2#6293411yescharacteristic
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. #49588C2semidirect
4. #49583C2semidirect
5. #47455C2semidirect
6. #46373C2semidirect
7. #43904C2semidirect
8. #43489C2semidirect
9. #39470C2semidirect
10. #39421C2semidirect
11. #39415C2semidirect
12. #39380C2semidirect
13. #39359C2semidirect
14. #39334C2semidirect
15. #38040C2semidirect
16. #38034C2semidirect
17. #37839C2semidirect
18. #37649C2semidirect
19. #37442C2semidirect
20. #37277C2semidirect
21. #37272C2semidirect
22. #36374C2semidirect
23. #36259C2semidirect
24. #35568C2semidirect
25. #35564C2semidirect
26. #35252C2semidirect
27. #35000C2semidirect
28. C2×#2415C2semidirect
29. #34202C2semidirect
31. C2×#562C22semidirect
32. C2×#554C22semidirect
35. C2×#547C22semidirect
37. C2×#546C22semidirect
39. C2×#544C22semidirect
40. C2×#543C22semidirect
42. C2×#542C22semidirect
43. C2×#542C22semidirect
45. C2×#540C22semidirect
48. C2×#538C22semidirect
49. C2×#538C22semidirect
50. C2×#538C22semidirect
52. C2×#537C22semidirect
53. C2×#537C22semidirect
54. C2×#537C22semidirect
56. C2×#535C22semidirect
59. C2×#532C22semidirect
61. C2×#529C22semidirect
64. C2×#525C22semidirect
66. C22×C22⋊Q8C22semidirect
68. C2×#520C22semidirect
69. C2×C4×#41C22semidirect
72. #2857C22semidirect
74. #2855C22semidirect
76. #2854C22semidirect
78. #2850C22semidirect
80. #2814C22semidirect
81. #2730C22semidirect
82. #2729C22semidirect
83. #2725C22semidirect
84. #2721C22semidirect
85. #2719C22semidirect
86. #2715C22semidirect
87. #2706C22semidirect
88. #2705C22semidirect
89. #2703C22semidirect
90. #2703C22semidirect
91. #2702C22semidirect
92. #2700C22semidirect
93. #2700C22semidirect
94. #2699C22semidirect
95. #2697C22semidirect
96. #2696C22semidirect
97. #2693C22semidirect
98. #2692C22semidirect
99. #2689C22semidirect
100. #2688C22semidirect
101. #2686C22semidirect
102. #2683C22semidirect
103. #2683C22semidirect
104. #2682C22semidirect
106. #2681C22semidirect
107. #2681C22semidirect
108. #2681C22semidirect
110. #2676C22semidirect
111. #2676C22semidirect
113. #2674C22semidirect
114. #2673C22semidirect
115. #2673C22semidirect
116. #2672C22semidirect
117. #2672C22semidirect
118. #2671C22semidirect
120. #2668C22semidirect
121. #2659C22semidirect
122. #2639C22semidirect
123. #2628C22semidirect
124. #2627C22semidirect
125. #2625C22semidirect
126. #2620C22semidirect
127. #2620C22semidirect
128. #2619C22semidirect
130. #2618C22semidirect
132. #2616C22semidirect
133. #2616C22semidirect
134. #2615C22semidirect
135. #2592C22semidirect
136. #2581C22semidirect
137. #2563C22semidirect
138. #2560C22semidirect
139. #2558C22semidirect
140. #2557C22semidirect
141. #2555C22semidirect
142. #2554C22semidirect
143. #2554C22semidirect
144. #2553C22semidirect
145. #2550C22semidirect
146. #2546C22semidirect
148. #2543C22semidirect
149. #2543C22semidirect
150. #2540C22semidirect
151. #2539C22semidirect
152. #2538C22semidirect
153. #2538C22semidirect
154. #2535C22semidirect
156. #2519C22semidirect
157. #2491C22semidirect
158. #2490C22semidirect
159. #2488C22semidirect
160. #2488C22semidirect
161. #2487C22semidirect
163. #2486C22semidirect
164. #2486C22semidirect
165. #2480C22semidirect
166. #2477C22semidirect
167. #2474C22semidirect
169. #2472C22semidirect
170. #2465C22semidirect
171. #2464C22semidirect
172. #2459C22semidirect
173. #2452C22semidirect
174. #2449C22semidirect
176. #2444C22semidirect
178. #2440C22semidirect
179. #2430C22semidirect
180. #2430C22semidirect
181. #2429C22semidirect
182. #2429C22semidirect
183. #2428C22semidirect
184. #2428C22semidirect
185. #2427C22semidirect
186. #2426C22semidirect
187. #2425C22semidirect
188. #2425C22semidirect
190. #2424C22semidirect
191. #2424C22semidirect
192. #2420C22semidirect
193. #2419C22semidirect
194. #2417C22semidirect
195. #2417C22semidirect
196. #2417C22semidirect
201. #2416C22semidirect
202. #2416C22semidirect
203. #2416C22semidirect
204. #2416C22semidirect
208. #2415C22semidirect
209. #2415C22semidirect
210. #2415C22semidirect
211. #2415C22semidirect
212. #2415C22semidirect
213. #2414C22semidirect
214. #2414C22semidirect
215. #2414C22semidirect
216. #2413C22semidirect
217. #2413C22semidirect
219. #2411C22semidirect
221. #2409C22semidirect
223. #2407C22semidirect
224. #2407C22semidirect
225. #2404C22semidirect
228. #2364C22semidirect
229. #2359C22semidirect
230. #2359C22semidirect
232. #2354C22semidirect
233. #2352C22semidirect
234. #2352C22semidirect
235. D4×C4⋊C4C22semidirect
236. #2339C22semidirect
237. #2324C22semidirect
238. #2324C22semidirect
239. #2323C22semidirect
240. #2323C22semidirect
241. #2317C22semidirect
242. #2317C22semidirect
243. #2311C22semidirect
244. #2311C22semidirect
245. #2311C22semidirect
246. #2309C22semidirect
248. C4×C22⋊Q8C22semidirect
249. C4×C22⋊Q8C22semidirect
250. C4×#121C22semidirect
251. C4×#121C22semidirect
252. #2297C22semidirect
253. C2×#391C22semidirect
254. C2×#389C22semidirect
255. C2×#389C22semidirect
256. C2×#389C22semidirect
257. C2×#388C22semidirect
259. C2×#380C22semidirect
260. #2274C22semidirect
330. #525D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35362
C2×#34602
#495882
#495832
#474552
#463732
#439042
#434892
#394702
#394212
#394152
#393802
#393592
#393342
#380402
#380342
#378392
#376492
#374422
#372772
#372722
#363742
#362592
#355682
#355642
#352522
#350002
C2×#24152
#342022