Finite Group Databasebeta

← #7681797

Subgroups — #7681797

Order 512.

4588 conjugacy classes of subgroups.

The subgroup lattice has 1027 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59448C214yesmaximal, complemented
2#59447C214yesmaximal, complemented
3#59255C218yesmaximal, complemented
4#45154C214yesmaximal, complemented
5#45153C214yesmaximal, complemented
6#43057C218yesmaximal, complemented
7#39475C214yesmaximal, complemented
8#37986C214yesmaximal, complemented
9#37982C214yesmaximal, complemented
10#36199C214yesmaximal, complemented
11#35630C211yesmaximal, characteristic, complemented
12#35630C211yesmaximal, characteristic, complemented
13#35627C211yesmaximal, characteristic, complemented
14#35555C211yesmaximal, characteristic, complemented
15#35333C211yesmaximal, characteristic
16#35307C211yesmaximal, characteristic
17#35307C211yesmaximal, characteristic
18#34948C211yesmaximal, characteristic, complemented
19C2×#2565C211yesmaximal, characteristic, complemented
20#34217C211yesmaximal, characteristic, complemented
21#34189C211yesmaximal, characteristic
22#34188C211yesmaximal, characteristic
23#34187C211yesmaximal, characteristic, complemented
24C4⋊C4×#41C211yesmaximal, characteristic
25C4×#536C211yesmaximal, characteristic
26C2×#536C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2855C2214yes—
33#2855C2214yes—
34#2851C2214yes—
35#2794C2218yes—
36#2791C2218yes—
37#2787C2218yes—
38#2770C2218yes—
39#2769C2218yes—
40#2767C2218yes—
41#2766C2218yes—
42#2765C2218yes—
43#2765C2218yes—
44#2744C2218yes—
45#2739C2218yes—
46#2719C2218yes—
47#2629C2214yes—
48#2625C2214yes—
49#2625C2214yes—
50#2606C2218yes—
51#2590C2218yes—
52#2585C2218yes—
53#2579C2214yes—
54#2579C2214yes—
55#2577C2218yes—
56#2573C2218yes—
57#2571C2214yes—
58#2571C2212yes—
59#2570C2214yes—
60#2570C2212yes—
61#2570C2214yes—
62#2570C2212yes—
63#2569C2214yes—
64#2566C2212yes—
65#2566C2212yes—
66#2565C2212yes—
67#2565C2212yes—
68#2565C2212yes—
69#2565C2214yes—
70#2565C2212yes—
71#2565C2214yes—
72#2565C2212yes—
73#2565C2212yes—
74#2552C2214yes—
75#2552C2212yes—
76#2530C2218yes—
77#2528C2218yes—
78#2528C2218yes—
79#2528C2218yes—
80#2524C2218yes—
81#2524C2218yes—
82#2524C2218yes—
83#2515C2218yes—
84#2514C2214yes—
85#2514C2214yes—
86#2514C2214yes—
87#2514C2214yes—
88#2511C2214yes—
89#2511C2214yes—
90#2511C2214yes—
91#2511C2214yes—
92#2509C2214yes—
93#2508C2214yes—
94#2507C2214yes—
95#2506C2214yes—
96#2505C2218yes—
97#2493C2218yes—
98#2493C2218yes—
99#2493C2218yes—
100#2484C2218yes—
101#2475C2218yes—
102#2475C2218yes—
103#2473C2218yes—
104#2473C2218yes—
105#2447C2214yes—
106#2447C2214yes—
107#2446C2214yes—
108#2446C2214yes—
109#2442C2214yes—
110#2419C2218yes—
111#2419C2218yes—
112#2402C2214yes—
113C2×#398C2214yes—
114#2371C2218yes—
115#2370C2214yes—
116#2370C2214yes—
117#2357C2214yes—
118#2356C2214yes—
119#2356C2214yes—
120#2356C2214yes—
121#2355C2214yes—
122#2355C2214yes—
123#2355C2214yes—
124#2354C2214yes—
125#2353C2218yes—
126#2352C2218yes—
127#2351C2212yes—
128Q8×C4⋊C4C2212yes—
129#2349C2212yes—
130#2349C2214yes—
131D4×C4⋊C4C2214yes—
132D4×C4⋊C4C2212yes—
133#2345C2214yes—
134#2345C2214yes—
135#2343C2218yes—
136#2330C2214yes—
137#2327C2212yes—
138#2326C2212yes—
139#2323C2214yes—
140#2322C2214yes—
141#2317C2211yescharacteristic
142#2317C2211yescharacteristic
143#2317C2211yescharacteristic
144#2316C2211yescharacteristic
145#2316C2211yescharacteristic
146#2314C2214yes—
147#2314C2214yes—
148#2313C2214yes—
149#2311C2211yescharacteristic
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155C4×C4⋊Q8C2212yes—
156C4×#125C2214yes—
157C4×#125C2214yes—
158C4×#124C2212yes—
159C4×C22⋊Q8C2214yes—
160C4×#123C2214yes—
161#2296C2211yescharacteristic
162#2296C2211yescharacteristic
163#2296C2211yescharacteristic
164#2296C2212yes—
165#2296C2212yes—
166#2296C2211yescharacteristic
167C2×#391C2211yescharacteristic
168C2×#391C2211yescharacteristic
169C2×#387C2214yes—
170#2285C2211yescharacteristic
171#2285C2211yescharacteristic
172#2285C2211yescharacteristic
173#2285C2212yes—
174#2285C2211yescharacteristic
175#2285C2214yes—
176C2×#384C2211yescharacteristic
177#2283C2214yes—
178#2283C2214yes—
179C2×#382C2211yescharacteristic
180#2274C2211yescharacteristic
181#2274C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C2×C4×C4⋊C4C2211yescharacteristic
186C2×C4×C4⋊C4C2212yes—
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189#536—28no—
190C2×C4⋊Q8C2312yes—
191C2×#125—28no—
192C2×#125C2312yes—
193C2×#125C2312yes—
194C2×#125C2312yes—
195C2×#125C2312yes—
196C2×#125C2314yes—
197C2×#125C2318yes—
198C2×#124C2312yes—
199C2×#123C2314yes—
200C2×C22⋊Q8C2314yes—
201C4×#41—28no—
202C4×#41—28no—
203C4×#41—28no—
204C2×C4×Q8—28no—
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2311yescharacteristic
230C2×#117C2312yes—
231C2×#117C2318yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2314yes—
240C22×C4⋊C4C2314yes—
241C22×C42C2312yes—
242C22×C42C2312yes—
243C22×C42C2312yes—
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#401C2318yes—
249#401C2318yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2318yes—
275#398C2318yes—
276#398C2314yes—
277#398C2314yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#396C2318yes—
287#396C2318yes—
288#391C2312yes—
289#391C2312yes—
290#391C2312yes—
291#391C2312yes—
292#391C2312yes—
293#391C2312yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2312yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#390C2312yes—
305#390C2312yes—
306#390C2312yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#389C2318yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2314yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#387C2314yes—
340#387C2314yes—
341#387C2314yes—
342#387C2314yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#386C2314yes—
378#386C2314yes—
379#386C2314yes—
380#385C2318yes—
381#385C2318yes—
382#385C2314yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#385C2314yes—
387#385C2314yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2314yes—
392#385C2314yes—
393#385C2314yes—
394#385C2314yes—
395#385C2314yes—
396#384C2312yes—
397#384C2312yes—
398#384C2314yes—
399#384C2312yes—
400#384C2312yes—
401#384C2312yes—
402#384C2312yes—
403#384C2312yes—
404#384C2312yes—
405#384C2312yes—
406#384C2314yes—
407#383C2318yes—
408#383C2318yes—
409#383C2318yes—
410#383C2318yes—
411#382C2312yes—
412#382C2314yes—
413#382C2312yes—
414#382C2314yes—
415#382C2312yes—
416#382C2312yes—
417#382C2312yes—
418#382C2312yes—
419#382C2312yes—
420#382C2312yes—
421#382C2312yes—
422#382C2318yes—
423#382C2314yes—
424#382C2318yes—
425#382C2318yes—
426#381C2314yes—
427#381C2314yes—
428#381C2314yes—
429#381C2318yes—
430#381C2318yes—
431#381C2318yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2312yes—
436#380C2312yes—
437#380C2312yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2312yes—
444#380C2314yes—
445#380C2318yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2318yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489#376C2312yes—
490#376C2318yes—
491#376C2318yes—
492C2×#95C2312yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C43C2312yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41#4118yes—
501C22×Q8—24no—
502C22×Q8—24no—
503C22×Q8—24no—
504C22×Q8C2412yes—
505C22×Q8C2412yes—
506C22×Q8C2411yescharacteristic
507C22×D4C2412yes—
508C22×D4C2411yescharacteristic
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2414yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2414yes—
519C23×C4C2412yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C4⋊Q8—28no—
524#125—28no—
525#125—28no—
526#125—28no—
527#125—28no—
528#125—416no—
529#125—48no—
530#124—28no—
531#123—216no—
532C22⋊Q8—216no—
533C4×Q8—28no—
534C4×Q8—28no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—24no—
540C4×Q8—24no—
541C4×D4—216no—
542C4×D4—28no—
543C4×D4—216no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—28no—
547C4×D4—24no—
548C4×D4—24no—
549#117—28no—
550#117—28no—
551#117—24no—
552#117—24no—
553#117—24no—
554#117—24no—
555#117—24no—
556#117—24no—
557#117—24no—
558#117—28no—
559#117—416no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—28no—
563C2×C4⋊C4—28no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4—48no—
568C2×C4⋊C4—48no—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C42—28no—
637C2×C42—28no—
638C2×C42—24no—
639C2×C42—28no—
640C2×C42—24no—
641C2×C42—28no—
642C2×C42#4118yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#95C2412yes—
673#95C2414yes—
674#95C2418yes—
675#95C2412yes—
676#95C2414yes—
677#95C2412yes—
678#95C2412yes—
679#95C2414yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2418yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718C24C2512yes—
719C24C2511yescharacteristic
720#41—232no—
721C2×Q8—22no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—24no—
726C2×Q8—22no—
727C2×Q8—24no—
728C2×Q8—24no—
729C2×Q8—416no—
730C2×Q8C2×#4114yes—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4C2×#4118yes—
736C2×D4C2×#4114yes—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—28no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—42no—
754C22×C4—44no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—42no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—42no—
766C22×C4C2×#4118yes—
767C22×C4C2×#4114yes—
768C22×C4C2×#4114yes—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C22×C42−1+414yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2511yescharacteristic
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—24no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—216no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—42no—
827C4⋊C4—44no—
828C4⋊C4—42no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—216no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C42—22no—
863C42—22no—
864C42—24no—
865C42—24no—
866C42—22no—
867C42—22no—
868C42—24no—
869C42—28no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—28no—
874C42—24no—
875C42—28no—
876C42—28no—
877C42—24no—
878C42—24no—
879C42—24no—
880C42—24no—
881C42—44no—
882C42—48no—
883C42—48no—
884C42—48no—
885C42—44no—
886C42—48no—
887C42C2×#4114yes—
888C42C2×#4114yes—
889C42C2×#4114yes—
890C42C2×#4114yes—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—24no—
896C23—24no—
897C23C22×#4114yes—
898C23C22×#4112yes—
899C23C22×#4112yes—
900C23C2×2−1+412yes—
901C23C2611yescharacteristic
902Q8—28no—
903Q8—48no—
904Q8—48no—
905D4—216no—
906D4—28no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—216no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—28no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—48no—
959C2×C4—416no—
960C2×C4—48no—
961C2×C4—48no—
962C2×C4—84no—
963C2×C4—84no—
964C2×C4—88no—
965C2×C4—84no—
966C2×C4—84no—
967C2×C4—84no—
968C2×C4#552116yes—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4114yes—
972C2×C4C22×#4112yes—
973C2×C4C22×#4112yes—
974C2×C4C22×#4112yes—
975C2×C4C22×#4112yes—
976C2×C4C22×#4112yes—
977C2×C4C22×#4112yes—
978C2×C4C2×2−1+412yes—
979C2×C4C2×2−1+412yes—
980C2×C4#58514yes—
981C22—24no—
982C22—22no—
983C22—22no—
984C22—24no—
985C22—28no—
986C22—24no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22C2×#55214yes—
991C22C23×#4111yescharacteristic
992C22C23×#4111yescharacteristic
993C22C22×2−1+411yescharacteristic
994C22C2×#58512yes—
995C222−1+612yes—
996C4—24no—
997C4—22no—
998C4—22no—
999C4—22no—
1000C4—22no—
1001C4—24no—
1002C4—44no—
1003C4—44no—
1004C4—42no—
1005C4—44no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—44no—
1010C4—44no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—44no—
1017C4C2×#55214yes—
1018C4C2×#55214yes—
1019C2—24no—
1020C2—44no—
1021C2C22×#55211yescharacteristic
1022C2#6281511yescharacteristic
1023C2#6286011yescharacteristic
1024C2#6295612yes—
1025C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59448C2semidirect
2. #59447C2semidirect
3. #59255C2semidirect
4. #45154C2semidirect
5. #45153C2semidirect
6. #43057C2semidirect
7. #39475C2semidirect
8. #37986C2semidirect
9. #37982C2semidirect
10. #36199C2semidirect
11. #35630C2semidirect
12. #35630C2semidirect
13. #35627C2semidirect
14. #35555C2semidirect
18. #34948C2semidirect
19. C2×#2565C2semidirect
20. #34217C2semidirect
23. #34187C2semidirect

Maximal subgroups

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

subgroupindex
#594482
#594472
#592552
#451542
#451532
#430572
#394752
#379862
#379822
#361992
#356302
#356272
#355552
#353332
#353072
#349482
C2×#25652
#342172
#341892
#341882
#341872
C4⋊C4×#412
C4×#5362