Finite Group Databasebeta

← #7679611

Subgroups — #7679611

Order 512.

5532 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C214yesmaximal, complemented
2#59425C214yesmaximal, complemented
3#59195C218yesmaximal, complemented
4#45391C214yesmaximal, complemented
5#45150C214yesmaximal, complemented
6#44474C218yesmaximal, complemented
7#39566C214yesmaximal, complemented
8#37974C214yesmaximal, complemented
9#37853C214yesmaximal, complemented
10#36167C214yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35629C211yesmaximal, characteristic, complemented
13#35629C211yesmaximal, characteristic, complemented
14#35628C211yesmaximal, characteristic, complemented
15#35334C211yesmaximal, characteristic, complemented
16#35307C211yesmaximal, characteristic, complemented
17#35305C211yesmaximal, characteristic
18C2×#2503C211yesmaximal, characteristic, complemented
19#34739C211yesmaximal, characteristic, complemented
20#34268C211yesmaximal, characteristic, complemented
21#34203C211yesmaximal, characteristic, complemented
22#34189C211yesmaximal, characteristic, complemented
23#34178C211yesmaximal, characteristic, complemented
24C22⋊C4×#41C211yesmaximal, characteristic
25C2×#2311C211yesmaximal, characteristic
26C23×#41C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic, complemented
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2211yescharacteristic, complemented
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2855C2214yescomplemented
37#2851C2214yescomplemented
38#2848C2214yes—
39#2796C2218yescomplemented
40#2789C2218yescomplemented
41#2758C2218yescomplemented
42#2751C2218yescomplemented
43#2747C2218yescomplemented
44#2746C2218yescomplemented
45#2745C2218yescomplemented
46#2743C2218yescomplemented
47#2742C2218yescomplemented
48#2740C2218yescomplemented
49#2738C2218yescomplemented
50#2737C2218yescomplemented
51#2628C2214yescomplemented
52#2625C2214yescomplemented
53#2616C2214yes—
54#2605C2218yescomplemented
55#2595C2218yescomplemented
56#2592C2214yescomplemented
57#2588C2218yescomplemented
58#2581C2214yescomplemented
59#2580C2214yescomplemented
60#2577C2218yescomplemented
61#2576C2218yescomplemented
62#2572C2218yescomplemented
63#2568C2214yescomplemented
64#2564C2218yescomplemented
65#2561C2218yes—
66#2530C2218yescomplemented
67#2526C2218yescomplemented
68#2516C2218yescomplemented
69#2516C2218yescomplemented
70#2514C2214yescomplemented
71#2514C2214yescomplemented
72#2513C2214yescomplemented
73#2513C2214yescomplemented
74#2510C2218yescomplemented
75#2510C2218yescomplemented
76#2505C2218yescomplemented
77#2503C2214yes—
78#2503C2212yes—
79#2503C2212yes—
80#2503C2214yescomplemented
81#2503C2212yescomplemented
82#2503C2212yescomplemented
83#2498C2218yescomplemented
84#2495C2214yescomplemented
85#2495C2214yescomplemented
86#2494C2214yescomplemented
87#2494C2214yescomplemented
88#2493C2218yes—
89#2493C2218yes—
90#2493C2218yescomplemented
91#2492C2214yescomplemented
92#2489C2214yescomplemented
93#2488C2218yescomplemented
94#2483C2218yes—
95#2482C2218yes—
96#2448C2214yescomplemented
97#2447C2214yescomplemented
98#2446C2214yescomplemented
99#2446C2214yescomplemented
100#2442C2212yes—
101#2441C2212yescomplemented
102#2440C2212yes—
103#2439C2212yescomplemented
104#2438C2218yes—
105#2438C2214yescomplemented
106#2437C2214yes—
107#2435C2212yes—
108#2434C2212yes—
109#2432C2212yes—
110#2432C2212yes—
111#2423C2214yescomplemented
112#2421C2214yescomplemented
113#2419C2218yescomplemented
114#2406C2214yes—
115#2405C2214yes—
116#2396C2214yescomplemented
117C2×#400C2214yescomplemented
118#2367C2214yescomplemented
119#2365C2214yescomplemented
120#2362C2214yescomplemented
121#2360C2214yes—
122#2359C2218yescomplemented
123#2357C2214yescomplemented
124#2356C2214yescomplemented
125#2353C2218yescomplemented
126#2345C2214yescomplemented
127#2345C2214yescomplemented
128#2344C2214yes—
129#2344C2214yes—
130#2344C2214yescomplemented
131#2343C2218yes—
132#2342C2214yes—
133#2342C2218yes—
134#2341C2212yes—
135Q8×C22⋊C4C2212yes—
136#2339C2212yes—
137#2339C2214yes—
138D4×C22⋊C4C2214yes—
139D4×C22⋊C4C2212yes—
140#2323C2214yescomplemented
141#2323C2214yescomplemented
142#2316C2211yescharacteristic, complemented
143#2316C2211yescharacteristic, complemented
144#2316C2211yescharacteristic, complemented
145#2314C2214yescomplemented
146#2313C2214yescomplemented
147#2311C2211yescharacteristic
148#2311C2211yescharacteristic
149#2311C2211yescharacteristic
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2311C2212yes—
153#2311C2214yes—
154#2311C2212yes—
155#2311C2211yescharacteristic
156#2311C2214yes—
157#2310C2211yescharacteristic, complemented
158C4×C22⋊Q8C2214yes—
159C4×C22⋊Q8C2214yes—
160C4×C22⋊Q8C2214yescomplemented
161#2297C2211yescharacteristic
162#2297C2211yescharacteristic
163#2297C2212yes—
164#2297C2212yes—
165#2296C2211yescharacteristic, complemented
166#2296C2211yescharacteristic, complemented
167C2×#391C2212yes—
168C2×#391C2211yescharacteristic, complemented
169C2×#391C2211yescharacteristic, complemented
170C2×#390C2212yes—
171C2×#386C2214yes—
172#2285C2211yescharacteristic, complemented
173#2283C2214yescomplemented
174C2×#382C2211yescharacteristic, complemented
175C2×#382C2211yescharacteristic, complemented
176#2280C2211yescharacteristic
177#2280C2212yes—
178#2280C2214yes—
179#2280C2211yescharacteristic
180C2×#381C2214yes—
181C2×#380C2214yes—
182#2274C2211yescharacteristic, complemented
183#2274C2211yescharacteristic, complemented
184#2274C2211yescharacteristic, complemented
185C2×C4×C22⋊C4C2212yes—
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41—28no—
188C22×#41—28no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2312yes—
192C22×#41C2311yescharacteristic
193C22×#41C2311yescharacteristic
194C22×#41C2312yes—
195C22×#41C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×D4C2312yes—
199C23×D4C2311yescharacteristic
200C24×C4C2312yes—
201C24×C4C2311yescharacteristic
202C24×C4C2312yes—
203#536—28no—
204#536—44no—
205#533—44no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×#125C2312yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×C22⋊Q8—28no—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223#519—44no—
224C4×#41—28no—
225C4×#41—44no—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2312yes—
235C2×#117—44no—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2318yes—
248C2×#117C2314yes—
249C22×C4⋊C4—28no—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2318yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2312yes—
269C22×C42C2312yes—
270#401C2318yes—
271#401C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#399C2318yes—
285#399C2314yes—
286#399C2318yes—
287#398C2314yes—
288#398C2318yes—
289#398C2314yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2314yes—
300#396C2314yes—
301#395C2318yes—
302#395C2318yes—
303#395C2314yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2318yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2318yes—
321#391C2314yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#390C2312yes—
332#390C2312yes—
333#390C2318yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2312yes—
349#389C2318yes—
350#389C2318yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#386C2314yes—
390#386C2314yes—
391#386C2318yes—
392#386C2314yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#386C2314yes—
397#386C2314yes—
398#386C2314yes—
399#386C2314yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2314yes—
411#385C2314yes—
412#385C2318yes—
413#385C2314yes—
414#385C2314yes—
415#384C2312yes—
416#383C2318yes—
417#383C2318yes—
418#383C2318yes—
419#382C2318yes—
420#382C2312yes—
421#382C2314yes—
422#382C2312yes—
423#382C2314yes—
424#382C2312yes—
425#382C2312yes—
426#382C2312yes—
427#381C2318yes—
428#381C2318yes—
429#381C2314yes—
430#381C2312yes—
431#381C2312yes—
432#381C2318yes—
433#381C2318yes—
434#381C2318yes—
435#381C2314yes—
436#381C2318yes—
437#381C2318yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2318yes—
442#380C2314yes—
443#380C2314yes—
444#380C2318yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2312yes—
456#380C2318yes—
457#380C2314yes—
458#379C2314yes—
459#379C2318yes—
460#379C2312yes—
461#379C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2311yescharacteristic
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493C4×C22⋊C4C2311yescharacteristic
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496#376C2318yes—
497C2×#95C2314yes—
498C2×#95C2312yes—
499C2×#95C2314yes—
500C2×#95C2318yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C25C2412yes—
505C25C2411yescharacteristic
506C2×#41—24no—
507C2×#41—28no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—44no—
520C2×#41—44no—
521C2×#41—42no—
522C2×#41—42no—
523C2×#41—464no—
524C2×#41#4118yes—
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—42no—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×D4—28no—
538C22×D4—24no—
539C22×D4—28no—
540C22×D4—24no—
541C22×D4—42no—
542C22×D4—44no—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2411yescharacteristic
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—28no—
553C23×C4—28no—
554C23×C4—28no—
555C23×C4—44no—
556C23×C4—48no—
557C23×C4#4118yes—
558C23×C4C2414yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2412yes—
570C23×C4C2414yes—
571C23×C4C2412yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2414yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2411yescharacteristic
580C4⋊Q8—28no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583#125—44no—
584#124—28no—
585#124—44no—
586#123—216no—
587#123—48no—
588C22⋊Q8—28no—
589C22⋊Q8—28no—
590C22⋊Q8—28no—
591C22⋊Q8—28no—
592C22⋊Q8—216no—
593C22⋊Q8—48no—
594C22⋊Q8—48no—
595C22⋊Q8—48no—
596C4×Q8—28no—
597C4×Q8—48no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×D4—216no—
602C4×D4—28no—
603C4×D4—44no—
604C4×D4—48no—
605#117—28no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—24no—
612#117—44no—
613#117—44no—
614#117—44no—
615#117—416no—
616#117—48no—
617#117—44no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—28no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C22⋊C4—28no—
663C2×C22⋊C4—48no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—44no—
666C2×C22⋊C4—416no—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C42—28no—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—44no—
702C2×C42—44no—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2414yes—
717C2×C42C2418yes—
718C2×C42C2418yes—
719C2×C42C2418yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722#95C2412yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2412yes—
730#95C2412yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762C24—22no—
763C24—22no—
764C24—24no—
765C24—24no—
766C24—24no—
767C24—28no—
768C24—42no—
769C24—42no—
770C24—44no—
771C24C2×#4114yes—
772C24C2512yes—
773C24C2511yescharacteristic
774C24C2512yes—
775C24C2511yescharacteristic
776C24C2511yescharacteristic
777#41—232no—
778#41—432no—
779#41—432no—
780#41—416no—
781#41—416no—
782#41—416no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—416no—
801C2×Q8—416no—
802C2×Q8C2×#4114yes—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—416no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—432no—
824C2×D4C2×#4118yes—
825C2×D4C2×#4114yes—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—232no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—22no—
835C22×C4—24no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—216no—
846C22×C4—28no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—28no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—28no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—432no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—42no—
878C22×C4—44no—
879C22×C4—42no—
880C22×C4—816no—
881C22×C4C2×#4118yes—
882C22×C4C2×#4114yes—
883C22×C4C2×#4114yes—
884C22×C4C2×#4114yes—
885C22×C4C2×#4114yes—
886C22×C4C2×#4114yes—
887C22×C4C2×#4114yes—
888C22×C4C2×#4114yes—
889C22×C4H(5,𝔽2)14yes—
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2514yes—
893C22×C4C2514yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2511yescharacteristic
906C22×C4C2512yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—216no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—48no—
932C4⋊C4—44no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—48no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—48no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—216no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—24no—
955C22⋊C4—28no—
956C22⋊C4—24no—
957C22⋊C4—28no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—48no—
975C42—22no—
976C42—24no—
977C42—22no—
978C42—28no—
979C42—24no—
980C42—24no—
981C42—22no—
982C42—22no—
983C42—24no—
984C42—24no—
985C42—24no—
986C42—24no—
987C42—24no—
988C42—44no—
989C42—44no—
990C42—48no—
991C42—48no—
992C42—48no—
993C42—48no—
994C23—21no—
995C23—21no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—21no—
1000C23—22no—
1001C23—21no—
1002C23—22no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—28no—
1008C23—28no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—44no—
1015C23—48no—
1016C23—48no—
1017C23—48no—
1018C23—416no—
1019C23—48no—
1020C23—84no—
1021C23—88no—
1022C23C22×#4114yes—
1023C23C22×#4112yes—
1024C23C22×#4112yes—
1025C23C22×#4112yes—
1026C23C22×#4112yes—
1027C23C2×H(5,𝔽2)12yes—
1028C23#58514yes—
1029C23C2611yescharacteristic
1030Q8—28no—
1031Q8—48no—
1032Q8—48no—
1033Q8—48no—
1034Q8—44no—
1035Q8—88no—
1036D4—216no—
1037D4—28no—
1038D4—48no—
1039D4—48no—
1040D4—48no—
1041D4—48no—
1042D4—44no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—28no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—28no—
1054C2×C4—216no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—28no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—416no—
1102C2×C4—48no—
1103C2×C4—84no—
1104C2×C4—88no—
1105C2×C4—84no—
1106C2×C4—88no—
1107C2×C4—84no—
1108C2×C4—84no—
1109C2×C4—84no—
1110C2×C4—88no—
1111C2×C4—88no—
1112C2×C4#551116yes—
1113C2×C4C22×#4114yes—
1114C2×C4C22×#4112yes—
1115C2×C4C22×#4112yes—
1116C2×C4C22×#4112yes—
1117C2×C4C22×#4112yes—
1118C2×C4C22×#4112yes—
1119C2×C4C22×#4112yes—
1120C2×C4C2×H(5,𝔽2)12yes—
1121C2×C4C2×H(5,𝔽2)12yes—
1122C22—24no—
1123C22—24no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—24no—
1128C22—24no—
1129C22—22no—
1130C22—28no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—24no—
1135C22—416no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—44no—
1140C22—42no—
1141C22—44no—
1142C22—42no—
1143C22—42no—
1144C22—44no—
1145C22—42no—
1146C22—816no—
1147C22C2×#55114yes—
1148C22#351014yes—
1149C22C23×#4111yescharacteristic
1150C22C23×#4111yescharacteristic
1151C22C22×H(5,𝔽2)11yescharacteristic
1152C22C2×#58512yes—
1153C222−1+612yes—
1154C4—22no—
1155C4—22no—
1156C4—24no—
1157C4—44no—
1158C4—44no—
1159C4—42no—
1160C4—42no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C4—42no—
1167C4—44no—
1168C4—42no—
1169C4—44no—
1170C4—42no—
1171C4—44no—
1172C4C2×#55114yes—
1173C4C2×#55114yes—
1174C2—24no—
1175C2—24no—
1176C2—42no—
1177C2—44no—
1178C2—82no—
1179C2C22×#55111yescharacteristic
1180C2C2×#351011yescharacteristic
1181C2#6286011yescharacteristic
1182C2#6292712yes—
1183C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59862C2semidirect
2. #59425C2semidirect
3. #59195C2semidirect
4. #45391C2semidirect
5. #45150C2semidirect
6. #44474C2semidirect
7. #39566C2semidirect
8. #37974C2semidirect
9. #37853C2semidirect
10. #36167C2semidirect
11. #35673C2semidirect
12. #35629C2semidirect
13. #35629C2semidirect
14. #35628C2semidirect
15. #35334C2semidirect
16. #35307C2semidirect
18. C2×#2503C2semidirect
19. #34739C2semidirect
20. #34268C2semidirect
21. #34203C2semidirect
22. #34189C2semidirect
23. #34178C2semidirect
29. C2×#533C22semidirect
31. C2×#519C22semidirect
36. #2855C22semidirect
37. #2851C22semidirect
39. #2796C22semidirect
40. #2789C22semidirect
41. #2758C22semidirect
42. #2751C22semidirect
43. #2747C22semidirect
44. #2746C22semidirect
45. #2745C22semidirect
46. #2743C22semidirect
47. #2742C22semidirect
48. #2740C22semidirect
49. #2738C22semidirect
50. #2737C22semidirect
51. #2628C22semidirect
52. #2625C22semidirect
54. #2605C22semidirect
55. #2595C22semidirect
56. #2592C22semidirect
57. #2588C22semidirect
58. #2581C22semidirect
59. #2580C22semidirect
60. #2577C22semidirect
61. #2576C22semidirect
62. #2572C22semidirect
63. #2568C22semidirect
64. #2564C22semidirect
66. #2530C22semidirect
67. #2526C22semidirect
68. #2516C22semidirect
69. #2516C22semidirect
70. #2514C22semidirect
71. #2514C22semidirect
72. #2513C22semidirect
73. #2513C22semidirect
74. #2510C22semidirect
75. #2510C22semidirect
76. #2505C22semidirect
80. #2503C22semidirect
81. #2503C22semidirect
82. #2503C22semidirect
83. #2498C22semidirect
84. #2495C22semidirect
85. #2495C22semidirect
86. #2494C22semidirect
87. #2494C22semidirect
90. #2493C22semidirect
91. #2492C22semidirect
92. #2489C22semidirect
93. #2488C22semidirect
96. #2448C22semidirect
97. #2447C22semidirect
98. #2446C22semidirect
99. #2446C22semidirect
101. #2441C22semidirect
103. #2439C22semidirect
105. #2438C22semidirect
111. #2423C22semidirect
112. #2421C22semidirect
113. #2419C22semidirect
116. #2396C22semidirect
117. C2×#400C22semidirect
118. #2367C22semidirect
119. #2365C22semidirect
120. #2362C22semidirect
122. #2359C22semidirect
123. #2357C22semidirect
124. #2356C22semidirect
125. #2353C22semidirect
126. #2345C22semidirect
127. #2345C22semidirect
130. #2344C22semidirect
140. #2323C22semidirect
141. #2323C22semidirect
142. #2316C22semidirect
143. #2316C22semidirect
144. #2316C22semidirect
145. #2314C22semidirect
146. #2313C22semidirect
157. #2310C22semidirect
160. C4×C22⋊Q8C22semidirect
165. #2296C22semidirect
166. #2296C22semidirect
168. C2×#391C22semidirect
169. C2×#391C22semidirect
172. #2285C22semidirect
173. #2283C22semidirect
174. C2×#382C22semidirect
175. C2×#382C22semidirect
182. #2274C22semidirect
183. #2274C22semidirect
184. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#594252
#591952
#453912
#451502
#444742
#395662
#379742
#378532
#361672
#356732
#356292
#356282
#353342
#353072
#353052
C2×#25032
#347392
#342682
#342032
#341892
#341782
C22⋊C4×#412
C2×#23112