Finite Group Databasebeta

← #7652669

Subgroups — #7652669

Order 512.

5472 conjugacy classes of subgroups.

The subgroup lattice has 1155 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42903C214yesmaximal, complemented
2#42860C214yesmaximal, complemented
3#42857C214yesmaximal, complemented
4#42835C214yesmaximal, complemented
5#41963C218yesmaximal, complemented
6#40225C214yesmaximal, complemented
7#40218C214yesmaximal, complemented
8#39790C214yesmaximal, complemented
9#39215C214yesmaximal, complemented
10#38397C218yesmaximal, complemented
11#35679C211yesmaximal, characteristic, complemented
12#35668C211yesmaximal, characteristic, complemented
13#35667C211yesmaximal, characteristic, complemented
14#35661C211yesmaximal, characteristic, complemented
15#35644C211yesmaximal, characteristic, complemented
16#35558C211yesmaximal, characteristic, complemented
17#35327C211yesmaximal, characteristic, complemented
18#35264C211yesmaximal, characteristic, complemented
19#35149C211yesmaximal, characteristic
20#34814C211yesmaximal, characteristic, complemented
21#34742C211yesmaximal, characteristic, complemented
22C2×#2432C211yesmaximal, characteristic, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34209C211yesmaximal, characteristic, complemented
25#34174C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2861C2212yescomplemented
40#2858C2212yescomplemented
41#2850C2212yescomplemented
42#2850C2212yescomplemented
43#2849C2214yes—
44#2830C2218yescomplemented
45#2829C2218yescomplemented
46#2808C2218yescomplemented
47#2803C2218yescomplemented
48#2803C2218yescomplemented
49#2800C2218yescomplemented
50#2800C2218yescomplemented
51#2797C2218yescomplemented
52#2788C2218yescomplemented
53#2787C2218yescomplemented
54#2781C2218yescomplemented
55#2780C2218yescomplemented
56#2770C2218yescomplemented
57#2768C2218yescomplemented
58#2750C2218yescomplemented
59#2727C2218yescomplemented
60#2715C2218yescomplemented
61#2710C2218yescomplemented
62#2662C2218yescomplemented
63#2652C2218yescomplemented
64#2651C2218yescomplemented
65#2651C2218yescomplemented
66#2649C2218yescomplemented
67#2648C2218yescomplemented
68#2641C2212yescomplemented
69#2640C2212yescomplemented
70#2620C2212yescomplemented
71#2620C2212yescomplemented
72#2613C2214yes—
73#2597C2218yescomplemented
74#2593C2218yescomplemented
75#2589C2218yescomplemented
76#2587C2218yescomplemented
77#2576C2218yescomplemented
78#2568C2212yescomplemented
79#2567C2212yescomplemented
80#2565C2212yescomplemented
81#2565C2212yescomplemented
82#2561C2214yes—
83#2554C2218yescomplemented
84#2546C2212yescomplemented
85#2546C2212yescomplemented
86#2545C2214yescomplemented
87#2545C2212yescomplemented
88#2545C2212yescomplemented
89#2544C2214yescomplemented
90#2538C2214yescomplemented
91#2536C2214yescomplemented
92#2534C2218yes—
93#2513C2214yescomplemented
94#2513C2214yescomplemented
95#2512C2214yescomplemented
96#2512C2214yescomplemented
97#2503C2214yes—
98#2497C2212yescomplemented
99#2496C2212yescomplemented
100#2495C2212yescomplemented
101#2494C2212yescomplemented
102#2493C2214yes—
103#2492C2214yescomplemented
104#2492C2214yescomplemented
105#2491C2214yescomplemented
106#2490C2214yescomplemented
107#2489C2214yescomplemented
108#2489C2214yescomplemented
109#2482C2218yes—
110#2480C2218yes—
111#2480C2214yes—
112#2472C2218yes—
113#2453C2214yescomplemented
114#2451C2214yescomplemented
115#2448C2214yescomplemented
116#2448C2214yescomplemented
117#2448C2214yescomplemented
118#2448C2214yescomplemented
119#2438C2218yes—
120#2432C2214yes—
121#2432C2214yes—
122#2432C2214yes—
123#2432C2214yes—
124#2432C2214yes—
125#2431C2214yes—
126#2429C2214yescomplemented
127#2429C2214yescomplemented
128#2429C2214yescomplemented
129#2426C2214yescomplemented
130#2423C2212yescomplemented
131#2422C2212yescomplemented
132#2421C2212yescomplemented
133#2420C2212yescomplemented
134#2419C2214yes—
135#2418C2214yes—
136#2413C2214yes—
137#2413C2218yes—
138#2411C2214yes—
139#2407C2214yes—
140#2407C2214yes—
141#2401C2214yescomplemented
142#2395C2214yescomplemented
143C2×#394C2214yes—
144#2367C2214yescomplemented
145#2365C2214yescomplemented
146#2365C2214yescomplemented
147#2365C2214yescomplemented
148#2359C2218yes—
149#2344C2218yes—
150#2341C2214yes—
151#2341C2214yes—
152#2341C2214yes—
153#2341C2214yes—
154#2337C2218yescomplemented
155#2334C2218yescomplemented
156#2327C2214yescomplemented
157#2323C2214yescomplemented
158#2317C2211yescharacteristic
159#2311C2211yescharacteristic
160#2310C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163#2309C2211yescharacteristic
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166#2309C2214yes—
167C4×C4⋊Q8C2214yescomplemented
168C4×#126C2214yescomplemented
169C4×C22⋊Q8C2214yescomplemented
170C4×#123C2214yescomplemented
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#385C2214yes—
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2214yes—
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41—28no—
188C22×#41—44no—
189C22×#41—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2314yes—
192C22×#41C2314yes—
193C23×Q8C2311yescharacteristic
194C23×Q8C2311yescharacteristic
195C23×D4C2311yescharacteristic
196C23×D4C2312yes—
197C24×C4C2311yescharacteristic
198C24×C4C2312yes—
199#544—44no—
200#536—28no—
201#536—44no—
202#535—44no—
203C2×C4⋊Q8—28no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127C2312yes—
212C2×#126C2314yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#124—44no—
217C2×#124C2312yes—
218C2×#124C2318yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224#525—44no—
225C2×#123C2314yes—
226C2×#123C2312yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×C22⋊Q8—44no—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#120C2314yes—
241C2×#120C2312yes—
242#519—44no—
243#519—44no—
244#519—44no—
245C4×#41—44no—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279#401C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#399C2318yes—
288#399C2318yes—
289#399C2314yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C2314yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#396C2314yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#395C2318yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2314yes—
331#393C2318yes—
332#393C2318yes—
333#392C2318yes—
334#392C2318yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2318yes—
348#391C2318yes—
349#391C2311yescharacteristic
350#391C2314yes—
351#391C2311yescharacteristic
352#390C2318yes—
353#390C2318yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2314yes—
359#390C2318yes—
360#390C2318yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2312yes—
365#390C2318yes—
366#390C2311yescharacteristic
367#390C2312yes—
368#390C2312yes—
369#390C2311yescharacteristic
370#390C2318yes—
371#390C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2314yes—
376#389C2312yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2314yes—
429#386C2314yes—
430#385C2314yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#384C2312yes—
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2311yescharacteristic
446#383C2314yes—
447#382C2311yescharacteristic
448#382C2312yes—
449#382C2311yescharacteristic
450#382C2318yes—
451#382C2312yes—
452#381C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2312yes—
457#381C2312yes—
458#381C2312yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2318yes—
463#380C2312yes—
464#380C2318yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2314yes—
470#379C2312yes—
471#379C2312yes—
472#379C2312yes—
473#379C2314yes—
474#379C2314yes—
475#379C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503#376C2312yes—
504C2×#95C2314yes—
505C2×#95C2312yes—
506C43C2312yes—
507C25C2411yescharacteristic
508C25C2412yes—
509C2×#41—216no—
510C2×#41—216no—
511C2×#41—24no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—48no—
515C2×#41—48no—
516C2×#41—48no—
517C2×#41—48no—
518C2×#41—464no—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8—24no—
523C22×Q8—24no—
524C22×Q8#4118yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×D4—28no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—44no—
536C22×D4—44no—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2418yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C23×C4—28no—
546C23×C4—24no—
547C23×C4—24no—
548C23×C4—24no—
549C23×C4—44no—
550C23×C4—44no—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2418yes—
561C23×C4C2414yes—
562C23×C4C2411yescharacteristic
563C4⋊Q8—216no—
564C4⋊Q8—28no—
565C4⋊Q8—28no—
566C4⋊Q8—28no—
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570#127—44no—
571#126—48no—
572#126—416no—
573#125—44no—
574#125—44no—
575#124—28no—
576#124—416no—
577#124—44no—
578#124—44no—
579#124—48no—
580#124—44no—
581#124—44no—
582#123—216no—
583#123—48no—
584#123—44no—
585#123—48no—
586C22⋊Q8—216no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589C22⋊Q8—48no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592C22⋊Q8—44no—
593#121—44no—
594#121—44no—
595#121—44no—
596#120—44no—
597#120—48no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×Q8—48no—
602C4×Q8—48no—
603C4×Q8—44no—
604C4×Q8—44no—
605C4×Q8—44no—
606C4×Q8—44no—
607C4×D4—44no—
608C4×D4—48no—
609C4×D4—48no—
610#117—24no—
611#117—24no—
612#117—24no—
613#117—24no—
614#117—24no—
615#117—24no—
616#117—24no—
617#117—44no—
618#117—48no—
619#117—48no—
620#117—48no—
621C2×C4⋊C4—216no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C22⋊C4—44no—
663C2×C22⋊C4—48no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—48no—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—44no—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2418yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2418yes—
726C2×C42C2414yes—
727C2×C42C2418yes—
728C2×C42C2414yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764C24—22no—
765C24—24no—
766C24—24no—
767C24—22no—
768C24—22no—
769C24—24no—
770C24—42no—
771C24—44no—
772C24—42no—
773C24—44no—
774C24C2512yes—
775C24C2514yes—
776C24C2512yes—
777C24C2511yescharacteristic
778#41—464no—
779#41—464no—
780#41—416no—
781C2×Q8—232no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—22no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—44no—
796C2×Q8—48no—
797C2×Q8—416no—
798C2×Q8C2×#4118yes—
799C2×Q8C2×#4118yes—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—216no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—24no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—48no—
814C2×D4—48no—
815C2×D4—432no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4—416no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—216no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—42no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—42no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—42no—
855C22×C4—432no—
856C22×C4—416no—
857C22×C4C2×#4118yes—
858C22×C4C2×#4114yes—
859C22×C4H(5,𝔽2)14yes—
860C22×C4H(5,𝔽2)14yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2514yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2514yes—
879C22×C4C2512yes—
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C4⋊C4—216no—
883C4⋊C4—216no—
884C4⋊C4—24no—
885C4⋊C4—216no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—216no—
928C22⋊C4—24no—
929C22⋊C4—216no—
930C22⋊C4—24no—
931C22⋊C4—28no—
932C22⋊C4—48no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C42—22no—
960C42—24no—
961C42—22no—
962C42—24no—
963C42—22no—
964C42—22no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—44no—
974C42—44no—
975C42—48no—
976C42—44no—
977C42—44no—
978C42—48no—
979C42—48no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—28no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—28no—
997C23—22no—
998C23—24no—
999C23—44no—
1000C23—44no—
1001C23—416no—
1002C23—48no—
1003C23—44no—
1004C23—84no—
1005C23—88no—
1006C23—84no—
1007C23—84no—
1008C23—84no—
1009C23C22×#4112yes—
1010C23C2×H(5,𝔽2)12yes—
1011C23C2×H(5,𝔽2)12yes—
1012C23C2611yescharacteristic
1013Q8—216no—
1014Q8—216no—
1015Q8—48no—
1016Q8—48no—
1017Q8—44no—
1018Q8—164no—
1019D4—432no—
1020D4—48no—
1021D4—48no—
1022D4—48no—
1023D4—44no—
1024D4—88no—
1025D4—164no—
1026D4—164no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—216no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—28no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—48no—
1077C2×C4—432no—
1078C2×C4—44no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—84no—
1084C2×C4—84no—
1085C2×C4—88no—
1086C2×C4#538116yes—
1087C2×C4C22×#4118yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4#58514yes—
1095C22—24no—
1096C22—22no—
1097C22—22no—
1098C22—24no—
1099C22—44no—
1100C22—42no—
1101C22—48no—
1102C22—42no—
1103C22—42no—
1104C22—44no—
1105C22—42no—
1106C22—42no—
1107C22—44no—
1108C22—42no—
1109C22—44no—
1110C22—42no—
1111C22—48no—
1112C22—42no—
1113C22—44no—
1114C22—42no—
1115C22—42no—
1116C22—816no—
1117C22—88no—
1118C22C2×#53814yes—
1119C22C23×#4111yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C22×H(5,𝔽2)11yescharacteristic
1122C22C2×#58512yes—
1123C222−1+612yes—
1124C4—24no—
1125C4—28no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—42no—
1139C4—44no—
1140C4—42no—
1141C4—42no—
1142C4—44no—
1143C4C2×#53814yes—
1144C4C2×#53814yes—
1145C2—24no—
1146C2—82no—
1147C2—84no—
1148C2—82no—
1149C2C22×#53811yescharacteristic
1150C2#6283611yescharacteristic
1151C2#6288711yescharacteristic
1152C2#6292512yes—
1153C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35149C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42903C2semidirect
2. #42860C2semidirect
3. #42857C2semidirect
4. #42835C2semidirect
5. #41963C2semidirect
6. #40225C2semidirect
7. #40218C2semidirect
8. #39790C2semidirect
9. #39215C2semidirect
10. #38397C2semidirect
11. #35679C2semidirect
12. #35668C2semidirect
13. #35667C2semidirect
14. #35661C2semidirect
15. #35644C2semidirect
16. #35558C2semidirect
17. #35327C2semidirect
18. #35264C2semidirect
20. #34814C2semidirect
21. #34742C2semidirect
22. C2×#2432C2semidirect
23. #34268C2semidirect
24. #34209C2semidirect
25. #34174C2semidirect
39. #2861C22semidirect
40. #2858C22semidirect
41. #2850C22semidirect
42. #2850C22semidirect
44. #2830C22semidirect
45. #2829C22semidirect
46. #2808C22semidirect
47. #2803C22semidirect
48. #2803C22semidirect
49. #2800C22semidirect
50. #2800C22semidirect
51. #2797C22semidirect
52. #2788C22semidirect
53. #2787C22semidirect
54. #2781C22semidirect
55. #2780C22semidirect
56. #2770C22semidirect
57. #2768C22semidirect
58. #2750C22semidirect
59. #2727C22semidirect
60. #2715C22semidirect
61. #2710C22semidirect
62. #2662C22semidirect
63. #2652C22semidirect
64. #2651C22semidirect
65. #2651C22semidirect
66. #2649C22semidirect
67. #2648C22semidirect
68. #2641C22semidirect
69. #2640C22semidirect
70. #2620C22semidirect
71. #2620C22semidirect
73. #2597C22semidirect
74. #2593C22semidirect
75. #2589C22semidirect
76. #2587C22semidirect
77. #2576C22semidirect
78. #2568C22semidirect
79. #2567C22semidirect
80. #2565C22semidirect
81. #2565C22semidirect
83. #2554C22semidirect
84. #2546C22semidirect
85. #2546C22semidirect
86. #2545C22semidirect
87. #2545C22semidirect
88. #2545C22semidirect
89. #2544C22semidirect
90. #2538C22semidirect
91. #2536C22semidirect
93. #2513C22semidirect
94. #2513C22semidirect
95. #2512C22semidirect
96. #2512C22semidirect
98. #2497C22semidirect
99. #2496C22semidirect
100. #2495C22semidirect
101. #2494C22semidirect
103. #2492C22semidirect
104. #2492C22semidirect
105. #2491C22semidirect
106. #2490C22semidirect
107. #2489C22semidirect
108. #2489C22semidirect
113. #2453C22semidirect
114. #2451C22semidirect
115. #2448C22semidirect
116. #2448C22semidirect
117. #2448C22semidirect
118. #2448C22semidirect
126. #2429C22semidirect
127. #2429C22semidirect
128. #2429C22semidirect
129. #2426C22semidirect
130. #2423C22semidirect
131. #2422C22semidirect
132. #2421C22semidirect
133. #2420C22semidirect
141. #2401C22semidirect
142. #2395C22semidirect
144. #2367C22semidirect
145. #2365C22semidirect
146. #2365C22semidirect
147. #2365C22semidirect
154. #2337C22semidirect
155. #2334C22semidirect
156. #2327C22semidirect
157. #2323C22semidirect
167. C4×C4⋊Q8C22semidirect
168. C4×#126C22semidirect
169. C4×C22⋊Q8C22semidirect
170. C4×#123C22semidirect

Maximal subgroups

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

subgroupindex
#429032
#428602
#428572
#428352
#419632
#402252
#402182
#397902
#392152
#383972
#356792
#356682
#356672
#356612
#356442
#355582
#353272
#352642
#351492
#348142
#347422
C2×#24322
#342682
#342092
#341742