Finite Group Databasebeta

← #7631213

Subgroups — #7631213

Order 512.

6172 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C214yesmaximal, complemented
2#36625C211yesmaximal, characteristic, complemented
3C2×#2856C211yesmaximal, characteristic
4#36587C214yesmaximal, complemented
5#36460C214yesmaximal, complemented
6#36302C214yesmaximal, complemented
7#36293C218yesmaximal, complemented
8#36117C214yesmaximal, complemented
9#36107C218yesmaximal, complemented
10#35295C214yesmaximal, complemented
11#35288C214yesmaximal, complemented
12#35286C211yesmaximal, characteristic, complemented
13#35285C211yesmaximal, characteristic, complemented
14#35271C214yesmaximal, complemented
15#35266C212yesmaximal, complemented
16#35262C212yesmaximal, complemented
17#34255C212yesmaximal, complemented
18#34214C211yesmaximal, characteristic, complemented
19#34210C211yesmaximal, characteristic, complemented
20#34204C212yesmaximal, complemented
21C2×C4×#117C211yesmaximal, characteristic, complemented
22C2×#533C2211yescharacteristic
23C22×#127C2211yescharacteristic
24C2×#529C2218yescomplemented
25C22×#121C2212yes—
26C22×#121C2214yes—
27C2×#518C2212yes—
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2861C2218yescomplemented
32#2860C2218yescomplemented
33#2860C2218yescomplemented
34#2859C2214yescomplemented
35#2858C2214yescomplemented
36#2857C2212yescomplemented
37#2857C2212yescomplemented
38#2856C2214yes—
39#2856C2212yes—
40#2856C2214yes—
41#2856C2212yes—
42#2856C2212yes—
43#2856C2212yes—
44#2855C2214yes—
45#2854C2218yescomplemented
46#2854C2218yescomplemented
47#2851C2212yescomplemented
48#2851C2212yescomplemented
49#2850C2218yescomplemented
50#2848C2214yes—
51#2647C2214yescomplemented
52#2644C2218yescomplemented
53#2641C2214yescomplemented
54#2624C2218yescomplemented
55#2597C22116yescomplemented
56#2571C2214yescomplemented
57#2559C22116yescomplemented
58#2552C2214yescomplemented
59#2548C2214yescomplemented
60#2548C2214yescomplemented
61#2531C22116yescomplemented
62#2526C22116yescomplemented
63#2513C2218yescomplemented
64#2513C2218yescomplemented
65#2512C2218yescomplemented
66#2504C2214yescomplemented
67#2501C2214yescomplemented
68#2500C2214yescomplemented
69#2500C2214yescomplemented
70#2490C2218yescomplemented
71#2482C2218yes—
72#2480C22116yes—
73#2479C22116yescomplemented
74#2476C22116yescomplemented
75#2454C2218yescomplemented
76#2448C2218yescomplemented
77#2447C2218yescomplemented
78#2444C22116yescomplemented
79#2442C2218yes—
80#2435C2218yes—
81#2427C2218yescomplemented
82#2426C2218yescomplemented
83#2425C22116yescomplemented
84#2420C2218yescomplemented
85#2405C2218yes—
86#2366C2214yescomplemented
87#2366C2214yescomplemented
88#2363C2218yescomplemented
89#2361C2218yescomplemented
90#2360C2218yes—
91#2357C2218yescomplemented
92#2355C2214yescomplemented
93#2354C2218yescomplemented
94Q8×C4⋊C4C2214yescomplemented
95#2342C22116yes—
96#2342C2218yes—
97D4×C22⋊C4C2218yes—
98D4×C22⋊C4C2218yes—
99#2330C2214yescomplemented
100#2328C2214yescomplemented
101#2324C2218yescomplemented
102#2319C2218yescomplemented
103#2317C2212yes—
104#2317C2212yes—
105#2316C2212yes—
106#2309C2212yes—
107#2309C2212yes—
108#2309C2212yes—
109C4×C4⋊Q8C2214yescomplemented
110C4×#127C2214yescomplemented
111C4×#124C2218yescomplemented
112C4×C22⋊Q8C2214yescomplemented
113C4×C22⋊Q8C2214yescomplemented
114C4×#121C2218yescomplemented
115C4×#121C2218yescomplemented
116#2296C2212yes—
117#2293C2218yescomplemented
118#2293C2218yescomplemented
119C2×#390C2212yes—
120C2×#390C2214yes—
121#2285C2211yescharacteristic
122C2×#384C2211yescharacteristic
123#2280C2212yes—
124#2274C2212yes—
125C4×#117C2211yescharacteristic
126C4×#117C2211yescharacteristic
127C4×#117C2214yes—
128C4×#117C2211yescharacteristic
129C4×#117C2211yescharacteristic
130C4×#117C2212yescomplemented
131C4×#117C2212yescomplemented
132C4×#117C2212yescomplemented
133C4×#117C2212yescomplemented
134C2×C4×C4⋊C4C2212yescomplemented
135C2×C4×C4⋊C4C2212yescomplemented
136C2×C4×C22⋊C4C2214yes—
137C2×#376C2212yescomplemented
138C2×C43C2212yescomplemented
139C23×D4C2312yes—
140C23×D4C2314yes—
141C23×D4C2314yes—
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144#533—28no—
145C2×C4⋊Q8C2312yes—
146C2×#127—28no—
147C2×#127C2312yes—
148C2×#127C2312yes—
149C2×#127C2314yes—
150#529—432no—
151C2×#126C23116yes—
152C2×#125C2312yes—
153C2×#125C2318yes—
154C2×#124C2318yes—
155C2×#124C2318yes—
156C2×#123C23116yes—
157C2×C22⋊Q8C2314yes—
158C2×C22⋊Q8C2314yes—
159C2×C22⋊Q8C2314yes—
160C2×#121—216no—
161C2×#121—416no—
162C2×#121C2314yes—
163C2×#121C2318yes—
164C2×#121C2314yes—
165C2×#121C2314yes—
166C2×#121C2314yes—
167C2×#121C2318yes—
168C2×#121C2318yes—
169C2×#121C2318yes—
170#518—216no—
171C2×C4×Q8C2314yes—
172C2×C4×Q8C2318yes—
173C2×C4×D4C2318yes—
174C2×C4×D4C2318yes—
175C2×C4×D4C2318yes—
176C2×C4×D4C2318yes—
177C2×C4×D4C23116yes—
178C2×#117—28no—
179C2×#117—28no—
180C2×#117C2311yescharacteristic
181C2×#117C2311yescharacteristic
182C2×#117C2311yescharacteristic
183C2×#117C2312yes—
184C2×#117C2312yes—
185C2×#117C2312yes—
186C2×#117C2312yes—
187C2×#117C2312yes—
188C2×#117C2312yes—
189C2×#117C2312yes—
190C2×#117C2311yescharacteristic
191C2×#117C2311yescharacteristic
192C2×#117C23116yes—
193C2×#117C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2314yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2318yes—
201C22×C22⋊C4C2314yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2318yes—
204C22×C42—28no—
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2312yes—
208C22×C42C2314yes—
209C22×C42C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2314yes—
217C22×C42C2311yescharacteristic
218#400C23116yes—
219#399C23116yes—
220#398C23116yes—
221#397C23116yes—
222#397C23116yes—
223#397C23116yes—
224#397C23116yes—
225#396C23116yes—
226#394C23116yes—
227#394C23116yes—
228#394C23116yes—
229#394C23116yes—
230#391C2318yes—
231#391C2314yes—
232#391C2314yes—
233#390C2318yes—
234#390C2318yes—
235#390C2318yes—
236#390C2318yes—
237#390C2318yes—
238#390C2314yes—
239#390C2314yes—
240#390C2318yes—
241#390C2314yes—
242#390C2314yes—
243#390C2314yes—
244#390C23116yes—
245#390C2318yes—
246#390C2318yes—
247#390C2314yes—
248#390C2318yes—
249#390C2318yes—
250#390C2318yes—
251#390C2318yes—
252#390C2318yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#389C2318yes—
258#389C2318yes—
259#389C2314yes—
260#389C23116yes—
261#389C2314yes—
262#389C2318yes—
263#389C2314yes—
264#389C2314yes—
265#388C23116yes—
266#388C23116yes—
267#388C23116yes—
268#388C23116yes—
269#388C23116yes—
270#388C23116yes—
271#388C23116yes—
272#388C23116yes—
273#388C23116yes—
274#388C23116yes—
275#388C23116yes—
276#387C23116yes—
277#387C2318yes—
278#387C2318yes—
279#386C23116yes—
280#386C23116yes—
281#386C23116yes—
282#386C23116yes—
283#386C23116yes—
284#385C2318yes—
285#385C2318yes—
286#385C23116yes—
287#385C2318yes—
288#385C2318yes—
289#385C2318yes—
290#384C2312yes—
291#384C2312yes—
292#384C2314yes—
293#384C2314yes—
294#384C2314yes—
295#384C2312yes—
296#382C2314yes—
297#382C2318yes—
298#382C2314yes—
299#382C2312yes—
300#381C23116yes—
301#381C2314yes—
302#380C2318yes—
303#380C23116yes—
304#380C2314yes—
305#380C2314yes—
306#380C2314yes—
307#380C2314yes—
308#380C2314yes—
309#379C2318yes—
310#379C2318yes—
311#379C2318yes—
312#379C2314yes—
313C4×C4⋊C4C2318yes—
314C4×C4⋊C4C2318yes—
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2314yes—
317C4×C4⋊C4C2314yes—
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2318yes—
320C4×C4⋊C4C2312yes—
321C4×C4⋊C4C2318yes—
322C4×C4⋊C4C2312yes—
323C4×C4⋊C4C2312yes—
324C4×C4⋊C4C2314yes—
325C4×C4⋊C4C2314yes—
326C4×C4⋊C4C2314yes—
327C4×C4⋊C4C2312yes—
328C4×C4⋊C4C2312yes—
329C4×C4⋊C4C2312yes—
330C4×C22⋊C4C2314yes—
331C4×C22⋊C4C2318yes—
332C4×C22⋊C4C23116yes—
333C4×C22⋊C4C2314yes—
334C4×C22⋊C4C23116yes—
335C4×C22⋊C4C2314yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343#376C2312yes—
344#376C2312yes—
345#376C2312yes—
346#376C2312yes—
347#376C2314yes—
348#376C2314yes—
349C2×#95C2314yes—
350C2×#95C2314yes—
351C43C2312yes—
352C43C2312yes—
353C43C2312yes—
354C43C2314yes—
355C43C2314yes—
356C43C2312yes—
357C25C2411yescharacteristic
358C25C2414yes—
359C22×Q8C2414yes—
360C22×D4—216no—
361C22×D4—28no—
362C22×D4—28no—
363C22×D4—28no—
364C22×D4—216no—
365C22×D4—48no—
366C22×D4—48no—
367C22×D4—416no—
368C22×D4C2418yes—
369C22×D4C2418yes—
370C22×D4C2414yes—
371C22×D4C2414yes—
372C22×D4C2418yes—
373C22×D4C2418yes—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—28no—
377C23×C4—28no—
378C23×C4—44no—
379C23×C4#4118yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2414yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2414yes—
394C23×C4C2412yes—
395C23×C4C24116yes—
396C23×C4C2411yescharacteristic
397C4⋊Q8—28no—
398#127—216no—
399#127—28no—
400#127—28no—
401#126—432no—
402#125—28no—
403#125—416no—
404#124—416no—
405#124—416no—
406#123—432no—
407C22⋊Q8—216no—
408C22⋊Q8—216no—
409C22⋊Q8—48no—
410#121—216no—
411#121—216no—
412#121—216no—
413#121—216no—
414#121—232no—
415#121—416no—
416#121—416no—
417#121—416no—
418C4×Q8—216no—
419C4×Q8—416no—
420C4×D4—232no—
421C4×D4—232no—
422C4×D4—416no—
423C4×D4—416no—
424C4×D4—432no—
425#117—28no—
426#117—28no—
427#117—24no—
428#117—24no—
429#117—24no—
430#117—24no—
431#117—24no—
432#117—28no—
433#117—28no—
434#117—28no—
435#117—28no—
436#117—28no—
437#117—432no—
438#117#4118yes—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—28no—
442C2×C4⋊C4—28no—
443C2×C4⋊C4—48no—
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2414yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C24116yes—
464C2×C4⋊C4C24116yes—
465C2×C4⋊C4C24116yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2412yes—
468C2×C22⋊C4—28no—
469C2×C22⋊C4—216no—
470C2×C22⋊C4—28no—
471C2×C22⋊C4—232no—
472C2×C22⋊C4—416no—
473C2×C22⋊C4C2414yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2414yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C24116yes—
481C2×C22⋊C4C24116yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C24116yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C24116yes—
493C2×C22⋊C4C24116yes—
494C2×C22⋊C4C2412yes—
495C2×C42—28no—
496C2×C42—28no—
497C2×C42—24no—
498C2×C42—216no—
499C2×C42—28no—
500C2×C42—28no—
501C2×C42—28no—
502C2×C42—24no—
503C2×C42—24no—
504C2×C42—24no—
505C2×C42—24no—
506C2×C42—48no—
507C2×C42#4118yes—
508C2×C42C2414yes—
509C2×C42C2414yes—
510C2×C42C2412yes—
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2414yes—
516C2×C42C2414yes—
517C2×C42C2414yes—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C2414yes—
521C2×C42C2414yes—
522C2×C42C2411yescharacteristic
523C2×C42C2412yes—
524C2×C42C2412yes—
525C2×C42C2411yescharacteristic
526C2×C42C2412yes—
527C2×C42C2412yes—
528C2×C42C2412yes—
529C2×C42C24116yes—
530C2×C42C2414yes—
531C2×C42C2414yes—
532C2×C42C2412yes—
533C2×C42C2412yes—
534C2×C42C2411yescharacteristic
535C2×C42C2411yescharacteristic
536#95C2414yes—
537#95C2414yes—
538#95C2414yes—
539#95C2414yes—
540#95C2414yes—
541#95C2414yes—
542#95C2414yes—
543#95C2414yes—
544#95C2418yes—
545#95C2418yes—
546#95C24116yes—
547#95C2418yes—
548#95C24116yes—
549#95C24116yes—
550#95C2418yes—
551#95C2418yes—
552#95C24116yes—
553C24—22no—
554C24—22no—
555C24—24no—
556C24—28no—
557C24—28no—
558C24—28no—
559C24—42no—
560C24—48no—
561C24—48no—
562C24C2×#4114yes—
563C24C2518yes—
564C24C2511yescharacteristic
565C24C2511yescharacteristic
566C24C2511yescharacteristic
567C2×Q8—28no—
568C2×Q8—28no—
569C2×Q8—28no—
570C2×D4—216no—
571C2×D4—232no—
572C2×D4—216no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4—28no—
579C2×D4—216no—
580C2×D4—216no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—48no—
584C2×D4—416no—
585C2×D4—48no—
586C2×D4—432no—
587C2×D4—832no—
588C2×D4—832no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—232no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—24no—
610C22×C4—28no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—28no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—232no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—432no—
626C22×C4—48no—
627C22×C4—416no—
628C22×C4—416no—
629C22×C4C2×#4114yes—
630C22×C4C2×#4118yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C4C2×#4114yes—
635C22×C4C2×#4114yes—
636C22×C4C2×#4114yes—
637C22×C4C2×#4114yes—
638C22×C4H(5,𝔽2)18yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2512yes—
642C22×C4C2518yes—
643C22×C4C2514yes—
644C22×C4C2518yes—
645C22×C4C2518yes—
646C22×C4C2512yes—
647C22×C4C2512yes—
648C22×C4C2512yes—
649C22×C4C2511yescharacteristic
650C22×C4C2514yes—
651C22×C4C2511yescharacteristic
652C22×C4C2512yes—
653C22×C4C2511yescharacteristic
654C22×C4C2511yescharacteristic
655C22×C4C2512yes—
656C4⋊C4—28no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—216no—
669C4⋊C4—28no—
670C4⋊C4—216no—
671C4⋊C4—216no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—48no—
675C4⋊C4—416no—
676C4⋊C4—416no—
677C4⋊C4—416no—
678C4⋊C4—48no—
679C4⋊C4C2×#4118yes—
680C22⋊C4—28no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—28no—
687C22⋊C4—216no—
688C22⋊C4—28no—
689C22⋊C4—232no—
690C22⋊C4—216no—
691C22⋊C4—216no—
692C22⋊C4—232no—
693C22⋊C4—416no—
694C22⋊C4—416no—
695C22⋊C4—416no—
696C22⋊C4—416no—
697C22⋊C4—416no—
698C22⋊C4—48no—
699C22⋊C4—416no—
700C22⋊C4—416no—
701C22⋊C4C2×#4118yes—
702C42—24no—
703C42—22no—
704C42—24no—
705C42—24no—
706C42—24no—
707C42—24no—
708C42—22no—
709C42—28no—
710C42—24no—
711C42—24no—
712C42—24no—
713C42—24no—
714C42—24no—
715C42—28no—
716C42—28no—
717C42—28no—
718C42—28no—
719C42—28no—
720C42—28no—
721C42—28no—
722C42—28no—
723C42—44no—
724C42—44no—
725C42—416no—
726C42C2×#4118yes—
727C42C2×#4114yes—
728C42C2×#4114yes—
729C42C2×#4118yes—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—216no—
745C23—216no—
746C23—44no—
747C23—48no—
748C23—48no—
749C23—416no—
750C23—816no—
751C23—88no—
752C23—816no—
753C23—88no—
754C23C22×#4112yes—
755C23C22×#4112yes—
756C23C22×#4112yes—
757C23C22×#4112yes—
758C23C22×#4112yes—
759C23C2×H(5,𝔽2)14yes—
760C23C2611yescharacteristic
761Q8—416no—
762D4—432no—
763D4—416no—
764D4—416no—
765D4—432no—
766D4—816no—
767D4—816no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—28no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—28no—
783C2×C4—216no—
784C2×C4—216no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—216no—
799C2×C4—28no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—48no—
808C2×C4—416no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—48no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—832no—
815C2×C4—88no—
816C2×C4#529116yescomplemented
817C2×C4C22×#4112yes—
818C2×C4C22×#4114yes—
819C2×C4C22×#4118yes—
820C2×C4C22×#4112yes—
821C2×C4C22×#4112yes—
822C2×C4C22×#4112yes—
823C2×C4C22×#4112yes—
824C2×C4C22×#4112yes—
825C2×C4C22×#4112yes—
826C2×C4C22×#4112yes—
827C2×C4C22×#4114yes—
828C2×C4C2×H(5,𝔽2)14yes—
829C2×C4C2×H(5,𝔽2)14yes—
830C2×C4#58514yes—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—24no—
835C22—24no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—416no—
843C22—42no—
844C22—42no—
845C22—416no—
846C22—48no—
847C22—416no—
848C22—48no—
849C22—48no—
850C22—1616no—
851C22C2×#52914yes—
852C22#350814yes—
853C22C23×#4111yescharacteristic
854C22C23×#4111yescharacteristic
855C22C23×#4111yescharacteristic
856C22C22×H(5,𝔽2)12yes—
857C22C2×#58512yes—
858C4—24no—
859C4—24no—
860C4—28no—
861C4—22no—
862C4—22no—
863C4—42no—
864C4—48no—
865C4—42no—
866C4—42no—
867C4—48no—
868C4—44no—
869C4—48no—
870C4—42no—
871C4—42no—
872C4C2×#52914yes—
873C4C2×#52914yes—
874C4#349418yes—
875C2—24no—
876C2—24no—
877C2—42no—
878C2—88no—
879C2C22×#52911yescharacteristic
880C2C2×#349412yes—
881C2C2×#350811yescharacteristic
882C2#6280012yes—
883C2#6281511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#2856C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36631C2semidirect
2. #36625C2semidirect
4. #36587C2semidirect
5. #36460C2semidirect
6. #36302C2semidirect
7. #36293C2semidirect
8. #36117C2semidirect
9. #36107C2semidirect
10. #35295C2semidirect
11. #35288C2semidirect
12. #35286C2semidirect
13. #35285C2semidirect
14. #35271C2semidirect
15. #35266C2semidirect
16. #35262C2semidirect
17. #34255C2semidirect
18. #34214C2semidirect
19. #34210C2semidirect
20. #34204C2semidirect
21. C2×C4×#117C2semidirect
24. C2×#529C22semidirect
31. #2861C22semidirect
32. #2860C22semidirect
33. #2860C22semidirect
34. #2859C22semidirect
35. #2858C22semidirect
36. #2857C22semidirect
37. #2857C22semidirect
45. #2854C22semidirect
46. #2854C22semidirect
47. #2851C22semidirect
48. #2851C22semidirect
49. #2850C22semidirect
51. #2647C22semidirect
52. #2644C22semidirect
53. #2641C22semidirect
54. #2624C22semidirect
55. #2597C22semidirect
56. #2571C22semidirect
57. #2559C22semidirect
58. #2552C22semidirect
59. #2548C22semidirect
60. #2548C22semidirect
61. #2531C22semidirect
62. #2526C22semidirect
63. #2513C22semidirect
64. #2513C22semidirect
65. #2512C22semidirect
66. #2504C22semidirect
67. #2501C22semidirect
68. #2500C22semidirect
69. #2500C22semidirect
70. #2490C22semidirect
73. #2479C22semidirect
74. #2476C22semidirect
75. #2454C22semidirect
76. #2448C22semidirect
77. #2447C22semidirect
78. #2444C22semidirect
81. #2427C22semidirect
82. #2426C22semidirect
83. #2425C22semidirect
84. #2420C22semidirect
86. #2366C22semidirect
87. #2366C22semidirect
88. #2363C22semidirect
89. #2361C22semidirect
91. #2357C22semidirect
92. #2355C22semidirect
93. #2354C22semidirect
94. Q8×C4⋊C4C22semidirect
99. #2330C22semidirect
100. #2328C22semidirect
101. #2324C22semidirect
102. #2319C22semidirect
109. C4×C4⋊Q8C22semidirect
110. C4×#127C22semidirect
111. C4×#124C22semidirect
112. C4×C22⋊Q8C22semidirect
113. C4×C22⋊Q8C22semidirect
114. C4×#121C22semidirect
115. C4×#121C22semidirect
117. #2293C22semidirect
118. #2293C22semidirect
130. C4×#117C22semidirect
131. C4×#117C22semidirect
132. C4×#117C22semidirect
133. C4×#117C22semidirect
134. C2×C4×C4⋊C4C22semidirect
135. C2×C4×C4⋊C4C22semidirect
137. C2×#376C22semidirect
138. C2×C43C22semidirect
816. C2×C4#529semidirect

Maximal subgroups

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

subgroupindex
#366312
#366252
C2×#28562
#365872
#364602
#363022
#362932
#361172
#361072
#352952
#352882
#352862
#352852
#352712
#352662
#352622
#342552
#342142
#342102
#342042
C2×C4×#1172