Finite Group Databasebeta

← #7672731

Subgroups — #7672731

Order 512.

6234 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59208C218yesmaximal, complemented
2#59028C218yesmaximal, complemented
3#39148C214yesmaximal, complemented
4#39147C214yesmaximal, complemented
5#37946C218yesmaximal, complemented
6C2×#2856C211yesmaximal, characteristic, complemented
7#36472C214yesmaximal, complemented
8#36460C214yesmaximal, complemented
9#36211C214yesmaximal, complemented
10#36182C214yesmaximal, complemented
11#35563C212yesmaximal, complemented
12#35540C212yesmaximal, complemented
13#35286C211yesmaximal, characteristic, complemented
14#35272C211yesmaximal, characteristic, complemented
15#35266C212yesmaximal, complemented
16#34275C212yesmaximal, complemented
17#34210C211yesmaximal, characteristic, complemented
18#34183C211yesmaximal, characteristic, complemented
19C4×#525C211yesmaximal, characteristic, complemented
20#34012C211yesmaximal, characteristic, complemented
21C2×#553C2218yescomplemented
22C2×#535C2212yes—
23C22×#127C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C22×#121C2214yes—
26C22×#121C2212yes—
27C2×#520C2212yes—
28C2×#518C2212yes—
29C2×C4×#41C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2860C2218yescomplemented
32#2859C2214yescomplemented
33#2856C2214yes—
34#2856C2214yes—
35#2856C2214yes—
36#2856C2214yes—
37#2856C2214yescomplemented
38#2757C22116yescomplemented
39#2749C22116yescomplemented
40#2701C22116yescomplemented
41#2688C22116yescomplemented
42#2647C2214yescomplemented
43#2644C2218yescomplemented
44#2619C2214yescomplemented
45#2603C22116yescomplemented
46#2571C2214yescomplemented
47#2566C2218yescomplemented
48#2559C22116yescomplemented
49#2552C2214yescomplemented
50#2548C2214yescomplemented
51#2541C2214yescomplemented
52#2535C2218yescomplemented
53#2534C2218yes—
54#2526C22116yescomplemented
55#2513C2218yescomplemented
56#2513C2218yescomplemented
57#2512C2218yescomplemented
58#2512C2218yescomplemented
59#2504C2218yescomplemented
60#2500C2218yescomplemented
61#2490C2218yescomplemented
62#2490C2218yescomplemented
63#2483C2218yes—
64#2480C22116yes—
65#2464C22116yescomplemented
66#2442C2218yes—
67#2428C2218yescomplemented
68#2426C2218yescomplemented
69#2422C2218yescomplemented
70#2422C2218yescomplemented
71#2422C2218yescomplemented
72#2420C2218yescomplemented
73#2420C2218yescomplemented
74#2420C2218yescomplemented
75#2416C2218yescomplemented
76#2416C2218yescomplemented
77#2414C2218yescomplemented
78#2414C2218yescomplemented
79#2408C2218yes—
80#2408C2218yes—
81#2405C2218yes—
82#2366C2214yescomplemented
83#2366C2214yescomplemented
84#2363C2218yescomplemented
85#2363C2218yescomplemented
86#2361C2218yescomplemented
87#2361C2218yescomplemented
88#2358C22116yes—
89#2357C2218yescomplemented
90Q8×C4⋊C4C2214yescomplemented
91D4×C4⋊C4C2218yes—
92D4×C4⋊C4C2214yescomplemented
93D4×C22⋊C4C2218yes—
94#2328C2214yescomplemented
95#2328C2214yescomplemented
96#2326C2214yescomplemented
97#2317C2212yes—
98#2317C2212yes—
99#2317C2214yescomplemented
100#2316C2212yes—
101#2309C2212yes—
102#2309C2212yes—
103C4×#127C2212yescomplemented
104C4×#127C2212yescomplemented
105C4×#127C2214yescomplemented
106C4×#124C2214yescomplemented
107C4×C22⋊Q8C2212yescomplemented
108C4×C22⋊Q8C2212yescomplemented
109C4×#123C2214yes—
110C4×#121C2212yescomplemented
111C4×#121C2212yescomplemented
112C4×#120C2214yes—
113#2297C2211yescharacteristic
114#2296C2211yescharacteristic
115C2×#390C2214yes—
116C2×#390C2212yes—
117#2290C2214yescomplemented
118#2285C2211yescharacteristic
119#2285C2211yescharacteristic
120#2285C2212yescomplemented
121#2285C2212yescomplemented
122#2285C2212yescomplemented
123C2×#384C2211yescharacteristic
124C2×#384C2212yescomplemented
125#2283C2214yes—
126#2283C2214yescomplemented
127#2283C2214yescomplemented
128#2280C2214yes—
129#2280C2211yescharacteristic
130#2280C2212yes—
131C42×D4C2214yescomplemented
132C4×#117C2211yescharacteristic
133C4×#117C2212yes—
134C4×#117C2214yescomplemented
135C22×#41C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2314yes—
138C23×D4C2314yes—
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141#553—432no—
142#535—216no—
143C2×#127—28no—
144C2×#127C2312yes—
145C2×#127C2314yes—
146C2×#127C2312yes—
147C2×#127C2314yes—
148C2×#126C23116yes—
149C2×#125C2318yes—
150C2×#124C2314yes—
151#525—28no—
152C2×#123C2312yes—
153C2×#123C23116yes—
154C2×C22⋊Q8C2312yes—
155C2×#121—48no—
156C2×#121—416no—
157C2×#121C2318yes—
158C2×#121C2318yes—
159C2×#121C2312yes—
160C2×#121C2318yes—
161C2×#121C2318yes—
162C2×#121C2318yes—
163C2×#121C2318yes—
164C2×#121C2318yes—
165C2×#121C2318yes—
166C2×#121C2318yes—
167C2×#121C23116yes—
168C2×#120C2318yes—
169C2×#120C2312yes—
170#520—48no—
171#518—48no—
172C4×#41—28no—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2314yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2312yes—
177C2×C4×D4C2314yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2318yes—
180C2×C4×D4C2314yes—
181C2×C4×D4C2314yes—
182C2×C4×D4C2314yes—
183C2×C4×D4C2314yes—
184C2×C4×D4C2318yes—
185C2×C4×D4C23116yes—
186C2×C4×D4C2314yes—
187C2×C4×D4C2318yes—
188C2×C4×D4C2314yes—
189C2×#117C2311yescharacteristic
190C2×#117C2311yescharacteristic
191C2×#117C2312yes—
192C2×#117C2312yes—
193C2×#117C2311yescharacteristic
194C2×#117C2312yes—
195C2×#117C2314yes—
196C2×#117C2314yes—
197C2×#117C2314yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2318yes—
202C22×C22⋊C4C2318yes—
203C22×C22⋊C4C2318yes—
204C22×C22⋊C4C2314yes—
205C22×C42—28no—
206C22×C42C2312yes—
207C22×C42C2312yes—
208C22×C42C2312yes—
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214#400C23116yes—
215#398C23116yes—
216#397C23116yes—
217#397C23116yes—
218#397C23116yes—
219#397C23116yes—
220#397C23116yes—
221#396C23116yes—
222#396C23116yes—
223#394C23116yes—
224#394C23116yes—
225#394C23116yes—
226#394C23116yes—
227#394C23116yes—
228#392C23116yes—
229#392C23116yes—
230#391C2311yescharacteristic
231#391C2311yescharacteristic
232#390C2311yescharacteristic
233#390C2314yes—
234#390C2314yes—
235#390C2318yes—
236#390C2318yes—
237#390C2314yes—
238#390C23116yes—
239#390C2318yes—
240#390C2318yes—
241#390C2318yes—
242#390C2318yes—
243#390C2318yes—
244#390C2314yes—
245#390C2311yescharacteristic
246#390C2318yes—
247#390C2318yes—
248#390C2318yes—
249#390C2318yes—
250#390C2318yes—
251#390C23116yes—
252#389C2318yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#389C23116yes—
258#389C2318yes—
259#389C2312yes—
260#389C2312yes—
261#388C23116yes—
262#388C2314yes—
263#388C23116yes—
264#388C23116yes—
265#388C23116yes—
266#388C23116yes—
267#388C23116yes—
268#388C2314yes—
269#387C2314yes—
270#387C2314yes—
271#386C23116yes—
272#386C23116yes—
273#386C23116yes—
274#386C23116yes—
275#386C23116yes—
276#386C2314yes—
277#386C23116yes—
278#386C2314yes—
279#386C2314yes—
280#385C23116yes—
281#385C23116yes—
282#385C2318yes—
283#385C2318yes—
284#385C23116yes—
285#385C2314yes—
286#385C2314yes—
287#385C2314yes—
288#384C2311yescharacteristic
289#384C2311yescharacteristic
290#384C2314yes—
291#384C2318yes—
292#384C2314yes—
293#384C2314yes—
294#384C2312yes—
295#384C2312yes—
296#384C2312yes—
297#383C2318yes—
298#382C2314yes—
299#382C2314yes—
300#382C2318yes—
301#382C2314yes—
302#382C2312yes—
303#382C2312yes—
304#382C2314yes—
305#381C23116yes—
306#381C2318yes—
307#381C2312yes—
308#381C2314yes—
309#380C2318yes—
310#380C2314yes—
311#380C2318yes—
312#380C2314yes—
313#380C2314yes—
314#380C2314yes—
315#380C2314yes—
316#380C2312yes—
317#380C2312yes—
318#380C2314yes—
319#379C2318yes—
320#379C2318yes—
321#379C2312yes—
322#379C2314yes—
323C4×C4⋊C4C2314yes—
324C4×C4⋊C4C2312yes—
325C4×C4⋊C4C2314yes—
326C4×C4⋊C4C2318yes—
327C4×C4⋊C4C2314yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2312yes—
334C4×C4⋊C4C2314yes—
335C4×C22⋊C4C2314yes—
336C4×C22⋊C4C23116yes—
337C4×C22⋊C4C2318yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343C4×C22⋊C4C2318yes—
344C4×C22⋊C4C2314yes—
345C4×C22⋊C4C2318yes—
346#376C2314yes—
347#376C2312yes—
348#376C2318yes—
349C43C2312yes—
350C43C2314yes—
351C25C2411yescharacteristic
352C25C2414yes—
353C2×#41—24no—
354C2×#41—24no—
355C2×#41#4118yes—
356C22×Q8C2411yescharacteristic
357C22×D4—28no—
358C22×D4—28no—
359C22×D4—216no—
360C22×D4—28no—
361C22×D4—48no—
362C22×D4—48no—
363C22×D4—48no—
364C22×D4—416no—
365C22×D4C2414yes—
366C22×D4C2418yes—
367C22×D4C2414yes—
368C22×D4C2414yes—
369C22×D4C2412yes—
370C22×D4C2411yescharacteristic
371C22×D4C24116yes—
372C22×D4C24116yes—
373C22×D4C2418yes—
374C23×C4—24no—
375C23×C4—28no—
376C23×C4—24no—
377C23×C4—28no—
378C23×C4—24no—
379C23×C4—44no—
380C23×C4C2411yescharacteristic
381C23×C4C2414yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2414yes—
392C23×C4C2418yes—
393C23×C4C2418yes—
394C23×C4C2418yes—
395C23×C4C2411yescharacteristic
396#127—216no—
397#127—28no—
398#127—28no—
399#127—216no—
400#126—432no—
401#125—416no—
402#124—216no—
403#123—28no—
404#123—432no—
405C22⋊Q8—28no—
406#121—28no—
407#121—232no—
408#121—232no—
409#121—416no—
410#121—432no—
411#121—416no—
412#121—416no—
413#121—416no—
414#121—416no—
415#121—416no—
416#121—416no—
417#120—28no—
418#120—232no—
419C4×Q8—28no—
420C4×Q8—48no—
421C4×D4—216no—
422C4×D4—216no—
423C4×D4—216no—
424C4×D4—28no—
425C4×D4—432no—
426C4×D4—416no—
427C4×D4—48no—
428C4×D4—48no—
429C4×D4—48no—
430C4×D4—48no—
431C4×D4—48no—
432C4×D4—416no—
433C4×D4—48no—
434C4×D4—416no—
435#117—24no—
436#117—24no—
437#117—28no—
438#117—24no—
439#117—28no—
440#117—216no—
441#117—28no—
442#117—48no—
443#117—48no—
444C2×C4⋊C4—28no—
445C2×C4⋊C4—48no—
446C2×C4⋊C4—48no—
447C2×C4⋊C4—416no—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C24116yes—
468C2×C4⋊C4C24116yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C24116yes—
471C2×C22⋊C4—416no—
472C2×C22⋊C4—416no—
473C2×C22⋊C4—48no—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C24116yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2414yes—
479C2×C22⋊C4C2414yes—
480C2×C22⋊C4C2412yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C24116yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C24116yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2414yes—
496C2×C22⋊C4C24116yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C24116yes—
499C2×C42—28no—
500C2×C42—24no—
501C2×C42—28no—
502C2×C42—28no—
503C2×C42—28no—
504C2×C42—28no—
505C2×C42—28no—
506C2×C42#4118yes—
507C2×C42C2412yes—
508C2×C42C2412yes—
509C2×C42C2414yes—
510C2×C42C2418yes—
511C2×C42C2412yes—
512C2×C42C2414yes—
513C2×C42C2414yes—
514C2×C42C2414yes—
515C2×C42C2414yes—
516C2×C42C2411yescharacteristic
517C2×C42C2412yes—
518C2×C42C2411yescharacteristic
519C2×C42C2412yes—
520C2×C42C2412yes—
521C2×C42C2412yes—
522C2×C42C2412yes—
523C2×C42C2418yes—
524C2×C42C2418yes—
525C2×C42C2411yescharacteristic
526C2×C42C2412yes—
527C2×C42C2411yescharacteristic
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2414yes—
535#95C2414yes—
536#95C2414yes—
537#95C2414yes—
538#95C2414yes—
539#95C2414yes—
540#95C2414yes—
541#95C2414yes—
542#95C24116yes—
543#95C24116yes—
544#95C24116yes—
545C24—24no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—28no—
550C24—28no—
551C24—28no—
552C24—42no—
553C24—48no—
554C24—48no—
555C24C2518yes—
556C24C2512yes—
557C24C2512yes—
558C24C2511yescharacteristic
559#41—232no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8C2×#4114yes—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—232no—
568C2×D4—232no—
569C2×D4—22no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—216no—
575C2×D4—216no—
576C2×D4—22no—
577C2×D4—28no—
578C2×D4—28no—
579C2×D4—216no—
580C2×D4—216no—
581C2×D4—44no—
582C2×D4—416no—
583C2×D4—48no—
584C2×D4—416no—
585C2×D4—416no—
586C2×D4—416no—
587C2×D4—48no—
588C2×D4—432no—
589C2×D4—832no—
590C2×D4—832no—
591C2×D4C2×#4118yes—
592C2×D4C2×#4114yes—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—28no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
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—24no—
620C22×C4—28no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—432no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—416no—
630C22×C4—416no—
631C22×C4—416no—
632C22×C4—416no—
633C22×C4C2×#4118yes—
634C22×C4C2×#4118yes—
635C22×C4C2×#4114yes—
636C22×C4C2×#4114yes—
637C22×C4H(5,𝔽2)18yes—
638C22×C4H(5,𝔽2)14yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2512yes—
642C22×C4C2514yes—
643C22×C4C2518yes—
644C22×C4C2514yes—
645C22×C4C2514yes—
646C22×C4C2512yes—
647C22×C4C2514yes—
648C22×C4C2518yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2512yes—
652C22×C4C2511yescharacteristic
653C22×C4C2511yescharacteristic
654C22×C4C2512yes—
655C4⋊C4—28no—
656C4⋊C4—24no—
657C4⋊C4—28no—
658C4⋊C4—24no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—24no—
663C4⋊C4—28no—
664C4⋊C4—216no—
665C4⋊C4—24no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—28no—
669C4⋊C4—28no—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—416no—
675C4⋊C4—44no—
676C4⋊C4—416no—
677C4⋊C4—416no—
678C22⋊C4—24no—
679C22⋊C4—28no—
680C22⋊C4—24no—
681C22⋊C4—28no—
682C22⋊C4—24no—
683C22⋊C4—28no—
684C22⋊C4—216no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—232no—
689C22⋊C4—232no—
690C22⋊C4—28no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—416no—
694C22⋊C4—416no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—416no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—416no—
701C22⋊C4—416no—
702C22⋊C4—416no—
703C42—22no—
704C42—24no—
705C42—24no—
706C42—24no—
707C42—24no—
708C42—22no—
709C42—24no—
710C42—24no—
711C42—28no—
712C42—24no—
713C42—28no—
714C42—24no—
715C42—28no—
716C42—216no—
717C42—28no—
718C42—28no—
719C42—48no—
720C42—48no—
721C42C2×#4114yes—
722C42C2×#4114yes—
723C42C2×#4118yes—
724C23—22no—
725C23—22no—
726C23—28no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—24no—
737C23—28no—
738C23—28no—
739C23—216no—
740C23—28no—
741C23—216no—
742C23—48no—
743C23—48no—
744C23—44no—
745C23—44no—
746C23—416no—
747C23—816no—
748C23—88no—
749C23—816no—
750C23—88no—
751C23C22×#4114yes—
752C23C22×#4112yes—
753C23C22×#4112yes—
754C23C2×H(5,𝔽2)14yes—
755C23C2×H(5,𝔽2)12yes—
756C23C2611yescharacteristic
757Q8—28no—
758D4—216no—
759D4—28no—
760D4—416no—
761D4—416no—
762D4—416no—
763D4—432no—
764D4—816no—
765D4—832no—
766D4—832no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—216no—
774C2×C4—216no—
775C2×C4—216no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—24no—
792C2×C4—216no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—48no—
806C2×C4—48no—
807C2×C4—416no—
808C2×C4—48no—
809C2×C4—88no—
810C2×C4—168no—
811C2×C4—168no—
812C2×C4—168no—
813C2×C4#553116yescomplemented
814C2×C4C22×#4114yes—
815C2×C4C22×#4114yes—
816C2×C4C22×#4112yes—
817C2×C4C22×#4112yes—
818C2×C4C22×#4112yes—
819C2×C4C22×#4112yes—
820C2×C4C22×#4114yes—
821C2×C4C2×H(5,𝔽2)14yes—
822C2×C4C2×H(5,𝔽2)12yes—
823C2×C4C2×H(5,𝔽2)12yes—
824C2×C4C2×H(5,𝔽2)14yes—
825C2×C4#58514yes—
826C22—24no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—24no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—416no—
836C22—42no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—416no—
844C22—416no—
845C22—48no—
846C22—48no—
847C22—48no—
848C22—1616no—
849C22C2×#55314yes—
850C22C23×#4111yescharacteristic
851C22C23×#4111yescharacteristic
852C22C22×H(5,𝔽2)12yes—
853C22C22×H(5,𝔽2)11yescharacteristic
854C22C2×#58512yes—
855C4—24no—
856C4—24no—
857C4—24no—
858C4—44no—
859C4—42no—
860C4—44no—
861C4—48no—
862C4—48no—
863C4—42no—
864C4—44no—
865C4—44no—
866C4—42no—
867C4—42no—
868C4C2×#55314yes—
869C4C2×#55314yes—
870C4#349418yes—
871C2—24no—
872C2—44no—
873C2—44no—
874C2—88no—
875C2C22×#55311yescharacteristic
876C2C2×#349412yes—
877C2#6280012yes—
878C2#6283211yescharacteristic
879C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59208C2semidirect
2. #59028C2semidirect
3. #39148C2semidirect
4. #39147C2semidirect
5. #37946C2semidirect
6. C2×#2856C2semidirect
7. #36472C2semidirect
8. #36460C2semidirect
9. #36211C2semidirect
10. #36182C2semidirect
11. #35563C2semidirect
12. #35540C2semidirect
13. #35286C2semidirect
14. #35272C2semidirect
15. #35266C2semidirect
16. #34275C2semidirect
17. #34210C2semidirect
18. #34183C2semidirect
19. C4×#525C2semidirect
20. #34012C2semidirect
21. C2×#553C22semidirect
31. #2860C22semidirect
32. #2859C22semidirect
37. #2856C22semidirect
38. #2757C22semidirect
39. #2749C22semidirect
40. #2701C22semidirect
41. #2688C22semidirect
42. #2647C22semidirect
43. #2644C22semidirect
44. #2619C22semidirect
45. #2603C22semidirect
46. #2571C22semidirect
47. #2566C22semidirect
48. #2559C22semidirect
49. #2552C22semidirect
50. #2548C22semidirect
51. #2541C22semidirect
52. #2535C22semidirect
54. #2526C22semidirect
55. #2513C22semidirect
56. #2513C22semidirect
57. #2512C22semidirect
58. #2512C22semidirect
59. #2504C22semidirect
60. #2500C22semidirect
61. #2490C22semidirect
62. #2490C22semidirect
65. #2464C22semidirect
67. #2428C22semidirect
68. #2426C22semidirect
69. #2422C22semidirect
70. #2422C22semidirect
71. #2422C22semidirect
72. #2420C22semidirect
73. #2420C22semidirect
74. #2420C22semidirect
75. #2416C22semidirect
76. #2416C22semidirect
77. #2414C22semidirect
78. #2414C22semidirect
82. #2366C22semidirect
83. #2366C22semidirect
84. #2363C22semidirect
85. #2363C22semidirect
86. #2361C22semidirect
87. #2361C22semidirect
89. #2357C22semidirect
90. Q8×C4⋊C4C22semidirect
92. D4×C4⋊C4C22semidirect
94. #2328C22semidirect
95. #2328C22semidirect
96. #2326C22semidirect
99. #2317C22semidirect
103. C4×#127C22semidirect
104. C4×#127C22semidirect
105. C4×#127C22semidirect
106. C4×#124C22semidirect
107. C4×C22⋊Q8C22semidirect
108. C4×C22⋊Q8C22semidirect
110. C4×#121C22semidirect
111. C4×#121C22semidirect
117. #2290C22semidirect
120. #2285C22semidirect
121. #2285C22semidirect
122. #2285C22semidirect
124. C2×#384C22semidirect
126. #2283C22semidirect
127. #2283C22semidirect
131. C42×D4C22semidirect
134. C4×#117C22semidirect
813. C2×C4#553semidirect

Maximal subgroups

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

subgroupindex
#592082
#590282
#391482
#391472
#379462
C2×#28562
#364722
#364602
#362112
#361822
#355632
#355402
#352862
#352722
#352662
#342752
#342102
#341832
C4×#5252
#340122