Finite Group Databasebeta

← #7658724

Subgroups — #7658724

Order 512.

9152 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C212yesmaximal, complemented
2#42985C214yesmaximal, complemented
3#42969C214yesmaximal, complemented
4#42883C214yesmaximal, complemented
5#41936C218yesmaximal, complemented
6#41932C218yesmaximal, complemented
7#40584C218yesmaximal, complemented
8#37454C212yesmaximal, complemented
9#37450C211yesmaximal, characteristic, complemented
10#37446C214yesmaximal, complemented
11#37437C212yesmaximal, complemented
12#36652C211yesmaximal, characteristic, complemented
13C2×#2815C212yesmaximal, complemented
14#35976C214yesmaximal, complemented
15#35691C214yesmaximal, complemented
16#35680C214yesmaximal, complemented
17#34172C211yesmaximal, characteristic, complemented
18C22×H(5,𝔽2)C2212yescomplemented
19C23×#41C2211yescharacteristic
20#3488—232no—
21C2×#550C2214yescomplemented
22C2×#548C2214yescomplemented
23C2×#546C2214yes—
24C2×#546C2218yescomplemented
25C2×D42C2214yescomplemented
26C2×D42C2218yescomplemented
27C2×D42C2214yescomplemented
28C2×#537C2214yescomplemented
29C2×#537C2212yescomplemented
30C2×#535C2214yescomplemented
31C2×#535C2212yescomplemented
32C2×#525C2212yescomplemented
33C2×#525C2214yescomplemented
34C22×#121C2214yescomplemented
35C22×#121C2212yescomplemented
36C2×#520C2212yescomplemented
37C2×#518C2212yescomplemented
38#2817C2211yescharacteristic, complemented
39#2816C2212yescomplemented
40#2816C2214yescomplemented
41#2815C2211yescharacteristic, complemented
42#2815C2214yescomplemented
43#2815C2212yescomplemented
44#2815C2218yescomplemented
45#2815C2218yescomplemented
46#2815C2218yescomplemented
47#2815C2212yescomplemented
48#2814C2214yescomplemented
49#2813C2214yescomplemented
50#2812C2214yescomplemented
51#2733C2218yescomplemented
52#2730C22116yescomplemented
53#2728C2218yescomplemented
54#2688C22116yescomplemented
55#2673C22116yescomplemented
56#2669C22116yescomplemented
57#2668C22116yescomplemented
58#2661C2218yescomplemented
59#2656C2218yescomplemented
60#2639C2218yescomplemented
61#2638C2218yescomplemented
62#2635C22116yescomplemented
63#2635C2218yescomplemented
64#2624C2214yescomplemented
65#2623C2218yescomplemented
66#2619C2214yescomplemented
67#2617C2218yescomplemented
68#2617C2218yescomplemented
69#2615C2214yescomplemented
70#2613C2218yescomplemented
71#2613C2218yescomplemented
72#2600C2218yescomplemented
73#2561C2214yescomplemented
74#2543C2218yescomplemented
75#2543C2218yescomplemented
76#2543C2218yescomplemented
77#2541C2214yescomplemented
78#2539C2214yescomplemented
79#2535C2214yescomplemented
80#2504C2214yescomplemented
81#2498C2218yescomplemented
82#2486C2214yescomplemented
83#2482C2218yescomplemented
84#2448C2218yescomplemented
85#2444C22116yescomplemented
86#2433C2214yescomplemented
87#2431C2218yescomplemented
88#2430C2218yescomplemented
89#2428C2218yescomplemented
90#2424C22116yescomplemented
91#2421C2218yescomplemented
92#2418C22116yescomplemented
93#2414C2218yescomplemented
94#2410C22116yescomplemented
95#2410C22116yescomplemented
96#2408C2214yescomplemented
97#2408C2218yescomplemented
98#2407C2218yescomplemented
99#2404C2218yescomplemented
100#2403C2214yescomplemented
101#2403C22116yescomplemented
102#2395C2214yescomplemented
103#2392C2214yescomplemented
104C2×#397C2218yescomplemented
105#2388C2214yescomplemented
106C2×#392C2218yescomplemented
107C2×#392C2218yescomplemented
108#2349C2214yescomplemented
109#2339C2214yescomplemented
110#2339C2218yescomplemented
111#2339C2214yescomplemented
112D4×C22⋊C4C2218yescomplemented
113#2310C2212yescomplemented
114#2308C2214yescomplemented
115#2280C2211yescharacteristic, complemented
116#2280C2211yescharacteristic, complemented
117C2×#381C2212yescomplemented
118C2×#381C2212yescomplemented
119C2×H(5,𝔽2)—216no—
120C2×H(5,𝔽2)—416no—
121C22×#41—48no—
122C22×#41D4116yescomplemented
123C22×#41C2312yes—
124C22×#41C2312yes—
125C22×#41C2314yes—
126C22×#41C2314yes—
127C22×#41C2314yes—
128C22×#41C2312yes—
129C23×Q8C2311yescharacteristic
130C23×D4C2314yes—
131C23×D4C2311yescharacteristic
132C23×D4C2314yes—
133C23×D4C2318yes—
134C23×D4C2312yes—
135C23×D4C2314yes—
136C23×D4C2318yes—
137C23×D4C2312yes—
138C23×D4C2318yes—
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141#550—232no—
142#548—232no—
143#546—232no—
144#546—264no—
145D42—232no—
146D42—264no—
147D42—416no—
148#537—232no—
149#537—216no—
150#535—232no—
151#535—216no—
152C2×#127C2318yes—
153C2×#127C2314yes—
154C2×#127C2314yes—
155C2×#124C2314yes—
156C2×#124C2318yes—
157#525—216no—
158#525—232no—
159C2×#123C2318yes—
160C2×#123C2314yes—
161C2×#123C2318yes—
162C2×C22⋊Q8C2312yes—
163C2×C22⋊Q8C2312yes—
164C2×C22⋊Q8C2314yes—
165C2×C22⋊Q8C2314yes—
166C2×C22⋊Q8C2318yes—
167C2×#121—232no—
168C2×#121—216no—
169C2×#121C2312yes—
170C2×#121C2314yes—
171C2×#121C2314yes—
172C2×#121C2314yes—
173C2×#121C2314yes—
174C2×#121C2314yes—
175C2×#121C2318yes—
176C2×#121C2318yes—
177C2×#121C2314yes—
178C2×#121C2314yes—
179C2×#121C2318yes—
180C2×#121C2312yes—
181C2×#121C2318yes—
182C2×#121C2318yes—
183C2×#121C2318yes—
184C2×#121C2314yes—
185C2×#121C2318yes—
186C2×#121C2318yes—
187C2×#121C23116yes—
188C2×#121C23116yes—
189C2×#120C2314yes—
190C2×#120C2318yes—
191C2×#120C2318yes—
192C2×#120C2318yes—
193C2×#120C2318yes—
194C2×#120C23116yes—
195C2×#120C2318yes—
196C2×#120C23116yes—
197#520—216no—
198#518—48no—
199C2×C4×Q8C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2318yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2312yes—
216C22×C22⋊C4C2314yes—
217C22×C22⋊C4C2318yes—
218C22×C22⋊C4C2314yes—
219C22×C22⋊C4C2314yes—
220C22×C22⋊C4C23116yes—
221#400C2314yes—
222#400C23116yes—
223#399C2318yes—
224#399C2314yes—
225#399C23116yes—
226#398C2314yes—
227#398C2318yes—
228#398C2314yes—
229#397C2318yes—
230#397C2314yes—
231#397C2318yes—
232#397C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2314yes—
236#397C23116yes—
237#397C23116yes—
238#397C2318yes—
239#396C2318yes—
240#395C2314yes—
241#394C23116yes—
242#394C2314yes—
243#394C2318yes—
244#394C2318yes—
245#394C23116yes—
246#394C23116yes—
247#394C2318yes—
248#394C2318yes—
249#394C23116yes—
250#394C2318yes—
251#394C2314yes—
252#394C2318yes—
253#393C2318yes—
254#393C2314yes—
255#392C2318yes—
256#392C2318yes—
257#392C23116yes—
258#392C2318yes—
259#392C23116yes—
260#392C23116yes—
261#392C2318yes—
262#392C2318yes—
263#392C2318yes—
264#392C2314yes—
265#392C2314yes—
266#392C2318yes—
267#392C23116yes—
268#392C2318yes—
269#392C23116yes—
270#392C2318yes—
271#392C23116yes—
272#392C2318yes—
273#391C2318yes—
274#391C2318yes—
275#390C2318yes—
276#390C2318yes—
277#390C23116yes—
278#389C2318yes—
279#388C23116yes—
280#388C23116yes—
281#388C23116yes—
282#388C23116yes—
283#387C23116yes—
284#386C23116yes—
285#386C23116yes—
286#386C23116yes—
287#386C23116yes—
288#386C23116yes—
289#386C23116yes—
290#386C23116yes—
291#386C23116yes—
292#386C23116yes—
293#386C23116yes—
294#385C23116yes—
295#385C23116yes—
296#382C2314yes—
297#381C2311yescharacteristic
298#381C2312yes—
299#381C2318yes—
300#381C2311yescharacteristic
301#381C2314yes—
302#381C2314yes—
303#381C2318yes—
304#381C2318yes—
305#380C2318yes—
306#380C2314yes—
307#380C2314yes—
308#380C2318yes—
309#379C2318yes—
310#379C2312yes—
311#379C2312yes—
312#379C23116yes—
313C4×C4⋊C4C2314yes—
314C4×C22⋊C4C2314yes—
315C4×C22⋊C4C2318yes—
316C4×C22⋊C4C2314yes—
317C2×#95C2318yes—
318C2×#95C2318yes—
319C2×#95C2318yes—
320C25C2418yes—
321C25C2412yes—
322C25C2414yes—
323C25C2411yescharacteristic
324H(5,𝔽2)—4128no—
325C2×#41—216no—
326C2×#41—216no—
327C2×#41—216no—
328C2×#41—28no—
329C2×#41—48no—
330C2×#41—416no—
331C2×#41—416no—
332C2×#41—48no—
333C2×#41—416no—
334C2×#41—464no—
335C2×#41C2×D4116yes—
336C2×#41C2×D4132yescomplemented
337C2×#41C2×D4116yescomplemented
338C22×Q8—44no—
339C22×Q8C2×D418yescomplemented
340C22×Q8C2412yes—
341C22×Q8C2412yes—
342C22×Q8C2412yes—
343C22×D4—28no—
344C22×D4—232no—
345C22×D4—216no—
346C22×D4—232no—
347C22×D4—216no—
348C22×D4—232no—
349C22×D4—216no—
350C22×D4—28no—
351C22×D4—48no—
352C22×D4—416no—
353C22×D4—416no—
354C22×D4—48no—
355C22×D4—432no—
356C22×D4—816no—
357C22×D4—816no—
358C22×D4—88no—
359C22×D4C2×D418yes—
360C22×D4C2×D4116yescomplemented
361C22×D4C2418yes—
362C22×D4C2414yes—
363C22×D4C2412yes—
364C22×D4C2411yescharacteristic
365C22×D4C2414yes—
366C22×D4C2414yes—
367C22×D4C2418yes—
368C22×D4C2418yes—
369C22×D4C2414yes—
370C22×D4C2418yes—
371C22×D4C2418yes—
372C22×D4C2418yes—
373C22×D4C2414yes—
374C22×D4C2414yes—
375C22×D4C2412yes—
376C22×D4C2418yes—
377C22×D4C2414yes—
378C22×D4C2418yes—
379C22×D4C24116yes—
380C22×D4C2418yes—
381C22×D4C2414yes—
382C22×D4C2411yescharacteristic
383C23×C4—44no—
384C23×C4—48no—
385C23×C4C2×D418yescomplemented
386C23×C4C2×D4116yescomplemented
387C23×C4C2414yes—
388C23×C4C2414yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2418yes—
392C23×C4C2418yes—
393C23×C4C2414yes—
394C23×C4C2418yes—
395C23×C4C2418yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2414yes—
399C23×C4C2411yescharacteristic
400#127—216no—
401#127—232no—
402#127—48no—
403#124—216no—
404#124—232no—
405#123—232no—
406#123—216no—
407#123—88no—
408C22⋊Q8—216no—
409C22⋊Q8—232no—
410C22⋊Q8—28no—
411C22⋊Q8—28no—
412C22⋊Q8—216no—
413#121—232no—
414#121—232no—
415#121—232no—
416#121—216no—
417#121—232no—
418#121—28no—
419#121—216no—
420#121—216no—
421#121—216no—
422#121—216no—
423#121—216no—
424#121—232no—
425#121—216no—
426#121—232no—
427#121—28no—
428#121—216no—
429#121—416no—
430#121—416no—
431#121—816no—
432#121—816no—
433#120—232no—
434#120—216no—
435#120—232no—
436#120—232no—
437#120—232no—
438#120—432no—
439#120—816no—
440#120—88no—
441C4×Q8—216no—
442C4×D4—232no—
443C4×D4—216no—
444C4×D4—216no—
445C4×D4—216no—
446C4×D4—232no—
447C4×D4—216no—
448C4×D4—232no—
449C4×D4—48no—
450C4×D4—48no—
451C4×D4—416no—
452#117—216no—
453#117—28no—
454#117—44no—
455#117—44no—
456C2×C4⋊C4—216no—
457C2×C4⋊C4—28no—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C24116yes—
471C2×C22⋊C4—232no—
472C2×C22⋊C4—216no—
473C2×C22⋊C4—48no—
474C2×C22⋊C4—48no—
475C2×C22⋊C4—816no—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2414yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2412yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2412yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C24116yes—
495C2×C22⋊C4C24116yes—
496C2×C22⋊C4C24116yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C24116yes—
501C2×C22⋊C4C24116yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2418yes—
504C2×C42C2414yes—
505C2×C42C2418yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508#95C2414yes—
509#95C2414yes—
510#95C2418yes—
511#95C2414yes—
512#95C2418yes—
513#95C24116yes—
514#95C24116yes—
515#95C24116yes—
516#95C2418yes—
517#95C2418yes—
518#95C2414yes—
519#95C24116yes—
520#95C2418yes—
521C24—28no—
522C24—28no—
523C24—216no—
524C24—232no—
525C24—42no—
526C24—48no—
527C24—44no—
528C24—48no—
529C24—48no—
530C24—48no—
531C24—416no—
532C24—48no—
533C24—48no—
534C24C22×D418yes—
535C24C22×D414yes—
536C24C2514yes—
537C24C2518yes—
538C24C2511yescharacteristic
539C24C2512yes—
540C24C2512yes—
541C24C2512yes—
542#41—264no—
543#41—464no—
544#41—432no—
545#41—464no—
546#41—432no—
547#41—464no—
548C2×Q8—24no—
549C2×Q8—28no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—416no—
553C2×Q8C22×D418yes—
554C2×Q8C22×D418yes—
555C2×D4—28no—
556C2×D4—216no—
557C2×D4—232no—
558C2×D4—28no—
559C2×D4—216no—
560C2×D4—28no—
561C2×D4—216no—
562C2×D4—232no—
563C2×D4—28no—
564C2×D4—216no—
565C2×D4—216no—
566C2×D4—216no—
567C2×D4—216no—
568C2×D4—28no—
569C2×D4—24no—
570C2×D4—216no—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—216no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—48no—
577C2×D4—416no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—416no—
583C2×D4—464no—
584C2×D4—432no—
585C2×D4—416no—
586C2×D4—44no—
587C2×D4—416no—
588C2×D4—416no—
589C2×D4—416no—
590C2×D4—48no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—44no—
597C2×D4—48no—
598C2×D4—416no—
599C2×D4—432no—
600C2×D4—4128no—
601C2×D4—464no—
602C2×D4—864no—
603C2×D4—832no—
604C2×D4—864no—
605C2×D4C22×D4116yes—
606C2×D4C22×D418yes—
607C2×D4C22×D414yes—
608C2×D4C22×D4116yes—
609C2×D4C22×D414yes—
610C2×D4H(5,𝔽2)18yes—
611C22×C4—216no—
612C22×C4—24no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—216no—
616C22×C4—216no—
617C22×C4—216no—
618C22×C4—28no—
619C22×C4—216no—
620C22×C4—416no—
621C22×C4—42no—
622C22×C4—432no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—48no—
626C22×C4—416no—
627C22×C4—416no—
628C22×C4—416no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—416no—
632C22×C4C22×D4116yes—
633C22×C4C22×D418yes—
634C22×C4C22×D414yes—
635C22×C4C22×D418yes—
636C22×C4C22×D418yes—
637C22×C4C22×D4116yes—
638C22×C4C22×D414yes—
639C22×C4C2514yes—
640C22×C4C2514yes—
641C22×C4C2518yes—
642C22×C4C2514yes—
643C22×C4C2518yes—
644C22×C4C2514yes—
645C22×C4C2514yes—
646C22×C4C2514yes—
647C22×C4C2512yes—
648C22×C4C2511yescharacteristic
649C22×C4C2511yescharacteristic
650C4⋊C4—24no—
651C4⋊C4—28no—
652C4⋊C4—216no—
653C4⋊C4—28no—
654C4⋊C4—24no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—48no—
662C4⋊C4—416no—
663C22⋊C4—28no—
664C22⋊C4—216no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—216no—
668C22⋊C4—216no—
669C22⋊C4—28no—
670C22⋊C4—216no—
671C22⋊C4—216no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—28no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—44no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—48no—
685C22⋊C4—416no—
686C22⋊C4—48no—
687C22⋊C4—416no—
688C22⋊C4—416no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C42—216no—
692C42—28no—
693C42—28no—
694C42—44no—
695C23—28no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—28no—
702C23—24no—
703C23—216no—
704C23—24no—
705C23—28no—
706C23—28no—
707C23—216no—
708C23—24no—
709C23—28no—
710C23—28no—
711C23—28no—
712C23—216no—
713C23—24no—
714C23—44no—
715C23—416no—
716C23—48no—
717C23—416no—
718C23—432no—
719C23—816no—
720C23—832no—
721C23—816no—
722C23—88no—
723C23—832no—
724C23—816no—
725C23—88no—
726C23—88no—
727C23—1616no—
728C23C23×D414yes—
729C23C23×D412yes—
730C23C23×D414yes—
731C23C23×D414yes—
732C23C2×H(5,𝔽2)18yes—
733C23C2611yescharacteristic
734Q8—216no—
735Q8—48no—
736Q8—48no—
737D4—216no—
738D4—232no—
739D4—28no—
740D4—416no—
741D4—416no—
742D4—48no—
743D4—432no—
744D4—416no—
745D4—416no—
746D4—432no—
747D4—416no—
748D4—432no—
749D4—416no—
750D4—88no—
751D4—816no—
752D4—816no—
753D4—816no—
754D4—816no—
755D4—816no—
756D4—832no—
757D4—168no—
758D4#534116yes—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—232no—
763C2×C4—28no—
764C2×C4—216no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—216no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—216no—
779C2×C4—24no—
780C2×C4—44no—
781C2×C4—48no—
782C2×C4—416no—
783C2×C4—48no—
784C2×C4—432no—
785C2×C4—416no—
786C2×C4—816no—
787C2×C4—816no—
788C2×C4—88no—
789C2×C4—168no—
790C2×C4C23×D418yes—
791C2×C4C23×D412yes—
792C2×C4C23×D414yes—
793C2×C4C23×D412yes—
794C2×C4C2×H(5,𝔽2)14yes—
795C22—216no—
796C22—28no—
797C22—24no—
798C22—24no—
799C22—28no—
800C22—24no—
801C22—22no—
802C22—24no—
803C22—24no—
804C22—48no—
805C22—44no—
806C22—48no—
807C22—48no—
808C22—416no—
809C22—416no—
810C22—48no—
811C22—44no—
812C22—48no—
813C22—44no—
814C22—48no—
815C22—48no—
816C22—44no—
817C22—816no—
818C22—88no—
819C22—1632no—
820C22—1616no—
821C22C2×#53418yes—
822C22C24×D411yescharacteristic
823C22C22×H(5,𝔽2)12yes—
824C22H(7,𝔽2)14yes—
825C4—24no—
826C4—28no—
827C4—22no—
828C4—44no—
829C4—48no—
830C4—44no—
831C4—44no—
832C4—48no—
833C4—44no—
834C4—44no—
835C4C2×#53414yes—
836C2—28no—
837C2—44no—
838C2—42no—
839C2—44no—
840C2—84no—
841C2—88no—
842C2C22×#53411yescharacteristic
843C2#6285212yes—
844C2#6304114yes—
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. C2×#3488C2semidirect
2. #42985C2semidirect
3. #42969C2semidirect
4. #42883C2semidirect
5. #41936C2semidirect
6. #41932C2semidirect
7. #40584C2semidirect
8. #37454C2semidirect
9. #37450C2semidirect
10. #37446C2semidirect
11. #37437C2semidirect
12. #36652C2semidirect
13. C2×#2815C2semidirect
14. #35976C2semidirect
15. #35691C2semidirect
16. #35680C2semidirect
17. #34172C2semidirect
18. C22×H(5,𝔽2)C22semidirect
21. C2×#550C22semidirect
22. C2×#548C22semidirect
24. C2×#546C22semidirect
25. C2×D42C22semidirect
26. C2×D42C22semidirect
27. C2×D42C22semidirect
28. C2×#537C22semidirect
29. C2×#537C22semidirect
30. C2×#535C22semidirect
31. C2×#535C22semidirect
32. C2×#525C22semidirect
33. C2×#525C22semidirect
34. C22×#121C22semidirect
35. C22×#121C22semidirect
36. C2×#520C22semidirect
37. C2×#518C22semidirect
38. #2817C22semidirect
39. #2816C22semidirect
40. #2816C22semidirect
41. #2815C22semidirect
42. #2815C22semidirect
43. #2815C22semidirect
44. #2815C22semidirect
45. #2815C22semidirect
46. #2815C22semidirect
47. #2815C22semidirect
48. #2814C22semidirect
49. #2813C22semidirect
50. #2812C22semidirect
51. #2733C22semidirect
52. #2730C22semidirect
53. #2728C22semidirect
54. #2688C22semidirect
55. #2673C22semidirect
56. #2669C22semidirect
57. #2668C22semidirect
58. #2661C22semidirect
59. #2656C22semidirect
60. #2639C22semidirect
61. #2638C22semidirect
62. #2635C22semidirect
63. #2635C22semidirect
64. #2624C22semidirect
65. #2623C22semidirect
66. #2619C22semidirect
67. #2617C22semidirect
68. #2617C22semidirect
69. #2615C22semidirect
70. #2613C22semidirect
71. #2613C22semidirect
72. #2600C22semidirect
73. #2561C22semidirect
74. #2543C22semidirect
75. #2543C22semidirect
76. #2543C22semidirect
77. #2541C22semidirect
78. #2539C22semidirect
79. #2535C22semidirect
80. #2504C22semidirect
81. #2498C22semidirect
82. #2486C22semidirect
83. #2482C22semidirect
84. #2448C22semidirect
85. #2444C22semidirect
86. #2433C22semidirect
87. #2431C22semidirect
88. #2430C22semidirect
89. #2428C22semidirect
90. #2424C22semidirect
91. #2421C22semidirect
92. #2418C22semidirect
93. #2414C22semidirect
94. #2410C22semidirect
95. #2410C22semidirect
96. #2408C22semidirect
97. #2408C22semidirect
98. #2407C22semidirect
99. #2404C22semidirect
100. #2403C22semidirect
101. #2403C22semidirect
102. #2395C22semidirect
103. #2392C22semidirect
104. C2×#397C22semidirect
105. #2388C22semidirect
106. C2×#392C22semidirect
107. C2×#392C22semidirect
108. #2349C22semidirect
109. #2339C22semidirect
110. #2339C22semidirect
111. #2339C22semidirect
112. D4×C22⋊C4C22semidirect
113. #2310C22semidirect
114. #2308C22semidirect
115. #2280C22semidirect
116. #2280C22semidirect
117. C2×#381C22semidirect
118. C2×#381C22semidirect
122. C22×#41D4semidirect
336. C2×#41C2×D4semidirect
337. C2×#41C2×D4semidirect
339. C22×Q8C2×D4semidirect
360. C22×D4C2×D4semidirect
385. C23×C4C2×D4semidirect
386. C23×C4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
#429852
#429692
#428832
#419362
#419322
#405842
#374542
#374502
#374462
#374372
#366522
C2×#28152
#359762
#356912
#356802
#341722