Finite Group Databasebeta

← #7687859

Subgroups — #7687859

Order 512.

11885 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3496C214yesmaximal, complemented
2#59816C211yesmaximal, characteristic, complemented
3#59313C212yesmaximal, complemented
4#59035C214yesmaximal, complemented
5#59015C218yesmaximal, complemented
6#45103C214yesmaximal, complemented
7#43017C218yesmaximal, complemented
8#39340C214yesmaximal, complemented
9#39338C218yesmaximal, complemented
10#36179C211yesmaximal, characteristic, complemented
11#36153C214yesmaximal, complemented
12#36127C212yesmaximal, complemented
13D4×#121C214yesmaximal, complemented
14#35750C214yesmaximal, complemented
15#34925C211yesmaximal, characteristic, complemented
16C2×#2537C212yesmaximal, complemented
17C4×D42C212yesmaximal, complemented
18C22×H(5,𝔽2)C2214yescomplemented
19#3496—264no—
20C2×#547C2214yescomplemented
21C2×#547C2214yescomplemented
22C2×#547C2218yescomplemented
23C2×#547C2212yescomplemented
24C2×#546C22116yescomplemented
25C2×#546C2218yescomplemented
26C2×#546C2218yescomplemented
27C2×D42C2212yes—
28C2×D42C2214yescomplemented
29C2×D42C2218yescomplemented
30C2×D42C2212yescomplemented
31C2×#537C2218yescomplemented
32C2×#534C22116yescomplemented
33C2×#532C2214yescomplemented
34C2×#532C2214yescomplemented
35C22×#121C2218yescomplemented
36C22×#121C2218yescomplemented
37C22×C4×D4C2214yescomplemented
38C22×C4×D4C2214yescomplemented
39#2868C2211yescharacteristic, complemented
40#2857C2214yescomplemented
41#2856C2212yescomplemented
42#2847C2218yescomplemented
43#2680C2218yescomplemented
44#2679C2214yescomplemented
45#2672C22116yescomplemented
46#2671C22116yescomplemented
47#2671C22116yescomplemented
48#2668C22116yescomplemented
49#2668C2218yescomplemented
50#2616C2214yescomplemented
51#2613C2218yescomplemented
52#2555C2214yescomplemented
53#2551C2211yescharacteristic, complemented
54#2547C2214yescomplemented
55#2542C2212yescomplemented
56#2542C2214yescomplemented
57#2541C2212yescomplemented
58#2537C2218yescomplemented
59#2537C2214yescomplemented
60#2537C2214yescomplemented
61#2537C2214yescomplemented
62#2537C2211yescharacteristic, complemented
63#2537C2218yescomplemented
64#2537C2212yescomplemented
65#2537C2218yescomplemented
66#2501C2214yescomplemented
67#2501C2218yescomplemented
68#2491C2214yescomplemented
69#2486C2218yescomplemented
70#2440C2218yescomplemented
71#2437C2218yescomplemented
72#2435C2214yescomplemented
73#2432C2218yescomplemented
74#2430C2218yescomplemented
75#2428C2214yescomplemented
76#2428C2218yescomplemented
77#2427C2218yescomplemented
78#2425C22116yescomplemented
79#2424C22116yescomplemented
80#2422C2218yescomplemented
81#2422C2218yescomplemented
82#2422C2218yescomplemented
83#2418C22116yescomplemented
84#2417C2218yescomplemented
85#2416C2218yescomplemented
86#2416C2218yescomplemented
87#2412C22116yescomplemented
88#2410C22116yescomplemented
89#2408C2214yescomplemented
90#2408C2218yescomplemented
91#2408C2218yescomplemented
92#2407C2218yescomplemented
93#2406C2218yescomplemented
94#2405C22116yescomplemented
95#2388C2214yescomplemented
96C2×#394C2218yescomplemented
97#2366C2212yescomplemented
98#2361C2214yescomplemented
99#2361C2214yescomplemented
100#2358C2218yescomplemented
101D4×C4⋊C4C2214yescomplemented
102D4×C4⋊C4C2214yescomplemented
103D4×C4⋊C4C2212yescomplemented
104D4×C4⋊C4C2212yescomplemented
105#2339C2214yescomplemented
106D4×C22⋊C4C2214yescomplemented
107D4×C22⋊C4C2214yescomplemented
108D4×C22⋊C4C2218yescomplemented
109C4×#127C2212yescomplemented
110C4×#127C2211yescharacteristic, complemented
111C4×#121C2214yescomplemented
112C4×#121C2214yescomplemented
113C4×#121C2214yescomplemented
114C4×#120C2218yescomplemented
115C2×#384C2212yescomplemented
116C2×#380C2218yescomplemented
117C42×D4C2212yescomplemented
118C42×D4C2211yescharacteristic, complemented
119C2×H(5,𝔽2)—264no—
120C2×H(5,𝔽2)—416no—
121C22×#41C2314yes—
122C22×#41C2314yes—
123C22×#41C2318yes—
124C22×#41C2318yes—
125C23×D4C2318yes—
126C23×D4C23116yes—
127C23×D4C2314yes—
128C23×D4C2314yes—
129C23×D4C2318yes—
130C23×D4C2314yes—
131C24×C4C2318yes—
132#547—264no—
133#547—232no—
134#547—232no—
135#547—48no—
136#546—264no—
137#546—264no—
138#546—2128no—
139D42—264no—
140D42—232no—
141D42—48no—
142D42D4132yescomplemented
143#537—264no—
144#534—2128no—
145#532—232no—
146#532—232no—
147C2×C4⋊Q8C2314yes—
148C2×C4⋊Q8C2314yes—
149C2×C4⋊Q8C2312yes—
150C2×#127C2311yescharacteristic
151C2×#127C2314yes—
152C2×#127C2312yes—
153C2×#124C2318yes—
154C2×#124C2318yes—
155C2×#123C23116yes—
156C2×#123C23116yes—
157C2×#123C23116yes—
158C2×#123C23116yes—
159C2×#123C2318yes—
160C2×C22⋊Q8C2318yes—
161C2×C22⋊Q8C23116yes—
162C2×C22⋊Q8C2318yes—
163C2×C22⋊Q8C2314yes—
164C2×#121—264no—
165C2×#121—264no—
166C2×#121C2318yes—
167C2×#121C2318yes—
168C2×#121C2318yes—
169C2×#121C2318yes—
170C2×#121C2314yes—
171C2×#121C2314yes—
172C2×#121C23116yes—
173C2×#121C23116yes—
174C2×#121C23116yes—
175C2×#121C23116yes—
176C2×#121C2318yes—
177C2×#121C2318yes—
178C2×#121C23116yes—
179C2×#121C2318yes—
180C2×#121C2314yes—
181C2×#121C2318yes—
182C2×#121C2314yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#120C23116yes—
186C2×#120C23116yes—
187C2×#120C23116yes—
188C2×#120C2318yes—
189C2×#120C2318yes—
190C2×C4×D4—232no—
191C2×C4×D4—416no—
192C2×C4×D4C2314yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2311yescharacteristic
196C2×C4×D4C2314yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2318yes—
199C2×C4×D4C2318yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C22×C4⋊C4C2318yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2318yes—
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2314yes—
218C22×C22⋊C4C2318yes—
219C22×C22⋊C4C23116yes—
220C22×C22⋊C4C23116yes—
221C22×C22⋊C4C2318yes—
222C22×C42C2312yes—
223C22×C42C2314yes—
224#399C2318yes—
225#399C23116yes—
226#398C23116yes—
227#397C23116yes—
228#397C23116yes—
229#396C23116yes—
230#395C2318yes—
231#395C2314yes—
232#394C2318yes—
233#394C23116yes—
234#394C2318yes—
235#394C23116yes—
236#394C2314yes—
237#394C23116yes—
238#394C2318yes—
239#394C23116yes—
240#394C2318yes—
241#394C2318yes—
242#394C23116yes—
243#394C23116yes—
244#393C2314yes—
245#392C2314yes—
246#392C23116yes—
247#392C2318yes—
248#392C2318yes—
249#391C2318yes—
250#390C2314yes—
251#390C2314yes—
252#390C2314yes—
253#390C2314yes—
254#390C2312yes—
255#390C2314yes—
256#390C2318yes—
257#390C2314yes—
258#390C2314yes—
259#390C2314yes—
260#389C2318yes—
261#389C2318yes—
262#389C2314yes—
263#389C2314yes—
264#389C2314yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#386C23116yes—
269#386C23116yes—
270#386C23116yes—
271#386C2318yes—
272#386C2318yes—
273#386C2318yes—
274#386C2318yes—
275#386C23116yes—
276#386C2318yes—
277#386C2318yes—
278#385C2318yes—
279#385C2318yes—
280#385C23116yes—
281#385C23116yes—
282#385C2318yes—
283#385C23116yes—
284#384C2312yes—
285#384C2311yescharacteristic
286#384C2312yes—
287#384C2314yes—
288#384C2312yes—
289#384C2318yes—
290#384C2314yes—
291#381C2318yes—
292#380C2314yes—
293#380C2318yes—
294#380C2318yes—
295#380C2314yes—
296#380C2318yes—
297#380C2314yes—
298#380C2318yes—
299#380C2318yes—
300#380C23116yes—
301#380C23116yes—
302#380C2314yes—
303#379C2318yes—
304#379C23116yes—
305#379C2318yes—
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2312yes—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C22⋊C4C2314yes—
312C4×C22⋊C4C2314yes—
313C4×C22⋊C4C2318yes—
314C4×C22⋊C4C2314yes—
315C4×C22⋊C4C2312yes—
316C4×C22⋊C4C2314yes—
317C4×C22⋊C4C2314yes—
318C2×#95C2318yes—
319C43C2311yescharacteristic
320C25C2418yes—
321C25C2418yes—
322H(5,𝔽2)—4256no—
323C2×#41—232no—
324C2×#41—232no—
325C2×#41—264no—
326C2×#41—216no—
327C2×#41—232no—
328C2×#41—232no—
329C2×#41—48no—
330C2×#41—416no—
331C2×#41—416no—
332C22×Q8C2414yes—
333C22×Q8C2414yes—
334C22×D4—216no—
335C22×D4—216no—
336C22×D4—264no—
337C22×D4—264no—
338C22×D4—264no—
339C22×D4—232no—
340C22×D4—232no—
341C22×D4—48no—
342C22×D4—48no—
343C22×D4—48no—
344C22×D4—416no—
345C22×D4—416no—
346C22×D4—416no—
347C22×D4—432no—
348C22×D4C2×D4132yescomplemented
349C22×D4C2×D4132yescomplemented
350C22×D4C2414yes—
351C22×D4C2418yes—
352C22×D4C2418yes—
353C22×D4C24116yes—
354C22×D4C2414yes—
355C22×D4C2418yes—
356C22×D4C2412yes—
357C22×D4C2414yes—
358C22×D4C2418yes—
359C22×D4C2414yes—
360C22×D4C2418yes—
361C22×D4C2412yes—
362C22×D4C24116yes—
363C22×D4C2414yes—
364C22×D4C2418yes—
365C22×D4C2411yescharacteristic
366C23×C4—232no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4C2418yes—
370C23×C4C2418yes—
371C23×C4C2414yes—
372C23×C4C2414yes—
373C23×C4C2412yes—
374C23×C4C24116yes—
375C23×C4C2414yes—
376C23×C4C2414yes—
377C23×C4C2418yes—
378C23×C4C2418yes—
379C23×C4C2414yes—
380C23×C4C2418yes—
381C4⋊Q8—216no—
382C4⋊Q8—216no—
383C4⋊Q8—44no—
384#127—216no—
385#127—24no—
386#127C2×D4116yescomplemented
387#124—232no—
388#124—232no—
389#123—264no—
390#123—264no—
391#123—264no—
392#123—264no—
393#123—416no—
394C22⋊Q8—232no—
395C22⋊Q8—232no—
396C22⋊Q8—264no—
397C22⋊Q8—48no—
398#121—232no—
399#121—216no—
400#121—264no—
401#121—232no—
402#121—232no—
403#121—264no—
404#121—264no—
405#121—232no—
406#121—232no—
407#121—264no—
408#121—232no—
409#121—216no—
410#121—264no—
411#121—232no—
412#121—48no—
413#121—416no—
414#121—48no—
415#121C2×D4132yescomplemented
416#121C2×D4132yescomplemented
417#120—264no—
418#120—264no—
419#120—264no—
420#120—416no—
421#120C2×D4164yescomplemented
422C4×D4—216no—
423C4×D4—232no—
424C4×D4—232no—
425C4×D4—24no—
426C4×D4—232no—
427C4×D4—232no—
428C4×D4—216no—
429C4×D4—232no—
430C4×D4—216no—
431C4×D4—216no—
432C4×D4—28no—
433C4×D4—216no—
434C4×D4—416no—
435C4×D4—48no—
436C4×D4—48no—
437C4×D4—44no—
438C4×D4—416no—
439C4×D4—48no—
440C4×D4—44no—
441C4×D4C2×D4116yescomplemented
442C4×D4C2×D4116yescomplemented
443C2×C4⋊C4—232no—
444C2×C4⋊C4—216no—
445C2×C4⋊C4—232no—
446C2×C4⋊C4—48no—
447C2×C4⋊C4—48no—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C24116yes—
455C2×C4⋊C4C24116yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2412yes—
468C2×C22⋊C4—264no—
469C2×C22⋊C4—232no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—416no—
472C2×C22⋊C4C2414yes—
473C2×C22⋊C4C24116yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C24116yes—
481C2×C22⋊C4C24116yes—
482C2×C22⋊C4C24116yes—
483C2×C22⋊C4C24116yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C2412yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2414yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2414yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2414yes—
498C2×C42—216no—
499C2×C42—28no—
500C2×C42C2414yes—
501C2×C42C2414yes—
502C2×C42C2414yes—
503C2×C42C2414yes—
504C2×C42C2412yes—
505C2×C42C2411yescharacteristic
506C2×C42C2412yes—
507C2×C42C2411yescharacteristic
508C2×C42C2412yes—
509C2×C42C2411yescharacteristic
510#95C2414yes—
511#95C2418yes—
512#95C24116yes—
513#95C2414yes—
514#95C2412yes—
515#95C2414yes—
516#95C2414yes—
517#95C2414yes—
518#95C2418yes—
519#95C2418yes—
520#95C2414yes—
521#95C24116yes—
522C24—216no—
523C24—216no—
524C24—232no—
525C24—48no—
526C24—48no—
527C24—48no—
528C24—48no—
529C24—48no—
530C24—48no—
531C24—416no—
532C24—48no—
533C24C22×D4132yes—
534C24C2514yes—
535C24C2518yes—
536C24C2514yes—
537C24C2512yes—
538#41—464no—
539#41—4128no—
540#41—4128no—
541#41—464no—
542C2×Q8—216no—
543C2×Q8—216no—
544C2×Q8—28no—
545C2×Q8—44no—
546C2×D4—216no—
547C2×D4—216no—
548C2×D4—2128no—
549C2×D4—232no—
550C2×D4—232no—
551C2×D4—232no—
552C2×D4—232no—
553C2×D4—216no—
554C2×D4—216no—
555C2×D4—216no—
556C2×D4—216no—
557C2×D4—232no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—216no—
561C2×D4—24no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—464no—
570C2×D4—48no—
571C2×D4—44no—
572C2×D4—48no—
573C2×D4—44no—
574C2×D4—48no—
575C2×D4—416no—
576C2×D4—48no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—416no—
580C2×D4—48no—
581C2×D4—416no—
582C2×D4—42no—
583C2×D4—48no—
584C2×D4—464no—
585C2×D4—4256no—
586C2×D4—4128no—
587C2×D4—864no—
588C2×D4C22×D4116yes—
589C2×D4C22×D418yes—
590C2×D4C22×D4132yes—
591C2×D4C22×D4116yes—
592C2×D4C22×D4116yes—
593C2×D4C22×D4132yes—
594C2×D4C22×D418yes—
595C2×D4H(5,𝔽2)14yes—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—232no—
601C22×C4—232no—
602C22×C4—24no—
603C22×C4—216no—
604C22×C4—216no—
605C22×C4—28no—
606C22×C4—232no—
607C22×C4—216no—
608C22×C4—216no—
609C22×C4—24no—
610C22×C4—28no—
611C22×C4—216no—
612C22×C4—28no—
613C22×C4—216no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—216no—
617C22×C4—216no—
618C22×C4—42no—
619C22×C4—416no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—864no—
629C22×C4C22×D4116yes—
630C22×C4C22×D4116yes—
631C22×C4C2514yes—
632C22×C4C2514yes—
633C22×C4C2518yes—
634C22×C4C2511yescharacteristic
635C22×C4C2512yes—
636C22×C4C2514yes—
637C22×C4C2518yes—
638C22×C4C2512yes—
639C22×C4C2514yes—
640C22×C4C2514yes—
641C22×C4C2511yescharacteristic
642C22×C4C2511yescharacteristic
643C22×C4C2512yes—
644C4⋊C4—28no—
645C4⋊C4—216no—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—232no—
649C4⋊C4—232no—
650C4⋊C4—216no—
651C4⋊C4—216no—
652C4⋊C4—24no—
653C4⋊C4—28no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—42no—
657C4⋊C4—48no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4C22×D418yes—
663C4⋊C4C22×D418yes—
664C22⋊C4—232no—
665C22⋊C4—216no—
666C22⋊C4—216no—
667C22⋊C4—232no—
668C22⋊C4—232no—
669C22⋊C4—232no—
670C22⋊C4—24no—
671C22⋊C4—216no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—232no—
675C22⋊C4—216no—
676C22⋊C4—28no—
677C22⋊C4—216no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—44no—
682C22⋊C4—48no—
683C22⋊C4—44no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4C22×D4116yes—
688C22⋊C4C22×D4132yes—
689C22⋊C4C22×D4116yes—
690C42—28no—
691C42—28no—
692C42—28no—
693C42—24no—
694C42—28no—
695C42—22no—
696C42—24no—
697C42—41no—
698C42C22×D418yes—
699C42H(5,𝔽2)14yescomplemented
700C23—22no—
701C23—24no—
702C23—22no—
703C23—28no—
704C23—24no—
705C23—24no—
706C23—28no—
707C23—24no—
708C23—28no—
709C23—28no—
710C23—24no—
711C23—24no—
712C23—28no—
713C23—28no—
714C23—24no—
715C23—264no—
716C23—28no—
717C23—24no—
718C23—24no—
719C23—28no—
720C23—24no—
721C23—432no—
722C23—432no—
723C23—432no—
724C23—816no—
725C23—816no—
726C23—816no—
727C23—816no—
728C23—832no—
729C23—832no—
730C23—168no—
731C23—168no—
732C23C23×D4116yes—
733C23C23×D418yes—
734C23C23×D418yes—
735C23C2×H(5,𝔽2)14yes—
736C23C2611yescharacteristic
737Q8—416no—
738Q8—416no—
739D4—264no—
740D4—232no—
741D4—216no—
742D4—232no—
743D4—432no—
744D4—416no—
745D4—432no—
746D4—416no—
747D4—464no—
748D4—432no—
749D4—432no—
750D4—416no—
751D4—84no—
752D4—816no—
753D4—832no—
754D4D42116yescomplemented
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—21no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—232no—
764C2×C4—232no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—216no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—28no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—48no—
784C2×C4—464no—
785C2×C4—432no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—432no—
789C2×C4—88no—
790C2×C4—816no—
791C2×C4—816no—
792C2×C4—816no—
793C2×C4C23×D414yes—
794C2×C4C23×D418yes—
795C2×C4C23×D418yes—
796C2×C4C23×D414yes—
797C2×C4C23×D414yes—
798C2×C4C2×H(5,𝔽2)12yes—
799C2×C4C2×H(5,𝔽2)12yes—
800C2×C4C2×H(5,𝔽2)14yes—
801C2×C4#58514yes—
802C22—28no—
803C22—28no—
804C22—24no—
805C22—24no—
806C22—216no—
807C22—28no—
808C22—28no—
809C22—216no—
810C22—28no—
811C22—216no—
812C22—44no—
813C22—48no—
814C22—44no—
815C22—48no—
816C22—44no—
817C22—48no—
818C22—44no—
819C22—48no—
820C22—48no—
821C22—48no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—864no—
826C22—1632no—
827C22C2×D4218yes—
828C22C24×D412yes—
829C22C22×H(5,𝔽2)11yescharacteristic
830C22C22×H(5,𝔽2)11yescharacteristic
831C22C2×#58512yes—
832C222−1+611yescharacteristic
833C4—24no—
834C4—28no—
835C4—22no—
836C4—28no—
837C4—44no—
838C4—44no—
839C4—48no—
840C4—41no—
841C4—42no—
842C4—44no—
843C4—48no—
844C4C2×D4214yes—
845C4#349618yescomplemented
846C2—28no—
847C2—48no—
848C2—416no—
849C2—84no—
850C2C22×D4211yescharacteristic
851C2C2×#349612yes—
852C2#6291411yescharacteristic
853C2#6298812yes—
854C2#6302411yescharacteristic
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×#3496C2semidirect
2. #59816C2semidirect
3. #59313C2semidirect
4. #59035C2semidirect
5. #59015C2semidirect
6. #45103C2semidirect
7. #43017C2semidirect
8. #39340C2semidirect
9. #39338C2semidirect
10. #36179C2semidirect
11. #36153C2semidirect
12. #36127C2semidirect
13. D4×#121C2semidirect
14. #35750C2semidirect
15. #34925C2semidirect
16. C2×#2537C2semidirect
17. C4×D42C2semidirect
18. C22×H(5,𝔽2)C22semidirect
20. C2×#547C22semidirect
21. C2×#547C22semidirect
22. C2×#547C22semidirect
23. C2×#547C22semidirect
24. C2×#546C22semidirect
25. C2×#546C22semidirect
26. C2×#546C22semidirect
28. C2×D42C22semidirect
29. C2×D42C22semidirect
30. C2×D42C22semidirect
31. C2×#537C22semidirect
32. C2×#534C22semidirect
33. C2×#532C22semidirect
34. C2×#532C22semidirect
35. C22×#121C22semidirect
36. C22×#121C22semidirect
37. C22×C4×D4C22semidirect
38. C22×C4×D4C22semidirect
39. #2868C22semidirect
40. #2857C22semidirect
41. #2856C22semidirect
42. #2847C22semidirect
43. #2680C22semidirect
44. #2679C22semidirect
45. #2672C22semidirect
46. #2671C22semidirect
47. #2671C22semidirect
48. #2668C22semidirect
49. #2668C22semidirect
50. #2616C22semidirect
51. #2613C22semidirect
52. #2555C22semidirect
53. #2551C22semidirect
54. #2547C22semidirect
55. #2542C22semidirect
56. #2542C22semidirect
57. #2541C22semidirect
58. #2537C22semidirect
59. #2537C22semidirect
60. #2537C22semidirect
61. #2537C22semidirect
62. #2537C22semidirect
63. #2537C22semidirect
64. #2537C22semidirect
65. #2537C22semidirect
66. #2501C22semidirect
67. #2501C22semidirect
68. #2491C22semidirect
69. #2486C22semidirect
70. #2440C22semidirect
71. #2437C22semidirect
72. #2435C22semidirect
73. #2432C22semidirect
74. #2430C22semidirect
75. #2428C22semidirect
76. #2428C22semidirect
77. #2427C22semidirect
78. #2425C22semidirect
79. #2424C22semidirect
80. #2422C22semidirect
81. #2422C22semidirect
82. #2422C22semidirect
83. #2418C22semidirect
84. #2417C22semidirect
85. #2416C22semidirect
86. #2416C22semidirect
87. #2412C22semidirect
88. #2410C22semidirect
89. #2408C22semidirect
90. #2408C22semidirect
91. #2408C22semidirect
92. #2407C22semidirect
93. #2406C22semidirect
94. #2405C22semidirect
95. #2388C22semidirect
96. C2×#394C22semidirect
97. #2366C22semidirect
98. #2361C22semidirect
99. #2361C22semidirect
100. #2358C22semidirect
101. D4×C4⋊C4C22semidirect
102. D4×C4⋊C4C22semidirect
103. D4×C4⋊C4C22semidirect
104. D4×C4⋊C4C22semidirect
105. #2339C22semidirect
106. D4×C22⋊C4C22semidirect
107. D4×C22⋊C4C22semidirect
108. D4×C22⋊C4C22semidirect
109. C4×#127C22semidirect
110. C4×#127C22semidirect
111. C4×#121C22semidirect
112. C4×#121C22semidirect
113. C4×#121C22semidirect
114. C4×#120C22semidirect
115. C2×#384C22semidirect
116. C2×#380C22semidirect
117. C42×D4C22semidirect
118. C42×D4C22semidirect
142. D42D4semidirect
348. C22×D4C2×D4semidirect
349. C22×D4C2×D4semidirect
386. #127C2×D4semidirect
415. #121C2×D4semidirect
416. #121C2×D4semidirect
421. #120C2×D4semidirect
441. C4×D4C2×D4semidirect
442. C4×D4C2×D4semidirect
699. C42H(5,𝔽2)semidirect
754. D4D42semidirect
845. C4#3496semidirect

Maximal subgroups

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

subgroupindex
C2×#34962
#598162
#593132
#590352
#590152
#451032
#430172
#393402
#393382
#361792
#361532
#361272
D4×#1212
#357502
#349252
C2×#25372
C4×D422