Finite Group Databasebeta

← #7711352

Subgroups — #7711352

Order 512.

6894 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#59822C212yesmaximal, complemented
3#59816C211yesmaximal, characteristic, complemented
4#59303C212yesmaximal, complemented
5#59126C212yesmaximal, complemented
6#46338C214yesmaximal, complemented
7#46089C214yesmaximal, complemented
8#40164C218yesmaximal, complemented
9#39191C214yesmaximal, complemented
10#38953C214yesmaximal, complemented
11#38026C218yesmaximal, complemented
12#37626C212yesmaximal, complemented
13#37249C214yesmaximal, complemented
14#36631C212yesmaximal, complemented
15#36160C214yesmaximal, complemented
16D4×#121C214yesmaximal, complemented
17#35076C214yesmaximal, complemented
18#34493C212yesmaximal, complemented
19C2×C4×#127C211yesmaximal, characteristic, complemented
20C2×#555C2214yescomplemented
21C2×D42C2212yes—
22C2×D42C2214yescomplemented
23C2×D42C2218yescomplemented
24C22×#127C2211yescharacteristic
25C2×#529C2214yescomplemented
26C22×#121C2214yescomplemented
27C22×C4×D4C2212yescomplemented
28C22×C4×D4C2214yescomplemented
29#2861C2214yescomplemented
30#2860C2214yescomplemented
31#2860C2214yescomplemented
32#2859C2212yescomplemented
33#2858C2212yescomplemented
34#2857C2212yescomplemented
35#2856C2212yes—
36#2854C2214yescomplemented
37#2854C2214yescomplemented
38#2850C2214yescomplemented
39#2847C2218yescomplemented
40#2828C2218yescomplemented
41#2804C2214yescomplemented
42#2795C2218yescomplemented
43#2753C22116yescomplemented
44#2733C2218yescomplemented
45#2714C22116yescomplemented
46#2711C22116yescomplemented
47#2685C22116yescomplemented
48#2679C2214yescomplemented
49#2670C22116yescomplemented
50#2670C22116yescomplemented
51#2669C2218yescomplemented
52#2635C2218yescomplemented
53#2635C2218yescomplemented
54#2624C2218yescomplemented
55#2619C2218yescomplemented
56#2591C2218yescomplemented
57#2580C2218yescomplemented
58#2571C2212yescomplemented
59#2563C2214yescomplemented
60#2548C2218yescomplemented
61#2541C2214yescomplemented
62#2541C2214yescomplemented
63#2539C2218yescomplemented
64#2537C2214yescomplemented
65#2537C2214yescomplemented
66#2537C2212yescomplemented
67#2500C2218yescomplemented
68#2497C2218yescomplemented
69#2487C2214yescomplemented
70#2487C2214yescomplemented
71#2485C2218yescomplemented
72#2472C22116yescomplemented
73#2459C22116yescomplemented
74#2433C2218yescomplemented
75#2428C2218yescomplemented
76#2428C2218yescomplemented
77#2424C22116yescomplemented
78#2420C2218yescomplemented
79#2416C2218yescomplemented
80#2416C2218yescomplemented
81#2414C2218yescomplemented
82#2414C2218yescomplemented
83#2414C2218yescomplemented
84#2414C2218yescomplemented
85#2410C22116yescomplemented
86#2408C2214yescomplemented
87#2408C2218yescomplemented
88#2408C2214yescomplemented
89#2408C2218yescomplemented
90#2408C2218yescomplemented
91#2405C2218yescomplemented
92#2403C2218yescomplemented
93#2375C2218yescomplemented
94#2366C2212yes—
95#2363C2218yescomplemented
96#2354C2214yescomplemented
97#2354C2214yescomplemented
98#2352C2218yescomplemented
99D4×C4⋊C4C2214yescomplemented
100D4×C22⋊C4C2218yescomplemented
101#2324C2218yescomplemented
102#2321C2218yescomplemented
103#2321C2218yescomplemented
104#2309C2218yescomplemented
105C4×C4⋊Q8C2212yescomplemented
106C4×#127C2211yescharacteristic
107C4×#127C2211yescharacteristic
108C4×#127C2212yescomplemented
109C4×#127C2212yescomplemented
110C4×#127C2214yescomplemented
111C4×#127C2212yescomplemented
112C4×#127C2211yescharacteristic, complemented
113C4×#127C2214yescomplemented
114C4×#127C2211yescharacteristic, complemented
115C4×#124C2214yescomplemented
116C4×#121C2214yescomplemented
117C4×#121C2214yescomplemented
118#2293C2214yescomplemented
119#2293C2214yescomplemented
120C2×#390C2212yescomplemented
121C2×#390C2214yescomplemented
122C2×#384C2211yescharacteristic, complemented
123#2280C2214yescomplemented
124C2×C43C2211yescharacteristic, complemented
125C23×D4C2314yes—
126C23×D4C2318yes—
127C23×D4C2312yes—
128C23×D4C2318yes—
129C23×D4C2314yes—
130C24×C4C2314yes—
131#555—416no—
132D42—216no—
133D42—416no—
134D42—432no—
135C2×C4⋊Q8C2312yes—
136C2×#127—28no—
137C2×#127C2312yes—
138C2×#127C2314yes—
139C2×#127C2311yescharacteristic
140C2×#127C2312yes—
141C2×#127C2318yes—
142C2×#127C2311yescharacteristic
143#529—416no—
144C2×#126C2318yes—
145C2×#125C2314yes—
146C2×#124C2314yes—
147C2×#124C2314yes—
148C2×#124C23116yes—
149C2×#123C2318yes—
150C2×C22⋊Q8C2314yes—
151C2×#121—416no—
152C2×#121C2318yes—
153C2×#121C2314yes—
154C2×#121C2314yes—
155C2×#121C2318yes—
156C2×#121C2318yes—
157C2×#121C2318yes—
158C2×#121C2314yes—
159C2×#121C2318yes—
160C2×#121C2318yes—
161C2×#121C2318yes—
162C2×#121C2318yes—
163C2×#121C2318yes—
164C2×#121C23116yes—
165C2×#120C2318yes—
166C2×#120C2318yes—
167C2×#120C23116yes—
168C2×#120C23116yes—
169C2×#120C23116yes—
170C2×C4×Q8C2314yes—
171C2×C4×D4—416no—
172C2×C4×D4—48no—
173C2×C4×D4C2314yes—
174C2×C4×D4C2314yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2314yes—
177C2×C4×D4C2318yes—
178C2×C4×D4C2312yes—
179C2×C4×D4C2314yes—
180C2×C4×D4C2312yes—
181C2×C4×D4C2314yes—
182C2×C4×D4C2312yes—
183C2×C4×D4C2314yes—
184C2×C4×D4C2318yes—
185C2×C4×D4C2312yes—
186C2×C4×D4C2314yes—
187C2×C4×D4C2318yes—
188C2×C4×D4C2314yes—
189C2×C4×D4C2318yes—
190C2×#117C2318yes—
191C2×#117C2318yes—
192C2×#117C2318yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2314yes—
195C22×C4⋊C4C2314yes—
196C22×C22⋊C4C2318yes—
197C22×C22⋊C4C2314yes—
198C22×C22⋊C4C2318yes—
199C22×C42C2311yescharacteristic
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204#400C2318yes—
205#400C2318yes—
206#399C2318yes—
207#399C2318yes—
208#397C23116yes—
209#396C23116yes—
210#394C2318yes—
211#394C23116yes—
212#394C23116yes—
213#394C2318yes—
214#394C23116yes—
215#394C23116yes—
216#394C23116yes—
217#394C23116yes—
218#394C23116yes—
219#394C23116yes—
220#393C23116yes—
221#392C23116yes—
222#392C23116yes—
223#392C2318yes—
224#392C23116yes—
225#392C2318yes—
226#392C23116yes—
227#392C23116yes—
228#391C2314yes—
229#391C2314yes—
230#390C2314yes—
231#390C2314yes—
232#390C2312yes—
233#390C2312yes—
234#390C2312yes—
235#390C2314yes—
236#390C2314yes—
237#390C2318yes—
238#390C2318yes—
239#390C2318yes—
240#390C2312yes—
241#390C2314yes—
242#390C2314yes—
243#390C2314yes—
244#390C2318yes—
245#390C2314yes—
246#390C23116yes—
247#390C2318yes—
248#390C23116yes—
249#390C23116yes—
250#390C2314yes—
251#390C2314yes—
252#390C2314yes—
253#390C2314yes—
254#390C2314yes—
255#390C2314yes—
256#390C2318yes—
257#389C2314yes—
258#389C2314yes—
259#389C2318yes—
260#389C2314yes—
261#389C2314yes—
262#389C2314yes—
263#389C2314yes—
264#389C2314yes—
265#389C2314yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C23116yes—
270#388C23116yes—
271#388C23116yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C23116yes—
278#388C23116yes—
279#387C23116yes—
280#386C23116yes—
281#386C23116yes—
282#386C2318yes—
283#386C2318yes—
284#386C23116yes—
285#386C2318yes—
286#386C23116yes—
287#386C2318yes—
288#385C2318yes—
289#385C2318yes—
290#385C23116yes—
291#384C2311yescharacteristic
292#384C2311yescharacteristic
293#384C2314yes—
294#384C2312yes—
295#384C2312yes—
296#384C2312yes—
297#382C2318yes—
298#382C2314yes—
299#381C2318yes—
300#380C2314yes—
301#380C2318yes—
302#380C2318yes—
303#380C2314yes—
304#380C2318yes—
305#380C2314yes—
306#380C2318yes—
307#380C2314yes—
308#379C2318yes—
309#379C23116yes—
310#379C2318yes—
311#379C2318yes—
312C4×C4⋊C4C2314yes—
313C4×C4⋊C4C2314yes—
314C4×C4⋊C4C2318yes—
315C4×C22⋊C4C2318yes—
316C4×C22⋊C4C2318yes—
317C4×C22⋊C4C2318yes—
318C4×C22⋊C4C2318yes—
319C43C2311yescharacteristic
320C43C2311yescharacteristic
321C43C2312yes—
322C43C2311yescharacteristic
323C43C2312yes—
324C43C2311yescharacteristic
325C25C2414yes—
326C25C2418yes—
327C22×Q8C2414yes—
328C22×D4—216no—
329C22×D4—28no—
330C22×D4—232no—
331C22×D4—216no—
332C22×D4—48no—
333C22×D4—44no—
334C22×D4—48no—
335C22×D4—416no—
336C22×D4—416no—
337C22×D4—416no—
338C22×D4—44no—
339C22×D4—416no—
340C22×D4—432no—
341C22×D4C2414yes—
342C22×D4C2418yes—
343C22×D4C2414yes—
344C22×D4C2414yes—
345C22×D4C2418yes—
346C22×D4C2414yes—
347C22×D4C2414yes—
348C22×D4C2412yes—
349C22×D4C2414yes—
350C22×D4C24116yes—
351C22×D4C24116yes—
352C22×D4C2418yes—
353C22×D4C24116yes—
354C22×D4C2412yes—
355C23×C4—216no—
356C23×C4—416no—
357C23×C4C2411yescharacteristic
358C23×C4C2411yescharacteristic
359C23×C4C2414yes—
360C23×C4C2414yes—
361C23×C4C2418yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C23×C4C2414yes—
366C23×C4C2414yes—
367C23×C4C2414yes—
368C23×C4C2418yes—
369C4⋊Q8—28no—
370#127—216no—
371#127—28no—
372#127—24no—
373#127—28no—
374#127—416no—
375#127#4118yes—
376#126—416no—
377#125—48no—
378#124—48no—
379#124—48no—
380#124—432no—
381#123—416no—
382C22⋊Q8—48no—
383#121—232no—
384#121—216no—
385#121—216no—
386#121—416no—
387#121—432no—
388#121—416no—
389#121—416no—
390#121—416no—
391#121—416no—
392#121—416no—
393#121—416no—
394#121—416no—
395#121—48no—
396#120—232no—
397#120—416no—
398#120—432no—
399#120—432no—
400#120—432no—
401C4×Q8—48no—
402C4×D4—232no—
403C4×D4—216no—
404C4×D4—216no—
405C4×D4—216no—
406C4×D4—216no—
407C4×D4—416no—
408C4×D4—48no—
409C4×D4—48no—
410C4×D4—416no—
411C4×D4—44no—
412C4×D4—48no—
413C4×D4—416no—
414C4×D4—44no—
415C4×D4—44no—
416C4×D4—48no—
417C4×D4—44no—
418C4×D4—48no—
419#117—416no—
420#117—416no—
421#117—416no—
422C2×C4⋊C4—48no—
423C2×C4⋊C4—48no—
424C2×C4⋊C4—44no—
425C2×C4⋊C4C2414yes—
426C2×C4⋊C4C2414yes—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2414yes—
429C2×C4⋊C4C2414yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2418yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2418yes—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4—48no—
447C2×C22⋊C4C2418yes—
448C2×C22⋊C4C2418yes—
449C2×C22⋊C4C2418yes—
450C2×C22⋊C4C2418yes—
451C2×C22⋊C4C2418yes—
452C2×C22⋊C4C2418yes—
453C2×C22⋊C4C2418yes—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2418yes—
456C2×C22⋊C4C2418yes—
457C2×C22⋊C4C2414yes—
458C2×C22⋊C4C2414yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2414yes—
461C2×C22⋊C4C2418yes—
462C2×C22⋊C4C2414yes—
463C2×C22⋊C4C24116yes—
464C2×C22⋊C4C24116yes—
465C2×C22⋊C4C24116yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C2418yes—
468C2×C22⋊C4C24116yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C24116yes—
471C2×C22⋊C4C24116yes—
472C2×C22⋊C4C2418yes—
473C2×C22⋊C4C2418yes—
474C2×C42—24no—
475C2×C42—28no—
476C2×C42—24no—
477C2×C42—28no—
478C2×C42—42no—
479C2×C42C2412yes—
480C2×C42C2418yes—
481C2×C42C2412yes—
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2412yes—
485C2×C42C2412yes—
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2412yes—
489C2×C42C2412yes—
490C2×C42C2412yes—
491C2×C42C2412yes—
492C2×C42C2412yes—
493C2×C42C2411yescharacteristic
494C2×C42C24116yes—
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2412yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504#95C2418yes—
505#95C24116yes—
506#95C2418yes—
507#95C2418yes—
508#95C24116yes—
509C24—28no—
510C24—28no—
511C24—216no—
512C24—216no—
513C24—48no—
514C24—44no—
515C24—48no—
516C24—416no—
517C24—416no—
518C24—48no—
519C24C2518yes—
520C24C2514yes—
521C24C2514yes—
522C24C2511yescharacteristic
523C2×Q8—28no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×D4—216no—
527C2×D4—28no—
528C2×D4—216no—
529C2×D4—216no—
530C2×D4—216no—
531C2×D4—232no—
532C2×D4—28no—
533C2×D4—24no—
534C2×D4—28no—
535C2×D4—28no—
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—216no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—464no—
548C2×D4—42no—
549C2×D4—48no—
550C2×D4—44no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—432no—
555C2×D4—44no—
556C2×D4—416no—
557C2×D4—416no—
558C2×D4—416no—
559C2×D4—416no—
560C2×D4—416no—
561C2×D4—48no—
562C2×D4—416no—
563C2×D4—44no—
564C2×D4—416no—
565C2×D4—416no—
566C2×D4—416no—
567C2×D4—864no—
568C2×D4—832no—
569C2×D4—864no—
570C2×D4C2×#41116yes—
571C2×D4C2×#4118yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—28no—
582C22×C4—216no—
583C22×C4—24no—
584C22×C4—28no—
585C22×C4—216no—
586C22×C4—216no—
587C22×C4—216no—
588C22×C4—216no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—42no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—416no—
598C22×C4—832no—
599C22×C4H(5,𝔽2)18yes—
600C22×C4H(5,𝔽2)14yes—
601C22×C4C2518yes—
602C22×C4C2518yes—
603C22×C4C2518yes—
604C22×C4C2514yes—
605C22×C4C2512yes—
606C22×C4C2514yes—
607C22×C4C2511yescharacteristic
608C22×C4C2511yescharacteristic
609C22×C4C2511yescharacteristic
610C22×C4C2511yescharacteristic
611C22×C4C2512yes—
612C22×C4C2512yes—
613C22×C4C2511yescharacteristic
614C22×C4C2512yes—
615C22×C4C2511yescharacteristic
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—216no—
624C4⋊C4—28no—
625C4⋊C4—48no—
626C4⋊C4—42no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—48no—
635C22⋊C4—216no—
636C22⋊C4—216no—
637C22⋊C4—216no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—216no—
642C22⋊C4—216no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—416no—
652C22⋊C4—416no—
653C22⋊C4—416no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—416no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—416no—
660C22⋊C4—416no—
661C22⋊C4—48no—
662C42—22no—
663C42—24no—
664C42—24no—
665C42—24no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—24no—
671C42—24no—
672C42—24no—
673C42—24no—
674C42—24no—
675C42—216no—
676C42—24no—
677C42—41no—
678C42—41no—
679C42—416no—
680C42C2×#4114yes—
681C42H(5,𝔽2)18yes—
682C23—21no—
683C23—22no—
684C23—21no—
685C23—28no—
686C23—24no—
687C23—28no—
688C23—24no—
689C23—28no—
690C23—24no—
691C23—28no—
692C23—28no—
693C23—28no—
694C23—28no—
695C23—28no—
696C23—24no—
697C23—28no—
698C23—28no—
699C23—28no—
700C23—24no—
701C23—432no—
702C23—416no—
703C23—416no—
704C23—88no—
705C23—816no—
706C23—832no—
707C23—816no—
708C23—816no—
709C23—816no—
710C23—1616no—
711C23C22×#4118yes—
712C23C2×H(5,𝔽2)14yes—
713C23C2×H(5,𝔽2)12yes—
714C23C2611yescharacteristic
715Q8—88no—
716D4—232no—
717D4—48no—
718D4—432no—
719D4—416no—
720D4—48no—
721D4—432no—
722D4—416no—
723D4—416no—
724D4—416no—
725D4—88no—
726D4—832no—
727D4—816no—
728D4—832no—
729D4—1616no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—216no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—48no—
763C2×C4—44no—
764C2×C4—432no—
765C2×C4—416no—
766C2×C4—416no—
767C2×C4—88no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4—816no—
771C2×C4C22×#4112yes—
772C2×C4C22×#4114yes—
773C2×C4C2×H(5,𝔽2)14yes—
774C2×C4C2×H(5,𝔽2)12yes—
775C2×C4C2×H(5,𝔽2)14yes—
776C2×C4C2×H(5,𝔽2)14yes—
777C2×C4C2×H(5,𝔽2)14yes—
778C2×C4C2×H(5,𝔽2)12yes—
779C2×C4C2×H(5,𝔽2)14yes—
780C2×C4#58512yes—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—24no—
785C22—216no—
786C22—28no—
787C22—44no—
788C22—44no—
789C22—48no—
790C22—44no—
791C22—48no—
792C22—48no—
793C22—44no—
794C22—48no—
795C22—48no—
796C22—48no—
797C22—44no—
798C22—48no—
799C22—48no—
800C22—48no—
801C22—48no—
802C22—832no—
803C22—1632no—
804C22#354914yes—
805C22C23×#4111yescharacteristic
806C22C22×H(5,𝔽2)11yescharacteristic
807C22C22×H(5,𝔽2)12yes—
808C22C22×H(5,𝔽2)12yes—
809C22C2×#58511yescharacteristic
810C4—22no—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—24no—
815C4—44no—
816C4—44no—
817C4—41no—
818C4—41no—
819C4—48no—
820C4—48no—
821C4—42no—
822C4—48no—
823C4#351918yes—
824C4#354314yes—
825C2—24no—
826C2—48no—
827C2—84no—
828C2—88no—
829C2C2×#354311yescharacteristic
830C2C2×#354911yescharacteristic
831C2C2×#351912yes—
832C2#6277311yescharacteristic
833C2#6283412yes—
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. #59864C2semidirect
2. #59822C2semidirect
3. #59816C2semidirect
4. #59303C2semidirect
5. #59126C2semidirect
6. #46338C2semidirect
7. #46089C2semidirect
8. #40164C2semidirect
9. #39191C2semidirect
10. #38953C2semidirect
11. #38026C2semidirect
12. #37626C2semidirect
13. #37249C2semidirect
14. #36631C2semidirect
15. #36160C2semidirect
16. D4×#121C2semidirect
17. #35076C2semidirect
18. #34493C2semidirect
19. C2×C4×#127C2semidirect
20. C2×#555C22semidirect
22. C2×D42C22semidirect
23. C2×D42C22semidirect
25. C2×#529C22semidirect
26. C22×#121C22semidirect
27. C22×C4×D4C22semidirect
28. C22×C4×D4C22semidirect
29. #2861C22semidirect
30. #2860C22semidirect
31. #2860C22semidirect
32. #2859C22semidirect
33. #2858C22semidirect
34. #2857C22semidirect
36. #2854C22semidirect
37. #2854C22semidirect
38. #2850C22semidirect
39. #2847C22semidirect
40. #2828C22semidirect
41. #2804C22semidirect
42. #2795C22semidirect
43. #2753C22semidirect
44. #2733C22semidirect
45. #2714C22semidirect
46. #2711C22semidirect
47. #2685C22semidirect
48. #2679C22semidirect
49. #2670C22semidirect
50. #2670C22semidirect
51. #2669C22semidirect
52. #2635C22semidirect
53. #2635C22semidirect
54. #2624C22semidirect
55. #2619C22semidirect
56. #2591C22semidirect
57. #2580C22semidirect
58. #2571C22semidirect
59. #2563C22semidirect
60. #2548C22semidirect
61. #2541C22semidirect
62. #2541C22semidirect
63. #2539C22semidirect
64. #2537C22semidirect
65. #2537C22semidirect
66. #2537C22semidirect
67. #2500C22semidirect
68. #2497C22semidirect
69. #2487C22semidirect
70. #2487C22semidirect
71. #2485C22semidirect
72. #2472C22semidirect
73. #2459C22semidirect
74. #2433C22semidirect
75. #2428C22semidirect
76. #2428C22semidirect
77. #2424C22semidirect
78. #2420C22semidirect
79. #2416C22semidirect
80. #2416C22semidirect
81. #2414C22semidirect
82. #2414C22semidirect
83. #2414C22semidirect
84. #2414C22semidirect
85. #2410C22semidirect
86. #2408C22semidirect
87. #2408C22semidirect
88. #2408C22semidirect
89. #2408C22semidirect
90. #2408C22semidirect
91. #2405C22semidirect
92. #2403C22semidirect
93. #2375C22semidirect
95. #2363C22semidirect
96. #2354C22semidirect
97. #2354C22semidirect
98. #2352C22semidirect
99. D4×C4⋊C4C22semidirect
100. D4×C22⋊C4C22semidirect
101. #2324C22semidirect
102. #2321C22semidirect
103. #2321C22semidirect
104. #2309C22semidirect
105. C4×C4⋊Q8C22semidirect
108. C4×#127C22semidirect
109. C4×#127C22semidirect
110. C4×#127C22semidirect
111. C4×#127C22semidirect
112. C4×#127C22semidirect
113. C4×#127C22semidirect
114. C4×#127C22semidirect
115. C4×#124C22semidirect
116. C4×#121C22semidirect
117. C4×#121C22semidirect
118. #2293C22semidirect
119. #2293C22semidirect
120. C2×#390C22semidirect
121. C2×#390C22semidirect
122. C2×#384C22semidirect
123. #2280C22semidirect
124. C2×C43C22semidirect

Maximal subgroups

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

subgroupindex
#598642
#598222
#598162
#593032
#591262
#463382
#460892
#401642
#391912
#389532
#380262
#376262
#372492
#366312
#361602
D4×#1212
#350762
#344932
C2×C4×#1272