Finite Group Databasebeta

← #7632734

Subgroups — #7632734

Order 512.

10876 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3500C211yesmaximal, characteristic, complemented
3C2×#3499C211yesmaximal, characteristic, complemented
4C2×C4×2−1+4C211yesmaximal, characteristic, complemented
5#36434C214yesmaximal, complemented
6#36218C2112yesmaximal, complemented
7#35821C2112yesmaximal, complemented
8#35771C214yesmaximal, complemented
9#35677C213yesmaximal, complemented
10#35667C213yesmaximal, complemented
11#35621C213yesmaximal, complemented
12#35533C213yesmaximal, complemented
13#35327C213yesmaximal, complemented
14#35178C213yesmaximal, complemented
15#34937C213yesmaximal, complemented
16C2×#2545C213yesmaximal, complemented
17#34259C211yesmaximal, characteristic, complemented
18#34258C211yesmaximal, characteristic, complemented
19C4⋊C4×#41C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C22×2−1+4C2211yescharacteristic
22C22×H(5,𝔽2)C2211yescharacteristic
23#3500—216no—
24#3500—216no—
25#3499—216no—
26C2×D4×Q8C2214yescomplemented
27C2×#548C2212yes—
28C2×#548C2214yes—
29C2×#548C2212yes—
30C2×#547C22112yescomplemented
31C2×#546C2216yes—
32C2×#546C22112yes—
33C2×#546C2216yes—
34C2×#536C2213yes—
35C2×#536C2213yes—
36C2×#536C2213yescomplemented
37C2×#536C2213yescomplemented
38C2×#535C2213yes—
39C2×#535C2213yes—
40C2×#532C2213yes—
41C2×#532C2213yes—
42C2×#532C2213yescomplemented
43C22×C4⋊Q8C2213yescomplemented
44C22×#124C2213yes—
45C22×#124C2213yes—
46C4×2−1+4—216no—
47C2×#520C2211yescharacteristic
48C2×#520C2213yescomplemented
49C2×#520C2216yescomplemented
50C2×#519C2213yescomplemented
51C2×#519C2212yescomplemented
52C2×C4×#41C2211yescharacteristic
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2213yescomplemented
56C2×C4×#41C2216yescomplemented
57C22×C4×Q8C2212yescomplemented
58C22×C4×Q8C2213yescomplemented
59#2854C22112yescomplemented
60#2850C22112yescomplemented
61#2620C22112yescomplemented
62#2618C22112yescomplemented
63#2548C2213yescomplemented
64#2548C2216yescomplemented
65#2547C2213yescomplemented
66#2546C2216yescomplemented
67#2546C2213yescomplemented
68#2545C2216yescomplemented
69#2545C22112yescomplemented
70#2545C2216yescomplemented
71#2545C2216yescomplemented
72#2545C2213yescomplemented
73#2545C2216yescomplemented
74#2545C22112yescomplemented
75#2545C2213yescomplemented
76#2544C2216yescomplemented
77#2544C2211yescharacteristic, complemented
78#2544C2213yescomplemented
79#2543C22112yescomplemented
80#2541C2213yescomplemented
81#2538C22112yescomplemented
82#2536C22112yescomplemented
83#2534C22112yescomplemented
84#2534C22112yescomplemented
85#2429C22112yescomplemented
86#2429C22112yescomplemented
87#2426C22112yescomplemented
88#2426C22112yescomplemented
89#2425C22124yescomplemented
90#2424C22124yescomplemented
91#2417C22112yescomplemented
92#2416C22112yescomplemented
93#2416C22112yescomplemented
94#2415C22112yescomplemented
95#2414C22112yescomplemented
96#2413C22124yescomplemented
97#2411C22124yescomplemented
98#2392C22112yescomplemented
99C2×#396C22112yescomplemented
100#2351C2212yescomplemented
101Q8×C4⋊C4C2212yescomplemented
102#2349C2216yescomplemented
103D4×C4⋊C4C2216yescomplemented
104#2341C2214yes—
105Q8×C22⋊C4C2214yescomplemented
106#2339C22112yescomplemented
107D4×C22⋊C4C22112yes—
108#2311C2213yes—
109#2311C2213yescomplemented
110#2310C2213yescomplemented
111#2309C2213yes—
112C4×#121C22112yescomplemented
113#2297C2213yes—
114#2297C2213yescomplemented
115#2296C2213yescomplemented
116#2296C2213yescomplemented
117C2×#391C2213yescomplemented
118C2×#390C2213yes—
119C2×#388C22112yescomplemented
120#2285C2213yescomplemented
121C2×C4×C4⋊C4C2213yescomplemented
122C2×2−1+4—28no—
123C2×2−1+4—28no—
124C2×2−1+4—28no—
125C2×2−1+4—28no—
126C2×2−1+4—28no—
127C2×2−1+4D4116yescomplemented
128C2×H(5,𝔽2)—28no—
129C2×H(5,𝔽2)—28no—
130C2×H(5,𝔽2)—28no—
131C22×#41C2313yes—
132C22×#41C2313yes—
133C22×#41C2312yes—
134C22×#41C2316yes—
135C22×#41C2313yes—
136C22×#41C2316yes—
137C22×#41C2311yescharacteristic
138C23×Q8C2313yes—
139C23×Q8C2312yes—
140C23×Q8C2313yes—
141C23×Q8C2312yes—
142C23×D4C2313yes—
143C23×D4C2316yes—
144D4×Q8—232no—
145#548—232no—
146#548—216no—
147#548—216no—
148#547—296no—
149#546—296no—
150#546—248no—
151#546—248no—
152#536—224no—
153#536—224no—
154#536—224no—
155#536—224no—
156#535—224no—
157#535—224no—
158#532—224no—
159#532—224no—
160#532—224no—
161C2×C4⋊Q8—224no—
162C2×C4⋊Q8C2313yes—
163C2×C4⋊Q8C2316yes—
164C2×C4⋊Q8C23112yes—
165C2×C4⋊Q8C2313yes—
166C2×C4⋊Q8C2313yes—
167C2×#127C2313yes—
168C2×#127C2313yes—
169C2×#127C2311yescharacteristic
170C2×#124—224no—
171C2×#124—224no—
172C2×#124C2316yes—
173C2×#124C2316yes—
174C2×#124C2313yes—
175C2×#124C2313yes—
176C2×#124C2316yes—
177C2×#124C2316yes—
178C2×#124C23112yes—
179C2×#124C2311yescharacteristic
180C2×#124C2311yescharacteristic
181C2×#124C2313yes—
182C2×#124C2313yes—
183C2×#123C23112yes—
184C2×#123C23112yes—
185C2×#123C23112yes—
186C2×#123C23112yes—
187C2×C22⋊Q8C23112yes—
188C2×C22⋊Q8C2316yes—
189C2×C22⋊Q8C2316yes—
190C2×C22⋊Q8C23112yes—
191C2×C22⋊Q8C23112yes—
192C2×#121C23112yes—
193C2×#121C2316yes—
194C2×#121C2316yes—
195C2×#121C2316yes—
196C2×#121C2316yes—
197C2×#121C23112yes—
198C2×#121C23112yes—
199C2×#121C23112yes—
200C2×#120C23112yes—
201C2×#120C23112yes—
202#520—28no—
203#520—248no—
204#520—224no—
205#519—216no—
206#519—224no—
207C4×#41—28no—
208C4×#41—28no—
209C4×#41—248no—
210C4×#41—224no—
211C4×#41D4116yescomplemented
212C2×C4×Q8—216no—
213C2×C4×Q8—224no—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2316yes—
218C2×C4×Q8C2313yes—
219C2×C4×Q8C2316yes—
220C2×C4×Q8C2316yes—
221C2×C4×Q8C2316yes—
222C2×C4×Q8C2316yes—
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2316yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C2316yes—
229C2×C4×D4C2316yes—
230C2×C4×D4C23112yes—
231C2×C4×D4C23112yes—
232C2×C4×D4C2316yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2316yes—
235C2×C4×D4C23112yes—
236C2×C4×D4C2313yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2313yes—
239C2×C4×D4C2313yes—
240C2×#117C2313yes—
241C2×#117C2313yes—
242C2×#117C2313yes—
243C2×#117C2316yes—
244C2×#117C23112yes—
245C2×#117C2316yes—
246C2×#117C2313yes—
247C22×C4⋊C4C2313yes—
248C22×C4⋊C4C2316yes—
249C22×C4⋊C4C23112yes—
250C22×C4⋊C4C2316yes—
251C22×C4⋊C4C2316yes—
252C22×C22⋊C4C2316yes—
253C22×C22⋊C4C23112yes—
254C22×C22⋊C4C2316yes—
255C22×C22⋊C4C23112yes—
256C22×C42C2316yes—
257C22×C42C2316yes—
258C22×C42C2313yes—
259C22×C42C2313yes—
260C22×C42C2313yes—
261#398C23124yes—
262#398C23112yes—
263#397C23112yes—
264#396C23112yes—
265#396C23124yes—
266#396C23124yes—
267#396C23112yes—
268#396C23124yes—
269#396C23124yes—
270#394C23124yes—
271#394C23112yes—
272#394C23124yes—
273#394C2314yes—
274#394C23112yes—
275#392C23112yes—
276#391C2313yes—
277#391C2316yes—
278#391C23112yes—
279#391C2313yes—
280#391C23112yes—
281#391C2311yescharacteristic
282#391C2313yes—
283#390C2313yes—
284#390C2316yes—
285#390C23112yes—
286#390C2313yes—
287#390C23112yes—
288#390C23124yes—
289#390C23112yes—
290#390C2313yes—
291#390C2311yescharacteristic
292#389C23124yes—
293#389C2316yes—
294#389C2316yes—
295#389C2316yes—
296#389C2316yes—
297#389C23112yes—
298#388C23124yes—
299#388C23124yes—
300#388C23112yes—
301#388C23124yes—
302#388C23124yes—
303#388C23112yes—
304#386C23112yes—
305#386C23112yes—
306#386C23112yes—
307#386C23112yes—
308#386C23124yes—
309#386C23112yes—
310#386C2314yes—
311#385C23112yes—
312#385C23112yes—
313#384C2316yes—
314#382C2316yes—
315#381C23112yes—
316#380C23112yes—
317#380C23112yes—
318#380C2316yes—
319#380C2316yes—
320#380C23112yes—
321#379C23112yes—
322C4×C4⋊C4C2316yes—
323C4×C4⋊C4C2316yes—
324C4×C4⋊C4C2311yescharacteristic
325C4×C4⋊C4C2313yes—
326C4×C4⋊C4C2313yes—
327C4×C4⋊C4C2313yes—
328C4×C4⋊C4C2316yes—
329C4×C22⋊C4C23112yes—
330C4×C22⋊C4C23112yes—
331C2×#95C23112yes—
332C2×#95C2316yes—
333C25C2416yes—
3342−1+4—2128no—
3352−1+4—464no—
336H(5,𝔽2)—464no—
337C2×#41—28no—
338C2×#41—28no—
339C2×#41—28no—
340C2×#41—224no—
341C2×#41—224no—
342C2×#41—224no—
343C2×#41—224no—
344C2×#41—224no—
345C2×#41—212no—
346C2×#41—212no—
347C2×#41—212no—
348C2×#41—212no—
349C2×#41—212no—
350C2×#41—212no—
351C2×#41—212no—
352C2×#41—212no—
353C2×#41C2×D4124yes—
354C2×#41C2×D4148yes—
355C2×#41C2×D418yes—
356C2×#41C2×D418yes—
357C2×#41#4118yes—
358C22×Q8—28no—
359C22×Q8—28no—
360C22×Q8—28no—
361C22×Q8—28no—
362C22×Q8—28no—
363C22×Q8—212no—
364C22×Q8—212no—
365C22×Q8—212no—
366C22×Q8—212no—
367C22×Q8—212no—
368C22×Q8C2×D4124yes—
369C22×Q8C2×D4116yes—
370C22×Q8C2416yes—
371C22×Q8C2413yes—
372C22×Q8C2411yescharacteristic
373C22×Q8C2416yes—
374C22×Q8C2413yes—
375C22×Q8C2411yescharacteristic
376C22×D4—224no—
377C22×D4—224no—
378C22×D4—224no—
379C22×D4—212no—
380C22×D4—212no—
381C22×D4—212no—
382C22×D4C2416yes—
383C22×D4C2416yes—
384C22×D4C2416yes—
385C22×D4C2413yes—
386C22×D4C2411yescharacteristic
387C22×D4C2414yes—
388C22×D4C2416yes—
389C22×D4C2411yescharacteristic
390C22×D4C2416yes—
391C22×D4C24112yes—
392C22×D4C2416yes—
393C22×D4C2413yes—
394C23×C4C2416yes—
395C23×C4C2416yes—
396C23×C4C2416yes—
397C23×C4C2416yes—
398C23×C4C2416yes—
399C23×C4C2416yes—
400C23×C4C2416yes—
401C23×C4C2416yes—
402C23×C4C2416yes—
403C23×C4C2412yes—
404C23×C4C2413yes—
405C23×C4C2413yes—
406C23×C4C2413yes—
407C4⋊Q8—212no—
408C4⋊Q8—224no—
409C4⋊Q8—248no—
410C4⋊Q8—212no—
411C4⋊Q8—212no—
412#127—24no—
413#127—212no—
414#127—212no—
415#124—212no—
416#124—224no—
417#124—248no—
418#124—212no—
419#124—24no—
420#124—212no—
421#124—212no—
422#124—224no—
423#124—224no—
424#124—224no—
425#124—24no—
426#123—248no—
427#123—248no—
428#123—248no—
429#123—248no—
430C22⋊Q8—248no—
431C22⋊Q8—248no—
432C22⋊Q8—248no—
433C22⋊Q8—224no—
434C22⋊Q8—224no—
435#121—248no—
436#121—248no—
437#121—224no—
438#121—224no—
439#121—248no—
440#121—224no—
441#121—224no—
442#121—424no—
443#120—248no—
444#120—248no—
445C4×Q8—28no—
446C4×Q8—28no—
447C4×Q8—28no—
448C4×Q8—224no—
449C4×Q8—224no—
450C4×Q8—224no—
451C4×Q8—212no—
452C4×Q8—224no—
453C4×Q8—224no—
454C4×Q8—212no—
455C4×Q8C2×D418yes—
456C4×Q8C2×D418yes—
457C4×D4—224no—
458C4×D4—224no—
459C4×D4—224no—
460C4×D4—224no—
461C4×D4—224no—
462C4×D4—248no—
463C4×D4—248no—
464C4×D4—248no—
465C4×D4—24no—
466C4×D4—212no—
467C4×D4—224no—
468C4×D4—224no—
469C4×D4C2×D4124yes—
470C4×D4C2×D4124yes—
471#117—212no—
472#117—212no—
473#117—212no—
474#117—224no—
475#117—248no—
476#117—224no—
477#117C2×D4124yes—
478C2×C4⋊C4—224no—
479C2×C4⋊C4—212no—
480C2×C4⋊C4—248no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—412no—
483C2×C4⋊C4C2412yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C2413yes—
486C2×C4⋊C4C24112yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C24112yes—
489C2×C4⋊C4C2416yes—
490C2×C4⋊C4C24124yes—
491C2×C4⋊C4C2411yescharacteristic
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C24112yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C24112yes—
501C2×C4⋊C4C2413yes—
502C2×C4⋊C4C2413yes—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—248no—
506C2×C22⋊C4—424no—
507C2×C22⋊C4C2416yes—
508C2×C22⋊C4C24112yes—
509C2×C22⋊C4C2416yes—
510C2×C22⋊C4C24112yes—
511C2×C22⋊C4C24112yes—
512C2×C22⋊C4C24112yes—
513C2×C22⋊C4C24124yes—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C2412yes—
517C2×C22⋊C4C2416yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2412yes—
521C2×C22⋊C4C2412yes—
522C2×C22⋊C4C24112yes—
523C2×C22⋊C4C24112yes—
524C2×C22⋊C4C24124yes—
525C2×C22⋊C4C24112yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C24112yes—
528C2×C22⋊C4C2416yes—
529C2×C42—224no—
530C2×C42—212no—
531C2×C42—212no—
532C2×C42—224no—
533C2×C42C2×D4124yes—
534C2×C42C2416yes—
535C2×C42C2416yes—
536C2×C42C24112yes—
537C2×C42C2413yes—
538C2×C42C2413yes—
539C2×C42C2416yes—
540C2×C42C2416yes—
541C2×C42C2416yes—
542C2×C42C2411yescharacteristic
543C2×C42C2411yescharacteristic
544C2×C42C2413yes—
545C2×C42C2413yes—
546C2×C42C2413yes—
547C2×C42C2411yescharacteristic
548#95C2412yes—
549#95C24112yes—
550#95C2416yes—
551#95C2416yes—
552#95C2416yes—
553#95C24124yes—
554#95C2414yes—
555#95C24112yes—
556#95C24112yes—
557#95C24112yes—
558C24—212no—
559C24—212no—
560C24—212no—
561C24—412no—
562C24—412no—
563C24C2516yes—
564C24C2512yes—
565C24C2512yes—
566C24C2513yes—
567#41—2192no—
568#41—296no—
569#41—432no—
570#41—496no—
571#41—448no—
572#41—448no—
573#41#121164yescomplemented
574C2×Q8—264no—
575C2×Q8—296no—
576C2×Q8—212no—
577C2×Q8—26no—
578C2×Q8—212no—
579C2×Q8—212no—
580C2×Q8—26no—
581C2×Q8—26no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—212no—
585C2×Q8—26no—
586C2×Q8—212no—
587C2×Q8—26no—
588C2×Q8—22no—
589C2×Q8—432no—
590C2×Q8—448no—
591C2×Q8C22×D4124yes—
592C2×Q8C22×D4112yes—
593C2×Q8C22×D414yes—
594C2×Q8C22×D414yes—
595C2×Q8C2×#4114yes—
596C2×D4—212no—
597C2×D4—212no—
598C2×D4—28no—
599C2×D4—212no—
600C2×D4—212no—
601C2×D4—212no—
602C2×D4—212no—
603C2×D4—212no—
604C2×D4—212no—
605C2×D4—224no—
606C2×D4—22no—
607C2×D4—212no—
608C2×D4—212no—
609C2×D4—26no—
610C2×D4—26no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—212no—
614C2×D4—212no—
615C2×D4—22no—
616C2×D4—212no—
617C2×D4—26no—
618C2×D4—22no—
619C2×D4—28no—
620C2×D4—44no—
621C2×D4—412no—
622C2×D4—412no—
623C2×D4—412no—
624C2×D4—412no—
625C2×D4—496no—
626C2×D4—448no—
627C2×D4C22×D4124yes—
628C2×D4C22×D414yes—
629C2×D4C22×D4112yes—
630C2×D4C22×D4112yes—
631C2×D4C2×#41112yes—
632C22×C4—212no—
633C22×C4—212no—
634C22×C4—212no—
635C22×C4—212no—
636C22×C4—212no—
637C22×C4—212no—
638C22×C4—212no—
639C22×C4—212no—
640C22×C4—212no—
641C22×C4—212no—
642C22×C4—24no—
643C22×C4—212no—
644C22×C4—212no—
645C22×C4—212no—
646C22×C4—212no—
647C22×C4—212no—
648C22×C4—212no—
649C22×C4—212no—
650C22×C4—212no—
651C22×C4—46no—
652C22×C4—46no—
653C22×C4—44no—
654C22×C4—46no—
655C22×C4—412no—
656C22×C4—46no—
657C22×C4—412no—
658C22×C4—46no—
659C22×C4C22×D4124yes—
660C22×C4C22×D4124yes—
661C22×C4C22×D4112yes—
662C22×C4C22×D4112yes—
663C22×C4C22×D4112yes—
664C22×C4C22×D4112yes—
665C22×C4C2×#41112yes—
666C22×C4C2512yes—
667C22×C4C2516yes—
668C22×C4C2512yes—
669C22×C4C2516yes—
670C22×C4C2516yes—
671C22×C4C2512yes—
672C22×C4C2516yes—
673C22×C4C2511yescharacteristic
674C22×C4C2513yes—
675C22×C4C2513yes—
676C22×C4C2511yescharacteristic
677C22×C4C2516yes—
678C22×C4C2512yes—
679C22×C4C2511yescharacteristic
680C22×C4C2513yes—
681C4⋊C4—224no—
682C4⋊C4—212no—
683C4⋊C4—212no—
684C4⋊C4—26no—
685C4⋊C4—224no—
686C4⋊C4—248no—
687C4⋊C4—212no—
688C4⋊C4—22no—
689C4⋊C4—212no—
690C4⋊C4—212no—
691C4⋊C4—224no—
692C4⋊C4—212no—
693C4⋊C4—212no—
694C4⋊C4—24no—
695C4⋊C4—212no—
696C4⋊C4—46no—
697C4⋊C4—46no—
698C4⋊C4—412no—
699C4⋊C4C22×D4112yes—
700C4⋊C4C22×D4112yes—
701C22⋊C4—212no—
702C22⋊C4—212no—
703C22⋊C4—212no—
704C22⋊C4—28no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—212no—
708C22⋊C4—212no—
709C22⋊C4—248no—
710C22⋊C4—224no—
711C22⋊C4—224no—
712C22⋊C4—24no—
713C22⋊C4—212no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—424no—
719C22⋊C4—412no—
720C22⋊C4—44no—
721C22⋊C4—412no—
722C22⋊C4C22×D4124yes—
723C42—212no—
724C42—22no—
725C42—22no—
726C42—212no—
727C42—224no—
728C42—212no—
729C42—26no—
730C42—26no—
731C42—212no—
732C42—212no—
733C42C22×D4112yes—
734C42C22×D414yes—
735C42C22×D4112yes—
736C42C22×D4112yes—
737C23—26no—
738C23—26no—
739C23—22no—
740C23—22no—
741C23—24no—
742C23—24no—
743C23—22no—
744C23—26no—
745C23—26no—
746C23—22no—
747C23—22no—
748C23—26no—
749C23—212no—
750C23—24no—
751C23—24no—
752C23—212no—
753C23—424no—
754C23—824no—
755C23—824no—
756C23—812no—
757C23—812no—
758C23C23×D414yes—
759C23C23×D416yes—
760C23C23×D416yes—
761C23C22×#4116yes—
762C23C2611yescharacteristic
763Q8—248no—
764Q8—224no—
765Q8—424no—
766Q8—412no—
767Q8—44no—
768Q8C2×#121116yes—
769D4—248no—
770D4—28no—
771D4—416no—
772D4—424no—
773D4—424no—
774D4—424no—
775D4—412no—
776D4—44no—
777D4—812no—
778D4—812no—
779D4—824no—
780D4C2×#121148yes—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—26no—
786C2×C4—26no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—248no—
790C2×C4—248no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—26no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—26no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—26no—
800C2×C4—22no—
801C2×C4—26no—
802C2×C4—212no—
803C2×C4—26no—
804C2×C4—26no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—26no—
808C2×C4—22no—
809C2×C4—26no—
810C2×C4—412no—
811C2×C4—412no—
812C2×C4—424no—
813C2×C4—48no—
814C2×C4—424no—
815C2×C4—424no—
816C2×C4—424no—
817C2×C4—812no—
818C2×C4—812no—
819C2×C4—812no—
820C2×C4C2×#121148yes—
821C2×C4C23×D412yes—
822C2×C4C23×D416yes—
823C2×C4C23×D416yes—
824C2×C4C23×D412yes—
825C2×C4C23×D4112yes—
826C2×C4C23×D412yes—
827C2×C4C23×D416yes—
828C2×C4C23×D416yes—
829C2×C4C23×D412yes—
830C2×C4C22×#4116yes—
831C2×C4C22×#4112yes—
832C2×C4#58514yes—
833C22—212no—
834C22—212no—
835C22—26no—
836C22—26no—
837C22—28no—
838C22—24no—
839C22—44no—
840C22—42no—
841C22—42no—
842C22—44no—
843C22—412no—
844C22—44no—
845C22—412no—
846C22—42no—
847C22—46no—
848C22—42no—
849C22—46no—
850C22—42no—
851C22—46no—
852C22—1624no—
853C22C22×#121112yes—
854C22C24×D411yescharacteristic
855C22C24×D411yescharacteristic
856C22C23×#4111yescharacteristic
857C22C2×#58512yes—
858C222−1+612yes—
859C4—24no—
860C4—22no—
861C4—26no—
862C4—22no—
863C4—26no—
864C4—212no—
865C4—46no—
866C4—42no—
867C4—46no—
868C4—46no—
869C4—42no—
870C4—42no—
871C4—46no—
872C4C22×#121112yes—
873C4C22×#12114yes—
874C2—212no—
875C2—44no—
876C2—82no—
877C2—86no—
878C2C23×#12111yescharacteristic
879C2#6281211yescharacteristic
880C2#6285911yescharacteristic
881C2#6299512yes—
882C2#6300212yes—
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×#3500C2semidirect
2. C2×#3500C2semidirect
3. C2×#3499C2semidirect
4. C2×C4×2−1+4C2semidirect
5. #36434C2semidirect
6. #36218C2semidirect
7. #35821C2semidirect
8. #35771C2semidirect
9. #35677C2semidirect
10. #35667C2semidirect
11. #35621C2semidirect
12. #35533C2semidirect
13. #35327C2semidirect
14. #35178C2semidirect
15. #34937C2semidirect
16. C2×#2545C2semidirect
17. #34259C2semidirect
18. #34258C2semidirect
19. C4⋊C4×#41C2semidirect
26. C2×D4×Q8C22semidirect
30. C2×#547C22semidirect
36. C2×#536C22semidirect
37. C2×#536C22semidirect
42. C2×#532C22semidirect
43. C22×C4⋊Q8C22semidirect
48. C2×#520C22semidirect
49. C2×#520C22semidirect
50. C2×#519C22semidirect
51. C2×#519C22semidirect
55. C2×C4×#41C22semidirect
56. C2×C4×#41C22semidirect
57. C22×C4×Q8C22semidirect
58. C22×C4×Q8C22semidirect
59. #2854C22semidirect
60. #2850C22semidirect
61. #2620C22semidirect
62. #2618C22semidirect
63. #2548C22semidirect
64. #2548C22semidirect
65. #2547C22semidirect
66. #2546C22semidirect
67. #2546C22semidirect
68. #2545C22semidirect
69. #2545C22semidirect
70. #2545C22semidirect
71. #2545C22semidirect
72. #2545C22semidirect
73. #2545C22semidirect
74. #2545C22semidirect
75. #2545C22semidirect
76. #2544C22semidirect
77. #2544C22semidirect
78. #2544C22semidirect
79. #2543C22semidirect
80. #2541C22semidirect
81. #2538C22semidirect
82. #2536C22semidirect
83. #2534C22semidirect
84. #2534C22semidirect
85. #2429C22semidirect
86. #2429C22semidirect
87. #2426C22semidirect
88. #2426C22semidirect
89. #2425C22semidirect
90. #2424C22semidirect
91. #2417C22semidirect
92. #2416C22semidirect
93. #2416C22semidirect
94. #2415C22semidirect
95. #2414C22semidirect
96. #2413C22semidirect
97. #2411C22semidirect
98. #2392C22semidirect
99. C2×#396C22semidirect
100. #2351C22semidirect
101. Q8×C4⋊C4C22semidirect
102. #2349C22semidirect
103. D4×C4⋊C4C22semidirect
105. Q8×C22⋊C4C22semidirect
106. #2339C22semidirect
109. #2311C22semidirect
110. #2310C22semidirect
112. C4×#121C22semidirect
114. #2297C22semidirect
115. #2296C22semidirect
116. #2296C22semidirect
117. C2×#391C22semidirect
119. C2×#388C22semidirect
120. #2285C22semidirect
121. C2×C4×C4⋊C4C22semidirect
127. C2×2−1+4D4semidirect
211. C4×#41D4semidirect
573. #41#121semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34992
C2×C4×2−1+42
#364342
#362182
#358212
#357712
#356772
#356672
#356212
#355332
#353272
#351782
#349372
C2×#25452
#342592
#342582
C4⋊C4×#412