Finite Group Databasebeta

← #7630868

Subgroups — #7630868

Order 512.

8286 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C211yesmaximal, characteristic, complemented
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3#36091C211yesmaximal, characteristic, complemented
4#36087C213yesmaximal, complemented
5#36082C211yesmaximal, characteristic, complemented
6#36080C213yesmaximal, complemented
7#36005C211yesmaximal, characteristic, complemented
8#36004C213yesmaximal, complemented
9#35983C211yesmaximal, characteristic, complemented
10#35982C213yesmaximal, complemented
11#35831C212yesmaximal, complemented
12#35823C216yesmaximal, complemented
13#35816C212yesmaximal, complemented
14#35808C216yesmaximal, complemented
15#35236C213yesmaximal, complemented
16#35233C213yesmaximal, complemented
17#35226C216yesmaximal, complemented
18#35225C216yesmaximal, complemented
19#34636C213yesmaximal, complemented
20#34614C213yesmaximal, complemented
21#34295C212yesmaximal, complemented
22#34293C212yesmaximal, complemented
23#34193C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25#3524—216no—
26C2×#559C2213yescomplemented
27C2×#557C2211yescharacteristic, complemented
28C2×#555C2213yescomplemented
29C2×#553C2213yescomplemented
30C2×#552C2213yescomplemented
31C2×#550C2211yescharacteristic
32C2×#550C2212yes—
33C2×#548C2211yescharacteristic
34C2×#548C2212yes—
35C2×#548C2211yescharacteristic, complemented
36C2×#542C2213yescomplemented
37C2×#540C2213yescomplemented
38C2×#529C2213yescomplemented
39C2×#529C2213yescomplemented
40C4×H(5,𝔽2)—216no—
41C2×#520C2211yescharacteristic
42C2×#520C2212yes—
43C2×#520C2213yes—
44C2×#520C2211yescharacteristic, complemented
45C2×#519C2211yescharacteristic, complemented
46C2×#518C2213yes—
47C2×#518C2216yes—
48C2×C4×#41C2213yes—
49C2×C4×#41C2212yes—
50C2×C4×#41C2211yescharacteristic
51C22×C4×D4C2216yes—
52C22×C4×D4C2213yes—
53#2849C22112yescomplemented
54#2848C2216yescomplemented
55#2847C2216yescomplemented
56#2638C2216yescomplemented
57#2637C2213yescomplemented
58#2637C2211yescharacteristic, complemented
59#2636C2216yescomplemented
60#2636C2213yescomplemented
61#2636C2213yescomplemented
62#2635C2216yescomplemented
63#2634C2213yescomplemented
64#2633C2213yescomplemented
65#2632C2213yescomplemented
66#2631C2213yescomplemented
67#2630C22112yescomplemented
68#2630C2216yescomplemented
69#2630C2216yescomplemented
70#2629C2216yescomplemented
71#2625C2213yescomplemented
72#2624C2213yescomplemented
73#2620C2216yescomplemented
74#2616C2213yes—
75#2615C2213yes—
76#2598C2216yescomplemented
77#2598C2216yescomplemented
78#2566C2216yescomplemented
79#2562C2216yescomplemented
80#2544C2216yescomplemented
81#2540C2216yescomplemented
82#2538C2216yescomplemented
83#2537C2216yescomplemented
84#2534C22112yescomplemented
85#2503C2213yescomplemented
86#2501C2213yescomplemented
87#2487C2213yescomplemented
88#2487C2213yescomplemented
89#2480C22112yescomplemented
90#2472C22112yescomplemented
91#2468C22112yescomplemented
92#2464C22112yescomplemented
93#2461C22112yescomplemented
94#2457C22112yescomplemented
95#2454C2216yescomplemented
96#2452C2216yescomplemented
97#2447C2216yescomplemented
98#2445C2216yescomplemented
99#2442C2216yescomplemented
100#2440C2216yescomplemented
101#2435C2213yes—
102#2435C2216yes—
103#2433C2216yes—
104#2433C2213yes—
105#2428C2216yescomplemented
106#2427C2216yescomplemented
107#2424C22112yescomplemented
108#2422C2216yescomplemented
109#2420C2216yescomplemented
110#2418C22112yescomplemented
111#2417C2216yescomplemented
112#2416C2216yescomplemented
113#2411C2216yescomplemented
114#2411C2216yescomplemented
115#2408C2213yes—
116#2408C2216yes—
117#2408C2216yes—
118#2408C2213yes—
119#2396C2216yescomplemented
120#2396C2216yescomplemented
121#2395C2213yescomplemented
122#2395C2213yescomplemented
123#2392C2216yescomplemented
124#2392C22112yescomplemented
125#2392C2216yescomplemented
126#2388C2213yes—
127#2388C2213yes—
128#2367C2216yescomplemented
129#2366C2216yescomplemented
130#2363C2216yescomplemented
131#2363C2216yescomplemented
132#2362C2216yescomplemented
133#2361C2216yescomplemented
134#2354C2216yescomplemented
135#2354C2216yescomplemented
136#2352C2216yescomplemented
137#2351C2212yescomplemented
138Q8×C4⋊C4C2212yescomplemented
139Q8×C4⋊C4C2212yescomplemented
140#2347C2213yescomplemented
141#2347C2213yescomplemented
142#2341C2211yescharacteristic
143#2341C2211yescharacteristic
144#2341C2212yes—
145#2341C2212yes—
146#2341C2212yescomplemented
147Q8×C22⋊C4C2212yescomplemented
148#2328C2216yescomplemented
149#2326C2216yescomplemented
150#2324C2216yescomplemented
151#2324C2216yescomplemented
152#2319C2216yescomplemented
153C4×C22⋊Q8C2216yescomplemented
154C4×#121C2216yescomplemented
155#2290C2216yescomplemented
156#2290C2216yescomplemented
157#2285C2213yescomplemented
158#2283C2213yescomplemented
159#2276C2212yescomplemented
160C2×H(5,𝔽2)—28no—
161C2×H(5,𝔽2)—216no—
162C22×#41C2313yes—
163C22×#41C2311yescharacteristic
164C22×#41C2311yescharacteristic
165C22×#41C2312yes—
166C23×Q8C2311yescharacteristic
167C23×D4C2313yes—
168C23×D4C2316yes—
169C24×C4C2316yes—
170#559—224no—
171#557—28no—
172#555—224no—
173#553—224no—
174#552—224no—
175#550—28no—
176#550—216no—
177#548—28no—
178#548—216no—
179#548—28no—
180#542—224no—
181#540—224no—
182C2×C4⋊Q8C2313yes—
183C2×#127C2316yes—
184C2×#127C2313yes—
185#529—224no—
186#529—224no—
187C2×#126C2311yescharacteristic
188C2×#126C2313yes—
189C2×#126C2316yes—
190C2×#125C2313yes—
191C2×#125C2313yes—
192C2×#125C2313yes—
193C2×#124C2316yes—
194C2×#124C2313yes—
195C2×#124C2313yes—
196C2×#124C2313yes—
197C2×#124C2316yes—
198C2×#123C2316yes—
199C2×#123C2313yes—
200C2×#123C2313yes—
201C2×#123C2316yes—
202C2×#123C23112yes—
203C2×C22⋊Q8C2313yes—
204C2×C22⋊Q8C2316yes—
205C2×C22⋊Q8C2313yes—
206C2×C22⋊Q8C2313yes—
207C2×C22⋊Q8C23112yes—
208C2×#121C2316yes—
209C2×#121C2316yes—
210C2×#121C2313yes—
211C2×#121C2316yes—
212C2×#121C2313yes—
213C2×#121C2313yes—
214C2×#121C2313yes—
215C2×#121C2313yes—
216C2×#121C2316yes—
217C2×#121C23112yes—
218C2×#120C2316yes—
219C2×#120C2316yes—
220C2×#120C23112yes—
221#520—28no—
222#520—216no—
223#520—28no—
224#520—224no—
225#519—28no—
226#518—248no—
227#518—224no—
228C4×#41—216no—
229C4×#41—224no—
230C4×#41D4116yescomplemented
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—248no—
244C2×C4×D4—224no—
245C2×C4×D4C2316yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C23112yes—
264C2×C4×D4C23112yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2313yes—
267C2×#117C2313yes—
268C2×#117C2313yes—
269C2×#117C2316yes—
270C2×#117C2316yes—
271C2×#117C2313yes—
272C2×#117C2316yes—
273C2×#117C2313yes—
274C2×#117C2316yes—
275C2×#117C2313yes—
276C22×C4⋊C4C2313yes—
277C22×C4⋊C4C2316yes—
278C22×C4⋊C4C2313yes—
279C22×C22⋊C4C2316yes—
280C22×C22⋊C4C23112yes—
281C22×C42C2316yes—
282C22×C42C2313yes—
283#400C2313yes—
284#400C2316yes—
285#400C2313yes—
286#400C2316yes—
287#399C2313yes—
288#399C2316yes—
289#399C2313yes—
290#399C2316yes—
291#398C2313yes—
292#398C2316yes—
293#398C23112yes—
294#398C2312yes—
295#398C2311yescharacteristic
296#398C2316yes—
297#397C2313yes—
298#397C23112yes—
299#397C2316yes—
300#397C2316yes—
301#397C2311yescharacteristic
302#397C2316yes—
303#396C2316yes—
304#396C23112yes—
305#396C2316yes—
306#396C23112yes—
307#396C23112yes—
308#396C2312yes—
309#396C2316yes—
310#395C2313yes—
311#395C2316yes—
312#395C2311yescharacteristic
313#394C2313yes—
314#394C2316yes—
315#394C2313yes—
316#394C23112yes—
317#394C23112yes—
318#394C23112yes—
319#394C23112yes—
320#394C2316yes—
321#394C2316yes—
322#394C2316yes—
323#394C2316yes—
324#394C2316yes—
325#394C2316yes—
326#394C2316yes—
327#393C2313yes—
328#393C2316yes—
329#393C2311yescharacteristic
330#392C2313yes—
331#392C2316yes—
332#392C23112yes—
333#392C2316yes—
334#392C2316yes—
335#392C2316yes—
336#392C2313yes—
337#391C2316yes—
338#391C2316yes—
339#390C2316yes—
340#390C2316yes—
341#390C2316yes—
342#390C2316yes—
343#390C2316yes—
344#390C2316yes—
345#390C23112yes—
346#390C23112yes—
347#390C2316yes—
348#390C2316yes—
349#389C2316yes—
350#389C2316yes—
351#389C2316yes—
352#389C2316yes—
353#389C2316yes—
354#389C2316yes—
355#388C23112yes—
356#388C23112yes—
357#388C23112yes—
358#388C23112yes—
359#388C23112yes—
360#388C23112yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#388C2312yes—
365#387C2316yes—
366#387C2316yes—
367#387C2316yes—
368#387C2312yes—
369#386C2316yes—
370#386C23112yes—
371#386C2316yes—
372#386C23112yes—
373#386C23112yes—
374#386C2316yes—
375#386C2316yes—
376#386C23112yes—
377#386C23112yes—
378#386C2316yes—
379#386C2316yes—
380#385C23112yes—
381#385C23112yes—
382#385C2316yes—
383#385C23112yes—
384#385C2316yes—
385#385C2316yes—
386#385C2316yes—
387#385C2316yes—
388#385C2316yes—
389#384C2316yes—
390#384C2316yes—
391#383C2313yes—
392#383C2313yes—
393#382C2316yes—
394#382C2311yescharacteristic
395#382C2313yes—
396#381C2316yes—
397#381C23112yes—
398#380C23112yes—
399#380C23112yes—
400#380C2316yes—
401#380C2316yes—
402#380C2316yes—
403#380C2313yes—
404#380C2313yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#379C2316yes—
409#379C2316yes—
410#379C23112yes—
411C4×C4⋊C4C2316yes—
412C4×C4⋊C4C2316yes—
413C4×C4⋊C4C2316yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2316yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C23112yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2313yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C23112yes—
426C4×C22⋊C4C23112yes—
427#376C2316yes—
428C25C2416yes—
429H(5,𝔽2)—2128no—
430C2×#41—28no—
431C2×#41—24no—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—212no—
436C2×#41—224no—
437C2×#41C2×D418yes—
438C2×#41#41116yes—
439C22×Q8—24no—
440C22×Q8—28no—
441C22×Q8C2411yescharacteristic
442C22×Q8C2413yes—
443C22×Q8C2413yes—
444C22×Q8C2411yescharacteristic
445C22×D4—224no—
446C22×D4—224no—
447C22×D4—224no—
448C22×D4—212no—
449C22×D4—224no—
450C22×D4C2413yes—
451C22×D4C2416yes—
452C22×D4C2413yes—
453C22×D4C2413yes—
454C22×D4C2416yes—
455C22×D4C2413yes—
456C22×D4C2416yes—
457C22×D4C2416yes—
458C22×D4C24112yes—
459C22×D4C2413yes—
460C22×D4C2416yes—
461C22×D4C2413yes—
462C23×C4—224no—
463C23×C4—812no—
464C23×C4C2413yes—
465C23×C4C2413yes—
466C23×C4C2413yes—
467C23×C4C2416yes—
468C23×C4C2416yes—
469C23×C4C24112yes—
470C23×C4C2416yes—
471C23×C4C2416yes—
472C23×C4C2416yes—
473C23×C4C2413yes—
474C23×C4C2413yes—
475C4⋊Q8—212no—
476#127—212no—
477#127—224no—
478#126—224no—
479#126—24no—
480#126—212no—
481#125—212no—
482#125—212no—
483#125—212no—
484#124—212no—
485#124—224no—
486#124—224no—
487#124—212no—
488#124—212no—
489#123—224no—
490#123—212no—
491#123—212no—
492#123—224no—
493#123—812no—
494C22⋊Q8—212no—
495C22⋊Q8—212no—
496C22⋊Q8—224no—
497C22⋊Q8—212no—
498C22⋊Q8—812no—
499#121—212no—
500#121—212no—
501#121—224no—
502#121—224no—
503#121—212no—
504#121—212no—
505#121—224no—
506#121—212no—
507#121—224no—
508#121—812no—
509#120—86no—
510#120—86no—
511#120—812no—
512C4×Q8—28no—
513C4×Q8—24no—
514C4×Q8—24no—
515C4×Q8—28no—
516C4×Q8—28no—
517C4×Q8—212no—
518C4×Q8—24no—
519C4×Q8—212no—
520C4×Q8—212no—
521C4×Q8—212no—
522C4×Q8C2×D418yes—
523C4×Q8C2×D418yes—
524C4×D4—224no—
525C4×D4—224no—
526C4×D4—224no—
527C4×D4—212no—
528C4×D4—212no—
529C4×D4—224no—
530C4×D4—224no—
531C4×D4—224no—
532C4×D4—224no—
533C4×D4—224no—
534C4×D4—212no—
535C4×D4—248no—
536C4×D4—224no—
537C4×D4—212no—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—212no—
541C4×D4—212no—
542C4×D4—212no—
543C4×D4—812no—
544C4×D4C2×D4124yes—
545C4×D4C2×D4124yes—
546#117—212no—
547#117—224no—
548#117—212no—
549#117—224no—
550#117—212no—
551#117—212no—
552#117—224no—
553#117—86no—
554#117C2×D4124yes—
555C2×C4⋊C4—212no—
556C2×C4⋊C4—224no—
557C2×C4⋊C4—212no—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2413yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2413yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C24112yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C24112yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2413yes—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—248no—
592C2×C22⋊C4C24112yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2411yescharacteristic
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2413yes—
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2411yescharacteristic
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2411yescharacteristic
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C24112yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C42—224no—
630C2×C42C2×D4124yes—
631C2×C42C2416yes—
632C2×C42C2416yes—
633C2×C42C2416yes—
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2412yes—
637C2×C42C2416yes—
638C2×C42C2416yes—
639C2×C42C24112yes—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2413yes—
643C2×C42C2411yescharacteristic
644#95C2412yes—
645#95C2416yes—
646#95C2416yes—
647#95C2416yes—
648#95C2416yes—
649#95C2411yescharacteristic
650#95C2411yescharacteristic
651#95C2412yes—
652#95C2416yes—
653#95C2412yes—
654#95C2412yes—
655#95C2416yes—
656#95C2413yes—
657#95C2413yes—
658#95C2416yes—
659#95C2416yes—
660#95C24112yes—
661#95C2416yes—
662#95C2412yes—
663#95C24112yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668C24—212no—
669C24—224no—
670C24—46no—
671C24—412no—
672C24—46no—
673C24C2511yescharacteristic
674C24C2513yes—
675C24C2513yes—
676C24C2516yes—
677#41—296no—
678#41—232no—
679#41—264no—
680#41—416no—
681C2×Q8—22no—
682C2×Q8—26no—
683C2×Q8—26no—
684C2×Q8—24no—
685C2×Q8—212no—
686C2×Q8—46no—
687C2×Q8—416no—
688C2×Q8C22×D414yes—
689C2×Q8C2×#4118yes—
690C2×D4—296no—
691C2×D4—2192no—
692C2×D4—212no—
693C2×D4—212no—
694C2×D4—212no—
695C2×D4—26no—
696C2×D4—212no—
697C2×D4—26no—
698C2×D4—212no—
699C2×D4—212no—
700C2×D4—224no—
701C2×D4—26no—
702C2×D4—212no—
703C2×D4—26no—
704C2×D4—26no—
705C2×D4—212no—
706C2×D4—212no—
707C2×D4—212no—
708C2×D4—212no—
709C2×D4—412no—
710C2×D4—46no—
711C2×D4—43no—
712C2×D4—46no—
713C2×D4—43no—
714C2×D4—412no—
715C2×D4—412no—
716C2×D4—46no—
717C2×D4—46no—
718C2×D4—43no—
719C2×D4—46no—
720C2×D4—43no—
721C2×D4C22×D4112yes—
722C2×D4C2×#41124yes—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—212no—
726C22×C4—212no—
727C22×C4—212no—
728C22×C4—26no—
729C22×C4—26no—
730C22×C4—212no—
731C22×C4—212no—
732C22×C4—212no—
733C22×C4—224no—
734C22×C4—212no—
735C22×C4—43no—
736C22×C4—46no—
737C22×C4—46no—
738C22×C4—46no—
739C22×C4—43no—
740C22×C4—46no—
741C22×C4—46no—
742C22×C4—412no—
743C22×C4—412no—
744C22×C4—412no—
745C22×C4—46no—
746C22×C4—46no—
747C22×C4—848no—
748C22×C4C22×D4112yes—
749C22×C4C22×D4112yes—
750C22×C4C22×D4112yes—
751C22×C4C2×#41124yes—
752C22×C4C2512yes—
753C22×C4C2512yes—
754C22×C4C2516yes—
755C22×C4C2512yes—
756C22×C4C2516yes—
757C22×C4C2511yescharacteristic
758C22×C4C2513yes—
759C22×C4C2516yes—
760C22×C4C2513yes—
761C22×C4C2511yescharacteristic
762C22×C4C2511yescharacteristic
763C22×C4C2513yes—
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2513yes—
767C22×C4C2513yes—
768C22×C4C2511yescharacteristic
769C22×C4C2512yes—
770C22×C4C2513yes—
771C4⋊C4—212no—
772C4⋊C4—26no—
773C4⋊C4—212no—
774C4⋊C4—26no—
775C4⋊C4—26no—
776C4⋊C4—24no—
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—26no—
780C4⋊C4—26no—
781C4⋊C4—26no—
782C4⋊C4—26no—
783C4⋊C4—212no—
784C4⋊C4—22no—
785C4⋊C4—26no—
786C4⋊C4—26no—
787C4⋊C4—22no—
788C4⋊C4—26no—
789C4⋊C4—24no—
790C4⋊C4—212no—
791C4⋊C4—212no—
792C4⋊C4—212no—
793C4⋊C4—42no—
794C4⋊C4—42no—
795C4⋊C4—46no—
796C4⋊C4—46no—
797C4⋊C4—412no—
798C4⋊C4—46no—
799C4⋊C4—412no—
800C4⋊C4—46no—
801C4⋊C4C22×D4112yes—
802C4⋊C4C22×D4112yes—
803C22⋊C4—212no—
804C22⋊C4—26no—
805C22⋊C4—212no—
806C22⋊C4—26no—
807C22⋊C4—212no—
808C22⋊C4—212no—
809C22⋊C4—224no—
810C22⋊C4—212no—
811C22⋊C4—224no—
812C22⋊C4—212no—
813C22⋊C4—22no—
814C22⋊C4—26no—
815C22⋊C4—26no—
816C22⋊C4—26no—
817C22⋊C4—26no—
818C22⋊C4—212no—
819C22⋊C4—22no—
820C22⋊C4—26no—
821C22⋊C4—22no—
822C22⋊C4—24no—
823C22⋊C4—212no—
824C22⋊C4—46no—
825C22⋊C4—42no—
826C22⋊C4—46no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—412no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4—46no—
833C22⋊C4—412no—
834C22⋊C4—46no—
835C22⋊C4—412no—
836C22⋊C4—46no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4C22×D4124yes—
840C42—24no—
841C42—212no—
842C42—212no—
843C42—212no—
844C42—26no—
845C42—26no—
846C42—212no—
847C42—212no—
848C42—412no—
849C42C22×D4112yes—
850C42C22×D414yes—
851C42C22×D4112yes—
852C42C22×D4112yes—
853C23—248no—
854C23—26no—
855C23—26no—
856C23—26no—
857C23—23no—
858C23—26no—
859C23—26no—
860C23—26no—
861C23—26no—
862C23—26no—
863C23—23no—
864C23—23no—
865C23—21no—
866C23—22no—
867C23—26no—
868C23—26no—
869C23—22no—
870C23—23no—
871C23—21no—
872C23—21no—
873C23—23no—
874C23—812no—
875C23—812no—
876C23—824no—
877C23—824no—
878C23C23×D416yes—
879C23C22×#41112yes—
880C23C2611yescharacteristic
881Q8—28no—
882Q8—412no—
883Q8—86no—
884Q8#525116yes—
885D4—224no—
886D4—248no—
887D4—224no—
888D4—248no—
889D4—412no—
890D4—86no—
891D4—812no—
892D4—86no—
893D4—86no—
894D4—812no—
895D4—812no—
896D4—824no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—23no—
901C2×C4—21no—
902C2×C4—26no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—23no—
906C2×C4—224no—
907C2×C4—248no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—23no—
911C2×C4—21no—
912C2×C4—23no—
913C2×C4—26no—
914C2×C4—23no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—26no—
919C2×C4—26no—
920C2×C4—22no—
921C2×C4—26no—
922C2×C4—26no—
923C2×C4—26no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—26no—
928C2×C4—26no—
929C2×C4—23no—
930C2×C4—22no—
931C2×C4—26no—
932C2×C4—22no—
933C2×C4—26no—
934C2×C4—26no—
935C2×C4—22no—
936C2×C4—23no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—412no—
941C2×C4—412no—
942C2×C4—424no—
943C2×C4—412no—
944C2×C4—412no—
945C2×C4—812no—
946C2×C4—812no—
947C2×C4—824no—
948C2×C4—812no—
949C2×C4C23×D416yes—
950C2×C4C23×D412yes—
951C2×C4C23×D412yes—
952C2×C4C23×D412yes—
953C2×C4C23×D416yes—
954C2×C4C23×D416yes—
955C2×C4C22×#4114yes—
956C2×C4C22×#41112yes—
957C22—26no—
958C22—26no—
959C22—212no—
960C22—212no—
961C22—26no—
962C22—212no—
963C22—46no—
964C22—46no—
965C22—46no—
966C22—46no—
967C22—46no—
968C22—46no—
969C22—41no—
970C22—43no—
971C22—43no—
972C22—41no—
973C22—46no—
974C22—42no—
975C22—42no—
976C22—46no—
977C22—41no—
978C22—43no—
979C22—848no—
980C22C24×D411yescharacteristic
981C22C23×#4112yes—
982C22H(7,𝔽2)12yes—
983C22H(7,𝔽2)11yescharacteristic
984C222−1+611yescharacteristic
985C4—22no—
986C4—26no—
987C4—22no—
988C4—26no—
989C4—22no—
990C4—24no—
991C4—46no—
992C4—43no—
993C4—41no—
994C4—42no—
995C4—43no—
996C4—41no—
997C4—42no—
998C4—42no—
999C4—46no—
1000C4—46no—
1001C4—41no—
1002C4—43no—
1003C4C2×#525112yes—
1004C2—46no—
1005C2—412no—
1006C2—83no—
1007C2—81no—
1008C2C22×#52511yescharacteristic
1009C2#6285211yescharacteristic
1010C2#6285311yescharacteristic
1011C2#6285712yes—
1012C2#6285812yes—
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×#3524C2semidirect
2. C2×C4×H(5,𝔽2)C2semidirect
3. #36091C2semidirect
4. #36087C2semidirect
5. #36082C2semidirect
6. #36080C2semidirect
7. #36005C2semidirect
8. #36004C2semidirect
9. #35983C2semidirect
10. #35982C2semidirect
11. #35831C2semidirect
12. #35823C2semidirect
13. #35816C2semidirect
14. #35808C2semidirect
15. #35236C2semidirect
16. #35233C2semidirect
17. #35226C2semidirect
18. #35225C2semidirect
19. #34636C2semidirect
20. #34614C2semidirect
21. #34295C2semidirect
22. #34293C2semidirect
23. #34193C2semidirect
26. C2×#559C22semidirect
27. C2×#557C22semidirect
28. C2×#555C22semidirect
29. C2×#553C22semidirect
30. C2×#552C22semidirect
35. C2×#548C22semidirect
36. C2×#542C22semidirect
37. C2×#540C22semidirect
38. C2×#529C22semidirect
39. C2×#529C22semidirect
44. C2×#520C22semidirect
45. C2×#519C22semidirect
53. #2849C22semidirect
54. #2848C22semidirect
55. #2847C22semidirect
56. #2638C22semidirect
57. #2637C22semidirect
58. #2637C22semidirect
59. #2636C22semidirect
60. #2636C22semidirect
61. #2636C22semidirect
62. #2635C22semidirect
63. #2634C22semidirect
64. #2633C22semidirect
65. #2632C22semidirect
66. #2631C22semidirect
67. #2630C22semidirect
68. #2630C22semidirect
69. #2630C22semidirect
70. #2629C22semidirect
71. #2625C22semidirect
72. #2624C22semidirect
73. #2620C22semidirect
76. #2598C22semidirect
77. #2598C22semidirect
78. #2566C22semidirect
79. #2562C22semidirect
80. #2544C22semidirect
81. #2540C22semidirect
82. #2538C22semidirect
83. #2537C22semidirect
84. #2534C22semidirect
85. #2503C22semidirect
86. #2501C22semidirect
87. #2487C22semidirect
88. #2487C22semidirect
89. #2480C22semidirect
90. #2472C22semidirect
91. #2468C22semidirect
92. #2464C22semidirect
93. #2461C22semidirect
94. #2457C22semidirect
95. #2454C22semidirect
96. #2452C22semidirect
97. #2447C22semidirect
98. #2445C22semidirect
99. #2442C22semidirect
100. #2440C22semidirect
105. #2428C22semidirect
106. #2427C22semidirect
107. #2424C22semidirect
108. #2422C22semidirect
109. #2420C22semidirect
110. #2418C22semidirect
111. #2417C22semidirect
112. #2416C22semidirect
113. #2411C22semidirect
114. #2411C22semidirect
119. #2396C22semidirect
120. #2396C22semidirect
121. #2395C22semidirect
122. #2395C22semidirect
123. #2392C22semidirect
124. #2392C22semidirect
125. #2392C22semidirect
128. #2367C22semidirect
129. #2366C22semidirect
130. #2363C22semidirect
131. #2363C22semidirect
132. #2362C22semidirect
133. #2361C22semidirect
134. #2354C22semidirect
135. #2354C22semidirect
136. #2352C22semidirect
137. #2351C22semidirect
138. Q8×C4⋊C4C22semidirect
139. Q8×C4⋊C4C22semidirect
140. #2347C22semidirect
141. #2347C22semidirect
146. #2341C22semidirect
147. Q8×C22⋊C4C22semidirect
148. #2328C22semidirect
149. #2326C22semidirect
150. #2324C22semidirect
151. #2324C22semidirect
152. #2319C22semidirect
153. C4×C22⋊Q8C22semidirect
154. C4×#121C22semidirect
155. #2290C22semidirect
156. #2290C22semidirect
157. #2285C22semidirect
158. #2283C22semidirect
159. #2276C22semidirect
230. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
C2×C4×H(5,𝔽2)2
#360912
#360872
#360822
#360802
#360052
#360042
#359832
#359822
#358312
#358232
#358162
#358082
#352362
#352332
#352262
#352252
#346362
#346142
#342952
#342932
#341932