Finite Group Databasebeta

← #7629677

Subgroups — #7629677

Order 512.

8751 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic, complemented
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3#36091C211yesmaximal, characteristic, complemented
4#36089C213yesmaximal, complemented
5#36083C213yesmaximal, complemented
6#36082C211yesmaximal, characteristic, complemented
7#36076C211yesmaximal, characteristic, complemented
8#36075C213yesmaximal, complemented
9#35996C211yesmaximal, characteristic, complemented
10#35995C213yesmaximal, complemented
11#35831C212yesmaximal, complemented
12#35823C216yesmaximal, complemented
13#35816C212yesmaximal, complemented
14#35808C216yesmaximal, complemented
15#34965C213yesmaximal, complemented
16#34935C213yesmaximal, complemented
17#34700C216yesmaximal, complemented
18#34681C216yesmaximal, complemented
19#34614C213yesmaximal, complemented
20#34547C213yesmaximal, complemented
21C4×#550C212yesmaximal, complemented
22C4×#548C212yesmaximal, complemented
23#34129C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25#3480—216no—
26C2×#559C2213yescomplemented
27C2×#557C2211yescharacteristic, complemented
28C2×#556C2213yescomplemented
29C2×#553C2213yescomplemented
30C2×#553C2213yescomplemented
31C2×#550C2212yes—
32C2×#550C2211yescharacteristic
33C2×#548C2212yes—
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic, complemented
36C2×#532C2213yescomplemented
37C2×#529C2213yescomplemented
38C2×#529C2213yescomplemented
39C2×#525C2216yescomplemented
40C4×H(5,𝔽2)—216no—
41C2×#520C2211yescharacteristic
42C2×#520C2212yes—
43C2×#520C2213yes—
44C2×#518C2213yes—
45C2×#518C2216yes—
46C2×C4×#41C2213yes—
47C2×C4×#41C2212yes—
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic, complemented
50C2×C4×#41C2213yescomplemented
51C22×C4×Q8C2211yescharacteristic, complemented
52C22×C4×D4C2213yes—
53C22×C4×D4C2216yes—
54#2637C2216yescomplemented
55#2636C2216yescomplemented
56#2630C22112yescomplemented
57#2629C2216yescomplemented
58#2625C2213yescomplemented
59#2624C2213yescomplemented
60#2620C2216yescomplemented
61#2616C2213yes—
62#2615C2213yes—
63#2603C2216yescomplemented
64#2603C2216yescomplemented
65#2566C2216yescomplemented
66#2544C2216yescomplemented
67#2538C2216yescomplemented
68#2537C2216yescomplemented
69#2536C2216yescomplemented
70#2535C2216yescomplemented
71#2534C2216yescomplemented
72#2534C2216yescomplemented
73#2504C2213yescomplemented
74#2502C2213yescomplemented
75#2486C2213yescomplemented
76#2486C2213yescomplemented
77#2480C22112yescomplemented
78#2472C22112yescomplemented
79#2468C22112yescomplemented
80#2464C22112yescomplemented
81#2461C22112yescomplemented
82#2457C22112yescomplemented
83#2454C2216yescomplemented
84#2452C2216yescomplemented
85#2447C2216yescomplemented
86#2445C2216yescomplemented
87#2442C2216yescomplemented
88#2440C2216yescomplemented
89#2435C2216yes—
90#2435C2213yes—
91#2433C2216yes—
92#2433C2213yes—
93#2428C2216yescomplemented
94#2427C2216yescomplemented
95#2424C22112yescomplemented
96#2422C2216yescomplemented
97#2420C2216yescomplemented
98#2418C22112yescomplemented
99#2417C2216yescomplemented
100#2416C2216yescomplemented
101#2411C22112yescomplemented
102#2408C2213yes—
103#2408C2213yes—
104#2408C2216yes—
105#2408C2216yes—
106#2399C2213yescomplemented
107#2398C2213yescomplemented
108#2398C2213yescomplemented
109#2397C2213yescomplemented
110#2396C2213yescomplemented
111#2396C2216yescomplemented
112#2396C2211yescharacteristic, complemented
113#2395C2216yescomplemented
114#2395C2213yescomplemented
115#2395C2213yescomplemented
116#2392C2216yescomplemented
117#2392C22112yescomplemented
118#2392C2213yescomplemented
119#2392C2213yescomplemented
120#2392C2216yescomplemented
121#2392C2216yescomplemented
122#2392C2216yescomplemented
123#2388C2213yes—
124#2388C2213yes—
125#2388C2216yescomplemented
126#2367C2216yescomplemented
127#2366C2216yescomplemented
128#2363C2216yescomplemented
129#2363C2216yescomplemented
130#2362C2216yescomplemented
131#2361C2216yescomplemented
132#2354C2216yescomplemented
133#2354C2216yescomplemented
134#2352C2216yescomplemented
135#2351C2212yescomplemented
136Q8×C4⋊C4C2212yescomplemented
137Q8×C4⋊C4C2212yescomplemented
138#2346C2213yescomplemented
139#2346C2213yescomplemented
140#2341C2211yescharacteristic
141#2341C2211yescharacteristic
142#2341C2212yes—
143#2341C2212yes—
144#2341C2212yescomplemented
145Q8×C22⋊C4C2212yescomplemented
146C4×#127C2216yescomplemented
147C4×#124C2216yescomplemented
148C4×C22⋊Q8C2216yescomplemented
149C4×#121C2216yescomplemented
150C4×#121C2216yescomplemented
151C4×#121C2216yescomplemented
152C4×#120C22112yescomplemented
153#2293C2216yescomplemented
154#2285C2213yescomplemented
155#2280C2216yescomplemented
156C42×Q8C2212yescomplemented
157C42×D4C2216yescomplemented
158C42×D4C2216yescomplemented
159C4×#117C2213yescomplemented
160C2×H(5,𝔽2)—28no—
161C2×H(5,𝔽2)—216no—
162C22×#41C2313yes—
163C22×#41C2311yescharacteristic
164C22×#41C2313yes—
165C22×#41C2311yescharacteristic
166C22×#41C2312yes—
167C23×Q8C2311yescharacteristic
168C23×D4C2313yes—
169C23×D4C2316yes—
170C24×C4C2316yes—
171#559—224no—
172#557—28no—
173#556—224no—
174#553—224no—
175#553—224no—
176#550—28no—
177#550—216no—
178#548—28no—
179#548—216no—
180#548—28no—
181#532—224no—
182C2×C4⋊Q8C2313yes—
183C2×#127C2316yes—
184C2×#127C2313yes—
185#529—224no—
186#529—224no—
187C2×#126C2316yes—
188C2×#126C2316yes—
189C2×#125C2313yes—
190C2×#125C2313yes—
191C2×#124C2313yes—
192C2×#124C2316yes—
193C2×#124C2313yes—
194C2×#124C2316yes—
195#525—424no—
196C2×#123C2316yes—
197C2×#123C2316yes—
198C2×#123C2316yes—
199C2×#123C2316yes—
200C2×C22⋊Q8C2316yes—
201C2×C22⋊Q8C2313yes—
202C2×C22⋊Q8C2313yes—
203C2×C22⋊Q8C23112yes—
204C2×#121C2316yes—
205C2×#121C2313yes—
206C2×#121C2316yes—
207C2×#121C2316yes—
208C2×#121C2313yes—
209C2×#121C2313yes—
210C2×#121C2313yes—
211C2×#121C2316yes—
212C2×#121C23112yes—
213C2×#120C2316yes—
214C2×#120C23112yes—
215C2×#120C2316yes—
216#520—28no—
217#520—216no—
218#520—224no—
219#518—248no—
220#518—224no—
221C4×#41—216no—
222C4×#41—28no—
223C4×#41—224no—
224C4×#41—224no—
225C4×#41D4116yescomplemented
226C2×C4×Q8—28no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2313yes—
233C2×C4×Q8C2313yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2313yes—
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—248no—
241C2×C4×D4—224no—
242C2×C4×D4C2313yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2313yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2316yes—
264C2×C4×D4C23112yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C23112yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×#117C2316yes—
272C2×#117C2313yes—
273C2×#117C2316yes—
274C2×#117C2313yes—
275C2×#117C2311yescharacteristic
276C2×#117C2313yes—
277C2×#117C2313yes—
278C2×#117C2316yes—
279C2×#117C2316yes—
280C2×#117C2313yes—
281C22×C4⋊C4C2313yes—
282C22×C4⋊C4C2316yes—
283C22×C4⋊C4C2313yes—
284C22×C22⋊C4C2316yes—
285C22×C22⋊C4C23112yes—
286C22×C42C2316yes—
287C22×C42C2313yes—
288C22×C42C2313yes—
289C22×C42C2313yes—
290#400C2313yes—
291#400C2311yescharacteristic
292#400C2316yes—
293#399C2313yes—
294#399C2311yescharacteristic
295#399C2316yes—
296#398C2313yes—
297#398C2316yes—
298#398C2316yes—
299#398C23112yes—
300#398C2312yes—
301#398C2316yes—
302#398C2313yes—
303#397C2313yes—
304#397C2316yes—
305#397C23112yes—
306#397C2316yes—
307#397C2316yes—
308#397C2316yes—
309#397C2313yes—
310#396C2316yes—
311#396C23112yes—
312#396C2316yes—
313#396C23112yes—
314#396C23112yes—
315#396C2312yes—
316#396C2316yes—
317#395C2313yes—
318#395C2311yescharacteristic
319#395C2316yes—
320#394C2313yes—
321#394C2316yes—
322#394C23112yes—
323#394C23112yes—
324#394C23112yes—
325#394C23112yes—
326#394C2316yes—
327#394C2316yes—
328#394C2313yes—
329#394C2316yes—
330#394C2316yes—
331#394C2316yes—
332#394C2316yes—
333#394C2316yes—
334#393C2313yes—
335#393C2311yescharacteristic
336#393C2316yes—
337#392C2313yes—
338#392C2316yes—
339#392C23112yes—
340#392C2316yes—
341#392C2316yes—
342#392C2313yes—
343#392C2316yes—
344#391C2316yes—
345#391C2316yes—
346#390C2316yes—
347#390C2316yes—
348#390C23112yes—
349#390C23112yes—
350#390C2316yes—
351#390C2316yes—
352#390C2316yes—
353#390C2316yes—
354#390C2316yes—
355#390C2316yes—
356#389C2316yes—
357#389C2316yes—
358#389C2316yes—
359#389C2316yes—
360#389C2316yes—
361#389C2316yes—
362#388C23112yes—
363#388C23112yes—
364#388C23112yes—
365#388C23112yes—
366#388C23112yes—
367#388C23112yes—
368#388C23112yes—
369#387C23112yes—
370#386C23112yes—
371#386C23112yes—
372#386C23112yes—
373#386C23112yes—
374#386C23112yes—
375#386C23112yes—
376#385C23112yes—
377#385C23112yes—
378#385C23112yes—
379#385C23112yes—
380#384C2316yes—
381#384C2316yes—
382#382C2316yes—
383#382C2316yes—
384#381C2316yes—
385#381C2316yes—
386#380C2316yes—
387#380C2313yes—
388#380C2313yes—
389#380C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C23112yes—
394#380C23112yes—
395#379C2316yes—
396#379C23112yes—
397#379C2316yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2316yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C23112yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426#376C2313yes—
427#376C2313yes—
428C43C2316yes—
429C25C2416yes—
430H(5,𝔽2)—2128no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—212no—
437C2×#41—212no—
438C2×#41—224no—
439C2×#41—212no—
440C2×#41—46no—
441C2×#41C2×D418yes—
442C2×#41#41116yescomplemented
443C22×Q8—24no—
444C22×Q8—28no—
445C22×Q8C2411yescharacteristic
446C22×Q8C2413yes—
447C22×Q8C2413yes—
448C22×Q8C2411yescharacteristic
449C22×D4—224no—
450C22×D4—224no—
451C22×D4—224no—
452C22×D4—212no—
453C22×D4—224no—
454C22×D4C2413yes—
455C22×D4C2416yes—
456C22×D4C2413yes—
457C22×D4C2416yes—
458C22×D4C2416yes—
459C22×D4C2413yes—
460C22×D4C2413yes—
461C22×D4C2413yes—
462C22×D4C2413yes—
463C22×D4C2416yes—
464C22×D4C2416yes—
465C22×D4C24112yes—
466C23×C4—224no—
467C23×C4—412no—
468C23×C4—412no—
469C23×C4C2413yes—
470C23×C4C2413yes—
471C23×C4C2413yes—
472C23×C4C2416yes—
473C23×C4C2413yes—
474C23×C4C2413yes—
475C23×C4C2416yes—
476C23×C4C2411yescharacteristic
477C23×C4C2416yes—
478C23×C4C24112yes—
479C23×C4C2416yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2413yes—
483C4⋊Q8—212no—
484#127—212no—
485#127—224no—
486#126—224no—
487#126—224no—
488#125—212no—
489#125—212no—
490#124—212no—
491#124—224no—
492#124—224no—
493#124—212no—
494#123—224no—
495#123—224no—
496#123—412no—
497#123—412no—
498C22⋊Q8—212no—
499C22⋊Q8—224no—
500C22⋊Q8—212no—
501C22⋊Q8—424no—
502#121—212no—
503#121—212no—
504#121—224no—
505#121—224no—
506#121—212no—
507#121—224no—
508#121—212no—
509#121—224no—
510#121—424no—
511#120—424no—
512#120—412no—
513#120—412no—
514C4×Q8—24no—
515C4×Q8—28no—
516C4×Q8—24no—
517C4×Q8—28no—
518C4×Q8—28no—
519C4×Q8—212no—
520C4×Q8—212no—
521C4×Q8—24no—
522C4×Q8—212no—
523C4×Q8—212no—
524C4×Q8—212no—
525C4×Q8C2×D418yes—
526C4×Q8C2×D418yes—
527C4×D4—224no—
528C4×D4—224no—
529C4×D4—224no—
530C4×D4—212no—
531C4×D4—212no—
532C4×D4—212no—
533C4×D4—212no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—212no—
541C4×D4—248no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—224no—
545C4×D4—224no—
546C4×D4—212no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—412no—
551C4×D4—412no—
552C4×D4—412no—
553C4×D4—424no—
554C4×D4C2×D4124yes—
555C4×D4C2×D4124yes—
556#117—212no—
557#117—212no—
558#117—224no—
559#117—212no—
560#117—24no—
561#117—224no—
562#117—212no—
563#117—412no—
564#117—412no—
565#117C2×D4124yes—
566C2×C4⋊C4—212no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—212no—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2413yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C24112yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C24112yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2413yes—
597C2×C4⋊C4C2413yes—
598C2×C22⋊C4—224no—
599C2×C22⋊C4—248no—
600C2×C22⋊C4C24112yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2411yescharacteristic
605C2×C22⋊C4C2411yescharacteristic
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C24112yes—
633C2×C22⋊C4C2416yes—
634C2×C42—224no—
635C2×C42—212no—
636C2×C42—212no—
637C2×C42C2×D4124yes—
638C2×C42C2416yes—
639C2×C42C2416yes—
640C2×C42C2413yes—
641C2×C42C2416yes—
642C2×C42C2413yes—
643C2×C42C2413yes—
644C2×C42C2413yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2411yescharacteristic
648C2×C42C2416yes—
649C2×C42C2413yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2416yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2411yescharacteristic
656C2×C42C2413yes—
657#95C2411yescharacteristic
658#95C2411yescharacteristic
659#95C2413yes—
660#95C2413yes—
661#95C2416yes—
662#95C2416yes—
663#95C2412yes—
664#95C2412yes—
665#95C2412yes—
666#95C2412yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C24112yes—
676#95C24112yes—
677#95C24112yes—
678C24—212no—
679C24—224no—
680C24—46no—
681C24—412no—
682C24—46no—
683C24C2513yes—
684C24C2513yes—
685C24C2516yes—
686C24C2511yescharacteristic
687#41—296no—
688#41—232no—
689#41—264no—
690#41—448no—
691#41—416no—
692C2×Q8—22no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—24no—
696C2×Q8—212no—
697C2×Q8—26no—
698C2×Q8—43no—
699C2×Q8—416no—
700C2×Q8C22×D414yes—
701C2×Q8C2×#4118yes—
702C2×D4—296no—
703C2×D4—2192no—
704C2×D4—212no—
705C2×D4—212no—
706C2×D4—212no—
707C2×D4—26no—
708C2×D4—26no—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—212no—
712C2×D4—26no—
713C2×D4—26no—
714C2×D4—212no—
715C2×D4—224no—
716C2×D4—26no—
717C2×D4—212no—
718C2×D4—26no—
719C2×D4—26no—
720C2×D4—212no—
721C2×D4—212no—
722C2×D4—212no—
723C2×D4—212no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—43no—
729C2×D4—43no—
730C2×D4—43no—
731C2×D4—412no—
732C2×D4—412no—
733C2×D4—412no—
734C2×D4C22×D4112yes—
735C2×D4C2×#41124yes—
736C22×C4—22no—
737C22×C4—212no—
738C22×C4—212no—
739C22×C4—212no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—22no—
743C22×C4—212no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—212no—
748C22×C4—212no—
749C22×C4—212no—
750C22×C4—212no—
751C22×C4—26no—
752C22×C4—26no—
753C22×C4—212no—
754C22×C4—212no—
755C22×C4—26no—
756C22×C4—26no—
757C22×C4—224no—
758C22×C4—46no—
759C22×C4—46no—
760C22×C4—46no—
761C22×C4—46no—
762C22×C4—46no—
763C22×C4—412no—
764C22×C4—46no—
765C22×C4—412no—
766C22×C4—46no—
767C22×C4—848no—
768C22×C4C22×D4112yes—
769C22×C4C22×D4112yes—
770C22×C4C22×D4112yes—
771C22×C4C2×#41124yes—
772C22×C4H(5,𝔽2)14yescomplemented
773C22×C4C2512yes—
774C22×C4C2516yes—
775C22×C4C2512yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2516yes—
779C22×C4C2513yes—
780C22×C4C2513yes—
781C22×C4C2516yes—
782C22×C4C2513yes—
783C22×C4C2511yescharacteristic
784C22×C4C2513yes—
785C22×C4C2513yes—
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2512yes—
790C22×C4C2513yes—
791C22×C4C2511yescharacteristic
792C4⋊C4—212no—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—26no—
796C4⋊C4—212no—
797C4⋊C4—24no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—26no—
802C4⋊C4—26no—
803C4⋊C4—26no—
804C4⋊C4—26no—
805C4⋊C4—26no—
806C4⋊C4—212no—
807C4⋊C4—24no—
808C4⋊C4—212no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—212no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—46no—
815C4⋊C4—412no—
816C4⋊C4—46no—
817C4⋊C4—46no—
818C4⋊C4—412no—
819C4⋊C4C22×D4112yes—
820C4⋊C4C22×D4112yes—
821C22⋊C4—212no—
822C22⋊C4—26no—
823C22⋊C4—26no—
824C22⋊C4—212no—
825C22⋊C4—212no—
826C22⋊C4—212no—
827C22⋊C4—224no—
828C22⋊C4—212no—
829C22⋊C4—212no—
830C22⋊C4—224no—
831C22⋊C4—212no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—26no—
835C22⋊C4—212no—
836C22⋊C4—26no—
837C22⋊C4—212no—
838C22⋊C4—24no—
839C22⋊C4—212no—
840C22⋊C4—212no—
841C22⋊C4—212no—
842C22⋊C4—24no—
843C22⋊C4—212no—
844C22⋊C4—46no—
845C22⋊C4—46no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—46no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—412no—
852C22⋊C4—412no—
853C22⋊C4—412no—
854C22⋊C4C22×D4124yes—
855C42—22no—
856C42—24no—
857C42—212no—
858C42—212no—
859C42—26no—
860C42—26no—
861C42—26no—
862C42—26no—
863C42—26no—
864C42—212no—
865C42—212no—
866C42—212no—
867C42—212no—
868C42—24no—
869C42—46no—
870C42C22×D4112yes—
871C42C22×D414yes—
872C42C22×D4112yes—
873C42C22×D4112yes—
874C23—248no—
875C23—26no—
876C23—21no—
877C23—22no—
878C23—26no—
879C23—26no—
880C23—26no—
881C23—23no—
882C23—26no—
883C23—22no—
884C23—26no—
885C23—26no—
886C23—26no—
887C23—23no—
888C23—21no—
889C23—23no—
890C23—26no—
891C23—23no—
892C23—23no—
893C23—26no—
894C23—812no—
895C23—824no—
896C23—824no—
897C23—812no—
898C23C23×D416yes—
899C23C22×#41112yes—
900C23C2×H(5,𝔽2)12yes—
901C23C2611yescharacteristic
902Q8—28no—
903Q8—412no—
904Q8—412no—
905Q8#525116yescomplemented
906D4—224no—
907D4—248no—
908D4—224no—
909D4—248no—
910D4—424no—
911D4—412no—
912D4—412no—
913D4—424no—
914D4—412no—
915D4—412no—
916D4—824no—
917D4—812no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—23no—
924C2×C4—26no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—23no—
928C2×C4—21no—
929C2×C4—224no—
930C2×C4—248no—
931C2×C4—224no—
932C2×C4—28no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—23no—
937C2×C4—23no—
938C2×C4—26no—
939C2×C4—23no—
940C2×C4—22no—
941C2×C4—26no—
942C2×C4—26no—
943C2×C4—22no—
944C2×C4—26no—
945C2×C4—26no—
946C2×C4—26no—
947C2×C4—26no—
948C2×C4—23no—
949C2×C4—22no—
950C2×C4—26no—
951C2×C4—22no—
952C2×C4—26no—
953C2×C4—26no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—23no—
958C2×C4—26no—
959C2×C4—412no—
960C2×C4—412no—
961C2×C4—412no—
962C2×C4—424no—
963C2×C4—412no—
964C2×C4—812no—
965C2×C4—86no—
966C2×C4—86no—
967C2×C4—824no—
968C2×C4—812no—
969C2×C4C23×D416yes—
970C2×C4C23×D412yes—
971C2×C4C23×D412yes—
972C2×C4C23×D416yes—
973C2×C4C23×D416yes—
974C2×C4C23×D412yes—
975C2×C4C22×#4114yes—
976C2×C4C22×#41112yes—
977C2×C4C2×H(5,𝔽2)12yes—
978C2×C4C2×H(5,𝔽2)12yes—
979C2×C4#58514yes—
980C2×C4#58512yes—
981C22—26no—
982C22—22no—
983C22—24no—
984C22—212no—
985C22—212no—
986C22—26no—
987C22—26no—
988C22—212no—
989C22—46no—
990C22—46no—
991C22—46no—
992C22—42no—
993C22—46no—
994C22—46no—
995C22—41no—
996C22—46no—
997C22—41no—
998C22—43no—
999C22—46no—
1000C22—46no—
1001C22—43no—
1002C22—43no—
1003C22—848no—
1004C22C24×D411yescharacteristic
1005C22C23×#4112yes—
1006C22C22×H(5,𝔽2)11yescharacteristic
1007C22C2×#58511yescharacteristic
1008C22C2×#58512yes—
1009C4—26no—
1010C4—22no—
1011C4—24no—
1012C4—22no—
1013C4—26no—
1014C4—22no—
1015C4—24no—
1016C4—46no—
1017C4—43no—
1018C4—46no—
1019C4—46no—
1020C4—42no—
1021C4—42no—
1022C4—41no—
1023C4—43no—
1024C4—41no—
1025C4—43no—
1026C4C2×#525112yes—
1027C4#348814yes—
1028C2—42no—
1029C2—46no—
1030C2—412no—
1031C2—83no—
1032C2C22×#52511yescharacteristic
1033C2C2×#348811yescharacteristic
1034C2#6280012yes—
1035C2#6281012yes—
1036C2#6281211yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3480C2semidirect
2. C2×C4×H(5,𝔽2)C2semidirect
3. #36091C2semidirect
4. #36089C2semidirect
5. #36083C2semidirect
6. #36082C2semidirect
7. #36076C2semidirect
8. #36075C2semidirect
9. #35996C2semidirect
10. #35995C2semidirect
11. #35831C2semidirect
12. #35823C2semidirect
13. #35816C2semidirect
14. #35808C2semidirect
15. #34965C2semidirect
16. #34935C2semidirect
17. #34700C2semidirect
18. #34681C2semidirect
19. #34614C2semidirect
20. #34547C2semidirect
21. C4×#550C2semidirect
22. C4×#548C2semidirect
23. #34129C2semidirect
26. C2×#559C22semidirect
27. C2×#557C22semidirect
28. C2×#556C22semidirect
29. C2×#553C22semidirect
30. C2×#553C22semidirect
35. C2×#548C22semidirect
36. C2×#532C22semidirect
37. C2×#529C22semidirect
38. C2×#529C22semidirect
39. C2×#525C22semidirect
49. C2×C4×#41C22semidirect
50. C2×C4×#41C22semidirect
51. C22×C4×Q8C22semidirect
54. #2637C22semidirect
55. #2636C22semidirect
56. #2630C22semidirect
57. #2629C22semidirect
58. #2625C22semidirect
59. #2624C22semidirect
60. #2620C22semidirect
63. #2603C22semidirect
64. #2603C22semidirect
65. #2566C22semidirect
66. #2544C22semidirect
67. #2538C22semidirect
68. #2537C22semidirect
69. #2536C22semidirect
70. #2535C22semidirect
71. #2534C22semidirect
72. #2534C22semidirect
73. #2504C22semidirect
74. #2502C22semidirect
75. #2486C22semidirect
76. #2486C22semidirect
77. #2480C22semidirect
78. #2472C22semidirect
79. #2468C22semidirect
80. #2464C22semidirect
81. #2461C22semidirect
82. #2457C22semidirect
83. #2454C22semidirect
84. #2452C22semidirect
85. #2447C22semidirect
86. #2445C22semidirect
87. #2442C22semidirect
88. #2440C22semidirect
93. #2428C22semidirect
94. #2427C22semidirect
95. #2424C22semidirect
96. #2422C22semidirect
97. #2420C22semidirect
98. #2418C22semidirect
99. #2417C22semidirect
100. #2416C22semidirect
101. #2411C22semidirect
106. #2399C22semidirect
107. #2398C22semidirect
108. #2398C22semidirect
109. #2397C22semidirect
110. #2396C22semidirect
111. #2396C22semidirect
112. #2396C22semidirect
113. #2395C22semidirect
114. #2395C22semidirect
115. #2395C22semidirect
116. #2392C22semidirect
117. #2392C22semidirect
118. #2392C22semidirect
119. #2392C22semidirect
120. #2392C22semidirect
121. #2392C22semidirect
122. #2392C22semidirect
125. #2388C22semidirect
126. #2367C22semidirect
127. #2366C22semidirect
128. #2363C22semidirect
129. #2363C22semidirect
130. #2362C22semidirect
131. #2361C22semidirect
132. #2354C22semidirect
133. #2354C22semidirect
134. #2352C22semidirect
135. #2351C22semidirect
136. Q8×C4⋊C4C22semidirect
137. Q8×C4⋊C4C22semidirect
138. #2346C22semidirect
139. #2346C22semidirect
144. #2341C22semidirect
145. Q8×C22⋊C4C22semidirect
146. C4×#127C22semidirect
147. C4×#124C22semidirect
148. C4×C22⋊Q8C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C4×#120C22semidirect
153. #2293C22semidirect
154. #2285C22semidirect
155. #2280C22semidirect
156. C42×Q8C22semidirect
157. C42×D4C22semidirect
158. C42×D4C22semidirect
159. C4×#117C22semidirect
225. C4×#41D4semidirect
442. C2×#41#41semidirect
772. C22×C4H(5,𝔽2)semidirect
905. Q8#525semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
C2×C4×H(5,𝔽2)2
#360912
#360892
#360832
#360822
#360762
#360752
#359962
#359952
#358312
#358232
#358162
#358082
#349652
#349352
#347002
#346812
#346142
#345472
C4×#5502
C4×#5482
#341292