Finite Group Databasebeta

← #7690692

Subgroups — #7690692

Order 512.

7927 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3523C211yesmaximal, characteristic, complemented
3#59550C216yesmaximal, complemented
4#59418C213yesmaximal, complemented
5#59144C213yesmaximal, complemented
6#59040C213yesmaximal, complemented
7#45175C216yesmaximal, complemented
8#45113C216yesmaximal, complemented
9#39468C213yesmaximal, complemented
10#39435C216yesmaximal, complemented
11#38908C213yesmaximal, complemented
12Q8×#121C212yesmaximal, complemented
13Q8×#121C211yesmaximal, characteristic, complemented
14#36446C211yesmaximal, characteristic, complemented
15#36445C211yesmaximal, characteristic, complemented
16#36406C213yesmaximal, complemented
17#36129C213yesmaximal, complemented
18#35723C212yesmaximal, complemented
19#35687C212yesmaximal, complemented
20#34889C213yesmaximal, complemented
21#34257C212yesmaximal, complemented
22C4×D4×Q8C211yesmaximal, characteristic, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3523—216no—
26#3499—216no—
27C2×#557C2213yes—
28C2×#557C2211yescharacteristic
29C2×#556C2213yes—
30C2×#552C2216yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#547C2213yes—
38C2×#547C2213yes—
39C2×#547C2216yes—
40C2×#541C2216yes—
41C2×#536C2216yes—
42C2×#533C2213yes—
43C2×#532C2213yes—
44C22×C4⋊Q8C2213yes—
45C2×#529C2213yes—
46C2×#519C2212yes—
47C2×C4×#41C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2212yes—
50#2862C2213yes—
51#2857C2216yes—
52#2857C2213yes—
53#2857C2213yes—
54#2715C22112yes—
55#2713C22112yes—
56#2707C22112yes—
57#2695C22112yes—
58#2694C22112yes—
59#2693C22112yes—
60#2691C22112yes—
61#2625C2216yes—
62#2616C2216yes—
63#2568C2213yes—
64#2559C2216yes—
65#2558C22112yes—
66#2557C2216yes—
67#2553C22112yes—
68#2553C22112yes—
69#2550C2213yes—
70#2550C2216yes—
71#2547C2213yes—
72#2546C2213yes—
73#2546C2216yes—
74#2544C2213yes—
75#2542C2213yes—
76#2540C2213yes—
77#2538C2213yes—
78#2538C2213yes—
79#2538C2216yes—
80#2535C2213yes—
81#2521C2216yes—
82#2499C2216yes—
83#2492C2213yes—
84#2490C2213yes—
85#2489C2216yes—
86#2489C2216yes—
87#2485C2216yes—
88#2473C22112yes—
89#2471C22112yes—
90#2464C2216yes—
91#2454C2216yes—
92#2451C2216yes—
93#2446C2216yes—
94#2446C2216yes—
95#2442C2216yes—
96#2442C2216yes—
97#2441C2216yes—
98#2439C2216yes—
99#2434C2216yes—
100#2432C2216yes—
101#2432C2216yes—
102#2429C2216yes—
103#2429C2216yes—
104#2429C2216yes—
105#2428C2211yescharacteristic
106#2427C2216yes—
107#2427C2213yes—
108#2426C2216yes—
109#2423C2216yes—
110#2421C2216yes—
111#2417C2216yes—
112#2417C2216yes—
113#2417C2216yes—
114#2417C2216yes—
115#2409C2216yes—
116#2407C2216yes—
117#2407C2216yes—
118#2395C2216yes—
119#2388C2216yes—
120#2367C2213yes—
121#2365C2213yes—
122#2362C2213yes—
123#2361C2213yes—
124#2360C2216yes—
125#2360C2216yes—
126#2360C2216yes—
127#2352C2216yes—
128#2352C2213yes—
129#2351C2211yescharacteristic
130Q8×C4⋊C4C2211yescharacteristic
131Q8×C4⋊C4C2212yes—
132D4×C4⋊C4C2213yes—
133#2341C2216yes—
134#2341C2212yes—
135#2341C2211yescharacteristic
136#2341C2216yes—
137Q8×C22⋊C4C2216yes—
138Q8×C22⋊C4C2216yes—
139Q8×C22⋊C4C2212yes—
140Q8×C22⋊C4C2212yes—
141Q8×C22⋊C4C2212yes—
142Q8×C22⋊C4C2211yescharacteristic
143Q8×C22⋊C4C2212yes—
144#2311C2216yes—
145#2311C2216yes—
146C4×C4⋊Q8C2213yes—
147C4×#124C2213yes—
148C4×#124C2213yes—
149C4×C22⋊Q8C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2216yes—
152C4×#121C2216yes—
153C4×#121C2213yes—
154C4×#121C2213yes—
155#2297C2216yes—
156#2297C2216yes—
157C42×Q8C2211yescharacteristic
158C42×D4C2213yes—
159C42×D4C2213yes—
160C2×2−1+4—216no—
161C2×2−1+4—216no—
162C2×2−1+4—48no—
163C22×#41C2316yes—
164C22×#41C2316yes—
165C22×#41C2316yes—
166C22×#41C2311yescharacteristic
167C23×Q8C2312yes—
168C23×Q8C2311yescharacteristic
169C23×Q8C2316yes—
170C23×Q8C2312yes—
171#557—224no—
172#557—28no—
173#556—224no—
174#552—248no—
175D4×Q8—216no—
176D4×Q8—216no—
177D4×Q8—28no—
178D4×Q8—48no—
179D4×Q8D4116yescomplemented
180#548—28no—
181#547—224no—
182#547—248no—
183#547—224no—
184#541—248no—
185#536—248no—
186#533—224no—
187#532—224no—
188C2×C4⋊Q8—224no—
189C2×C4⋊Q8C2313yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2313yes—
192C2×C4⋊Q8C2316yes—
193C2×C4⋊Q8C2316yes—
194C2×C4⋊Q8C2316yes—
195C2×C4⋊Q8C2316yes—
196C2×C4⋊Q8C2313yes—
197C2×#127C2311yescharacteristic
198#529—224no—
199C2×#126C2316yes—
200C2×#126C23112yes—
201C2×#125C2313yes—
202C2×#125C2316yes—
203C2×#125C2316yes—
204C2×#125C23112yes—
205C2×#124C2313yes—
206C2×#124C2313yes—
207C2×#124C2316yes—
208C2×#124C2313yes—
209C2×#123C2316yes—
210C2×#123C23112yes—
211C2×#123C23112yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2313yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2313yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C2316yes—
223C2×C22⋊Q8C2316yes—
224C2×#121C2313yes—
225C2×#121C2311yescharacteristic
226C2×#121C2313yes—
227C2×#121C2313yes—
228C2×#121C2316yes—
229C2×#121C2312yes—
230C2×#121C2311yescharacteristic
231#519—216no—
232C4×#41—28no—
233C2×C4×Q8—28no—
234C2×C4×Q8—48no—
235C2×C4×Q8C2313yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2316yes—
242C2×C4×Q8C2316yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2316yes—
245C2×C4×Q8C2313yes—
246C2×C4×Q8C2313yes—
247C2×C4×Q8C2316yes—
248C2×C4×Q8C2316yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2313yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×#117C2316yes—
263C2×#117C2316yes—
264C2×#117C2313yes—
265C2×#117C2316yes—
266C22×C4⋊C4C2313yes—
267C22×C4⋊C4C2316yes—
268C22×C4⋊C4C2316yes—
269C22×C4⋊C4C2316yes—
270C22×C42C2313yes—
271C22×C42C2313yes—
272C22×C42C2316yes—
273#400C23112yes—
274#400C23112yes—
275#400C2316yes—
276#399C2316yes—
277#399C23112yes—
278#398C23112yes—
279#398C2316yes—
280#398C23112yes—
281#398C23112yes—
282#398C23112yes—
283#397C2316yes—
284#397C23112yes—
285#397C2316yes—
286#397C2316yes—
287#397C23112yes—
288#396C23112yes—
289#396C23112yes—
290#396C23112yes—
291#396C23112yes—
292#395C23112yes—
293#395C2316yes—
294#394C2316yes—
295#394C23112yes—
296#394C23112yes—
297#394C2316yes—
298#394C2316yes—
299#394C2312yes—
300#394C2316yes—
301#393C2316yes—
302#392C2312yes—
303#392C2316yes—
304#392C2316yes—
305#391C2316yes—
306#391C2316yes—
307#391C2316yes—
308#391C23112yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#391C2316yes—
315#391C2313yes—
316#391C2316yes—
317#391C2316yes—
318#391C2313yes—
319#391C2313yes—
320#391C2313yes—
321#390C2313yes—
322#390C2316yes—
323#390C23112yes—
324#390C2313yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2313yes—
329#390C2311yescharacteristic
330#390C2316yes—
331#389C2316yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C23112yes—
336#389C23112yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C2316yes—
341#389C2313yes—
342#389C2313yes—
343#389C2313yes—
344#389C2311yescharacteristic
345#389C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C23112yes—
351#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yes—
355#387C2316yes—
356#387C23112yes—
357#387C23112yes—
358#387C23112yes—
359#387C23112yes—
360#387C2316yes—
361#386C23112yes—
362#386C2316yes—
363#386C2316yes—
364#386C2316yes—
365#386C23112yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2312yes—
371#385C23112yes—
372#385C23112yes—
373#385C23112yes—
374#385C2316yes—
375#385C23112yes—
376#385C2316yes—
377#384C2313yes—
378#384C2316yes—
379#382C2313yes—
380#382C2316yes—
381#382C2316yes—
382#382C2313yes—
383#380C2313yes—
384#380C2316yes—
385#380C2316yes—
386#380C23112yes—
387#380C2316yes—
388#380C23112yes—
389#380C2316yes—
390#380C2313yes—
391#380C2316yes—
392#380C2313yes—
393#380C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C23112yes—
397#380C2313yes—
398C4×C4⋊C4C2313yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2313yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2313yes—
409C4×C22⋊C4C2313yes—
410C4×C22⋊C4C23112yes—
411C4×C22⋊C4C23112yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2311yescharacteristic
424C4×C22⋊C4C2316yes—
425C43C2313yes—
4262−1+4—4128no—
427C2×#41—24no—
428C2×#41—224no—
429C2×#41—24no—
430C2×#41—224no—
431C2×#41—224no—
432C2×#41—224no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—412no—
436C2×#41—412no—
437C2×#41—412no—
438C2×#41#4118yes—
439C22×Q8—28no—
440C22×Q8—28no—
441C22×Q8—24no—
442C22×Q8—224no—
443C22×Q8—28no—
444C22×Q8—24no—
445C22×Q8—28no—
446C22×Q8—24no—
447C22×Q8—28no—
448C22×Q8—224no—
449C22×Q8—412no—
450C22×Q8C2×D4116yes—
451C22×Q8C2413yes—
452C22×Q8C2413yes—
453C22×Q8C2416yes—
454C22×Q8C2416yes—
455C22×Q8C2416yes—
456C22×Q8C2411yescharacteristic
457C22×D4C2411yescharacteristic
458C22×D4C2412yes—
459C22×D4C2412yes—
460C22×D4C2413yes—
461C22×D4C2412yes—
462C22×D4C2416yes—
463C22×D4C2416yes—
464C22×D4C2412yes—
465C22×D4C2411yescharacteristic
466C22×D4C2413yes—
467C23×C4C2413yes—
468C23×C4C2413yes—
469C23×C4C2411yescharacteristic
470C23×C4C2416yes—
471C23×C4C2413yes—
472C23×C4C2413yes—
473C23×C4C24112yes—
474C23×C4C2412yes—
475C23×C4C2416yes—
476C23×C4C2413yes—
477C23×C4C2416yes—
478C4⋊Q8—224no—
479C4⋊Q8—224no—
480C4⋊Q8—212no—
481C4⋊Q8—224no—
482C4⋊Q8—212no—
483C4⋊Q8—212no—
484C4⋊Q8—412no—
485C4⋊Q8C2×D4124yes—
486#127—24no—
487#126—224no—
488#126—248no—
489#125—212no—
490#125—224no—
491#125—248no—
492#125—224no—
493#124—212no—
494#124—212no—
495#124—224no—
496#124—46no—
497#123—248no—
498#123—224no—
499#123—248no—
500C22⋊Q8—224no—
501C22⋊Q8—224no—
502C22⋊Q8—224no—
503C22⋊Q8—224no—
504C22⋊Q8—212no—
505C22⋊Q8—212no—
506C22⋊Q8—224no—
507C22⋊Q8—212no—
508C22⋊Q8—412no—
509C22⋊Q8—412no—
510C22⋊Q8—412no—
511C22⋊Q8C2×D4148yes—
512#121—24no—
513#121—212no—
514#121—212no—
515#121—212no—
516#121—24no—
517#121—224no—
518#121—28no—
519C4×Q8—24no—
520C4×Q8—24no—
521C4×Q8—224no—
522C4×Q8—28no—
523C4×Q8—224no—
524C4×Q8—24no—
525C4×Q8—24no—
526C4×Q8—28no—
527C4×Q8—212no—
528C4×Q8—224no—
529C4×Q8—212no—
530C4×Q8—212no—
531C4×Q8—412no—
532C4×Q8—412no—
533C4×Q8C2×D418yes—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—212no—
537C4×D4—212no—
538C4×D4—24no—
539C4×D4—212no—
540C4×D4—212no—
541C4×D4—212no—
542C4×D4—46no—
543C4×D4—46no—
544C4×D4—412no—
545C4×D4C2×D4124yes—
546#117—224no—
547#117—224no—
548#117—212no—
549#117—224no—
550C2×C4⋊C4—212no—
551C2×C4⋊C4—224no—
552C2×C4⋊C4—224no—
553C2×C4⋊C4—412no—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2416yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C24112yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C24112yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C24112yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2413yes—
580C2×C4⋊C4C24112yes—
581C2×C4⋊C4C24112yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2411yescharacteristic
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2413yes—
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C24112yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2411yescharacteristic
617C2×C42—212no—
618C2×C42—212no—
619C2×C42—412no—
620C2×C42C2413yes—
621C2×C42C24112yes—
622C2×C42C2413yes—
623C2×C42C2416yes—
624C2×C42C2413yes—
625C2×C42C2413yes—
626C2×C42C2416yes—
627C2×C42C2413yes—
628C2×C42C2411yescharacteristic
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2411yescharacteristic
634C2×C42C2416yes—
635C2×C42C2416yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638#95C2411yescharacteristic
639#95C2411yescharacteristic
640#95C2416yes—
641#95C2416yes—
642#95C2412yes—
643#95C2413yes—
644#95C2413yes—
645#95C2413yes—
646#95C2413yes—
647#95C2416yes—
648#95C2416yes—
649#95C2416yes—
650#95C24112yes—
651#95C24112yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C24112yes—
662#95C2416yes—
663#95C24112yes—
664C24C2512yes—
665C24C2512yes—
666C24C2513yes—
667C24C2511yescharacteristic
668#41—232no—
669#41—496no—
670#41—496no—
671#41—496no—
672C2×Q8—264no—
673C2×Q8—26no—
674C2×Q8—26no—
675C2×Q8—212no—
676C2×Q8—212no—
677C2×Q8—212no—
678C2×Q8—26no—
679C2×Q8—212no—
680C2×Q8—212no—
681C2×Q8—212no—
682C2×Q8—26no—
683C2×Q8—212no—
684C2×Q8—26no—
685C2×Q8—26no—
686C2×Q8—46no—
687C2×Q8—496no—
688C2×Q8—416no—
689C2×Q8—432no—
690C2×Q8C22×D4124yes—
691C2×Q8C22×D414yes—
692C2×Q8C2×#4114yes—
693C2×Q8H(5,𝔽2)14yes—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—212no—
697C2×D4—24no—
698C2×D4—26no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—26no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—26no—
705C2×D4—22no—
706C2×D4—212no—
707C2×D4—24no—
708C2×D4—26no—
709C2×D4—22no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—42no—
716C2×D4—43no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—46no—
720C2×D4—42no—
721C2×D4—46no—
722C2×D4C22×D414yes—
723C2×D4C2×#41112yes—
724C22×C4—26no—
725C22×C4—212no—
726C22×C4—212no—
727C22×C4—26no—
728C22×C4—224no—
729C22×C4—26no—
730C22×C4—22no—
731C22×C4—26no—
732C22×C4—26no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—224no—
736C22×C4—212no—
737C22×C4—26no—
738C22×C4—212no—
739C22×C4—26no—
740C22×C4—212no—
741C22×C4—24no—
742C22×C4—26no—
743C22×C4—24no—
744C22×C4—22no—
745C22×C4—26no—
746C22×C4—22no—
747C22×C4—26no—
748C22×C4—42no—
749C22×C4—43no—
750C22×C4—43no—
751C22×C4—412no—
752C22×C4—46no—
753C22×C4—46no—
754C22×C4—46no—
755C22×C4C22×D4124yes—
756C22×C4C2×#41112yes—
757C22×C4C2511yescharacteristic
758C22×C4C2513yes—
759C22×C4C2513yes—
760C22×C4C2516yes—
761C22×C4C2513yes—
762C22×C4C2512yes—
763C22×C4C2516yes—
764C22×C4C2511yescharacteristic
765C22×C4C2516yes—
766C22×C4C2513yes—
767C22×C4C2513yes—
768C22×C4C2513yes—
769C22×C4C2516yes—
770C22×C4C2511yescharacteristic
771C22×C4C2511yescharacteristic
772C22×C4C2512yes—
773C22×C4C2511yescharacteristic
774C22×C4C2513yes—
775C22×C4C2511yescharacteristic
776C4⋊C4—212no—
777C4⋊C4—26no—
778C4⋊C4—26no—
779C4⋊C4—212no—
780C4⋊C4—224no—
781C4⋊C4—212no—
782C4⋊C4—26no—
783C4⋊C4—212no—
784C4⋊C4—212no—
785C4⋊C4—212no—
786C4⋊C4—212no—
787C4⋊C4—212no—
788C4⋊C4—22no—
789C4⋊C4—224no—
790C4⋊C4—212no—
791C4⋊C4—26no—
792C4⋊C4—26no—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—26no—
796C4⋊C4—24no—
797C4⋊C4—212no—
798C4⋊C4—26no—
799C4⋊C4—412no—
800C4⋊C4—46no—
801C4⋊C4—43no—
802C4⋊C4—46no—
803C4⋊C4—412no—
804C4⋊C4—412no—
805C4⋊C4C22×D4112yes—
806C4⋊C4C22×D4112yes—
807C4⋊C4C22×D4124yes—
808C4⋊C42−1+414yescomplemented
809C22⋊C4—24no—
810C22⋊C4—212no—
811C22⋊C4—212no—
812C22⋊C4—212no—
813C22⋊C4—26no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—212no—
819C22⋊C4—22no—
820C22⋊C4—24no—
821C22⋊C4—26no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—212no—
825C22⋊C4—42no—
826C22⋊C4—46no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—46no—
830C22⋊C4—43no—
831C22⋊C4—43no—
832C22⋊C4—46no—
833C22⋊C4—46no—
834C22⋊C4—412no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4C22×D4124yes—
838C22⋊C42−1+414yescomplemented
839C42—22no—
840C42—26no—
841C42—26no—
842C42—26no—
843C42—26no—
844C42—26no—
845C42—224no—
846C42—212no—
847C42—26no—
848C42—26no—
849C42—212no—
850C42—22no—
851C42—26no—
852C42—26no—
853C42—46no—
854C42—46no—
855C42—43no—
856C42C22×D4112yes—
857C23—21no—
858C23—23no—
859C23—21no—
860C23—22no—
861C23—21no—
862C23—22no—
863C23—23no—
864C23—23no—
865C23—22no—
866C23—23no—
867C23—22no—
868C23—21no—
869C23—23no—
870C23—21no—
871C23—22no—
872C23—23no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23C23×D414yes—
883C23C22×#4116yes—
884C23C2×2−1+412yes—
885C23C2611yescharacteristic
886Q8—248no—
887Q8—424no—
888Q8—412no—
889Q8—424no—
890Q8—412no—
891Q8#546116yes—
892D4—224no—
893D4—28no—
894D4—48no—
895D4—48no—
896D4—48no—
897D4—424no—
898D4—48no—
899D4—412no—
900D4—424no—
901D4—44no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—26no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—26no—
908C2×C4—21no—
909C2×C4—23no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—23no—
913C2×C4—21no—
914C2×C4—248no—
915C2×C4—224no—
916C2×C4—23no—
917C2×C4—21no—
918C2×C4—26no—
919C2×C4—22no—
920C2×C4—23no—
921C2×C4—23no—
922C2×C4—26no—
923C2×C4—21no—
924C2×C4—23no—
925C2×C4—23no—
926C2×C4—26no—
927C2×C4—23no—
928C2×C4—26no—
929C2×C4—23no—
930C2×C4—26no—
931C2×C4—21no—
932C2×C4—23no—
933C2×C4—21no—
934C2×C4—23no—
935C2×C4—22no—
936C2×C4—26no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—23no—
940C2×C4—26no—
941C2×C4—26no—
942C2×C4—21no—
943C2×C4—23no—
944C2×C4—21no—
945C2×C4—23no—
946C2×C4—23no—
947C2×C4—22no—
948C2×C4—26no—
949C2×C4—412no—
950C2×C4—48no—
951C2×C4—412no—
952C2×C4—448no—
953C2×C4—412no—
954C2×C4—424no—
955C2×C4—44no—
956C2×C4—412no—
957C2×C4—812no—
958C2×C4C23×D416yes—
959C2×C4C23×D4112yes—
960C2×C4C23×D416yes—
961C2×C4C23×D412yes—
962C2×C4C22×#4112yes—
963C2×C4C22×#4116yes—
964C2×C4C2×H(5,𝔽2)16yes—
965C2×C4C2×2−1+412yes—
966C2×C4C2×2−1+414yes—
967C2×C4C2×2−1+412yes—
968C2×C4C2×2−1+412yes—
969C2×C4#58512yes—
970C22—22no—
971C22—24no—
972C22—26no—
973C22—22no—
974C22—24no—
975C22—22no—
976C22—26no—
977C22—24no—
978C22—26no—
979C22—43no—
980C22—41no—
981C22—42no—
982C22—42no—
983C22—43no—
984C22—41no—
985C22—43no—
986C22—42no—
987C22—42no—
988C22—41no—
989C22—43no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22C24×D411yescharacteristic
999C22C23×#4111yescharacteristic
1000C22C22×H(5,𝔽2)11yescharacteristic
1001C22C22×2−1+411yescharacteristic
1002C22C22×2−1+411yescharacteristic
1003C22C2×#58511yescharacteristic
1004C222−1+611yescharacteristic
1005C4—22no—
1006C4—26no—
1007C4—22no—
1008C4—24no—
1009C4—22no—
1010C4—212no—
1011C4—43no—
1012C4—42no—
1013C4—41no—
1014C4—41no—
1015C4—43no—
1016C4—46no—
1017C4—43no—
1018C4—46no—
1019C4—43no—
1020C4—46no—
1021C4—43no—
1022C4C2×#546112yes—
1023C4#349714yes—
1024C2—42no—
1025C2—44no—
1026C2—46no—
1027C2—82no—
1028C2C22×#54611yescharacteristic
1029C2C2×#349711yescharacteristic
1030C2#6280511yescharacteristic
1031C2#6292211yescharacteristic
1032C2D4×2−1+411yescharacteristic
1033C2#6300111yescharacteristic
1034C2#6301611yescharacteristic
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×#3499C2semidirect
2. C2×#3523C2semidirect
3. #59550C2semidirect
4. #59418C2semidirect
5. #59144C2semidirect
6. #59040C2semidirect
7. #45175C2semidirect
8. #45113C2semidirect
9. #39468C2semidirect
10. #39435C2semidirect
11. #38908C2semidirect
12. Q8×#121C2semidirect
13. Q8×#121C2semidirect
14. #36446C2semidirect
15. #36445C2semidirect
16. #36406C2semidirect
17. #36129C2semidirect
18. #35723C2semidirect
19. #35687C2semidirect
20. #34889C2semidirect
21. #34257C2semidirect
22. C4×D4×Q8C2semidirect
23. C4×#548C2semidirect
179. D4×Q8D4semidirect
808. C4⋊C42−1+4semidirect
838. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#35232
#595502
#594182
#591442
#590402
#451752
#451132
#394682
#394352
#389082
Q8×#1212
#364462
#364452
#364062
#361292
#357232
#356872
#348892
#342572
C4×D4×Q82
C4×#5482