Finite Group Databasebeta

← #10580253

Subgroups — #10580253

Order 512.

6278 conjugacy classes of subgroups.

The subgroup lattice has 1049 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#62148C212yesmaximal, complemented
4#62133C216yesmaximal, complemented
5#62000C212yesmaximal, complemented
6#61985C216yesmaximal, complemented
7#61900C212yesmaximal, complemented
8#61837C212yesmaximal, complemented
9#61730C216yesmaximal, complemented
10#61595C216yesmaximal, complemented
11#61447C2112yesmaximal, complemented
12#61435C214yesmaximal, complemented
13#60952C213yesmaximal, complemented
14#60943C213yesmaximal, complemented
15#60562C213yesmaximal, complemented
16#60536C213yesmaximal, complemented
17#60278C211yesmaximal, characteristic, complemented
18#3523C2212yes—
19#3520C2216yes—
20#3518—21no—
21#3515—23no—
22#3511C2213yescomplemented
23#3509C2213yescomplemented
24#3503C2211yescharacteristic, complemented
25#3499C2211yescharacteristic, complemented
26#3495—23no—
27#3489—21no—
28#3482—21no—
29#3482—23no—
30#3482—23no—
31#3482—21no—
32#3482C2216yes—
33#3482C2216yes—
34#3482C2212yes—
35#3482C2212yes—
36#3482C2212yescomplemented
37#3482C2216yescomplemented
38Q8×#41—21no—
39C2×#557C2211yescharacteristic
40#3475—23no—
41C2×#556C2213yes—
42C2×#552—23no—
43C2×D4×Q8C2211yescharacteristic
44C2×#548—21no—
45C2×#547C2213yes—
46#3461—23no—
47#3444C2213yes—
48C2×#533C2213yes—
49C2×#533C2213yes—
50C2×#529—23no—
51C4×2−1+4—21no—
52C2×C4×#41C2213yes—
53C2×C4×#41C2211yescharacteristic
54C22×C4×Q8—21no—
55#3398C22112yescomplemented
56#3395C2214yescomplemented
57#3386C22112yescomplemented
58Q8×D8C2214yescomplemented
59#3374C22112yescomplemented
60#3367C22112yescomplemented
61#3359C2214yescomplemented
62#3359C2214yescomplemented
63#3353C22112yescomplemented
64#3349C22124yescomplemented
65#3342C22112yescomplemented
66#3330C22112yescomplemented
67#3328C22112yescomplemented
68#3315C22124yescomplemented
69#3313C22124yescomplemented
70#3302C22112yescomplemented
71#3302C22112yescomplemented
72#3283C22112yescomplemented
73#3276C22112yescomplemented
74#3269C22124yescomplemented
75#3255C2216yescomplemented
76#3254C2216yescomplemented
77#3249C22112yescomplemented
78#3239C2216yes—
79#3237C2216yescomplemented
80#3230C2216yes—
81#3230C2216yescomplemented
82#3218C2216yes—
83#3216C2216yescomplemented
84#3209C2216yes—
85#3209C2216yescomplemented
86#3196C22112yes—
87#3189C22112yes—
88#3172C22112yescomplemented
89#3170C22112yescomplemented
90#3116C22112yescomplemented
91#3113C2216yes—
92#3110C2216yes—
93#3108C2216yes—
94#3107C22112yescomplemented
95#3107C22112yescomplemented
96#3107C2216yescomplemented
97#3106C2216yescomplemented
98#3105C2216yes—
99#3104C2213yes—
100#3104C2216yes—
101#3104C22112yescomplemented
102#3103C2213yes—
103#3102C22112yescomplemented
104#3101C2213yes—
105#3100C2211yescharacteristic
106#3095C2216yes—
107#3091C2216yes—
108#3079C2216yescomplemented
109#3076C2216yescomplemented
110#3039C2216yescomplemented
111#3035C2216yescomplemented
112#3007C2216yes—
113#3002C2216yes—
114#2991C2212yescomplemented
115#2990C2216yescomplemented
116#2984C2212yes—
117#2974C2216yes—
118#2965C2216yescomplemented
119C8×#41C2212yescomplemented
120C4×#137C22112yescomplemented
121C4×#135C22112yescomplemented
122#2920C2213yes—
123C2×#431C2213yes—
124C2×2−1+4—21no—
125C22×#41D411yescharacteristic
126C22×#41C2313yes—
127C23×Q8—21no—
128C2×#137C23112yes—
129C2×#135C23112yes—
130Q82—21no—
131#557—21no—
132#557—23no—
133#557—23no—
134#557C2312yes—
135#557C2312yes—
136#557C2316yes—
137#557C2316yes—
138#556—23no—
139#556—26no—
140#556—23no—
141#556—23no—
142#556—26no—
143#556C2316yes—
144#556C2316yes—
145#556C2316yes—
146#556C2316yes—
147#556C23112yes—
148#555—23no—
149#554—23no—
150#554—23no—
151#554—26no—
152#553—26no—
153#552—26no—
154#552—26no—
155#552—26no—
156#552—212no—
157#552—212no—
158#552—26no—
159#552—26no—
160#552—212no—
161#552—26no—
162#552—26no—
163#552C23112yes—
164#551—212no—
165D4×Q8—22no—
166D4×Q8—21no—
167D4×Q8—23no—
168D4×Q8—21no—
169D4×Q8C2316yes—
170D4×Q8C2312yes—
171D4×Q8C2312yes—
172D4×Q8C2316yes—
173#548—22no—
174#548—22no—
175#548—26no—
176#548—26no—
177#548—22no—
178#548C23112yes—
179#547—26no—
180#547—23no—
181#547—26no—
182#547—23no—
183#547—23no—
184#547C2316yes—
185#547C23112yes—
186#547C2316yes—
187#547C2316yes—
188#547C2316yes—
189#546—26no—
190#544—23no—
191#542—26no—
192#542—26no—
193#541—26no—
194#541—26no—
195#539—212no—
196#537—23no—
197#536—23no—
198#536—23no—
199#533—26no—
200#533—23no—
201#533—23no—
202#533—23no—
203#533—23no—
204#533—23no—
205#533—23no—
206#533—23no—
207#533—23no—
208#533C2313yes—
209#533C2316yes—
210#533C2316yes—
211#533C2316yes—
212#533C2313yes—
213#533C2316yes—
214#533C2316yes—
215#533C2316yes—
216#533C2316yes—
217#533C2313yes—
218#532C2313yes—
219#532C2311yescharacteristic
220#532C2313yes—
221C2×C4⋊Q8C2313yes—
222C2×C4⋊Q8C2313yes—
223C2×C4⋊Q8C2313yes—
224C2×C4⋊Q8C2313yes—
225#529—26no—
226#529—212no—
227#529—26no—
228#529—26no—
229#529—212no—
230#529—26no—
231#529—212no—
232#529—26no—
233#529—23no—
234#529—23no—
235#529—23no—
236#529—23no—
237#529C2316yes—
238#529C2316yes—
239C2×#126—26no—
240C2×#125—23no—
241C2×#125—23no—
242C2×#125—23no—
243C2×#124—23no—
244#525—23no—
245#525—23no—
246#525C2316yes—
247C2×#123—26no—
248C2×C22⋊Q8—23no—
249C2×C22⋊Q8—23no—
250C2×C22⋊Q8—23no—
251C2×C22⋊Q8C2316yes—
252C2×C22⋊Q8C2316yes—
253C2×#121—23no—
254#520—21no—
255#520—26no—
256#520—23no—
257#519—22no—
258#519—23no—
259C4×#41—26no—
260C4×#41—23no—
261C4×#41—23no—
262C4×#41—23no—
263C4×#41—23no—
264C4×#41—23no—
265C4×#41—23no—
266C4×#41D411yescharacteristic
267C4×#41D413yes—
268C4×#41D413yes—
269C4×#41D411yescharacteristic
270C4×#41C2316yes—
271C4×#41C2316yes—
272C4×#41C2316yes—
273C4×#41C2316yes—
274C4×#41C2316yes—
275C4×#41C2311yescharacteristic
276C4×#41C2313yes—
277C4×#41C2311yescharacteristic
278C4×#41C2313yes—
279C2×C4×Q8—21no—
280C2×C4×Q8—22no—
281C2×C4×Q8—26no—
282C2×C4×Q8—22no—
283C2×C4×Q8—26no—
284C2×C4×Q8—22no—
285C2×C4×Q8—23no—
286C2×C4×Q8—23no—
287C2×C4×Q8—23no—
288C2×C4×Q8D411yescharacteristic
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2316yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×D4—23no—
294C2×C4×D4—23no—
295C2×C4×D4D413yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×#117—23no—
300C2×#117—23no—
301C2×#117—23no—
302C2×#117D413yes—
303C2×#117C2313yes—
304C22×C4⋊C4—23no—
305C22×C42—23no—
306C22×C42C2313yes—
307#501C23112yes—
308#500C23112yes—
309#497C23112yes—
310#494C23112yes—
311#491C23112yes—
312#489C23112yes—
313#487C23112yes—
314#487C23112yes—
315#485C23112yes—
316#485C23124yes—
317#485C23124yes—
318#484C23124yes—
319#484C2316yes—
320#484C23112yes—
321#483C2316yes—
322#482C23112yes—
323#481C2316yes—
324#480C2312yes—
325#479C23112yes—
326#478C23112yes—
327#477C2316yes—
328#477C23112yes—
329#477C23124yes—
330#476C2316yes—
331#475C23112yes—
332#475C2316yes—
333#475C23112yes—
334#474C23112yes—
335#474C2312yes—
336#474C23112yes—
337#470C23124yes—
338#468C23124yes—
339#467C23124yes—
340#467C23124yes—
341#464C23112yes—
342#463C23112yes—
343#462C23112yes—
344#462C2316yes—
345#462C23112yes—
346#462C23124yes—
347#462C23112yes—
348#461C23112yes—
349#461C2316yes—
350#461C23112yes—
351#460C2316yes—
352#459C2312yes—
353#452C23112yes—
354#452C23124yes—
355#452C23124yes—
356#451C23124yes—
357#451C2316yes—
358#451C23112yes—
359#450C2316yes—
360#449C23112yes—
361#448C2316yes—
362#447C2312yes—
363#446C23112yes—
364C8×Q8C2314yes—
365#441C23124yes—
366#440C23124yes—
367C4×Q16C23112yes—
368C4×Q16C23112yes—
369C4×Q16C23124yes—
370C4×SD16C23112yes—
371C4×SD16C23112yes—
372C4×SD16C23112yes—
373C4×SD16C23112yes—
374C4×D8C23112yes—
375C4×D8C2314yes—
376#436C23112yes—
377#435C23124yes—
378C8×D4C23112yes—
379#432C2316yes—
380#432C2316yes—
381#431C2311yescharacteristic
382#431C2313yes—
383#431C2316yes—
384#431C2316yes—
385#431C2316yes—
386#431C2316yes—
387#428C23112yes—
388#427C23112yes—
389#423C2316yes—
390C2×C4⋊C8C2316yes—
391#419C23112yes—
392#417C23112yes—
393#416C23112yes—
394#416C23112yes—
395#407C2316yes—
396C2×C22⋊C8C2316yes—
397C4×M16C2316yes—
398C2×C4×C8C2316yes—
3992−1+4—48no—
400C2×#41—26no—
401C2×#41—21no—
402C2×#41—23no—
403C2×#41—23no—
404C2×#41—23no—
405C2×#41—412no—
406C2×#41—44no—
407C2×#41C2×D411yescharacteristic
408C2×#41C2×D411yescharacteristic
409C2×#41C2×D413yes—
410C2×#41C2×D413yes—
411C2×#41C2416yes—
412C2×#41C2416yes—
413C2×#41C2416yes—
414C22×Q8—26no—
415C22×Q8—22no—
416C22×Q8—22no—
417C22×Q8—23no—
418C22×Q8—23no—
419C22×Q8—48no—
420C22×Q8C2×D411yescharacteristic
421C22×Q8C2413yes—
422C22×Q8C2416yes—
423C22×D4—23no—
424C22×D4C2×D413yes—
425C22×D4C2411yescharacteristic
426C23×C4—23no—
427C23×C4—23no—
428C23×C4—21no—
429C23×C4C2×D413yes—
430C23×C4C2×D413yes—
431C23×C4C2413yes—
432#137—424no—
433#135—424no—
434C2×Q16C24112yes—
435C2×Q16C24124yes—
436C2×SD16C24112yes—
437C2×SD16C24112yes—
438C2×D8C2414yes—
439C2×M16C24112yes—
440C22×C8C24112yes—
441C4⋊Q8—26no—
442C4⋊Q8—26no—
443C4⋊Q8—23no—
444C4⋊Q8—23no—
445C4⋊Q8—23no—
446C4⋊Q8—23no—
447C4⋊Q8—23no—
448C4⋊Q8—23no—
449C4⋊Q8—23no—
450C4⋊Q8—23no—
451C4⋊Q8C2413yes—
452C4⋊Q8C2416yes—
453C4⋊Q8C2416yes—
454C4⋊Q8C2416yes—
455C4⋊Q8C2413yes—
456C4⋊Q8C2416yes—
457C4⋊Q8C2416yes—
458C4⋊Q8C2416yes—
459C4⋊Q8C2411yescharacteristic
460#127C2411yescharacteristic
461#126—212no—
462#126—212no—
463#126—212no—
464#126—212no—
465#126—212no—
466#126—212no—
467#126—212no—
468#126—26no—
469#126—26no—
470#125—26no—
471#125—26no—
472#125—212no—
473#125—212no—
474#125—26no—
475#125—212no—
476#125—23no—
477#125—26no—
478#125—26no—
479#125—26no—
480#125—26no—
481#125—26no—
482#125—26no—
483#125—26no—
484#125—23no—
485#125C2416yes—
486#124—26no—
487#124—26no—
488#124—212no—
489#124—26no—
490#124—212no—
491#124—21no—
492#124—23no—
493#124C2416yes—
494#123—212no—
495#123—26no—
496#123—26no—
497#123—26no—
498#123—212no—
499#123—212no—
500#123—212no—
501#123—212no—
502#123—212no—
503#123—212no—
504C22⋊Q8—26no—
505C22⋊Q8—23no—
506C22⋊Q8—26no—
507C22⋊Q8—26no—
508C22⋊Q8—26no—
509C22⋊Q8—26no—
510C22⋊Q8—26no—
511C22⋊Q8—26no—
512C22⋊Q8—26no—
513C22⋊Q8—26no—
514C22⋊Q8—26no—
515C22⋊Q8—26no—
516C22⋊Q8—26no—
517C22⋊Q8—23no—
518C22⋊Q8—23no—
519C22⋊Q8—23no—
520C22⋊Q8—26no—
521C22⋊Q8—26no—
522C22⋊Q8—212no—
523C22⋊Q8—26no—
524C22⋊Q8—26no—
525C22⋊Q8—212no—
526C22⋊Q8—212no—
527C22⋊Q8C2416yes—
528C22⋊Q8C24112yes—
529C22⋊Q8C24112yes—
530C22⋊Q8C24112yes—
531C22⋊Q8C2416yes—
532#121—26no—
533#121—26no—
534#121—212no—
535#121—212no—
536#121—26no—
537#121—21no—
538#121—23no—
539#121—23no—
540#121—23no—
541#121C2412yes—
542#121C2416yes—
543#120—26no—
544C4×Q8—26no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—26no—
548C4×Q8—212no—
549C4×Q8—26no—
550C4×Q8—26no—
551C4×Q8—26no—
552C4×Q8—26no—
553C4×Q8—26no—
554C4×Q8—26no—
555C4×Q8—26no—
556C4×Q8—26no—
557C4×Q8—23no—
558C4×Q8—26no—
559C4×Q8—26no—
560C4×Q8—23no—
561C4×Q8—23no—
562C4×Q8—23no—
563C4×Q8—23no—
564C4×Q8—26no—
565C4×Q8—26no—
566C4×Q8—23no—
567C4×Q8—23no—
568C4×Q8—23no—
569C4×Q8C2×D411yescharacteristic
570C4×Q8C2×D413yes—
571C4×Q8C2×D411yescharacteristic
572C4×Q8C2×D413yes—
573C4×Q8C2×D411yescharacteristic
574C4×Q8C2×D413yes—
575C4×Q8C2416yes—
576C4×Q8C2416yes—
577C4×Q8C2416yes—
578C4×Q8C2416yes—
579C4×Q8C2416yes—
580C4×Q8C24112yes—
581C4×Q8C2416yes—
582C4×Q8C2411yescharacteristic
583C4×Q8C2413yes—
584C4×D4—26no—
585C4×D4—26no—
586C4×D4—26no—
587C4×D4—26no—
588C4×D4—26no—
589C4×D4—26no—
590C4×D4—26no—
591C4×D4—26no—
592C4×D4—26no—
593C4×D4—26no—
594C4×D4—26no—
595C4×D4—26no—
596C4×D4—26no—
597C4×D4—26no—
598C4×D4—26no—
599C4×D4—212no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—23no—
603C4×D4—23no—
604C4×D4—21no—
605C4×D4—23no—
606C4×D4—23no—
607C4×D4—23no—
608C4×D4C2×D413yes—
609C4×D4C2×D413yes—
610C4×D4C2×D416yes—
611C4×D4C2×D413yes—
612C4×D4C2×D416yes—
613C4×D4C2×D413yes—
614C4×D4C2×D413yes—
615C4×D4C2×D416yes—
616C4×D4C2×D413yes—
617C4×D4C2412yes—
618C4×D4C2412yes—
619C4×D4C2416yes—
620C4×D4C2416yes—
621C4×D4C2412yes—
622C4×D4C2416yes—
623C4×D4C2413yes—
624C4×D4C2413yes—
625C4×D4C2416yes—
626#117—23no—
627#117—26no—
628#117—26no—
629#117—26no—
630#117—26no—
631#117—26no—
632#117—26no—
633#117—26no—
634#117—23no—
635#117—23no—
636#117—23no—
637#117—26no—
638#117—212no—
639#117—26no—
640#117—26no—
641#117—26no—
642#117—26no—
643#117—26no—
644#117—26no—
645#117—26no—
646#117C2×D413yes—
647#117C2×D413yes—
648#117C2×D416yes—
649#117C2×D413yes—
650#117C2×D416yes—
651#117C2×D413yes—
652#117C2416yes—
653#117C2416yes—
654#117C2416yes—
655C2×C4⋊C4—23no—
656C2×C4⋊C4—26no—
657C2×C4⋊C4—23no—
658C2×C4⋊C4—23no—
659C2×C4⋊C4—23no—
660C2×C4⋊C4—23no—
661C2×C4⋊C4—23no—
662C2×C4⋊C4—23no—
663C2×C4⋊C4—23no—
664C2×C4⋊C4—26no—
665C2×C4⋊C4—26no—
666C2×C4⋊C4—26no—
667C2×C4⋊C4—212no—
668C2×C4⋊C4—26no—
669C2×C4⋊C4—26no—
670C2×C4⋊C4C2×D413yes—
671C2×C4⋊C4C2×D413yes—
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2416yes—
675C2×C22⋊C4—26no—
676C2×C22⋊C4—26no—
677C2×C22⋊C4—23no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—23no—
680C2×C22⋊C4C2×D416yes—
681C2×C42—23no—
682C2×C42—23no—
683C2×C42—26no—
684C2×C42—23no—
685C2×C42—26no—
686C2×C42—26no—
687C2×C42—26no—
688C2×C42—26no—
689C2×C42—26no—
690C2×C42C2×D413yes—
691C2×C42C2×D413yes—
692C2×C42C2×D413yes—
693C2×C42C2×D413yes—
694C2×C42C2×D413yes—
695C2×C42C2×D413yes—
696C2×C42C2413yes—
697C2×C42C2411yescharacteristic
698C2×C42C2413yes—
699C2×C42C2413yes—
700C2×C42C2413yes—
701C2×C42C2413yes—
702#107C2414yes—
703#107C24112yes—
704#107C24124yes—
705#106C24112yes—
706#106C24112yes—
707C4⋊C8C2412yes—
708C4⋊C8C2416yes—
709C4⋊C8C24112yes—
710C4⋊C8C24112yes—
711#103C24112yes—
712#103C24112yes—
713#103C24112yes—
714#103C24112yes—
715#103C24124yes—
716#103C24124yes—
717#102C2414yes—
718#102C2414yes—
719#102C24112yes—
720#102C24112yes—
721C22⋊C8C2412yes—
722C22⋊C8C2416yes—
723C22⋊C8C24112yes—
724C22⋊C8C24112yes—
725#97C24112yes—
726C4×C8C2412yes—
727C4×C8C2416yes—
728C4×C8C24112yes—
729C24—21no—
730C24C22×D413yes—
731#41—24no—
732#41—24no—
733#41—212no—
734#41—212no—
735#41—46no—
736#41—46no—
737#41—46no—
738#41—46no—
739#41—412no—
740#41—412no—
741#41—412no—
742#41—412no—
743#41—424no—
744#41—44no—
745C2×Q8—24no—
746C2×Q8—21no—
747C2×Q8—26no—
748C2×Q8—26no—
749C2×Q8—23no—
750C2×Q8—26no—
751C2×Q8—23no—
752C2×Q8—26no—
753C2×Q8—46no—
754C2×Q8—412no—
755C2×Q8—412no—
756C2×Q8—412no—
757C2×Q8—424no—
758C2×Q8—48no—
759C2×Q8—48no—
760C2×Q8C22×D413yes—
761C2×Q8C22×D411yescharacteristic
762C2×Q8C2516yes—
763C2×Q8C2516yes—
764C2×D4—24no—
765C2×D4—22no—
766C2×D4—26no—
767C2×D4—26no—
768C2×D4—26no—
769C2×D4—26no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—46no—
774C2×D4—412no—
775C2×D4C22×D413yes—
776C2×D4C22×D413yes—
777C2×D4C22×D416yes—
778C2×D4C2512yes—
779C2×D4C2512yes—
780C22×C4—212no—
781C22×C4—21no—
782C22×C4—23no—
783C22×C4—23no—
784C22×C4—26no—
785C22×C4—26no—
786C22×C4—22no—
787C22×C4—26no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—26no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—26no—
795C22×C4—46no—
796C22×C4—46no—
797C22×C4—412no—
798C22×C4—412no—
799C22×C4—44no—
800C22×C4C22×D413yes—
801C22×C4C22×D413yes—
802C22×C4C22×D413yes—
803C22×C4C22×D413yes—
804C22×C4C22×D413yes—
805C22×C4C22×D413yes—
806C22×C4C22×D413yes—
807C22×C4C22×D413yes—
808C22×C4C22×D413yes—
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D413yes—
811C22×C4C22×D413yes—
812C22×C4C22×D413yes—
813C22×C4C22×D413yes—
814C22×C4C22×D411yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2513yes—
817C22×C4C2513yes—
818Q16—412no—
819Q16—424no—
820SD16—224no—
821SD16—412no—
822D8—28no—
823M16—412no—
824C2×C8—412no—
825C2×C8C2514yes—
826C2×C8C25112yes—
827C4⋊C4—26no—
828C4⋊C4—26no—
829C4⋊C4—212no—
830C4⋊C4—212no—
831C4⋊C4—23no—
832C4⋊C4—23no—
833C4⋊C4—23no—
834C4⋊C4—26no—
835C4⋊C4—212no—
836C4⋊C4—26no—
837C4⋊C4—26no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—26no—
841C4⋊C4—26no—
842C4⋊C4—26no—
843C4⋊C4—26no—
844C4⋊C4—26no—
845C4⋊C4—26no—
846C4⋊C4—26no—
847C4⋊C4—26no—
848C4⋊C4—212no—
849C4⋊C4—21no—
850C4⋊C4—23no—
851C4⋊C4—26no—
852C4⋊C4—21no—
853C4⋊C4—26no—
854C4⋊C4—26no—
855C4⋊C4—26no—
856C4⋊C4—26no—
857C4⋊C4C22×D413yes—
858C4⋊C4C22×D416yes—
859C4⋊C4C22×D413yes—
860C4⋊C4C22×D413yes—
861C4⋊C4C22×D413yes—
862C4⋊C4C22×D416yes—
863C4⋊C4C2512yes—
864C4⋊C4C2512yes—
865C4⋊C4C2516yes—
866C4⋊C4C2516yes—
867C22⋊C4—26no—
868C22⋊C4—212no—
869C22⋊C4—212no—
870C22⋊C4—212no—
871C22⋊C4—26no—
872C22⋊C4—26no—
873C22⋊C4—26no—
874C22⋊C4—26no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—26no—
878C22⋊C4—26no—
879C22⋊C4—26no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—26no—
883C22⋊C4—26no—
884C22⋊C4—26no—
885C22⋊C4C22×D416yes—
886C22⋊C4C22×D416yes—
887C22⋊C4C22×D416yes—
888C22⋊C4C22×D416yes—
889C42—26no—
890C42—26no—
891C42—26no—
892C42—26no—
893C42—26no—
894C42—212no—
895C42—26no—
896C42—26no—
897C42—26no—
898C42—26no—
899C42C22×D413yes—
900C42C22×D413yes—
901C42C22×D411yescharacteristic
902C42C22×D413yes—
903C42C22×D413yes—
904C42C22×D413yes—
905C42C22×D413yes—
906C42C22×D413yes—
907C42C22×D413yes—
908C42C22×D413yes—
909C42C22×D413yes—
910C42C22×D411yescharacteristic
911C42C2513yes—
912C42C2513yes—
913C42C2511yescharacteristic
914C42C2511yescharacteristic
915C23—24no—
916C23—22no—
917C23—26no—
918C23—22no—
919C23—43no—
920C23—43no—
921C23—42no—
922C23—42no—
923C23C23×D413yes—
924C23C23×D413yes—
925C23C23×D411yescharacteristic
926Q8—26no—
927Q8—212no—
928Q8—26no—
929Q8—26no—
930Q8—412no—
931Q8—46no—
932Q8—46no—
933Q8—412no—
934Q8—412no—
935Q8—42no—
936Q8—86no—
937Q8#57514yes—
938D4—24no—
939D4—22no—
940D4—24no—
941D4—26no—
942D4—26no—
943D4—46no—
944D4—42no—
945D4—412no—
946D4—412no—
947D4—412no—
948D4—44no—
949D4—42no—
950D4—86no—
951D4#58514yes—
952C2×C4—26no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—22no—
956C2×C4—26no—
957C2×C4—26no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—26no—
969C2×C4—43no—
970C2×C4—41no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—43no—
975C2×C4—412no—
976C2×C4—412no—
977C2×C4—412no—
978C2×C4—46no—
979C2×C4—46no—
980C2×C4—412no—
981C2×C4—42no—
982C2×C4—412no—
983C2×C4—412no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—86no—
988C2×C4—86no—
989C2×C4#57814yes—
990C2×C4C23×D413yes—
991C2×C4C23×D413yes—
992C2×C4C23×D413yes—
993C2×C4C23×D413yes—
994C2×C4C23×D411yescharacteristic
995C2×C4C23×D411yescharacteristic
996C2×C4C23×D411yescharacteristic
997C2×C4C23×D413yes—
998C2×C4C23×D413yes—
999C2×C4C23×D411yescharacteristic
1000C2×C4C23×D411yescharacteristic
1001C2×C4C2611yescharacteristic
1002C8—24no—
1003C8—212no—
1004C22—21no—
1005C22—21no—
1006C22—23no—
1007C22—23no—
1008C22—24no—
1009C22—23no—
1010C22—23no—
1011C22—23no—
1012C22—23no—
1013C22—48no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—86no—
1020C22C2×#57812yes—
1021C22C24×D411yescharacteristic
1022C4—23no—
1023C4—21no—
1024C4—23no—
1025C4—21no—
1026C4—21no—
1027C4—23no—
1028C4—23no—
1029C4—23no—
1030C4—46no—
1031C4—46no—
1032C4—46no—
1033C4—46no—
1034C4—42no—
1035C4—42no—
1036C4C2×#57516yes—
1037C4C2×#57812yes—
1038C4C2×#57812yes—
1039C4C2×#58512yes—
1040C2—22no—
1041C2—43no—
1042C2—43no—
1043C2—44no—
1044C2—82no—
1045C2#6281111yescharacteristic
1046C2C22×#57511yescharacteristic
1047C2C22×#57811yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62805C2semidirect
2. C2×#3482C2semidirect
3. #62148C2semidirect
4. #62133C2semidirect
5. #62000C2semidirect
6. #61985C2semidirect
7. #61900C2semidirect
8. #61837C2semidirect
9. #61730C2semidirect
10. #61595C2semidirect
11. #61447C2semidirect
12. #61435C2semidirect
13. #60952C2semidirect
14. #60943C2semidirect
15. #60562C2semidirect
16. #60536C2semidirect
17. #60278C2semidirect
22. #3511C22semidirect
23. #3509C22semidirect
24. #3503C22semidirect
25. #3499C22semidirect
36. #3482C22semidirect
37. #3482C22semidirect
55. #3398C22semidirect
56. #3395C22semidirect
57. #3386C22semidirect
58. Q8×D8C22semidirect
59. #3374C22semidirect
60. #3367C22semidirect
61. #3359C22semidirect
62. #3359C22semidirect
63. #3353C22semidirect
64. #3349C22semidirect
65. #3342C22semidirect
66. #3330C22semidirect
67. #3328C22semidirect
68. #3315C22semidirect
69. #3313C22semidirect
70. #3302C22semidirect
71. #3302C22semidirect
72. #3283C22semidirect
73. #3276C22semidirect
74. #3269C22semidirect
75. #3255C22semidirect
76. #3254C22semidirect
77. #3249C22semidirect
79. #3237C22semidirect
81. #3230C22semidirect
83. #3216C22semidirect
85. #3209C22semidirect
88. #3172C22semidirect
89. #3170C22semidirect
90. #3116C22semidirect
94. #3107C22semidirect
95. #3107C22semidirect
96. #3107C22semidirect
97. #3106C22semidirect
101. #3104C22semidirect
103. #3102C22semidirect
108. #3079C22semidirect
109. #3076C22semidirect
110. #3039C22semidirect
111. #3035C22semidirect
114. #2991C22semidirect
115. #2990C22semidirect
118. #2965C22semidirect
119. C8×#41C22semidirect
120. C4×#137C22semidirect
121. C4×#135C22semidirect

Maximal subgroups

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

subgroupindex
#628052
C2×#34822
#621482
#621332
#620002
#619852
#619002
#618372
#617302
#615952
#614472
#614352
#609522
#609432
#605622
#605362
#602782