Finite Group Databasebeta

← #6344234

Subgroups — #6344234

Order 512.

2787 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62833C211yesmaximal, characteristic
2#60294C211yesmaximal, characteristic, complemented
3#60269C211yesmaximal, characteristic, complemented
4#17775C214yesmaximal, complemented
5#17774C214yesmaximal, complemented
6#17767C214yesmaximal, complemented
7#17765C212yesmaximal, complemented
8#17761C212yesmaximal, complemented
9#17759C214yesmaximal, complemented
10#17753C211yesmaximal, characteristic, complemented
11C2×#1556C211yesmaximal, characteristic, complemented
12#17727C212yesmaximal, complemented
13#17723C212yesmaximal, complemented
14#17713C211yesmaximal, characteristic, complemented
15C2×#1549C211yesmaximal, characteristic, complemented
16#3552—22no—
17#3552—22no—
18#3552—22no—
19#3552C414yes—
20#3544—22no—
21#3544C414yes—
22#3511—21no—
23#3511C412yes—
24#3511C2212yes—
25#3511C2212yes—
26#3509—21no—
27#3509C2212yes—
28#3503—21no—
29#3503C412yes—
30#3503C2212yes—
31#3503C2212yes—
32#3499—21no—
33#3499C2212yes—
34#3492—22no—
35#3492C414yes—
36#3486—22no—
37#3444C2211yescharacteristic
38#3444C2211yescharacteristic
39C22×C4⋊Q8C2211yescharacteristic
40#2995—22no—
41#2992—22no—
42#2990C2214yes—
43#2990C2214yes—
44#2989C2214yes—
45#2989C2212yes—
46#2988C2212yes—
47#2985—21no—
48#2981—21no—
49#2977—22no—
50#2968—22no—
51#2966—22no—
52#2961—21no—
53#2933—22no—
54#2932—21no—
55#2925C2212yes—
56#2925C2214yes—
57C2×#432C2211yescharacteristic
58C2×#432C2211yescharacteristic
59C2×#431C2211yescharacteristic
60#2906C2212yes—
61C2×#423C2211yescharacteristic
62#1561C2214yescomplemented
63#1559C2212yes—
64#1559C2214yescomplemented
65#1557C2212yes—
66#1557C2214yescomplemented
67#1556C2214yes—
68#1556C2214yes—
69#1556C2214yescomplemented
70#1554C2212yes—
71#1554C2214yescomplemented
72#1553C2212yes—
73#1553C2214yescomplemented
74#1552C2212yes—
75#1552C2212yes—
76#1552C2214yescomplemented
77#1552C2214yescomplemented
78#1551C2212yes—
79#1551C2212yes—
80#1550C2212yes—
81#1550C2214yescomplemented
82#1549C2212yes—
83#1549C2214yes—
84#1549C2212yes—
85#1549C2214yescomplemented
86#1547C2212yes—
87#1547C2214yescomplemented
88#1546C2214yescomplemented
89#1544C2214yescomplemented
90#1542C2211yescharacteristic
91#1542C2211yescharacteristic
92#1542C2214yescomplemented
93#1540C2211yescharacteristic
94#1540C2211yescharacteristic
95#1540C2214yescomplemented
96C2×#332C2214yes—
97C2×#332C2212yes—
98C2×#332C2212yes—
99C2×#332C2214yescomplemented
100C2×2−1+4—22no—
101C23×Q8—21no—
102C2×#131—22no—
103C22×M16—21no—
104#563—28no—
105#563—28no—
106Q82—22no—
107Q82C2×C414yes—
108#557—22no—
109#557—22no—
110#557—22no—
111#557C2×C414yes—
112#556—22no—
113#556—22no—
114#556—22no—
115#556C2×C414yes—
116#555—22no—
117#555C2×C414yes—
118#554—24no—
119#554—24no—
120#554—22no—
121#554—24no—
122#554—22no—
123#554C2×C414yes—
124#554C2×C418yes—
125#554C2×C414yes—
126#553—24no—
127#553—24no—
128#553—24no—
129#553C2×C418yes—
130#552—24no—
131#552—24no—
132#552—24no—
133#552C2×C418yes—
134D4×Q8—24no—
135D4×Q8—24no—
136D4×Q8—22no—
137D4×Q8—24no—
138D4×Q8—24no—
139D4×Q8—22no—
140D4×Q8—22no—
141D4×Q8C2×C414yes—
142#548—24no—
143#548—24no—
144#548—24no—
145#548—24no—
146#547—24no—
147#547—24no—
148#547—24no—
149#547—22no—
150#547—22no—
151#547—22no—
152#547C2×C418yes—
153#547C2×C414yes—
154#544—24no—
155#544—24no—
156#544—22no—
157#544—24no—
158#544C2×C414yes—
159#544C2×C418yes—
160#542—24no—
161#542—24no—
162#542—24no—
163#542C2×C418yes—
164#541—24no—
165#541—24no—
166#539—28no—
167#539—28no—
168#537—22no—
169#537C2×C414yes—
170#536—22no—
171#536—24no—
172#536—28no—
173#536—22no—
174#536—24no—
175#533—22no—
176#533—22no—
177#533C2×C411yescharacteristic
178#533D411yescharacteristic
179#533D411yescharacteristic
180#533C2311yescharacteristic
181#533C2314yes—
182#533C2311yescharacteristic
183#533C2314yes—
184#533C2311yescharacteristic
185#532—22no—
186#532C2×C411yescharacteristic
187#532D411yescharacteristic
188#532D411yescharacteristic
189#532C2311yescharacteristic
190#532C2311yescharacteristic
191#532C2314yes—
192#532C2311yescharacteristic
193C2×C4⋊Q8—22no—
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8—21no—
196C2×C4⋊Q8—21no—
197C2×C4⋊Q8—21no—
198C2×C4⋊Q8—21no—
199C2×C4⋊Q8—21no—
200C2×C4⋊Q8C2×C412yes—
201C2×C4⋊Q8C2×C412yes—
202C2×C4⋊Q8C2×C412yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2312yes—
207#529—21no—
208#529—21no—
209#529—21no—
210#529—21no—
211#529C2×C412yes—
212#529C2×C412yes—
213#529C2×C412yes—
214#529C2×C412yes—
215#529D412yes—
216#529D412yes—
217#529D412yes—
218#529D412yes—
219#525—21no—
220#525—21no—
221#525—28no—
222#525C2×C412yes—
223#525C2×C412yes—
224#525D412yes—
225#525D412yes—
226#520—22no—
227#520—22no—
228#520C2×C414yes—
229#520C2×C414yes—
230#519—22no—
231C4×#41—21no—
232C4×#41—21no—
233C4×#41C2×C412yes—
234C4×#41C2312yes—
235C4×#41C2312yes—
236C4×#41C2312yes—
237C22×C4⋊C4—21no—
238C22×C4⋊C4C2×C412yes—
239C22×C42C2311yescharacteristic
240#446—24no—
241#446—24no—
242#446—22no—
243#446—24no—
244C8×Q8—22no—
245#436—24no—
246#436—22no—
247#435—24no—
248#435—24no—
249#435—24no—
250#435—24no—
251#435—24no—
252#435—24no—
253#435—24no—
254C8×D4—24no—
255C8×D4—24no—
256C8×D4—22no—
257C8×D4—24no—
258#433—24no—
259#433—24no—
260#433—24no—
261#432—21no—
262#432—21no—
263#432—21no—
264#432—21no—
265#432C2312yes—
266#432C2312yes—
267#432C2314yes—
268#432C2314yes—
269#432C2312yes—
270#432C2312yes—
271#431—21no—
272#431—21no—
273#431C2311yescharacteristic
274#431C2311yescharacteristic
275#431C2314yes—
276#431C2314yes—
277#431C2312yes—
278#424—22no—
279#424—24no—
280#423—21no—
281#423—21no—
282#423C2314yes—
283#423C2312yes—
284#423C2312yes—
285#423C2314yes—
286C2×C4⋊C8—21no—
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2312yes—
290C2×C4⋊C8C2312yes—
291C2×C4⋊C8C2312yes—
292C2×C4⋊C8C2314yes—
293C2×C4⋊C8C2314yes—
294#408—22no—
295#408—24no—
296C2×C22⋊C8—21no—
297C2×C22⋊C8—21no—
298C2×C22⋊C8—21no—
299#405—22no—
300#405—24no—
301C2×#97—21no—
302C2×#97—21no—
303C2×C4×C8—21no—
304#333C2312yes—
305#333C2312yes—
306#333C2314yes—
307#332C2314yes—
308#332C2314yes—
309#332C2314yes—
310#332C2314yes—
311#332C2314yes—
312#332C2314yes—
313#332C2314yes—
314#332C2314yes—
315#332C2312yes—
316#332C2314yes—
317#332C2312yes—
318#332C2312yes—
319#332C2312yes—
320#332C2314yes—
321#331C2312yes—
322#331C2312yes—
323#331C2314yes—
3242−1+4—88no—
325C2×#41—28no—
326C2×#41—24no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—24no—
330C2×#41C22×C412yes—
331C2×#41C22×C412yes—
332C2×#41C2×D412yes—
333C2×#41C2×D412yes—
334C22×Q8—24no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—24no—
342C22×Q8—84no—
343C23×C4—22no—
344C23×C4C22×C411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347#131—84no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—24no—
351C2×M16—24no—
352C2×M16—82no—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—22no—
356C22×C8—24no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—24no—
360C4⋊Q8—24no—
361C4⋊Q8—24no—
362C4⋊Q8—24no—
363C4⋊Q8—28no—
364C4⋊Q8—28no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8—24no—
378C4⋊Q8—24no—
379C4⋊Q8C22⋊C411yescharacteristic
380C4⋊Q8C22⋊C411yescharacteristic
381C4⋊Q8C22⋊C411yescharacteristic
382C4⋊Q8C22×C414yes—
383C4⋊Q8C22×C414yes—
384C4⋊Q8C22×C414yes—
385C4⋊Q8C22×C418yes—
386C4⋊Q8C2411yescharacteristic
387C4⋊Q8C2414yes—
388C4⋊Q8C2411yescharacteristic
389C4⋊Q8C2411yescharacteristic
390#127C22⋊C411yescharacteristic
391#127C2411yescharacteristic
392#126—28no—
393#126—28no—
394#126—28no—
395#126—28no—
396#126—22no—
397#126—22no—
398#126C22⋊C414yes—
399#126C22⋊C414yes—
400#125—24no—
401#125—24no—
402#125—28no—
403#125—28no—
404#125—28no—
405#125—28no—
406#125—21no—
407#125—21no—
408#125—24no—
409#125C22⋊C412yes—
410#125C22⋊C412yes—
411#125C22⋊C412yes—
412#125C22×C412yes—
413#125C22×C418yes—
414#124—24no—
415#124—28no—
416#124—28no—
417#124—21no—
418#124—21no—
419#124—24no—
420#124C22⋊C412yes—
421#124C22⋊C412yes—
422#124C22⋊C412yes—
423#124C22×C412yes—
424#123—28no—
425#123—22no—
426#123—22no—
427#123—22no—
428#123—28no—
429#123—28no—
430#123—28no—
431#123—28no—
432#123—28no—
433#123C22⋊C414yes—
434#123C22⋊C414yes—
435#123C22⋊C414yes—
436C22⋊Q8—24no—
437C22⋊Q8—24no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8—24no—
445C22⋊Q8—24no—
446C22⋊Q8—24no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C22⋊Q8—28no—
455C22⋊Q8—28no—
456C22⋊Q8—28no—
457C22⋊Q8C22⋊C412yes—
458C22⋊Q8C22⋊C412yes—
459C22⋊Q8C22⋊C412yes—
460C22⋊Q8C22⋊C412yes—
461C22⋊Q8C22⋊C412yes—
462C22⋊Q8C22⋊C412yes—
463C22⋊Q8C22×C412yes—
464C22⋊Q8C22×C412yes—
465C22⋊Q8C22×C418yes—
466#121—28no—
467#121—28no—
468#121—24no—
469#121—24no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—24no—
475#121C22⋊C412yes—
476#121C22⋊C412yes—
477#121C22⋊C412yes—
478#121C22⋊C412yes—
479#121C22⋊C412yes—
480#121C22⋊C412yes—
481#121C22×C412yes—
482#121C22×C412yes—
483#121C22×C418yes—
484#120—22no—
485#120C22⋊C414yes—
486C4×Q8—24no—
487C4×Q8—24no—
488C4×Q8—24no—
489C4×Q8—24no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—24no—
497C4×Q8C22×C412yes—
498C4×Q8C22×C412yes—
499C4×Q8C22×C418yes—
500C4×Q8C22×C412yes—
501C4×Q8C22×C412yes—
502C4×Q8C2×D412yes—
503C4×Q8C2×D412yes—
504C4×Q8C2×D412yes—
505C4×Q8C2×D412yes—
506C4×D4—28no—
507C4×D4—24no—
508C4×D4—28no—
509C4×D4—24no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—24no—
523C4×D4C22×C412yes—
524C4×D4C22×C412yes—
525C4×D4C22×C418yes—
526C4×D4C22×C414yes—
527C4×D4C22×C414yes—
528C4×D4C22×C412yes—
529C4×D4C22×C412yes—
530C4×D4C2×D414yes—
531C4×D4C2×D414yes—
532C4×D4C2×D414yes—
533C4×D4C2×D414yes—
534C4×D4C2×D412yes—
535C4×D4C2×D412yes—
536C4×D4C2×D412yes—
537C4×D4C2×D412yes—
538#117—21no—
539#117—21no—
540#117—24no—
541#117—24no—
542#117—24no—
543#117—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117C22×C412yes—
548#117C22×C418yes—
549#117C22×C412yes—
550#117C22×C414yes—
551#117C2×D412yes—
552#117C2×D412yes—
553#117C2×D414yes—
554#117C2×D414yes—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4C22×C414yes—
568C2×C4⋊C4C22×C414yes—
569C2×C4⋊C4C22×C414yes—
570C2×C4⋊C4C22×C418yes—
571C2×C42—22no—
572C2×C42C22×C411yescharacteristic
573C2×C42C22×C411yescharacteristic
574C2×C42C22×C411yescharacteristic
575C2×C42C2×D411yescharacteristic
576C2×C42C2×D411yescharacteristic
577C2×C42C2×D411yescharacteristic
578C2×C42C2×D411yescharacteristic
579C2×C42C2×D411yescharacteristic
580C2×C42C2×D411yescharacteristic
581C2×C42C2414yes—
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585C4⋊C8—22no—
586C4⋊C8—22no—
587C4⋊C8—22no—
588C4⋊C8—21no—
589C4⋊C8—24no—
590C4⋊C8—22no—
591C4⋊C8—21no—
592C4⋊C8—22no—
593C4⋊C8—24no—
594C4⋊C8—24no—
595C4⋊C8—24no—
596C4⋊C8C2412yes—
597C4⋊C8C2412yes—
598C4⋊C8C2414yes—
599C4⋊C8C2414yes—
600C4⋊C8C2412yes—
601C4⋊C8C2412yes—
602C22⋊C8—22no—
603C22⋊C8—22no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—22no—
607C22⋊C8—22no—
608C22⋊C8—22no—
609C22⋊C8—24no—
610C22⋊C8—24no—
611C22⋊C8—24no—
612C22⋊C8—24no—
613#97—22no—
614#97—22no—
615#97—22no—
616#97—22no—
617#97—24no—
618#97—24no—
619C4×C8—22no—
620C4×C8—21no—
621C4×C8—21no—
622C4×C8—24no—
623C4×C8—24no—
624C24C2×C22⋊C411yescharacteristic
625#41—24no—
626#41—24no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—42no—
632#41—42no—
633#41—84no—
634#41—84no—
635#41—816no—
636#41—88no—
637C2×Q8—24no—
638C2×Q8—28no—
639C2×Q8—24no—
640C2×Q8—24no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—21no—
644C2×Q8—48no—
645C2×Q8—82no—
646C2×Q8—82no—
647C2×Q8—84no—
648C2×Q8—84no—
649C2×Q8—84no—
650C2×Q8—84no—
651C2×Q8—84no—
652C2×Q8—84no—
653C2×Q8—88no—
654C2×Q8C2×C22⋊C412yes—
655C2×Q8C2×C22⋊C412yes—
656C2×Q8C2×C22⋊C412yes—
657C2×Q8C23×C412yes—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—28no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C2×C22⋊C414yes—
665C2×D4C2×C22⋊C412yes—
666C2×D4C2×C22⋊C414yes—
667C2×D4C2×C22⋊C412yes—
668C2×D4C2×C22⋊C414yes—
669C2×D4C2×C22⋊C412yes—
670C2×D4C23×C412yes—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—28no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—84no—
684C22×C4C2×C22⋊C411yescharacteristic
685C22×C4C2×C22⋊C411yescharacteristic
686C22×C4C2×C22⋊C411yescharacteristic
687C22×C4C2×C22⋊C411yescharacteristic
688C22×C4C2×C22⋊C411yescharacteristic
689C22×C4C2×C22⋊C411yescharacteristic
690C22×C4C2×C22⋊C411yescharacteristic
691C22×C4C2×C22⋊C411yescharacteristic
692C22×C4C2×C22⋊C411yescharacteristic
693C22×C4C23×C411yescharacteristic
694C22×C4C23×C411yescharacteristic
695C22×C4C23×C411yescharacteristic
696C22×C4C23×C414yes—
697C22×C4C22×D411yescharacteristic
698C22×C4C22×D411yescharacteristic
699C22×C4C22×D411yescharacteristic
700C22×C4C22×D411yescharacteristic
701C22×C4C22×D411yescharacteristic
702C22×C4C22×D414yes—
703C22×C4C22×D414yes—
704C22×C4C22×D411yescharacteristic
705M16—44no—
706M16—84no—
707M16—82no—
708M16—84no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—24no—
713C2×C8—24no—
714C2×C8—22no—
715C2×C8—42no—
716C2×C8—42no—
717C2×C8—84no—
718C2×C8—82no—
719C2×C8—82no—
720C2×C8—82no—
721C2×C8—84no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—24no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4C2×C22⋊C412yes—
746C4⋊C4C2×C22⋊C412yes—
747C4⋊C4C2×C22⋊C412yes—
748C4⋊C4C2×C22⋊C412yes—
749C4⋊C4C2×C22⋊C414yes—
750C4⋊C4C2×C22⋊C414yes—
751C4⋊C4C2×C22⋊C412yes—
752C4⋊C4C2×C22⋊C414yes—
753C4⋊C4C2×C22⋊C414yes—
754C4⋊C4C2×C22⋊C412yes—
755C4⋊C4C2×C22⋊C414yes—
756C4⋊C4C2×C22⋊C414yes—
757C4⋊C4C23×C418yes—
758C4⋊C4C23×C412yes—
759C4⋊C4C23×C412yes—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C22⋊C4—28no—
763C22⋊C4—22no—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—28no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4C2×C22⋊C414yes—
774C22⋊C4C2×C22⋊C414yes—
775C22⋊C4C2×C22⋊C414yes—
776C22⋊C4C2×C22⋊C414yes—
777C22⋊C4C2×C22⋊C414yes—
778C22⋊C4C2×C22⋊C414yes—
779C22⋊C4C2×C22⋊C414yes—
780C22⋊C4C2×C22⋊C414yes—
781C22⋊C4C2×C22⋊C414yes—
782C42—22no—
783C42—22no—
784C42—22no—
785C42—28no—
786C42—28no—
787C42C2×C22⋊C411yescharacteristic
788C42C2×C22⋊C411yescharacteristic
789C42C2×C22⋊C411yescharacteristic
790C42C2×C22⋊C411yescharacteristic
791C42C2×C22⋊C411yescharacteristic
792C42C2×C22⋊C411yescharacteristic
793C42C23×C411yescharacteristic
794C42C23×C411yescharacteristic
795C42C23×C411yescharacteristic
796C42C23×C414yes—
797C42C22×D411yescharacteristic
798C42C22×D411yescharacteristic
799C42C22×D414yes—
800C42C22×D414yes—
801C42C22×D411yescharacteristic
802C42C22×D411yescharacteristic
803C42C22×D411yescharacteristic
804C42C22×D411yescharacteristic
805C42C2511yescharacteristic
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23C22×C22⋊C414yes—
811C23C22×C22⋊C411yescharacteristic
812C23C22×C22⋊C411yescharacteristic
813C23C22×C22⋊C411yescharacteristic
814Q8—24no—
815Q8—42no—
816Q8—42no—
817Q8—42no—
818Q8—48no—
819Q8—44no—
820Q8—44no—
821Q8—42no—
822Q8—41no—
823Q8—41no—
824Q8—84no—
825Q8—84no—
826Q8—88no—
827D4—28no—
828D4—28no—
829D4—24no—
830D4—42no—
831D4—42no—
832D4—44no—
833D4—42no—
834D4—44no—
835D4—44no—
836D4—44no—
837D4—42no—
838D4—41no—
839D4—41no—
840D4—88no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—24no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—44no—
873C2×C4—88no—
874C2×C4—84no—
875C2×C4—84no—
876C2×C4—88no—
877C2×C4C22×C22⋊C411yescharacteristic
878C2×C4C22×C22⋊C411yescharacteristic
879C2×C4C22×C22⋊C414yes—
880C2×C4C22×C22⋊C414yes—
881C2×C4C22×C22⋊C411yescharacteristic
882C2×C4C22×C22⋊C411yescharacteristic
883C2×C4C22×C22⋊C411yescharacteristic
884C2×C4C22×C22⋊C411yescharacteristic
885C2×C4C22×C22⋊C411yescharacteristic
886C2×C4C22×C22⋊C411yescharacteristic
887C2×C4C22×C22⋊C414yes—
888C2×C4C22×C22⋊C411yescharacteristic
889C2×C4#57712yes—
890C2×C4#57812yes—
891C2×C4C24×C411yescharacteristic
892C2×C4C23×D411yescharacteristic
893C2×C4C23×D411yescharacteristic
894C8—42no—
895C8—44no—
896C8—42no—
897C8—42no—
898C8—44no—
899C8—42no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—24no—
906C22—21no—
907C22—24no—
908C22—21no—
909C22—24no—
910C22—44no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22#288912yes—
915C22#289812yes—
916C22C23×C22⋊C411yescharacteristic
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—24no—
922C4—21no—
923C4—21no—
924C4—24no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—24no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—48no—
933C4#289812yes—
934C4C2×#57711yescharacteristic
935C4C2×#57811yescharacteristic
936C4#358512yes—
937C2—22no—
938C2—22no—
939C2—44no—
940C2—41no—
941C2—82no—
942C2C2×#288911yescharacteristic
943C2C2×#289811yescharacteristic
944C2#6008711yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
prime radical#62833C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60294C2semidirect
3. #60269C2semidirect
4. #17775C2semidirect
5. #17774C2semidirect
6. #17767C2semidirect
7. #17765C2semidirect
8. #17761C2semidirect
9. #17759C2semidirect
10. #17753C2semidirect
11. C2×#1556C2semidirect
12. #17727C2semidirect
13. #17723C2semidirect
14. #17713C2semidirect
15. C2×#1549C2semidirect
62. #1561C22semidirect
64. #1559C22semidirect
66. #1557C22semidirect
69. #1556C22semidirect
71. #1554C22semidirect
73. #1553C22semidirect
76. #1552C22semidirect
77. #1552C22semidirect
81. #1550C22semidirect
85. #1549C22semidirect
87. #1547C22semidirect
88. #1546C22semidirect
89. #1544C22semidirect
92. #1542C22semidirect
95. #1540C22semidirect
99. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
#628332
#602942
#602692
#177752
#177742
#177672
#177652
#177612
#177592
#177532
C2×#15562
#177272
#177232
#177132
C2×#15492