Finite Group Databasebeta

← #6343216

Subgroups — #6343216

Order 512.

2925 conjugacy classes of subgroups.

The subgroup lattice has 1119 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62748C211yesmaximal, characteristic
2#60265C211yesmaximal, characteristic, complemented
3#60210C211yesmaximal, characteristic, complemented
4#17521C214yesmaximal, complemented
5#17517C214yesmaximal, complemented
6#17515C212yesmaximal, complemented
7#17511C212yesmaximal, complemented
8#17510C212yesmaximal, complemented
9#17507C212yesmaximal, complemented
10#17505C214yesmaximal, complemented
11#17500C211yesmaximal, characteristic, complemented
12#17487C211yesmaximal, characteristic, complemented
13#17468C214yesmaximal, complemented
14C2×#1483C211yesmaximal, characteristic, complemented
15C2×#1480C211yesmaximal, characteristic, complemented
16#3562—22no—
17#3561—21no—
18#3560—22no—
19#3559C412yes—
20#3558—21no—
21#3558C412yes—
22#3554C412yes—
23#3552C412yes—
24#3546C412yes—
25#3543C412yes—
26#3537C412yes—
27#3536C412yes—
28#3534—22no—
29#3529—22no—
30#3481C2214yes—
31#3480C2212yes—
32D4×#41—22no—
33D4×#41C2212yes—
34#3460C2214yes—
35#3459—22no—
36#3455—21no—
37#3449—21no—
38#3444C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#529C2211yescharacteristic
41#2994—22no—
42#2992—22no—
43#2990C2214yescomplemented
44#2989C2212yescomplemented
45#2988C2212yescomplemented
46#2969—22no—
47#2968—22no—
48#2965C2214yescomplemented
49#2965C2212yescomplemented
50C8×#41C2212yescomplemented
51#2962—21no—
52#2962—21no—
53#2935—21no—
54#2935—21no—
55#2933—22no—
56#2929—22no—
57#2925C2212yescomplemented
58#2922C2212yescomplemented
59#2920C2211yescharacteristic, complemented
60C2×#431C2211yescharacteristic, complemented
61#2906C2212yescomplemented
62C22×C4⋊C8C2211yescharacteristic, complemented
63C4×#131C2212yescomplemented
64C2×C4×M16C2211yescharacteristic, complemented
65#1496C2214yescomplemented
66#1495C2214yescomplemented
67#1494C2214yescomplemented
68#1494C2214yescomplemented
69#1492C2212yescomplemented
70#1492C2212yescomplemented
71#1492C2214yescomplemented
72#1490C2212yescomplemented
73#1490C2212yescomplemented
74#1490C2214yescomplemented
75#1489C2214yescomplemented
76#1488C2214yescomplemented
77#1487C2211yescharacteristic, complemented
78#1487C2211yescharacteristic, complemented
79#1486C2211yescharacteristic, complemented
80#1486C2211yescharacteristic, complemented
81#1486C2214yescomplemented
82#1484C2214yescomplemented
83#1484C2214yescomplemented
84#1483C2212yescomplemented
85#1483C2212yescomplemented
86#1483C2212yescomplemented
87#1483C2212yescomplemented
88#1483C2214yescomplemented
89#1482C2214yescomplemented
90#1482C2214yescomplemented
91#1480C2212yescomplemented
92#1480C2212yescomplemented
93#1480C2212yescomplemented
94#1480C2212yescomplemented
95#1480C2214yescomplemented
96#1478C2214yescomplemented
97#1477C2214yescomplemented
98#1476C2214yescomplemented
99C2×Q8⋊C8C2212yescomplemented
100C2×D4⋊C8C2214yescomplemented
101C2×D4⋊C8C2212yescomplemented
102C2×D4⋊C8C2214yescomplemented
103C22×#41—22no—
104C22×#41—21no—
105C2×#131—22no—
106C2×#131—22no—
107C22×M16—21no—
108C23×C8—21no—
109#563—24no—
110#563—22no—
111#562—22no—
112#562—22no—
113#562—24no—
114#562—24no—
115H(3,𝔽4)—22no—
116#560—24no—
117#560—24no—
118#560—24no—
119#559—22no—
120#559C2×C412yes—
121#559C2×C414yes—
122#557C2×C412yes—
123#556—22no—
124#556C2×C412yes—
125#554C2×C414yes—
126#554C2×C414yes—
127#553—24no—
128#553—24no—
129#553C2×C414yes—
130#553C2×C414yes—
131#553C2×C414yes—
132#551—24no—
133#551—24no—
134#550—22no—
135#550C2×C412yes—
136#550C2×C412yes—
137D4×Q8—22no—
138D4×Q8C2×C412yes—
139#548—22no—
140#548—22no—
141#548—22no—
142#548C2×C414yes—
143#547—24no—
144#547—22no—
145#547C2×C414yes—
146#547C2×C412yes—
147#546—24no—
148#546—24no—
149#546—22no—
150#546—22no—
151#546—24no—
152#546—24no—
153#546—22no—
154#546C2×C414yes—
155#546C2×C414yes—
156D42—22no—
157D42—24no—
158D42C2×C414yes—
159D42C2×C412yes—
160D42C2×C414yes—
161#544C2×C414yes—
162#543—22no—
163#542—22no—
164#542—22no—
165#542—24no—
166#542C2×C414yes—
167#542C2×C414yes—
168#541—22no—
169#540—22no—
170#540—24no—
171#540C2×C414yes—
172#540C2×C414yes—
173#539—24no—
174#539—24no—
175#539—24no—
176#539—22no—
177#539—22no—
178#538—24no—
179#538—24no—
180#538—22no—
181#538—22no—
182#538—22no—
183#538—22no—
184#538—24no—
185#538—24no—
186#537—22no—
187#537—22no—
188#537C2×C414yes—
189#536—22no—
190#536—22no—
191#535—22no—
192#535—22no—
193#535C2×C414yes—
194#535C2×C414yes—
195#534—24no—
196#534—22no—
197#534—22no—
198#534—22no—
199#533C2×C411yescharacteristic
200#533D411yescharacteristic
201#533D411yescharacteristic
202#532—22no—
203#532—24no—
204#532—21no—
205#532—21no—
206#532—21no—
207#532—21no—
208#532C2×C412yes—
209#532C2×C412yes—
210#532C2×C411yescharacteristic
211#532D411yescharacteristic
212#532D411yescharacteristic
213#532C2312yes—
214#532C2312yes—
215#532C2314yes—
216C2×C4⋊Q8C2×C411yescharacteristic
217C2×#127C2×C411yescharacteristic
218#529—24no—
219#529—24no—
220#529—24no—
221#529—21no—
222#529—21no—
223#529—21no—
224#529—21no—
225#529C2×C412yes—
226#529C2×C412yes—
227#529C2×C412yes—
228#529C2×C412yes—
229#529D412yes—
230#529D412yes—
231#529D412yes—
232#529D412yes—
233#529C2312yes—
234#529C2312yes—
235#529C2314yes—
236C2×#126—21no—
237C2×#125C2×C411yescharacteristic
238C2×#124—21no—
239C2×#124C2×C411yescharacteristic
240#525—24no—
241#525—24no—
242#525—24no—
243#525—24no—
244#525—22no—
245#525—24no—
246#525C2×C412yes—
247#525D412yes—
248#525D412yes—
249C2×#123—21no—
250C2×C22⋊Q8C2×C411yescharacteristic
251C2×#121—21no—
252C2×#121C2×C411yescharacteristic
253C2×#121C2×C412yes—
254C4×#41—22no—
255C4×#41C2314yes—
256C4×#41C2312yes—
257C4×#41C2312yes—
258C4×#41C2312yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4—24no—
262C2×C4×D4—21no—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×#117—21no—
267C22×C42C2311yescharacteristic
268#446—24no—
269#446—22no—
270#446—22no—
271#446—24no—
272C8×Q8—22no—
273C8×Q8—22no—
274#436—24no—
275#436—22no—
276#436—22no—
277#435—24no—
278#435—24no—
279#435—24no—
280#435—24no—
281#435—24no—
282#435—24no—
283C8×D4—24no—
284C8×D4—24no—
285C8×D4—24no—
286C8×D4—22no—
287C8×D4—22no—
288#433—24no—
289#433—24no—
290#432—21no—
291#432C2312yes—
292#432C2314yes—
293#431—21no—
294#431—21no—
295#431—21no—
296#431C2312yes—
297#431C2314yes—
298#431C2311yescharacteristic
299#431C2312yes—
300#431C2311yescharacteristic
301#431C2314yes—
302#431C2314yes—
303#424—22no—
304#424—24no—
305#424—22no—
306#423C2311yescharacteristic
307#423C2314yes—
308#423C2311yescharacteristic
309C2×C4⋊C8—21no—
310C2×C4⋊C8—21no—
311C2×C4⋊C8—21no—
312C2×C4⋊C8—21no—
313C2×C4⋊C8C2312yes—
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2312yes—
317C2×C4⋊C8C2314yes—
318#408—22no—
319#408—22no—
320#407—21no—
321C2×C22⋊C8—21no—
322#405—22no—
323#405—24no—
324#405—22no—
325C4×M16—21no—
326C4×M16—21no—
327C4×M16—21no—
328C4×M16C2311yescharacteristic
329C4×M16C2311yescharacteristic
330C4×M16C2312yes—
331C4×M16C2314yes—
332C2×#97—21no—
333C2×C4×C8C2312yes—
334C2×C4×C8C2312yes—
335C2×C4×C8C2314yes—
336Q8⋊C8C2312yes—
337Q8⋊C8C2312yes—
338Q8⋊C8C2312yes—
339Q8⋊C8C2312yes—
340Q8⋊C8C2314yes—
341Q8⋊C8C2314yes—
342D4⋊C8C2312yes—
343D4⋊C8C2314yes—
344D4⋊C8C2314yes—
345D4⋊C8C2312yes—
346D4⋊C8C2314yes—
347D4⋊C8C2314yes—
348D4⋊C8C2314yes—
349D4⋊C8C2312yes—
350D4⋊C8C2312yes—
351D4⋊C8C2314yes—
352D4⋊C8C2314yes—
353D4⋊C8C2314yes—
354D4⋊C8C2314yes—
355D4⋊C8C2314yes—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—24no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—24no—
363C2×#41—22no—
364C2×#41—82no—
365C2×#41—82no—
366C2×#41—84no—
367C2×#41—84no—
368C2×#41C22×C414yes—
369C2×#41C22×C412yes—
370C2×#41C2×D412yes—
371C2×#41C2×D412yes—
372C22×Q8—22no—
373C22×Q8—21no—
374C22×Q8C22×C411yescharacteristic
375C22×D4—21no—
376C22×D4—22no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—22no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4C22×C411yescharacteristic
383C22×D4C22×C412yes—
384C22×D4C22×C414yes—
385C23×C4—21no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4C22×C411yescharacteristic
389C23×C4C2×D411yescharacteristic
390C23×C4C2×D411yescharacteristic
391#131—48no—
392#131—84no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—22no—
396C2×M16—21no—
397C2×M16—24no—
398C2×M16—21no—
399C2×M16—24no—
400C2×M16—44no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—24no—
405C22×C8—21no—
406C22×C8—22no—
407C22×C8—21no—
408C22×C8—24no—
409C22×C8—82no—
410C4⋊Q8—22no—
411C4⋊Q8—24no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414C4⋊Q8C22⋊C411yescharacteristic
415C4⋊Q8C22⋊C411yescharacteristic
416C4⋊Q8C22⋊C411yescharacteristic
417C4⋊Q8C22×C412yes—
418C4⋊Q8C22×C412yes—
419C4⋊Q8C22×C414yes—
420#127—22no—
421#127—24no—
422#127—21no—
423#127—21no—
424#127C22⋊C411yescharacteristic
425#127C22×C412yes—
426#127C22×C412yes—
427#127C22×C414yes—
428#126—24no—
429#126—24no—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
434#126—22no—
435#126—22no—
436#126—22no—
437#126—22no—
438#126—24no—
439#126C22⋊C414yes—
440#126C22⋊C414yes—
441#125—24no—
442#125—24no—
443#125—24no—
444#125—21no—
445#125—21no—
446#125C22⋊C412yes—
447#125C22⋊C412yes—
448#125C22⋊C412yes—
449#125C22×C412yes—
450#125C22×C412yes—
451#125C22×C414yes—
452#124—24no—
453#124—24no—
454#124—22no—
455#124—22no—
456#124—24no—
457#124—24no—
458#124—24no—
459#124—22no—
460#124—22no—
461#124—21no—
462#124—21no—
463#124—22no—
464#124—22no—
465#124—24no—
466#124C22⋊C412yes—
467#124C22⋊C412yes—
468#124C22⋊C412yes—
469#124C22×C412yes—
470#124C22×C412yes—
471#124C22×C414yes—
472#123—22no—
473#123—22no—
474#123—22no—
475#123—22no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123C22⋊C414yes—
495#123C22⋊C414yes—
496#123C22⋊C414yes—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8C22⋊C412yes—
515C22⋊Q8C22⋊C412yes—
516C22⋊Q8C22⋊C412yes—
517C22⋊Q8C22⋊C412yes—
518C22⋊Q8C22⋊C412yes—
519C22⋊Q8C22⋊C412yes—
520C22⋊Q8C22×C412yes—
521C22⋊Q8C22×C412yes—
522C22⋊Q8C22×C414yes—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—24no—
527#121—24no—
528#121—24no—
529#121—24no—
530#121—22no—
531#121—22no—
532#121—21no—
533#121—21no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—22no—
542#121—22no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—24no—
547#121—24no—
548#121—24no—
549#121—24no—
550#121—24no—
551#121—24no—
552#121—24no—
553#121C22⋊C412yes—
554#121C22⋊C412yes—
555#121C22⋊C412yes—
556#121C22⋊C412yes—
557#121C22⋊C412yes—
558#121C22⋊C412yes—
559#121C22×C412yes—
560#121C22×C412yes—
561#121C22×C414yes—
562#121C22×C414yes—
563#121C22×C414yes—
564#121C22×C414yes—
565#121C22×C414yes—
566#120—24no—
567#120—24no—
568#120—24no—
569#120—24no—
570#120—24no—
571#120—24no—
572#120—24no—
573#120—24no—
574#120—24no—
575#120—24no—
576#120—24no—
577#120C22⋊C414yes—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8C22×C412yes—
583C4×Q8C22×C414yes—
584C4×Q8C22×C412yes—
585C4×Q8C22×C412yes—
586C4×Q8C2×D412yes—
587C4×Q8C2×D412yes—
588C4×Q8C2×D412yes—
589C4×Q8C2×D412yes—
590C4×Q8C2412yes—
591C4×D4—24no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—24no—
596C4×D4—22no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—24no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—21no—
612C4×D4—24no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—22no—
616C4×D4—24no—
617C4×D4C22×C412yes—
618C4×D4C22×C414yes—
619C4×D4C22×C414yes—
620C4×D4C22×C414yes—
621C4×D4C22×C414yes—
622C4×D4C22×C414yes—
623C4×D4C22×C414yes—
624C4×D4C22×C412yes—
625C4×D4C22×C412yes—
626C4×D4C2×D414yes—
627C4×D4C2×D412yes—
628C4×D4C2×D412yes—
629C4×D4C2×D414yes—
630C4×D4C2×D414yes—
631C4×D4C2×D414yes—
632C4×D4C2×D412yes—
633C4×D4C2×D412yes—
634C4×D4C2412yes—
635C4×D4C2414yes—
636#117—22no—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—24no—
641#117—24no—
642#117C22×C414yes—
643#117C22×C412yes—
644#117C22×C414yes—
645#117C2×D412yes—
646#117C2×D414yes—
647#117C2×D412yes—
648#117C2×D414yes—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—24no—
655C2×C4⋊C4C22×C412yes—
656C2×C4⋊C4C22×C411yescharacteristic
657C2×C4⋊C4C22×C414yes—
658C2×C4⋊C4C22×C411yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—24no—
669C2×C42—21no—
670C2×C42—24no—
671C2×C42C22×C411yescharacteristic
672C2×C42C22×C411yescharacteristic
673C2×C42C22×C411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C4⋊C8—22no—
685C4⋊C8—21no—
686C4⋊C8—22no—
687C4⋊C8—21no—
688C4⋊C8—21no—
689C4⋊C8—22no—
690C4⋊C8—21no—
691C4⋊C8—24no—
692C4⋊C8—21no—
693C4⋊C8—24no—
694C4⋊C8—21no—
695C4⋊C8—24no—
696C4⋊C8—24no—
697C4⋊C8C2412yes—
698C4⋊C8C2412yes—
699C4⋊C8C2412yes—
700C4⋊C8C2412yes—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—22no—
704C22⋊C8—22no—
705C22⋊C8—22no—
706C22⋊C8—24no—
707C22⋊C8—24no—
708C22⋊C8—24no—
709C22⋊C8—24no—
710#97—21no—
711#97—21no—
712#97—22no—
713#97—22no—
714#97—24no—
715#97—24no—
716C4×C8—22no—
717C4×C8—22no—
718C4×C8—24no—
719C4×C8—22no—
720C4×C8—24no—
721C4×C8C2412yes—
722C4×C8C2412yes—
723C4×C8C2412yes—
724C4×C8C2412yes—
725C24—21no—
726C24—22no—
727C24—24no—
728C24C2×C22⋊C411yescharacteristic
729#41—24no—
730#41—24no—
731#41—44no—
732#41—44no—
733#41—48no—
734#41—44no—
735#41—44no—
736#41—82no—
737#41—84no—
738#41—82no—
739#41—84no—
740#41—84no—
741#41—84no—
742#41—88no—
743#41—84no—
744#41—84no—
745C2×Q8—22no—
746C2×Q8—21no—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—42no—
750C2×Q8—82no—
751C2×Q8—84no—
752C2×Q8C2×C22⋊C412yes—
753C2×Q8C2×C22⋊C412yes—
754C2×Q8C2×C22⋊C412yes—
755C2×Q8C23×C412yes—
756C2×D4—22no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—22no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—44no—
774C2×D4—42no—
775C2×D4—48no—
776C2×D4—82no—
777C2×D4—82no—
778C2×D4—84no—
779C2×D4—88no—
780C2×D4—88no—
781C2×D4—82no—
782C2×D4—84no—
783C2×D4C2×C22⋊C414yes—
784C2×D4C2×C22⋊C414yes—
785C2×D4C2×C22⋊C412yes—
786C2×D4C2×C22⋊C412yes—
787C2×D4C2×C22⋊C412yes—
788C2×D4C2×C22⋊C414yes—
789C2×D4C23×C412yes—
790C2×D4C23×C414yes—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—82no—
811C22×C4—84no—
812C22×C4—82no—
813C22×C4—84no—
814C22×C4C2×C22⋊C411yescharacteristic
815C22×C4C2×C22⋊C411yescharacteristic
816C22×C4C2×C22⋊C411yescharacteristic
817C22×C4C2×C22⋊C411yescharacteristic
818C22×C4C2×C22⋊C411yescharacteristic
819C22×C4C2×C22⋊C411yescharacteristic
820C22×C4C2×C22⋊C411yescharacteristic
821C22×C4C2×C22⋊C411yescharacteristic
822C22×C4C2×C22⋊C411yescharacteristic
823C22×C4C23×C411yescharacteristic
824C22×C4C23×C411yescharacteristic
825C22×C4C23×C411yescharacteristic
826C22×C4C23×C414yes—
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D414yes—
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D414yes—
834C22×C4C22×D411yescharacteristic
835M16—24no—
836M16—44no—
837M16—48no—
838M16—42no—
839M16—42no—
840M16—42no—
841M16—84no—
842C2×C8—22no—
843C2×C8—22no—
844C2×C8—22no—
845C2×C8—22no—
846C2×C8—22no—
847C2×C8—22no—
848C2×C8—22no—
849C2×C8—22no—
850C2×C8—44no—
851C2×C8—48no—
852C2×C8—44no—
853C2×C8—44no—
854C2×C8—81no—
855C2×C8—82no—
856C2×C8—81no—
857C2×C8—84no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4C2×C22⋊C414yes—
878C4⋊C4C2×C22⋊C414yes—
879C4⋊C4C2×C22⋊C414yes—
880C4⋊C4C2×C22⋊C412yes—
881C4⋊C4C2×C22⋊C412yes—
882C4⋊C4C2×C22⋊C412yes—
883C4⋊C4C2×C22⋊C412yes—
884C4⋊C4C2×C22⋊C414yes—
885C4⋊C4C2×C22⋊C414yes—
886C4⋊C4C2×C22⋊C412yes—
887C4⋊C4C2×C22⋊C414yes—
888C4⋊C4C2×C22⋊C412yes—
889C4⋊C4C23×C412yes—
890C4⋊C4C23×C414yes—
891C4⋊C4C23×C412yes—
892C22⋊C4—22no—
893C22⋊C4—24no—
894C22⋊C4—22no—
895C22⋊C4—24no—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—22no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—22no—
915C22⋊C4—24no—
916C22⋊C4C2×C22⋊C414yes—
917C22⋊C4C2×C22⋊C414yes—
918C22⋊C4C2×C22⋊C414yes—
919C22⋊C4C2×C22⋊C414yes—
920C22⋊C4C2×C22⋊C414yes—
921C22⋊C4C2×C22⋊C414yes—
922C22⋊C4C2×C22⋊C414yes—
923C22⋊C4C2×C22⋊C414yes—
924C22⋊C4C2×C22⋊C414yes—
925C42—22no—
926C42—24no—
927C42—24no—
928C42—22no—
929C42C2×C22⋊C411yescharacteristic
930C42C2×C22⋊C411yescharacteristic
931C42C2×C22⋊C411yescharacteristic
932C42C2×C22⋊C411yescharacteristic
933C42C2×C22⋊C411yescharacteristic
934C42C2×C22⋊C411yescharacteristic
935C42C23×C411yescharacteristic
936C42C23×C411yescharacteristic
937C42C23×C411yescharacteristic
938C42C23×C414yes—
939C42C22×D411yescharacteristic
940C42C22×D411yescharacteristic
941C42C22×D414yes—
942C42C22×D411yescharacteristic
943C42C22×D411yescharacteristic
944C42C22×D414yes—
945C42C22×D411yescharacteristic
946C42C22×D411yescharacteristic
947C42C2511yescharacteristic
948C23—22no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—41no—
953C23—42no—
954C23—44no—
955C23—82no—
956C23—84no—
957C23—81no—
958C23—82no—
959C23—84no—
960C23—81no—
961C23—84no—
962C23C22×C22⋊C414yes—
963C23C22×C22⋊C411yescharacteristic
964C23C22×C22⋊C411yescharacteristic
965C23C22×C22⋊C411yescharacteristic
966Q8—24no—
967Q8—24no—
968Q8—42no—
969Q8—42no—
970Q8—44no—
971Q8—81no—
972Q8—82no—
973Q8—84no—
974D4—28no—
975D4—28no—
976D4—24no—
977D4—24no—
978D4—28no—
979D4—42no—
980D4—44no—
981D4—42no—
982D4—48no—
983D4—44no—
984D4—44no—
985D4—82no—
986D4—81no—
987D4—84no—
988D4—82no—
989D4—82no—
990D4—84no—
991D4—82no—
992D4—84no—
993D4—82no—
994D4—84no—
995D4—84no—
996D4—84no—
997D4—84no—
998D4—84no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—28no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—41no—
1019C2×C4—44no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—42no—
1027C2×C4—44no—
1028C2×C4—42no—
1029C2×C4—44no—
1030C2×C4—42no—
1031C2×C4—44no—
1032C2×C4—84no—
1033C2×C4—84no—
1034C2×C4—84no—
1035C2×C4—84no—
1036C2×C4—84no—
1037C2×C4—82no—
1038C2×C4—84no—
1039C2×C4—81no—
1040C2×C4—81no—
1041C2×C4C22×C22⋊C414yes—
1042C2×C4C22×C22⋊C414yes—
1043C2×C4C22×C22⋊C411yescharacteristic
1044C2×C4C22×C22⋊C411yescharacteristic
1045C2×C4C22×C22⋊C411yescharacteristic
1046C2×C4C22×C22⋊C411yescharacteristic
1047C2×C4C22×C22⋊C411yescharacteristic
1048C2×C4C22×C22⋊C411yescharacteristic
1049C2×C4C22×C22⋊C411yescharacteristic
1050C2×C4C22×C22⋊C411yescharacteristic
1051C2×C4C22×C22⋊C414yes—
1052C2×C4C22×C22⋊C411yescharacteristic
1053C2×C4#57612yes—
1054C2×C4#57712yes—
1055C2×C4C24×C411yescharacteristic
1056C2×C4C23×D411yescharacteristic
1057C2×C4C23×D411yescharacteristic
1058C8—24no—
1059C8—42no—
1060C8—42no—
1061C8—42no—
1062C8—42no—
1063C8—42no—
1064C8—42no—
1065C8—42no—
1066C22—21no—
1067C22—21no—
1068C22—21no—
1069C22—21no—
1070C22—21no—
1071C22—24no—
1072C22—21no—
1073C22—24no—
1074C22—21no—
1075C22—24no—
1076C22—44no—
1077C22—44no—
1078C22—42no—
1079C22—42no—
1080C22—44no—
1081C22—44no—
1082C22—42no—
1083C22—164no—
1084C22—162no—
1085C22—168no—
1086C22#289712yes—
1087C22#290112yes—
1088C22C23×C22⋊C411yescharacteristic
1089C4—21no—
1090C4—21no—
1091C4—21no—
1092C4—24no—
1093C4—21no—
1094C4—21no—
1095C4—24no—
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—24no—
1101C4—42no—
1102C4—42no—
1103C4—44no—
1104C4—42no—
1105C4#289712yes—
1106C4#357312yes—
1107C4C2×#57611yescharacteristic
1108C4C2×#57711yescharacteristic
1109C2—22no—
1110C2—22no—
1111C2—41no—
1112C2—44no—
1113C2—84no—
1114C2—82no—
1115C2#6006511yescharacteristic
1116C2C2×#289711yescharacteristic
1117C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62748C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60265C2semidirect
3. #60210C2semidirect
4. #17521C2semidirect
5. #17517C2semidirect
6. #17515C2semidirect
7. #17511C2semidirect
8. #17510C2semidirect
9. #17507C2semidirect
10. #17505C2semidirect
11. #17500C2semidirect
12. #17487C2semidirect
13. #17468C2semidirect
14. C2×#1483C2semidirect
15. C2×#1480C2semidirect
43. #2990C22semidirect
44. #2989C22semidirect
45. #2988C22semidirect
48. #2965C22semidirect
49. #2965C22semidirect
50. C8×#41C22semidirect
57. #2925C22semidirect
58. #2922C22semidirect
59. #2920C22semidirect
60. C2×#431C22semidirect
61. #2906C22semidirect
62. C22×C4⋊C8C22semidirect
63. C4×#131C22semidirect
64. C2×C4×M16C22semidirect
65. #1496C22semidirect
66. #1495C22semidirect
67. #1494C22semidirect
68. #1494C22semidirect
69. #1492C22semidirect
70. #1492C22semidirect
71. #1492C22semidirect
72. #1490C22semidirect
73. #1490C22semidirect
74. #1490C22semidirect
75. #1489C22semidirect
76. #1488C22semidirect
77. #1487C22semidirect
78. #1487C22semidirect
79. #1486C22semidirect
80. #1486C22semidirect
81. #1486C22semidirect
82. #1484C22semidirect
83. #1484C22semidirect
84. #1483C22semidirect
85. #1483C22semidirect
86. #1483C22semidirect
87. #1483C22semidirect
88. #1483C22semidirect
89. #1482C22semidirect
90. #1482C22semidirect
91. #1480C22semidirect
92. #1480C22semidirect
93. #1480C22semidirect
94. #1480C22semidirect
95. #1480C22semidirect
96. #1478C22semidirect
97. #1477C22semidirect
98. #1476C22semidirect
99. C2×Q8⋊C8C22semidirect
100. C2×D4⋊C8C22semidirect
101. C2×D4⋊C8C22semidirect
102. C2×D4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627482
#602652
#602102
#175212
#175172
#175152
#175112
#175102
#175072
#175052
#175002
#174872
#174682
C2×#14832
C2×#14802