Finite Group Databasebeta

← #6343243

Subgroups — #6343243

Order 512.

2872 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C211yesmaximal, characteristic
2#60282C211yesmaximal, characteristic, complemented
3C2×#2922C211yesmaximal, characteristic, complemented
4#17524C218yesmaximal, complemented
5#17521C218yesmaximal, complemented
6#17502C212yesmaximal, complemented
7#17488C212yesmaximal, complemented
8#17487C212yesmaximal, complemented
9#17482C212yesmaximal, complemented
10#17480C212yesmaximal, complemented
11C2×#1494C212yesmaximal, complemented
12#3521—24no—
13#3515C414yes—
14#3514C414yes—
15#3507C412yes—
16#3505C412yes—
17#3505C412yes—
18#3501C411yescharacteristic
19#3496C411yescharacteristic
20#3493—21no—
21#3491—21no—
22#3491—21no—
23#3485—21no—
24#3482C2214yes—
25#3481C2214yes—
26#3475—24no—
27#3461—21no—
28#3459—21no—
29#3459—21no—
30#3444C2212yes—
31C2×#529C2212yes—
32C2×#529C2212yes—
33C4×H(5,𝔽2)—21no—
34C2×C4×#41C2211yescharacteristic
35#2990C2218yescomplemented
36#2983—21no—
37#2973—21no—
38#2973—21no—
39#2972—21no—
40#2970—24no—
41#2922—24no—
42#2922C2218yescomplemented
43#2920C2212yescomplemented
44C2×#433—21no—
45C2×#433—21no—
46C2×#432C2212yescomplemented
47C2×#432C2212yescomplemented
48C2×#431C2211yescharacteristic, complemented
49C2×#431C2211yescharacteristic, complemented
50C2×#431C2211yescharacteristic, complemented
51C2×#431C2211yescharacteristic, complemented
52C2×#424—21no—
53C2×#408—21no—
54C2×C4×M16C2211yescharacteristic, complemented
55C22×C4×C8C2211yescharacteristic, complemented
56#1497C2214yescomplemented
57#1496C2214yescomplemented
58#1495C2218yescomplemented
59#1494C2214yescomplemented
60#1494C2214yescomplemented
61#1494C2218yescomplemented
62#1494C2214yescomplemented
63#1494C2214yescomplemented
64#1491C2214yescomplemented
65#1490C2214yescomplemented
66#1488C2218yescomplemented
67#1487C2214yescomplemented
68#1486C2214yescomplemented
69#1483C2218yescomplemented
70#1482C2218yescomplemented
71#1481C2214yescomplemented
72#1480C2214yescomplemented
73#1479C2214yescomplemented
74#1478C2214yescomplemented
75#1477C2218yescomplemented
76C2×Q8⋊C8C2214yescomplemented
77C2×D4⋊C8C2214yescomplemented
78C2×H(5,𝔽2)—21no—
79C22×#41D411yescharacteristic
80C22×M16—21no—
81C23×C8—21no—
82#559C2×C414yes—
83#557C2×C414yes—
84#556—24no—
85#556—24no—
86#556C2×C414yes—
87#555—24no—
88#554—24no—
89#554C2×C414yes—
90#554C2×C414yes—
91#553—24no—
92#553—24no—
93#553—24no—
94#553C2×C414yes—
95#553C2×C414yes—
96#552—24no—
97#552—24no—
98#552—24no—
99#552—24no—
100#552—24no—
101#552—24no—
102#552C2×C414yes—
103#552C2×C414yes—
104#551—24no—
105#551—24no—
106#551—24no—
107#551—24no—
108#551—24no—
109#551—24no—
110D4×Q8C2×C414yes—
111#548C2×C414yes—
112#548C2×C414yes—
113#547—24no—
114#547—24no—
115#547C2×C414yes—
116#546—24no—
117#546—24no—
118#546—24no—
119#546C2×C414yes—
120#546C2×C414yes—
121D42C2×C414yes—
122#544—21no—
123#543—21no—
124#543—21no—
125#542—24no—
126#541—24no—
127#539—24no—
128#539—24no—
129#539—22no—
130#539—22no—
131#539—22no—
132#539—22no—
133#538—24no—
134#538—24no—
135#538—22no—
136#538—22no—
137#537—21no—
138#536—22no—
139#534—22no—
140#534—22no—
141#534—21no—
142#534—21no—
143#533—24no—
144#533C2×C412yes—
145#533C2×C412yes—
146#533C2312yes—
147#532C2×C412yes—
148#532C2×C412yes—
149#532C2312yes—
150#529—24no—
151#529—24no—
152#529—24no—
153#529—22no—
154#529—22no—
155#529—22no—
156#529—22no—
157#529—22no—
158#529—22no—
159#529—22no—
160#529—22no—
161#529—22no—
162#529—22no—
163#529—22no—
164#529—22no—
165#529C2×C414yes—
166#529C2×C414yes—
167#529C2×C414yes—
168#529C2×C414yes—
169#529C2×C414yes—
170#529C2314yes—
171#529C2314yes—
172#529C2314yes—
173C2×#126—22no—
174C2×#126—22no—
175C2×#125C2×C412yes—
176C2×#125C2×C412yes—
177C2×#124C2×C412yes—
178C2×#124C2×C412yes—
179#525—22no—
180#525—22no—
181#525—24no—
182#525—24no—
183#525C2×C414yes—
184C2×#123—22no—
185C2×#123—22no—
186C2×C22⋊Q8C2×C412yes—
187C2×C22⋊Q8C2×C412yes—
188C2×#121C2×C412yes—
189C2×#121C2×C412yes—
190#520—24no—
191#520—22no—
192#518—21no—
193#518—24no—
194#518—22no—
195#518—22no—
196C4×#41—24no—
197C4×#41—22no—
198C4×#41—22no—
199C4×#41C2×C414yes—
200C4×#41D414yes—
201C4×#41D414yes—
202C4×#41C2314yes—
203C4×#41C2314yes—
204C2×C4×Q8C2×C411yescharacteristic
205C2×C4×Q8D411yescharacteristic
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2312yes—
208C2×C4×D4—22no—
209C2×C4×D4—22no—
210C2×C4×D4—24no—
211C2×C4×D4C2×C411yescharacteristic
212C2×C4×D4C2×C411yescharacteristic
213C2×C4×D4C2×C411yescharacteristic
214C2×C4×D4D411yescharacteristic
215C2×C4×D4D411yescharacteristic
216C2×C4×D4D411yescharacteristic
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×#117—22no—
220C2×#117—22no—
221C2×#117D411yescharacteristic
222C2×#117D411yescharacteristic
223C2×#117D411yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#446—28no—
228#435—28no—
229#435—28no—
230C8×D4—28no—
231#433—28no—
232#433—28no—
233#432—22no—
234#432—22no—
235#432—22no—
236#432—22no—
237#432—22no—
238#432C2314yes—
239#432C2314yes—
240#432C2314yes—
241#431—22no—
242#431—22no—
243#431—22no—
244#431—22no—
245#431—22no—
246#431C2314yes—
247#431C2314yes—
248#431C2314yes—
249#431C2314yes—
250#431C2314yes—
251#424—28no—
252#423C2314yes—
253C2×C4⋊C8—21no—
254C2×C4⋊C8—21no—
255C2×C4⋊C8—21no—
256C2×C4⋊C8—21no—
257C2×C4⋊C8C2314yes—
258C2×C4⋊C8C2314yes—
259#408—28no—
260#407—22no—
261C2×C22⋊C8—21no—
262C2×C22⋊C8—21no—
263C2×C22⋊C8—21no—
264C2×C22⋊C8—21no—
265C2×C22⋊C8—22no—
266C2×C22⋊C8—22no—
267C4×M16—22no—
268C4×M16—22no—
269C4×M16C2314yes—
270C2×#97—21no—
271C2×#97—22no—
272C2×#97—22no—
273C2×C4×C8—21no—
274C2×C4×C8—22no—
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2314yes—
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280Q8⋊C8C2318yes—
281Q8⋊C8C2318yes—
282Q8⋊C8C2318yes—
283Q8⋊C8C2318yes—
284D4⋊C8C2318yes—
285D4⋊C8C2318yes—
286D4⋊C8C2318yes—
287D4⋊C8C2318yes—
288H(5,𝔽2)—48no—
289C2×#41—24no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—44no—
293C2×#41C22⋊C414yes—
294C2×#41C22×C414yes—
295C2×#41C2×D414yes—
296C22×Q8C22⋊C411yescharacteristic
297C22×Q8C22×C412yes—
298C22×Q8C22×C412yes—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4C22⋊C411yescharacteristic
303C22×D4C22⋊C411yescharacteristic
304C22×D4C22⋊C411yescharacteristic
305C22×D4C22×C412yes—
306C22×D4C22×C412yes—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4C22×C411yescharacteristic
310C23×C4C22×C411yescharacteristic
311C23×C4C22×C411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—44no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—24no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—24no—
327C22×C8—24no—
328C22×C8—44no—
329C4⋊Q8—24no—
330C4⋊Q8—24no—
331C4⋊Q8C22×C412yes—
332C4⋊Q8C22×C412yes—
333C4⋊Q8C22×C412yes—
334#127C22×C412yes—
335#126—24no—
336#126—24no—
337#126—24no—
338#126—24no—
339#126—24no—
340#126—24no—
341#126—24no—
342#126—24no—
343#126—24no—
344#126—24no—
345#126—24no—
346#126—24no—
347#126—24no—
348#126—24no—
349#125—24no—
350#125—24no—
351#125—24no—
352#125—24no—
353#125—24no—
354#125—22no—
355#125—22no—
356#125—22no—
357#125—22no—
358#125—22no—
359#125—22no—
360#125C22×C414yes—
361#125C22×C414yes—
362#125C22×C414yes—
363#124—24no—
364#124—24no—
365#124—24no—
366#124—22no—
367#124—22no—
368#124—22no—
369#124—22no—
370#124—22no—
371#124—22no—
372#124C22×C414yes—
373#124C22×C414yes—
374#124C22×C414yes—
375#123—24no—
376#123—24no—
377#123—24no—
378#123—24no—
379#123—24no—
380#123—24no—
381#123—24no—
382#123—24no—
383#123—24no—
384#123—24no—
385#123—24no—
386#123—24no—
387#123—24no—
388#123—24no—
389#123—24no—
390#123—24no—
391#123—24no—
392#123—24no—
393#123—24no—
394C22⋊Q8—24no—
395C22⋊Q8—24no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—24no—
405C22⋊Q8—24no—
406C22⋊Q8—24no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410C22⋊Q8—24no—
411C22⋊Q8—24no—
412C22⋊Q8—24no—
413C22⋊Q8C22×C414yes—
414C22⋊Q8C22×C414yes—
415C22⋊Q8C22×C414yes—
416C22⋊Q8C22×C414yes—
417#121—24no—
418#121—24no—
419#121—24no—
420#121—24no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—24no—
430#121—24no—
431#121—24no—
432#121C22×C414yes—
433#121C22×C414yes—
434#121C22×C414yes—
435#121C22×C414yes—
436#120—24no—
437#120—24no—
438#120—24no—
439#120—24no—
440#120—24no—
441C4×Q8—24no—
442C4×Q8—22no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8C22⋊C414yes—
451C4×Q8C22⋊C414yes—
452C4×Q8C22×C414yes—
453C4×Q8C22×C414yes—
454C4×Q8C22×C414yes—
455C4×Q8C22×C414yes—
456C4×Q8C2×D414yes—
457C4×Q8C2414yes—
458C4×D4—24no—
459C4×D4—24no—
460C4×D4—24no—
461C4×D4—24no—
462C4×D4—24no—
463C4×D4—24no—
464C4×D4—24no—
465C4×D4—24no—
466C4×D4—24no—
467C4×D4—24no—
468C4×D4—24no—
469C4×D4—24no—
470C4×D4—24no—
471C4×D4—24no—
472C4×D4—24no—
473C4×D4—24no—
474C4×D4—24no—
475C4×D4—24no—
476C4×D4—24no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4C22⋊C414yes—
486C4×D4C22⋊C414yes—
487C4×D4C22⋊C414yes—
488C4×D4C22⋊C414yes—
489C4×D4C22⋊C414yes—
490C4×D4C22⋊C414yes—
491C4×D4C22×C414yes—
492C4×D4C22×C414yes—
493C4×D4C22×C414yes—
494C4×D4C22×C414yes—
495C4×D4C22×C414yes—
496C4×D4C22×C414yes—
497C4×D4C2×D414yes—
498C4×D4C2×D414yes—
499C4×D4C2×D414yes—
500C4×D4C2414yes—
501#117—22no—
502#117—22no—
503#117—24no—
504#117—24no—
505#117—24no—
506#117—24no—
507#117—24no—
508#117—24no—
509#117—24no—
510#117—24no—
511#117—24no—
512#117—24no—
513#117—24no—
514#117—24no—
515#117C22⋊C414yes—
516#117C22⋊C414yes—
517#117C22⋊C414yes—
518#117C22×C414yes—
519#117C2×D414yes—
520#117C2×D414yes—
521#117C2×D414yes—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4C22⋊C411yescharacteristic
532C2×C4⋊C4C22⋊C411yescharacteristic
533C2×C4⋊C4C22⋊C411yescharacteristic
534C2×C4⋊C4C22⋊C411yescharacteristic
535C2×C4⋊C4C22⋊C411yescharacteristic
536C2×C4⋊C4C22⋊C411yescharacteristic
537C2×C4⋊C4C22×C412yes—
538C2×C4⋊C4C22×C412yes—
539C2×C4⋊C4C22×C412yes—
540C2×C4⋊C4C22×C412yes—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4C22⋊C411yescharacteristic
554C2×C22⋊C4C22⋊C411yescharacteristic
555C2×C22⋊C4C22⋊C411yescharacteristic
556C2×C22⋊C4C22⋊C411yescharacteristic
557C2×C22⋊C4C22⋊C411yescharacteristic
558C2×C22⋊C4C22⋊C411yescharacteristic
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—24no—
562C2×C42C22×C411yescharacteristic
563C2×C42C22×C411yescharacteristic
564C2×C42C22×C411yescharacteristic
565C2×C42C22×C412yes—
566C2×C42C22×C412yes—
567C2×C42C22×C412yes—
568C2×C42C2×D412yes—
569C2×C42C2×D412yes—
570C2×C42C2×D411yescharacteristic
571C2×C42C2×D411yescharacteristic
572C2×C42C2×D411yescharacteristic
573C2×C42C2×D411yescharacteristic
574C2×C42C2×D411yescharacteristic
575C2×C42C2×D411yescharacteristic
576C2×C42C2×D412yes—
577C2×C42C2×D412yes—
578C2×C42C2×D412yes—
579C2×C42C2×D412yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2411yescharacteristic
584C4⋊C8—24no—
585C4⋊C8—24no—
586C4⋊C8—24no—
587C4⋊C8—24no—
588C4⋊C8—24no—
589C4⋊C8—24no—
590C4⋊C8—24no—
591C4⋊C8C2418yes—
592C22⋊C8—24no—
593C22⋊C8—24no—
594C22⋊C8—24no—
595C22⋊C8—24no—
596C22⋊C8—24no—
597C22⋊C8—24no—
598C22⋊C8—24no—
599C22⋊C8—24no—
600#97—24no—
601#97—24no—
602#97—24no—
603#97—24no—
604C4×C8—21no—
605C4×C8—21no—
606C4×C8—24no—
607C4×C8—21no—
608C4×C8—21no—
609C4×C8—24no—
610C4×C8C2412yes—
611C4×C8C2412yes—
612C4×C8C2412yes—
613C4×C8C2412yes—
614C24—22no—
615C24—22no—
616C24C2×C22⋊C411yescharacteristic
617C24C2×C22⋊C411yescharacteristic
618C24C2×C22⋊C411yescharacteristic
619#41—48no—
620#41—48no—
621#41—48no—
622#41—48no—
623#41—416no—
624#41—84no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—42no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8C2×C22⋊C414yes—
633C2×Q8C23×C414yes—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—42no—
648C2×D4—416no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4C2×C22⋊C414yes—
652C2×D4C2×C22⋊C414yes—
653C2×D4C2×C22⋊C414yes—
654C2×D4C23×C414yes—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—84no—
676C22×C4—84no—
677C22×C4C2×C22⋊C412yes—
678C22×C4C2×C22⋊C411yescharacteristic
679C22×C4C2×C22⋊C411yescharacteristic
680C22×C4C2×C22⋊C411yescharacteristic
681C22×C4C2×C22⋊C412yes—
682C22×C4C2×C22⋊C412yes—
683C22×C4C2×C22⋊C412yes—
684C22×C4C2×C22⋊C411yescharacteristic
685C22×C4C2×C22⋊C411yescharacteristic
686C22×C4C2×C22⋊C411yescharacteristic
687C22×C4C2×C22⋊C412yes—
688C22×C4C2×C22⋊C412yes—
689C22×C4C2×C22⋊C412yes—
690C22×C4C2×C22⋊C412yes—
691C22×C4C2×C22⋊C411yescharacteristic
692C22×C4C2×C22⋊C411yescharacteristic
693C22×C4C2×C22⋊C411yescharacteristic
694C22×C4C2×C22⋊C412yes—
695C22×C4C23×C411yescharacteristic
696C22×C4C23×C412yes—
697C22×C4C23×C412yes—
698C22×C4C23×C412yes—
699C22×C4C22×D411yescharacteristic
700C22×C4C22×D412yes—
701C22×C4C22×D411yescharacteristic
702C22×C4C22×D412yes—
703C22×C4C22×D412yes—
704C22×C4C22×D412yes—
705C22×C4C22×D412yes—
706C22×C4C22×D412yes—
707M16—48no—
708M16—84no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—28no—
714C2×C8—42no—
715C2×C8—42no—
716C2×C8—48no—
717C2×C8—42no—
718C2×C8—42no—
719C2×C8—84no—
720C2×C8—84no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—24no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4C2×C22⋊C414yes—
744C4⋊C4C2×C22⋊C414yes—
745C4⋊C4C2×C22⋊C414yes—
746C4⋊C4C2×C22⋊C414yes—
747C4⋊C4C2×C22⋊C414yes—
748C4⋊C4C2×C22⋊C414yes—
749C4⋊C4C23×C414yes—
750C4⋊C4C23×C414yes—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4C2×C22⋊C414yes—
771C22⋊C4C2×C22⋊C414yes—
772C22⋊C4C2×C22⋊C414yes—
773C22⋊C4C2×C22⋊C414yes—
774C22⋊C4C2×C22⋊C414yes—
775C22⋊C4C2×C22⋊C414yes—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—24no—
781C42C2×C22⋊C412yes—
782C42C2×C22⋊C412yes—
783C42C2×C22⋊C412yes—
784C42C2×C22⋊C412yes—
785C42C2×C22⋊C412yes—
786C42C2×C22⋊C412yes—
787C42C2×C22⋊C412yes—
788C42C2×C22⋊C412yes—
789C42C2×C22⋊C412yes—
790C42C23×C411yescharacteristic
791C42C23×C412yes—
792C42C23×C412yes—
793C42C23×C412yes—
794C42C22×D411yescharacteristic
795C42C22×D412yes—
796C42C22×D412yes—
797C42C22×D412yes—
798C42C22×D412yes—
799C42C22×D411yescharacteristic
800C42C22×D412yes—
801C42C22×D412yes—
802C42C2511yescharacteristic
803C23—22no—
804C23—22no—
805C23—24no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—44no—
813C23—44no—
814C23—82no—
815C23—82no—
816C23—82no—
817C23—82no—
818C23#42114yes—
819C23C22×C22⋊C412yes—
820C23C22×C22⋊C412yes—
821C23C22×C22⋊C411yescharacteristic
822C23C22×C22⋊C412yes—
823Q8—28no—
824Q8—44no—
825Q8—44no—
826Q8—82no—
827Q8—82no—
828Q8—82no—
829D4—28no—
830D4—28no—
831D4—28no—
832D4—44no—
833D4—44no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—82no—
838D4—82no—
839D4—82no—
840D4—84no—
841D4—84no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—48no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—48no—
879C2×C4—84no—
880C2×C4—84no—
881C2×C4—84no—
882C2×C4—82no—
883C2×C4—82no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4C22×C22⋊C412yes—
887C2×C4C22×C22⋊C412yes—
888C2×C4C22×C22⋊C412yes—
889C2×C4C22×C22⋊C412yes—
890C2×C4C22×C22⋊C411yescharacteristic
891C2×C4C22×C22⋊C411yescharacteristic
892C2×C4C22×C22⋊C411yescharacteristic
893C2×C4C22×C22⋊C412yes—
894C2×C4C22×C22⋊C412yes—
895C2×C4C22×C22⋊C412yes—
896C2×C4C22×C22⋊C412yes—
897C2×C4C22×C22⋊C412yes—
898C2×C4C24×C411yescharacteristic
899C2×C4C23×D411yescharacteristic
900C2×C4C23×D411yescharacteristic
901C8—42no—
902C8—42no—
903C8—42no—
904C8—42no—
905C8—48no—
906C22—21no—
907C22—22no—
908C22—21no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—82no—
921C22—82no—
922C22—164no—
923C22—164no—
924C22C2×#42112yes—
925C22C2×#42114yes—
926C22C23×C22⋊C411yescharacteristic
927C4—21no—
928C4—22no—
929C4—22no—
930C4—22no—
931C4—21no—
932C4—22no—
933C4—22no—
934C4—22no—
935C4—21no—
936C4—21no—
937C4—22no—
938C4—22no—
939C4—22no—
940C4—44no—
941C4—44no—
942C4—44no—
943C4#357312yes—
944C4#358412yes—
945C2—22no—
946C2—24no—
947C2—42no—
948C2—42no—
949C2—84no—
950C2#6006511yescharacteristic
951C2#6008611yescharacteristic
952C2C22×#42111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62781C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60282C2semidirect
3. C2×#2922C2semidirect
4. #17524C2semidirect
5. #17521C2semidirect
6. #17502C2semidirect
7. #17488C2semidirect
8. #17487C2semidirect
9. #17482C2semidirect
10. #17480C2semidirect
11. C2×#1494C2semidirect
35. #2990C22semidirect
42. #2922C22semidirect
43. #2920C22semidirect
46. C2×#432C22semidirect
47. C2×#432C22semidirect
48. C2×#431C22semidirect
49. C2×#431C22semidirect
50. C2×#431C22semidirect
51. C2×#431C22semidirect
54. C2×C4×M16C22semidirect
55. C22×C4×C8C22semidirect
56. #1497C22semidirect
57. #1496C22semidirect
58. #1495C22semidirect
59. #1494C22semidirect
60. #1494C22semidirect
61. #1494C22semidirect
62. #1494C22semidirect
63. #1494C22semidirect
64. #1491C22semidirect
65. #1490C22semidirect
66. #1488C22semidirect
67. #1487C22semidirect
68. #1486C22semidirect
69. #1483C22semidirect
70. #1482C22semidirect
71. #1481C22semidirect
72. #1480C22semidirect
73. #1479C22semidirect
74. #1478C22semidirect
75. #1477C22semidirect
76. C2×Q8⋊C8C22semidirect
77. C2×D4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627812
#602822
C2×#29222
#175242
#175212
#175022
#174882
#174872
#174822
#174802
C2×#14942