Finite Group Databasebeta

← #6343201

Subgroups — #6343201

Order 512.

2888 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C211yesmaximal, characteristic
2C2×#2990C211yesmaximal, characteristic, complemented
3#60123C211yesmaximal, characteristic, complemented
4#17524C218yesmaximal, complemented
5#17521C218yesmaximal, complemented
6#17502C212yesmaximal, complemented
7#17494C212yesmaximal, complemented
8#17492C212yesmaximal, complemented
9#17466C212yesmaximal, complemented
10#17465C212yesmaximal, complemented
11C2×#1483C212yesmaximal, 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#2990—24no—
36#2990C2218yescomplemented
37C2×#446—21no—
38C2×#435—21no—
39C2×#435—21no—
40C2×C8×D4—21no—
41#2923—24no—
42#2922C2218yescomplemented
43#2921—21no—
44#2921—21no—
45#2920C2212yescomplemented
46#2920C2212yescomplemented
47C2×#432C2211yescharacteristic, complemented
48C2×#432C2211yescharacteristic, complemented
49C2×#431C2211yescharacteristic, complemented
50#2905—21no—
51C2×#423C2211yescharacteristic, complemented
52C22×C4⋊C8C2211yescharacteristic, complemented
53C22×C4⋊C8C2211yescharacteristic, complemented
54#2879—21no—
55C2×C4×M16C2212yescomplemented
56#1497C2214yescomplemented
57#1496C2214yescomplemented
58#1495C2218yescomplemented
59#1494C2218yescomplemented
60#1491C2214yescomplemented
61#1490C2214yescomplemented
62#1488C2218yescomplemented
63#1487C2214yescomplemented
64#1486C2214yescomplemented
65#1483C2214yescomplemented
66#1483C2214yescomplemented
67#1483C2218yescomplemented
68#1483C2214yescomplemented
69#1483C2214yescomplemented
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—22no—
81C22×M16—21no—
82C23×C8—21no—
83C23×C8—21no—
84#559C2×C414yes—
85#557C2×C414yes—
86#556—24no—
87#556—24no—
88#556C2×C414yes—
89#555—24no—
90#554—24no—
91#554C2×C414yes—
92#554C2×C414yes—
93#553—24no—
94#553—24no—
95#553—24no—
96#553C2×C414yes—
97#553C2×C414yes—
98#552—24no—
99#552—24no—
100#552—24no—
101#552—24no—
102#552—24no—
103#552—24no—
104#552C2×C414yes—
105#552C2×C414yes—
106#551—24no—
107#551—24no—
108#551—24no—
109#551—24no—
110#551—24no—
111#551—24no—
112D4×Q8C2×C414yes—
113#548C2×C414yes—
114#548C2×C414yes—
115#547—24no—
116#547—24no—
117#547C2×C414yes—
118#546—24no—
119#546—24no—
120#546—24no—
121#546C2×C414yes—
122#546C2×C414yes—
123D42C2×C414yes—
124#544—21no—
125#543—21no—
126#543—21no—
127#542—24no—
128#541—24no—
129#539—24no—
130#539—24no—
131#539—22no—
132#539—22no—
133#539—22no—
134#539—22no—
135#538—24no—
136#538—24no—
137#538—22no—
138#538—22no—
139#537—21no—
140#536—22no—
141#534—22no—
142#534—22no—
143#534—21no—
144#534—21no—
145#533—24no—
146#533C2×C412yes—
147#533C2×C412yes—
148#533C2312yes—
149#532C2×C412yes—
150#532C2×C412yes—
151#532C2312yes—
152#529—24no—
153#529—24no—
154#529—24no—
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#529—22no—
166#529—22no—
167#529C2×C414yes—
168#529C2×C414yes—
169#529C2×C414yes—
170#529C2×C414yes—
171#529C2×C414yes—
172#529C2314yes—
173#529C2314yes—
174#529C2314yes—
175C2×#126—22no—
176C2×#126—22no—
177C2×#125C2×C412yes—
178C2×#125C2×C412yes—
179C2×#124C2×C412yes—
180C2×#124C2×C412yes—
181#525—22no—
182#525—22no—
183#525—24no—
184#525—24no—
185#525C2×C414yes—
186C2×#123—22no—
187C2×#123—22no—
188C2×C22⋊Q8C2×C412yes—
189C2×C22⋊Q8C2×C412yes—
190C2×#121C2×C412yes—
191C2×#121C2×C412yes—
192#520—24no—
193#520—22no—
194#518—21no—
195#518—24no—
196#518—22no—
197#518—22no—
198C4×#41—24no—
199C4×#41—22no—
200C4×#41—22no—
201C4×#41C2×C414yes—
202C4×#41D414yes—
203C4×#41D414yes—
204C4×#41C2314yes—
205C4×#41C2314yes—
206C2×C4×Q8C2×C411yescharacteristic
207C2×C4×Q8D411yescharacteristic
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2312yes—
210C2×C4×D4—22no—
211C2×C4×D4—22no—
212C2×C4×D4—24no—
213C2×C4×D4C2×C411yescharacteristic
214C2×C4×D4C2×C411yescharacteristic
215C2×C4×D4C2×C411yescharacteristic
216C2×C4×D4D411yescharacteristic
217C2×C4×D4D411yescharacteristic
218C2×C4×D4D411yescharacteristic
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×#117—22no—
222C2×#117—22no—
223C2×#117D411yescharacteristic
224C2×#117D411yescharacteristic
225C2×#117D411yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#446—28no—
230#435—28no—
231#435—28no—
232C8×D4—28no—
233#433—28no—
234#433—28no—
235#432—22no—
236#432—22no—
237#432—22no—
238#432—22no—
239#432—22no—
240#432—22no—
241#432C2314yes—
242#432C2314yes—
243#431—22no—
244#431C2314yes—
245#431C2314yes—
246#431C2314yes—
247#431C2314yes—
248#431C2314yes—
249#424—28no—
250#423—22no—
251#423—22no—
252#423—22no—
253#423C2314yes—
254C2×C4⋊C8—21no—
255C2×C4⋊C8—21no—
256C2×C4⋊C8—22no—
257C2×C4⋊C8—22no—
258C2×C4⋊C8—21no—
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2314yes—
263C2×C4⋊C8C2314yes—
264C2×C4⋊C8C2311yescharacteristic
265#408—28no—
266#407—22no—
267#407—22no—
268C2×C22⋊C8—21no—
269C2×C22⋊C8—21no—
270C2×C22⋊C8—21no—
271C4×M16—22no—
272C4×M16—22no—
273C4×M16C2314yes—
274C4×M16C2314yes—
275C2×#97—22no—
276C2×#97—21no—
277C2×#97—21no—
278C2×C4×C8—21no—
279C2×C4×C8C2314yes—
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—24no—
321C2×M16—48no—
322C2×M16—82no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—24no—
327C22×C8—21no—
328C22×C8—24no—
329C22×C8—24no—
330C22×C8—82no—
331C22×C8—82no—
332C4⋊Q8—24no—
333C4⋊Q8—24no—
334C4⋊Q8C22×C412yes—
335C4⋊Q8C22×C412yes—
336C4⋊Q8C22×C412yes—
337#127C22×C412yes—
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#126—24no—
350#126—24no—
351#126—24no—
352#125—24no—
353#125—24no—
354#125—24no—
355#125—24no—
356#125—24no—
357#125—22no—
358#125—22no—
359#125—22no—
360#125—22no—
361#125—22no—
362#125—22no—
363#125C22×C414yes—
364#125C22×C414yes—
365#125C22×C414yes—
366#124—24no—
367#124—24no—
368#124—24no—
369#124—22no—
370#124—22no—
371#124—22no—
372#124—22no—
373#124—22no—
374#124—22no—
375#124C22×C414yes—
376#124C22×C414yes—
377#124C22×C414yes—
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—
394#123—24no—
395#123—24no—
396#123—24no—
397C22⋊Q8—24no—
398C22⋊Q8—24no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410C22⋊Q8—24no—
411C22⋊Q8—24no—
412C22⋊Q8—24no—
413C22⋊Q8—24no—
414C22⋊Q8—24no—
415C22⋊Q8—24no—
416C22⋊Q8C22×C414yes—
417C22⋊Q8C22×C414yes—
418C22⋊Q8C22×C414yes—
419C22⋊Q8C22×C414yes—
420#121—24no—
421#121—24no—
422#121—24no—
423#121—24no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—22no—
430#121—22no—
431#121—22no—
432#121—24no—
433#121—24no—
434#121—24no—
435#121C22×C414yes—
436#121C22×C414yes—
437#121C22×C414yes—
438#121C22×C414yes—
439#120—24no—
440#120—24no—
441#120—24no—
442#120—24no—
443#120—24no—
444C4×Q8—24no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8C22⋊C414yes—
454C4×Q8C22⋊C414yes—
455C4×Q8C22×C414yes—
456C4×Q8C22×C414yes—
457C4×Q8C22×C414yes—
458C4×Q8C22×C414yes—
459C4×Q8C2×D414yes—
460C4×Q8C2414yes—
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—24no—
478C4×D4—24no—
479C4×D4—24no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
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×D4C22×C414yes—
498C4×D4C22×C414yes—
499C4×D4C22×C414yes—
500C4×D4C2×D414yes—
501C4×D4C2×D414yes—
502C4×D4C2×D414yes—
503C4×D4C2414yes—
504#117—22no—
505#117—22no—
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#117—24no—
516#117—24no—
517#117—24no—
518#117C22⋊C414yes—
519#117C22⋊C414yes—
520#117C22⋊C414yes—
521#117C22×C414yes—
522#117C2×D414yes—
523#117C2×D414yes—
524#117C2×D414yes—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4C22⋊C411yescharacteristic
535C2×C4⋊C4C22⋊C411yescharacteristic
536C2×C4⋊C4C22⋊C411yescharacteristic
537C2×C4⋊C4C22⋊C411yescharacteristic
538C2×C4⋊C4C22⋊C411yescharacteristic
539C2×C4⋊C4C22⋊C411yescharacteristic
540C2×C4⋊C4C22×C412yes—
541C2×C4⋊C4C22×C412yes—
542C2×C4⋊C4C22×C412yes—
543C2×C4⋊C4C22×C412yes—
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—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4C22⋊C411yescharacteristic
557C2×C22⋊C4C22⋊C411yescharacteristic
558C2×C22⋊C4C22⋊C411yescharacteristic
559C2×C22⋊C4C22⋊C411yescharacteristic
560C2×C22⋊C4C22⋊C411yescharacteristic
561C2×C22⋊C4C22⋊C411yescharacteristic
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—24no—
565C2×C42C22×C411yescharacteristic
566C2×C42C22×C411yescharacteristic
567C2×C42C22×C411yescharacteristic
568C2×C42C22×C412yes—
569C2×C42C22×C412yes—
570C2×C42C22×C412yes—
571C2×C42C2×D412yes—
572C2×C42C2×D412yes—
573C2×C42C2×D411yescharacteristic
574C2×C42C2×D411yescharacteristic
575C2×C42C2×D411yescharacteristic
576C2×C42C2×D411yescharacteristic
577C2×C42C2×D411yescharacteristic
578C2×C42C2×D411yescharacteristic
579C2×C42C2×D412yes—
580C2×C42C2×D412yes—
581C2×C42C2×D412yes—
582C2×C42C2×D412yes—
583C2×C42C2412yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2411yescharacteristic
587C4⋊C8—21no—
588C4⋊C8—21no—
589C4⋊C8—21no—
590C4⋊C8—24no—
591C4⋊C8—24no—
592C4⋊C8—24no—
593C4⋊C8—21no—
594C4⋊C8—24no—
595C4⋊C8—24no—
596C4⋊C8—24no—
597C4⋊C8—24no—
598C4⋊C8C2412yes—
599C4⋊C8C2412yes—
600C4⋊C8C2412yes—
601C4⋊C8C2412yes—
602C22⋊C8—24no—
603C22⋊C8—24no—
604C22⋊C8—24no—
605C22⋊C8—24no—
606C22⋊C8—24no—
607C22⋊C8—24no—
608C22⋊C8—24no—
609#97—24no—
610#97—24no—
611#97—24no—
612#97—24no—
613C4×C8—24no—
614C4×C8—24no—
615C4×C8C2418yes—
616C24—22no—
617C24—22no—
618C24C2×C22⋊C411yescharacteristic
619C24C2×C22⋊C411yescharacteristic
620C24C2×C22⋊C411yescharacteristic
621#41—48no—
622#41—48no—
623#41—48no—
624#41—48no—
625#41—416no—
626#41—82no—
627#41—82no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—42no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8C2×C22⋊C414yes—
636C2×Q8C23×C414yes—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—416no—
652C2×D4—48no—
653C2×D4—48no—
654C2×D4C2×C22⋊C414yes—
655C2×D4C2×C22⋊C414yes—
656C2×D4C2×C22⋊C414yes—
657C2×D4C23×C414yes—
658C22×C4—24no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—82no—
682C22×C4—82no—
683C22×C4—82no—
684C22×C4—82no—
685C22×C4C2×C22⋊C412yes—
686C22×C4C2×C22⋊C411yescharacteristic
687C22×C4C2×C22⋊C411yescharacteristic
688C22×C4C2×C22⋊C411yescharacteristic
689C22×C4C2×C22⋊C412yes—
690C22×C4C2×C22⋊C412yes—
691C22×C4C2×C22⋊C412yes—
692C22×C4C2×C22⋊C411yescharacteristic
693C22×C4C2×C22⋊C411yescharacteristic
694C22×C4C2×C22⋊C411yescharacteristic
695C22×C4C2×C22⋊C412yes—
696C22×C4C2×C22⋊C412yes—
697C22×C4C2×C22⋊C412yes—
698C22×C4C2×C22⋊C412yes—
699C22×C4C2×C22⋊C411yescharacteristic
700C22×C4C2×C22⋊C411yescharacteristic
701C22×C4C2×C22⋊C411yescharacteristic
702C22×C4C2×C22⋊C412yes—
703C22×C4C23×C411yescharacteristic
704C22×C4C23×C412yes—
705C22×C4C23×C412yes—
706C22×C4C23×C412yes—
707C22×C4C22×D411yescharacteristic
708C22×C4C22×D412yes—
709C22×C4C22×D412yes—
710C22×C4C22×D412yes—
711C22×C4C22×D412yes—
712C22×C4C22×D411yescharacteristic
713C22×C4C22×D412yes—
714C22×C4C22×D412yes—
715M16—48no—
716M16—48no—
717M16—84no—
718C2×C8—28no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—22no—
723C2×C8—42no—
724C2×C8—42no—
725C2×C8—42no—
726C2×C8—42no—
727C2×C8—48no—
728C2×C8—84no—
729C2×C8—84no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—22no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4—24no—
748C4⋊C4—22no—
749C4⋊C4—22no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4C2×C22⋊C414yes—
753C4⋊C4C2×C22⋊C414yes—
754C4⋊C4C2×C22⋊C414yes—
755C4⋊C4C2×C22⋊C414yes—
756C4⋊C4C2×C22⋊C414yes—
757C4⋊C4C2×C22⋊C414yes—
758C4⋊C4C23×C414yes—
759C4⋊C4C23×C414yes—
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⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4C2×C22⋊C414yes—
780C22⋊C4C2×C22⋊C414yes—
781C22⋊C4C2×C22⋊C414yes—
782C22⋊C4C2×C22⋊C414yes—
783C22⋊C4C2×C22⋊C414yes—
784C22⋊C4C2×C22⋊C414yes—
785C42—24no—
786C42—24no—
787C42—24no—
788C42—24no—
789C42—24no—
790C42C2×C22⋊C412yes—
791C42C2×C22⋊C412yes—
792C42C2×C22⋊C412yes—
793C42C2×C22⋊C412yes—
794C42C2×C22⋊C412yes—
795C42C2×C22⋊C412yes—
796C42C2×C22⋊C412yes—
797C42C2×C22⋊C412yes—
798C42C2×C22⋊C412yes—
799C42C23×C411yescharacteristic
800C42C23×C412yes—
801C42C23×C412yes—
802C42C23×C412yes—
803C42C22×D412yes—
804C42C22×D411yescharacteristic
805C42C22×D412yes—
806C42C22×D412yes—
807C42C22×D412yes—
808C42C22×D412yes—
809C42C22×D412yes—
810C42C22×D411yescharacteristic
811C42C2511yescharacteristic
812C23—22no—
813C23—22no—
814C23—24no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—44no—
822C23—44no—
823C23—82no—
824C23—82no—
825C23—82no—
826C23—82no—
827C23#42114yes—
828C23C22×C22⋊C412yes—
829C23C22×C22⋊C412yes—
830C23C22×C22⋊C411yescharacteristic
831C23C22×C22⋊C412yes—
832Q8—28no—
833Q8—44no—
834Q8—44no—
835Q8—82no—
836Q8—82no—
837Q8—82no—
838D4—28no—
839D4—28no—
840D4—28no—
841D4—44no—
842D4—44no—
843D4—48no—
844D4—48no—
845D4—48no—
846D4—82no—
847D4—82no—
848D4—82no—
849D4—84no—
850D4—84no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—48no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—84no—
894C2×C4—84no—
895C2×C4—84no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—82no—
900C2×C4C22×C22⋊C412yes—
901C2×C4C22×C22⋊C412yes—
902C2×C4C22×C22⋊C412yes—
903C2×C4C22×C22⋊C412yes—
904C2×C4C22×C22⋊C411yescharacteristic
905C2×C4C22×C22⋊C411yescharacteristic
906C2×C4C22×C22⋊C411yescharacteristic
907C2×C4C22×C22⋊C412yes—
908C2×C4C22×C22⋊C412yes—
909C2×C4C22×C22⋊C412yes—
910C2×C4C22×C22⋊C412yes—
911C2×C4C22×C22⋊C412yes—
912C2×C4C24×C411yescharacteristic
913C2×C4C23×D411yescharacteristic
914C2×C4C23×D411yescharacteristic
915C8—48no—
916C8—42no—
917C8—42no—
918C8—42no—
919C8—42no—
920C22—21no—
921C22—22no—
922C22—21no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—82no—
936C22—164no—
937C22—164no—
938C22C2×#42112yes—
939C22C2×#42114yes—
940C22C23×C22⋊C411yescharacteristic
941C4—21no—
942C4—22no—
943C4—22no—
944C4—22no—
945C4—21no—
946C4—22no—
947C4—22no—
948C4—22no—
949C4—21no—
950C4—21no—
951C4—22no—
952C4—22no—
953C4—22no—
954C4—44no—
955C4—44no—
956C4—44no—
957C4#357312yes—
958C4#358511yescharacteristic
959C4#358611yescharacteristic
960C2—22no—
961C2—24no—
962C2—42no—
963C2—42no—
964C2—84no—
965C2#6006511yescharacteristic
966C2#6008911yescharacteristic
967C2C22×#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. C2×#2990C2semidirect
3. #60123C2semidirect
4. #17524C2semidirect
5. #17521C2semidirect
6. #17502C2semidirect
7. #17494C2semidirect
8. #17492C2semidirect
9. #17466C2semidirect
10. #17465C2semidirect
11. C2×#1483C2semidirect
36. #2990C22semidirect
42. #2922C22semidirect
45. #2920C22semidirect
46. #2920C22semidirect
47. C2×#432C22semidirect
48. C2×#432C22semidirect
49. C2×#431C22semidirect
51. C2×#423C22semidirect
52. C22×C4⋊C8C22semidirect
53. C22×C4⋊C8C22semidirect
55. C2×C4×M16C22semidirect
56. #1497C22semidirect
57. #1496C22semidirect
58. #1495C22semidirect
59. #1494C22semidirect
60. #1491C22semidirect
61. #1490C22semidirect
62. #1488C22semidirect
63. #1487C22semidirect
64. #1486C22semidirect
65. #1483C22semidirect
66. #1483C22semidirect
67. #1483C22semidirect
68. #1483C22semidirect
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
C2×#29902
#601232
#175242
#175212
#175022
#174942
#174922
#174662
#174652
C2×#14832