Finite Group Databasebeta

← #6343633

Subgroups — #6343633

Order 512.

2936 conjugacy classes of subgroups.

The subgroup lattice has 977 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62814C211yesmaximal, characteristic
2C2×#2924C211yesmaximal, characteristic, complemented
3#34177C211yesmaximal, characteristic, complemented
4#17609C218yesmaximal, complemented
5#17604C218yesmaximal, complemented
6#17591C212yesmaximal, complemented
7#17587C212yesmaximal, complemented
8#17586C212yesmaximal, complemented
9#17576C212yesmaximal, complemented
10#17571C212yesmaximal, complemented
11C2×#1516C212yesmaximal, complemented
12#3495C414yescomplemented
13#3495C2214yes—
14#3494C414yescomplemented
15#3494C2214yes—
16#3493—21no—
17#3493—21no—
18#3492—21no—
19#3492—21no—
20#3491—21no—
21#3491—21no—
22#3490—21no—
23#3490—21no—
24#3475—24no—
25#3475—24no—
26#3458C411yescharacteristic, complemented
27#3455C412yescomplemented
28#3455C412yescomplemented
29#3449C411yescharacteristic, complemented
30#3444C2212yes—
31#3444C2212yes—
32C2×#525C2212yes—
33#3428C412yescomplemented
34C22×#117C2211yescharacteristic
35#2924—24no—
36#2924C2218yescomplemented
37C2×#433—21no—
38C2×#433—21no—
39C2×#432C2211yescharacteristic, complemented
40C2×#432C2211yescharacteristic, complemented
41C2×#431C2211yescharacteristic, complemented
42C2×#431C2211yescharacteristic, complemented
43C2×#424—21no—
44C2×#407C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46C2×#405—21no—
47#2343—24no—
48#2343C2218yescomplemented
49#2315—21no—
50#2313—21no—
51#2313—21no—
52#2283C2212yescomplemented
53#2283C2212yescomplemented
54C2×#381C2212yes—
55#2273—21no—
56#1521C2218yescomplemented
57#1518C2214yescomplemented
58#1517C2214yescomplemented
59#1516C2218yes—
60#1516C2214yescomplemented
61#1516C2214yescomplemented
62#1516C2214yescomplemented
63#1516C2214yescomplemented
64#1515C2214yescomplemented
65#1514C2214yescomplemented
66#1512C2218yescomplemented
67#1511C2214yescomplemented
68#1510C2214yescomplemented
69#1509C2218yescomplemented
70#1506C2214yescomplemented
71#1505C2214yescomplemented
72#1504C2218yes—
73#1503C2214yescomplemented
74#1502C2214yescomplemented
75#1500C2218yescomplemented
76C2×#328C2214yescomplemented
77C2×#327C2214yescomplemented
78C22×#41C2×C412yes—
79C24×C4C2311yescharacteristic
80C22×M16—21no—
81C23×C8—21no—
82#556—24no—
83#556—24no—
84#555—24no—
85#555—24no—
86#554—24no—
87#554—24no—
88#553—24no—
89#553—24no—
90#553—24no—
91#553—24no—
92#552—24no—
93#552—24no—
94#552—24no—
95#552—24no—
96#552—24no—
97#552—24no—
98#552—24no—
99#552—24no—
100#551—24no—
101#551—24no—
102#551—24no—
103#551—24no—
104#551—24no—
105#551—24no—
106#551—24no—
107#551—24no—
108#547—24no—
109#547—24no—
110#546—24no—
111#546—24no—
112#546—24no—
113#546—24no—
114#544—21no—
115#544—21no—
116#544C2×C414yescomplemented
117#544C2×C414yescomplemented
118#543—21no—
119#543—21no—
120#542C2×C414yescomplemented
121#542C2×C414yescomplemented
122#542C2×C414yescomplemented
123#542C2×C414yescomplemented
124#541C2×C414yescomplemented
125#541C2×C414yescomplemented
126#540C2×C414yescomplemented
127#540C2×C414yescomplemented
128#539—22no—
129#539—22no—
130#539—22no—
131#539—22no—
132#538—22no—
133#538—22no—
134#538—22no—
135#538—22no—
136#537—21no—
137#537—21no—
138#536C2×C414yescomplemented
139#535C2×C414yescomplemented
140#534—21no—
141#534—21no—
142#533—24no—
143#533C2×C412yescomplemented
144#533C2×C412yescomplemented
145#533C2×C412yescomplemented
146#533C2×C412yescomplemented
147#533C2312yes—
148#533C2312yes—
149#532C2×C412yescomplemented
150#532C2×C412yescomplemented
151#532C2×C412yescomplemented
152#532C2×C412yescomplemented
153#532C2312yes—
154#532C2312yes—
155#529—24no—
156#529—24no—
157#529—24no—
158#529—24no—
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×C414yescomplemented
168#529C2×C414yescomplemented
169#529C2314yes—
170#529C2314yes—
171#525—22no—
172#525—22no—
173#525—22no—
174#525—22no—
175#525—22no—
176#525—22no—
177#525—22no—
178#525—22no—
179#525—24no—
180#525C2×C414yes—
181#525C2×C414yes—
182#525C2314yes—
183#525C2314yes—
184C2×#123—22no—
185C2×C22⋊Q8C2×C412yes—
186C2×C22⋊Q8C2312yes—
187C2×#121C2×C412yes—
188C2×#121C2312yes—
189C2×#120—22no—
190#520—22no—
191#520—22no—
192#520C2×C414yescomplemented
193#520C2×C414yescomplemented
194#519C2×C414yescomplemented
195#518—22no—
196#518—22no—
197#518C2×C414yescomplemented
198C4×#41—24no—
199C4×#41—22no—
200C4×#41—22no—
201C4×#41—22no—
202C4×#41—22no—
203C4×#41C2×C414yescomplemented
204C4×#41C2×C414yescomplemented
205C2×C4×D4—22no—
206C2×C4×D4—22no—
207C2×#117—24no—
208C2×#117C2×C412yes—
209C2×#117C2×C411yescharacteristic
210C2×#117C2×C411yescharacteristic
211C2×#117C2×C411yescharacteristic
212C2×#117C2×C411yescharacteristic
213C2×#117C2×C414yes—
214C2×#117D411yescharacteristic
215C2×#117D411yescharacteristic
216C2×#117D411yescharacteristic
217C2×#117D411yescharacteristic
218C2×#117D414yes—
219C2×#117D414yes—
220C2×#117C2314yes—
221C22×C4⋊C4D411yescharacteristic
222C22×C4⋊C4D411yescharacteristic
223C22×C22⋊C4—22no—
224C22×C22⋊C4D411yescharacteristic
225C22×C22⋊C4D411yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228#433—28no—
229#433—28no—
230#432—22no—
231#432—22no—
232#432C2314yes—
233#432C2314yes—
234#431—22no—
235#431—22no—
236#431C2314yes—
237#431C2314yes—
238#424—28no—
239C2×C4⋊C8—21no—
240C2×C4⋊C8—21no—
241C2×C4⋊C8—21no—
242C2×C4⋊C8—21no—
243#407—22no—
244#407C2314yes—
245C2×C22⋊C8—21no—
246C2×C22⋊C8—22no—
247C2×C22⋊C8—21no—
248C2×C22⋊C8C2311yescharacteristic
249C2×C22⋊C8C2311yescharacteristic
250C2×C22⋊C8C2314yes—
251C2×C22⋊C8C2311yescharacteristic
252C2×C22⋊C8C2311yescharacteristic
253#405—28no—
254C2×#97—21no—
255C2×#97—21no—
256C2×C4×C8—21no—
257C2×C4×C8—21no—
258#387—28no—
259#387—28no—
260#385—28no—
261#383—22no—
262#383C2314yes—
263#382—22no—
264#382C2314yes—
265#381—22no—
266#381—22no—
267#381C2314yes—
268#381C2314yes—
269#380—22no—
270#380—22no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4C2314yes—
273C4×C22⋊C4—22no—
274C4×C22⋊C4—22no—
275C4×C22⋊C4—28no—
276#376—22no—
277#376C2314yes—
278C2×#95—22no—
279C2×#95C2314yes—
280#328C2318yes—
281#328C2318yes—
282#328C2318yes—
283#328C2318yes—
284#327C2318yes—
285#327C2318yes—
286#327C2318yes—
287#327C2318yes—
288C25C2×D411yescharacteristic
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—48no—
296C2×#41C22×C414yes—
297C2×#41C22×C414yes—
298C22×Q8C22×C412yes—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4C22×C412yes—
303C23×C4—22no—
304C23×C4—24no—
305C23×C4—44no—
306C23×C4C22×C411yescharacteristic
307C23×C4C22×C412yes—
308C23×C4C22×C411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D412yes—
314C23×C4C2×D412yes—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C2×M16—24no—
321C2×M16—44no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—24no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—44no—
328C4⋊Q8—24no—
329C4⋊Q8—24no—
330C4⋊Q8C22×C412yes—
331C4⋊Q8C22×C412yes—
332C4⋊Q8C22×C412yes—
333C4⋊Q8C22×C412yes—
334C4⋊Q8C22×C412yes—
335C4⋊Q8C22×C412yes—
336#127C22×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#125—24no—
351#125—24no—
352#125—24no—
353#125—24no—
354#125—24no—
355#125—24no—
356#125—22no—
357#125—22no—
358#125—22no—
359#125—22no—
360#125C22×C414yes—
361#125C22×C414yes—
362#124—24no—
363#124—24no—
364#124—24no—
365#124—24no—
366#124—22no—
367#124—22no—
368#124—22no—
369#124—22no—
370#124C22×C414yes—
371#124C22×C414yes—
372#123—24no—
373#123—24no—
374#123—24no—
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—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—24no—
403C22⋊Q8—24no—
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⋊Q8C22×C414yes—
413C22⋊Q8C22×C414yes—
414C22⋊Q8C22×C414yes—
415C22⋊Q8C2414yes—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—24no—
429#121—24no—
430#121—24no—
431#121—24no—
432#121—24no—
433#121—24no—
434#121C22×C414yes—
435#121C22×C414yes—
436#121C22×C414yes—
437#121C2414yes—
438#120—24no—
439#120—24no—
440#120—24no—
441#120—24no—
442#120—24no—
443#120—24no—
444C4×Q8—24no—
445C4×Q8—24no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8C22×C414yes—
455C4×Q8C22×C414yes—
456C4×Q8C22×C414yes—
457C4×Q8C22×C414yes—
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—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—
492#117—22no—
493#117—22no—
494#117—22no—
495#117—22no—
496#117—22no—
497#117—22no—
498#117—24no—
499#117—24no—
500#117—24no—
501#117—24no—
502#117—24no—
503#117—24no—
504#117—24no—
505#117—24no—
506#117—24no—
507#117—24no—
508#117C22⋊C414yes—
509#117C22⋊C414yes—
510#117C22⋊C414yes—
511#117C22⋊C414yes—
512#117C22⋊C414yes—
513#117C22⋊C414yes—
514#117C22⋊C414yes—
515#117C22⋊C414yes—
516#117C22×C414yes—
517#117C22×C414yes—
518#117C22×C414yes—
519#117C22×C414yes—
520#117C22×C414yes—
521#117C22×C414yes—
522#117C2×D414yes—
523#117C2×D414yes—
524#117C2×D414yes—
525#117C2×D414yes—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4C22⋊C411yescharacteristic
533C2×C4⋊C4C22⋊C411yescharacteristic
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⋊C414yes—
541C2×C4⋊C4C22⋊C414yes—
542C2×C4⋊C4C22×C412yes—
543C2×C4⋊C4C22×C412yes—
544C2×C4⋊C4C2×D414yes—
545C2×C4⋊C4C2×D414yes—
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⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—48no—
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×C22⋊C4C22⋊C411yescharacteristic
563C2×C22⋊C4C22⋊C411yescharacteristic
564C2×C22⋊C4C22⋊C414yes—
565C2×C22⋊C4C22⋊C414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C42—22no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42C22×C411yescharacteristic
574C2×C42C22×C411yescharacteristic
575C2×C42C22×C412yes—
576C2×C42C22×C412yes—
577C2×C42C22×C411yescharacteristic
578C2×C42C22×C411yescharacteristic
579C2×C42C2×D412yes—
580C2×C42C2×D412yes—
581C2×C42C2×D412yes—
582C2×C42C2×D412yes—
583C2×C42C2×D411yescharacteristic
584C2×C42C2×D411yescharacteristic
585C2×C42C2×D411yescharacteristic
586C2×C42C2×D411yescharacteristic
587C2×C42C2412yes—
588C2×C42C2412yes—
589C4⋊C8—24no—
590C4⋊C8—24no—
591C4⋊C8—24no—
592C4⋊C8—24no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—24no—
596C22⋊C8—24no—
597C22⋊C8—21no—
598C22⋊C8—21no—
599C22⋊C8C2412yes—
600C22⋊C8C2412yes—
601C22⋊C8C2412yes—
602C22⋊C8C2412yes—
603#97—24no—
604#97—24no—
605C4×C8—24no—
606C4×C8—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95C2418yes—
615C24—24no—
616C24—22no—
617C24—42no—
618C24—81no—
619C24C2×C22⋊C412yes—
620C24C2×C22⋊C411yescharacteristic
621C24C2×C22⋊C411yescharacteristic
622C24C22×D411yescharacteristic
623C24C22×D412yes—
624#41—48no—
625#41—48no—
626#41—48no—
627#41—48no—
628#41—84no—
629#41—84no—
630#41—84no—
631#41—84no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—44no—
638C2×Q8C23×C414yes—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—44no—
651C2×D4—48no—
652C2×D4—84no—
653C2×D4—84no—
654C2×D4C23×C414yes—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—44no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—44no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—48no—
678C22×C4—48no—
679C22×C4—81no—
680C22×C4—81no—
681C22×C4—84no—
682C22×C4—84no—
683C22×C4C2×C22⋊C412yes—
684C22×C4C2×C22⋊C412yes—
685C22×C4C2×C22⋊C411yescharacteristic
686C22×C4C2×C22⋊C411yescharacteristic
687C22×C4C2×C22⋊C412yes—
688C22×C4C2×C22⋊C412yes—
689C22×C4C2×C22⋊C411yescharacteristic
690C22×C4C2×C22⋊C411yescharacteristic
691C22×C4C2×C22⋊C411yescharacteristic
692C22×C4C2×C22⋊C411yescharacteristic
693C22×C4C2×C22⋊C412yes—
694C22×C4C2×C22⋊C412yes—
695C22×C4C2×C22⋊C411yescharacteristic
696C22×C4C2×C22⋊C411yescharacteristic
697C22×C4C2×C22⋊C411yescharacteristic
698C22×C4C2×C22⋊C411yescharacteristic
699C22×C4C2×C22⋊C412yes—
700C22×C4C2×C22⋊C412yes—
701C22×C4C2×C22⋊C412yes—
702C22×C4C23×C411yescharacteristic
703C22×C4C23×C412yes—
704C22×C4C23×C411yescharacteristic
705C22×C4C23×C412yes—
706C22×C4C22×D412yes—
707C22×C4C22×D412yes—
708C22×C4C22×D411yescharacteristic
709C22×C4C22×D412yes—
710C22×C4C22×D411yescharacteristic
711C22×C4C22×D412yes—
712C22×C4C22×D412yes—
713C22×C4C22×D412yes—
714C22×C4C22×D411yescharacteristic
715C22×C4C22×D412yes—
716C22×C4C2511yescharacteristic
717M16—48no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C2×C8—42no—
724C2×C8—48no—
725C2×C8—42no—
726C2×C8—42no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—84no—
750C4⋊C4—84no—
751C4⋊C4C2×C22⋊C414yes—
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⋊C4C2×C22⋊C414yes—
759C4⋊C4C23×C414yes—
760C4⋊C4C23×C414yes—
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⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4C2×C22⋊C414yes—
782C22⋊C4C2×C22⋊C414yes—
783C22⋊C4C2×C22⋊C414yes—
784C22⋊C4C2×C22⋊C414yes—
785C22⋊C4C2×C22⋊C414yes—
786C22⋊C4C2×C22⋊C414yes—
787C22⋊C4C2×C22⋊C414yes—
788C22⋊C4C2×C22⋊C414yes—
789C42—24no—
790C42—24no—
791C42—24no—
792C42—24no—
793C42—24no—
794C42—24no—
795C42—84no—
796C42—84no—
797C42C2×C22⋊C412yes—
798C42C2×C22⋊C412yes—
799C42C2×C22⋊C412yes—
800C42C2×C22⋊C412yes—
801C42C2×C22⋊C412yes—
802C42C2×C22⋊C412yes—
803C42C2×C22⋊C412yes—
804C42C2×C22⋊C412yes—
805C42C23×C412yes—
806C42C23×C412yes—
807C42C23×C412yes—
808C42C23×C412yes—
809C42C22×D412yes—
810C42C22×D412yes—
811C42C22×D412yes—
812C42C22×D412yes—
813C23—22no—
814C23—24no—
815C23—22no—
816C23—24no—
817C23—24no—
818C23—22no—
819C23—24no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—41no—
826C23—42no—
827C23—41no—
828C23—44no—
829C23—82no—
830C23—82no—
831C23—88no—
832C23#41014yes—
833C23C22×C22⋊C412yes—
834C23C22×C22⋊C411yescharacteristic
835C23C22×C22⋊C411yescharacteristic
836C23C22×C22⋊C412yes—
837C23C23×D411yescharacteristic
838Q8—44no—
839Q8—44no—
840Q8—82no—
841Q8—82no—
842Q8—82no—
843Q8—82no—
844D4—44no—
845D4—44no—
846D4—48no—
847D4—48no—
848D4—48no—
849D4—48no—
850D4—82no—
851D4—82no—
852D4—82no—
853D4—82no—
854D4—84no—
855D4—84no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—48no—
894C2×C4—48no—
895C2×C4—44no—
896C2×C4—48no—
897C2×C4—48no—
898C2×C4—48no—
899C2×C4—84no—
900C2×C4—84no—
901C2×C4—84no—
902C2×C4—84no—
903C2×C4—82no—
904C2×C4—82no—
905C2×C4—168no—
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×C4C22×C22⋊C411yescharacteristic
913C2×C4C22×C22⋊C412yes—
914C2×C4C22×C22⋊C412yes—
915C2×C4C22×C22⋊C412yes—
916C2×C4C22×C22⋊C412yes—
917C2×C4C22×C22⋊C412yes—
918C2×C4C24×C411yescharacteristic
919C2×C4C23×D411yescharacteristic
920C8—42no—
921C8—42no—
922C8—42no—
923C8—42no—
924C22—21no—
925C22—21no—
926C22—22no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—21no—
931C22—22no—
932C22—21no—
933C22—22no—
934C22—21no—
935C22—22no—
936C22—44no—
937C22—48no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—44no—
942C22—84no—
943C22—82no—
944C22—164no—
945C22C2×#41014yes—
946C22C2×#41012yes—
947C22C23×C22⋊C411yescharacteristic
948C22#358412yes—
949C4—21no—
950C4—21no—
951C4—22no—
952C4—21no—
953C4—22no—
954C4—21no—
955C4—22no—
956C4—22no—
957C4—22no—
958C4—22no—
959C4—22no—
960C4—22no—
961C4—22no—
962C4—22no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—88no—
967C2—22no—
968C2—24no—
969C2—22no—
970C2—41no—
971C2—42no—
972C2—84no—
973C2C22×#41011yescharacteristic
974C2#6008611yescharacteristic
975C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62814C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2924C2semidirect
3. #34177C2semidirect
4. #17609C2semidirect
5. #17604C2semidirect
6. #17591C2semidirect
7. #17587C2semidirect
8. #17586C2semidirect
9. #17576C2semidirect
10. #17571C2semidirect
11. C2×#1516C2semidirect
12. #3495C4semidirect
14. #3494C4semidirect
26. #3458C4semidirect
27. #3455C4semidirect
28. #3455C4semidirect
29. #3449C4semidirect
33. #3428C4semidirect
36. #2924C22semidirect
39. C2×#432C22semidirect
40. C2×#432C22semidirect
41. C2×#431C22semidirect
42. C2×#431C22semidirect
48. #2343C22semidirect
52. #2283C22semidirect
53. #2283C22semidirect
56. #1521C22semidirect
57. #1518C22semidirect
58. #1517C22semidirect
60. #1516C22semidirect
61. #1516C22semidirect
62. #1516C22semidirect
63. #1516C22semidirect
64. #1515C22semidirect
65. #1514C22semidirect
66. #1512C22semidirect
67. #1511C22semidirect
68. #1510C22semidirect
69. #1509C22semidirect
70. #1506C22semidirect
71. #1505C22semidirect
73. #1503C22semidirect
74. #1502C22semidirect
75. #1500C22semidirect
76. C2×#328C22semidirect
77. C2×#327C22semidirect
116. #544C2×C4semidirect
117. #544C2×C4semidirect
120. #542C2×C4semidirect
121. #542C2×C4semidirect
122. #542C2×C4semidirect
123. #542C2×C4semidirect
124. #541C2×C4semidirect
125. #541C2×C4semidirect
126. #540C2×C4semidirect
127. #540C2×C4semidirect
138. #536C2×C4semidirect
139. #535C2×C4semidirect
143. #533C2×C4semidirect
144. #533C2×C4semidirect
145. #533C2×C4semidirect
146. #533C2×C4semidirect
149. #532C2×C4semidirect
150. #532C2×C4semidirect
151. #532C2×C4semidirect
152. #532C2×C4semidirect
167. #529C2×C4semidirect
168. #529C2×C4semidirect
192. #520C2×C4semidirect
193. #520C2×C4semidirect
194. #519C2×C4semidirect
197. #518C2×C4semidirect
203. C4×#41C2×C4semidirect
204. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628142
C2×#29242
#341772
#176092
#176042
#175912
#175872
#175862
#175762
#175712
C2×#15162