Finite Group Databasebeta

← #6343401

Subgroups — #6343401

Order 512.

3240 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62773C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3C2×#2318C211yesmaximal, characteristic, complemented
4#17598C218yesmaximal, complemented
5#17597C218yesmaximal, complemented
6#17593C212yesmaximal, complemented
7#17592C212yesmaximal, complemented
8#17588C212yesmaximal, complemented
9#17587C212yesmaximal, complemented
10#17542C212yesmaximal, complemented
11C2×#1504C212yesmaximal, complemented
12#3520C2214yes—
13#3519C2214yes—
14#3513—24no—
15#3506C412yescomplemented
16#3505C412yescomplemented
17#3505C412yescomplemented
18#3501C411yescharacteristic, complemented
19#3496C411yescharacteristic, complemented
20#3492—21no—
21#3490—21no—
22#3490—21no—
23#3484—21no—
24#3481—24no—
25#3475C414yescomplemented
26D4×#41C414yescomplemented
27#3460—21no—
28#3459—21no—
29#3459—21no—
30#3444C2212yes—
31C2×#525C2212yes—
32C2×#525C2212yes—
33C4×H(5,𝔽2)—21no—
34C22×C4×D4C2211yescharacteristic
35#2975—21no—
36#2974C2218yescomplemented
37#2973—21no—
38#2973—21no—
39#2972—21no—
40D4×M16—24no—
41#2920C2212yescomplemented
42C2×#407C2212yescomplemented
43C2×#407C2212yescomplemented
44#2318—24no—
45#2318C2218yescomplemented
46C2×#388—21no—
47C2×#387—21no—
48C2×#386—21no—
49C2×#385—21no—
50C2×#383C2211yescharacteristic, complemented
51C2×#382C2211yescharacteristic, complemented
52C2×#381C2211yescharacteristic, complemented
53C2×#380C2211yescharacteristic, complemented
54C2×C4×C22⋊C4C2211yescharacteristic, complemented
55C22×#95C2211yescharacteristic, complemented
56#1521C2218yescomplemented
57#1520C2214yescomplemented
58#1519C2214yescomplemented
59#1518C2214yescomplemented
60#1517C2214yescomplemented
61#1516C2218yescomplemented
62#1515C2214yescomplemented
63#1514C2214yescomplemented
64#1513C2218yescomplemented
65#1512C2218yescomplemented
66#1511C2214yescomplemented
67#1510C2214yescomplemented
68#1508C2214yescomplemented
69#1507C2214yescomplemented
70#1504C2214yescomplemented
71#1504C2214yescomplemented
72#1504C2218yescomplemented
73#1504C2214yescomplemented
74#1504C2214yescomplemented
75#1501C2218yescomplemented
76C2×#328C2214yescomplemented
77C2×#327C2214yescomplemented
78C2×H(5,𝔽2)—21no—
79C22×#41C2×C412yes—
80C22×#41C2×C412yescomplemented
81C23×D4D411yescharacteristic
82C24×C4—21no—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×M16—22no—
86C22×M16—22no—
87#559—24no—
88#556C2×C414yescomplemented
89#555C2×C414yescomplemented
90#554—24no—
91#554—24no—
92#554C2×C414yescomplemented
93#553—24no—
94#553—24no—
95#553—24no—
96#553—24no—
97#553C2×C414yescomplemented
98#553C2×C414yescomplemented
99#552—24no—
100#552C2×C414yescomplemented
101#552C2×C414yescomplemented
102#551—24no—
103#551—24no—
104#551—24no—
105#551—24no—
106#551—24no—
107#551—24no—
108#550C2×C414yescomplemented
109D4×Q8C2×C414yescomplemented
110#548C2×C414yescomplemented
111#548C2×C414yescomplemented
112#547—24no—
113#547C2×C414yescomplemented
114#547C2×C414yescomplemented
115#546—24no—
116#546—24no—
117#546—24no—
118#546—24no—
119#546—24no—
120#546—24no—
121#546—24no—
122#546C2×C414yescomplemented
123#546C2×C414yescomplemented
124D42—24no—
125D42—24no—
126D42C2×C414yescomplemented
127#544—21no—
128#543—21no—
129#543—21no—
130#542—24no—
131#540—24no—
132#539—24no—
133#539—24no—
134#539—22no—
135#539—22no—
136#538—24no—
137#538—24no—
138#538—22no—
139#538—22no—
140#538—22no—
141#538—22no—
142#537—21no—
143#535—22no—
144#534—22no—
145#534—22no—
146#534—21no—
147#534—21no—
148#533C2×C412yescomplemented
149#533C2×C412yescomplemented
150#533C2312yes—
151#532—24no—
152#532C2×C412yescomplemented
153#532C2×C412yescomplemented
154#532C2312yes—
155#529—24no—
156#529—24no—
157#529—24no—
158#529—22no—
159#529—22no—
160#529—22no—
161#529—22no—
162#529C2×C414yescomplemented
163#529C2314yes—
164#525—22no—
165#525—22no—
166#525—22no—
167#525—22no—
168#525—22no—
169#525—22no—
170#525—22no—
171#525—22no—
172#525—22no—
173#525—22no—
174#525—24no—
175#525—24no—
176#525C2×C414yes—
177#525C2×C414yes—
178#525C2×C414yescomplemented
179#525C2×C414yescomplemented
180#525C2314yes—
181#525C2314yes—
182#525C2314yes—
183C2×#123—22no—
184C2×#123—22no—
185C2×C22⋊Q8C2×C412yes—
186C2×C22⋊Q8C2×C412yescomplemented
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2312yes—
189C2×#121C2×C412yes—
190C2×#121C2×C412yescomplemented
191C2×#121C2312yes—
192C2×#121C2312yes—
193C2×#120—22no—
194C2×#120—22no—
195#520—24no—
196#520—22no—
197#518—21no—
198#518—24no—
199#518—22no—
200#518—22no—
201C4×#41—24no—
202C4×#41—22no—
203C4×#41—22no—
204C4×#41C2×C414yescomplemented
205C2×C4×D4—22no—
206C2×C4×D4—22no—
207C2×C4×D4—22no—
208C2×C4×D4—22no—
209C2×C4×D4—24no—
210C2×C4×D4C2×C414yes—
211C2×C4×D4C2×C411yescharacteristic
212C2×C4×D4C2×C411yescharacteristic
213C2×C4×D4C2×C411yescharacteristic
214C2×C4×D4C2×C411yescharacteristic
215C2×C4×D4D411yescharacteristic
216C2×C4×D4D414yes—
217C2×C4×D4D411yescharacteristic
218C2×C4×D4D411yescharacteristic
219C2×C4×D4D411yescharacteristic
220C2×C4×D4D414yes—
221C2×C4×D4C2314yes—
222C2×#117C2×C412yes—
223C2×#117C2×C412yescomplemented
224C22×C4⋊C4—21no—
225C22×C4⋊C4—21no—
226C22×C4⋊C4D411yescharacteristic
227C22×C22⋊C4—21no—
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C22⋊C4D411yescharacteristic
231C22×C22⋊C4D411yescharacteristic
232C22×C42—21no—
233C22×C42C2311yescharacteristic
234#436—28no—
235#435—28no—
236#435—28no—
237C8×D4—28no—
238#432—22no—
239#432C2314yes—
240#431—22no—
241#431C2314yes—
242#423—22no—
243#407—22no—
244#407—22no—
245#407—22no—
246#407—22no—
247#407C2314yes—
248#407C2314yes—
249#407C2314yes—
250C2×C22⋊C8—22no—
251C2×C22⋊C8—22no—
252C2×C22⋊C8C2314yes—
253C2×C22⋊C8C2314yes—
254C4×M16—22no—
255#388—28no—
256#387—28no—
257#386—28no—
258#385—28no—
259#383—22no—
260#383C2314yes—
261#382—22no—
262#382C2314yes—
263#381—22no—
264#381C2314yes—
265#380—22no—
266#380C2314yes—
267C4×C22⋊C4—22no—
268C4×C22⋊C4C2314yes—
269C2×#95—22no—
270C2×#95—21no—
271C2×#95—21no—
272C2×#95—21no—
273C2×#95—21no—
274C2×#95—21no—
275C2×#95C2314yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280#328C2318yes—
281#328C2318yes—
282#328C2318yes—
283#328C2318yes—
284#327C2318yes—
285#327C2318yes—
286#327C2318yes—
287#327C2318yes—
288C25C2×D411yescharacteristic
289C25C2×D411yescharacteristic
290H(5,𝔽2)—48no—
291C2×#41—24no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—84no—
299C2×#41—84no—
300C2×#41C22×C414yes—
301C2×#41C22×C414yes—
302C2×#41C22×C414yescomplemented
303C22×Q8C22×C412yes—
304C22×Q8C22×C412yescomplemented
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—24no—
312C22×D4—44no—
313C22×D4C22⋊C411yescharacteristic
314C22×D4C22⋊C411yescharacteristic
315C22×D4C22⋊C411yescharacteristic
316C22×D4C22⋊C411yescharacteristic
317C22×D4C22⋊C414yes—
318C22×D4C22×C412yes—
319C22×D4C22×C412yescomplemented
320C22×D4C2×D414yes—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—24no—
328C23×C4—44no—
329C23×C4—82no—
330C23×C4—82no—
331C23×C4—82no—
332C23×C4—82no—
333C23×C4C22×C412yes—
334C23×C4C22×C412yes—
335C23×C4C22×C411yescharacteristic
336C23×C4C22×C411yescharacteristic
337C23×C4C22×C411yescharacteristic
338C23×C4C22×C411yescharacteristic
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D412yes—
344C23×C4C2×D412yes—
345C23×C4C2×D412yes—
346C23×C4C2×D412yes—
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2411yescharacteristic
352C23×C4C2412yes—
353C23×C4C2412yes—
354C2×M16—24no—
355C2×M16—24no—
356C2×M16—24no—
357C2×M16—84no—
358C2×M16—84no—
359C22×C8—24no—
360C22×C8—24no—
361C4⋊Q8—24no—
362C4⋊Q8C22×C412yescomplemented
363C4⋊Q8C22×C412yescomplemented
364C4⋊Q8C22×C412yescomplemented
365#127—24no—
366#127C22×C412yescomplemented
367#126—24no—
368#126—24no—
369#126—24no—
370#126—24no—
371#126—24no—
372#126—24no—
373#126—24no—
374#126—24no—
375#125—24no—
376#125—24no—
377#125—24no—
378#125—22no—
379#125—22no—
380#125C22×C414yescomplemented
381#124—24no—
382#124—24no—
383#124—24no—
384#124—24no—
385#124—24no—
386#124—22no—
387#124—22no—
388#124C22×C414yescomplemented
389#123—24no—
390#123—24no—
391#123—24no—
392#123—24no—
393#123—24no—
394#123—24no—
395#123—24no—
396#123—24no—
397#123—24no—
398#123—24no—
399#123—24no—
400#123—24no—
401#123—24no—
402#123—24no—
403#123—24no—
404#123—24no—
405#123—24no—
406#123—24no—
407#123—24no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—24no—
421C22⋊Q8—24no—
422C22⋊Q8—24no—
423C22⋊Q8—24no—
424C22⋊Q8—24no—
425C22⋊Q8—24no—
426C22⋊Q8—24no—
427C22⋊Q8C22×C414yes—
428C22⋊Q8C22×C414yes—
429C22⋊Q8C22×C414yes—
430C22⋊Q8C22×C414yescomplemented
431C22⋊Q8C22×C414yescomplemented
432C22⋊Q8C2414yes—
433#121—24no—
434#121—24no—
435#121—24no—
436#121—24no—
437#121—24no—
438#121—24no—
439#121—22no—
440#121—22no—
441#121—22no—
442#121—22no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121—22no—
448#121—22no—
449#121—22no—
450#121—22no—
451#121—24no—
452#121—24no—
453#121—24no—
454#121—24no—
455#121—24no—
456#121C22×C414yes—
457#121C22×C414yes—
458#121C22×C414yes—
459#121C22×C414yescomplemented
460#121C22×C414yescomplemented
461#121C2414yes—
462#120—24no—
463#120—24no—
464#120—24no—
465#120—24no—
466#120—24no—
467#120—24no—
468#120—24no—
469#120—24no—
470#120—24no—
471#120—24no—
472#120—24no—
473C4×Q8—24no—
474C4×Q8—22no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8C22×C414yescomplemented
479C4×Q8C22×C414yescomplemented
480C4×D4—24no—
481C4×D4—24no—
482C4×D4—24no—
483C4×D4—24no—
484C4×D4—24no—
485C4×D4—24no—
486C4×D4—24no—
487C4×D4—24no—
488C4×D4—24no—
489C4×D4—24no—
490C4×D4—24no—
491C4×D4—24no—
492C4×D4—24no—
493C4×D4—24no—
494C4×D4—24no—
495C4×D4—24no—
496C4×D4—24no—
497C4×D4—24no—
498C4×D4—24no—
499C4×D4—24no—
500C4×D4—24no—
501C4×D4—24no—
502C4×D4—24no—
503C4×D4—24no—
504C4×D4—24no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4C22⋊C414yes—
510C4×D4C22⋊C414yes—
511C4×D4C22⋊C414yes—
512C4×D4C22⋊C414yes—
513C4×D4C22⋊C414yes—
514C4×D4C22⋊C414yes—
515C4×D4C22⋊C414yes—
516C4×D4C22⋊C414yes—
517C4×D4C22×C414yes—
518C4×D4C22×C414yes—
519C4×D4C22×C414yes—
520C4×D4C22×C414yes—
521C4×D4C22×C414yescomplemented
522C4×D4C22×C414yescomplemented
523C4×D4C2×D414yes—
524C4×D4C2×D414yes—
525C4×D4C2×D414yes—
526C4×D4C2×D414yes—
527#117—22no—
528#117—22no—
529#117—22no—
530#117—22no—
531#117—22no—
532#117—22no—
533#117—24no—
534#117—24no—
535#117—24no—
536#117—24no—
537#117—24no—
538#117—24no—
539#117C22×C414yes—
540#117C22×C414yes—
541#117C22×C414yescomplemented
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—82no—
550C2×C4⋊C4—82no—
551C2×C4⋊C4C22⋊C411yescharacteristic
552C2×C4⋊C4C22⋊C411yescharacteristic
553C2×C4⋊C4C22⋊C411yescharacteristic
554C2×C4⋊C4C22⋊C411yescharacteristic
555C2×C4⋊C4C22⋊C414yes—
556C2×C4⋊C4C22×C412yes—
557C2×C4⋊C4C22×C412yes—
558C2×C4⋊C4C22×C412yescomplemented
559C2×C4⋊C4C22×C412yescomplemented
560C2×C4⋊C4C2×D414yes—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—44no—
577C2×C22⋊C4—82no—
578C2×C22⋊C4—82no—
579C2×C22⋊C4C22⋊C411yescharacteristic
580C2×C22⋊C4C22⋊C411yescharacteristic
581C2×C22⋊C4C22⋊C411yescharacteristic
582C2×C22⋊C4C22⋊C411yescharacteristic
583C2×C22⋊C4C22⋊C411yescharacteristic
584C2×C22⋊C4C22⋊C411yescharacteristic
585C2×C22⋊C4C22⋊C411yescharacteristic
586C2×C22⋊C4C22⋊C411yescharacteristic
587C2×C22⋊C4C22⋊C414yes—
588C2×C22⋊C4C22⋊C414yes—
589C2×C22⋊C4C2×D414yes—
590C2×C22⋊C4C2×D414yes—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—24no—
594C2×C42—24no—
595C2×C42—82no—
596C2×C42C22×C412yes—
597C2×C42C22×C411yescharacteristic
598C2×C42C22×C411yescharacteristic
599C2×C42C2×D412yes—
600C2×C42C2×D411yescharacteristic
601C2×C42C2×D412yes—
602C2×C42C2×D411yescharacteristic
603C2×C42C2412yes—
604C4⋊C8—24no—
605C4⋊C8—24no—
606C22⋊C8—24no—
607C22⋊C8—24no—
608C22⋊C8—24no—
609C22⋊C8—24no—
610C22⋊C8—24no—
611C22⋊C8C2418yes—
612#97—24no—
613C4×C8—24no—
614#95—21no—
615#95—21no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—21no—
622#95—21no—
623#95C2412yes—
624#95C2412yes—
625#95C2412yes—
626#95C2412yes—
627C24—24no—
628C24—22no—
629C24—22no—
630C24—41no—
631C24—42no—
632C24—41no—
633C24—41no—
634C24—42no—
635C24—42no—
636C24—41no—
637C24C2×C22⋊C412yes—
638C24C2×C22⋊C411yescharacteristic
639C24C2×C22⋊C412yes—
640C24C2×C22⋊C411yescharacteristic
641C24C2×C22⋊C411yescharacteristic
642C24C2×C22⋊C411yescharacteristic
643C24C22×D411yescharacteristic
644C24C22×D412yes—
645C24C22×D412yes—
646#41—48no—
647#41—48no—
648#41—416no—
649#41—82no—
650#41—82no—
651#41—84no—
652#41—84no—
653#41—84no—
654#41—84no—
655#41—84no—
656#41—84no—
657C2×Q8—22no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—82no—
662C2×Q8—82no—
663C2×Q8C23×C414yes—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—416no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—82no—
687C2×D4—82no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—84no—
693C2×D4—84no—
694C2×D4C2×C22⋊C414yes—
695C2×D4C2×C22⋊C414yes—
696C2×D4C2×C22⋊C414yes—
697C2×D4C2×C22⋊C414yes—
698C2×D4C23×C414yes—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—42no—
715C22×C4—41no—
716C22×C4—42no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—42no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—41no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—48no—
737C22×C4—81no—
738C22×C4—81no—
739C22×C4—81no—
740C22×C4—81no—
741C22×C4—82no—
742C22×C4—82no—
743C22×C4—81no—
744C22×C4—81no—
745C22×C4—81no—
746C22×C4—81no—
747C22×C4—82no—
748C22×C4—82no—
749C22×C4—84no—
750C22×C4—84no—
751C22×C4—84no—
752C22×C4—84no—
753C22×C4—816no—
754C22×C4C2×C22⋊C411yescharacteristic
755C22×C4C2×C22⋊C411yescharacteristic
756C22×C4C2×C22⋊C412yes—
757C22×C4C2×C22⋊C412yes—
758C22×C4C2×C22⋊C412yes—
759C22×C4C2×C22⋊C412yes—
760C22×C4C2×C22⋊C411yescharacteristic
761C22×C4C2×C22⋊C412yes—
762C22×C4C2×C22⋊C411yescharacteristic
763C22×C4C2×C22⋊C412yes—
764C22×C4C2×C22⋊C412yes—
765C22×C4C2×C22⋊C412yes—
766C22×C4C2×C22⋊C411yescharacteristic
767C22×C4C2×C22⋊C411yescharacteristic
768C22×C4C2×C22⋊C411yescharacteristic
769C22×C4C2×C22⋊C411yescharacteristic
770C22×C4C2×C22⋊C412yes—
771C22×C4C2×C22⋊C412yes—
772C22×C4C2×C22⋊C412yes—
773C22×C4C2×C22⋊C412yes—
774C22×C4C23×C411yescharacteristic
775C22×C4C23×C411yescharacteristic
776C22×C4C23×C412yes—
777C22×C4C23×C412yes—
778C22×C4C23×C412yes—
779C22×C4C23×C412yes—
780C22×C4C22×D412yes—
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D412yes—
784C22×C4C22×D412yes—
785C22×C4C22×D412yes—
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D412yes—
788C22×C4C22×D412yes—
789C22×C4C22×D412yes—
790C22×C4C22×D412yes—
791C22×C4C2511yescharacteristic
792M16—48no—
793M16—84no—
794M16—84no—
795C2×C8—28no—
796C2×C8—84no—
797C2×C8—84no—
798C4⋊C4—22no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—84no—
817C4⋊C4—84no—
818C4⋊C4C2×C22⋊C414yes—
819C4⋊C4C2×C22⋊C414yes—
820C4⋊C4C2×C22⋊C414yes—
821C4⋊C4C2×C22⋊C414yes—
822C4⋊C4C23×C414yes—
823C4⋊C4C23×C414yes—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—24no—
829C22⋊C4—24no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—48no—
844C22⋊C4—84no—
845C22⋊C4—84no—
846C22⋊C4C2×C22⋊C414yes—
847C22⋊C4C2×C22⋊C414yes—
848C22⋊C4C2×C22⋊C414yes—
849C22⋊C4C2×C22⋊C414yes—
850C22⋊C4C2×C22⋊C414yes—
851C22⋊C4C2×C22⋊C414yes—
852C22⋊C4C2×C22⋊C414yes—
853C22⋊C4C2×C22⋊C414yes—
854C42—24no—
855C42—24no—
856C42—24no—
857C42—24no—
858C42—24no—
859C42—84no—
860C42C2×C22⋊C412yes—
861C42C2×C22⋊C412yes—
862C42C2×C22⋊C412yes—
863C42C2×C22⋊C412yes—
864C42C23×C412yes—
865C42C23×C412yes—
866C42C22×D412yes—
867C42C22×D412yes—
868C23—21no—
869C23—21no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—24no—
875C23—24no—
876C23—24no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—24no—
881C23—22no—
882C23—22no—
883C23—24no—
884C23—42no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—42no—
889C23—41no—
890C23—42no—
891C23—41no—
892C23—41no—
893C23—42no—
894C23—42no—
895C23—41no—
896C23—42no—
897C23—41no—
898C23—48no—
899C23—48no—
900C23—44no—
901C23—44no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—82no—
906C23—84no—
907C23—84no—
908C23#42114yes—
909C23C22×C22⋊C412yes—
910C23C22×C22⋊C412yes—
911C23C22×C22⋊C412yes—
912C23C22×C22⋊C411yescharacteristic
913C23C22×C22⋊C411yescharacteristic
914C23C22×C22⋊C412yes—
915C23C23×D411yescharacteristic
916Q8—44no—
917Q8—44no—
918Q8—82no—
919Q8—82no—
920Q8—82no—
921D4—28no—
922D4—28no—
923D4—44no—
924D4—44no—
925D4—44no—
926D4—44no—
927D4—48no—
928D4—44no—
929D4—44no—
930D4—48no—
931D4—48no—
932D4—48no—
933D4—82no—
934D4—82no—
935D4—82no—
936D4—84no—
937D4—84no—
938D4—84no—
939D4—84no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—41no—
978C2×C4—42no—
979C2×C4—41no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—84no—
999C2×C4—84no—
1000C2×C4—84no—
1001C2×C4—82no—
1002C2×C4—82no—
1003C2×C4—82no—
1004C2×C4—82no—
1005C2×C4—84no—
1006C2×C4—84no—
1007C2×C4—84no—
1008C2×C4—84no—
1009C2×C4—816no—
1010C2×C4C22×C22⋊C411yescharacteristic
1011C2×C4C22×C22⋊C412yes—
1012C2×C4C22×C22⋊C412yes—
1013C2×C4C22×C22⋊C412yes—
1014C2×C4C22×C22⋊C412yes—
1015C2×C4C22×C22⋊C411yescharacteristic
1016C2×C4C22×C22⋊C412yes—
1017C2×C4C22×C22⋊C412yes—
1018C2×C4C22×C22⋊C412yes—
1019C2×C4C22×C22⋊C412yes—
1020C2×C4C24×C411yescharacteristic
1021C2×C4C23×D411yescharacteristic
1022C8—48no—
1023C22—24no—
1024C22—24no—
1025C22—21no—
1026C22—21no—
1027C22—22no—
1028C22—21no—
1029C22—21no—
1030C22—22no—
1031C22—21no—
1032C22—21no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—48no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—82no—
1051C22—82no—
1052C22—84no—
1053C22—82no—
1054C22—82no—
1055C22—164no—
1056C22—164no—
1057C22#288312yes—
1058C22C2×#42112yes—
1059C22C2×#42114yes—
1060C22C23×C22⋊C411yescharacteristic
1061C22#358511yescharacteristic
1062C22#358611yescharacteristic
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—22no—
1068C4—22no—
1069C4—22no—
1070C4—22no—
1071C4—22no—
1072C4—22no—
1073C4—22no—
1074C4—22no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4—82no—
1079C4—82no—
1080C4—82no—
1081C4—82no—
1082C2—21no—
1083C2—21no—
1084C2—22no—
1085C2—22no—
1086C2—24no—
1087C2—42no—
1088C2—42no—
1089C2—42no—
1090C2—84no—
1091C2C2×#288311yescharacteristic
1092C2#6008911yescharacteristic
1093C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62773C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. C2×#2318C2semidirect
4. #17598C2semidirect
5. #17597C2semidirect
6. #17593C2semidirect
7. #17592C2semidirect
8. #17588C2semidirect
9. #17587C2semidirect
10. #17542C2semidirect
11. C2×#1504C2semidirect
15. #3506C4semidirect
16. #3505C4semidirect
17. #3505C4semidirect
18. #3501C4semidirect
19. #3496C4semidirect
25. #3475C4semidirect
26. D4×#41C4semidirect
36. #2974C22semidirect
41. #2920C22semidirect
42. C2×#407C22semidirect
43. C2×#407C22semidirect
45. #2318C22semidirect
50. C2×#383C22semidirect
51. C2×#382C22semidirect
52. C2×#381C22semidirect
53. C2×#380C22semidirect
54. C2×C4×C22⋊C4C22semidirect
55. C22×#95C22semidirect
56. #1521C22semidirect
57. #1520C22semidirect
58. #1519C22semidirect
59. #1518C22semidirect
60. #1517C22semidirect
61. #1516C22semidirect
62. #1515C22semidirect
63. #1514C22semidirect
64. #1513C22semidirect
65. #1512C22semidirect
66. #1511C22semidirect
67. #1510C22semidirect
68. #1508C22semidirect
69. #1507C22semidirect
70. #1504C22semidirect
71. #1504C22semidirect
72. #1504C22semidirect
73. #1504C22semidirect
74. #1504C22semidirect
75. #1501C22semidirect
76. C2×#328C22semidirect
77. C2×#327C22semidirect
80. C22×#41C2×C4semidirect
88. #556C2×C4semidirect
89. #555C2×C4semidirect
92. #554C2×C4semidirect
97. #553C2×C4semidirect
98. #553C2×C4semidirect
100. #552C2×C4semidirect
101. #552C2×C4semidirect
108. #550C2×C4semidirect
109. D4×Q8C2×C4semidirect
110. #548C2×C4semidirect
111. #548C2×C4semidirect
113. #547C2×C4semidirect
114. #547C2×C4semidirect
122. #546C2×C4semidirect
123. #546C2×C4semidirect
126. D42C2×C4semidirect
148. #533C2×C4semidirect
149. #533C2×C4semidirect
152. #532C2×C4semidirect
153. #532C2×C4semidirect
162. #529C2×C4semidirect
178. #525C2×C4semidirect
179. #525C2×C4semidirect
186. C2×C22⋊Q8C2×C4semidirect
190. C2×#121C2×C4semidirect
204. C4×#41C2×C4semidirect
223. C2×#117C2×C4semidirect
302. C2×#41C22×C4semidirect
304. C22×Q8C22×C4semidirect
319. C22×D4C22×C4semidirect
362. C4⋊Q8C22×C4semidirect
363. C4⋊Q8C22×C4semidirect
364. C4⋊Q8C22×C4semidirect
366. #127C22×C4semidirect
380. #125C22×C4semidirect
388. #124C22×C4semidirect
430. C22⋊Q8C22×C4semidirect
431. C22⋊Q8C22×C4semidirect
459. #121C22×C4semidirect
460. #121C22×C4semidirect
478. C4×Q8C22×C4semidirect
479. C4×Q8C22×C4semidirect
521. C4×D4C22×C4semidirect
522. C4×D4C22×C4semidirect
541. #117C22×C4semidirect
558. C2×C4⋊C4C22×C4semidirect
559. C2×C4⋊C4C22×C4semidirect

Maximal subgroups

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

subgroupindex
#627732
#602302
C2×#23182
#175982
#175972
#175932
#175922
#175882
#175872
#175422
C2×#15042