Finite Group Databasebeta

← #224892

Subgroups — #224892

Order 512.

1036 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36579C211yesmaximal, characteristic
2Q8×C22⋊C8C211yesmaximal, characteristic, complemented
3#13927C211yesmaximal, characteristic, complemented
4#9716C211yesmaximal, characteristic
5#9714C211yesmaximal, characteristic, complemented
6#9713C211yesmaximal, characteristic
7#9681C211yesmaximal, characteristic
8#9681C211yesmaximal, characteristic
9#9679C211yesmaximal, characteristic, complemented
10#8577C211yesmaximal, characteristic
11#8576C211yesmaximal, characteristic, complemented
12#8574C211yesmaximal, characteristic, complemented
13#8221C211yesmaximal, characteristic, complemented
14#8220C211yesmaximal, characteristic
15C4×#328C211yesmaximal, characteristic, complemented
16C2×#556C411yescharacteristic, complemented
17C22×C4×Q8C2211yescharacteristic
18C2×C8×Q8—21no—
19#2857C2211yescharacteristic
20#2850C2211yescharacteristic
21#2850C2211yescharacteristic
22#2592C411yescharacteristic, complemented
23#2592C411yescharacteristic, complemented
24#2581C411yescharacteristic, complemented
25#2581C411yescharacteristic, complemented
26#2568C411yescharacteristic, complemented
27#2538C411yescharacteristic, complemented
28#2481—21no—
29#2481—21no—
30#2469—21no—
31#2469—21no—
32#2421—21no—
33#2409—21no—
34#2362—21no—
35#2355C411yescharacteristic, complemented
36#2352—21no—
37C4×C22⋊Q8C2211yescharacteristic
38C4×C22⋊Q8C2211yescharacteristic
39C4×#121C2211yescharacteristic
40C2×#387—21no—
41#1984—21no—
42#1984—21no—
43#1984—21no—
44#1797C2211yescharacteristic
45#1797C2211yescharacteristic
46#1797C2211yescharacteristic
47C4×C22⋊C8C2211yescharacteristic
48C4×C22⋊C8C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50C2×#328C2211yescharacteristic
51C2×#328C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62#1446—21no—
63#1441—21no—
64#1436—21no—
65C4⋊#95C2211yescharacteristic
66#1434C2211yescharacteristic
67#1434C2211yescharacteristic
68#1434C2211yescharacteristic
69#1434C2211yescharacteristic
70C4×#95C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C23×Q8D411yescharacteristic
76#556—44no—
77C2×C4⋊Q8C2×C411yescharacteristic
78C2×#126—21no—
79C2×#126—21no—
80C2×#124C2×C411yescharacteristic
81C2×#124C2×C411yescharacteristic
82C2×C22⋊Q8—21no—
83C2×C22⋊Q8—21no—
84C2×C22⋊Q8C2311yescharacteristic
85C2×C22⋊Q8C2311yescharacteristic
86C2×#121C2311yescharacteristic
87C2×C4×Q8—44no—
88C2×C4×Q8C2×C411yescharacteristic
89C2×C4×Q8C2×C411yescharacteristic
90C2×C4×Q8C2×C411yescharacteristic
91C2×C4×Q8C2×C411yescharacteristic
92C2×C4×Q8C2×C411yescharacteristic
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8D411yescharacteristic
95C2×C4×Q8D411yescharacteristic
96C2×C4×Q8D411yescharacteristic
97C2×C4×Q8D411yescharacteristic
98C2×C4×D4—21no—
99C2×C4×D4C2×C411yescharacteristic
100C2×#117—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4D411yescharacteristic
103C22×C4⋊C4D411yescharacteristic
104C22×C4⋊C4D411yescharacteristic
105C22×C42—21no—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C8×Q8—44no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C22⋊C8C2311yescharacteristic
114C2×C22⋊C8C2311yescharacteristic
115C2×C22⋊C8C2311yescharacteristic
116C2×C22⋊C8C2311yescharacteristic
117C2×C4×C8—21no—
118C2×C4×C8—21no—
119C2×C4×C8—21no—
120#400—21no—
121#400—21no—
122#400—21no—
123#400—21no—
124#397—21no—
125#397—21no—
126#396—21no—
127#396—21no—
128#395—21no—
129#395—21no—
130#393—21no—
131#393—21no—
132#391—21no—
133#391—21no—
134#391C2×C411yescharacteristic
135#391C2×C411yescharacteristic
136#391C2×C411yescharacteristic
137#391C2×C411yescharacteristic
138#391C2×C411yescharacteristic
139#391C2×C411yescharacteristic
140#390C2×C411yescharacteristic
141#390C2×C411yescharacteristic
142#390C2×C411yescharacteristic
143#389—21no—
144#389—21no—
145#389C2×C411yescharacteristic
146#389C2×C411yescharacteristic
147#389C2×C411yescharacteristic
148#388—21no—
149#388—21no—
150#388—21no—
151#388—21no—
152#388—21no—
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157#387—21no—
158#387—21no—
159#387—21no—
160#387—21no—
161#387—21no—
162#387—21no—
163#387—21no—
164#387—21no—
165#387—44no—
166#386—21no—
167#386—21no—
168#386—21no—
169#386—21no—
170#386—21no—
171#385—21no—
172#385—21no—
173#384C2×C411yescharacteristic
174#382—21no—
175#382C2×C411yescharacteristic
176#382C2×C411yescharacteristic
177#380—21no—
178#380—21no—
179#380—21no—
180#380C2311yescharacteristic
181C4×C4⋊C4—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4—21no—
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#328—22no—
211#328—22no—
212#328—22no—
213#328—22no—
214#328—41no—
215#328—41no—
216#328—41no—
217#328—41no—
218#327—22no—
219#327—22no—
220#327—41no—
221#327—41no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—42no—
225C22×Q8—42no—
226C22×Q8C22⋊C411yescharacteristic
227C22×Q8C22⋊C411yescharacteristic
228C22×Q8C22⋊C411yescharacteristic
229C22×Q8C22⋊C411yescharacteristic
230C22×Q8C22×C411yescharacteristic
231C22×Q8C22×C411yescharacteristic
232C22×D4—21no—
233C22×D4C22×C411yescharacteristic
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2411yescharacteristic
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8—42no—
251#126—44no—
252#126—44no—
253#124—42no—
254#124—42no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—44no—
264C22⋊Q8—44no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269C4×Q8—24no—
270C4×Q8—24no—
271C4×Q8—42no—
272C4×Q8—42no—
273C4×Q8—42no—
274C4×Q8—42no—
275C4×Q8—42no—
276C4×Q8—42no—
277C4×Q8—42no—
278C4×Q8—42no—
279C4×D4—42no—
280C4×D4—42no—
281C4×D4—42no—
282#117—44no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4C22⋊C411yescharacteristic
301C2×C4⋊C4C22⋊C411yescharacteristic
302C2×C4⋊C4C22⋊C411yescharacteristic
303C2×C4⋊C4C22⋊C411yescharacteristic
304C2×C4⋊C4C22⋊C411yescharacteristic
305C2×C4⋊C4C22⋊C411yescharacteristic
306C2×C4⋊C4C22⋊C411yescharacteristic
307C2×C4⋊C4C22⋊C411yescharacteristic
308C2×C4⋊C4C22⋊C411yescharacteristic
309C2×C4⋊C4C22⋊C411yescharacteristic
310C2×C4⋊C4C22⋊C411yescharacteristic
311C2×C4⋊C4C22⋊C411yescharacteristic
312C2×C4⋊C4C22×C411yescharacteristic
313C2×C4⋊C4C22×C411yescharacteristic
314C2×C4⋊C4C22×C411yescharacteristic
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—81no—
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C22×C411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C4⋊C8—42no—
356C4⋊C8—42no—
357C4⋊C8—42no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8#4112yes—
366C4×C8—42no—
367C4×C8—42no—
368C4×C8—42no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—81no—
409#95#4112yes—
410C24—21no—
411C24C22×D411yescharacteristic
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—48no—
433C2×Q8—48no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—42no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C411yescharacteristic
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4#13512yes—
519C22×C4#13512yes—
520C22×C4C23×C411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4H(5,𝔽2)11yescharacteristic
525C22×C42−1+411yescharacteristic
526C2×C8—22no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—81no—
570C4⋊C4—84no—
571C4⋊C4#9914yes—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—42no—
604C42—42no—
605C42—42no—
606C42—81no—
607C42—81no—
608C42—84no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23C22×C22⋊C411yescharacteristic
621C23#54811yescharacteristic
622C23#55011yescharacteristic
623C23C2×#13511yescharacteristic
624C23C2×#13511yescharacteristic
625C23#57711yescharacteristic
626C23#57811yescharacteristic
627Q8—28no—
628Q8—44no—
629Q8—44no—
630Q8—44no—
631Q8—81no—
632Q8—81no—
633Q8—81no—
634Q8—81no—
635D4—81no—
636D4—81no—
637D4—81no—
638D4—81no—
639D4—81no—
640D4—81no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4C2×#9912yes—
742C2×C4C2×#9912yes—
743C2×C4C2×#9912yes—
744C2×C4#41612yes—
745C2×C4#41612yes—
746C2×C4#42112yes—
747C2×C4C4×#4111yescharacteristic
748C2×C4#52011yescharacteristic
749C2×C4#54811yescharacteristic
750C2×C4#55011yescharacteristic
751C8—42no—
752C8—81no—
753C8—81no—
754C8—81no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22#234111yescharacteristic
775C22C22×#9911yescharacteristic
776C22#288411yescharacteristic
777C22C2×#41611yescharacteristic
778C22#289811yescharacteristic
779C22C2×#42111yescharacteristic
780C22#290111yescharacteristic
781C22#336011yescharacteristic
782C22#336411yescharacteristic
783C22#339311yescharacteristic
784C22#339411yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—82no—
802C4—82no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4—161no—
811C4—161no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—161no—
817C2#1757211yescharacteristic
818C2#1760111yescharacteristic
819C2#1760811yescharacteristic
820C2#1761611yescharacteristic
821C2#2253411yescharacteristic
822C2#2254111yescharacteristic
823C2#2255111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊C8C2semidirect
3. #13927C2semidirect
5. #9714C2semidirect
9. #9679C2semidirect
11. #8576C2semidirect
12. #8574C2semidirect
13. #8221C2semidirect
15. C4×#328C2semidirect
16. C2×#556C4semidirect
22. #2592C4semidirect
23. #2592C4semidirect
24. #2581C4semidirect
25. #2581C4semidirect
26. #2568C4semidirect
27. #2538C4semidirect
35. #2355C4semidirect

Maximal subgroups

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

subgroupindex
#365792
Q8×C22⋊C82
#139272
#97162
#97142
#97132
#96812
#96792
#85772
#85762
#85742
#82212
#82202
C4×#3282