Finite Group Databasebeta

← #224894

Subgroups — #224894

Order 512.

1079 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36580C211yesmaximal, characteristic
2Q8×C22⋊C8C211yesmaximal, characteristic, complemented
3#13927C211yesmaximal, characteristic, complemented
4#9716C211yesmaximal, characteristic, complemented
5#9715C211yesmaximal, characteristic
6#9713C211yesmaximal, characteristic, complemented
7#9681C211yesmaximal, characteristic, complemented
8#9681C211yesmaximal, characteristic, complemented
9#9680C211yesmaximal, characteristic
10#8578C211yesmaximal, characteristic, complemented
11#8575C211yesmaximal, characteristic, complemented
12#8573C211yesmaximal, characteristic, complemented
13#8221C211yesmaximal, characteristic, complemented
14#8220C211yesmaximal, characteristic, complemented
15C4×#327C211yesmaximal, characteristic, complemented
16C2×#559C411yescharacteristic, complemented
17C22×C4×Q8C2211yescharacteristic
18C2×C8×Q8—21no—
19#2856C2211yescharacteristic
20#2850C2211yescharacteristic
21#2850C2211yescharacteristic
22#2592C411yescharacteristic, complemented
23#2592C411yescharacteristic, complemented
24#2582C411yescharacteristic, complemented
25#2580C411yescharacteristic, complemented
26#2580C411yescharacteristic, complemented
27#2548C411yescharacteristic, complemented
28#2458—21no—
29#2458—21no—
30#2448—21no—
31#2443—21no—
32#2443—21no—
33#2436—21no—
34#2367—21no—
35#2361—21no—
36#2355C411yescharacteristic, complemented
37C4×C22⋊Q8C2211yescharacteristic
38C4×#121C2211yescharacteristic
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×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
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#559—44no—
77C2×#127C2×C411yescharacteristic
78C2×#124—21no—
79C2×#124—21no—
80C2×#124C2×C411yescharacteristic
81C2×#124C2×C411yescharacteristic
82C2×#123—21no—
83C2×#123—21no—
84C2×C22⋊Q8C2311yescharacteristic
85C2×#121—21no—
86C2×#121—21no—
87C2×#121C2311yescharacteristic
88C2×#121C2311yescharacteristic
89C2×C4×Q8—44no—
90C2×C4×Q8C2×C411yescharacteristic
91C2×C4×Q8C2×C411yescharacteristic
92C2×C4×Q8C2×C411yescharacteristic
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8C2×C411yescharacteristic
95C2×C4×Q8D411yescharacteristic
96C2×C4×Q8D411yescharacteristic
97C2×C4×Q8D411yescharacteristic
98C2×C4×Q8D411yescharacteristic
99C2×C4×D4—21no—
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4C2×C411yescharacteristic
103C2×C4×D4C2×C411yescharacteristic
104C22×C4⋊C4—21no—
105C22×C4⋊C4D411yescharacteristic
106C22×C4⋊C4D411yescharacteristic
107C22×C4⋊C4D411yescharacteristic
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C8×Q8—44no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C22⋊C8C2311yescharacteristic
117C2×C22⋊C8C2311yescharacteristic
118C2×C22⋊C8C2311yescharacteristic
119C2×C22⋊C8C2311yescharacteristic
120C2×C4×C8—21no—
121C2×C4×C8—21no—
122C2×C4×C8—21no—
123#399—21no—
124#399—21no—
125#398—21no—
126#398—21no—
127#397—21no—
128#397—21no—
129#394—21no—
130#394—21no—
131#393—21no—
132#393—21no—
133#393—21no—
134#393—21no—
135#391—21no—
136#391—21no—
137#391C2×C411yescharacteristic
138#391C2×C411yescharacteristic
139#391C2×C411yescharacteristic
140#390—21no—
141#390—21no—
142#390—21no—
143#390C2×C411yescharacteristic
144#390C2×C411yescharacteristic
145#390C2×C411yescharacteristic
146#390C2×C411yescharacteristic
147#390C2×C411yescharacteristic
148#390C2×C411yescharacteristic
149#389—21no—
150#389C2×C411yescharacteristic
151#389C2×C411yescharacteristic
152#389C2×C411yescharacteristic
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#387—21no—
164#387—21no—
165#387—21no—
166#387—44no—
167#386—21no—
168#386—21no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#385—21no—
174#385—21no—
175#385—21no—
176#385—21no—
177#385—21no—
178#384C2×C411yescharacteristic
179#382C2×C411yescharacteristic
180#382C2×C411yescharacteristic
181#380C2311yescharacteristic
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—41no—
213#328—41no—
214#327—22no—
215#327—22no—
216#327—22no—
217#327—22no—
218#327—41no—
219#327—41no—
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×D4—21no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—21no—
235C22×D4C22×C411yescharacteristic
236C22×D4C22×C411yescharacteristic
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2411yescharacteristic
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254#127—42no—
255#124—42no—
256#124—42no—
257#124—44no—
258#124—44no—
259#123—44no—
260#123—44no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—42no—
274#121—42no—
275#121—81no—
276#121—81no—
277C4×Q8—24no—
278C4×Q8—24no—
279C4×Q8—42no—
280C4×Q8—42no—
281C4×Q8—42no—
282C4×Q8—42no—
283C4×Q8—42no—
284C4×Q8—42no—
285C4×Q8—42no—
286C4×D4—42no—
287C4×D4—42no—
288C4×D4—44no—
289C4×D4—81no—
290C4×D4—81no—
291C4×D4—81no—
292C4×D4—81no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—81no—
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×C4⋊C4C22⋊C411yescharacteristic
318C2×C4⋊C4C22×C411yescharacteristic
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C4⋊C4C22×C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
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×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42—81no—
355C2×C42C22×C411yescharacteristic
356C2×C42C22×C411yescharacteristic
357C2×C42C22×C411yescharacteristic
358C2×C42C22×C411yescharacteristic
359C2×C42C22×C411yescharacteristic
360C2×C42C22×C411yescharacteristic
361C2×C42C2×D411yescharacteristic
362C2×C42C2×D411yescharacteristic
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C4⋊C8—42no—
368C4⋊C8—42no—
369C4⋊C8—42no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8#4112yes—
378C4×C8—42no—
379C4×C8—42no—
380C4×C8—42no—
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—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—81no—
415#95#4112yes—
416C24—21no—
417C24—21no—
418C24C22×D411yescharacteristic
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—48no—
436C2×Q8—48no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—81no—
462C2×D4—81no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—42no—
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×C4—41no—
507C22×C4—41no—
508C22×C4—42no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4#13512yes—
540C22×C4#13512yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4C2×#4111yescharacteristic
545C22×C4H(5,𝔽2)11yescharacteristic
546C22×C42−1+411yescharacteristic
547C2×C8—22no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4—81no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4—84no—
587C4⋊C4#9914yes—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—42no—
627C42—42no—
628C42—81no—
629C42—81no—
630C42—84no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23C22×C22⋊C411yescharacteristic
650C23#54811yescharacteristic
651C23#55011yescharacteristic
652C23C2×#13511yescharacteristic
653C23C2×#13511yescharacteristic
654C23#57611yescharacteristic
655C23#57711yescharacteristic
656Q8—28no—
657Q8—44no—
658Q8—44no—
659Q8—44no—
660Q8—81no—
661Q8—81no—
662D4—81no—
663D4—81no—
664D4—81no—
665D4—81no—
666D4—84no—
667D4—81no—
668D4—81no—
669D4—81no—
670D4—81no—
671D4—81no—
672D4—81no—
673D4—81no—
674D4—81no—
675D4—162no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—162no—
773C2×C4—162no—
774C2×C4C2×#9912yes—
775C2×C4C2×#9912yes—
776C2×C4C2×#9912yes—
777C2×C4#41612yes—
778C2×C4#41612yes—
779C2×C4#42112yes—
780C2×C4C4×#4111yescharacteristic
781C2×C4#52011yescharacteristic
782C2×C4#54811yescharacteristic
783C2×C4#55011yescharacteristic
784C8—42no—
785C8—81no—
786C8—81no—
787C8—81no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22#234111yescharacteristic
815C22C22×#9911yescharacteristic
816C22#288411yescharacteristic
817C22C2×#41611yescharacteristic
818C22#289711yescharacteristic
819C22C2×#42111yescharacteristic
820C22#290111yescharacteristic
821C22#336111yescharacteristic
822C22#336511yescharacteristic
823C22#339411yescharacteristic
824C22#339611yescharacteristic
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—82no—
842C4—82no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4—81no—
849C4—161no—
850C4—161no—
851C2—21no—
852C2—21no—
853C2—21no—
854C2—21no—
855C2—161no—
856C2—161no—
857C2#1757211yescharacteristic
858C2#1760211yescharacteristic
859C2#1760311yescharacteristic
860C2#1761611yescharacteristic
861C2#2253411yescharacteristic
862C2#2254311yescharacteristic
863C2#2255111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#2856C22
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
4. #9716C2semidirect
6. #9713C2semidirect
7. #9681C2semidirect
8. #9681C2semidirect
10. #8578C2semidirect
11. #8575C2semidirect
12. #8573C2semidirect
13. #8221C2semidirect
14. #8220C2semidirect
15. C4×#327C2semidirect
16. C2×#559C4semidirect
22. #2592C4semidirect
23. #2592C4semidirect
24. #2582C4semidirect
25. #2580C4semidirect
26. #2580C4semidirect
27. #2548C4semidirect
36. #2355C4semidirect

Maximal subgroups

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

subgroupindex
#365802
Q8×C22⋊C82
#139272
#97162
#97152
#97132
#96812
#96802
#85782
#85752
#85732
#82212
#82202
C4×#3272