Finite Group Databasebeta

← #188524

Subgroups — #188524

Order 512.

1056 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34224C211yesmaximal, characteristic
2#21951C211yesmaximal, characteristic, complemented
3C2×#1521C211yesmaximal, characteristic
4C2×#1500C211yesmaximal, characteristic
5#13964C211yesmaximal, characteristic, complemented
6#8578C211yesmaximal, characteristic, complemented
7#8577C211yesmaximal, characteristic
8#8576C211yesmaximal, characteristic, complemented
9#8575C211yesmaximal, characteristic
10#8574C211yesmaximal, characteristic, complemented
11#8573C211yesmaximal, characteristic
12#8572C211yesmaximal, characteristic, complemented
13#8571C211yesmaximal, characteristic
14#8025C211yesmaximal, characteristic, complemented
15#8013C211yesmaximal, characteristic, complemented
16C2×#529C2211yescharacteristic
17C2×#431C2211yescharacteristic
18C2×#431C2211yescharacteristic
19#2373—21no—
20#2373—21no—
21#2370C411yescharacteristic, complemented
22#2370C411yescharacteristic, complemented
23#2367C411yescharacteristic, complemented
24#2367C411yescharacteristic, complemented
25#2357C411yescharacteristic, complemented
26#2356C411yescharacteristic, complemented
27#2351C411yescharacteristic, complemented
28#2349C411yescharacteristic, complemented
29#2347—21no—
30#2343—21no—
31#2322—21no—
32#2322—21no—
33#2318—21no—
34C4×C22⋊Q8C2211yescharacteristic
35C4×C22⋊Q8C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38#2283C2211yescharacteristic
39C2×#383C2211yescharacteristic
40#2275—21no—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×#376C2211yescharacteristic
43#1939—21no—
44#1939—21no—
45#1939—21no—
46#1939—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1521—24no—
52#1500—24no—
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61#1441—21no—
62#1441—21no—
63#1436—21no—
64#1436—21no—
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67#1434C2211yescharacteristic
68#1434C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77#529—22no—
78#529—22no—
79#529D414yes—
80#529Q814yes—
81C2×#126—21no—
82C2×#125C2×C411yescharacteristic
83C2×#124C2×C411yescharacteristic
84C2×#123—21no—
85C2×C22⋊Q8C2311yescharacteristic
86C2×#121C2311yescharacteristic
87C2×C4×Q8C2×C411yescharacteristic
88C2×C4×Q8C2×C411yescharacteristic
89C2×C4×Q8C2×C411yescharacteristic
90C2×C4×D4—21no—
91C2×C4×D4—21no—
92C2×C4×D4—21no—
93C2×C4×D4C2×C411yescharacteristic
94C2×C4×D4C2×C411yescharacteristic
95C2×C4×D4C2×C411yescharacteristic
96C2×#117—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4D411yescharacteristic
100C22×C4⋊C4D411yescharacteristic
101C22×C42—21no—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105#431—22no—
106#431—22no—
107#431—22no—
108#431—22no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C22⋊C8C2311yescharacteristic
116C2×C22⋊C8C2311yescharacteristic
117C2×C22⋊C8C2311yescharacteristic
118C2×C22⋊C8C2311yescharacteristic
119C2×C4×C8—21no—
120C2×C4×C8—21no—
121#391C2×C411yescharacteristic
122#391C2×C411yescharacteristic
123#390C2×C411yescharacteristic
124#390C2×C411yescharacteristic
125#389—21no—
126#389—21no—
127#389—21no—
128#389—21no—
129#389C2×C411yescharacteristic
130#389C2×C411yescharacteristic
131#389C2×C411yescharacteristic
132#389C2×C411yescharacteristic
133#388—21no—
134#388—21no—
135#388—21no—
136#388—21no—
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#386—21no—
150#386—21no—
151#385—21no—
152#385—21no—
153#385—21no—
154#385—21no—
155#385—21no—
156#385—21no—
157#383—21no—
158#383—21no—
159#383—22no—
160#383—22no—
161#382—21no—
162#382C2×C411yescharacteristic
163#382C2×C411yescharacteristic
164#381—21no—
165#381—21no—
166#380—21no—
167#380C2311yescharacteristic
168#380C2311yescharacteristic
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4D411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C4⋊C4D411yescharacteristic
187C4×C4⋊C4D411yescharacteristic
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196#376—21no—
197#376—21no—
198#376—22no—
199#376—22no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95D411yescharacteristic
211C2×#95D411yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216#336—21no—
217#336—21no—
218#336—21no—
219#336—21no—
220#328—22no—
221#328—22no—
222#328—22no—
223#328—22no—
224#327—22no—
225#327—22no—
226#327—22no—
227#327—22no—
228C22×Q8C22×C411yescharacteristic
229C22×D4—21no—
230C22×D4C22×C411yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2411yescharacteristic
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249#126—24no—
250#126—24no—
251#125—22no—
252#125C4⋊C414yescomplemented
253#124—22no—
254#124C4⋊C414yescomplemented
255#123—24no—
256#123—24no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8C2×D412yes—
260C22⋊Q8C2×Q812yes—
261#121—21no—
262#121—21no—
263#121C2×D412yes—
264#121C2×Q812yes—
265C4×Q8—22no—
266C4×Q8—81no—
267C4×Q8—81no—
268C4×Q8C4⋊C414yescomplemented
269C4×D4—24no—
270C4×D4—24no—
271C4×D4—22no—
272C4×D4—42no—
273C4×D4—42no—
274C4×D4—42no—
275C4×D4—42no—
276C4×D4—81no—
277C4×D4—81no—
278C4×D4C4⋊C414yescomplemented
279#117—24no—
280#117—24no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
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—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
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×C22⋊C4—21no—
316C2×C22⋊C4—21no—
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×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—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—81no—
341C2×C42—81no—
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D412yes—
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×Q812yes—
356C2×C42#4112yes—
357C2×C42#4112yes—
358C4⋊C8—42no—
359C4⋊C8—42no—
360C4⋊C8—81no—
361C4⋊C8—81no—
362C4⋊C8—81no—
363C4⋊C8—81no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C4×C8—42no—
373C4×C8—42no—
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—21no—
400#95—21no—
401#95—21no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—81no—
410#95—81no—
411#95C22⋊C411yescharacteristic
412#95C22⋊C411yescharacteristic
413#95C22⋊C411yescharacteristic
414#95C22⋊C411yescharacteristic
415#95C22⋊C411yescharacteristic
416#95C22⋊C411yescharacteristic
417#95C22⋊C411yescharacteristic
418#95C22⋊C411yescharacteristic
419C24—21no—
420C24C22×D411yescharacteristic
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8C2×C4⋊C412yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4C2×C4⋊C412yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
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—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
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—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4C2×C22⋊C411yescharacteristic
502C22×C4C2×C22⋊C411yescharacteristic
503C22×C4C2×C22⋊C411yescharacteristic
504C22×C4C2×C22⋊C411yescharacteristic
505C22×C4C2×C22⋊C411yescharacteristic
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×C4#12112yes—
514C22×C4#12112yes—
515C22×C4C22⋊Q812yes—
516C22×C4C22⋊Q812yes—
517C22×C4#13512yes—
518C22×C4#13512yes—
519C22×C4C23×C411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×Q811yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C2×C8—41no—
526C2×C8—41no—
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—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—84no—
563C4⋊C4—84no—
564C4⋊C4C2×C4⋊C412yes—
565C4⋊C4C2×C4⋊C412yes—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—42no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—42no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C42—24no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—42no—
593C42—48no—
594C42—42no—
595C42—81no—
596C42—81no—
597C42—81no—
598C42—81no—
599C42—81no—
600C42—81no—
601C42C2×C4⋊C412yes—
602C42C2×C4⋊C412yes—
603C42#11712yes—
604C42#11712yes—
605C42#12112yes—
606C42#12112yes—
607C42C22⋊Q812yes—
608C42C22⋊Q812yes—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23C22×C22⋊C411yescharacteristic
621C23C2×#12111yescharacteristic
622C23C2×C22⋊Q811yescharacteristic
623C23C2×#13511yescharacteristic
624C23C2×#13511yescharacteristic
625C23#57511yescharacteristic
626C23#57511yescharacteristic
627Q8—42no—
628Q8—42no—
629D4—42no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—42no—
634D4—42no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
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—22no—
654C2×C4—22no—
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—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
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—84no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
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—162no—
738C2×C4—162no—
739C2×C4#38012yes—
740C2×C4#38012yes—
741C2×C4#38012yes—
742C2×C4#38012yes—
743C2×C4#41612yes—
744C2×C4#41612yes—
745C2×C4C22×C4⋊C411yescharacteristic
746C2×C4C2×#11711yescharacteristic
747C2×C4C2×#12111yescharacteristic
748C2×C4C2×C22⋊Q811yescharacteristic
749C8—81no—
750C8—81no—
751C8—81no—
752C8—81no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22C2×#38011yescharacteristic
773C22#288311yescharacteristic
774C22#288411yescharacteristic
775C22C2×#41611yescharacteristic
776C22#289611yescharacteristic
777C22#290111yescharacteristic
778C22#290111yescharacteristic
779C22#303511yescharacteristic
780C22#303511yescharacteristic
781C22#307611yescharacteristic
782C22#307611yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—82no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—161no—
809C4—161no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—82no—
815C2#1761511yescharacteristic
816C2#1761611yescharacteristic
817C2#1762311yescharacteristic
818C2#1762411yescharacteristic
819C2#2063411yescharacteristic
820C2#2064511yescharacteristic
821C2#2065511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21951C2semidirect
5. #13964C2semidirect
6. #8578C2semidirect
8. #8576C2semidirect
10. #8574C2semidirect
12. #8572C2semidirect
14. #8025C2semidirect
15. #8013C2semidirect
21. #2370C4semidirect
22. #2370C4semidirect
23. #2367C4semidirect
24. #2367C4semidirect
25. #2357C4semidirect
26. #2356C4semidirect
27. #2351C4semidirect
28. #2349C4semidirect
252. #125C4⋊C4semidirect
254. #124C4⋊C4semidirect
268. C4×Q8C4⋊C4semidirect
278. C4×D4C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
#342242
#219512
C2×#15212
C2×#15002
#139642
#85782
#85772
#85762
#85752
#85742
#85732
#85722
#85712
#80252
#80132