Finite Group Databasebeta

← #221582

Subgroups — #221582

Order 512.

1087 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34691C211yesmaximal, characteristic
2#22797C211yesmaximal, characteristic
3C4×#436C211yesmaximal, characteristic
4C2×#1485C211yesmaximal, characteristic, complemented
5C2×#1491C211yesmaximal, characteristic, complemented
6#9677C211yesmaximal, characteristic, complemented
7#9637C211yesmaximal, characteristic, complemented
8#9077C211yesmaximal, characteristic, complemented
9#9077C211yesmaximal, characteristic, complemented
10#8941C211yesmaximal, characteristic, complemented
11#8938C211yesmaximal, characteristic, complemented
12#8568C211yesmaximal, characteristic, complemented
13#8314C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8176C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C2×#436—21no—
19C2×#432C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#2473—21no—
24#2465—21no—
25#2462—21no—
26#2451C411yescharacteristic
27#2449—21no—
28#2446C411yescharacteristic
29#2440C411yescharacteristic
30#2434C411yescharacteristic
31#2429C411yescharacteristic
32#2423C411yescharacteristic
33#2417C411yescharacteristic
34#2409C411yescharacteristic
35#2399—21no—
36#2396—21no—
37C4×C4⋊Q8C2211yescharacteristic
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41#2295C2211yescharacteristic
42#2290—21no—
43C42×D4C2211yescharacteristic
44#1955—21no—
45#1924—21no—
46#1923—21no—
47#1842C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1771—21no—
51#1770—21no—
52#1767C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54#1753—21no—
55#1753—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C42×C8C2211yescharacteristic
59#1491—24no—
60#1485—24no—
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×Q8⋊C8C2211yescharacteristic
64C2×Q8⋊C8C2211yescharacteristic
65C2×Q8⋊C8C2211yescharacteristic
66C2×Q8⋊C8C2211yescharacteristic
67C2×Q8⋊C8C2211yescharacteristic
68C2×Q8⋊C8C2211yescharacteristic
69C2×Q8⋊C8C2211yescharacteristic
70C2×Q8⋊C8C2211yescharacteristic
71C2×Q8⋊C8C2211yescharacteristic
72C2×Q8⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C22×M16—21no—
79C22×M16—21no—
80#533—22no—
81#533—22no—
82#533—41no—
83#533—41no—
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×C4⋊Q8C2×C411yescharacteristic
87C2×#125—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×C22⋊Q8C2×C411yescharacteristic
91C2×C22⋊Q8C2×C411yescharacteristic
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×C4×Q8—21no—
95C2×C4×Q8—21no—
96C2×C4×Q8—21no—
97C2×C4×Q8—22no—
98C2×C4×Q8—22no—
99C2×C4×Q8—41no—
100C2×C4×Q8—41no—
101C2×C4×Q8C2×C411yescharacteristic
102C2×C4×Q8C2×C411yescharacteristic
103C2×C4×Q8C2311yescharacteristic
104C2×C4×Q8C2311yescharacteristic
105C2×C4×Q8C2311yescharacteristic
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C2×C4×D4D411yescharacteristic
109C2×#117—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4C2×C411yescharacteristic
112C22×C42—21no—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115#436—28no—
116#432—22no—
117#432—41no—
118#431—22no—
119#431—41no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8C2311yescharacteristic
124C2×C4⋊C8C2311yescharacteristic
125C2×C4⋊C8C2311yescharacteristic
126C2×C4⋊C8C2311yescharacteristic
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—21no—
133C4×M16—22no—
134C4×M16—22no—
135C4×M16—41no—
136C4×M16—41no—
137C2×#97—21no—
138C2×#97—21no—
139C2×#97—21no—
140C2×#97—21no—
141C2×C4×C8—21no—
142C2×C4×C8—21no—
143C2×C4×C8—21no—
144C2×C4×C8C2311yescharacteristic
145C2×C4×C8C2311yescharacteristic
146C2×C4×C8C2311yescharacteristic
147C2×C4×C8C2311yescharacteristic
148#400—21no—
149#399—21no—
150#398—21no—
151#398—21no—
152#398—21no—
153#398—21no—
154#398—21no—
155#398—21no—
156#396—21no—
157#396—21no—
158#395—21no—
159#395—21no—
160#395—21no—
161#395—21no—
162#395—21no—
163#393—21no—
164#391—21no—
165#391C2×C411yescharacteristic
166#391C2×C411yescharacteristic
167#391C2×C411yescharacteristic
168#391C2×C411yescharacteristic
169#391C2×C411yescharacteristic
170#391C2×C411yescharacteristic
171#389—21no—
172#389—21no—
173#389—21no—
174#389C2×C411yescharacteristic
175#389C2×C411yescharacteristic
176#389C2×C411yescharacteristic
177#389C2×C411yescharacteristic
178#388—21no—
179#388—21no—
180#387—21no—
181#387—21no—
182#387—21no—
183#387—21no—
184#387—21no—
185#387—21no—
186#387—21no—
187#387—21no—
188#386—21no—
189#386—21no—
190#385—21no—
191#385—21no—
192#385—21no—
193#385—21no—
194#385—21no—
195#385—21no—
196#384C2×C411yescharacteristic
197#380—21no—
198#380C2×C411yescharacteristic
199#380C2×C411yescharacteristic
200C4×C4⋊C4—21no—
201C4×C4⋊C4—21no—
202C4×C4⋊C4—21no—
203C4×C4⋊C4—21no—
204C4×C4⋊C4—21no—
205C4×C4⋊C4C2×C411yescharacteristic
206C4×C4⋊C4D411yescharacteristic
207C4×C4⋊C4D411yescharacteristic
208C4×C4⋊C4C2311yescharacteristic
209C4×C22⋊C4—21no—
210C4×C22⋊C4—21no—
211C4×C22⋊C4C2×C411yescharacteristic
212C4×C22⋊C4C2×C411yescharacteristic
213C4×C22⋊C4D411yescharacteristic
214C4×C22⋊C4D411yescharacteristic
215C4×C22⋊C4D411yescharacteristic
216C4×C22⋊C4D411yescharacteristic
217#376—21no—
218C43C2311yescharacteristic
219#336—21no—
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225Q8⋊C8—22no—
226Q8⋊C8—22no—
227Q8⋊C8—22no—
228Q8⋊C8—22no—
229Q8⋊C8—22no—
230Q8⋊C8—22no—
231Q8⋊C8—22no—
232Q8⋊C8—41no—
233Q8⋊C8—41no—
234Q8⋊C8—41no—
235Q8⋊C8—41no—
236Q8⋊C8D414yescomplemented
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—41no—
242C22×Q8—41no—
243C22×Q8—41no—
244C22×Q8—41no—
245C22×Q8C22×C411yescharacteristic
246C22×Q8C22×C411yescharacteristic
247C22×Q8C22×C411yescharacteristic
248C22×D4C22⋊C411yescharacteristic
249C23×C4—21no—
250C23×C4—21no—
251C23×C4C22×C411yescharacteristic
252C23×C4C22×C411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C2×M16—24no—
258C2×M16—24no—
259C2×M16—42no—
260C2×M16—42no—
261C2×M16—42no—
262C2×M16—42no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8—41no—
275C4⋊Q8—41no—
276C4⋊Q8—41no—
277#125—42no—
278#125—42no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—41no—
283C22⋊Q8—41no—
284C22⋊Q8—41no—
285C22⋊Q8—41no—
286C22⋊Q8—41no—
287C22⋊Q8—42no—
288C22⋊Q8—42no—
289C22⋊Q8—44no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—42no—
303C4×Q8—42no—
304C4×Q8—42no—
305C4×Q8—42no—
306C4×Q8—41no—
307C4×Q8—41no—
308C4×Q8—42no—
309C4×Q8—42no—
310C4×Q8C2×D412yes—
311C4×Q8#4112yes—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—41no—
316C4×D4—41no—
317#117—42no—
318#117—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4C22⋊C411yescharacteristic
345C2×C4⋊C4C22⋊C411yescharacteristic
346C2×C4⋊C4C22⋊C411yescharacteristic
347C2×C4⋊C4C22×C411yescharacteristic
348C2×C4⋊C4C22×C411yescharacteristic
349C2×C4⋊C4C22×C411yescharacteristic
350C2×C4⋊C4C22×C411yescharacteristic
351C2×C4⋊C4C22×C411yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4C22⋊C411yescharacteristic
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C22⋊C4C22⋊C411yescharacteristic
361C2×C22⋊C4C22⋊C411yescharacteristic
362C2×C22⋊C4C22⋊C411yescharacteristic
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42C22×C411yescharacteristic
381C2×C42C22×C411yescharacteristic
382C2×C42C22×C411yescharacteristic
383C2×C42C22×C411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2411yescharacteristic
393C4⋊C8—24no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—42no—
402C4⋊C8—81no—
403C4⋊C8C2×D412yes—
404C22⋊C8—24no—
405C22⋊C8—24no—
406C22⋊C8—42no—
407C22⋊C8—42no—
408C22⋊C8—81no—
409C22⋊C8—81no—
410#97—42no—
411#97—42no—
412#97—42no—
413#97—42no—
414C4×C8—24no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—42no—
423C4×C8—42no—
424C4×C8C2×D412yes—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95C22⋊C411yescharacteristic
445#95C22⋊C411yescharacteristic
446#95C22⋊C411yescharacteristic
447#95C22⋊C411yescharacteristic
448#95C22⋊C411yescharacteristic
449#95C22⋊C411yescharacteristic
450C24C2×C22⋊C411yescharacteristic
451C24C2×C22⋊C411yescharacteristic
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—42no—
477C2×Q8—81no—
478C2×Q8C4×D412yes—
479C2×Q8#13112yes—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
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×C4C23×C411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542M16—48no—
543M16—48no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C4⋊C4—21no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—41no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—81no—
602C4⋊C4—81no—
603C4⋊C4—81no—
604C4⋊C4C4×D412yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—81no—
616C22⋊C4#10414yes—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—22no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—22no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—22no—
638C42—41no—
639C42—42no—
640C42—42no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42#13712yes—
648C42#13712yes—
649C42C22×D411yescharacteristic
650C42C2×#4111yescharacteristic
651C42H(5,𝔽2)11yescharacteristic
652C42H(5,𝔽2)11yescharacteristic
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23C2×#10412yes—
667C23C22×C22⋊C411yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—48no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—84no—
682D4—44no—
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—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—48no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
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—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—84no—
757C2×C4#41912yes—
758C2×C4#41912yes—
759C2×C4C2×#10412yes—
760C2×C4C2×#10412yes—
761C2×C4C2×C4×D411yescharacteristic
762C2×C4#51811yescharacteristic
763C2×C4D4211yescharacteristic
764C2×C4D4211yescharacteristic
765C2×C4#54611yescharacteristic
766C2×C4#54611yescharacteristic
767C2×C4C2×#13111yescharacteristic
768C2×C4#56811yescharacteristic
769C2×C4#56811yescharacteristic
770C2×C4#56811yescharacteristic
771C2×C4C2×#13711yescharacteristic
772C2×C4C2×#13711yescharacteristic
773C2×C4#57711yescharacteristic
774C2×C4#57811yescharacteristic
775C8—24no—
776C8—42no—
777C8—42no—
778C8—42no—
779C8—42no—
780C8—81no—
781C8—81no—
782C8—81no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22D4×C22⋊C411yescharacteristic
798C22#287911yescharacteristic
799C22#288011yescharacteristic
800C22C2×#41911yescharacteristic
801C22#289811yescharacteristic
802C22C22×#10411yescharacteristic
803C22#290111yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—21no—
808C4—21no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4#293011yescharacteristic
825C4#293311yescharacteristic
826C4#297611yescharacteristic
827C4#297811yescharacteristic
828C4#327611yescharacteristic
829C4#327811yescharacteristic
830C4#332811yescharacteristic
831C4#332911yescharacteristic
832C2—42no—
833C2—81no—
834C2#1750111yescharacteristic
835C2#1750611yescharacteristic
836C2#1751411yescharacteristic
837C2#1751911yescharacteristic
838C2#2240011yescharacteristic
839C2#2243011yescharacteristic
840C2D4×#10411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×D4C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1485C2semidirect
5. C2×#1491C2semidirect
6. #9677C2semidirect
7. #9637C2semidirect
8. #9077C2semidirect
9. #9077C2semidirect
10. #8941C2semidirect
11. #8938C2semidirect
12. #8568C2semidirect
13. #8314C2semidirect
14. #8311C2semidirect
15. #8176C2semidirect
236. Q8⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#346912
#227972
C4×#4362
C2×#14852
C2×#14912
#96772
#96372
#90772
#89412
#89382
#85682
#83142
#83112
#81762