Finite Group Databasebeta

← #221678

Subgroups — #221678

Order 512.

1061 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34929C211yesmaximal, characteristic
2#22749C211yesmaximal, characteristic
3C4×#435C211yesmaximal, characteristic
4C2×#1493C211yesmaximal, characteristic, complemented
5C2×#1485C211yesmaximal, characteristic, complemented
6#9677C211yesmaximal, characteristic, complemented
7#9647C211yesmaximal, characteristic, complemented
8#9077C211yesmaximal, characteristic, complemented
9#9071C211yesmaximal, characteristic, complemented
10#8942C211yesmaximal, characteristic, complemented
11#8938C211yesmaximal, characteristic, complemented
12#8566C211yesmaximal, characteristic, complemented
13#8314C211yesmaximal, characteristic, complemented
14#8314C211yesmaximal, characteristic, complemented
15#8173C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C2×#533C2211yescharacteristic
18C2×#435—21no—
19C2×#431C2211yescharacteristic
20C2×#423C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23#2556—21no—
24#2556—21no—
25#2551C411yescharacteristic
26#2546C411yescharacteristic
27#2542C411yescharacteristic
28#2538C411yescharacteristic
29#2506—21no—
30#2492C411yescharacteristic
31#2492C411yescharacteristic
32#2452—21no—
33#2429C411yescharacteristic
34#2429C411yescharacteristic
35#2396—21no—
36#2396—21no—
37C4×C4⋊Q8—21no—
38C4×C4⋊Q8C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41#2293—21no—
42C42×Q8C2211yescharacteristic
43C42×D4C2211yescharacteristic
44#1924—21no—
45#1916—21no—
46#1870—21no—
47#1831C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1771—21no—
51#1767C2211yescharacteristic
52C4×C4⋊C8C2211yescharacteristic
53#1753—21no—
54#1753—21no—
55#1752—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C4×#97C2211yescharacteristic
59#1493—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
77C22×M16—21no—
78C22×M16—21no—
79C23×C8—21no—
80#533—22no—
81#533—22no—
82#533—22no—
83#533—22no—
84#533—41no—
85#533—41no—
86#533—41no—
87#533—41no—
88C2×C4⋊Q8—21no—
89C2×C4⋊Q8C2×C411yescharacteristic
90C2×C4⋊Q8C2×C411yescharacteristic
91C2×C4⋊Q8C2×C411yescharacteristic
92C2×C4⋊Q8C2×C411yescharacteristic
93C2×C4⋊Q8C2×C411yescharacteristic
94C2×#125—21no—
95C2×#125—21no—
96C2×C22⋊Q8—21no—
97C2×C22⋊Q8—21no—
98C2×C22⋊Q8C2×C411yescharacteristic
99C2×C22⋊Q8C2×C411yescharacteristic
100C2×C22⋊Q8C2×C411yescharacteristic
101C2×C22⋊Q8C2×C411yescharacteristic
102C2×C22⋊Q8C2×C411yescharacteristic
103C2×C22⋊Q8C2×C411yescharacteristic
104C2×C4×Q8—21no—
105C2×C4×Q8—21no—
106C2×C4×Q8C2×C411yescharacteristic
107C2×C4×Q8C2×C411yescharacteristic
108C2×C4×Q8C2311yescharacteristic
109C2×C4×Q8C2311yescharacteristic
110C2×C4×Q8C2311yescharacteristic
111C2×C4×D4C2×C411yescharacteristic
112C2×C4×D4D411yescharacteristic
113C2×C4×D4D411yescharacteristic
114C2×#117—21no—
115C2×#117—21no—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118#435—28no—
119#431—22no—
120#431—41no—
121#423—22no—
122#423—41no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8C2311yescharacteristic
126C2×C4⋊C8C2311yescharacteristic
127C2×C4⋊C8C2311yescharacteristic
128C2×C4⋊C8C2311yescharacteristic
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C4×M16—22no—
135C4×M16—41no—
136C2×#97—21no—
137C2×#97—21no—
138C2×#97—21no—
139C2×#97—21no—
140C2×C4×C8—22no—
141C2×C4×C8—21no—
142C2×C4×C8—21no—
143C2×C4×C8—41no—
144C2×C4×C8C2311yescharacteristic
145C2×C4×C8C2311yescharacteristic
146C2×C4×C8C2311yescharacteristic
147C2×C4×C8C2311yescharacteristic
148#400—21no—
149#400—21no—
150#399—21no—
151#399—21no—
152#398—21no—
153#398—21no—
154#398—21no—
155#398—21no—
156#396—21no—
157#396—21no—
158#396—21no—
159#396—21no—
160#395—21no—
161#395—21no—
162#393—21no—
163#393—21no—
164#391—21no—
165#391—21no—
166#391C2×C411yescharacteristic
167#391C2×C411yescharacteristic
168#391C2×C411yescharacteristic
169#391C2×C411yescharacteristic
170#390—21no—
171#390—21no—
172#389—21no—
173#389—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389C2×C411yescharacteristic
181#389C2×C411yescharacteristic
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#387—21no—
187#387—21no—
188#385—21no—
189#385—21no—
190#384—21no—
191#384C2×C411yescharacteristic
192#380C2×C411yescharacteristic
193#380C2×C411yescharacteristic
194C4×C4⋊C4—21no—
195C4×C4⋊C4—21no—
196C4×C4⋊C4—21no—
197C4×C4⋊C4—21no—
198C4×C4⋊C4—21no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4—21no—
201C4×C4⋊C4C2×C411yescharacteristic
202C4×C4⋊C4C2×C411yescharacteristic
203C4×C4⋊C4C2×C411yescharacteristic
204C4×C4⋊C4D411yescharacteristic
205C4×C4⋊C4D411yescharacteristic
206C4×C4⋊C4C2311yescharacteristic
207C4×C22⋊C4—21no—
208C4×C22⋊C4—21no—
209C4×C22⋊C4C2×C411yescharacteristic
210C4×C22⋊C4C2×C411yescharacteristic
211C4×C22⋊C4D411yescharacteristic
212C4×C22⋊C4D411yescharacteristic
213C4×C22⋊C4D411yescharacteristic
214C4×C22⋊C4D411yescharacteristic
215C43—21no—
216C43C2311yescharacteristic
217#336—21no—
218#336—21no—
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×Q8C22×C411yescharacteristic
240C22×Q8C22×C411yescharacteristic
241C22×Q8C22×C411yescharacteristic
242C22×D4C22⋊C411yescharacteristic
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C2×M16—24no—
250C2×M16—42no—
251C2×M16—42no—
252C2×M16—42no—
253C2×M16—42no—
254C2×M16—81no—
255C22×C8—21no—
256C22×C8—24no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—42no—
265C22×C8—42no—
266C4⋊Q8—22no—
267C4⋊Q8—22no—
268C4⋊Q8—22no—
269C4⋊Q8—22no—
270C4⋊Q8—41no—
271C4⋊Q8—41no—
272C4⋊Q8—41no—
273C4⋊Q8—41no—
274C4⋊Q8—41no—
275C4⋊Q8—41no—
276C4⋊Q8—44no—
277#125—42no—
278#125—42no—
279#125—42no—
280#125—42no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—41no—
288C22⋊Q8—41no—
289C22⋊Q8—41no—
290C22⋊Q8—41no—
291C22⋊Q8—41no—
292C22⋊Q8—41no—
293C22⋊Q8—42no—
294C22⋊Q8—42no—
295C22⋊Q8—42no—
296C22⋊Q8—42no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—22no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—42no—
309C4×Q8—42no—
310C4×Q8—42no—
311C4×Q8—42no—
312C4×Q8—41no—
313C4×Q8—41no—
314C4×Q8—41no—
315C4×Q8C2×D412yes—
316C4×Q8#4112yes—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—24no—
320C4×D4—41no—
321C4×D4—41no—
322#117—42no—
323#117—42no—
324#117—42no—
325#117—42no—
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—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C22⋊C411yescharacteristic
350C2×C4⋊C4C22⋊C411yescharacteristic
351C2×C4⋊C4C22⋊C411yescharacteristic
352C2×C4⋊C4C22×C411yescharacteristic
353C2×C4⋊C4C22×C411yescharacteristic
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C22⋊C4C22⋊C411yescharacteristic
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C22×C411yescharacteristic
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C22×C411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2411yescharacteristic
400C4⋊C8—24no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—42no—
409C4⋊C8C2×D412yes—
410C22⋊C8—24no—
411C22⋊C8—24no—
412C22⋊C8—42no—
413C22⋊C8—42no—
414C22⋊C8—81no—
415#97—24no—
416#97—42no—
417#97—42no—
418#97—81no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—42no—
427C4×C8—42no—
428C4×C8C2×D412yes—
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—21no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—81no—
474C2×Q8—81no—
475C2×Q8C4×D412yes—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—41no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
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—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C2×C22⋊C411yescharacteristic
521C22×C4C2×C22⋊C411yescharacteristic
522C22×C4C2×C22⋊C411yescharacteristic
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C411yescharacteristic
527C22×C4#13712yes—
528C22×C4#13712yes—
529C22×C4C23×C411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532M16—48no—
533M16—84no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—48no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
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—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—41no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4#10414yes—
596C4⋊C4C4×D412yes—
597C4⋊C4#13112yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—22no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—22no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—22no—
635C42—41no—
636C42—42no—
637C42—42no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—42no—
645C42—81no—
646C42C22×D411yescharacteristic
647C42C2×#4111yescharacteristic
648C42H(5,𝔽2)11yescharacteristic
649C42H(5,𝔽2)11yescharacteristic
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23#41912yes—
664C23C22×C22⋊C411yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—84no—
678Q8—84no—
679D4—44no—
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—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
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—21no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
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#41912yes—
753C2×C4C2×#10412yes—
754C2×C4C2×#10412yes—
755C2×C4C2×#10412yes—
756C2×C4C2×C4×D411yescharacteristic
757C2×C4#51811yescharacteristic
758C2×C4D4211yescharacteristic
759C2×C4D4211yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4C2×#13111yescharacteristic
763C2×C4#56811yescharacteristic
764C2×C4#56811yescharacteristic
765C2×C4#56811yescharacteristic
766C2×C4C2×#13711yescharacteristic
767C2×C4C2×#13711yescharacteristic
768C2×C4#57711yescharacteristic
769C2×C4#57811yescharacteristic
770C8—24no—
771C8—42no—
772C8—42no—
773C8—42no—
774C8—42no—
775C8—81no—
776C8—81no—
777C8—81no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22D4×C22⋊C411yescharacteristic
793C22#287911yescharacteristic
794C22#288011yescharacteristic
795C22C2×#41911yescharacteristic
796C22#289811yescharacteristic
797C22C22×#10411yescharacteristic
798C22#290111yescharacteristic
799C4—22no—
800C4—22no—
801C4—21no—
802C4—21no—
803C4—22no—
804C4—22no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—42no—
812C4—41no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4#293211yescharacteristic
820C4#293511yescharacteristic
821C4#298011yescharacteristic
822C4#298111yescharacteristic
823C4#326611yescharacteristic
824C4#327011yescharacteristic
825C4#331211yescharacteristic
826C4#332011yescharacteristic
827C2—42no—
828C2—81no—
829C2#1750111yescharacteristic
830C2#1750611yescharacteristic
831C2#1751411yescharacteristic
832C2#1751811yescharacteristic
833C2#2240311yescharacteristic
834C2#2242511yescharacteristic
835C2D4×#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×#1493C2semidirect
5. C2×#1485C2semidirect
6. #9677C2semidirect
7. #9647C2semidirect
8. #9077C2semidirect
9. #9071C2semidirect
10. #8942C2semidirect
11. #8938C2semidirect
12. #8566C2semidirect
13. #8314C2semidirect
14. #8314C2semidirect
15. #8173C2semidirect
236. Q8⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#349292
#227492
C4×#4352
C2×#14932
C2×#14852
#96772
#96472
#90772
#90712
#89422
#89382
#85662
#83142
#81732