Finite Group Databasebeta

← #223480

Subgroups — #223480

Order 512.

1115 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34763C211yesmaximal, characteristic
2#22648C211yesmaximal, characteristic, complemented
3C4×C8×D4C211yesmaximal, characteristic, complemented
4#9870C211yesmaximal, characteristic, complemented
5#9869C211yesmaximal, characteristic, complemented
6#9072C211yesmaximal, characteristic, complemented
7#9072C211yesmaximal, characteristic, complemented
8#8944C211yesmaximal, characteristic, complemented
9#8939C211yesmaximal, characteristic, complemented
10#8709C211yesmaximal, characteristic, complemented
11#8706C211yesmaximal, characteristic, complemented
12#8567C211yesmaximal, characteristic, complemented
13#8177C211yesmaximal, characteristic, complemented
14#7897C211yesmaximal, characteristic, complemented
15C2×#1279C211yesmaximal, characteristic, complemented
16C2×#529—21no—
17C2×#435—21no—
18C2×C8×D4—21no—
19C2×#423C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23#2521—21no—
24#2519—21no—
25#2512C411yescharacteristic
26#2506C411yescharacteristic
27#2501C411yescharacteristic
28#2496C411yescharacteristic
29#2491C411yescharacteristic
30#2488—21no—
31#2486C411yescharacteristic
32#2440C411yescharacteristic
33#2425—21no—
34#2416C411yescharacteristic
35#2396—21no—
36#2395—21no—
37C4×C4⋊Q8C2211yescharacteristic
38C4×#123—21no—
39C4×#121C2211yescharacteristic
40C4×#121C2211yescharacteristic
41#2293C2211yescharacteristic
42#2285C2211yescharacteristic
43C42×D4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45#1940—21no—
46#1851—21no—
47#1850—21no—
48#1842C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51C8×C4⋊C4—21no—
52#1767C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C8×C22⋊C4—21no—
55C8×C22⋊C4—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C42×C8C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63#1279C2211yescharacteristic
64#1279C2211yescharacteristic
65#1279C2211yescharacteristic
66#1279C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C22×M16—21no—
76C23×C8—21no—
77C23×C8—21no—
78C23×C8—21no—
79C2×C4⋊Q8C2×C411yescharacteristic
80#529—44no—
81#529—44no—
82C2×#126—21no—
83C2×#126—21no—
84C2×#125—21no—
85C2×#124—21no—
86C2×#123—21no—
87C2×#123—21no—
88C2×#123—21no—
89C2×C22⋊Q8—21no—
90C2×#121—21no—
91C2×#121C2×C411yescharacteristic
92C2×#121C2×C411yescharacteristic
93C2×C4×Q8—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4D411yescharacteristic
98C2×C4×D4D411yescharacteristic
99C2×C4×D4C2311yescharacteristic
100C2×#117—21no—
101C2×#117—21no—
102C22×C4⋊C4C2×C411yescharacteristic
103C22×C4⋊C4C2×C411yescharacteristic
104C22×C42—21no—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#435—44no—
108C8×D4—28no—
109#423—22no—
110#423—41no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—41no—
118C2×C4⋊C8C2311yescharacteristic
119C2×C4⋊C8C2311yescharacteristic
120C2×C4⋊C8C2311yescharacteristic
121C2×C4⋊C8C2311yescharacteristic
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×#97—21no—
127C2×C4×C8—21no—
128C2×C4×C8—22no—
129C2×C4×C8—22no—
130C2×C4×C8—21no—
131C2×C4×C8—21no—
132C2×C4×C8—21no—
133C2×C4×C8—41no—
134C2×C4×C8—41no—
135C2×C4×C8C2311yescharacteristic
136C2×C4×C8C2311yescharacteristic
137C2×C4×C8C2311yescharacteristic
138C2×C4×C8C2311yescharacteristic
139#400—21no—
140#400—21no—
141#399—21no—
142#399—21no—
143#398—21no—
144#398—21no—
145#398—21no—
146#397—21no—
147#397—21no—
148#397—21no—
149#396—21no—
150#396—21no—
151#395—21no—
152#394—21no—
153#394—21no—
154#393—21no—
155#391—21no—
156#390C2×C411yescharacteristic
157#390C2×C411yescharacteristic
158#390C2×C411yescharacteristic
159#390C2×C411yescharacteristic
160#389—21no—
161#389C2×C411yescharacteristic
162#389C2×C411yescharacteristic
163#389C2×C411yescharacteristic
164#389C2×C411yescharacteristic
165#389C2×C411yescharacteristic
166#389C2×C411yescharacteristic
167#388—21no—
168#388—21no—
169#388—21no—
170#388—21no—
171#388—21no—
172#388—21no—
173#387—21no—
174#387—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#385—21no—
179#384C2×C411yescharacteristic
180#384C2×C411yescharacteristic
181#384C2×C411yescharacteristic
182#382—21no—
183#381—21no—
184#380—21no—
185#380C2×C411yescharacteristic
186#380C2×C411yescharacteristic
187#380C2×C411yescharacteristic
188#380C2×C411yescharacteristic
189C4×C4⋊C4—21no—
190C4×C4⋊C4—21no—
191C4×C4⋊C4—21no—
192C4×C4⋊C4—21no—
193C4×C4⋊C4C2×C411yescharacteristic
194C4×C4⋊C4C2×C411yescharacteristic
195C4×C4⋊C4C2×C411yescharacteristic
196C4×C4⋊C4D411yescharacteristic
197C4×C4⋊C4D411yescharacteristic
198C4×C4⋊C4C2311yescharacteristic
199C4×C4⋊C4C2311yescharacteristic
200C4×C4⋊C4C2311yescharacteristic
201C4×C22⋊C4—21no—
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204C4×C22⋊C4C2×C411yescharacteristic
205C4×C22⋊C4C2×C411yescharacteristic
206C4×C22⋊C4D411yescharacteristic
207C4×C22⋊C4D411yescharacteristic
208C4×C22⋊C4D411yescharacteristic
209C4×C22⋊C4D411yescharacteristic
210C2×#95—21no—
211C43C2311yescharacteristic
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216#336—21no—
217#336—21no—
218D4⋊C8—22no—
219D4⋊C8—22no—
220D4⋊C8—41no—
221D4⋊C8—41no—
222C22×Q8—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C22⋊C411yescharacteristic
226C22×D4C22×C411yescharacteristic
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4C22×C411yescharacteristic
231C23×C4C22×C411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C2×M16—42no—
237C2×M16—42no—
238C2×M16—81no—
239C22×C8—21no—
240C22×C8—24no—
241C22×C8—24no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—42no—
250C22×C8—42no—
251C22×C8—42no—
252C22×C8—42no—
253C22×C8—42no—
254C22×C8—42no—
255C22×C8—81no—
256C4⋊Q8—22no—
257C4⋊Q8—41no—
258#126—44no—
259#126—44no—
260#125—44no—
261#124—44no—
262#123—44no—
263#123—44no—
264#123—44no—
265C22⋊Q8—44no—
266#121—22no—
267#121—22no—
268#121—22no—
269#121—41no—
270#121—44no—
271C4×Q8—42no—
272C4×Q8—42no—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—24no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—42no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284C4×D4D814yes—
285C4×D4SD1614yes—
286#117—42no—
287#117—42no—
288#117—42no—
289#117—42no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
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—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—41no—
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×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×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4C22⋊C411yescharacteristic
335C2×C22⋊C4C22⋊C411yescharacteristic
336C2×C22⋊C4C22⋊C411yescharacteristic
337C2×C22⋊C4C22⋊C411yescharacteristic
338C2×C22⋊C4C22⋊C411yescharacteristic
339C2×C22⋊C4C22⋊C411yescharacteristic
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42C22×C411yescharacteristic
356C2×C42C22×C411yescharacteristic
357C2×C42C22×C411yescharacteristic
358C2×C42C22×C411yescharacteristic
359C2×C42C2×D411yescharacteristic
360C2×C42C2×D411yescharacteristic
361C2×C42C2×D411yescharacteristic
362C2×C42C2×D411yescharacteristic
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2411yescharacteristic
368C4⋊C8—24no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—42no—
377C4⋊C8—42no—
378C4⋊C8—42no—
379C4⋊C8—81no—
380C4⋊C8#4112yes—
381C22⋊C8—24no—
382C22⋊C8—24no—
383C22⋊C8—42no—
384C22⋊C8—42no—
385#97—42no—
386C4×C8—24no—
387C4×C8—21no—
388C4×C8—21no—
389C4×C8—21no—
390C4×C8—21no—
391C4×C8—21no—
392C4×C8—21no—
393C4×C8—21no—
394C4×C8—42no—
395C4×C8—42no—
396C4×C8—42no—
397C4×C8#4112yes—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95C22⋊C411yescharacteristic
414#95C22⋊C411yescharacteristic
415#95C22⋊C411yescharacteristic
416#95C22⋊C411yescharacteristic
417#95C22⋊C411yescharacteristic
418#95C22⋊C411yescharacteristic
419C24—21no—
420C24C2×C22⋊C411yescharacteristic
421C24C2×C22⋊C411yescharacteristic
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—81no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—81no—
439C2×D4#10214yes—
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—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—81no—
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4#13112yes—
496C22×C4#13112yes—
497C22×C4C2×D812yes—
498C22×C4C2×D812yes—
499C22×C4C2×SD1612yes—
500C22×C4C2×SD1612yes—
501C22×C4C23×C411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504M16—84no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—48no—
513C2×C8—48no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—84no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4#10214yes—
563C4⋊C4#13112yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4#10214yes—
584C22⋊C4#10214yes—
585C22⋊C4#10414yes—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—22no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—42no—
613C42—42no—
614C42C2×D812yes—
615C42C2×SD1612yes—
616C42C2×#4111yescharacteristic
617C42C2×#4111yescharacteristic
618C42H(5,𝔽2)11yescharacteristic
619C422−1+411yescharacteristic
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23#40812yes—
638C23C2×#10212yes—
639C23C2×#10212yes—
640C23C2×#10412yes—
641C23C22×C22⋊C411yescharacteristic
642Q8—84no—
643D4—28no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—84no—
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—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
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—84no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4#40812yes—
723C2×C4C2×#10212yes—
724C2×C4C2×#10212yes—
725C2×C4C2×#10212yes—
726C2×C4C2×#10212yes—
727C2×C4C2×#10412yes—
728C2×C4C2×#10412yes—
729C2×C4C4×#4111yescharacteristic
730C2×C4#52011yescharacteristic
731C2×C4#54611yescharacteristic
732C2×C4#54611yescharacteristic
733C2×C4#54711yescharacteristic
734C2×C4#54711yescharacteristic
735C2×C4C2×#13111yescharacteristic
736C2×C4C2×#13111yescharacteristic
737C2×C4C2×#13111yescharacteristic
738C2×C4#56811yescharacteristic
739C2×C4C22×D811yescharacteristic
740C2×C4C22×SD1611yescharacteristic
741C2×C4#57711yescharacteristic
742C2×C4#57811yescharacteristic
743C8—24no—
744C8—42no—
745C8—42no—
746C8—42no—
747C8—42no—
748C8—81no—
749C8—81no—
750C8—81no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22#149214yes—
772C22#233911yescharacteristic
773C22C2×#40811yescharacteristic
774C22#288011yescharacteristic
775C22C22×#10211yescharacteristic
776C22#289811yescharacteristic
777C22C22×#10411yescharacteristic
778C22#290111yescharacteristic
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—21no—
786C4—21no—
787C4—22no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—41no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4#296611yescharacteristic
799C4#296811yescharacteristic
800C4#299211yescharacteristic
801C4#299411yescharacteristic
802C4#329411yescharacteristic
803C4#329811yescharacteristic
804C4#333411yescharacteristic
805C4#333511yescharacteristic
806C2—24no—
807C2—42no—
808C2—161no—
809C2C2×#149211yescharacteristic
810C2#1748411yescharacteristic
811C2#1750711yescharacteristic
812C2#1751911yescharacteristic
813C2#2247011yescharacteristic
814C2#2248511yescharacteristic
815C2#2250511yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radical#2416C4
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
2. #22648C2semidirect
3. C4×C8×D4C2semidirect
4. #9870C2semidirect
5. #9869C2semidirect
6. #9072C2semidirect
7. #9072C2semidirect
8. #8944C2semidirect
9. #8939C2semidirect
10. #8709C2semidirect
11. #8706C2semidirect
12. #8567C2semidirect
13. #8177C2semidirect
14. #7897C2semidirect
15. C2×#1279C2semidirect

Maximal subgroups

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

subgroupindex
#347632
#226482
C4×C8×D42
#98702
#98692
#90722
#89442
#89392
#87092
#87062
#85672
#81772
#78972
C2×#12792