Finite Group Databasebeta

← #207022

Subgroups — #207022

Order 512.

1212 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35253C211yesmaximal, characteristic
2#20379C211yesmaximal, characteristic
3#13962C211yesmaximal, characteristic
4#9889C211yesmaximal, characteristic, complemented
5#9888C211yesmaximal, characteristic, complemented
6#9887C211yesmaximal, characteristic, complemented
7#9887C211yesmaximal, characteristic, complemented
8#9886C211yesmaximal, characteristic, complemented
9#9886C211yesmaximal, characteristic, complemented
10#9885C211yesmaximal, characteristic, complemented
11#9884C211yesmaximal, characteristic, complemented
12#8024C211yesmaximal, characteristic
13#8020C211yesmaximal, characteristic
14#8015C211yesmaximal, characteristic
15C2×#1294C211yesmaximal, characteristic
16C2×#544C411yescharacteristic, complemented
17C22×#117C2211yescharacteristic
18C2×#407C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C2×#405—21no—
21#2857C2211yescharacteristic
22#2857C2211yescharacteristic
23#2851C2211yescharacteristic
24#2851C2211yescharacteristic
25#2629C411yescharacteristic, complemented
26#2629C411yescharacteristic, complemented
27#2628C411yescharacteristic, complemented
28#2628C411yescharacteristic, complemented
29#2442—21no—
30#2441—21no—
31#2440—21no—
32#2439—21no—
33#2438—21no—
34#2438—21no—
35#2437—21no—
36#2437—21no—
37#2317C411yescharacteristic, complemented
38#2317C411yescharacteristic, complemented
39#2316C411yescharacteristic, complemented
40C2×#385—21no—
41#2280C2211yescharacteristic
42C2×#381C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1750—21no—
46#1750—21no—
47#1749C2211yescharacteristic
48#1749C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50C4×C22⋊C8C2211yescharacteristic
51#1729—21no—
52#1441—21no—
53#1441—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56#1434C2211yescharacteristic
57#1434C2211yescharacteristic
58C22⋊#95—21no—
59#1294C2211yescharacteristic
60#1294C2211yescharacteristic
61#1294C2211yescharacteristic
62#1294C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C22×M16—21no—
78C23×C8—21no—
79#544—44no—
80C2×C4⋊Q8—21no—
81C2×C4⋊Q8C2×C411yescharacteristic, complemented
82C2×C4⋊Q8C2×C411yescharacteristic, complemented
83C2×#125—21no—
84C2×#125C2×C411yescharacteristic, complemented
85C2×#125C2×C411yescharacteristic, complemented
86C2×C22⋊Q8—21no—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×#117—44no—
91C2×#117C2×C411yescharacteristic
92C2×#117C2×C411yescharacteristic
93C2×#117C2×C411yescharacteristic
94C2×#117C2×C411yescharacteristic
95C2×#117C2×C411yescharacteristic
96C2×#117C2×C411yescharacteristic
97C2×#117D411yescharacteristic
98C2×#117D411yescharacteristic
99C2×#117D411yescharacteristic
100C2×#117D411yescharacteristic
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4C2×C411yescharacteristic
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4D411yescharacteristic
106C22×C4⋊C4D411yescharacteristic
107C22×C22⋊C4—21no—
108C22×C22⋊C4—21no—
109C22×C22⋊C4D411yescharacteristic
110C22×C22⋊C4D411yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113#407—22no—
114#407Q814yescomplemented
115C2×C22⋊C8—21no—
116C2×C22⋊C8—21no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8Q814yescomplemented
119C2×C22⋊C8C2311yescharacteristic
120C2×C22⋊C8C2311yescharacteristic
121C2×C22⋊C8C2311yescharacteristic
122C2×C22⋊C8C2311yescharacteristic
123#405—44no—
124C2×#97—21no—
125C2×#97—21no—
126C2×C4×C8—21no—
127C2×C4×C8—21no—
128#400—21no—
129#400—21no—
130#399—21no—
131#399—21no—
132#398—21no—
133#398—21no—
134#398—21no—
135#398—21no—
136#396—21no—
137#396—21no—
138#396—21no—
139#396—21no—
140#395—21no—
141#395—21no—
142#393—21no—
143#393—21no—
144#391—21no—
145#391—21no—
146#389—21no—
147#389—21no—
148#389—21no—
149#389—21no—
150#389—21no—
151#389—21no—
152#389C2×C411yescharacteristic, complemented
153#389C2×C411yescharacteristic, complemented
154#389C2×C411yescharacteristic, complemented
155#389C2×C411yescharacteristic, complemented
156#389C2×C411yescharacteristic, complemented
157#389C2×C411yescharacteristic, complemented
158#389C2×C411yescharacteristic, complemented
159#389C2×C411yescharacteristic, complemented
160#387—21no—
161#387—21no—
162#387—21no—
163#387—21no—
164#385—21no—
165#385—21no—
166#385—21no—
167#385—21no—
168#385—21no—
169#385—21no—
170#385—21no—
171#385—21no—
172#385—44no—
173#384—21no—
174#384C2×C411yescharacteristic, complemented
175#384C2×C411yescharacteristic, complemented
176#382—21no—
177#382C2×C411yescharacteristic, complemented
178#382C2×C411yescharacteristic, complemented
179#381—21no—
180#381—22no—
181#381—22no—
182#380—21no—
183#380—21no—
184#380—21no—
185#380—21no—
186#380—21no—
187#380—21no—
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190#380C2×C411yescharacteristic
191#380C2×C411yescharacteristic
192#380C2311yescharacteristic
193#380C2311yescharacteristic
194#380C2311yescharacteristic
195#380C2311yescharacteristic
196#379—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C2×#95—21no—
200C2×#95—22no—
201C2×#95—22no—
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×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214#336—21no—
215#336—21no—
216#336—21no—
217#336—21no—
218C25C2×D411yescharacteristic
219C22×Q8—21no—
220C22×Q8—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—81no—
235C23×C4—81no—
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×Q812yes—
246C23×C4C2×Q812yes—
247C23×C4#4112yes—
248C23×C4#4112yes—
249C23×C4C2411yescharacteristic
250C2×M16—24no—
251C2×M16—42no—
252C2×M16—42no—
253C22×C8—24no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—42no—
259C22×C8—42no—
260C4⋊Q8—42no—
261C4⋊Q8—42no—
262C4⋊Q8—44no—
263#125—42no—
264#125—42no—
265#125—44no—
266C22⋊Q8—44no—
267C22⋊Q8—44no—
268C22⋊Q8—81no—
269C22⋊Q8—81no—
270C22⋊Q8—81no—
271C22⋊Q8—81no—
272#117—24no—
273#117—24no—
274#117—42no—
275#117—42no—
276#117—42no—
277#117—42no—
278#117—42no—
279#117—42no—
280#117—42no—
281#117—42no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
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—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—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—81no—
311C2×C4⋊C4—81no—
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×C4⋊C4C22×C411yescharacteristic
324C2×C4⋊C4C22×C411yescharacteristic
325C2×C4⋊C4C22×C411yescharacteristic
326C2×C4⋊C4C22×C411yescharacteristic
327C2×C4⋊C4C22×C411yescharacteristic
328C2×C22⋊C4—24no—
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—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—81no—
344C2×C22⋊C4—81no—
345C2×C22⋊C4C22⋊C411yescharacteristic
346C2×C22⋊C4C22⋊C411yescharacteristic
347C2×C22⋊C4C22⋊C411yescharacteristic
348C2×C22⋊C4C22⋊C411yescharacteristic
349C2×C22⋊C4C22⋊C411yescharacteristic
350C2×C22⋊C4C22⋊C411yescharacteristic
351C2×C22⋊C4C22⋊C411yescharacteristic
352C2×C22⋊C4C22⋊C411yescharacteristic
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42C22×C411yescharacteristic
358C2×C42C22×C411yescharacteristic
359C2×C42C22×C411yescharacteristic
360C2×C42C22×C411yescharacteristic
361C2×C42C2×D411yescharacteristic
362C2×C42C2×D411yescharacteristic
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C22⋊C8—24no—
366C22⋊C8—24no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8C2×Q812yes—
372C22⋊C8C2×Q812yes—
373C22⋊C8C2×Q812yes—
374C22⋊C8C2×Q812yes—
375#97—42no—
376#97—42no—
377C4×C8—42no—
378C4×C8—42no—
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—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—81no—
414#95—81no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—41no—
422C24—41no—
423C24C2×C22⋊C411yescharacteristic
424C24C2×C22⋊C411yescharacteristic
425C24#12412yes—
426C24C4⋊Q812yes—
427C24C22×D411yescharacteristic
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—81no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—81no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
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—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
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—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
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—41no—
481C22×C4—41no—
482C22×C4—48no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
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—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4—84no—
512C22×C4—84no—
513C22×C4—84no—
514C22×C4—84no—
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
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×C4C4×Q812yes—
526C22×C4C4×Q812yes—
527C22×C4C4×Q812yes—
528C22×C4C4×Q812yes—
529C22×C4C22⋊Q812yes—
530C22×C4C22⋊Q812yes—
531C22×C4C22⋊Q812yes—
532C22×C4C22⋊Q812yes—
533C22×C4#12412yes—
534C22×C4C4⋊Q812yes—
535C22×C4C23×C411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×Q811yescharacteristic
538C22×C4C22×Q811yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541M16—48no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—48no—
553C2×C8—41no—
554C2×C8—41no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
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—81no—
580C4⋊C4—81no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4—81no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4—81no—
587C4⋊C4—81no—
588C4⋊C4—81no—
589C4⋊C4—81no—
590C4⋊C4—81no—
591C4⋊C4—84no—
592C4⋊C4—84no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—84no—
615C22⋊C4#9914yes—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—42no—
625C42—42no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—21no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#39112yes—
657C23#39112yes—
658C23C2×#9912yes—
659C23#41012yes—
660C23C22×C22⋊C411yescharacteristic
661C23C2×#12411yescharacteristic
662C23C2×C4⋊Q811yescharacteristic
663C23#57611yescharacteristic
664C23#57711yescharacteristic
665C23#57711yescharacteristic
666C23#57811yescharacteristic
667Q8—162no—
668Q8—162no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
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—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
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—81no—
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—816no—
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—81no—
773C2×C4—81no—
774C2×C4—162no—
775C2×C4—162no—
776C2×C4#39112yes—
777C2×C4#39112yes—
778C2×C4C2×#9912yes—
779C2×C4C2×#9912yes—
780C2×C4C2×C4×Q811yescharacteristic
781C2×C4C2×C4×Q811yescharacteristic
782C2×C4C2×C22⋊Q811yescharacteristic
783C2×C4C2×C22⋊Q811yescharacteristic
784C8—42no—
785C8—42no—
786C8—42no—
787C8—42no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—22no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—22no—
797C22—21no—
798C22—21no—
799C22—22no—
800C22—21no—
801C22—21no—
802C22—22no—
803C22—21no—
804C22—21no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22#199614yes—
818C22C2×#39111yescharacteristic
819C22C22×#9911yescharacteristic
820C22C2×#41011yescharacteristic
821C22#289711yescharacteristic
822C22#289811yescharacteristic
823C22#290111yescharacteristic
824C22#290111yescharacteristic
825C22#313611yescharacteristic
826C22#313711yescharacteristic
827C22#316311yescharacteristic
828C22#316411yescharacteristic
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—82no—
844C4—82no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4—81no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—161no—
854C4—161no—
855C2—21no—
856C2—21no—
857C2—21no—
858C2—21no—
859C2—24no—
860C2—42no—
861C2#1760311yescharacteristic
862C2#1760411yescharacteristic
863C2#1760811yescharacteristic
864C2#1760911yescharacteristic
865C2#2130711yescharacteristic
866C2#2132611yescharacteristic
867C2C2×#199611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #9889C2semidirect
5. #9888C2semidirect
6. #9887C2semidirect
7. #9887C2semidirect
8. #9886C2semidirect
9. #9886C2semidirect
10. #9885C2semidirect
11. #9884C2semidirect
16. C2×#544C4semidirect
25. #2629C4semidirect
26. #2629C4semidirect
27. #2628C4semidirect
28. #2628C4semidirect
37. #2317C4semidirect
38. #2317C4semidirect
39. #2316C4semidirect
81. C2×C4⋊Q8C2×C4semidirect
82. C2×C4⋊Q8C2×C4semidirect
84. C2×#125C2×C4semidirect
85. C2×#125C2×C4semidirect
114. #407Q8semidirect
118. C2×C22⋊C8Q8semidirect
152. #389C2×C4semidirect
153. #389C2×C4semidirect
154. #389C2×C4semidirect
155. #389C2×C4semidirect
156. #389C2×C4semidirect
157. #389C2×C4semidirect
158. #389C2×C4semidirect
159. #389C2×C4semidirect
174. #384C2×C4semidirect
175. #384C2×C4semidirect
177. #382C2×C4semidirect
178. #382C2×C4semidirect

Maximal subgroups

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

subgroupindex
#352532
#203792
#139622
#98892
#98882
#98872
#98862
#98852
#98842
#80242
#80202
#80152
C2×#12942