Finite Group Databasebeta

← #216022

Subgroups — #216022

Order 512.

1037 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35253C211yesmaximal, characteristic
2#20716C211yesmaximal, characteristic
3#13944C211yesmaximal, characteristic
4#9913C211yesmaximal, characteristic, complemented
5#9912C211yesmaximal, characteristic, complemented
6#9910C211yesmaximal, characteristic, complemented
7#9908C211yesmaximal, characteristic, complemented
8#9888C211yesmaximal, characteristic, complemented
9#9887C211yesmaximal, characteristic, complemented
10#9886C211yesmaximal, characteristic, complemented
11#9884C211yesmaximal, characteristic, complemented
12#8715C211yesmaximal, characteristic
13#8715C211yesmaximal, characteristic
14#8713C211yesmaximal, characteristic
15#8712C211yesmaximal, characteristic
16C2×#544C411yescharacteristic, complemented
17C22×#117C2211yescharacteristic
18C2×#433—21no—
19#2857C2211yescharacteristic
20#2857C2211yescharacteristic
21#2851C2211yescharacteristic
22#2851C2211yescharacteristic
23#2629C411yescharacteristic, complemented
24#2629C411yescharacteristic, complemented
25#2628C411yescharacteristic, complemented
26#2628C411yescharacteristic, complemented
27#2442—21no—
28#2441—21no—
29#2440—21no—
30#2439—21no—
31#2438—21no—
32#2438—21no—
33#2437—21no—
34#2437—21no—
35#2317C411yescharacteristic, complemented
36#2317C411yescharacteristic, complemented
37#2316C411yescharacteristic, complemented
38C2×#387—21no—
39#2280C2211yescharacteristic
40C2×#380C2211yescharacteristic
41#1818—21no—
42#1798—21no—
43#1797C2211yescharacteristic
44#1797C2211yescharacteristic
45#1779C2211yescharacteristic
46#1779C2211yescharacteristic
47#1750—21no—
48#1749C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50#1445—21no—
51#1439—21no—
52#1437—21no—
53C4⋊#95C2211yescharacteristic
54#1434C2211yescharacteristic
55#1434C2211yescharacteristic
56C22⋊#95C2211yescharacteristic
57C22⋊#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
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×C4C2311yescharacteristic
76#544—44no—
77C2×C4⋊Q8—21no—
78C2×C4⋊Q8C2×C411yescharacteristic
79C2×C4⋊Q8C2×C411yescharacteristic
80C2×#125—21no—
81C2×#125C2×C411yescharacteristic
82C2×#125C2×C411yescharacteristic
83C2×C22⋊Q8—21no—
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8—21no—
87C2×#117—44no—
88C2×#117C2×C411yescharacteristic
89C2×#117C2×C411yescharacteristic
90C2×#117C2×C411yescharacteristic
91C2×#117C2×C411yescharacteristic
92C2×#117C2×C411yescharacteristic
93C2×#117C2×C411yescharacteristic
94C2×#117D411yescharacteristic
95C2×#117D411yescharacteristic
96C2×#117D411yescharacteristic
97C2×#117D411yescharacteristic
98C22×C4⋊C4—21no—
99C22×C4⋊C4C2×C411yescharacteristic
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C4⋊C4D411yescharacteristic
102C22×C4⋊C4D411yescharacteristic
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4D411yescharacteristic
107C22×C22⋊C4D411yescharacteristic
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111#433—44no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×C22⋊C8—21no—
115C2×C22⋊C8—21no—
116C2×C22⋊C8—21no—
117C2×C22⋊C8—21no—
118C2×C22⋊C8C2311yescharacteristic
119C2×C22⋊C8C2311yescharacteristic
120C2×C22⋊C8C2311yescharacteristic
121C2×C22⋊C8C2311yescharacteristic
122C2×#97—21no—
123C2×C4×C8—21no—
124#400—21no—
125#400—21no—
126#399—21no—
127#399—21no—
128#398—21no—
129#398—21no—
130#398—21no—
131#398—21no—
132#396—21no—
133#396—21no—
134#396—21no—
135#396—21no—
136#395—21no—
137#395—21no—
138#393—21no—
139#393—21no—
140#391—21no—
141#391—21no—
142#389—21no—
143#389—21no—
144#389—21no—
145#389—21no—
146#389—21no—
147#389—21no—
148#389C2×C411yescharacteristic
149#389C2×C411yescharacteristic
150#389C2×C411yescharacteristic
151#389C2×C411yescharacteristic
152#389C2×C411yescharacteristic
153#389C2×C411yescharacteristic
154#389C2×C411yescharacteristic
155#389C2×C411yescharacteristic
156#387—21no—
157#387—21no—
158#387—21no—
159#387—21no—
160#387—44no—
161#385—21no—
162#385—21no—
163#385—21no—
164#385—21no—
165#385—21no—
166#385—21no—
167#385—21no—
168#385—21no—
169#384—21no—
170#384C2×C411yescharacteristic
171#384C2×C411yescharacteristic
172#382—21no—
173#382C2×C411yescharacteristic
174#382C2×C411yescharacteristic
175#381—21no—
176#380—21no—
177#380—21no—
178#380—21no—
179#380—21no—
180#380—21no—
181#380—21no—
182#380C2×C411yescharacteristic
183#380C2×C411yescharacteristic
184#380C2×C411yescharacteristic
185#380C2×C411yescharacteristic
186#380C2311yescharacteristic
187#380C2311yescharacteristic
188#380C2311yescharacteristic
189#380C2311yescharacteristic
190#379—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210C25C2×D411yescharacteristic
211C22×Q8—21no—
212C22×Q8—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2411yescharacteristic
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8—42no—
240C4⋊Q8—42no—
241C4⋊Q8—44no—
242#125—42no—
243#125—42no—
244#125—44no—
245C22⋊Q8—44no—
246C22⋊Q8—44no—
247C22⋊Q8—81no—
248C22⋊Q8—81no—
249C22⋊Q8—81no—
250C22⋊Q8—81no—
251#117—24no—
252#117—24no—
253#117—42no—
254#117—42no—
255#117—42no—
256#117—42no—
257#117—42no—
258#117—42no—
259#117—42no—
260#117—42no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4C22⋊C411yescharacteristic
289C2×C4⋊C4C22⋊C411yescharacteristic
290C2×C4⋊C4C22⋊C411yescharacteristic
291C2×C4⋊C4C22⋊C411yescharacteristic
292C2×C4⋊C4C22⋊C411yescharacteristic
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C4⋊C4C22×C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—81no—
321C2×C22⋊C4—81no—
322C2×C22⋊C4—81no—
323C2×C22⋊C4—81no—
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C22⋊C4C22⋊C411yescharacteristic
328C2×C22⋊C4C22⋊C411yescharacteristic
329C2×C22⋊C4C22⋊C411yescharacteristic
330C2×C22⋊C4C22⋊C411yescharacteristic
331C2×C22⋊C4C22⋊C411yescharacteristic
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—81no—
339C2×C42C22×C411yescharacteristic
340C2×C42C22×C411yescharacteristic
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C4⋊C8—42no—
348C4⋊C8—42no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—42no—
358C22⋊C8—42no—
359C22⋊C8—42no—
360C22⋊C8—42no—
361#97—42no—
362C4×C8—42no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
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—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—81no—
398#95—81no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24C2×C22⋊C411yescharacteristic
410C24C2×C22⋊C411yescharacteristic
411C24C22×D411yescharacteristic
412C2×Q8—42no—
413C2×Q8—42no—
414C2×Q8—81no—
415C2×Q8—81no—
416C2×Q8—81no—
417C2×Q8—81no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
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—41no—
454C22×C4—41no—
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—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
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—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
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—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
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×C4C23×C411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C42−1+411yescharacteristic
515C22×C42−1+411yescharacteristic
516C22×C42−1+411yescharacteristic
517C22×C42−1+411yescharacteristic
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—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4—84no—
566C4⋊C4#9914yes—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—42no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—42no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—42no—
600C42—42no—
601C42—84no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23#41012yes—
636C23C22×C22⋊C411yescharacteristic
637C23#53611yescharacteristic
638C23#53611yescharacteristic
639C23#57611yescharacteristic
640C23#57711yescharacteristic
641C23#57711yescharacteristic
642C23#57811yescharacteristic
643Q8—162no—
644Q8—162no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
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—21no—
667C2×C4—21no—
668C2×C4—21no—
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—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
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—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
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—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—162no—
751C2×C4—162no—
752C2×C4C2×#9912yes—
753C2×C4C2×#9912yes—
754C2×C4C2×#9912yes—
755C2×C4#51911yescharacteristic
756C2×C4#51911yescharacteristic
757C2×C4#53611yescharacteristic
758C2×C4#53611yescharacteristic
759C8—81no—
760C8—81no—
761C8—81no—
762C8—81no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22#231011yescharacteristic
794C22C22×#9911yescharacteristic
795C22C2×#41011yescharacteristic
796C22#289711yescharacteristic
797C22#289811yescharacteristic
798C22#290111yescharacteristic
799C22#290111yescharacteristic
800C22#324111yescharacteristic
801C22#324211yescharacteristic
802C22#324311yescharacteristic
803C22#324411yescharacteristic
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—82no—
819C4—82no—
820C4—81no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4—161no—
829C4—161no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—42no—
835C2—81no—
836C2#1760411yescharacteristic
837C2#1760811yescharacteristic
838C2#1760911yescharacteristic
839C2#1761111yescharacteristic
840C2#2182511yescharacteristic
841C2#2184311yescharacteristic
842C2#2184611yescharacteristic
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. #9913C2semidirect
5. #9912C2semidirect
6. #9910C2semidirect
7. #9908C2semidirect
8. #9888C2semidirect
9. #9887C2semidirect
10. #9886C2semidirect
11. #9884C2semidirect
16. C2×#544C4semidirect
23. #2629C4semidirect
24. #2629C4semidirect
25. #2628C4semidirect
26. #2628C4semidirect
35. #2317C4semidirect
36. #2317C4semidirect
37. #2316C4semidirect

Maximal subgroups

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

subgroupindex
#352532
#207162
#139442
#99132
#99122
#99102
#99082
#98882
#98872
#98862
#98842
#87152
#87132
#87122