Finite Group Databasebeta

← #191087

Subgroups — #191087

Order 512.

1041 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34245C211yesmaximal, characteristic
2#21904C211yesmaximal, characteristic
3#14351C211yesmaximal, characteristic
4#8715C211yesmaximal, characteristic
5#8715C211yesmaximal, characteristic
6#8578C211yesmaximal, characteristic, complemented
7#8576C211yesmaximal, characteristic, complemented
8#8574C211yesmaximal, characteristic, complemented
9#8572C211yesmaximal, characteristic, complemented
10#8329C211yesmaximal, characteristic
11#8329C211yesmaximal, characteristic
12#8221C211yesmaximal, characteristic, complemented
13#8221C211yesmaximal, characteristic, complemented
14#8217C211yesmaximal, characteristic, complemented
15#8217C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2211yescharacteristic
17#2368—21no—
18#2368—21no—
19#2362C411yescharacteristic, complemented
20#2362C411yescharacteristic, complemented
21#2362C411yescharacteristic, complemented
22#2362C411yescharacteristic, complemented
23#2344C411yescharacteristic, complemented
24#2344C411yescharacteristic, complemented
25#2342—21no—
26#2342—21no—
27Q8×C22⋊C4C411yescharacteristic, complemented
28Q8×C22⋊C4C411yescharacteristic, complemented
29#2332—21no—
30#2332—21no—
31#2313—21no—
32C4×C22⋊Q8C2211yescharacteristic
33C4×C22⋊Q8C2211yescharacteristic
34C4×C22⋊Q8C2211yescharacteristic
35C4×C22⋊Q8C2211yescharacteristic
36#2280C2211yescharacteristic
37#2274—21no—
38C2×C4×C22⋊C4C2211yescharacteristic
39#1924—21no—
40#1924—21no—
41#1923—21no—
42#1923—21no—
43#1797C2211yescharacteristic
44#1797C2211yescharacteristic
45#1779C2211yescharacteristic
46#1779C2211yescharacteristic
47#1749C2211yescharacteristic
48C4×C22⋊C8C2211yescharacteristic
49C2×#328C2211yescharacteristic
50C2×#328C2211yescharacteristic
51C2×#328C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57#1443—21no—
58#1442—21no—
59#1440—21no—
60#1439—21no—
61C4⋊#95C2211yescharacteristic
62#1434C2211yescharacteristic
63#1434C2211yescharacteristic
64#1434C2211yescharacteristic
65C22⋊#95C2211yescharacteristic
66C22⋊#95C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C23×Q8C2×C411yescharacteristic
76C24×C4C2311yescharacteristic
77C2×C22⋊Q8—21no—
78C2×C22⋊Q8—21no—
79C2×C22⋊Q8—22no—
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8C2×C411yescharacteristic
84C2×C22⋊Q8C2×C411yescharacteristic
85C2×C22⋊Q8C2311yescharacteristic
86C2×C22⋊Q8C2311yescharacteristic
87C2×C4×Q8C2×C411yescharacteristic
88C2×C4×Q8C2×C411yescharacteristic
89C2×C4×Q8C2×C411yescharacteristic
90C2×C4×Q8C2×C411yescharacteristic
91C2×#117—21no—
92C2×#117—21no—
93C2×#117C2×C411yescharacteristic
94C2×#117C2×C411yescharacteristic
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4C2×C411yescharacteristic
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4D411yescharacteristic
102C22×C22⋊C4D411yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C22⋊C8—21no—
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C2×C22⋊C8—21no—
111C2×C22⋊C8C2311yescharacteristic
112C2×C22⋊C8C2311yescharacteristic
113C2×C22⋊C8C2311yescharacteristic
114C2×C22⋊C8C2311yescharacteristic
115C2×#97—21no—
116C2×C4×C8—21no—
117#391—21no—
118#391—21no—
119#391—21no—
120#391—21no—
121#391C2×C411yescharacteristic
122#391C2×C411yescharacteristic
123#391C2×C411yescharacteristic
124#391C2×C411yescharacteristic
125#389C2×C411yescharacteristic
126#389C2×C411yescharacteristic
127#389C2×C411yescharacteristic
128#389C2×C411yescharacteristic
129#388—21no—
130#388—21no—
131#388—21no—
132#388—21no—
133#388—21no—
134#388—21no—
135#388—21no—
136#388—21no—
137#387—21no—
138#387—21no—
139#387—21no—
140#387—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#385—21no—
150#385—21no—
151#385—21no—
152#385—21no—
153#381—21no—
154#381—21no—
155#381—21no—
156#380—21no—
157#380—21no—
158#380C2×C411yescharacteristic
159#380C2×C411yescharacteristic
160#380C2311yescharacteristic
161#380C2311yescharacteristic
162#379—21no—
163C4×C4⋊C4—21no—
164C4×C4⋊C4—21no—
165C4×C4⋊C4—21no—
166C4×C4⋊C4—21no—
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4C2×C411yescharacteristic
172C4×C4⋊C4C2×C411yescharacteristic
173C4×C4⋊C4C2×C411yescharacteristic
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C22⋊C4—21no—
176C4×C22⋊C4—21no—
177C4×C22⋊C4—21no—
178C4×C22⋊C4—21no—
179C4×C22⋊C4—21no—
180C4×C22⋊C4—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—21no—
183C4×C22⋊C4C2×C411yescharacteristic
184C4×C22⋊C4C2×C411yescharacteristic
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4D411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95D411yescharacteristic
201C2×#95D411yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#328—22no—
211#328—22no—
212#328—22no—
213#328—22no—
214#328—22no—
215#328—22no—
216#328—22no—
217#328—22no—
218C25C2×D411yescharacteristic
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—21no—
222C22×Q8—81no—
223C22×Q8—81no—
224C22×Q8C22×C411yescharacteristic
225C22×Q8C22×C411yescharacteristic
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—81no—
237C23×C4—81no—
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2411yescharacteristic
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—24no—
255C22⋊Q8—24no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—22no—
263C22⋊Q8—22no—
264C22⋊Q8#4112yes—
265C22⋊Q8#4112yes—
266C22⋊Q8#4112yes—
267C22⋊Q8#4112yes—
268C4×Q8—81no—
269C4×Q8—81no—
270C4×Q8—81no—
271C4×Q8—81no—
272#117—44no—
273#117—44no—
274#117—81no—
275#117—81no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
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—42no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4—81no—
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×C22⋊C4—24no—
303C2×C22⋊C4—24no—
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—81no—
319C2×C22⋊C4—81no—
320C2×C22⋊C4—81no—
321C2×C22⋊C4—81no—
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
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×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—81no—
341C2×C42—81no—
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C4⋊C8—81no—
351C4⋊C8—81no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—81no—
361C22⋊C8—81no—
362C22⋊C8—81no—
363C22⋊C8—81no—
364#97—81no—
365C4×C8—81no—
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—21no—
392#95—21no—
393#95—21no—
394#95—42no—
395#95—81no—
396#95—81no—
397#95—81no—
398#95—81no—
399#95—81no—
400#95—81no—
401#95—81no—
402#95—81no—
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411C24—22no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24C2×C22⋊C411yescharacteristic
422C24C2×C22⋊C411yescharacteristic
423C24C22×D411yescharacteristic
424C2×Q8—24no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—84no—
434C2×Q8—84no—
435C2×Q8#11712yes—
436C2×Q8#11712yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
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—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
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—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—42no—
486C22×C4—42no—
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—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—82no—
516C22×C4—82no—
517C22×C4—82no—
518C22×C4—82no—
519C22×C4—81no—
520C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C23×C411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—81no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4—84no—
571C4⋊C4#11712yes—
572C4⋊C4#11712yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—42no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—42no—
606C42—42no—
607C42—42no—
608C42—42no—
609C42—81no—
610C42—81no—
611C42—81no—
612C42—81no—
613C42—81no—
614C42—81no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23#42112yes—
649C23C22×C22⋊C411yescharacteristic
650C23#52511yescharacteristic
651C23#52511yescharacteristic
652C23#57711yescharacteristic
653C23#57711yescharacteristic
654C23#57811yescharacteristic
655C23#57811yescharacteristic
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—84no—
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—21no—
679C2×C4—21no—
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—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
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—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
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—84no—
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—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
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#42112yes—
771C2×C4C2×#11711yescharacteristic
772C2×C4C2×#11711yescharacteristic
773C2×C4#52511yescharacteristic
774C2×C4#52511yescharacteristic
775C8—81no—
776C8—81no—
777C8—81no—
778C8—81no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22#228011yescharacteristic
810C22#288311yescharacteristic
811C22#288311yescharacteristic
812C22#289811yescharacteristic
813C22#289811yescharacteristic
814C22C2×#42111yescharacteristic
815C22C2×#42111yescharacteristic
816C22#312111yescharacteristic
817C22#312111yescharacteristic
818C22#312611yescharacteristic
819C22#312711yescharacteristic
820C4—22no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—42no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—161no—
843C4—161no—
844C4—161no—
845C4—161no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—21no—
850C2—42no—
851C2—81no—
852C2#1759811yescharacteristic
853C2#1759811yescharacteristic
854C2#1759811yescharacteristic
855C2#1760011yescharacteristic
856C2#2072411yescharacteristic
857C2#2074511yescharacteristic
858C2#2074811yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #8578C2semidirect
7. #8576C2semidirect
8. #8574C2semidirect
9. #8572C2semidirect
12. #8221C2semidirect
13. #8221C2semidirect
14. #8217C2semidirect
15. #8217C2semidirect
19. #2362C4semidirect
20. #2362C4semidirect
21. #2362C4semidirect
22. #2362C4semidirect
23. #2344C4semidirect
24. #2344C4semidirect
27. Q8×C22⋊C4C4semidirect
28. Q8×C22⋊C4C4semidirect

Maximal subgroups

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

subgroupindex
#342452
#219042
#143512
#87152
#85782
#85762
#85742
#85722
#83292
#82212
#82172