Finite Group Databasebeta

← #216851

Subgroups — #216851

Order 512.

1042 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35086C211yesmaximal, characteristic
2#21904C211yesmaximal, characteristic
3#13782C211yesmaximal, characteristic
4#9887C211yesmaximal, characteristic, complemented
5#9886C211yesmaximal, characteristic, complemented
6#9683C211yesmaximal, characteristic, complemented
7#9679C211yesmaximal, characteristic, complemented
8#9146C211yesmaximal, characteristic
9#9146C211yesmaximal, characteristic
10#9143C211yesmaximal, characteristic
11#9143C211yesmaximal, characteristic
12#8578C211yesmaximal, characteristic, complemented
13#8576C211yesmaximal, characteristic, complemented
14#8574C211yesmaximal, characteristic, complemented
15#8572C211yesmaximal, characteristic, complemented
16#2857C2211yescharacteristic
17#2851C2211yescharacteristic
18#2848C2211yescharacteristic
19#2848C2211yescharacteristic
20#2652—21no—
21#2652—21no—
22#2505—21no—
23#2505—21no—
24#2496C411yescharacteristic, complemented
25#2496C411yescharacteristic, complemented
26#2489C411yescharacteristic, complemented
27#2489C411yescharacteristic, complemented
28#2480—21no—
29#2480—21no—
30#2429C411yescharacteristic, complemented
31#2429C411yescharacteristic, complemented
32#2421C411yescharacteristic, complemented
33#2421C411yescharacteristic, complemented
34#2334—21no—
35#2334—21no—
36C4×C22⋊Q8C2211yescharacteristic
37C4×C22⋊Q8C2211yescharacteristic
38C2×#385—21no—
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41C22×#95C2211yescharacteristic
42#1924—21no—
43#1924—21no—
44#1923—21no—
45#1923—21no—
46#1797C2211yescharacteristic
47#1797C2211yescharacteristic
48#1779C2211yescharacteristic
49#1779C2211yescharacteristic
50#1749C2211yescharacteristic
51C4×C22⋊C8C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434C2211yescharacteristic
65#1434C2211yescharacteristic
66C22⋊#95—21no—
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C2×C4⋊Q8C2×C411yescharacteristic, complemented
78C2×#126—21no—
79C2×#126—21no—
80C2×#125C2×C411yescharacteristic, complemented
81C2×C22⋊Q8C2×C411yescharacteristic
82C2×C22⋊Q8C2×C411yescharacteristic
83C2×C22⋊Q8C2×C411yescharacteristic
84C2×C22⋊Q8C2×C411yescharacteristic
85C2×C22⋊Q8C2311yescharacteristic
86C2×C22⋊Q8C2311yescharacteristic
87C2×C4×Q8C2×C411yescharacteristic, complemented
88C2×C4×Q8C2×C411yescharacteristic, complemented
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4D411yescharacteristic
93C22×C22⋊C4D411yescharacteristic
94C22×C42—21no—
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C22⋊C8—21no—
100C2×C22⋊C8—21no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8C2311yescharacteristic
104C2×C22⋊C8C2311yescharacteristic
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×#97—21no—
108C2×C4×C8—21no—
109#400—21no—
110#400—21no—
111#400—21no—
112#400—21no—
113#400—21no—
114#400—21no—
115#398—21no—
116#398—21no—
117#397—21no—
118#397—21no—
119#397—21no—
120#397—21no—
121#397—21no—
122#397—21no—
123#396—21no—
124#396—21no—
125#391C2×C411yescharacteristic, complemented
126#391C2×C411yescharacteristic, complemented
127#391C2×C411yescharacteristic, complemented
128#391C2×C411yescharacteristic, complemented
129#389—21no—
130#389—21no—
131#389—21no—
132#389—21no—
133#389C2×C411yescharacteristic, complemented
134#389C2×C411yescharacteristic, complemented
135#389C2×C411yescharacteristic, complemented
136#389C2×C411yescharacteristic, complemented
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#385—28no—
152#385—21no—
153#385—21no—
154#385—21no—
155#385—21no—
156#385—21no—
157#385—21no—
158#385—21no—
159#385—21no—
160#385—21no—
161#385—21no—
162#384C2×C411yescharacteristic, complemented
163#382—21no—
164#382—21no—
165#382C2×C411yescharacteristic, complemented
166#380—21no—
167#380—21no—
168#380C2×C411yescharacteristic
169#380C2×C411yescharacteristic
170#380C2×C411yescharacteristic
171#380C2×C411yescharacteristic
172#380C2311yescharacteristic
173#380C2311yescharacteristic
174#379—21no—
175#379—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C2×C411yescharacteristic, complemented
179C4×C4⋊C4C2×C411yescharacteristic, complemented
180C4×C22⋊C4—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—41no—
183C4×C22⋊C4—41no—
184C4×C22⋊C4C2×C411yescharacteristic
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4C2×C411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—41no—
200C2×#95—41no—
201C2×#95D411yescharacteristic
202C2×#95D411yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#328—41no—
212#328—41no—
213#328—41no—
214#328—41no—
215#328—41no—
216#328—41no—
217#328—41no—
218#328—41no—
219C25C2×D411yescharacteristic
220C22×Q8C22×C411yescharacteristic
221C22×Q8C22×C411yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—24no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—81no—
234C23×C4—81no—
235C23×C4—81no—
236C23×C4—81no—
237C23×C4—81no—
238C23×C4—81no—
239C23×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2411yescharacteristic
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C4⋊Q8—81no—
254#126—44no—
255#126—44no—
256#125—81no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—81no—
266C22⋊Q8—81no—
267C22⋊Q8—81no—
268C22⋊Q8—81no—
269C4×Q8—81no—
270C4×Q8—81no—
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—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—21no—
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—81no—
292C2×C4⋊C4—81no—
293C2×C4⋊C4—81no—
294C2×C4⋊C4—81no—
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×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
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—21no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—42no—
331C2×C42—81no—
332C2×C42—81no—
333C2×C42—81no—
334C2×C42—81no—
335C2×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C22×C411yescharacteristic
338C2×C42C22×C411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C4⋊C8—81no—
344C4⋊C8—81no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—81no—
354C22⋊C8—81no—
355C22⋊C8—81no—
356C22⋊C8—81no—
357#97—81no—
358C4×C8—81no—
359#95—24no—
360#95—24no—
361#95—21no—
362#95—21no—
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—81no—
393#95—81no—
394#95—81no—
395#95—81no—
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95C22⋊C411yescharacteristic
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—41no—
413C24—41no—
414C24C2×C22⋊C411yescharacteristic
415C24C2×C22⋊C411yescharacteristic
416C24C22×D411yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
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—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—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—41no—
486C22×C4—41no—
487C22×C4—48no—
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—82no—
501C22×C4—82no—
502C22×C4—82no—
503C22×C4—82no—
504C22×C4—84no—
505C22×C4—84no—
506C22×C4—84no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C23×C411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
523C22×C4H(5,𝔽2)11yescharacteristic
524C22×C42−1+411yescharacteristic
525C22×C42−1+411yescharacteristic
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
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—81no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—48no—
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—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C22⋊C4#10414yes—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—42no—
602C42—42no—
603C42—81no—
604C42—81no—
605C42—84no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—24no—
611C23—24no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23C2×#10412yes—
639C23#42112yes—
640C23C22×C22⋊C411yescharacteristic
641C23#53511yescharacteristic
642C23#53611yescharacteristic
643C23#57711yescharacteristic
644C23#57711yescharacteristic
645C23#57811yescharacteristic
646C23#57811yescharacteristic
647Q8—81no—
648Q8—81no—
649Q8—81no—
650Q8—81no—
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—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
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—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
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—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—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—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—816no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4C2×#10412yes—
759C2×C4C2×#10412yes—
760C2×C4#52011yescharacteristic
761C2×C4#52011yescharacteristic
762C2×C4#53711yescharacteristic
763C2×C4#53711yescharacteristic
764C8—81no—
765C8—81no—
766C8—81no—
767C8—81no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22#231111yescharacteristic
799C22#288311yescharacteristic
800C22#288311yescharacteristic
801C22#289811yescharacteristic
802C22#289811yescharacteristic
803C22C22×#10411yescharacteristic
804C22C2×#42111yescharacteristic
805C22#322211yescharacteristic
806C22#322311yescharacteristic
807C22#324211yescharacteristic
808C22#324211yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—22no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4—81no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—42no—
840C2—42no—
841C2#1754811yescharacteristic
842C2#1754811yescharacteristic
843C2#1759811yescharacteristic
844C2#1759811yescharacteristic
845C2#2187311yescharacteristic
846C2#2187611yescharacteristic
847C2#2189911yescharacteristic
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
4. #9887C2semidirect
5. #9886C2semidirect
6. #9683C2semidirect
7. #9679C2semidirect
12. #8578C2semidirect
13. #8576C2semidirect
14. #8574C2semidirect
15. #8572C2semidirect
24. #2496C4semidirect
25. #2496C4semidirect
26. #2489C4semidirect
27. #2489C4semidirect
30. #2429C4semidirect
31. #2429C4semidirect
32. #2421C4semidirect
33. #2421C4semidirect
77. C2×C4⋊Q8C2×C4semidirect
80. C2×#125C2×C4semidirect
87. C2×C4×Q8C2×C4semidirect
88. C2×C4×Q8C2×C4semidirect
125. #391C2×C4semidirect
126. #391C2×C4semidirect
127. #391C2×C4semidirect
128. #391C2×C4semidirect
133. #389C2×C4semidirect
134. #389C2×C4semidirect
135. #389C2×C4semidirect
136. #389C2×C4semidirect
162. #384C2×C4semidirect
165. #382C2×C4semidirect
178. C4×C4⋊C4C2×C4semidirect
179. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#350862
#219042
#137822
#98872
#98862
#96832
#96792
#91462
#91432
#85782
#85762
#85742
#85722