Finite Group Databasebeta

← #216848

Subgroups — #216848

Order 512.

1087 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35080C211yesmaximal, characteristic
2#21904C211yesmaximal, characteristic, complemented
3#13782C211yesmaximal, characteristic, complemented
4#9889C211yesmaximal, characteristic, complemented
5#9884C211yesmaximal, characteristic, complemented
6#9682C211yesmaximal, characteristic, complemented
7#9681C211yesmaximal, characteristic, complemented
8#9150C211yesmaximal, characteristic
9#9147C211yesmaximal, characteristic
10#9146C211yesmaximal, characteristic, complemented
11#9143C211yesmaximal, characteristic, complemented
12#8578C211yesmaximal, characteristic, complemented
13#8576C211yesmaximal, characteristic, complemented
14#8573C211yesmaximal, characteristic, complemented
15#8571C211yesmaximal, characteristic, complemented
16#2857C2211yescharacteristic
17#2850C2211yescharacteristic
18#2848C2211yescharacteristic
19#2847C2211yescharacteristic
20#2653—21no—
21#2649—21no—
22#2510—21no—
23#2495C411yescharacteristic, complemented
24#2494C411yescharacteristic, complemented
25#2492C411yescharacteristic, complemented
26#2491C411yescharacteristic, complemented
27#2472—21no—
28#2450—21no—
29#2427C411yescharacteristic, complemented
30#2426C411yescharacteristic, complemented
31#2423C411yescharacteristic, complemented
32#2422C411yescharacteristic, complemented
33#2418—21no—
34#2337—21no—
35#2335—21no—
36C4×C22⋊Q8C2211yescharacteristic
37C4×#121C2211yescharacteristic
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×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
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×#124—21no—
79C2×#124C2×C411yescharacteristic, complemented
80C2×#123—21no—
81C2×C22⋊Q8—21no—
82C2×C22⋊Q8C2×C411yescharacteristic
83C2×C22⋊Q8C2×C411yescharacteristic
84C2×C22⋊Q8C2311yescharacteristic
85C2×#121C2×C411yescharacteristic
86C2×#121C2×C411yescharacteristic
87C2×#121C2311yescharacteristic
88C2×#120—21no—
89C2×C4×Q8C2×C411yescharacteristic, complemented
90C2×C4×D4—21no—
91C2×C4×D4C2×C411yescharacteristic, complemented
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4D411yescharacteristic
96C22×C22⋊C4D411yescharacteristic
97C22×C42—21no—
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8—21no—
105C2×C22⋊C8—21no—
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×C22⋊C8C2311yescharacteristic
109C2×C22⋊C8C2311yescharacteristic
110C2×#97—21no—
111C2×C4×C8—21no—
112#401—21no—
113#400—21no—
114#400—21no—
115#399—21no—
116#398—21no—
117#397—21no—
118#397—21no—
119#397—21no—
120#397—21no—
121#396—21no—
122#394—21no—
123#394—21no—
124#394—21no—
125#394—21no—
126#393—21no—
127#393—21no—
128#391—21no—
129#391—21no—
130#391C2×C411yescharacteristic, complemented
131#391C2×C411yescharacteristic, complemented
132#390—21no—
133#390C2×C411yescharacteristic, complemented
134#390C2×C411yescharacteristic, complemented
135#389—21no—
136#389C2×C411yescharacteristic, complemented
137#389C2×C411yescharacteristic, complemented
138#389C2×C411yescharacteristic, complemented
139#389C2×C411yescharacteristic, complemented
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#388—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#386—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#385—28no—
160#385—21no—
161#385—21no—
162#385—21no—
163#385—21no—
164#385—21no—
165#384C2×C411yescharacteristic, complemented
166#383—21no—
167#382C2×C411yescharacteristic, complemented
168#380—21no—
169#380—21no—
170#380C2×C411yescharacteristic
171#380C2×C411yescharacteristic
172#380C2×C411yescharacteristic
173#380C2×C411yescharacteristic
174#380C2311yescharacteristic
175#380C2311yescharacteristic
176#379—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#327—41no—
216#327—41no—
217#327—41no—
218#327—41no—
219C25C2×D411yescharacteristic
220C22×Q8—21no—
221C22×Q8C22×C411yescharacteristic
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C22×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—24no—
235C23×C4—21no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—81no—
239C23×C4—81no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2411yescharacteristic
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C4⋊Q8—81no—
259#124—44no—
260#124—81no—
261#123—44no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—81no—
267C22⋊Q8—81no—
268C22⋊Q8—81no—
269C22⋊Q8—81no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—81no—
275#121—81no—
276#120—81no—
277#120—81no—
278C4×Q8—81no—
279C4×D4—81no—
280C4×D4—81no—
281C4×D4—81no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
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—81no—
296C2×C4⋊C4—81no—
297C2×C4⋊C4—81no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
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—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
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—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4C22⋊C411yescharacteristic
330C2×C22⋊C4C22⋊C411yescharacteristic
331C2×C22⋊C4C22⋊C411yescharacteristic
332C2×C22⋊C4C22⋊C411yescharacteristic
333C2×C22⋊C4C22⋊C411yescharacteristic
334C2×C22⋊C4C22⋊C411yescharacteristic
335C2×C22⋊C4C22⋊C411yescharacteristic
336C2×C22⋊C4C22⋊C411yescharacteristic
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—42no—
341C2×C42—81no—
342C2×C42—81no—
343C2×C42—81no—
344C2×C42—81no—
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C22×C411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C4⋊C8—81no—
354C4⋊C8—81no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—81no—
364C22⋊C8—81no—
365C22⋊C8—81no—
366C22⋊C8—81no—
367#97—81no—
368C4×C8—81no—
369#95—24no—
370#95—24no—
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—21no—
395#95—21no—
396#95—21no—
397#95—42no—
398#95—81no—
399#95—81no—
400#95—81no—
401#95—81no—
402#95C22⋊C411yescharacteristic
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—41no—
420C24—41no—
421C24C2×C22⋊C411yescharacteristic
422C24C2×C22⋊C411yescharacteristic
423C24C22×D411yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—42no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4—81no—
446C2×D4—81no—
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—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
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—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—48no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4C2×C22⋊C411yescharacteristic
542C22×C4C2×C22⋊C411yescharacteristic
543C22×C4C2×C22⋊C411yescharacteristic
544C22×C4C23×C411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4H(5,𝔽2)11yescharacteristic
547C22×C4H(5,𝔽2)11yescharacteristic
548C22×C42−1+411yescharacteristic
549C22×C42−1+411yescharacteristic
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—81no—
581C4⋊C4—81no—
582C4⋊C4—84no—
583C4⋊C4—84no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—48no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4#10414yes—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—42no—
625C42—81no—
626C42—81no—
627C42—84no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—24no—
633C23—24no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C2×#10412yes—
668C23#42112yes—
669C23C22×C22⋊C411yescharacteristic
670C23#53511yescharacteristic
671C23#53611yescharacteristic
672C23#57611yescharacteristic
673C23#57711yescharacteristic
674C23#57711yescharacteristic
675C23#57811yescharacteristic
676Q8—81no—
677Q8—81no—
678Q8—162no—
679D4—81no—
680D4—81no—
681D4—81no—
682D4—81no—
683D4—81no—
684D4—81no—
685D4—162no—
686D4—162no—
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—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
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—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—816no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—162no—
792C2×C4C2×#10412yes—
793C2×C4C2×#10412yes—
794C2×C4#52011yescharacteristic
795C2×C4#52011yescharacteristic
796C2×C4#53711yescharacteristic
797C2×C4#53711yescharacteristic
798C8—81no—
799C8—81no—
800C8—81no—
801C8—81no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22#231111yescharacteristic
840C22#288311yescharacteristic
841C22#288311yescharacteristic
842C22#289711yescharacteristic
843C22#289811yescharacteristic
844C22C22×#10411yescharacteristic
845C22C2×#42111yescharacteristic
846C22#322411yescharacteristic
847C22#322511yescharacteristic
848C22#324311yescharacteristic
849C22#324411yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—22no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C2—21no—
876C2—21no—
877C2—21no—
878C2—21no—
879C2—42no—
880C2—42no—
881C2—161no—
882C2#1754711yescharacteristic
883C2#1754811yescharacteristic
884C2#1759711yescharacteristic
885C2#1759811yescharacteristic
886C2#2187111yescharacteristic
887C2#2187611yescharacteristic
888C2#2189911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#2847C22
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
2. #21904C2semidirect
3. #13782C2semidirect
4. #9889C2semidirect
5. #9884C2semidirect
6. #9682C2semidirect
7. #9681C2semidirect
10. #9146C2semidirect
11. #9143C2semidirect
12. #8578C2semidirect
13. #8576C2semidirect
14. #8573C2semidirect
15. #8571C2semidirect
23. #2495C4semidirect
24. #2494C4semidirect
25. #2492C4semidirect
26. #2491C4semidirect
29. #2427C4semidirect
30. #2426C4semidirect
31. #2423C4semidirect
32. #2422C4semidirect
77. C2×C4⋊Q8C2×C4semidirect
79. C2×#124C2×C4semidirect
89. C2×C4×Q8C2×C4semidirect
91. C2×C4×D4C2×C4semidirect
130. #391C2×C4semidirect
131. #391C2×C4semidirect
133. #390C2×C4semidirect
134. #390C2×C4semidirect
136. #389C2×C4semidirect
137. #389C2×C4semidirect
138. #389C2×C4semidirect
139. #389C2×C4semidirect
165. #384C2×C4semidirect
167. #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
#350802
#219042
#137822
#98892
#98842
#96822
#96812
#91502
#91472
#91462
#91432
#85782
#85762
#85732
#85712