Finite Group Databasebeta

← #30608695

Subgroups — #30608695

Order 15616.

1434 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840713C211yesmaximal, characteristic
2C2×#16840711C211yesmaximal, characteristic
3#21460999C211yesmaximal, characteristic
4#21460999C211yesmaximal, characteristic
5#21460999C211yesmaximal, characteristic
6#21460999C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460998C211yesmaximal, characteristic
9#21460997C211yesmaximal, characteristic
10#21460996C211yesmaximal, characteristic
11#21460994C211yesmaximal, characteristic
12C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
13#95×#6923C211yesmaximal, characteristic
14#95×#6923C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26#16840713C418yescomplemented
27#16840711C418yescomplemented
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839649C411yescharacteristic, complemented
50#16839648C411yescharacteristic, complemented
51#16839647C411yescharacteristic, complemented
52#16839646C411yescharacteristic, complemented
53#16839645C411yescharacteristic, complemented
54#16839644C411yescharacteristic, complemented
55#16839643C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#387C411yescharacteristic, complemented
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C2×C4⋊#6923—41no—
70C2×C4⋊#6923—41no—
71C2×C4⋊#6923—41no—
72C2×C4⋊#6923—41no—
73C2×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923C2×C414yes—
78C2×C4⋊#6923C2×C414yes—
79C2×C4⋊#6923C2×C414yes—
80C2×C4⋊#6923C2×C414yes—
81C2×C4×#6923—22no—
82C2×C4×#6923—22no—
83C2×C4×#6923—22no—
84C2×C4×#6923—41no—
85C2×C4×#6923—41no—
86C2×C4×#6923—41no—
87C2×C4×#6923—41no—
88C2×C4×#6923—41no—
89C2×C4×#6923—41no—
90C2×C4×#6923—41no—
91C2×C4×#6923—41no—
92C2×C4×#6923—41no—
93C2×C4×#6923—41no—
94C2×C4×#6923—41no—
95C2×C4×#6923—41no—
96C2×C4×#6923C2×C414yes—
97C2×C4×#6923C2×C414yes—
98C2×C4×#6923Q814yes—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—22no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4—41no—
111(C2×#6923)⋊C4C2×C414yes—
112(C2×#6923)⋊C4C2×C414yes—
113(C2×#6923)⋊C4C2×C414yes—
114(C2×#6923)⋊C4C2×C414yes—
115(C2×#6923)⋊C4C2×C414yes—
116(C2×#6923)⋊C4C2×C414yes—
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic
125C2×C4⋊Dic61C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C4⋊C4×D61—41no—
131C4⋊C4×D61—41no—
132C4⋊C4×D61C2×C414yes—
133C4⋊C4×D61C2×C414yes—
134C2×C4×Dic61C2×C411yescharacteristic
135C2×C4×Dic61C2×C411yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C42×D61—41no—
138C42×D61—41no—
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151C2×C4⋊C4×C61C2×C411yescharacteristic
152C2×C4⋊C4×C61C2×C411yescharacteristic
153C2×C42×C61C2×C411yescharacteristic
154#95×C61C2×C411yescharacteristic
155#95×C61C2×C411yescharacteristic
156#95×C61C2×C411yescharacteristic
157#95×C61C2×C411yescharacteristic
158C23×D61C2411yescharacteristic
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923C22×C412yes—
204C22×#6923C22×C412yes—
205C22×#6923C22×C412yes—
206C22×#6923C22×C412yes—
207C22×#6923C22×C412yes—
208C22×#6923C22×C412yes—
209C22×#6923C22×C412yes—
210C22×#6923C22×C412yes—
211C22×#6923C2×Q812yes—
212C22×#6923C2×Q812yes—
213C22×#6923#4112yes—
214C22×#6923#4112yes—
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61C22×C412yes—
264C2×C4×D61C22×C412yes—
265C2×C4×D61C22×C412yes—
266C2×C4×D61C22×C412yes—
267C2×C4×D61C22×C412yes—
268C2×C4×D61C22×C412yes—
269C2×C4×D61C2×Q812yes—
270C2×C4×D61#4112yes—
271C4⋊#6923—44no—
272C4⋊#6923—44no—
273C4⋊#6923—44no—
274C4⋊#6923—44no—
275C4×#6923—44no—
276C4×#6923—44no—
277C4×#6923—44no—
278C4×#6923—44no—
279C4×#6923—44no—
280C4×#6923—44no—
281C4⋊C4×C61—41no—
282C4⋊C4×C61C4214yescomplemented
283C42×C61—41no—
284C4⋊Dic61—41no—
285C4⋊Dic61C4214yescomplemented
286#11758196—41no—
287#11758196—41no—
288#11758196C4214yescomplemented
289#11758196C4214yescomplemented
290C4×Dic61—41no—
291C4×Dic61—41no—
292C4×Dic61—41no—
293C23×C61C23×C411yescharacteristic
294C22×D61C23×C411yescharacteristic
295C22×D61C23×C411yescharacteristic
296C22×D61C22×Q811yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61C2×#4111yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61H(5,𝔽2)11yescharacteristic
301C22×D61H(5,𝔽2)11yescharacteristic
302C22×D61H(5,𝔽2)11yescharacteristic
303C22×D61H(5,𝔽2)11yescharacteristic
304C22×D61H(5,𝔽2)11yescharacteristic
305C22×D612−1+411yescharacteristic
306C22×D612−1+411yescharacteristic
307C22×D612−1+411yescharacteristic
308C2×#6923—22no—
309C2×#6923—22no—
310C2×#6923—22no—
311C2×#6923—22no—
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—22no—
321C2×#6923—22no—
322C2×#6923—22no—
323C2×#6923—22no—
324C2×#6923—22no—
325C2×#6923—22no—
326C2×#6923—22no—
327C2×#6923—22no—
328C2×#6923—22no—
329C2×#6923—22no—
330C2×#6923—22no—
331C2×#6923—22no—
332C2×#6923—22no—
333C2×#6923—22no—
334C2×#6923—22no—
335C2×#6923—22no—
336C2×#6923—22no—
337C2×#6923—22no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923C4×Q814yes—
363C2×#6923C4×Q814yes—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61C2×C4212yes—
382C2×C4×C61C2×C4212yes—
383C2×C4×C61C2×C4212yes—
384C2×C4×C61C4×Q812yes—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61C2×C4212yes—
403C2×Dic61C2×C4212yes—
404C2×Dic61C2×C4212yes—
405C2×Dic61C4×Q812yes—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434#13792—611nomaximal, Sylow
435C22×C61C22×C4211yescharacteristic
436C22×C61C2×C4×Q811yescharacteristic
437C22×C61C4×#4111yescharacteristic
438C22×C61#51811yescharacteristic
439C22×C61#52011yescharacteristic
440C22×C61#52011yescharacteristic
441C22×C61#52011yescharacteristic
442C2×D61C2×C4×Q811yescharacteristic
443C2×D61C2×C4×Q811yescharacteristic
444C2×D61C4×#4111yescharacteristic
445C2×D61C4×#4111yescharacteristic
446C2×D61#51811yescharacteristic
447C2×D61#51811yescharacteristic
448C2×D61#51811yescharacteristic
449C2×D61#51911yescharacteristic
450C2×D61#52011yescharacteristic
451C2×D61#52011yescharacteristic
452C2×D61#52011yescharacteristic
453C2×D61#52011yescharacteristic
454C2×D61#53811yescharacteristic
455C2×D61#53811yescharacteristic
456C2×D61#53811yescharacteristic
457C2×D61#53911yescharacteristic
458C2×D61#53911yescharacteristic
459C2×D61#53911yescharacteristic
460C2×D61#54011yescharacteristic
461C2×D61#54011yescharacteristic
462C2×D61#54111yescharacteristic
463C2×D61#54111yescharacteristic
464C2×D61#54211yescharacteristic
465C2×D61#54211yescharacteristic
466C2×D61#54311yescharacteristic
467C2×D61#54411yescharacteristic
468C2×D61#54411yescharacteristic
469C2×D61#54411yescharacteristic
470#6923—24no—
471#6923—24no—
472#6923—42no—
473#6923—42no—
474#6923—42no—
475#6923—42no—
476#6923—42no—
477#6923—42no—
478C4×C61—22no—
479C4×C61—22no—
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485Dic61—22no—
486Dic61—22no—
487Dic61—22no—
488Dic61—22no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492C2×#389—611no—
493C2×#387—611no—
494C2×#387—611no—
495#1436—611no—
496#1436—611no—
497#1436—611no—
498#1436—611no—
499#1436—611no—
500#1436—611no—
501C4⋊#95—611no—
502C4⋊#95—611no—
503#1434—611no—
504C4×#95—611no—
505C4×#95—611no—
506C4×#95—611no—
507C2×C61C42×Q811yescharacteristic
508C2×C61#227411yescharacteristic
509C2×C61#227511yescharacteristic
510C2×C61#232911yescharacteristic
511C2×C61#233011yescharacteristic
512C2×C61#233411yescharacteristic
513C2×C61#233511yescharacteristic
514D61#232911yescharacteristic
515D61#232911yescharacteristic
516D61#233011yescharacteristic
517D61#233111yescharacteristic
518D61#233311yescharacteristic
519D61#233411yescharacteristic
520D61#233511yescharacteristic
521D61#233611yescharacteristic
522C22×C4⋊C4—611no—
523C22×C4⋊C4—611no—
524C22×C4⋊C4—611no—
525C22×C4⋊C4—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—611no—
528C22×C42—611no—
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42—611no—
533C22×C42—611no—
534C22×C42—611no—
535#389—618no—
536#387—618no—
537#387—611no—
538#387—611no—
539#387—611no—
540#387—611no—
541#387—611no—
542#387—611no—
543#387—611no—
544#387#692311yescharacteristic, complemented
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C61#1379211yescharacteristic, complemented, Sylow
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—614no—
587C2×C4⋊C4—614no—
588C2×C4⋊C4—614no—
589C2×C4⋊C4—614no—
590C2×C4⋊C4—614no—
591C2×C4⋊C4—614no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—2441no—
596C2×C4⋊C4—2441no—
597C2×C4⋊C4—2441no—
598C2×C4⋊C4—2441no—
599C2×C4⋊C4—2441no—
600C2×C4⋊C4—2441no—
601C2×C4⋊C4—2441no—
602C2×C4⋊C4—2441no—
603C2×C4⋊C4—2441no—
604C2×C4⋊C4—2441no—
605C2×C4⋊C4C2×#692311yescharacteristic
606C2×C4⋊C4C2×#692311yescharacteristic
607C2×C42—614no—
608C2×C42—614no—
609C2×C42—614no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—2441no—
617C2×C42—2441no—
618C2×C42—2441no—
619C2×C42—2441no—
620C2×C42—2441no—
621C2×C42—2441no—
622C2×C42—2441no—
623C2×C42—2441no—
624C2×C42—2441no—
625C2×C42—2441no—
626C2×C42—2441no—
627C2×C42—2441no—
628C2×C42—2441no—
629C2×C42—2441no—
630C2×C42C2×#692311yescharacteristic
631#95—614no—
632#95—614no—
633#95—614no—
634#95—614no—
635#95—614no—
636#95—614no—
637#95—611no—
638#95—611no—
639#95—611no—
640#95—611no—
641#95—611no—
642#95—611no—
643#95—611no—
644#95—611no—
645#95—611no—
646#95—611no—
647#95—611no—
648#95—611no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—2441no—
656#95—2441no—
657#95—2441no—
658#95—2441no—
659#95—2441no—
660#95—2441no—
661#95C2×#692311yescharacteristic
662#95C2×#692311yescharacteristic
663#95C2×#692311yescharacteristic
664#95C2×#692311yescharacteristic
665C24—611no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4C22×#692311yescharacteristic
772C22×C4C22×#692311yescharacteristic
773C22×C4C22×#692311yescharacteristic
774C22×C4C22×#692311yescharacteristic
775C22×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777C22×C4C22×#692311yescharacteristic
778C4⋊C4—41no—
779C4⋊C4—614no—
780C4⋊C4—614no—
781C4⋊C4—614no—
782C4⋊C4—2441no—
783C4⋊C4—2441no—
784C4⋊C4—2441no—
785C4⋊C4—2444no—
786C4⋊C4—2444no—
787C4⋊C4—2444no—
788C4⋊C4—2444no—
789C4⋊C4C4×#692314yescomplemented
790C42—41no—
791C42—2441no—
792C42—2441no—
793C42—2441no—
794C42—2444no—
795C42—2444no—
796C42—2444no—
797C42—2444no—
798C42—2444no—
799C42—2444no—
800C23—611no—
801C23—611no—
802C23—611no—
803C23—611no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23C23×#692311yescharacteristic
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—614no—
833C2×C4—614no—
834C2×C4—612no—
835C2×C4—612no—
836C2×C4—612no—
837C2×C4—612no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4C2×C4×#692312yes—
938C2×C4C2×C4×#692312yes—
939C2×C4C2×C4×#692312yes—
940C2×C4Q8×#692312yes—
941C22—611no—
942C22—611no—
943C22—611no—
944C22—611no—
945C22—611no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—611no—
953C22—611no—
954C22—611no—
955C22—611no—
956C22—611no—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22C22×C4×#692311yescharacteristic
970C22C2×Q8×#692311yescharacteristic
971C22#41×#692311yescharacteristic
972C22#1684082911yescharacteristic
973C22#1684083111yescharacteristic
974C22#1684083111yescharacteristic
975C22#1684083111yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—1224no—
984C4—1224no—
985C4—1222no—
986C4—1222no—
987C4—1222no—
988C4—1222no—
989C4—2442no—
990C4—2442no—
991C4—2442no—
992C4—2442no—
993C4—2442no—
994C4—2442no—
995C4—2441no—
996C4—2441no—
997C4—2441no—
998C2—611no—
999C2—611no—
1000C2—611no—
1001C2—611no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2C4×Q8×#692311yescharacteristic
1007C2#2146225611yescharacteristic
1008C2#2146225811yescharacteristic
1009C2#2146231211yescharacteristic
1010C2#2146231311yescharacteristic
1011C2#2146231711yescharacteristic
1012C2#2146231811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#387C4
socleC23×C61C23×C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#13792
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
26. #16840713C4semidirect
27. #16840711C4semidirect
49. #16839649C4semidirect
50. #16839648C4semidirect
51. #16839647C4semidirect
52. #16839646C4semidirect
53. #16839645C4semidirect
54. #16839644C4semidirect
55. #16839643C4semidirect
60. C61×#387C4semidirect
282. C4⋊C4×C61C42semidirect
285. C4⋊Dic61C42semidirect
288. #11758196C42semidirect
289. #11758196C42semidirect
544. #387#6923semidirect
567. C61#13792semidirect
789. C4⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407112
#214609992
#214609982
#214609972
#214609962
#214609942
C4×(C2×#6923)⋊C42
#95×#69232
#387×D612
#1379261