Finite Group Databasebeta

← #30609396

Subgroups — #30609396

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461008C211yesmaximal, characteristic, complemented
2#21461006C211yesmaximal, characteristic, complemented
3#21461004C211yesmaximal, characteristic, complemented
4#21461004C211yesmaximal, characteristic, complemented
5#21461002C211yesmaximal, characteristic
6#21461002C211yesmaximal, characteristic
7#21461000C211yesmaximal, characteristic
8#21461000C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic, complemented
10#21460996C211yesmaximal, characteristic, complemented
11#21460994C211yesmaximal, characteristic, complemented
12#21460994C211yesmaximal, characteristic, complemented
13#21460993C211yesmaximal, characteristic
14#21460993C211yesmaximal, characteristic
15#385×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C22⋊#6923C2211yescharacteristic
19C22×C22⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C2×(C2×#6923)⋊C4C2211yescharacteristic
25C2×(C2×#6923)⋊C4C2211yescharacteristic
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
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
44C23×C4×D61C2211yescharacteristic
45C2×C4⋊C4×D61C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C22⋊C4×D61C2211yescharacteristic
48C2×C22⋊C4×D61C2211yescharacteristic
49#16839637C411yescharacteristic, complemented
50#16839636C411yescharacteristic, complemented
51#16839636C411yescharacteristic, complemented
52#16839635C411yescharacteristic, complemented
53#16839634C411yescharacteristic, complemented
54#16839633C411yescharacteristic, complemented
55#16839633C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58C61×#385C411yescharacteristic, complemented
59C23×#6923C2311yescharacteristic
60C23×#6923C2311yescharacteristic
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C2×C4⋊#6923—22no—
68C2×C4⋊#6923—22no—
69C2×C4⋊#6923—41no—
70C2×C4⋊#6923—41no—
71C2×C4⋊#6923—41no—
72C2×C4⋊#6923—41no—
73C2×C22⋊#6923—22no—
74C2×C22⋊#6923—22no—
75C2×C22⋊#6923—22no—
76C2×C22⋊#6923—22no—
77C2×C22⋊#6923—22no—
78C2×C22⋊#6923—41no—
79C2×C22⋊#6923—41no—
80C2×C22⋊#6923—41no—
81C2×C22⋊#6923—41no—
82C2×C22⋊#6923—41no—
83C2×C22⋊#6923—41no—
84C2×C22⋊#6923Q814yes—
85C2×C4×#6923—22no—
86C2×C4×#6923—22no—
87C2×C4×#6923—22no—
88C2×C4×#6923—41no—
89C2×C4×#6923—41no—
90C2×C4×#6923—41no—
91(C2×#6923)⋊C4—22no—
92(C2×#6923)⋊C4—22no—
93(C2×#6923)⋊C4—22no—
94(C2×#6923)⋊C4—41no—
95(C2×#6923)⋊C4—41no—
96(C2×#6923)⋊C4—41no—
97(C2×#6923)⋊C4—41no—
98(C2×#6923)⋊C4—41no—
99(C2×#6923)⋊C4—41no—
100(C2×#6923)⋊C4—41no—
101(C2×#6923)⋊C4—41no—
102(C2×#6923)⋊C4—41no—
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4—41no—
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—
111C24×D61C2311yescharacteristic
112C23×Dic61C2×C411yescharacteristic
113C22×C4×D61—41no—
114C22×C4×D61—41no—
115C22×C4×D61—41no—
116C22×C4×D61—41no—
117C22×C4×D61—41no—
118C22×C4×D61—41no—
119C22×C4×D61C2×C411yescharacteristic
120C22×C4×D61C2×C411yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127C2×C4⋊Dic61C2×C411yescharacteristic
128C2×C4⋊Dic61C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C4⋊C4×D61—41no—
134C4⋊C4×D61—41no—
135C4⋊C4×D61—41no—
136C4⋊C4×D61—41no—
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×C22⋊Dic61C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C22⋊C4×D61—22no—
144C22⋊C4×D61—22no—
145C22⋊C4×D61—41no—
146C22⋊C4×D61—41no—
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151#14519684C2×C411yescharacteristic
152#14519684C2×C411yescharacteristic
153C23×C4×C61C2×C411yescharacteristic
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C4⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158#95×C61C2×C411yescharacteristic
159#95×C61C2×C411yescharacteristic
160C24×C61C22×C411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61C22×C411yescharacteristic
174C23×D61C2×Q812yes—
175C23×D61#4112yes—
176C23×D61C2411yescharacteristic
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×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923C2×Q812yes—
230C22×#6923C2×Q812yes—
231C22×#6923#4112yes—
232C22×#6923#4112yes—
233C22×C4×C61—41no—
234C22×C4×C61—41no—
235C22×C4×C61—41no—
236C22×C4×C61C22×C411yescharacteristic
237C22×C4×C61C22×C411yescharacteristic
238C22×C4×C61C22×C411yescharacteristic
239C22×C4×C61C22×C411yescharacteristic
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×Dic61—41no—
243C22×Dic61—41no—
244C22×Dic61—41no—
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C22×C411yescharacteristic
248C22×Dic61C22×C411yescharacteristic
249C22×Dic61C22×C411yescharacteristic
250C22×Dic61C22×C411yescharacteristic
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×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—41no—
286C2×C4×D61—41no—
287C2×C4×D61—41no—
288C2×C4×D61—41no—
289C2×C4×D61—41no—
290C2×C4×D61—41no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61#4112yes—
296C2×C4×D61#4112yes—
297C22⋊#6923—44no—
298C22⋊#6923—44no—
299C22⋊#6923—44no—
300C22⋊#6923—44no—
301C4⋊#6923—44no—
302C4⋊#6923—44no—
303C4×#6923—44no—
304C4×#6923—44no—
305C4⋊C4×C61—41no—
306C4⋊C4×C61—41no—
307C22⋊C4×C61—22no—
308C22⋊C4×C61—41no—
309C22⋊Dic61—22no—
310C22⋊Dic61—41no—
311#11758198—22no—
312#11758198—22no—
313#11758198—41no—
314#11758198—41no—
315C4⋊Dic61—41no—
316C4⋊Dic61—41no—
317#11758196—41no—
318#11758196—41no—
319#11758196—41no—
320#11758196—41no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61C4×Q812yes—
328C23×C61C23×C411yescharacteristic
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61C4×Q812yes—
364C22×D61C22×Q811yescharacteristic
365C22×D61C2×#4111yescharacteristic
366C22×D61C2×#4111yescharacteristic
367C22×D61C2×#4111yescharacteristic
368C22×D61C2×#4111yescharacteristic
369C22×D61C2×#4111yescharacteristic
370C22×D61H(5,𝔽2)11yescharacteristic
371C22×D61H(5,𝔽2)11yescharacteristic
372C22×D61H(5,𝔽2)11yescharacteristic
373C22×D61H(5,𝔽2)11yescharacteristic
374C22×D61H(5,𝔽2)11yescharacteristic
375C22×D61H(5,𝔽2)11yescharacteristic
376C22×D61H(5,𝔽2)11yescharacteristic
377C22×D612−1+411yescharacteristic
378C2×#6923—22no—
379C2×#6923—22no—
380C2×#6923—22no—
381C2×#6923—22no—
382C2×#6923—22no—
383C2×#6923—22no—
384C2×#6923—22no—
385C2×#6923—22no—
386C2×#6923—22no—
387C2×#6923—22no—
388C2×#6923—22no—
389C2×#6923—22no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×#6923—41no—
427C2×#6923—41no—
428C2×#6923—41no—
429C2×#6923—41no—
430C2×#6923—41no—
431C2×#6923—41no—
432C2×#6923—41no—
433C2×#6923—41no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—44no—
452C2×C4×C61#11712yes—
453C2×Dic61—21no—
454C2×Dic61—21no—
455C2×Dic61—21no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61—21no—
468C2×Dic61—21no—
469C2×Dic61—21no—
470C2×Dic61—44no—
471C2×Dic61#11712yes—
472C4×D61—22no—
473C4×D61—22no—
474C4×D61—22no—
475C4×D61—22no—
476C4×D61—44no—
477C4×D61—44no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483C4×D61—41no—
484C4×D61—41no—
485C4×D61—41no—
486C4×D61—41no—
487C4×D61—41no—
488C4×D61—41no—
489C4×D61—41no—
490C4×D61—41no—
491C4×D61—41no—
492C4×D61—41no—
493C4×D61—41no—
494C4×D61—41no—
495C4×D61—41no—
496C4×D61—41no—
497C4×D61—41no—
498#14456—611nomaximal, Sylow
499C22×C61—22no—
500C22×C61—22no—
501C22×C61—22no—
502C22×C61—41no—
503C22×C61—41no—
504C22×C61—41no—
505C22×C61—41no—
506C22×C61C2×#11711yescharacteristic
507C22×C61C2×C4×Q811yescharacteristic
508C22×C61C4×#4111yescharacteristic
509C22×C61#51811yescharacteristic
510C22×C61#51811yescharacteristic
511C22×C61#51811yescharacteristic
512C22×C61#52011yescharacteristic
513C2×D61—22no—
514C2×D61—22no—
515C2×D61—22no—
516C2×D61—41no—
517C2×D61—41no—
518C2×D61—41no—
519C2×D61—41no—
520C2×D61—42no—
521C2×D61—42no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61#53811yescharacteristic
529C2×D61#53811yescharacteristic
530C2×D61#53911yescharacteristic
531C2×D61#53911yescharacteristic
532C2×D61#54011yescharacteristic
533C2×D61#54011yescharacteristic
534C2×D61#54011yescharacteristic
535C2×D61#54211yescharacteristic
536C2×D61#54211yescharacteristic
537C2×D61#54211yescharacteristic
538C2×D61#54311yescharacteristic
539C2×D61#54411yescharacteristic
540C2×D61#55111yescharacteristic
541C2×D61#55111yescharacteristic
542C2×D61#55111yescharacteristic
543C2×D61#55111yescharacteristic
544C2×D61#55311yescharacteristic
545C2×D61#55311yescharacteristic
546C2×D61#55311yescharacteristic
547C2×D61#55311yescharacteristic
548C2×D61#55411yescharacteristic
549C2×D61#55411yescharacteristic
550C2×D61#55411yescharacteristic
551C2×D61#55411yescharacteristic
552C2×D61#56011yescharacteristic
553C2×D61#56011yescharacteristic
554C2×D61#56011yescharacteristic
555C2×D61H(3,𝔽4)11yescharacteristic
556#6923—42no—
557#6923—42no—
558#6923—42no—
559#6923—42no—
560#6923—81no—
561#6923—81no—
562#6923—81no—
563#6923—81no—
564C4×C61—22no—
565C4×C61—41no—
566C4×C61—41no—
567C4×C61—41no—
568C4×C61—41no—
569C4×C61—41no—
570Dic61—22no—
571Dic61—41no—
572Dic61—41no—
573Dic61—41no—
574Dic61—41no—
575Dic61—41no—
576C2×#385—611no—
577#1445—611no—
578#1443—611no—
579#1441—611no—
580#1441—611no—
581#1439—611no—
582#1439—611no—
583#1437—611no—
584#1437—611no—
585#1436—611no—
586C4⋊#95—611no—
587#1434—611no—
588#1434—611no—
589C22⋊#95—611no—
590C22⋊#95—611no—
591C2×C61—42no—
592C2×C61#231911yescharacteristic
593C2×C61#232911yescharacteristic
594C2×C61#233511yescharacteristic
595C2×C61#234511yescharacteristic
596C2×C61#235311yescharacteristic
597C2×C61#236811yescharacteristic
598C2×C61#237511yescharacteristic
599D61—42no—
600D61#274611yescharacteristic
601D61#274811yescharacteristic
602D61#274911yescharacteristic
603D61#275311yescharacteristic
604D61#275711yescharacteristic
605D61#276311yescharacteristic
606D61#278011yescharacteristic
607D61#279011yescharacteristic
608C24×C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊C4—611no—
612C22×C4⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C42—611no—
620C22×C42—611no—
621#385—611no—
622#385—611no—
623#385—611no—
624#385—611no—
625#385—611no—
626#385—611no—
627#385—611no—
628#385#692311yescharacteristic, complemented
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C61#1445611yescharacteristic, complemented, Sylow
652C25—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—2441no—
671C23×C4—2441no—
672C23×C4—2441no—
673C23×C4—2441no—
674C23×C4—2441no—
675C23×C4—2441no—
676C23×C4C2×#692311yescharacteristic
677C2×C4⋊C4—611no—
678C2×C4⋊C4—611no—
679C2×C4⋊C4—611no—
680C2×C4⋊C4—611no—
681C2×C4⋊C4—611no—
682C2×C4⋊C4—611no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—2441no—
686C2×C4⋊C4—2441no—
687C2×C4⋊C4—2441no—
688C2×C4⋊C4—2441no—
689C2×C4⋊C4—2441no—
690C2×C4⋊C4—2441no—
691C2×C4⋊C4—2441no—
692C2×C4⋊C4—2441no—
693C2×C4⋊C4C2×#692311yescharacteristic
694C2×C4⋊C4C2×#692311yescharacteristic
695C2×C22⋊C4—611no—
696C2×C22⋊C4—611no—
697C2×C22⋊C4—611no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—611no—
700C2×C22⋊C4—611no—
701C2×C22⋊C4—611no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—2441no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4C2×#692311yescharacteristic
718C2×C22⋊C4C2×#692311yescharacteristic
719C2×C42—1222no—
720C2×C42—1222no—
721C2×C42—1222no—
722C2×C42—2441no—
723C2×C42—2441no—
724C2×C42—2441no—
725#95—611no—
726#95—611no—
727#95—611no—
728#95—611no—
729#95—611no—
730#95—611no—
731#95—1222no—
732#95—1222no—
733#95—1222no—
734#95—2441no—
735#95—2441no—
736#95—2441no—
737#95—2441no—
738#95—2441no—
739#95—2441no—
740#95—2441no—
741#95—2441no—
742#95—2441no—
743#95—2441no—
744#95—2441no—
745#95—2441no—
746#95—2441no—
747#95—2441no—
748#95—2441no—
749#95—2441no—
750#95—2441no—
751#95C2×#692311yescharacteristic
752#95C2×#692311yescharacteristic
753C24—611no—
754C24—612no—
755C24—612no—
756C24—611no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24C22×#692311yescharacteristic
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—611no—
774C22×C4—612no—
775C22×C4—612no—
776C22×C4—612no—
777C22×C4—612no—
778C22×C4—612no—
779C22×C4—612no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—2441no—
872C22×C4—2441no—
873C22×C4—2441no—
874C22×C4—2441no—
875C22×C4—2441no—
876C22×C4—2441no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2441no—
882C22×C4—2441no—
883C22×C4—2441no—
884C22×C4C22×#692311yescharacteristic
885C22×C4C22×#692311yescharacteristic
886C22×C4C22×#692311yescharacteristic
887C22×C4C22×#692311yescharacteristic
888C22×C4C22×#692311yescharacteristic
889C22×C4C22×#692311yescharacteristic
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—2441no—
893C4⋊C4—2441no—
894C4⋊C4—2441no—
895C4⋊C4—2441no—
896C4⋊C4—2441no—
897C4⋊C4—2441no—
898C4⋊C4—2444no—
899C4⋊C4—2444no—
900C22⋊C4—22no—
901C22⋊C4—41no—
902C22⋊C4—1222no—
903C22⋊C4—1222no—
904C22⋊C4—1222no—
905C22⋊C4—2441no—
906C22⋊C4—2441no—
907C22⋊C4—2441no—
908C22⋊C4—2444no—
909C22⋊C4—2444no—
910C22⋊C4—2444no—
911C22⋊C4—2444no—
912C42—2444no—
913C42—2444no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—611no—
921C23—611no—
922C23—611no—
923C23—611no—
924C23—611no—
925C23—611no—
926C23—611no—
927C23—611no—
928C23—611no—
929C23—611no—
930C23—611no—
931C23—611no—
932C23—611no—
933C23—611no—
934C23—612no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1221no—
948C23—1221no—
949C23—1221no—
950C23—1221no—
951C23—1221no—
952C23—1221no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23Q8×#692312yes—
970C23C23×#692311yescharacteristic
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—44no—
989C2×C4—612no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1221no—
995C2×C4—1221no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—1222no—
1003C2×C4—1222no—
1004C2×C4—1222no—
1005C2×C4—1222no—
1006C2×C4—1222no—
1007C2×C4—1222no—
1008C2×C4—1221no—
1009C2×C4—1221no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2444no—
1044C2×C4—2444no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2444no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4#1451985612yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—611no—
1099C22—611no—
1100C22—611no—
1101C22—611no—
1102C22—611no—
1103C22—611no—
1104C22—611no—
1105C22—611no—
1106C22—611no—
1107C22—611no—
1108C22—611no—
1109C22—611no—
1110C22—611no—
1111C22—611no—
1112C22—611no—
1113C22—611no—
1114C22—611no—
1115C22—611no—
1116C22—611no—
1117C22—611no—
1118C22—611no—
1119C22—611no—
1120C22—611no—
1121C22—611no—
1122C22—611no—
1123C22—611no—
1124C22—611no—
1125C22—611no—
1126C22—1222no—
1127C22—1222no—
1128C22—1222no—
1129C22—2442no—
1130C22—2442no—
1131C22—2442no—
1132C22—2442no—
1133C22—2442no—
1134C22—2442no—
1135C22—2442no—
1136C22—2442no—
1137C22—2441no—
1138C22—2441no—
1139C22—2441no—
1140C22—2441no—
1141C22C2×#1451985611yescharacteristic
1142C22C2×Q8×#692311yescharacteristic
1143C22#41×#692311yescharacteristic
1144C22#1684082911yescharacteristic
1145C22#1684082911yescharacteristic
1146C22#1684082911yescharacteristic
1147C22#1684083111yescharacteristic
1148C4—22no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—1222no—
1155C4—4881no—
1156C4—4881no—
1157C4—4881no—
1158C4—4881no—
1159C4—2442no—
1160C4—2442no—
1161C4—2442no—
1162C4—2442no—
1163C4—2441no—
1164C4—2441no—
1165C4—2441no—
1166C4—2441no—
1167C4—2441no—
1168C2—42no—
1169C2—611no—
1170C2—611no—
1171C2—611no—
1172C2—611no—
1173C2—611no—
1174C2—611no—
1175C2—611no—
1176C2—611no—
1177C2—2442no—
1178C2#2146230211yescharacteristic
1179C2#2146231211yescharacteristic
1180C2#2146231811yescharacteristic
1181C2#2146232811yescharacteristic
1182C2#2146233611yescharacteristic
1183C2#2146235111yescharacteristic
1184C2#2146235811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#385C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#385#6923
hypocenterC61#14456
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #21461008C2semidirect
2. #21461006C2semidirect
3. #21461004C2semidirect
4. #21461004C2semidirect
9. #21460999C2semidirect
10. #21460996C2semidirect
11. #21460994C2semidirect
12. #21460994C2semidirect
49. #16839637C4semidirect
50. #16839636C4semidirect
51. #16839636C4semidirect
52. #16839635C4semidirect
53. #16839634C4semidirect
54. #16839633C4semidirect
55. #16839633C4semidirect
58. C61×#385C4semidirect
628. #385#6923semidirect
651. C61#14456semidirect

Maximal subgroups

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

subgroupindex
#214610082
#214610062
#214610042
#214610022
#214610002
#214609992
#214609962
#214609942
#214609932
#385×D612
#1445661