Finite Group Databasebeta

← #30609398

Subgroups — #30609398

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461008C211yesmaximal, characteristic
2#21461007C211yesmaximal, characteristic
3#21461005C211yesmaximal, characteristic
4#21461004C211yesmaximal, characteristic
5#21461004C211yesmaximal, characteristic
6#21461004C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460999C211yesmaximal, characteristic
9#21460998C211yesmaximal, characteristic
10#21460998C211yesmaximal, characteristic
11#21460998C211yesmaximal, characteristic
12#21460997C211yesmaximal, characteristic
13#21460996C211yesmaximal, characteristic
14#21460995C211yesmaximal, characteristic
15#389×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C2×(C2×#6923)⋊C4C2211yescharacteristic
23C2×(C2×#6923)⋊C4C2211yescharacteristic
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
44C2×C4⋊C4×D61C2211yescharacteristic
45C2×C4⋊C4×D61C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839661C411yescharacteristic, complemented
50#16839660C411yescharacteristic, complemented
51#16839659C411yescharacteristic, complemented
52#16839659C411yescharacteristic, complemented
53#16839658C411yescharacteristic, complemented
54#16839657C411yescharacteristic, complemented
55#16839657C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58C61×#389C411yescharacteristic, 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×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923Q814yes—
79C2×C4×#6923—22no—
80C2×C4×#6923—41no—
81C2×C4×#6923—41no—
82C2×C4×#6923—41no—
83C2×C4×#6923—41no—
84C2×C4×#6923—41no—
85(C2×#6923)⋊C4—22no—
86(C2×#6923)⋊C4—22no—
87(C2×#6923)⋊C4—22no—
88(C2×#6923)⋊C4—22no—
89(C2×#6923)⋊C4—22no—
90(C2×#6923)⋊C4—22no—
91(C2×#6923)⋊C4—22no—
92(C2×#6923)⋊C4—41no—
93(C2×#6923)⋊C4—41no—
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)⋊C4Q814yes—
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×C4⋊Dic61C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C4⋊C4×D61—22no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61—41no—
129C4⋊C4×D61—41no—
130C4⋊C4×D61—41no—
131C4⋊C4×D61—41no—
132C4⋊C4×D61—41no—
133C4⋊C4×D61—41no—
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
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C4⋊C4×C61C2×C411yescharacteristic
147C2×C4⋊C4×C61C2×C411yescharacteristic
148C2×C4⋊C4×C61C2×C411yescharacteristic
149C2×C42×C61C2×C411yescharacteristic
150#95×C61C2×C411yescharacteristic
151#95×C61C2×C411yescharacteristic
152C23×D61C2411yescharacteristic
153C22×#6923—21no—
154C22×#6923—21no—
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923—21no—
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×#6923—21no—
204C22×#6923—21no—
205C22×#6923C2×Q812yes—
206C22×#6923C2×Q812yes—
207C22×#6923C2×Q812yes—
208C22×#6923C2×Q812yes—
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
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×D61C2×Q812yes—
260C2×C4×D61C2×Q812yes—
261C2×C4×D61#4112yes—
262C2×C4×D61#4112yes—
263C2×C4×D61#4112yes—
264C2×C4×D61#4112yes—
265C4⋊#6923—44no—
266C4⋊#6923—44no—
267C4⋊#6923—44no—
268C4⋊#6923—44no—
269C4×#6923—44no—
270C4×#6923—44no—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—41no—
273C4⋊C4×C61—41no—
274C4⋊C4×C61—41no—
275C42×C61—41no—
276C4⋊Dic61—22no—
277C4⋊Dic61—41no—
278C4⋊Dic61—41no—
279C4⋊Dic61—41no—
280#11758196—22no—
281#11758196—22no—
282#11758196—41no—
283#11758196—41no—
284#11758196—41no—
285#11758196—41no—
286#11758196—41no—
287#11758196—41no—
288C4×Dic61—41no—
289C4×Dic61—41no—
290C4×Dic61—41no—
291C23×C61C23×C411yescharacteristic
292C22×D61C22×Q811yescharacteristic
293C22×D61C22×Q811yescharacteristic
294C22×D61C2×#4111yescharacteristic
295C22×D61C2×#4111yescharacteristic
296C22×D61C2×#4111yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61H(5,𝔽2)11yescharacteristic
299C22×D61H(5,𝔽2)11yescharacteristic
300C22×D61H(5,𝔽2)11yescharacteristic
301C22×D61H(5,𝔽2)11yescharacteristic
302C22×D61H(5,𝔽2)11yescharacteristic
303C22×D61H(5,𝔽2)11yescharacteristic
304C22×D612−1+411yescharacteristic
305C22×D612−1+411yescharacteristic
306C2×#6923—22no—
307C2×#6923—22no—
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—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
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×C4×C61—21no—
363C2×C4×C61—21no—
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#11712yes—
381C2×C4×C61C4×Q812yes—
382C2×C4×C61C4×Q812yes—
383C2×Dic61—21no—
384C2×Dic61—21no—
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#11712yes—
402C2×Dic61C4×Q812yes—
403C2×Dic61C4×Q812yes—
404C4×D61—22no—
405C4×D61—22no—
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—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
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—
432#14458—611nomaximal, Sylow
433C22×C61C2×#11711yescharacteristic
434C22×C61C2×C4×Q811yescharacteristic
435C22×C61C2×C4×Q811yescharacteristic
436C22×C61#51811yescharacteristic
437C22×C61#51811yescharacteristic
438C22×C61#52011yescharacteristic
439C22×C61#52011yescharacteristic
440C2×D61#53811yescharacteristic
441C2×D61#53811yescharacteristic
442C2×D61#53811yescharacteristic
443C2×D61#53911yescharacteristic
444C2×D61#53911yescharacteristic
445C2×D61#53911yescharacteristic
446C2×D61#54011yescharacteristic
447C2×D61#54111yescharacteristic
448C2×D61#54311yescharacteristic
449C2×D61#54411yescharacteristic
450C2×D61#54411yescharacteristic
451C2×D61#54411yescharacteristic
452C2×D61#55311yescharacteristic
453C2×D61#55311yescharacteristic
454C2×D61#55411yescharacteristic
455C2×D61#55411yescharacteristic
456C2×D61#55411yescharacteristic
457C2×D61#55411yescharacteristic
458C2×D61#55411yescharacteristic
459C2×D61#55511yescharacteristic
460C2×D61#55611yescharacteristic
461C2×D61#55711yescharacteristic
462C2×D61Q8211yescharacteristic
463C2×D61#55911yescharacteristic
464C2×D61#56011yescharacteristic
465C2×D61#56011yescharacteristic
466C2×D61#56211yescharacteristic
467C2×D61#56211yescharacteristic
468#6923—42no—
469#6923—42no—
470#6923—42no—
471#6923—42no—
472#6923—81no—
473#6923—81no—
474#6923—81no—
475#6923—81no—
476C4×C61—22no—
477C4×C61—22no—
478C4×C61—22no—
479C4×C61—41no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—41no—
483Dic61—22no—
484Dic61—22no—
485Dic61—22no—
486Dic61—41no—
487Dic61—41no—
488Dic61—41no—
489Dic61—41no—
490C2×#389—611no—
491#1445—611no—
492#1444—611no—
493#1442—611no—
494#1441—611no—
495#1441—611no—
496#1441—611no—
497#1436—611no—
498#1436—611no—
499#1436—611no—
500#1436—611no—
501#1436—611no—
502C4⋊#95—611no—
503C4⋊#95—611no—
504#1434—611no—
505C2×C61#231811yescharacteristic
506C2×C61#232911yescharacteristic
507C2×C61#233011yescharacteristic
508C2×C61#234511yescharacteristic
509C2×C61#235511yescharacteristic
510C2×C61#236911yescharacteristic
511C2×C61#237711yescharacteristic
512D61#278011yescharacteristic
513D61#278311yescharacteristic
514D61#278811yescharacteristic
515D61#279211yescharacteristic
516D61#280211yescharacteristic
517D61#280311yescharacteristic
518D61#280611yescharacteristic
519D61#280711yescharacteristic
520C22×C4⋊C4—611no—
521C22×C4⋊C4—611no—
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—
531#389—611no—
532#389—611no—
533#389—611no—
534#389—611no—
535#389—611no—
536#389—611no—
537#389—611no—
538#389#692311yescharacteristic, complemented
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
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—
563C61#1445811yescharacteristic, complemented, Sylow
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
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—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—614no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4—1222no—
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⋊C4—2441no—
606C2×C4⋊C4—2441no—
607C2×C4⋊C4—2441no—
608C2×C4⋊C4—2441no—
609C2×C4⋊C4—2441no—
610C2×C4⋊C4—2441no—
611C2×C4⋊C4C2×#692311yescharacteristic
612C2×C4⋊C4C2×#692311yescharacteristic
613C2×C4⋊C4C2×#692311yescharacteristic
614C2×C4⋊C4C2×#692311yescharacteristic
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—1222no—
619C2×C42—2441no—
620C2×C42—2441no—
621C2×C42—2441no—
622C2×C42—2441no—
623C2×C42—2441no—
624C2×C42—2441no—
625C2×C42—2441no—
626C2×C42C2×#692311yescharacteristic
627#95—614no—
628#95—611no—
629#95—611no—
630#95—611no—
631#95—611no—
632#95—611no—
633#95—611no—
634#95—1222no—
635#95—1222no—
636#95—1222no—
637#95—1222no—
638#95—1222no—
639#95—1222no—
640#95—1222no—
641#95—2441no—
642#95—2441no—
643#95—2441no—
644#95—2441no—
645#95—2441no—
646#95—2441no—
647#95—2441no—
648#95—2441no—
649#95—2441no—
650#95—2441no—
651#95—2441no—
652#95—2441no—
653#95—2441no—
654#95—2441no—
655#95C2×#692311yescharacteristic
656#95C2×#692311yescharacteristic
657C24—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
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×C4C22×#692311yescharacteristic
764C22×C4C22×#692311yescharacteristic
765C22×C4C22×#692311yescharacteristic
766C22×C4C22×#692311yescharacteristic
767C22×C4C22×#692311yescharacteristic
768C22×C4C22×#692311yescharacteristic
769C22×C4C22×#692311yescharacteristic
770C4⋊C4—22no—
771C4⋊C4—41no—
772C4⋊C4—41no—
773C4⋊C4—41no—
774C4⋊C4—1222no—
775C4⋊C4—1222no—
776C4⋊C4—1222no—
777C4⋊C4—2441no—
778C4⋊C4—2441no—
779C4⋊C4—2441no—
780C4⋊C4—2441no—
781C4⋊C4—2441no—
782C4⋊C4—2441no—
783C4⋊C4—2441no—
784C4⋊C4—2441no—
785C4⋊C4—2441no—
786C4⋊C4—2444no—
787C4⋊C4—2444no—
788C4⋊C4—2444no—
789C4⋊C4—2444no—
790C42—41no—
791C42—2441no—
792C42—2441no—
793C42—2441no—
794C42—2444no—
795C42—2444no—
796C23—611no—
797C23—611no—
798C23—611no—
799C23—611no—
800C23—611no—
801C23—611no—
802C23—611no—
803C23—611no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23C23×#692311yescharacteristic
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
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—612no—
830C2×C4—612no—
831C2×C4—612no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
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—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
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—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
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#1451985612yes—
935C2×C4Q8×#692312yes—
936C2×C4Q8×#692312yes—
937C22—611no—
938C22—611no—
939C22—611no—
940C22—611no—
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—
965C22C2×#1451985611yescharacteristic
966C22C2×Q8×#692311yescharacteristic
967C22C2×Q8×#692311yescharacteristic
968C22#1684082911yescharacteristic
969C22#1684082911yescharacteristic
970C22#1684083111yescharacteristic
971C22#1684083111yescharacteristic
972C4—22no—
973C4—22no—
974C4—22no—
975C4—41no—
976C4—41no—
977C4—41no—
978C4—41no—
979C4—1222no—
980C4—1222no—
981C4—1222no—
982C4—4881no—
983C4—4881no—
984C4—4881no—
985C4—4881no—
986C4—2442no—
987C4—2442no—
988C4—2442no—
989C4—2442no—
990C4—2441no—
991C4—2441no—
992C4—2441no—
993C4—2441no—
994C2—611no—
995C2—611no—
996C2—611no—
997C2—611no—
998C2—611no—
999C2—611no—
1000C2—611no—
1001C2—611no—
1002C2#2146230111yescharacteristic
1003C2#2146231211yescharacteristic
1004C2#2146231311yescharacteristic
1005C2#2146232811yescharacteristic
1006C2#2146233811yescharacteristic
1007C2#2146235211yescharacteristic
1008C2#2146236011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#389C4
prime radical, cosocleC23×D61C24
hypercenter#389#6923
hypocenterC61#14458
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. #16839661C4semidirect
50. #16839660C4semidirect
51. #16839659C4semidirect
52. #16839659C4semidirect
53. #16839658C4semidirect
54. #16839657C4semidirect
55. #16839657C4semidirect
58. C61×#389C4semidirect
538. #389#6923semidirect
563. C61#14458semidirect

Maximal subgroups

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

subgroupindex
#214610082
#214610072
#214610052
#214610042
#214609992
#214609982
#214609972
#214609962
#214609952
#389×D612
#1445861