Finite Group Databasebeta

← #30609422

Subgroups — #30609422

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461008C211yesmaximal, characteristic
2#21461008C211yesmaximal, characteristic
3#21461006C211yesmaximal, characteristic
4#21461005C211yesmaximal, characteristic
5#21461005C211yesmaximal, characteristic
6#21461004C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460999C211yesmaximal, characteristic
9#21460996C211yesmaximal, characteristic
10#21460995C211yesmaximal, characteristic
11#21460995C211yesmaximal, characteristic
12#21460994C211yesmaximal, characteristic
13#21460994C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4×#6923C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20C2×(C2×#6923)⋊C4C2211yescharacteristic
21C2×(C2×#6923)⋊C4C2211yescharacteristic
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×C42×D61C2211yescharacteristic
47#16839649C411yescharacteristic, complemented
48#16839648C411yescharacteristic, complemented
49#16839647C411yescharacteristic, complemented
50#16839646C411yescharacteristic, complemented
51#16839645C411yescharacteristic, complemented
52#16839644C411yescharacteristic, complemented
53#16839643C411yescharacteristic, complemented
54#95×D61C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58C61×#387C411yescharacteristic, 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—22no—
70C2×C4⋊#6923—41no—
71C2×C4⋊#6923—41no—
72C2×C4⋊#6923—41no—
73C2×C4×#6923—22no—
74C2×C4×#6923—22no—
75C2×C4×#6923—22no—
76C2×C4×#6923—22no—
77C2×C4×#6923—41no—
78C2×C4×#6923—41no—
79(C2×#6923)⋊C4—22no—
80(C2×#6923)⋊C4—22no—
81(C2×#6923)⋊C4—22no—
82(C2×#6923)⋊C4—22no—
83(C2×#6923)⋊C4—22no—
84(C2×#6923)⋊C4—22no—
85(C2×#6923)⋊C4—22no—
86(C2×#6923)⋊C4—22no—
87(C2×#6923)⋊C4—22no—
88(C2×#6923)⋊C4—41no—
89(C2×#6923)⋊C4—41no—
90(C2×#6923)⋊C4—41no—
91(C2×#6923)⋊C4—41no—
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—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109C22×C4×D61C2311yescharacteristic
110C2×C4⋊Dic61C2×C411yescharacteristic
111C2×C4⋊Dic61C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C4⋊C4×D61—22no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—41no—
119C4⋊C4×D61—41no—
120C2×C4×Dic61C2×C411yescharacteristic
121C2×C4×Dic61C2×C411yescharacteristic
122C2×C4×Dic61C2×C411yescharacteristic
123C42×D61—41no—
124C42×D61—41no—
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C42×C61C2×C411yescharacteristic
140#95×C61C2×C411yescharacteristic
141#95×C61C2×C411yescharacteristic
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C23×D61C2411yescharacteristic
145C22×#6923—21no—
146C22×#6923—21no—
147C22×#6923—21no—
148C22×#6923—21no—
149C22×#6923—21no—
150C22×#6923—21no—
151C22×#6923—21no—
152C22×#6923—21no—
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#4112yes—
198C22×#6923#4112yes—
199C22×#6923#4112yes—
200C22×#6923#4112yes—
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C22×C411yescharacteristic
208C22×Dic61C22×C411yescharacteristic
209C22×Dic61C22×C411yescharacteristic
210C22×Dic61C22×C411yescharacteristic
211C22×Dic61C22×C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
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#4112yes—
256C2×C4×D61#4112yes—
257C4⋊#6923—44no—
258C4⋊#6923—44no—
259C4×#6923—44no—
260C4×#6923—44no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—41no—
263C42×C61—41no—
264C4⋊Dic61—22no—
265C4⋊Dic61—41no—
266#11758196—22no—
267#11758196—22no—
268#11758196—41no—
269#11758196—41no—
270C4×Dic61—41no—
271C4×Dic61—41no—
272C4×Dic61—41no—
273C23×C61C23×C411yescharacteristic
274C22×D61C2×#4111yescharacteristic
275C22×D61C2×#4111yescharacteristic
276C22×D61C2×#4111yescharacteristic
277C22×D61C2×#4111yescharacteristic
278C22×D61C2×#4111yescharacteristic
279C22×D61C2×#4111yescharacteristic
280C22×D61H(5,𝔽2)11yescharacteristic
281C22×D61H(5,𝔽2)11yescharacteristic
282C22×D61H(5,𝔽2)11yescharacteristic
283C22×D61H(5,𝔽2)11yescharacteristic
284C22×D612−1+411yescharacteristic
285C22×D612−1+411yescharacteristic
286C22×D612−1+411yescharacteristic
287C22×D612−1+411yescharacteristic
288C2×#6923—22no—
289C2×#6923—22no—
290C2×#6923—22no—
291C2×#6923—22no—
292C2×#6923—22no—
293C2×#6923—22no—
294C2×#6923—22no—
295C2×#6923—22no—
296C2×#6923—22no—
297C2×#6923—22no—
298C2×#6923—22no—
299C2×#6923—22no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
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×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61#11712yes—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61#11712yes—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—41no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61—41no—
398C4×D61—41no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414#14482—611nomaximal, Sylow
415C22×C61C2×#11711yescharacteristic
416C22×C61C4×#4111yescharacteristic
417C22×C61C4×#4111yescharacteristic
418C22×C61#51811yescharacteristic
419C22×C61#51911yescharacteristic
420C22×C61#52011yescharacteristic
421C22×C61#52011yescharacteristic
422C2×D61#53811yescharacteristic
423C2×D61#53911yescharacteristic
424C2×D61#53911yescharacteristic
425C2×D61#53911yescharacteristic
426C2×D61#54011yescharacteristic
427C2×D61#54011yescharacteristic
428C2×D61#54011yescharacteristic
429C2×D61#54211yescharacteristic
430C2×D61#54211yescharacteristic
431C2×D61#54211yescharacteristic
432C2×D61#54211yescharacteristic
433C2×D61#54211yescharacteristic
434C2×D61#55111yescharacteristic
435C2×D61#55111yescharacteristic
436C2×D61#55111yescharacteristic
437C2×D61#55211yescharacteristic
438C2×D61#55211yescharacteristic
439C2×D61#55211yescharacteristic
440C2×D61#55211yescharacteristic
441C2×D61#55211yescharacteristic
442C2×D61#55311yescharacteristic
443C2×D61#55611yescharacteristic
444C2×D61#55611yescharacteristic
445C2×D61#55611yescharacteristic
446C2×D61#56211yescharacteristic
447C2×D61#56311yescharacteristic
448C2×D61#56311yescharacteristic
449C2×D61#56411yescharacteristic
450#6923—42no—
451#6923—42no—
452#6923—42no—
453#6923—42no—
454#6923—81no—
455#6923—81no—
456#6923—81no—
457#6923—81no—
458C4×C61—22no—
459C4×C61—41no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—41no—
465Dic61—22no—
466Dic61—41no—
467Dic61—41no—
468Dic61—41no—
469Dic61—41no—
470Dic61—41no—
471Dic61—41no—
472C2×#387—611no—
473#1445—611no—
474#1445—611no—
475#1443—611no—
476#1442—611no—
477#1442—611no—
478#1441—611no—
479#1436—611no—
480#1436—611no—
481C4⋊#95—611no—
482#1434—611no—
483#1434—611no—
484#1434—611no—
485#1434—611no—
486#1434—611no—
487C2×C61#231911yescharacteristic
488C2×C61#233211yescharacteristic
489C2×C61#233511yescharacteristic
490C2×C61#234311yescharacteristic
491C2×C61#235611yescharacteristic
492C2×C61#237311yescharacteristic
493C2×C61#238211yescharacteristic
494D61#273811yescharacteristic
495D61#273811yescharacteristic
496D61#274011yescharacteristic
497D61#274111yescharacteristic
498D61#275911yescharacteristic
499D61#276711yescharacteristic
500D61#276711yescharacteristic
501D61#279311yescharacteristic
502C22×C4⋊C4—611no—
503C22×C4⋊C4—611no—
504C22×C4⋊C4—611no—
505C22×C4⋊C4—611no—
506C22×C42—611no—
507C22×C42—611no—
508C22×C42—611no—
509#387—611no—
510#387—611no—
511#387—611no—
512#387—611no—
513#387—611no—
514#387—611no—
515#387—611no—
516#387#692311yescharacteristic, complemented
517C2×#95—611no—
518C2×#95—611no—
519C2×#95—611no—
520C2×#95—611no—
521C2×#95—611no—
522C2×#95—611no—
523C2×#95—611no—
524C2×#95—611no—
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95—611no—
530C2×#95—611no—
531C2×#95—611no—
532C2×#95—611no—
533C2×#95—611no—
534C2×#95—611no—
535C2×#95—611no—
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C61#1448211yescharacteristic, complemented, Sylow
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4—1222no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—2441no—
573C2×C4⋊C4—2441no—
574C2×C4⋊C4—2441no—
575C2×C4⋊C4—2441no—
576C2×C4⋊C4—2441no—
577C2×C4⋊C4C2×#692311yescharacteristic
578C2×C4⋊C4C2×#692311yescharacteristic
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—1222no—
583C2×C42—1222no—
584C2×C42—1222no—
585C2×C42—1222no—
586C2×C42—2441no—
587C2×C42—2441no—
588C2×C42—2441no—
589C2×C42—2441no—
590C2×C42C2×#692311yescharacteristic
591#95—611no—
592#95—611no—
593#95—611no—
594#95—611no—
595#95—611no—
596#95—611no—
597#95—611no—
598#95—611no—
599#95—611no—
600#95—611no—
601#95—611no—
602#95—611no—
603#95—1222no—
604#95—1222no—
605#95—1222no—
606#95—1222no—
607#95—1222no—
608#95—1222no—
609#95—1222no—
610#95—1222no—
611#95—1222no—
612#95—2441no—
613#95—2441no—
614#95—2441no—
615#95—2441no—
616#95—2441no—
617#95—2441no—
618#95—2441no—
619#95—2441no—
620#95—2441no—
621#95—2441no—
622#95—2441no—
623#95—2441no—
624#95—2441no—
625#95—2441no—
626#95—2441no—
627#95C2×#692311yescharacteristic
628#95C2×#692311yescharacteristic
629#95C2×#692311yescharacteristic
630#95C2×#692311yescharacteristic
631C24—611no—
632C22×C4—611no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
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×C4C22×#692311yescharacteristic
738C22×C4C22×#692311yescharacteristic
739C22×C4C22×#692311yescharacteristic
740C22×C4C22×#692311yescharacteristic
741C22×C4C22×#692311yescharacteristic
742C22×C4C22×#692311yescharacteristic
743C22×C4C22×#692311yescharacteristic
744C4⋊C4—22no—
745C4⋊C4—41no—
746C4⋊C4—1222no—
747C4⋊C4—1222no—
748C4⋊C4—1222no—
749C4⋊C4—2441no—
750C4⋊C4—2441no—
751C4⋊C4—2441no—
752C4⋊C4—2444no—
753C4⋊C4—2444no—
754C42—41no—
755C42—2441no—
756C42—2441no—
757C42—2441no—
758C42—2444no—
759C42—2444no—
760C23—611no—
761C23—611no—
762C23—611no—
763C23—611no—
764C23—611no—
765C23—611no—
766C23—611no—
767C23—611no—
768C23—611no—
769C23—611no—
770C23—611no—
771C23—611no—
772C23—611no—
773C23—611no—
774C23C23×#692311yescharacteristic
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—612no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
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#1451985612yes—
901C22—611no—
902C22—611no—
903C22—611no—
904C22—611no—
905C22—611no—
906C22—611no—
907C22—611no—
908C22—611no—
909C22—611no—
910C22—611no—
911C22—611no—
912C22—611no—
913C22—611no—
914C22—611no—
915C22—611no—
916C22—611no—
917C22—611no—
918C22—611no—
919C22—611no—
920C22—611no—
921C22—611no—
922C22—611no—
923C22—611no—
924C22—611no—
925C22—611no—
926C22—611no—
927C22—611no—
928C22—611no—
929C22C2×#1451985611yescharacteristic
930C22#41×#692311yescharacteristic
931C22#41×#692311yescharacteristic
932C22#1684082911yescharacteristic
933C22#1684083011yescharacteristic
934C22#1684083111yescharacteristic
935C22#1684083111yescharacteristic
936C4—22no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—41no—
942C4—41no—
943C4—1222no—
944C4—4881no—
945C4—4881no—
946C4—4881no—
947C4—4881no—
948C4—2442no—
949C4—2442no—
950C4—2442no—
951C4—2442no—
952C4—2441no—
953C4—2441no—
954C4—2441no—
955C4—2441no—
956C4—2441no—
957C4—2441no—
958C2—611no—
959C2—611no—
960C2—611no—
961C2—611no—
962C2—611no—
963C2—611no—
964C2—611no—
965C2—611no—
966C2#2146230211yescharacteristic
967C2#2146231511yescharacteristic
968C2#2146231811yescharacteristic
969C2#2146232611yescharacteristic
970C2#2146233911yescharacteristic
971C2#2146235611yescharacteristic
972C2#2146236511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#14482
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
47. #16839649C4semidirect
48. #16839648C4semidirect
49. #16839647C4semidirect
50. #16839646C4semidirect
51. #16839645C4semidirect
52. #16839644C4semidirect
53. #16839643C4semidirect
58. C61×#387C4semidirect
516. #387#6923semidirect
545. C61#14482semidirect

Maximal subgroups

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

subgroupindex
#214610082
#214610062
#214610052
#214610042
#214609992
#214609962
#214609952
#214609942
#387×D612
#1448261