Finite Group Databasebeta

← #30609418

Subgroups — #30609418

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461007C211yesmaximal, characteristic
2#21461006C211yesmaximal, characteristic
3#21461005C211yesmaximal, characteristic
4#21461005C211yesmaximal, characteristic
5#21461005C211yesmaximal, characteristic
6#21461005C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460999C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460997C211yesmaximal, characteristic
11#21460995C211yesmaximal, characteristic
12#21460994C211yesmaximal, characteristic
13#21460994C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#383×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×C42×D61C2211yescharacteristic
45#16839630C411yescharacteristic, complemented
46#16839629C411yescharacteristic, complemented
47#16839629C411yescharacteristic, complemented
48#16839629C411yescharacteristic, complemented
49#16839629C411yescharacteristic, complemented
50#16839629C411yescharacteristic, complemented
51#16839629C411yescharacteristic, complemented
52#95×D61C2211yescharacteristic
53#95×D61C2211yescharacteristic
54#95×D61C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58C61×#383C411yescharacteristic, 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—22no—
71C2×C4⋊#6923—22no—
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⋊#6923—41no—
79C2×C4×#6923—22no—
80C2×C4×#6923—22no—
81C2×C4×#6923—22no—
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—22no—
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)⋊C4—41no—
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
117C42×D61—22no—
118C42×D61—22no—
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
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×C42×C61C2×C411yescharacteristic
138#95×C61C2×C411yescharacteristic
139#95×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×#6923—44no—
262C4×#6923—44no—
263C42×C61—22no—
264C4×Dic61—22no—
265C4×Dic61—22no—
266C4×Dic61—22no—
267C23×C61C23×C411yescharacteristic
268C22×D61C2×#4111yescharacteristic
269C22×D61C2×#4111yescharacteristic
270C22×D61C2×#4111yescharacteristic
271C22×D61C2×#4111yescharacteristic
272C22×D61C2×#4111yescharacteristic
273C22×D61C2×#4111yescharacteristic
274C22×D61H(5,𝔽2)11yescharacteristic
275C22×D61H(5,𝔽2)11yescharacteristic
276C22×D61H(5,𝔽2)11yescharacteristic
277C22×D61H(5,𝔽2)11yescharacteristic
278C22×D612−1+411yescharacteristic
279C22×D612−1+411yescharacteristic
280C22×D612−1+411yescharacteristic
281C22×D612−1+411yescharacteristic
282C2×#6923—22no—
283C2×#6923—22no—
284C2×#6923—22no—
285C2×#6923—22no—
286C2×#6923—22no—
287C2×#6923—22no—
288C2×#6923—22no—
289C2×#6923—22no—
290C2×#6923—22no—
291C2×#6923—22no—
292C2×#6923—22no—
293C2×#6923—22no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
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×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
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#11712yes—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
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#11712yes—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—41no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—41no—
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—
408#14478—611nomaximal, Sylow
409C22×C61C2×#11711yescharacteristic
410C22×C61C4×#4111yescharacteristic
411C22×C61C4×#4111yescharacteristic
412C22×C61#52011yescharacteristic
413C22×C61#52011yescharacteristic
414C22×C61#52011yescharacteristic
415C22×C61#52011yescharacteristic
416C2×D61#53811yescharacteristic
417C2×D61#53811yescharacteristic
418C2×D61#53911yescharacteristic
419C2×D61#53911yescharacteristic
420C2×D61#54011yescharacteristic
421C2×D61#54111yescharacteristic
422C2×D61#54111yescharacteristic
423C2×D61#54111yescharacteristic
424C2×D61#54211yescharacteristic
425C2×D61#54211yescharacteristic
426C2×D61#54211yescharacteristic
427C2×D61#54211yescharacteristic
428C2×D61#55111yescharacteristic
429C2×D61#55111yescharacteristic
430C2×D61#55111yescharacteristic
431C2×D61#55211yescharacteristic
432C2×D61#55211yescharacteristic
433C2×D61#55211yescharacteristic
434C2×D61#55211yescharacteristic
435C2×D61#55211yescharacteristic
436C2×D61#55311yescharacteristic
437C2×D61#55511yescharacteristic
438C2×D61#55511yescharacteristic
439C2×D61#55611yescharacteristic
440C2×D61#56011yescharacteristic
441C2×D61#56311yescharacteristic
442C2×D61#56311yescharacteristic
443C2×D61#56311yescharacteristic
444#6923—42no—
445#6923—42no—
446#6923—42no—
447#6923—42no—
448#6923—81no—
449#6923—81no—
450#6923—81no—
451#6923—81no—
452C4×C61—22no—
453C4×C61—41no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61—41no—
457C4×C61—41no—
458C4×C61—41no—
459Dic61—22no—
460Dic61—41no—
461Dic61—41no—
462Dic61—41no—
463Dic61—41no—
464Dic61—41no—
465Dic61—41no—
466C2×#383—611no—
467#1444—611no—
468#1443—611no—
469#1442—611no—
470#1442—611no—
471#1442—611no—
472#1442—611no—
473#1436—611no—
474#1436—611no—
475#1436—611no—
476C4⋊#95—611no—
477#1434—611no—
478#1434—611no—
479#1434—611no—
480#1434—611no—
481C2×C61#231411yescharacteristic
482C2×C61#233411yescharacteristic
483C2×C61#233411yescharacteristic
484C2×C61#234311yescharacteristic
485C2×C61#234611yescharacteristic
486C2×C61#237311yescharacteristic
487C2×C61#238311yescharacteristic
488D61#273711yescharacteristic
489D61#273811yescharacteristic
490D61#275611yescharacteristic
491D61#275811yescharacteristic
492D61#276411yescharacteristic
493D61#276611yescharacteristic
494D61#276911yescharacteristic
495D61#277511yescharacteristic
496C22×C4⋊C4—611no—
497C22×C4⋊C4—611no—
498C22×C4⋊C4—611no—
499C22×C4⋊C4—611no—
500C22×C42—611no—
501C22×C42—611no—
502C22×C42—611no—
503#383—611no—
504#383—611no—
505#383—611no—
506#383—611no—
507#383—611no—
508#383—611no—
509#383—611no—
510#383#692311yescharacteristic, complemented
511C2×#95—611no—
512C2×#95—611no—
513C2×#95—611no—
514C2×#95—611no—
515C2×#95—611no—
516C2×#95—611no—
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—
539C61#1447811yescharacteristic, complemented, Sylow
540C23×C4—611no—
541C23×C4—611no—
542C23×C4—611no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—611no—
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—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—2441no—
561C2×C4⋊C4—2441no—
562C2×C4⋊C4—2441no—
563C2×C4⋊C4—2441no—
564C2×C4⋊C4—2441no—
565C2×C4⋊C4—2441no—
566C2×C4⋊C4—2441no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—1222no—
571C2×C42—1222no—
572C2×C42—1222no—
573C2×C42—1222no—
574C2×C42—1222no—
575C2×C42—2441no—
576C2×C42—2441no—
577C2×C42—2441no—
578C2×C42C2×#692311yescharacteristic
579#95—611no—
580#95—611no—
581#95—611no—
582#95—611no—
583#95—611no—
584#95—611no—
585#95—611no—
586#95—611no—
587#95—611no—
588#95—611no—
589#95—611no—
590#95—611no—
591#95—611no—
592#95—611no—
593#95—611no—
594#95—611no—
595#95—611no—
596#95—611no—
597#95—1222no—
598#95—1222no—
599#95—1222no—
600#95—1222no—
601#95—1222no—
602#95—1222no—
603#95—1222no—
604#95—1222no—
605#95—2441no—
606#95—2441no—
607#95—2441no—
608#95—2441no—
609#95—2441no—
610#95—2441no—
611#95—2441no—
612#95—2441no—
613#95—2441no—
614#95—2441no—
615#95—2441no—
616#95—2441no—
617#95—2441no—
618#95—2441no—
619#95C2×#692311yescharacteristic
620#95C2×#692311yescharacteristic
621#95C2×#692311yescharacteristic
622#95C2×#692311yescharacteristic
623#95C2×#692311yescharacteristic
624#95C2×#692311yescharacteristic
625C24—611no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
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×C4C22×#692311yescharacteristic
732C22×C4C22×#692311yescharacteristic
733C22×C4C22×#692311yescharacteristic
734C22×C4C22×#692311yescharacteristic
735C22×C4C22×#692311yescharacteristic
736C22×C4C22×#692311yescharacteristic
737C22×C4C22×#692311yescharacteristic
738C4⋊C4—2444no—
739C4⋊C4—2444no—
740C4⋊C4—2444no—
741C4⋊C4—2444no—
742C42—22no—
743C42—1222no—
744C42—1222no—
745C42—1222no—
746C42—2444no—
747C42—2444no—
748C23—611no—
749C23—611no—
750C23—611no—
751C23—611no—
752C23—611no—
753C23—611no—
754C23—611no—
755C23—611no—
756C23—611no—
757C23—611no—
758C23—611no—
759C23—611no—
760C23—611no—
761C23—611no—
762C23C23×#692311yescharacteristic
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
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—612no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
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#1451985612yes—
889C22—611no—
890C22—611no—
891C22—611no—
892C22—611no—
893C22—611no—
894C22—611no—
895C22—611no—
896C22—611no—
897C22—611no—
898C22—611no—
899C22—611no—
900C22—611no—
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—
917C22C2×#1451985611yescharacteristic
918C22#41×#692311yescharacteristic
919C22#41×#692311yescharacteristic
920C22#1684083111yescharacteristic
921C22#1684083111yescharacteristic
922C22#1684083111yescharacteristic
923C22#1684083111yescharacteristic
924C4—22no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—1222no—
932C4—4881no—
933C4—4881no—
934C4—4881no—
935C4—4881no—
936C4—2442no—
937C4—2442no—
938C4—2442no—
939C4—2442no—
940C4—2441no—
941C4—2441no—
942C4—2441no—
943C4—2441no—
944C4—2441no—
945C4—2441no—
946C2—611no—
947C2—611no—
948C2—611no—
949C2—611no—
950C2—611no—
951C2—611no—
952C2—611no—
953C2—611no—
954C2#2146229711yescharacteristic
955C2#2146231711yescharacteristic
956C2#2146231711yescharacteristic
957C2#2146232611yescharacteristic
958C2#2146232911yescharacteristic
959C2#2146235611yescharacteristic
960C2#2146236611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#383C4
prime radical, cosocleC23×D61C24
hypercenter#383#6923
hypocenterC61#14478
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
45. #16839630C4semidirect
46. #16839629C4semidirect
47. #16839629C4semidirect
48. #16839629C4semidirect
49. #16839629C4semidirect
50. #16839629C4semidirect
51. #16839629C4semidirect
58. C61×#383C4semidirect
510. #383#6923semidirect
539. C61#14478semidirect

Maximal subgroups

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

subgroupindex
#214610072
#214610062
#214610052
#214609992
#214609972
#214609952
#214609942
#383×D612
#1447861