Finite Group Databasebeta

← #30609326

Subgroups — #30609326

Order 15616.

1246 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840711C211yesmaximal, characteristic
2C2×#16840706C211yesmaximal, characteristic
3#21461008C211yesmaximal, characteristic
4#21461008C211yesmaximal, characteristic
5#21461007C211yesmaximal, characteristic
6#21461005C211yesmaximal, characteristic
7#21461004C211yesmaximal, characteristic
8#21461004C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic
11#21460998C211yesmaximal, characteristic
12#21460998C211yesmaximal, 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
22#16840711—24no—
23#16840706—24no—
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×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C4⋊C4×D61C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839661C411yescharacteristic, complemented
52#16839660C411yescharacteristic, complemented
53#16839659C411yescharacteristic, complemented
54#16839659C411yescharacteristic, complemented
55#16839658C411yescharacteristic, complemented
56#16839657C411yescharacteristic, complemented
57#16839657C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#389C411yescharacteristic, complemented
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C2×C4⋊#6923—22no—
70C2×C4⋊#6923—22no—
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—22no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923—41no—
81C2×C4×#6923—22no—
82C2×C4×#6923—22no—
83C2×C4×#6923—41no—
84C2×C4×#6923—41no—
85C2×C4×#6923—41no—
86C2×C4×#6923—41no—
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—22no—
94(C2×#6923)⋊C4—22no—
95(C2×#6923)⋊C4—22no—
96(C2×#6923)⋊C4—22no—
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)⋊C4D414yes—
108(C2×#6923)⋊C4Q814yes—
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×C4⋊Dic61C2×C411yescharacteristic
118C2×C4⋊Dic61C2×C411yescharacteristic
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C4⋊C4×D61—22no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61—41no—
133C4⋊C4×D61—41no—
134C4⋊C4×D61—41no—
135C4⋊C4×D61—41no—
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C42×D61—22no—
140C42×D61—22no—
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147C2×C4⋊C4×C61C2×C411yescharacteristic
148C2×C4⋊C4×C61C2×C411yescharacteristic
149C2×C4⋊C4×C61C2×C411yescharacteristic
150C2×C4⋊C4×C61C2×C411yescharacteristic
151C2×C42×C61C2×C411yescharacteristic
152#95×C61C2×C411yescharacteristic
153#95×C61C2×C411yescharacteristic
154C23×D61C2411yescharacteristic
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×#6923—21no—
206C22×#6923—21no—
207C22×#6923C2×D412yes—
208C22×#6923C2×D412yes—
209C22×#6923C2×Q812yes—
210C22×#6923C2×Q812yes—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
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×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2×Q812yes—
263C2×C4×D61#4112yes—
264C2×C4×D61#4112yes—
265C2×C4×D61#4112yes—
266C2×C4×D61#4112yes—
267C4⋊#6923—44no—
268C4⋊#6923—44no—
269C4⋊#6923—44no—
270C4⋊#6923—44no—
271C4×#6923—44no—
272C4×#6923—44no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—22no—
275C4⋊C4×C61—41no—
276C4⋊C4×C61—41no—
277C42×C61—22no—
278C4⋊Dic61—22no—
279C4⋊Dic61—22no—
280C4⋊Dic61—41no—
281C4⋊Dic61—41no—
282#11758196—22no—
283#11758196—22no—
284#11758196—22no—
285#11758196—22no—
286#11758196—41no—
287#11758196—41no—
288#11758196—41no—
289#11758196—41no—
290C4×Dic61—22no—
291C4×Dic61—22no—
292C4×Dic61—22no—
293C23×C61C23×C411yescharacteristic
294C22×D61C22×D411yescharacteristic
295C22×D61C22×Q811yescharacteristic
296C22×D61C2×#4111yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61C2×#4111yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61H(5,𝔽2)11yescharacteristic
301C22×D61H(5,𝔽2)11yescharacteristic
302C22×D61H(5,𝔽2)11yescharacteristic
303C22×D61H(5,𝔽2)11yescharacteristic
304C22×D612−1+411yescharacteristic
305C22×D612−1+411yescharacteristic
306C22×D612−1+411yescharacteristic
307C22×D612−1+411yescharacteristic
308C2×#6923—22no—
309C2×#6923—22no—
310C2×#6923—22no—
311C2×#6923—22no—
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—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×#6923—41no—
363C2×#6923—41no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61#11712yes—
383C2×C4×C61C4×D412yes—
384C2×C4×C61C4×Q812yes—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61#11712yes—
404C2×Dic61C4×D412yes—
405C2×Dic61C4×Q812yes—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—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—
432C4×D61—41no—
433C4×D61—41no—
434#14386—611nomaximal, Sylow
435C22×C61C2×#11711yescharacteristic
436C22×C61C2×C4×D411yescharacteristic
437C22×C61C2×C4×Q811yescharacteristic
438C22×C61#51811yescharacteristic
439C22×C61#51911yescharacteristic
440C22×C61#52011yescharacteristic
441C22×C61#52011yescharacteristic
442C2×D61#53511yescharacteristic
443C2×D61#53711yescharacteristic
444C2×D61#53811yescharacteristic
445C2×D61#53811yescharacteristic
446C2×D61#53911yescharacteristic
447C2×D61#53911yescharacteristic
448C2×D61#54011yescharacteristic
449C2×D61#54211yescharacteristic
450C2×D61#54211yescharacteristic
451C2×D61#54211yescharacteristic
452C2×D61#54411yescharacteristic
453C2×D61#54411yescharacteristic
454C2×D61#54611yescharacteristic
455C2×D61#54711yescharacteristic
456C2×D61#54711yescharacteristic
457C2×D61D4×Q811yescharacteristic
458C2×D61#55211yescharacteristic
459C2×D61#55211yescharacteristic
460C2×D61#55211yescharacteristic
461C2×D61#55411yescharacteristic
462C2×D61#55411yescharacteristic
463C2×D61#55611yescharacteristic
464C2×D61#55711yescharacteristic
465C2×D61#55911yescharacteristic
466C2×D61#56211yescharacteristic
467C2×D61#56311yescharacteristic
468C2×D61#56311yescharacteristic
469C2×D61#56411yescharacteristic
470#6923—42no—
471#6923—42no—
472#6923—42no—
473#6923—42no—
474#6923—81no—
475#6923—81no—
476#6923—81no—
477#6923—81no—
478C4×C61—22no—
479C4×C61—22no—
480C4×C61—22no—
481C4×C61—41no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485Dic61—22no—
486Dic61—22no—
487Dic61—22no—
488Dic61—41no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492C2×#389—611no—
493C2×#387—611no—
494C2×#382—611no—
495#1445—611no—
496#1445—611no—
497#1444—611no—
498#1442—611no—
499#1441—611no—
500#1441—611no—
501#1436—611no—
502#1436—611no—
503#1436—611no—
504#1436—611no—
505C4⋊#95—611no—
506#1434—611no—
507C2×C61#231811yescharacteristic
508C2×C61#232411yescharacteristic
509C2×C61#233111yescharacteristic
510C2×C61#234411yescharacteristic
511C2×C61#235511yescharacteristic
512C2×C61#236011yescharacteristic
513C2×C61#238211yescharacteristic
514D61#271011yescharacteristic
515D61#271511yescharacteristic
516D61#272011yescharacteristic
517D61#272611yescharacteristic
518D61#276711yescharacteristic
519D61#276811yescharacteristic
520D61#277311yescharacteristic
521D61#277411yescharacteristic
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×C4⋊C4—611no—
529C22×C4⋊C4—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42—611no—
533#389—611no—
534#389—611no—
535#389—611no—
536#389—611no—
537#389—611no—
538#389—611no—
539#389—611no—
540#389#692311yescharacteristic, complemented
541#387—1224no—
542#382—1224no—
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—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C61#1438611yescharacteristic, complemented, Sylow
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—1222no—
596C2×C4⋊C4—1222no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
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⋊C4—2441no—
612C2×C4⋊C4—2441no—
613C2×C4⋊C4—2441no—
614C2×C4⋊C4—2441no—
615C2×C4⋊C4C2×#692311yescharacteristic
616C2×C4⋊C4C2×#692311yescharacteristic
617C2×C4⋊C4C2×#692311yescharacteristic
618C2×C4⋊C4C2×#692311yescharacteristic
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625C2×C42—1222no—
626C2×C42—2441no—
627C2×C42—2441no—
628C2×C42—2441no—
629C2×C42—2441no—
630C2×C42C2×#692311yescharacteristic
631#95—614no—
632#95—614no—
633#95—611no—
634#95—611no—
635#95—611no—
636#95—611no—
637#95—611no—
638#95—611no—
639#95—1222no—
640#95—1222no—
641#95—1222no—
642#95—1222no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—2441no—
650#95—2441no—
651#95—2441no—
652#95—2441no—
653#95—2441no—
654#95—2441no—
655#95—2441no—
656#95—2441no—
657#95—2441no—
658#95—2441no—
659#95C2×#692311yescharacteristic
660#95C2×#692311yescharacteristic
661C24—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
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×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4C22×#692311yescharacteristic
768C22×C4C22×#692311yescharacteristic
769C22×C4C22×#692311yescharacteristic
770C22×C4C22×#692311yescharacteristic
771C22×C4C22×#692311yescharacteristic
772C22×C4C22×#692311yescharacteristic
773C22×C4C22×#692311yescharacteristic
774C4⋊C4—22no—
775C4⋊C4—22no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—1222no—
779C4⋊C4—1222no—
780C4⋊C4—1222no—
781C4⋊C4—1222no—
782C4⋊C4—1222no—
783C4⋊C4—1222no—
784C4⋊C4—2441no—
785C4⋊C4—2441no—
786C4⋊C4—2441no—
787C4⋊C4—2441no—
788C4⋊C4—2441no—
789C4⋊C4—2441no—
790C4⋊C4—2444no—
791C4⋊C4—2444no—
792C4⋊C4—2444no—
793C4⋊C4—2444no—
794C42—22no—
795C42—1222no—
796C42—1222no—
797C42—1222no—
798C42—2444no—
799C42—2444no—
800C23—611no—
801C23—611no—
802C23—611no—
803C23—611no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23C23×#692311yescharacteristic
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—612no—
834C2×C4—612no—
835C2×C4—612no—
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—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
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—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4#1451985612yes—
939C2×C4D4×#692312yes—
940C2×C4Q8×#692312yes—
941C22—611no—
942C22—611no—
943C22—611no—
944C22—611no—
945C22—611no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—611no—
953C22—611no—
954C22—611no—
955C22—611no—
956C22—611no—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22C2×#1451985611yescharacteristic
970C22C2×D4×#692311yescharacteristic
971C22C2×Q8×#692311yescharacteristic
972C22#1684082911yescharacteristic
973C22#1684083011yescharacteristic
974C22#1684083111yescharacteristic
975C22#1684083111yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—1222no—
984C4—1222no—
985C4—1222no—
986C4—4881no—
987C4—4881no—
988C4—4881no—
989C4—4881no—
990C4—2442no—
991C4—2442no—
992C4—2442no—
993C4—2442no—
994C4—2441no—
995C4—2441no—
996C4—2441no—
997C4—2441no—
998C2—611no—
999C2—611no—
1000C2—611no—
1001C2—611no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2#2146230111yescharacteristic
1007C2#2146230711yescharacteristic
1008C2#2146231411yescharacteristic
1009C2#2146232711yescharacteristic
1010C2#2146233811yescharacteristic
1011C2#2146234311yescharacteristic
1012C2#2146236511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#389C4
prime radical, cosocleC23×D61C24
hypercenter#389#6923
hypocenterC61#14386
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
51. #16839661C4semidirect
52. #16839660C4semidirect
53. #16839659C4semidirect
54. #16839659C4semidirect
55. #16839658C4semidirect
56. #16839657C4semidirect
57. #16839657C4semidirect
60. C61×#389C4semidirect
540. #389#6923semidirect
567. C61#14386semidirect

Maximal subgroups

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

subgroupindex
C2×#168407112
C2×#168407062
#214610082
#214610072
#214610052
#214610042
#214609992
#214609982
#214609962
#214609952
#389×D612
#1438661