Finite Group Databasebeta

← #30608748

Subgroups — #30608748

Order 15616.

1514 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×C4⋊C4×#6923C211yesmaximal, characteristic
3#21460999C211yesmaximal, characteristic
4#21460999C211yesmaximal, characteristic
5#21460999C211yesmaximal, characteristic
6#21460998C211yesmaximal, characteristic
7#21460996C211yesmaximal, characteristic
8#21460994C211yesmaximal, characteristic
9#21460994C211yesmaximal, characteristic
10C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
11C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
12#95×#6923C211yesmaximal, characteristic
13#95×#6923C211yesmaximal, characteristic
14#95×#6923C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4×#6923C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26#16840711C418yescomplemented
27C4⋊C4×#6923C418yescomplemented
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×C42×D61C2211yescharacteristic
49#16839649C411yescharacteristic, complemented
50#16839648C411yescharacteristic, complemented
51#16839647C411yescharacteristic, complemented
52#16839646C411yescharacteristic, complemented
53#16839645C411yescharacteristic, complemented
54#16839644C411yescharacteristic, complemented
55#16839643C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#387C411yescharacteristic, 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—41no—
72C2×C4⋊#6923—41no—
73C2×C4⋊#6923C2×C414yes—
74C2×C4⋊#6923C2×C414yes—
75C2×C4×#6923—22no—
76C2×C4×#6923—22no—
77C2×C4×#6923—22no—
78C2×C4×#6923—22no—
79C2×C4×#6923—22no—
80C2×C4×#6923—22no—
81C2×C4×#6923—22no—
82C2×C4×#6923—22no—
83C2×C4×#6923—22no—
84C2×C4×#6923—22no—
85C2×C4×#6923—41no—
86C2×C4×#6923—41no—
87C2×C4×#6923—41no—
88C2×C4×#6923—41no—
89C2×C4×#6923—41no—
90C2×C4×#6923—41no—
91C2×C4×#6923—41no—
92C2×C4×#6923—41no—
93C2×C4×#6923—41no—
94C2×C4×#6923—41no—
95C2×C4×#6923C2×C414yes—
96C2×C4×#6923C2×C414yes—
97C2×C4×#6923C2×C414yes—
98C2×C4×#6923C2×C414yes—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—22no—
105(C2×#6923)⋊C4—22no—
106(C2×#6923)⋊C4—22no—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4C2×C414yes—
111(C2×#6923)⋊C4C2×C414yes—
112(C2×#6923)⋊C4C2×C414yes—
113(C2×#6923)⋊C4C2×C414yes—
114(C2×#6923)⋊C4C2×C414yes—
115(C2×#6923)⋊C4C2×C414yes—
116(C2×#6923)⋊C4Q814yes—
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic
125C2×C4⋊Dic61C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C4⋊C4×D61—41no—
131C4⋊C4×D61—41no—
132C4⋊C4×D61C2×C414yes—
133C4⋊C4×D61C2×C414yes—
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
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151C2×C4⋊C4×C61C2×C411yescharacteristic
152C2×C4⋊C4×C61C2×C411yescharacteristic
153C2×C42×C61C2×C411yescharacteristic
154#95×C61C2×C411yescharacteristic
155#95×C61C2×C411yescharacteristic
156#95×C61C2×C411yescharacteristic
157#95×C61C2×C411yescharacteristic
158C23×D61C2411yescharacteristic
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×#6923C22×C412yes—
200C22×#6923C22×C412yes—
201C22×#6923C22×C412yes—
202C22×#6923C22×C412yes—
203C22×#6923C22×C412yes—
204C22×#6923C22×C412yes—
205C22×#6923C22×C412yes—
206C22×#6923C22×C412yes—
207C22×#6923C2×Q812yes—
208C22×#6923C2×Q812yes—
209C22×#6923#4112yes—
210C22×#6923#4112yes—
211C22×#6923#4112yes—
212C22×#6923#4112yes—
213C22×#6923#4112yes—
214C22×#6923#4112yes—
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
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×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61C22×C412yes—
264C2×C4×D61C22×C412yes—
265C2×C4×D61C22×C412yes—
266C2×C4×D61C22×C412yes—
267C2×C4×D61C22×C412yes—
268C2×C4×D61C22×C412yes—
269C2×C4×D61C2×Q812yes—
270C2×C4×D61#4112yes—
271C4⋊#6923—28no—
272C4⋊#6923—44no—
273C4×#6923—28no—
274C4×#6923—44no—
275C4×#6923—44no—
276C4×#6923—44no—
277C4×#6923—44no—
278C4×#6923—44no—
279C4×#6923—44no—
280C4×#6923—44no—
281C4⋊C4×C61—41no—
282C4⋊C4×C61C4214yescomplemented
283C42×C61—41no—
284C4⋊Dic61—41no—
285C4⋊Dic61C4214yescomplemented
286#11758196—41no—
287#11758196—41no—
288#11758196C4214yescomplemented
289#11758196C4214yescomplemented
290C4×Dic61—41no—
291C4×Dic61—41no—
292C4×Dic61—41no—
293C23×C61C23×C411yescharacteristic
294C22×D61C23×C411yescharacteristic
295C22×D61C23×C411yescharacteristic
296C22×D61C22×Q811yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61C2×#4111yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61C2×#4111yescharacteristic
301C22×D61C2×#4111yescharacteristic
302C22×D61C2×#4111yescharacteristic
303C22×D61C2×#4111yescharacteristic
304C22×D61H(5,𝔽2)11yescharacteristic
305C22×D61H(5,𝔽2)11yescharacteristic
306C22×D61H(5,𝔽2)11yescharacteristic
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—22no—
321C2×#6923—22no—
322C2×#6923—22no—
323C2×#6923—22no—
324C2×#6923—22no—
325C2×#6923—22no—
326C2×#6923—22no—
327C2×#6923—22no—
328C2×#6923—22no—
329C2×#6923—22no—
330C2×#6923—22no—
331C2×#6923—22no—
332C2×#6923—22no—
333C2×#6923—22no—
334C2×#6923—22no—
335C2×#6923—22no—
336C2×#6923—22no—
337C2×#6923—22no—
338C2×#6923—22no—
339C2×#6923—22no—
340C2×#6923—22no—
341C2×#6923—22no—
342C2×#6923—22no—
343C2×#6923—22no—
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#11714yes—
361C2×#6923#11714yes—
362C2×#6923C4×Q814yes—
363C2×#6923C4×Q814yes—
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×C61C2×C4212yes—
382C2×C4×C61C2×C4212yes—
383C2×C4×C61C2×C4212yes—
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×Dic61C2×C4212yes—
403C2×Dic61C2×C4212yes—
404C2×Dic61C2×C4212yes—
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—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
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#13819—611nomaximal, Sylow
435C22×C61C22×C4211yescharacteristic
436C22×C61C2×C4×Q811yescharacteristic
437C22×C61C4×#4111yescharacteristic
438C22×C61C4×#4111yescharacteristic
439C22×C61C4×#4111yescharacteristic
440C22×C61#51811yescharacteristic
441C22×C61#52011yescharacteristic
442C2×D61C2×#11711yescharacteristic
443C2×D61C2×#11711yescharacteristic
444C2×D61C2×C4×Q811yescharacteristic
445C2×D61C2×C4×Q811yescharacteristic
446C2×D61C4×#4111yescharacteristic
447C2×D61C4×#4111yescharacteristic
448C2×D61C4×#4111yescharacteristic
449C2×D61C4×#4111yescharacteristic
450C2×D61#51811yescharacteristic
451C2×D61#51811yescharacteristic
452C2×D61#52011yescharacteristic
453C2×D61#52011yescharacteristic
454C2×D61#55111yescharacteristic
455C2×D61#55111yescharacteristic
456C2×D61#55111yescharacteristic
457C2×D61#55111yescharacteristic
458C2×D61#55211yescharacteristic
459C2×D61#55211yescharacteristic
460C2×D61#55311yescharacteristic
461C2×D61#55311yescharacteristic
462C2×D61#55311yescharacteristic
463C2×D61#55311yescharacteristic
464C2×D61#55411yescharacteristic
465C2×D61#55411yescharacteristic
466C2×D61#55411yescharacteristic
467C2×D61#55611yescharacteristic
468C2×D61#55711yescharacteristic
469C2×D61#55911yescharacteristic
470#6923—24no—
471#6923—24no—
472#6923—24no—
473#6923—24no—
474#6923—42no—
475#6923—42no—
476#6923—42no—
477#6923—42no—
478C4×C61—22no—
479C4×C61—22no—
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485Dic61—22no—
486Dic61—22no—
487Dic61—22no—
488Dic61—22no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492C2×#387—611no—
493C2×#387—611no—
494C2×C4×C4⋊C4—611no—
495#1436—611no—
496#1436—611no—
497#1436—611no—
498#1436—611no—
499C4⋊#95—611no—
500#1434—611no—
501#1434—611no—
502C4×#95—611no—
503C4×#95—611no—
504C4×#95—611no—
505C4×#95—611no—
506C4×#95—611no—
507C2×C61C4×#11711yescharacteristic
508C2×C61C42×Q811yescharacteristic
509C2×C61#227511yescharacteristic
510C2×C61#236811yescharacteristic
511C2×C61#237011yescharacteristic
512C2×C61#237311yescharacteristic
513C2×C61#237411yescharacteristic
514D61#234311yescharacteristic
515D61#234511yescharacteristic
516D61#235311yescharacteristic
517D61#235511yescharacteristic
518D61#236811yescharacteristic
519D61#237011yescharacteristic
520D61#237311yescharacteristic
521D61#237411yescharacteristic
522C22×C4⋊C4—611no—
523C22×C4⋊C4—611no—
524C22×C4⋊C4—611no—
525C22×C4⋊C4—611no—
526C22×C42—611no—
527C22×C42—611no—
528C22×C42—611no—
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42—611no—
533C22×C42—611no—
534C22×C42—611no—
535#387—618no—
536#387—611no—
537#387—611no—
538#387—611no—
539#387—611no—
540#387—611no—
541#387—611no—
542#387—611no—
543#387#692311yescharacteristic, complemented
544C4×C4⋊C4—618no—
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#1381911yescharacteristic, 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—614no—
587C2×C4⋊C4—614no—
588C2×C4⋊C4—614no—
589C2×C4⋊C4—614no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1222no—
595C2×C4⋊C4—2441no—
596C2×C4⋊C4—2441no—
597C2×C4⋊C4—2441no—
598C2×C4⋊C4—2441no—
599C2×C4⋊C4C2×#692311yescharacteristic
600C2×C4⋊C4C2×#692311yescharacteristic
601C2×C42—614no—
602C2×C42—614no—
603C2×C42—614no—
604C2×C42—614no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—1222no—
609C2×C42—1222no—
610C2×C42—1222no—
611C2×C42—1222no—
612C2×C42—1222no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—1222no—
617C2×C42—1222no—
618C2×C42—2441no—
619C2×C42—2441no—
620C2×C42—2441no—
621C2×C42—2441no—
622C2×C42—2441no—
623C2×C42—2441no—
624C2×C42—2441no—
625C2×C42—2441no—
626C2×C42—2441no—
627C2×C42—2441no—
628C2×C42—2441no—
629C2×C42—2441no—
630C2×C42C2×#692311yescharacteristic
631#95—614no—
632#95—614no—
633#95—614no—
634#95—614no—
635#95—614no—
636#95—614no—
637#95—614no—
638#95—611no—
639#95—611no—
640#95—611no—
641#95—611no—
642#95—611no—
643#95—611no—
644#95—611no—
645#95—611no—
646#95—611no—
647#95—611no—
648#95—611no—
649#95—611no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—1222no—
656#95—1222no—
657#95—1222no—
658#95—1222no—
659#95—2441no—
660#95—2441no—
661#95C2×#692311yescharacteristic
662#95C2×#692311yescharacteristic
663#95C2×#692311yescharacteristic
664#95C2×#692311yescharacteristic
665C24—611no—
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—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
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×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4C22×#692311yescharacteristic
772C22×C4C22×#692311yescharacteristic
773C22×C4C22×#692311yescharacteristic
774C22×C4C22×#692311yescharacteristic
775C22×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777C22×C4C22×#692311yescharacteristic
778C4⋊C4—41no—
779C4⋊C4—614no—
780C4⋊C4—614no—
781C4⋊C4—614no—
782C4⋊C4—1228no—
783C4⋊C4—2441no—
784C4⋊C4—2441no—
785C4⋊C4—2441no—
786C4⋊C4—2444no—
787C4⋊C4C4×#692314yescomplemented
788C42—41no—
789C42—1228no—
790C42—2441no—
791C42—2441no—
792C42—2441no—
793C42—2444no—
794C42—2444no—
795C42—2444no—
796C42—2444no—
797C42—2444no—
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—614no—
833C2×C4—614no—
834C2×C4—614no—
835C2×C4—614no—
836C2×C4—612no—
837C2×C4—612no—
838C2×C4—612no—
839C2×C4—612no—
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—1222no—
849C2×C4—1222no—
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—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—1221no—
903C2×C4—1221no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
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×C4C2×C4×#692312yes—
938C2×C4C2×C4×#692312yes—
939C2×C4C2×C4×#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—
969C22C22×C4×#692311yescharacteristic
970C22C2×Q8×#692311yescharacteristic
971C22#41×#692311yescharacteristic
972C22#41×#692311yescharacteristic
973C22#41×#692311yescharacteristic
974C22#1684082911yescharacteristic
975C22#1684083111yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—1224no—
984C4—1224no—
985C4—1224no—
986C4—1224no—
987C4—1222no—
988C4—1222no—
989C4—1222no—
990C4—1222no—
991C4—2442no—
992C4—2442no—
993C4—2442no—
994C4—2442no—
995C4—2441no—
996C4—2441no—
997C4—2441no—
998C2—611no—
999C2—611no—
1000C2—611no—
1001C2—611no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2#117×#692311yescharacteristic
1007C2C4×Q8×#692311yescharacteristic
1008C2#2146225811yescharacteristic
1009C2#2146235111yescharacteristic
1010C2#2146235311yescharacteristic
1011C2#2146235611yescharacteristic
1012C2#2146235711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#387C4
socleC23×C61C23×C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#13819
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
26. #16840711C4semidirect
27. C4⋊C4×#6923C4semidirect
49. #16839649C4semidirect
50. #16839648C4semidirect
51. #16839647C4semidirect
52. #16839646C4semidirect
53. #16839645C4semidirect
54. #16839644C4semidirect
55. #16839643C4semidirect
60. C61×#387C4semidirect
282. C4⋊C4×C61C42semidirect
285. C4⋊Dic61C42semidirect
288. #11758196C42semidirect
289. #11758196C42semidirect
543. #387#6923semidirect
567. C61#13819semidirect
787. C4⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407112
C2×C4⋊C4×#69232
#214609992
#214609982
#214609962
#214609942
C4×(C2×#6923)⋊C42
#95×#69232
#387×D612
#1381961