Finite Group Databasebeta

← #30608687

Subgroups — #30608687

Order 15616.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×#16840712C211yesmaximal, characteristic
3C2×C4⋊C4×#6923C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊#6923C211yesmaximal, characteristic
5#21461000C211yesmaximal, characteristic
6#21461000C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic, complemented
8#21460999C211yesmaximal, characteristic, complemented
9#21460998C211yesmaximal, characteristic, complemented
10#21460998C211yesmaximal, characteristic, complemented
11#21460996C211yesmaximal, characteristic, complemented
12#21460994C211yesmaximal, characteristic, complemented
13#21460993C211yesmaximal, characteristic
14#95×#6923C211yesmaximal, characteristic, complemented
15#385×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C22⋊#6923C2211yescharacteristic
19C22×C22⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26C22×C4×#6923C2211yescharacteristic
27C22×C4×#6923C2211yescharacteristic
28#16840712C418yescomplemented
29#16840712C418yescomplemented
30C4⋊C4×#6923—24no—
31C4×C22⋊#6923—24no—
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×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C23×C4×D61C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C4⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61C2211yescharacteristic
52C2×C22⋊C4×D61C2211yescharacteristic
53#16839637C411yescharacteristic, complemented
54#16839636C411yescharacteristic, complemented
55#16839636C411yescharacteristic, complemented
56#16839635C411yescharacteristic, complemented
57#16839634C411yescharacteristic, complemented
58#16839633C411yescharacteristic, complemented
59#16839633C411yescharacteristic, complemented
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#385C411yescharacteristic, complemented
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C4⋊#6923C2×C414yescomplemented
76C2×C4⋊#6923C2×C414yescomplemented
77C2×C22⋊#6923—22no—
78C2×C22⋊#6923—22no—
79C2×C22⋊#6923—22no—
80C2×C22⋊#6923—22no—
81C2×C22⋊#6923—41no—
82C2×C22⋊#6923—41no—
83C2×C22⋊#6923—41no—
84C2×C22⋊#6923—41no—
85C2×C22⋊#6923C2×C414yes—
86C2×C22⋊#6923C2×C414yes—
87C2×C22⋊#6923C2×C414yes—
88C2×C22⋊#6923C2×C414yes—
89C2×C4×#6923—22no—
90C2×C4×#6923—22no—
91C2×C4×#6923—22no—
92C2×C4×#6923—22no—
93C2×C4×#6923—22no—
94C2×C4×#6923—41no—
95C2×C4×#6923—41no—
96C2×C4×#6923—41no—
97C2×C4×#6923—41no—
98C2×C4×#6923—41no—
99C2×C4×#6923—41no—
100C2×C4×#6923—41no—
101C2×C4×#6923—41no—
102C2×C4×#6923—41no—
103C2×C4×#6923—41no—
104C2×C4×#6923C2×C414yescomplemented
105C2×C4×#6923C2×C414yescomplemented
106C2×C4×#6923D414yes—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—22no—
109(C2×#6923)⋊C4—22no—
110(C2×#6923)⋊C4—22no—
111(C2×#6923)⋊C4—22no—
112(C2×#6923)⋊C4—22no—
113(C2×#6923)⋊C4—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4—41no—
117(C2×#6923)⋊C4—41no—
118(C2×#6923)⋊C4—41no—
119(C2×#6923)⋊C4C2×C414yescomplemented
120(C2×#6923)⋊C4C2×C414yescomplemented
121(C2×#6923)⋊C4C2×C414yescomplemented
122(C2×#6923)⋊C4C2×C414yescomplemented
123C24×D61C2311yescharacteristic
124C23×Dic61C2×C411yescharacteristic
125C22×C4×D61—22no—
126C22×C4×D61—22no—
127C22×C4×D61—41no—
128C22×C4×D61—41no—
129C22×C4×D61—41no—
130C22×C4×D61—41no—
131C22×C4×D61C2×C411yescharacteristic
132C22×C4×D61C2×C411yescharacteristic
133C22×C4×D61C2311yescharacteristic
134C22×C4×D61C2311yescharacteristic
135C22×C4×D61C2311yescharacteristic
136C22×C4×D61C2311yescharacteristic
137C22×C4×D61C2311yescharacteristic
138C22×C4×D61C2311yescharacteristic
139C2×C4⋊Dic61C2×C411yescharacteristic
140C2×C4⋊Dic61C2×C411yescharacteristic
141C2×#11758196C2×C411yescharacteristic
142C2×#11758196C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C4⋊C4×D61—22no—
146C4⋊C4×D61—22no—
147C4⋊C4×D61—41no—
148C4⋊C4×D61—41no—
149C2×C22⋊Dic61C2×C411yescharacteristic
150C2×C22⋊Dic61C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C22⋊C4×D61—41no—
156C22⋊C4×D61—41no—
157C22⋊C4×D61C2×C414yes—
158C22⋊C4×D61C2×C414yes—
159#14519684C2×C411yescharacteristic
160#14519684C2×C411yescharacteristic
161#14519684C2×C411yescharacteristic
162#14519684C2×C411yescharacteristic
163#14519684C2×C411yescharacteristic
164#14519684C2×C411yescharacteristic
165C23×C4×C61C2×C411yescharacteristic
166C2×C4⋊C4×C61C2×C411yescharacteristic
167C2×C4⋊C4×C61C2×C411yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170#95×C61C2×C411yescharacteristic
171#95×C61C2×C411yescharacteristic
172C24×C61C22×C411yescharacteristic
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61C22×C411yescharacteristic
186C23×D61C22×C412yes—
187C23×D61C22×C412yes—
188C23×D61C2411yescharacteristic
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×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923—21no—
232C22×#6923—21no—
233C22×#6923C22×C412yes—
234C22×#6923C22×C412yes—
235C22×#6923C22×C412yes—
236C22×#6923C22×C412yes—
237C22×#6923C22×C412yes—
238C22×#6923C22×C412yes—
239C22×#6923C22×C412yes—
240C22×#6923C22×C412yes—
241C22×#6923C2×D412yes—
242C22×#6923C2×D412yes—
243C22×#6923#4112yes—
244C22×#6923#4112yes—
245C22×C4×C61—22no—
246C22×C4×C61—41no—
247C22×C4×C61—41no—
248C22×C4×C61C22×C411yescharacteristic
249C22×C4×C61C22×C411yescharacteristic
250C22×C4×C61C22×C411yescharacteristic
251C22×C4×C61C22×C411yescharacteristic
252C22×C4×C61C22×C411yescharacteristic
253C22×C4×C61C22×C411yescharacteristic
254C22×Dic61—22no—
255C22×Dic61—41no—
256C22×Dic61—41no—
257C22×Dic61C22×C411yescharacteristic
258C22×Dic61C22×C411yescharacteristic
259C22×Dic61C22×C411yescharacteristic
260C22×Dic61C22×C411yescharacteristic
261C22×Dic61C22×C411yescharacteristic
262C22×Dic61C22×C411yescharacteristic
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—21no—
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—21no—
292C2×C4×D61—21no—
293C2×C4×D61—22no—
294C2×C4×D61—22no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—41no—
300C2×C4×D61—41no—
301C2×C4×D61—41no—
302C2×C4×D61—41no—
303C2×C4×D61C22×C412yes—
304C2×C4×D61C22×C412yes—
305C2×C4×D61C22×C412yes—
306C2×C4×D61C22×C412yes—
307C2×C4×D61C2×D412yes—
308C2×C4×D61#4112yes—
309C22⋊#6923—28no—
310C22⋊#6923—28no—
311C22⋊#6923—44no—
312C22⋊#6923—44no—
313C4⋊#6923—28no—
314C4⋊#6923—44no—
315C4×#6923—28no—
316C4×#6923—44no—
317C4×#6923—44no—
318C4×#6923—44no—
319C4×#6923—44no—
320C4×#6923—44no—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—41no—
323C22⋊C4×C61—41no—
324C22⋊C4×C61C4214yescomplemented
325C22⋊Dic61—41no—
326C22⋊Dic61C4214yescomplemented
327#11758198—41no—
328#11758198—41no—
329#11758198C4214yescomplemented
330#11758198C4214yescomplemented
331C4⋊Dic61—22no—
332C4⋊Dic61—41no—
333#11758196—22no—
334#11758196—22no—
335#11758196—41no—
336#11758196—41no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61C2×C4212yes—
344C23×C61C23×C411yescharacteristic
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61C2×C4212yes—
380C22×D61C23×C411yescharacteristic
381C22×D61C23×C411yescharacteristic
382C22×D61C22×D411yescharacteristic
383C22×D61C2×#4111yescharacteristic
384C22×D61C2×#4111yescharacteristic
385C22×D61C2×#4111yescharacteristic
386C22×D61H(5,𝔽2)11yescharacteristic
387C22×D61H(5,𝔽2)11yescharacteristic
388C22×D61H(5,𝔽2)11yescharacteristic
389C22×D61H(5,𝔽2)11yescharacteristic
390C22×D61H(5,𝔽2)11yescharacteristic
391C22×D612−1+411yescharacteristic
392C22×D612−1+411yescharacteristic
393C22×D612−1+411yescharacteristic
394C2×#6923—22no—
395C2×#6923—22no—
396C2×#6923—22no—
397C2×#6923—22no—
398C2×#6923—22no—
399C2×#6923—22no—
400C2×#6923—22no—
401C2×#6923—22no—
402C2×#6923—22no—
403C2×#6923—22no—
404C2×#6923—22no—
405C2×#6923—22no—
406C2×#6923—22no—
407C2×#6923—22no—
408C2×#6923—22no—
409C2×#6923—22no—
410C2×#6923—22no—
411C2×#6923—22no—
412C2×#6923—22no—
413C2×#6923—22no—
414C2×#6923—22no—
415C2×#6923—22no—
416C2×#6923—22no—
417C2×#6923—22no—
418C2×#6923—22no—
419C2×#6923—22no—
420C2×#6923—22no—
421C2×#6923—22no—
422C2×#6923—22no—
423C2×#6923—22no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×#6923—41no—
427C2×#6923—41no—
428C2×#6923—41no—
429C2×#6923—41no—
430C2×#6923—41no—
431C2×#6923—41no—
432C2×#6923—41no—
433C2×#6923—41no—
434C2×#6923—41no—
435C2×#6923—41no—
436C2×#6923—41no—
437C2×#6923—41no—
438C2×#6923—41no—
439C2×#6923—41no—
440C2×#6923—41no—
441C2×#6923—41no—
442C2×#6923—41no—
443C2×#6923—41no—
444C2×#6923—41no—
445C2×#6923—41no—
446C2×#6923—41no—
447C2×#6923—41no—
448C2×#6923C4×D414yes—
449C2×#6923C4×D414yes—
450C2×C4×C61—21no—
451C2×C4×C61—21no—
452C2×C4×C61—21no—
453C2×C4×C61—21no—
454C2×C4×C61—21no—
455C2×C4×C61—21no—
456C2×C4×C61—21no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—44no—
466C2×C4×C61C2×C4212yes—
467C2×C4×C61C2×C4212yes—
468C2×C4×C61C4×D412yes—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61—21no—
472C2×Dic61—21no—
473C2×Dic61—21no—
474C2×Dic61—21no—
475C2×Dic61—21no—
476C2×Dic61—21no—
477C2×Dic61—21no—
478C2×Dic61—21no—
479C2×Dic61—21no—
480C2×Dic61—21no—
481C2×Dic61—21no—
482C2×Dic61—21no—
483C2×Dic61—21no—
484C2×Dic61—44no—
485C2×Dic61C2×C4212yes—
486C2×Dic61C2×C4212yes—
487C2×Dic61C4×D412yes—
488C4×D61—22no—
489C4×D61—22no—
490C4×D61—22no—
491C4×D61—22no—
492C4×D61—22no—
493C4×D61—22no—
494C4×D61—22no—
495C4×D61—22no—
496C4×D61—22no—
497C4×D61—22no—
498C4×D61—22no—
499C4×D61—22no—
500C4×D61—44no—
501C4×D61—44no—
502C4×D61—41no—
503C4×D61—41no—
504C4×D61—41no—
505C4×D61—41no—
506C4×D61—41no—
507C4×D61—41no—
508C4×D61—41no—
509C4×D61—41no—
510C4×D61—41no—
511C4×D61—41no—
512C4×D61—41no—
513C4×D61—41no—
514#13789—611nomaximal, Sylow
515C22×C61—22no—
516C22×C61—22no—
517C22×C61—22no—
518C22×C61—41no—
519C22×C61—41no—
520C22×C61—41no—
521C22×C61—41no—
522C22×C61C22×C4211yescharacteristic
523C22×C61C2×C4×D411yescharacteristic
524C22×C61C4×#4111yescharacteristic
525C22×C61#51811yescharacteristic
526C22×C61#51811yescharacteristic
527C22×C61#51911yescharacteristic
528C22×C61#52011yescharacteristic
529C2×D61—22no—
530C2×D61—22no—
531C2×D61—22no—
532C2×D61—41no—
533C2×D61—41no—
534C2×D61—41no—
535C2×D61—41no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61C2×C4×D411yescharacteristic
545C2×D61C2×C4×D411yescharacteristic
546C2×D61C4×#4111yescharacteristic
547C2×D61C4×#4111yescharacteristic
548C2×D61#51811yescharacteristic
549C2×D61#51811yescharacteristic
550C2×D61#52011yescharacteristic
551C2×D61#52011yescharacteristic
552C2×D61#52011yescharacteristic
553C2×D61#52011yescharacteristic
554C2×D61#52011yescharacteristic
555C2×D61#52011yescharacteristic
556C2×D61#53411yescharacteristic
557C2×D61#53511yescharacteristic
558C2×D61#53611yescharacteristic
559C2×D61#53711yescharacteristic
560C2×D61#53811yescharacteristic
561C2×D61#53811yescharacteristic
562C2×D61#53811yescharacteristic
563C2×D61#53911yescharacteristic
564C2×D61#53911yescharacteristic
565C2×D61#53911yescharacteristic
566C2×D61#54011yescharacteristic
567C2×D61#54111yescharacteristic
568C2×D61#54211yescharacteristic
569C2×D61#54211yescharacteristic
570C2×D61#54211yescharacteristic
571C2×D61#54211yescharacteristic
572#6923—24no—
573#6923—24no—
574#6923—42no—
575#6923—42no—
576#6923—42no—
577#6923—42no—
578#6923—42no—
579#6923—42no—
580C4×C61—22no—
581C4×C61—22no—
582C4×C61—22no—
583C4×C61—41no—
584C4×C61—41no—
585C4×C61—41no—
586Dic61—22no—
587Dic61—22no—
588Dic61—22no—
589Dic61—41no—
590Dic61—41no—
591Dic61—41no—
592C2×#388—611no—
593C2×#388—611no—
594C2×#385—611no—
595C2×C4×C4⋊C4—611no—
596C2×C4×C22⋊C4—611no—
597#1437—611no—
598#1437—611no—
599#1436—611no—
600#1436—611no—
601#1436—611no—
602#1436—611no—
603C4⋊#95—611no—
604#1434—611no—
605C22⋊#95—611no—
606C4×#95—611no—
607C2×C61—42no—
608C2×C61C42×D411yescharacteristic
609C2×C61#227411yescharacteristic
610C2×C61#227511yescharacteristic
611C2×C61#232111yescharacteristic
612C2×C61#232311yescharacteristic
613C2×C61#233211yescharacteristic
614C2×C61#233511yescharacteristic
615D61—42no—
616D61#232211yescharacteristic
617D61#232411yescharacteristic
618D61#232511yescharacteristic
619D61#232611yescharacteristic
620D61#233411yescharacteristic
621D61#233411yescharacteristic
622D61#233511yescharacteristic
623D61#233711yescharacteristic
624C24×C4—611no—
625C22×C4⋊C4—611no—
626C22×C4⋊C4—611no—
627C22×C4⋊C4—611no—
628C22×C4⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C42—611no—
636C22×C42—611no—
637C22×C42—611no—
638C22×C42—611no—
639C22×C42—611no—
640C22×C42—611no—
641#388—618no—
642#388—618no—
643#385—611no—
644#385—611no—
645#385—611no—
646#385—611no—
647#385—611no—
648#385—611no—
649#385—611no—
650#385#692311yescharacteristic, complemented
651C4×C4⋊C4—1224no—
652C4×C22⋊C4—1224no—
653C2×#95—611no—
654C2×#95—611no—
655C2×#95—611no—
656C2×#95—611no—
657C2×#95—611no—
658C2×#95—611no—
659C2×#95—611no—
660C2×#95—611no—
661C2×#95—611no—
662C2×#95—611no—
663C2×#95—611no—
664C2×#95—611no—
665C2×#95—611no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C61#1378911yescharacteristic, complemented, Sylow
672C25—611no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—611no—
682C23×C4—611no—
683C23×C4—611no—
684C23×C4—611no—
685C23×C4—611no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—611no—
689C23×C4—611no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—2441no—
693C23×C4—2441no—
694C23×C4—2441no—
695C23×C4—2441no—
696C23×C4C2×#692311yescharacteristic
697C2×C4⋊C4—614no—
698C2×C4⋊C4—611no—
699C2×C4⋊C4—611no—
700C2×C4⋊C4—611no—
701C2×C4⋊C4—614no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—1222no—
706C2×C4⋊C4—1222no—
707C2×C4⋊C4—1222no—
708C2×C4⋊C4—1222no—
709C2×C4⋊C4—2441no—
710C2×C4⋊C4—2441no—
711C2×C4⋊C4—2441no—
712C2×C4⋊C4—2441no—
713C2×C4⋊C4C2×#692311yescharacteristic
714C2×C4⋊C4C2×#692311yescharacteristic
715C2×C22⋊C4—611no—
716C2×C22⋊C4—611no—
717C2×C22⋊C4—611no—
718C2×C22⋊C4—614no—
719C2×C22⋊C4—614no—
720C2×C22⋊C4—614no—
721C2×C22⋊C4—614no—
722C2×C22⋊C4—614no—
723C2×C22⋊C4—614no—
724C2×C22⋊C4—611no—
725C2×C22⋊C4—611no—
726C2×C22⋊C4—611no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—2441no—
732C2×C22⋊C4—2441no—
733C2×C22⋊C4—2441no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4—2441no—
736C2×C22⋊C4—2441no—
737C2×C22⋊C4C2×#692311yescharacteristic
738C2×C22⋊C4C2×#692311yescharacteristic
739C2×C42—614no—
740C2×C42—614no—
741C2×C42—614no—
742C2×C42—1222no—
743C2×C42—1222no—
744C2×C42—1222no—
745C2×C42—1222no—
746C2×C42—1222no—
747C2×C42—2441no—
748C2×C42—2441no—
749C2×C42—2441no—
750C2×C42—2441no—
751C2×C42—2441no—
752C2×C42—2441no—
753C2×C42—2441no—
754C2×C42—2441no—
755C2×C42—2441no—
756C2×C42—2441no—
757#95—614no—
758#95—614no—
759#95—614no—
760#95—614no—
761#95—611no—
762#95—611no—
763#95—611no—
764#95—611no—
765#95—611no—
766#95—611no—
767#95—1222no—
768#95—1222no—
769#95—1222no—
770#95—1222no—
771#95—1222no—
772#95—1222no—
773#95—2441no—
774#95—2441no—
775#95—2441no—
776#95—2441no—
777#95—2441no—
778#95—2441no—
779#95C2×#692311yescharacteristic
780#95C2×#692311yescharacteristic
781C24—611no—
782C24—612no—
783C24—612no—
784C24—611no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—1221no—
790C24—1221no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24C22×#692311yescharacteristic
798C22×C4—22no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—612no—
802C22×C4—612no—
803C22×C4—612no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—612no—
816C22×C4—612no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—612no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—1222no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1222no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1222no—
902C22×C4—2441no—
903C22×C4—2441no—
904C22×C4—2441no—
905C22×C4—2441no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4—2444no—
909C22×C4—2444no—
910C22×C4—2441no—
911C22×C4—2441no—
912C22×C4C22×#692311yescharacteristic
913C22×C4C22×#692311yescharacteristic
914C22×C4C22×#692311yescharacteristic
915C22×C4C22×#692311yescharacteristic
916C22×C4C22×#692311yescharacteristic
917C22×C4C22×#692311yescharacteristic
918C4⋊C4—22no—
919C4⋊C4—41no—
920C4⋊C4—1222no—
921C4⋊C4—1222no—
922C4⋊C4—1228no—
923C4⋊C4—1222no—
924C4⋊C4—2441no—
925C4⋊C4—2441no—
926C4⋊C4—2441no—
927C4⋊C4—2444no—
928C22⋊C4—41no—
929C22⋊C4—614no—
930C22⋊C4—614no—
931C22⋊C4—614no—
932C22⋊C4—1228no—
933C22⋊C4—1228no—
934C22⋊C4—2441no—
935C22⋊C4—2441no—
936C22⋊C4—2441no—
937C22⋊C4—2444no—
938C22⋊C4—2444no—
939C22⋊C4C4×#692314yescomplemented
940C42—1228no—
941C42—2444no—
942C42—2444no—
943C42—2444no—
944C42—2444no—
945C42—2444no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—611no—
953C23—611no—
954C23—611no—
955C23—611no—
956C23—611no—
957C23—611no—
958C23—611no—
959C23—611no—
960C23—611no—
961C23—611no—
962C23—611no—
963C23—611no—
964C23—611no—
965C23—611no—
966C23—612no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1221no—
980C23—1221no—
981C23—1221no—
982C23—1221no—
983C23—1221no—
984C23—1221no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23—2441no—
991C23—2441no—
992C23—2441no—
993C23—2441no—
994C23—2441no—
995C23—2441no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23C2×C4×#692312yes—
1002C23C23×#692311yescharacteristic
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—44no—
1019C2×C4—614no—
1020C2×C4—614no—
1021C2×C4—612no—
1022C2×C4—612no—
1023C2×C4—612no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1221no—
1049C2×C4—1221no—
1050C2×C4—1221no—
1051C2×C4—1221no—
1052C2×C4—1221no—
1053C2×C4—1221no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—1222no—
1067C2×C4—1222no—
1068C2×C4—1222no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1221no—
1073C2×C4—1221no—
1074C2×C4—1221no—
1075C2×C4—1221no—
1076C2×C4—1221no—
1077C2×C4—1221no—
1078C2×C4—1221no—
1079C2×C4—1221no—
1080C2×C4—1221no—
1081C2×C4—2444no—
1082C2×C4—2444no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2444no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C2×C4—2441no—
1111C2×C4—2441no—
1112C2×C4—2441no—
1113C2×C4—2441no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4C2×C4×#692312yes—
1121C2×C4C2×C4×#692312yes—
1122C2×C4D4×#692312yes—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—611no—
1131C22—611no—
1132C22—611no—
1133C22—611no—
1134C22—611no—
1135C22—611no—
1136C22—611no—
1137C22—611no—
1138C22—611no—
1139C22—611no—
1140C22—611no—
1141C22—611no—
1142C22—611no—
1143C22—611no—
1144C22—611no—
1145C22—611no—
1146C22—611no—
1147C22—611no—
1148C22—611no—
1149C22—611no—
1150C22—611no—
1151C22—611no—
1152C22—611no—
1153C22—611no—
1154C22—611no—
1155C22—611no—
1156C22—611no—
1157C22—611no—
1158C22—1222no—
1159C22—1222no—
1160C22—1222no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22—2442no—
1168C22—2442no—
1169C22—2441no—
1170C22—2441no—
1171C22—2441no—
1172C22—2441no—
1173C22C22×C4×#692311yescharacteristic
1174C22C2×D4×#692311yescharacteristic
1175C22#41×#692311yescharacteristic
1176C22#1684082911yescharacteristic
1177C22#1684082911yescharacteristic
1178C22#1684083011yescharacteristic
1179C22#1684083111yescharacteristic
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—1224no—
1187C4—1224no—
1188C4—1222no—
1189C4—1222no—
1190C4—1222no—
1191C4—2442no—
1192C4—2442no—
1193C4—2442no—
1194C4—2442no—
1195C4—2442no—
1196C4—2442no—
1197C4—2441no—
1198C4—2441no—
1199C4—2441no—
1200C2—42no—
1201C2—611no—
1202C2—611no—
1203C2—611no—
1204C2—611no—
1205C2—611no—
1206C2—611no—
1207C2—611no—
1208C2—611no—
1209C2—2442no—
1210C2C4×D4×#692311yescharacteristic
1211C2#2146225711yescharacteristic
1212C2#2146225811yescharacteristic
1213C2#2146230411yescharacteristic
1214C2#2146230611yescharacteristic
1215C2#2146231511yescharacteristic
1216C2#2146231811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#385C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#385#6923
hypocenterC61#13789
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×#6923C2semidirect
7. #21460999C2semidirect
8. #21460999C2semidirect
9. #21460998C2semidirect
10. #21460998C2semidirect
11. #21460996C2semidirect
12. #21460994C2semidirect
14. #95×#6923C2semidirect
28. #16840712C4semidirect
29. #16840712C4semidirect
53. #16839637C4semidirect
54. #16839636C4semidirect
55. #16839636C4semidirect
56. #16839635C4semidirect
57. #16839634C4semidirect
58. #16839633C4semidirect
59. #16839633C4semidirect
62. C61×#385C4semidirect
75. C2×C4⋊#6923C2×C4semidirect
76. C2×C4⋊#6923C2×C4semidirect
104. C2×C4×#6923C2×C4semidirect
105. C2×C4×#6923C2×C4semidirect
119. (C2×#6923)⋊C4C2×C4semidirect
120. (C2×#6923)⋊C4C2×C4semidirect
121. (C2×#6923)⋊C4C2×C4semidirect
122. (C2×#6923)⋊C4C2×C4semidirect
324. C22⋊C4×C61C42semidirect
326. C22⋊Dic61C42semidirect
329. #11758198C42semidirect
330. #11758198C42semidirect
650. #385#6923semidirect
671. C61#13789semidirect
939. C22⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×C4⋊C4×#69232
C2×C4×C22⋊#69232
#214610002
#214609992
#214609982
#214609962
#214609942
#214609932
#95×#69232
#385×D612
#1378961