Finite Group Databasebeta

← #30609415

Subgroups — #30609415

Order 15616.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×#16840709C211yesmaximal, characteristic
3#21461008C211yesmaximal, characteristic, complemented
4#21461004C211yesmaximal, characteristic, complemented
5#21461004C211yesmaximal, characteristic, complemented
6#21461004C211yesmaximal, characteristic, complemented
7#21461003C211yesmaximal, characteristic
8#21461003C211yesmaximal, characteristic
9#21460998C211yesmaximal, characteristic, complemented
10#21460997C211yesmaximal, characteristic, complemented
11#21460996C211yesmaximal, characteristic, complemented
12#21460995C211yesmaximal, characteristic, complemented
13#21460992C211yesmaximal, characteristic
14#21460992C211yesmaximal, characteristic
15C2×#126×D61C211yesmaximal, characteristic
16C24×#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24#16840712—24no—
25#16840709—24no—
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×#14519772C411yescharacteristic, complemented
47C2×#14519772C411yescharacteristic, complemented
48C2×#14519772C411yescharacteristic, complemented
49C2×#14519771C411yescharacteristic, complemented
50C2×#14519770C411yescharacteristic, complemented
51C2×#14519770C411yescharacteristic, complemented
52C2×#14519770C411yescharacteristic, complemented
53#126×D61—24no—
54#126×D61—24no—
55C2×C4⋊C4×D61C2211yescharacteristic
56C2×C4⋊C4×D61C2211yescharacteristic
57C2×C4⋊C4×D61C2211yescharacteristic
58C2×C22⋊C4×D61C2211yescharacteristic
59C2×C22⋊C4×D61C2211yescharacteristic
60C2×C22⋊C4×D61C2211yescharacteristic
61C2×C42×D61C2211yescharacteristic
62C2×#126×C61C411yescharacteristic, complemented
63C23×#6923—22no—
64C23×#6923—22no—
65C23×#6923—22no—
66C23×#6923—41no—
67C23×#6923—41no—
68C23×#6923—41no—
69C23×#6923—41no—
70C23×#6923C2311yescharacteristic
71C23×#6923C2311yescharacteristic
72C23×#6923C2311yescharacteristic
73C23×#6923C2311yescharacteristic
74C23×#6923C2311yescharacteristic
75C23×#6923C2311yescharacteristic
76C23×#6923C2311yescharacteristic
77C23×#6923C2311yescharacteristic
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—41no—
85C2×C4⋊#6923—41no—
86C2×C4⋊#6923—41no—
87C2×C22⋊#6923—22no—
88C2×C22⋊#6923—22no—
89C2×C22⋊#6923—22no—
90C2×C22⋊#6923—22no—
91C2×C22⋊#6923—22no—
92C2×C22⋊#6923—41no—
93C2×C22⋊#6923—41no—
94C2×C22⋊#6923—41no—
95C2×C22⋊#6923—41no—
96C2×C4×#6923—22no—
97C2×C4×#6923—22no—
98C2×C4×#6923—41no—
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—41no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4—41no—
110(C2×#6923)⋊C4—41no—
111(C2×#6923)⋊C4—41no—
112(C2×#6923)⋊C4—41no—
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—
119C24×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126#14519772—24no—
127#14519772—24no—
128#14519772—24no—
129#14519771—24no—
130#14519770—24no—
131#14519770—24no—
132#14519770—24no—
133C2×C4⋊Dic61C2×C411yescharacteristic, complemented
134C2×C4⋊Dic61C2×C411yescharacteristic, complemented
135C2×C4⋊Dic61C2×C411yescharacteristic, complemented
136C2×#11758196C2×C411yescharacteristic, complemented
137C2×#11758196C2×C411yescharacteristic, complemented
138C2×#11758196C2×C411yescharacteristic, complemented
139C2×#11758196C2×C411yescharacteristic, complemented
140C2×#11758196C2×C411yescharacteristic, complemented
141C2×#11758196C2×C411yescharacteristic, complemented
142C4⋊C4×D61—22no—
143C4⋊C4×D61—22no—
144C4⋊C4×D61—22no—
145C4⋊C4×D61—22no—
146C4⋊C4×D61—22no—
147C4⋊C4×D61—22no—
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×C22⋊Dic61C2×C411yescharacteristic
150C2×C22⋊Dic61C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C22⋊C4×D61—22no—
158C22⋊C4×D61—22no—
159C22⋊C4×D61—22no—
160C22⋊C4×D61—22no—
161C22⋊C4×D61D414yes—
162C22⋊C4×D61D414yes—
163C2×C4×Dic61C2×C411yescharacteristic, complemented
164C2×C4×Dic61C2×C411yescharacteristic, complemented
165C2×C4×Dic61C2×C411yescharacteristic, complemented
166C42×D61—22no—
167C42×D61—22no—
168#126×C61—24no—
169C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
170C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
171C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
172C2×C22⋊C4×C61C2×C411yescharacteristic
173C2×C22⋊C4×C61C2×C411yescharacteristic
174C2×C22⋊C4×C61C2×C411yescharacteristic
175C2×C42×C61C2×C411yescharacteristic, complemented
176C24×C61C22×C411yescharacteristic
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×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61C22×C411yescharacteristic
190C23×D61C2×D412yes—
191C23×D61C2×D412yes—
192C23×D61C2411yescharacteristic
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×#6923—21no—
234C22×#6923—21no—
235C22×#6923—21no—
236C22×#6923—21no—
237C22×#6923—21no—
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—21no—
245C22×#6923—44no—
246C22×#6923—44no—
247C22×#6923—44no—
248C22×#6923—44no—
249C22×#6923—44no—
250C22×#6923—44no—
251C22×#6923—44no—
252C22×#6923#4112yes—
253C22×#6923#4112yes—
254C22×#6923#4112yes—
255C22×#6923#4112yes—
256C22×C4×C61C22×C411yescharacteristic
257C22×C4×C61C22×C411yescharacteristic
258C22×C4×C61C22×C411yescharacteristic
259C22×C4×C61C22×C411yescharacteristic
260C22×C4×C61C22×C411yescharacteristic
261C22×C4×C61C22×C411yescharacteristic
262C22×Dic61C22×C411yescharacteristic
263C22×Dic61C22×C411yescharacteristic
264C22×Dic61C22×C411yescharacteristic
265C22×Dic61C22×C411yescharacteristic
266C22×Dic61C22×C411yescharacteristic
267C22×Dic61C22×C411yescharacteristic
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—21no—
294C2×C4×D61—21no—
295C2×C4×D61—21no—
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—21no—
300C2×C4×D61C2×D412yes—
301C2×C4×D61C2×D412yes—
302C2×C4×D61C2×D412yes—
303C2×C4×D61C2×D412yes—
304C22⋊#6923—44no—
305C22⋊#6923—44no—
306C22⋊#6923—44no—
307C4⋊#6923—44no—
308C4⋊#6923—44no—
309C4⋊#6923—44no—
310C4×#6923—44no—
311C4⋊C4×C61—22no—
312C4⋊C4×C61—22no—
313C4⋊C4×C61—22no—
314C22⋊C4×C61—22no—
315C22⋊C4×C61—22no—
316C22⋊C4×C61C22⋊C414yes—
317C42×C61—22no—
318C22⋊Dic61—22no—
319C22⋊Dic61—22no—
320C22⋊Dic61C22⋊C414yes—
321#11758198—22no—
322#11758198—22no—
323#11758198—22no—
324#11758198—22no—
325#11758198C22⋊C414yes—
326#11758198C22⋊C414yes—
327C4⋊Dic61—22no—
328C4⋊Dic61—22no—
329C4⋊Dic61—22no—
330#11758196—22no—
331#11758196—22no—
332#11758196—22no—
333#11758196—22no—
334#11758196—22no—
335#11758196—22no—
336C4×Dic61—22no—
337C4×Dic61—22no—
338C4×Dic61—22no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61C2×C22⋊C412yes—
346C23×C61C23×C411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
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—22no—
364C22×D61—22no—
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×D61—41no—
380C22×D61—41no—
381C22×D61C2×C22⋊C412yes—
382C22×D61C22×D411yescharacteristic
383C22×D61C22×D411yescharacteristic
384C22×D61C2×#4111yescharacteristic
385C22×D61C2×#4111yescharacteristic
386C22×D61C2×#4111yescharacteristic
387C22×D61C2×#4111yescharacteristic
388C22×D61H(5,𝔽2)11yescharacteristic
389C22×D61H(5,𝔽2)11yescharacteristic
390C22×D61H(5,𝔽2)11yescharacteristic
391C22×D61H(5,𝔽2)11yescharacteristic
392C22×D612−1+411yescharacteristic
393C22×D612−1+411yescharacteristic
394C22×D612−1+411yescharacteristic
395C22×D612−1+411yescharacteristic
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—416no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
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×#6923—41no—
449C2×#6923—41no—
450C2×#6923—41no—
451C2×#6923—41no—
452C2×#6923—41no—
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—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61C2×C22⋊C412yes—
470C2×C4×C61C2×C22⋊C412yes—
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—21no—
485C2×Dic61—21no—
486C2×Dic61—21no—
487C2×Dic61C2×C22⋊C412yes—
488C2×Dic61C2×C22⋊C412yes—
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—41no—
498C4×D61—41no—
499C4×D61—41no—
500C4×D61—41no—
501C4×D61—41no—
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—
513#14475—611nomaximal, Sylow
514C22×C61—22no—
515C22×C61—22no—
516C22×C61—22no—
517C22×C61—41no—
518C22×C61—41no—
519C22×C61—41no—
520C22×C61—41no—
521C22×C61C22×C22⋊C411yescharacteristic
522C22×C61C4×#4111yescharacteristic
523C22×C61C4×#4111yescharacteristic
524C22×C61#52011yescharacteristic
525C22×C61#52011yescharacteristic
526C22×C61#52011yescharacteristic
527C22×C61#52011yescharacteristic
528C2×D61—22no—
529C2×D61—22no—
530C2×D61—22no—
531C2×D61—41no—
532C2×D61—41no—
533C2×D61—41no—
534C2×D61—41no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61#53511yescharacteristic
544C2×D61#53611yescharacteristic
545C2×D61#53711yescharacteristic
546C2×D61#53711yescharacteristic
547C2×D61#53811yescharacteristic
548C2×D61#53811yescharacteristic
549C2×D61#53911yescharacteristic
550C2×D61#53911yescharacteristic
551C2×D61#54111yescharacteristic
552C2×D61#54111yescharacteristic
553C2×D61#54211yescharacteristic
554C2×D61#54211yescharacteristic
555C2×D61#54611yescharacteristic
556C2×D61#54611yescharacteristic
557C2×D61#54611yescharacteristic
558C2×D61#54611yescharacteristic
559C2×D61#54711yescharacteristic
560C2×D61#54711yescharacteristic
561C2×D61#54711yescharacteristic
562C2×D61#54711yescharacteristic
563C2×D61#55111yescharacteristic
564C2×D61#55211yescharacteristic
565C2×D61#55311yescharacteristic
566C2×D61#55611yescharacteristic
567C2×D61#56011yescharacteristic
568C2×D61#56311yescharacteristic
569C2×D61#56311yescharacteristic
570C2×D61#56311yescharacteristic
571#6923—42no—
572#6923—42no—
573#6923—42no—
574#6923—42no—
575#6923—81no—
576#6923—81no—
577#6923—81no—
578#6923—81no—
579C4×C61—22no—
580C4×C61—22no—
581C4×C61—41no—
582C4×C61—41no—
583C4×C61—41no—
584C4×C61—41no—
585Dic61—22no—
586Dic61—22no—
587Dic61—41no—
588Dic61—41no—
589Dic61—41no—
590Dic61—41no—
591C22×#126—611no—
592C2×#388—611no—
593C2×#385—611no—
594#1445—611no—
595#1441—611no—
596#1441—611no—
597#1441—611no—
598#1440—611no—
599#1440—611no—
600#1436—611no—
601C4⋊#95—611no—
602C4⋊#95—611no—
603#1434—611no—
604C22⋊#95—611no—
605C22⋊#95—611no—
606C2×C61—42no—
607C2×C61#231111yescharacteristic
608C2×C61#233411yescharacteristic
609C2×C61#233411yescharacteristic
610C2×C61#233911yescharacteristic
611C2×C61#233911yescharacteristic
612C2×C61#237311yescharacteristic
613C2×C61#238311yescharacteristic
614D61—42no—
615D61#268511yescharacteristic
616D61#268911yescharacteristic
617D61#269111yescharacteristic
618D61#269511yescharacteristic
619D61#269811yescharacteristic
620D61#271511yescharacteristic
621D61#271811yescharacteristic
622D61#272211yescharacteristic
623C24×C4—611no—
624C2×#126—611no—
625C2×#126—611no—
626C2×#126—611no—
627C2×#126—611no—
628C2×#126—611no—
629C2×#126—611no—
630C2×#126—611no—
631C2×#126—1224no—
632C2×#126—1224no—
633C2×#126#692311yescharacteristic, complemented
634C22×C4⋊C4—611no—
635C22×C4⋊C4—611no—
636C22×C4⋊C4—611no—
637C22×C4⋊C4—611no—
638C22×C4⋊C4—611no—
639C22×C4⋊C4—611no—
640C22×C22⋊C4—611no—
641C22×C22⋊C4—611no—
642C22×C22⋊C4—611no—
643C22×C22⋊C4—611no—
644C22×C22⋊C4—611no—
645C22×C22⋊C4—611no—
646C22×C42—611no—
647C22×C42—611no—
648#388—1224no—
649#385—1224no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
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—
670C61#1447511yescharacteristic, complemented, Sylow
671C25—611no—
672C23×C4—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—1222no—
687C23×C4—1222no—
688C23×C4—1222no—
689C23×C4—2441no—
690C23×C4—2441no—
691C23×C4—2441no—
692C23×C4—2441no—
693#126—24no—
694#126—1224no—
695#126—1224no—
696#126—1224no—
697#126—1224no—
698#126—1224no—
699#126—1224no—
700#126—1224no—
701C2×C4⋊C4—611no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—1222no—
711C2×C4⋊C4—1222no—
712C2×C4⋊C4—1222no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C4⋊C4—1222no—
716C2×C4⋊C4—1222no—
717C2×C4⋊C4—1222no—
718C2×C4⋊C4—1222no—
719C2×C4⋊C4—1222no—
720C2×C4⋊C4—1222no—
721C2×C4⋊C4—1222no—
722C2×C4⋊C4—2441no—
723C2×C4⋊C4—2441no—
724C2×C4⋊C4—2441no—
725C2×C4⋊C4C2×#692311yescharacteristic, complemented
726C2×C4⋊C4C2×#692311yescharacteristic, complemented
727C2×C4⋊C4C2×#692311yescharacteristic, complemented
728C2×C22⋊C4—611no—
729C2×C22⋊C4—611no—
730C2×C22⋊C4—611no—
731C2×C22⋊C4—614no—
732C2×C22⋊C4—614no—
733C2×C22⋊C4—611no—
734C2×C22⋊C4—611no—
735C2×C22⋊C4—611no—
736C2×C22⋊C4—611no—
737C2×C22⋊C4—611no—
738C2×C22⋊C4—611no—
739C2×C22⋊C4—1222no—
740C2×C22⋊C4—1222no—
741C2×C22⋊C4—1222no—
742C2×C22⋊C4—1222no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C22⋊C4—1222no—
747C2×C22⋊C4—1222no—
748C2×C22⋊C4—2441no—
749C2×C22⋊C4—2441no—
750C2×C22⋊C4—2441no—
751C2×C22⋊C4—2441no—
752C2×C22⋊C4C2×#692311yescharacteristic
753C2×C22⋊C4C2×#692311yescharacteristic
754C2×C22⋊C4C2×#692311yescharacteristic
755C2×C42—611no—
756C2×C42—611no—
757C2×C42—611no—
758C2×C42—1222no—
759C2×C42—1222no—
760C2×C42—1222no—
761C2×C42—1222no—
762C2×C42—2441no—
763C2×C42C2×#692311yescharacteristic, complemented
764#95—1222no—
765#95—1222no—
766#95—1222no—
767#95—1222no—
768#95—1222no—
769#95—1222no—
770#95—1222no—
771#95—1222no—
772#95—2441no—
773#95—2441no—
774#95—2441no—
775#95—2441no—
776#95—2441no—
777#95—2441no—
778#95—2441no—
779#95—2441no—
780#95—2441no—
781#95—2441no—
782#95—2441no—
783#95—2441no—
784C24—611no—
785C24—612no—
786C24—612no—
787C24—611no—
788C24—1221no—
789C24—1221no—
790C24—1221no—
791C24—1221no—
792C24—1221no—
793C24—1221no—
794C24—1221no—
795C24—1221no—
796C24—1221no—
797C24—1221no—
798C24—1221no—
799C24—1221no—
800C24C22×#692311yescharacteristic
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—612no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
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—1221no—
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—2444no—
900C22×C4—2444no—
901C22×C4—2444no—
902C22×C4—2444no—
903C22×C4—2444no—
904C22×C4—2444no—
905C22×C4—2444no—
906C22×C4C22×#692311yescharacteristic
907C22×C4C22×#692311yescharacteristic
908C22×C4C22×#692311yescharacteristic
909C22×C4C22×#692311yescharacteristic
910C22×C4C22×#692311yescharacteristic
911C22×C4C22×#692311yescharacteristic
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—1222no—
916C4⋊C4—1222no—
917C4⋊C4—1222no—
918C4⋊C4—1222no—
919C4⋊C4—1222no—
920C4⋊C4—1222no—
921C4⋊C4—1222no—
922C4⋊C4—1222no—
923C4⋊C4—1222no—
924C4⋊C4—2444no—
925C4⋊C4—2444no—
926C4⋊C4—2444no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—614no—
930C22⋊C4—614no—
931C22⋊C4—614no—
932C22⋊C4—1222no—
933C22⋊C4—1222no—
934C22⋊C4—1222no—
935C22⋊C4—1222no—
936C22⋊C4—1222no—
937C22⋊C4—1222no—
938C22⋊C4—2444no—
939C22⋊C4—2444no—
940C22⋊C4—2444no—
941C22⋊C4C22⋊#692314yes—
942C42—22no—
943C42—1222no—
944C42—1222no—
945C42—1222no—
946C42—2444no—
947C23—21no—
948C23—21no—
949C23—21no—
950C23—21no—
951C23—21no—
952C23—21no—
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—611no—
967C23—612no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1222no—
980C23—1221no—
981C23—1221no—
982C23—1221no—
983C23—1221no—
984C23—1221no—
985C23—1221no—
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—
1001C23—2441no—
1002C23C2×C22⋊#692312yes—
1003C23C23×#692311yescharacteristic
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—21no—
1019C2×C4—21no—
1020C2×C4—612no—
1021C2×C4—612no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1221no—
1031C2×C4—1221no—
1032C2×C4—1221no—
1033C2×C4—1221no—
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—1221no—
1047C2×C4—1221no—
1048C2×C4—1221no—
1049C2×C4—1221no—
1050C2×C4—1221no—
1051C2×C4—1221no—
1052C2×C4—1221no—
1053C2×C4—1221no—
1054C2×C4—1221no—
1055C2×C4—1221no—
1056C2×C4—1221no—
1057C2×C4—1221no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
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—2441no—
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—24416no—
1119C2×C4C2×C22⋊#692312yes—
1120C2×C4C2×C22⋊#692312yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—611no—
1129C22—611no—
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—1222no—
1157C22—1222no—
1158C22—1222no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22—2442no—
1165C22—2442no—
1166C22—2442no—
1167C22—2441no—
1168C22—2441no—
1169C22—2441no—
1170C22—2441no—
1171C22C22×C22⋊#692311yescharacteristic
1172C22#41×#692311yescharacteristic
1173C22#41×#692311yescharacteristic
1174C22#1684083111yescharacteristic
1175C22#1684083111yescharacteristic
1176C22#1684083111yescharacteristic
1177C22#1684083111yescharacteristic
1178C4—22no—
1179C4—22no—
1180C4—41no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—1222no—
1185C4—1222no—
1186C4—4881no—
1187C4—4881no—
1188C4—4881no—
1189C4—4881no—
1190C4—2442no—
1191C4—2442no—
1192C4—2442no—
1193C4—2442no—
1194C4—2441no—
1195C4—2441no—
1196C4—2441no—
1197C4—2441no—
1198C2—42no—
1199C2—611no—
1200C2—611no—
1201C2—611no—
1202C2—611no—
1203C2—611no—
1204C2—611no—
1205C2—611no—
1206C2—611no—
1207C2—2442no—
1208C2#2146229411yescharacteristic
1209C2#2146231711yescharacteristic
1210C2#2146231711yescharacteristic
1211C2#2146232211yescharacteristic
1212C2#2146232211yescharacteristic
1213C2#2146235611yescharacteristic
1214C2#2146236611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#126×C61C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC2×#126#6923
hypocenterC61#14475
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
3. #21461008C2semidirect
4. #21461004C2semidirect
5. #21461004C2semidirect
6. #21461004C2semidirect
9. #21460998C2semidirect
10. #21460997C2semidirect
11. #21460996C2semidirect
12. #21460995C2semidirect
46. C2×#14519772C4semidirect
47. C2×#14519772C4semidirect
48. C2×#14519772C4semidirect
49. C2×#14519771C4semidirect
50. C2×#14519770C4semidirect
51. C2×#14519770C4semidirect
52. C2×#14519770C4semidirect
62. C2×#126×C61C4semidirect
133. C2×C4⋊Dic61C2×C4semidirect
134. C2×C4⋊Dic61C2×C4semidirect
135. C2×C4⋊Dic61C2×C4semidirect
136. C2×#11758196C2×C4semidirect
137. C2×#11758196C2×C4semidirect
138. C2×#11758196C2×C4semidirect
139. C2×#11758196C2×C4semidirect
140. C2×#11758196C2×C4semidirect
141. C2×#11758196C2×C4semidirect
163. C2×C4×Dic61C2×C4semidirect
164. C2×C4×Dic61C2×C4semidirect
165. C2×C4×Dic61C2×C4semidirect
169. C2×C4⋊C4×C61C2×C4semidirect
170. C2×C4⋊C4×C61C2×C4semidirect
171. C2×C4⋊C4×C61C2×C4semidirect
175. C2×C42×C61C2×C4semidirect
633. C2×#126#6923semidirect
670. C61#14475semidirect
725. C2×C4⋊C4C2×#6923semidirect
726. C2×C4⋊C4C2×#6923semidirect
727. C2×C4⋊C4C2×#6923semidirect
763. C2×C42C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×#168407092
#214610082
#214610042
#214610032
#214609982
#214609972
#214609962
#214609952
#214609922
C2×#126×D612
#1447561