Finite Group Databasebeta

← #16831483

Subgroups — #16831483

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271817C211yesmaximal, characteristic, complemented
2#14271522C211yesmaximal, characteristic, complemented
3#14271496C211yesmaximal, characteristic, complemented
4#14271474C211yesmaximal, characteristic, complemented
5#14271458C211yesmaximal, characteristic, complemented
6#14271411C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271308C211yesmaximal, characteristic, complemented
10#14271302C211yesmaximal, characteristic, complemented
11#14271261C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271164C211yesmaximal, characteristic, complemented
14C2×#11745183C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×#90807—21no—
19C29×#124—21no—
20C29×#124C2211yescharacteristic
21C29×C22⋊Q8—21no—
22C29×C22⋊Q8C2211yescharacteristic
23C29×#121—21no—
24C29×#121C2211yescharacteristic
25C4×Q8×C29C2211yescharacteristic
26C4×D4×C29—21no—
27C4×D4×C29C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29C2×#90784C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745292C2211yescharacteristic
33C2×C4⋊Dic29C2211yescharacteristic
34C2×C4⋊Dic29C2211yescharacteristic
35C2×#90777C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745259—21no—
38#11745248—21no—
39#11745248—21no—
40C4×D116C2211yescharacteristic
41#11745231C2211yescharacteristic
42#11745183C2211yescharacteristic
43#11745183C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745180C2211yescharacteristic
51C22⋊#6597C2211yescharacteristic
52C22⋊#6597C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745155C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58#11745151C2211yescharacteristic
59#41×C29—22no—
60#41×C29—41no—
61C2×Q8×C29—21no—
62C2×Q8×C29—22no—
63C2×Q8×C29—41no—
64C2×Q8×C29C2311yescharacteristic
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29D411yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C22×C4×C29—21no—
71C22×C4×C29—21no—
72C22×C4×C29C2311yescharacteristic
73C22×C4×C29C2311yescharacteristic
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C22×Dic29—21no—
77C22×Dic29—21no—
78#90807—44no—
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×Dic58—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29D411yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C22⋊C4×C29—21no—
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊C4×C29D411yescharacteristic
91C22⋊C4×C29D411yescharacteristic
92C42×C29—21no—
93C42×C29C2311yescharacteristic
94#90784—22no—
95#90784—41no—
96#90782—41no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100C4⋊Dic29—21no—
101C4⋊Dic29—21no—
102C4⋊Dic29—21no—
103C4⋊Dic29C2311yescharacteristic
104C4⋊Dic29C2311yescharacteristic
105C4⋊Dic29C2311yescharacteristic
106#90777—41no—
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C2×#6597C2311yescharacteristic
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C23×C29C2×D411yescharacteristic
115C22×D29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—21no—
119Q8×C29—42no—
120Q8×C29#4112yescomplemented
121D4×C29—22no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—42no—
125D4×C29—42no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—42no—
134C2×C4×C29—42no—
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2411yescharacteristic
140C22⋊D29—42no—
141C22⋊D29—42no—
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29—21no—
145C2×Dic29—42no—
146C2×Dic29—42no—
147D116—21no—
148D116—21no—
149C4×D29—42no—
150Dic58—42no—
151#6597—21no—
152#6597—21no—
153#6597—21no—
154#6597—21no—
155#3308—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29AGL(1,ℤ/8)12yes—
165C22×C29C22×D411yescharacteristic
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—22no—
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29C2×#4111yescharacteristic
177C4×C29H(5,𝔽2)11yescharacteristic
178Dic29—41no—
179Dic29—41no—
180Dic29—41no—
181#548D2911yescharacteristic, complemented
182#547—291no—
183#489—291no—
184#484—291no—
185#480—291no—
186#477—291no—
187#468—291no—
188#466—291no—
189#463—291no—
190#449—291no—
191#448—291no—
192#440—291no—
193#435—291no—
194#417—291no—
195C2×#103—291no—
196C2×C29—22no—
197C2×C29—41no—
198C2×C29—81no—
199C2×C29#54611yescharacteristic
200C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
201C2×C29#57811yescharacteristic
202D29—81no—
203C2×#41—581no—
204C2×#41C2×D2911yescharacteristic
205C22×Q8C2×D2911yescharacteristic
206C2×SD16—291no—
207C2×SD16—291no—
208C2×D8—291no—
209C2×M16—291no—
210C22×C8—291no—
211C4⋊Q8—291no—
212#124—21no—
213#124C2×D2911yescharacteristic
214#123—581no—
215#123—581no—
216C22⋊Q8—21no—
217C22⋊Q8—581no—
218C22⋊Q8C2×D2911yescharacteristic
219#121—21no—
220#121—291no—
221#121—291no—
222#121C2×D2911yescharacteristic
223C4×Q8C2×D2911yescharacteristic
224C4×D4—21no—
225C4×D4—291no—
226C4×D4C2×D2911yescharacteristic
227C2×C4⋊C4—291no—
228C2×C4⋊C4—291no—
229#107—291no—
230#107—291no—
231#107—291no—
232C4⋊C8—291no—
233#103—291no—
234#103—291no—
235#103—291no—
236#103—291no—
237#103—291no—
238#103—291no—
239#102—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243C22⋊C8—291no—
244C22⋊C8—291no—
245#97—291no—
246C29#330811yescharacteristic, complemented, Sylow
247#41—22no—
248#41—41no—
249#41—1164no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—581no—
254C2×Q8C22×D2911yescharacteristic
255C2×Q8C22×D2911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4C22⋊D2911yescharacteristic
262C2×D4C22×D2911yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—581no—
266C22×C4—581no—
267C22×C4—581no—
268C22×C4C22×D2911yescharacteristic
269C22×C4C22×D2911yescharacteristic
270SD16—582no—
271SD16—1161no—
272D8—1161no—
273M16—1161no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—291no—
278C2×C8—1161no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—291no—
282C4⋊C4—291no—
283C4⋊C4—291no—
284C4⋊C4—581no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4C22⋊D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4C22⋊D2911yescharacteristic
297C22⋊C4C22⋊D2911yescharacteristic
298C42—21no—
299C42C22×D2911yescharacteristic
300C23—21no—
301C23—581no—
302C23C2×C22⋊D2911yescharacteristic
303C23C2×C22⋊D2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—1162no—
309Q8#9080712yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—581no—
316D4—581no—
317D4—1162no—
318D4—1162no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—1162no—
332C2×C4—1162no—
333C2×C4—1162no—
334C2×C4C2×C22⋊D2911yescharacteristic
335C2×C4C2×C22⋊D2911yescharacteristic
336C2×C4C2×C22⋊D2911yescharacteristic
337C2×C4C2×C22⋊D2911yescharacteristic
338C2×C4C23×D2911yescharacteristic
339C8—581no—
340C8—581no—
341C8—581no—
342C8—581no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1161no—
352C22—1161no—
353C22—1161no—
354C22#1174531112yes—
355C22C22×C22⋊D2911yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—1161no—
364C4—1161no—
365C4—1161no—
366C4C2×#9080711yescharacteristic
367C4#1174535911yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—2321no—
372C2#1427180711yescharacteristic
373C2C2×#1174531111yescharacteristic
374C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#548C2
socleC22×C29C22×D4
hypercenter#548D29
hypocenterC29#3308
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14271817C2semidirect
2. #14271522C2semidirect
3. #14271496C2semidirect
4. #14271474C2semidirect
5. #14271458C2semidirect
6. #14271411C2semidirect
7. #14271397C2semidirect
8. #14271375C2semidirect
9. #14271308C2semidirect
10. #14271302C2semidirect
11. #14271261C2semidirect
12. #14271235C2semidirect
13. #14271164C2semidirect
14. C2×#11745183C2semidirect
15. C29×#548C2semidirect
120. Q8×C29#41semidirect
181. #548D29semidirect
246. C29#3308semidirect
309. Q8#90807semidirect

Maximal subgroups

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

subgroupindex
#142718172
#142715222
#142714962
#142714742
#142714582
#142714112
#142713972
#142713752
#142713082
#142713022
#142712612
#142712352
#142711642
C2×#117451832
C29×#5482
#330829