Finite Group Databasebeta

← #16831480

Subgroups — #16831480

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#14271825C211yesmaximal, characteristic, complemented
2#14271816C211yesmaximal, characteristic, complemented
3#14271525C211yesmaximal, characteristic, complemented
4#14271500C211yesmaximal, characteristic, complemented
5#14271478C211yesmaximal, characteristic, complemented
6#14271410C211yesmaximal, characteristic, complemented
7#14271400C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271303C211yesmaximal, characteristic, complemented
11#14271261C211yesmaximal, characteristic, complemented
12#14271233C211yesmaximal, characteristic, complemented
13#14271163C211yesmaximal, characteristic, complemented
14#103×D29C211yesmaximal, characteristic, complemented
15C29×#477C211yesmaximal, characteristic, complemented
16C2×#90809—21no—
17C2×#90809C2211yescharacteristic
18C2×Q8×D29C2211yescharacteristic
19C29×C4⋊Q8C2211yescharacteristic
20C4×Q8×C29C2211yescharacteristic
21#11745308—21no—
22C2×#90784C2211yescharacteristic
23C2×D232C2211yescharacteristic
24C2×#90773C2211yescharacteristic
25C2×#90772C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic
27#11745259—21no—
28#11745259C2211yescharacteristic
29#11745257—21no—
30#11745257C2211yescharacteristic
31#11745257C2211yescharacteristic
32#11745257C2211yescharacteristic
33#11745256—21no—
34#11745256—21no—
35C4⋊C4×D29C2211yescharacteristic
36C4⋊C4×D29C2211yescharacteristic
37#11745237—21no—
38#11745237C2211yescharacteristic
39C4×D116—21no—
40C4×D116C2211yescharacteristic
41C4×D116C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×C4⋊C8C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×#103C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745158C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×Q8×C29—21no—
60C2×Q8×C29C2311yescharacteristic
61#90809—22no—
62#90809—41no—
63#90809—44no—
64Q8×D29—22no—
65Q8×D29—41no—
66C2×D116—21no—
67C2×D116—21no—
68C2×D116—21no—
69C2×D116—21no—
70C2×D116D411yescharacteristic
71C2×D116C2311yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×C4×D29C2311yescharacteristic
80C2×Dic58—21no—
81C2×Dic58C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C4⋊C4×C29—21no—
85C4⋊C4×C29—21no—
86C4⋊C4×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C42×C29—21no—
90C42×C29C2311yescharacteristic
91#90784—22no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781—21no—
99#90781D411yescharacteristic
100#90781D411yescharacteristic
101C4⋊Dic29—21no—
102C4⋊Dic29D411yescharacteristic
103C4⋊Dic29C2311yescharacteristic
104#90779—21no—
105#90779—21no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—41no—
109#90773—41no—
110#90772—41no—
111C8×D29—41no—
112C22×D29—21no—
113C22×D29—21no—
114C22×D29C2×D411yescharacteristic
115C22×D29C2×D411yescharacteristic
116Q8×C29—21no—
117Q8×C29—42no—
118Q8×C29#4112yescomplemented
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130D116—22no—
131D116—21no—
132D116—21no—
133D116—21no—
134D116—21no—
135D116—42no—
136D116—42no—
137D116—42no—
138D116—42no—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—42no—
144C4×D29—42no—
145C4×D29—42no—
146C4×D29—42no—
147C4×D29—42no—
148Dic58—21no—
149Dic58—21no—
150Dic58—42no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3308—291nomaximal, Sylow
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29AGL(1,ℤ/8)12yes—
169C4×C29—22no—
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29C2×#4111yescharacteristic
176C4×C29H(5,𝔽2)11yescharacteristic
177Dic29—21no—
178Dic29—21no—
179Dic29—41no—
180Dic29—41no—
181#548—291no—
182#547—291no—
183#489—291no—
184#484—291no—
185#480—291no—
186#477D2911yescharacteristic, complemented
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#54611yescharacteristic
197C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C29#57811yescharacteristic
199D29—22no—
200D29—41no—
201D29—81no—
202D29—81no—
203C2×#41—291no—
204C2×#41—581no—
205C22×Q8—291no—
206C2×SD16—291no—
207C2×SD16—291no—
208C2×D8—291no—
209C2×M16—291no—
210C22×C8—291no—
211C4⋊Q8C2×D2911yescharacteristic
212#124—291no—
213#124—581no—
214#123—581no—
215#123—581no—
216C22⋊Q8—291no—
217C22⋊Q8—581no—
218C22⋊Q8—581no—
219#121—291no—
220#121—291no—
221#121—291no—
222#121—581no—
223C4×Q8C2×D2911yescharacteristic
224C4×D4—291no—
225C4×D4—291no—
226C4×D4—581no—
227C2×C4⋊C4—291no—
228C2×C4⋊C4—291no—
229#107—291no—
230#107C2×D2911yescharacteristic
231#107C2×D2911yescharacteristic
232C4⋊C8C2×D2911yescharacteristic
233#103—291no—
234#103—291no—
235#103—291no—
236#103—291no—
237#103C2×D2911yescharacteristic
238#103C2×D2911yescharacteristic
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—582no—
248#41—1161no—
249#41—1164no—
250C2×Q8—21no—
251C2×Q8—291no—
252C2×Q8—581no—
253C2×Q8—582no—
254C2×Q8—1161no—
255C2×Q8C22×D2911yescharacteristic
256C2×D4—291no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C22×C4—291no—
264C22×C4—291no—
265C22×C4—581no—
266C22×C4—581no—
267C22×C4—581no—
268C22×C4—581no—
269C22×C4—581no—
270SD16—582no—
271SD16—1161no—
272D8—1161no—
273M16—1161no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—1161no—
277C2×C8C22×D2911yescharacteristic
278C2×C8C22×D2911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—291no—
282C4⋊C4—291no—
283C4⋊C4—581no—
284C4⋊C4—581no—
285C4⋊C4—581no—
286C4⋊C4C22×D2911yescharacteristic
287C4⋊C4C22×D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
289C22⋊C4—291no—
290C22⋊C4—291no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C42—21no—
299C42C22×D2911yescharacteristic
300C23—291no—
301C23—291no—
302C23—581no—
303C23—581no—
304Q8—21no—
305Q8—42no—
306Q8—581no—
307Q8—581no—
308Q8—1162no—
309Q8#9080912yescomplemented
310D4—582no—
311D4—581no—
312D4—581no—
313D4—581no—
314D4—581no—
315D4—1162no—
316D4—1162no—
317D4—1162no—
318D4—1162no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—291no—
324C2×C4—291no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—1162no—
332C2×C4—1162no—
333C2×C4—1162no—
334C2×C4—1162no—
335C2×C4—1162no—
336C2×C4D4×D2911yescharacteristic
337C2×C4D4×D2911yescharacteristic
338C2×C4C23×D2911yescharacteristic
339C8—21no—
340C8—21no—
341C8—581no—
342C8—581no—
343C22—292no—
344C22—581no—
345C22—581no—
346C22—581no—
347C22—581no—
348C22—581no—
349C22—1161no—
350C22—1161no—
351C22—1161no—
352C22—1161no—
353C22—1161no—
354C22—1161no—
355C22C2×D4×D2911yescharacteristic
356C4—22no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—581no—
363C4—581no—
364C4—1161no—
365C4—1161no—
366C4C2×#9080911yescharacteristic
367C4#1174536411yescharacteristic
368C2—582no—
369C2—1161no—
370C2—2321no—
371C2—2321no—
372C2#1427180411yescharacteristic
373C2AGL(1,ℤ/8)×D2911yescharacteristic
374C2#1427197611yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#477C2
socleC22×C29C22×D4
hypercenter#477D29
hypocenterC29#3308
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #14271825C2semidirect
2. #14271816C2semidirect
3. #14271525C2semidirect
4. #14271500C2semidirect
5. #14271478C2semidirect
6. #14271410C2semidirect
7. #14271400C2semidirect
8. #14271379C2semidirect
9. #14271311C2semidirect
10. #14271303C2semidirect
11. #14271261C2semidirect
12. #14271233C2semidirect
13. #14271163C2semidirect
14. #103×D29C2semidirect
15. C29×#477C2semidirect
118. Q8×C29#41semidirect
186. #477D29semidirect
246. C29#3308semidirect
309. Q8#90809semidirect

Maximal subgroups

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

subgroupindex
#142718252
#142718162
#142715252
#142715002
#142714782
#142714102
#142714002
#142713792
#142713112
#142713032
#142712612
#142712332
#142711632
#103×D292
C29×#4772
#330829