Finite Group Databasebeta

← #16832224

Subgroups — #16832224

Order 3712.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271890C211yesmaximal, characteristic, complemented
2#14271834C211yesmaximal, characteristic
3#14271529C211yesmaximal, characteristic, complemented
4#14271526C211yesmaximal, characteristic, complemented
5#14271508C211yesmaximal, characteristic, complemented
6#14271462C211yesmaximal, characteristic, complemented
7#14271442C211yesmaximal, characteristic, complemented
8#14271364C211yesmaximal, characteristic, complemented
9#14271362C211yesmaximal, characteristic, complemented
10#14271362C211yesmaximal, characteristic, complemented
11#14271292C211yesmaximal, characteristic, complemented
12#14271263C211yesmaximal, characteristic, complemented
13#14271262C211yesmaximal, characteristic, complemented
14#14271250C211yesmaximal, characteristic, complemented
15C29×#478C211yesmaximal, characteristic, complemented
16C2×#90805—21no—
17C29×#125C2211yescharacteristic
18C4×D4×C29C2211yescharacteristic
19#11745302C2211yescharacteristic
20#11745302C2211yescharacteristic
21C2×#90783C2211yescharacteristic
22#11745292—21no—
23C2×#90773C2211yescharacteristic
24C2×#90773C2211yescharacteristic
25#11745255C2211yescharacteristic
26#11745255C2211yescharacteristic
27#11745252C2211yescharacteristic
28#11745251—21no—
29#11745251—21no—
30#11745250—21no—
31#11745250C2211yescharacteristic
32#11745249—21no—
33#11745249C2211yescharacteristic
34#11745249C2211yescharacteristic
35#11745246—21no—
36#11745246—21no—
37#11745236C2211yescharacteristic
38C4×Dic58C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C29×#107C2211yescharacteristic
41C29×#106C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#102C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745163C2211yescharacteristic
49#11745162C2211yescharacteristic
50#11745162C2211yescharacteristic
51C8×Dic29C2211yescharacteristic
52#11745158C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C22×C4×C29—21no—
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65#90805—44no—
66C2×D116—21no—
67C2×D116—21no—
68C2×D116C2311yescharacteristic
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×Dic58—21no—
73C2×Dic58D411yescharacteristic
74C2×Dic58C2311yescharacteristic
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C42×C29C2311yescharacteristic
84#90783—22no—
85#90781—21no—
86#90781—21no—
87C4⋊Dic29—21no—
88C4⋊Dic29D411yescharacteristic
89C4⋊Dic29C2311yescharacteristic
90#90779—21no—
91#90779—21no—
92#90779—21no—
93#90779—21no—
94#90779—21no—
95#90779D411yescharacteristic
96#90779D411yescharacteristic
97C4×Dic29—21no—
98C4×Dic29—21no—
99C4×Dic29—21no—
100C4×Dic29C2311yescharacteristic
101C4×Dic29C2311yescharacteristic
102C2×#6597C2311yescharacteristic
103C2×#6597C2311yescharacteristic
104#90773—22no—
105#90773—22no—
106C23×C29—21no—
107C22×D29—21no—
108C22×D29—21no—
109D4×C29—21no—
110D4×C29—21no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—42no—
115C2×C4×C29C2×D411yescharacteristic
116C2×C4×C29C2×D411yescharacteristic
117C2×C4×C29C2411yescharacteristic
118C22⋊D29—42no—
119C22⋊D29—42no—
120C22⋊D29—81no—
121C22⋊D29—81no—
122C2×Dic29—21no—
123C2×Dic29—21no—
124C2×Dic29C2×D411yescharacteristic
125C2×Dic29C2×D411yescharacteristic
126C2×Dic29C2×D411yescharacteristic
127C2×Dic29C2×D411yescharacteristic
128D116—21no—
129D116—21no—
130D116—21no—
131D116—21no—
132D116—42no—
133D116—81no—
134C4×D29—42no—
135C4×D29—42no—
136Dic58—21no—
137Dic58—22no—
138Dic58—42no—
139Dic58#4112yescomplemented
140C8×C29—21no—
141C8×C29—21no—
142#6597—21no—
143#6597—21no—
144#3368—291nomaximal, Sylow
145C22×C29—41no—
146C22×C29—41no—
147C22×C29—41no—
148C22×C29C22×D411yescharacteristic
149C2×D29—41no—
150C2×D29—41no—
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C4×C29—21no—
156C4×C29—21no—
157C4×C29—41no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29C2×#4111yescharacteristic
161C4×C292−1+411yescharacteristic
162Dic29—22no—
163Dic29—21no—
164Dic29—21no—
165Dic29—21no—
166Dic29—41no—
167Dic29AGL(1,ℤ/8)12yes—
168#557—291no—
169#550—291no—
170#490—291no—
171#490—291no—
172#486—291no—
173#478—291no—
174#478D2911yescharacteristic, complemented
175#474—291no—
176#460—291no—
177#460—291no—
178#460—291no—
179#446—291no—
180#440—291no—
181#440—291no—
182C4×SD16—291no—
183C2×C29—81no—
184C2×C29#54811yescharacteristic
185C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C29#57711yescharacteristic
187D29—81no—
188D29—81no—
189C2×#41—581no—
190C2×SD16—291no—
191C2×SD16—291no—
192C2×SD16—291no—
193C4⋊Q8—291no—
194C4⋊Q8—581no—
195#127—291no—
196#127—291no—
197#127—291no—
198#125—291no—
199#125—581no—
200#125—581no—
201#125C2×D2911yescharacteristic
202#121—581no—
203#121—581no—
204#121—581no—
205C4×Q8—291no—
206C4×Q8—291no—
207C4×Q8—291no—
208C4×Q8—291no—
209C4×Q8—581no—
210C4×D4—291no—
211C4×D4—291no—
212C4×D4C2×D2911yescharacteristic
213#107—291no—
214#107C2×D2911yescharacteristic
215#106C2×D2911yescharacteristic
216C4⋊C8—291no—
217C4⋊C8—291no—
218C4⋊C8C2×D2911yescharacteristic
219#103—291no—
220#102—291no—
221#102—291no—
222#102—291no—
223#102—291no—
224#102—291no—
225#102—291no—
226#102—291no—
227#102C2×D2911yescharacteristic
228#102C2×D2911yescharacteristic
229#97—291no—
230#97—291no—
231C4×C8—291no—
232C29#336811yescharacteristic, complemented, Sylow
233#41—1164no—
234C2×Q8—291no—
235C2×Q8—291no—
236C2×Q8—581no—
237C2×D4—291no—
238C2×D4—291no—
239C2×D4—581no—
240C2×D4—581no—
241C2×D4—581no—
242C2×D4—581no—
243C2×D4—581no—
244C2×D4—581no—
245C2×D4C22×D2911yescharacteristic
246C22×C4—21no—
247C22×C4—581no—
248C22×C4—581no—
249SD16—582no—
250SD16—582no—
251SD16—582no—
252C2×C8—291no—
253C2×C8—291no—
254C2×C8C22×D2911yescharacteristic
255C2×C8C22×D2911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—291no—
259C4⋊C4—291no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4C22×D2911yescharacteristic
269C4⋊C4C22×D2911yescharacteristic
270C4⋊C4C22×D2911yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C42—291no—
275C42—291no—
276C42—581no—
277C42—581no—
278C42—581no—
279C42C22×D2911yescharacteristic
280C23—21no—
281C23—581no—
282C23—581no—
283Q8—292no—
284Q8—582no—
285Q8—581no—
286Q8—1162no—
287D4—21no—
288D4—21no—
289D4—581no—
290D4—581no—
291D4—581no—
292D4—581no—
293D4—1162no—
294D4—1162no—
295D4—1162no—
296D4—2321no—
297D4—2321no—
298D4—2321no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—291no—
304C2×C4—291no—
305C2×C4—291no—
306C2×C4—291no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—1162no—
310C2×C4—1162no—
311C2×C4D4×D2911yescharacteristic
312C2×C4D4×D2911yescharacteristic
313C2×C4C23×D2911yescharacteristic
314C8—21no—
315C8—21no—
316C8—581no—
317C8—581no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1161no—
322C22—1161no—
323C22—1161no—
324C22—1161no—
325C22—1161no—
326C22—1161no—
327C22C2×D4×D2911yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—292no—
334C4—582no—
335C4—581no—
336C4—581no—
337C4—581no—
338C4—1161no—
339C4#1174536211yescharacteristic
340C4#41×D2911yescharacteristic
341C2—81no—
342C2—2321no—
343C2—2321no—
344C2#1427182311yescharacteristic
345C2AGL(1,ℤ/8)×D2911yescharacteristic
346C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#478C2
socleC22×C29C22×D4
prime radical#14271834C2
hypercenter#478D29
hypocenterC29#3368
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14271890C2semidirect
3. #14271529C2semidirect
4. #14271526C2semidirect
5. #14271508C2semidirect
6. #14271462C2semidirect
7. #14271442C2semidirect
8. #14271364C2semidirect
9. #14271362C2semidirect
10. #14271362C2semidirect
11. #14271292C2semidirect
12. #14271263C2semidirect
13. #14271262C2semidirect
14. #14271250C2semidirect
15. C29×#478C2semidirect
139. Dic58#41semidirect
174. #478D29semidirect
232. C29#3368semidirect

Maximal subgroups

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

subgroupindex
#142718902
#142718342
#142715292
#142715262
#142715082
#142714622
#142714422
#142713642
#142713622
#142712922
#142712632
#142712622
#142712502
C29×#4782
#336829