Finite Group Databasebeta

← #16817996

Subgroups — #16817996

Order 3712.

334 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271127C211yesmaximal, characteristic, complemented
2C2×#11745179C211yesmaximal, characteristic, complemented
3#14270900C212yesmaximal, complemented
4#14270897C212yesmaximal, complemented
5C29×#525C211yesmaximal, characteristic
6C2×#41×C29C411yescharacteristic, complemented
7C23×C4×C29C2211yescharacteristic
8C23×Dic29—21no—
9C29×#123—21no—
10C29×C22⋊Q8C411yescharacteristic, complemented
11C29×C22⋊Q8C2211yescharacteristic
12C29×#121C411yescharacteristic, complemented
13C29×#121C2211yescharacteristic
14C29×#120—21no—
15C4×D4×C29—21no—
16C4×D4×C29—21no—
17C29×#117C411yescharacteristic, complemented
18C2×#90777—21no—
19#11745179—21no—
20#11745179C2212yes—
21C22⋊#6597—21no—
22C22⋊#6597C2212yes—
23C24×C29D411yescharacteristic
24#41×C29—42no—
25C2×Q8×C29C2×C411yescharacteristic, complemented
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29—21no—
29C2×D4×C29C2×C411yescharacteristic, complemented
30C22×C4×C29—21no—
31C22×C4×C29—42no—
32C22×C4×C29C2×C411yescharacteristic
33C22×C4×C29C2×C411yescharacteristic
34C22×C4×C29D411yescharacteristic
35C22×C4×C29D411yescharacteristic
36C22×C4×C29D411yescharacteristic
37C22×C4×C29C2311yescharacteristic
38C22×Dic29—24no—
39C22×Dic29—22no—
40C22×Dic29—42no—
41C22×Dic29—42no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29C2×C411yescharacteristic, complemented
45C4⋊C4×C29C2×C411yescharacteristic, complemented
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—21no—
50C22⋊C4×C29—21no—
51C42×C29—21no—
52#90777—42no—
53C2×#6597—22no—
54C23×C29—22no—
55C23×C29—22no—
56C23×C29—21no—
57C23×C29—21no—
58C23×C29—21no—
59C23×C29C22⋊C411yescharacteristic
60C23×C29C22⋊C411yescharacteristic
61C23×C29C2×D411yescharacteristic
62Q8×C29—41no—
63D4×C29—41no—
64D4×C29—42no—
65D4×C29—42no—
66D4×C29—41no—
67D4×C29—41no—
68C2×C4×C29—22no—
69C2×C4×C29—22no—
70C2×C4×C29—21no—
71C2×C4×C29—21no—
72C2×C4×C29—21no—
73C2×C4×C29—41no—
74C2×C4×C29—41no—
75C2×C4×C29—41no—
76C2×C4×C29—41no—
77C2×C4×C29—42no—
78C2×C4×C29C22⋊C411yescharacteristic
79C2×C4×C29C22⋊C411yescharacteristic
80C2×C4×C29C22×C411yescharacteristic
81C2×C4×C29C2×D411yescharacteristic
82C2×Dic29—24no—
83C2×Dic29—48no—
84C2×Dic29—42no—
85C2×Dic29—42no—
86#6597—42no—
87#1504—291nomaximal, Sylow
88C22×C29—24no—
89C22×C29—24no—
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—21no—
93C22×C29—21no—
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29#9912yes—
100C22×C29#10412yes—
101C22×C29C2×C22⋊C411yescharacteristic
102C22×C29AGL(1,ℤ/8)11yescharacteristic
103C22×C29#13711yescharacteristic
104C4×C29—21no—
105C4×C29—21no—
106C4×C29—21no—
107C4×C29—21no—
108C4×C29—41no—
109C4×C29—41no—
110C4×C29—41no—
111Dic29—44no—
112#525D2911yescharacteristic
113#407—291no—
114C2×#95—291no—
115#328—292no—
116#327—292no—
117C2×C29—21no—
118C2×C29—22no—
119C2×C29—22no—
120C2×C29—21no—
121C2×C29—81no—
122C2×C29C2×#9911yescharacteristic
123C2×C29#41711yescharacteristic
124C2×C29C2×#10411yescharacteristic
125C2×#41Dic2911yescharacteristic, complemented
126C23×C4—581no—
127C23×C4C2×D2911yescharacteristic
128C2×M16—581no—
129#123—21no—
130C22⋊Q8Dic2911yescharacteristic, complemented
131C22⋊Q8C2×D2911yescharacteristic
132#121Dic2911yescharacteristic, complemented
133#121C2×D2911yescharacteristic
134#120—21no—
135C4×D4—21no—
136C4×D4—21no—
137#117Dic2911yescharacteristic, complemented
138C22⋊C8—292no—
139C22⋊C8—581no—
140#95—292no—
141#95—581no—
142C29#150411yescharacteristic, complemented, Sylow
143C24C22⋊D2911yescharacteristic
144#41—42no—
145C2×Q8C2×Dic2911yescharacteristic, complemented
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C2×Dic2911yescharacteristic, complemented
150C22×C4—21no—
151C22×C4—42no—
152C22×C4—584no—
153C22×C4—582no—
154C22×C4—1162no—
155C22×C4—1162no—
156C22×C4C2×Dic2911yescharacteristic
157C22×C4C2×Dic2911yescharacteristic
158C22×C4C22⋊D2911yescharacteristic
159C22×C4C22⋊D2911yescharacteristic
160C22×C4C22⋊D2911yescharacteristic
161C22×C4C22×D2911yescharacteristic
162M16—1162no—
163C2×C8—582no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4C2×Dic2911yescharacteristic, complemented
167C4⋊C4C2×Dic2911yescharacteristic, complemented
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C42—21no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23—21no—
179C23C22⋊Dic2911yescharacteristic
180C23C22⋊Dic2911yescharacteristic
181C23C2×C22⋊D2911yescharacteristic
182Q8—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—42no—
187D4—42no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—584no—
199C2×C4—1168no—
200C2×C4—1162no—
201C2×C4—1162no—
202C2×C4C22⋊Dic2911yescharacteristic
203C2×C4C22⋊Dic2911yescharacteristic
204C2×C4C22×Dic2911yescharacteristic
205C2×C4C2×C22⋊D2911yescharacteristic
206C8—1162no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22#1174518212yes—
219C22#1174518512yes—
220C22#1174531111yescharacteristic
221C22#1174531311yescharacteristic
222C22C2×C22⋊Dic2911yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—1164no—
231C2—21no—
232C2—21no—
233C2—22no—
234C2—22no—
235C2—81no—
236C2C2×#1174518211yescharacteristic
237C2#1427116411yescharacteristic
238C2C2×#1174518511yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#525C2
socleC22×C29C2×C22⋊C4
cosocleC22×C4×C29C23
hypercenter#525D29
hypocenterC29#1504
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14271127C2semidirect
2. C2×#11745179C2semidirect
3. #14270900C2semidirect
4. #14270897C2semidirect
6. C2×#41×C29C4semidirect
10. C29×C22⋊Q8C4semidirect
12. C29×#121C4semidirect
17. C29×#117C4semidirect
25. C2×Q8×C29C2×C4semidirect
29. C2×D4×C29C2×C4semidirect
44. C4⋊C4×C29C2×C4semidirect
45. C4⋊C4×C29C2×C4semidirect
125. C2×#41Dic29semidirect
130. C22⋊Q8Dic29semidirect
132. #121Dic29semidirect
137. #117Dic29semidirect
142. C29#1504semidirect
145. C2×Q8C2×Dic29semidirect
149. C2×D4C2×Dic29semidirect
166. C4⋊C4C2×Dic29semidirect
167. C4⋊C4C2×Dic29semidirect

Maximal subgroups

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

subgroupindex
#142711272
C2×#117451792
#142709002
#142708972
C29×#5252
#150429