Finite Group Databasebeta

← #16834871

Subgroups — #16834871

Order 3712.

284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272181C211yesmaximal, characteristic, complemented
2C4×C4⋊#1181C211yesmaximal, characteristic, complemented
3#14272015C212yesmaximal, complemented
4#14272014C212yesmaximal, complemented
5#14271710C211yesmaximal, characteristic
6C2×#90805—21no—
7C2×C4⋊#1181—21no—
8C2×C4×#1181—21no—
9C4×D4×C29C411yescharacteristic, complemented
10#11745302C411yescharacteristic, complemented
11#11745300C2211yescharacteristic
12C4×C22⋊D29—21no—
13#11745257C2211yescharacteristic
14#11745250C411yescharacteristic, complemented
15#11745247—21no—
16#11745246—21no—
17C4×D116C411yescharacteristic, complemented
18C42×D29C2211yescharacteristic
19(C2×#1181)⋊C4C2212yes—
20#11745220—21no—
21#11745219C2212yes—
22C4×#6599—21no—
23C22×#1181—22no—
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29—21no—
26C2×C22⋊D29—21no—
27C2×C22⋊D29—21no—
28C2×C22⋊D29—21no—
29#90805—42no—
30#90805—42no—
31C2×D116—21no—
32C2×D116C2×C411yescharacteristic
33C2×C4×D29—21no—
34C2×C4×D29D411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29C2311yescharacteristic
37C2×Dic58—21no—
38C2×#6599—22no—
39C4⋊#1181—24no—
40C4×#1181—42no—
41C4⋊C4×C29C2×C411yescharacteristic
42C22⋊C4×C29—21no—
43C42×C29C2×C411yescharacteristic
44C22⋊Dic29—21no—
45#90781—21no—
46#90781—21no—
47C4⋊Dic29C2×C411yescharacteristic
48#90779—21no—
49C4×Dic29C2×C411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29D411yescharacteristic
52C23×C29—21no—
53C22×D29—21no—
54C22×D29C2×D411yescharacteristic
55C2×#1181—24no—
56C2×#1181—42no—
57C2×#1181—42no—
58D4×C29—41no—
59C2×C4×C29—21no—
60C2×C4×C29—42no—
61C2×C4×C29C22⋊C411yescharacteristic
62C2×C4×C29C22⋊C411yescharacteristic
63C2×C4×C29C22×C411yescharacteristic
64C22⋊D29—41no—
65C22⋊D29—41no—
66C22⋊D29—42no—
67C22⋊D29—42no—
68C2×Dic29—21no—
69C2×Dic29C22⋊C411yescharacteristic
70C2×Dic29C22⋊C411yescharacteristic
71C2×Dic29C2×D411yescharacteristic
72D116—41no—
73D116—41no—
74D116—41no—
75C4×D29—22no—
76C4×D29—41no—
77C4×D29—42no—
78C4×D29D812yes—
79C4×D29SD1612yes—
80Dic58—42no—
81#6599—42no—
82#1502—291nomaximal, Sylow
83C22×C29—41no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29C2×C22⋊C411yescharacteristic
87C2×D29—21no—
88C2×D29—21no—
89C2×D29—41no—
90C2×D29—41no—
91C2×D29—41no—
92C2×D29C2×D811yescharacteristic
93C2×D29C2×SD1611yescharacteristic
94#1181—44no—
95C4×C29—21no—
96C4×C29—21no—
97C4×C29—41no—
98C4×C29#10212yes—
99Dic29—21no—
100Dic29—41no—
101Dic29#10212yes—
102Dic29#10412yes—
103#532—291no—
104#431—291no—
105C4×C4⋊C4—291no—
106#327—292no—
107#327—292no—
108C2×C29—81no—
109C2×C29#41011yescharacteristic
110C2×C29C2×#10211yescharacteristic
111C2×C29C2×#10411yescharacteristic
112D29—21no—
113D29—21no—
114D29—81no—
115C2×#41—581no—
116C4⋊Q8—291no—
117#127—291no—
118#124—581no—
119#121—291no—
120#121—291no—
121#121—581no—
122C4×D4—291no—
123C4×D4—581no—
124C4×D4#118111yescharacteristic, complemented
125C2×C4⋊C4—581no—
126C2×C42—291no—
127C2×C42—581no—
128C4⋊C8—581no—
129C22⋊C8—292no—
130C4×C8—581no—
131#95—292no—
132C29#150211yescharacteristic, complemented, Sylow
133#41—1162no—
134#41—1162no—
135C2×Q8—581no—
136C2×D4—291no—
137C2×D4—581no—
138C2×D4—581no—
139C2×D4—581no—
140C2×D4—581no—
141C2×D4C2×#118111yescharacteristic
142C22×C4—21no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—291no—
146C22×C4—582no—
147C22×C4—581no—
148C2×C8—582no—
149C4⋊C4—291no—
150C4⋊C4—581no—
151C4⋊C4—584no—
152C4⋊C4C2×#118111yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C42—291no—
158C42—291no—
159C42—291no—
160C42—1162no—
161C42C2×#118111yescharacteristic
162C23—21no—
163C23—291no—
164C23—581no—
165Q8—1162no—
166D4—41no—
167D4—1161no—
168D4—1161no—
169D4—1161no—
170D4—1162no—
171D4—1162no—
172D4—1161no—
173D4—1161no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—292no—
179C2×C4—292no—
180C2×C4—291no—
181C2×C4—582no—
182C2×C4—584no—
183C2×C4—581no—
184C2×C4—1161no—
185C2×C4—1162no—
186C2×C4—1162no—
187C2×C4—1162no—
188C2×C4C22⋊#118111yescharacteristic
189C2×C4C22⋊#118111yescharacteristic
190C2×C4C22×#118111yescharacteristic
191C8—1162no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—291no—
196C22—291no—
197C22—581no—
198C22—581no—
199C22—1161no—
200C22—1161no—
201C22—1161no—
202C22C2×C22⋊#118111yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—292no—
207C4—292no—
208C4—581no—
209C4—1164no—
210C4—1161no—
211C4#1174522312yes—
212C2—81no—
213C2—581no—
214C2—581no—
215C2—2321no—
216C2#1427214211yescharacteristic
217C2C2×#1174522311yescharacteristic
218C2D29⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radical#14271710C2
cosocleC2×C4×D29C23
hypercenterC4×D4#1181
hypocenterC29#1502
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272181C2semidirect
2. C4×C4⋊#1181C2semidirect
3. #14272015C2semidirect
4. #14272014C2semidirect
9. C4×D4×C29C4semidirect
10. #11745302C4semidirect
14. #11745250C4semidirect
17. C4×D116C4semidirect
124. C4×D4#1181semidirect
132. C29#1502semidirect

Maximal subgroups

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

subgroupindex
#142721812
C4×C4⋊#11812
#142720152
#142720142
#142717102
#150229