Finite Group Databasebeta

← #16834917

Subgroups — #16834917

Order 3712.

284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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
1D29⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#14272106C211yesmaximal, characteristic, complemented
3#14272016C212yesmaximal, complemented
4#14272014C212yesmaximal, complemented
5#14271673C211yesmaximal, characteristic
6C2×#90807C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×D29⋊C8—21no—
10C29×#121C411yescharacteristic, complemented
11#11745300C2211yescharacteristic
12#11745299—21no—
13D4×Dic29—21no—
14#11745286C411yescharacteristic, complemented
15#11745259C2211yescharacteristic
16#11745254C411yescharacteristic, complemented
17#11745245—21no—
18#11745243—21no—
19C22⋊#6599—21no—
20(C2×#1181)⋊C4—21no—
21(C2×#1181)⋊C4C2212yes—
22#11745219C2212yes—
23C23×D29D411yescharacteristic
24C22×#1181—22no—
25C2×D4×C29—21no—
26C2×D4×C29C2×C411yescharacteristic
27C22×C4×C29C2×C411yescharacteristic
28C2×C22⋊D29—21no—
29C2×C22⋊D29—21no—
30C22×Dic29—21no—
31C22×Dic29D411yescharacteristic
32#90807—42no—
33C2×C4×D29—42no—
34C2×C4×D29C2×C411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29C2311yescharacteristic
38C2×Dic58C2×C411yescharacteristic
39C22⋊#1181—42no—
40C2×#6599—22no—
41D29⋊C8—42no—
42C4⋊C4×C29C2×C411yescharacteristic
43C22⋊C4×C29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46#90781—21no—
47#90781—21no—
48C4⋊Dic29—21no—
49C4⋊Dic29C2×C411yescharacteristic
50#90779—21no—
51C4×Dic29—21no—
52C23×C29—21no—
53C23×C29C22⋊C411yescharacteristic
54C22×D29—22no—
55C22×D29—22no—
56C22×D29—41no—
57C22×D29C22⋊C411yescharacteristic
58C22×D29C2×D411yescharacteristic
59C2×#1181—42no—
60C2×#1181—42no—
61C2×#1181—42no—
62D4×C29—41no—
63D4×C29—42no—
64C2×C4×C29—21no—
65C2×C4×C29—41no—
66C2×C4×C29C22⋊C411yescharacteristic
67C2×C4×C29C22×C411yescharacteristic
68C22⋊D29—42no—
69C22⋊D29—42no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—41no—
73C2×Dic29—42no—
74C2×Dic29C22⋊C411yescharacteristic
75C2×Dic29C2×D411yescharacteristic
76C4×D29—22no—
77C4×D29—22no—
78C4×D29—41no—
79C4×D29—41no—
80Dic58—41no—
81#6599—42no—
82#1516—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—21no—
85C22×C29—21no—
86C22×C29—41no—
87C22×C29—41no—
88C22×C29—41no—
89C22×C29C2×C22⋊C411yescharacteristic
90C2×D29—21no—
91C2×D29—21no—
92C2×D29—21no—
93C2×D29—21no—
94C2×D29—44no—
95C2×D29#9912yes—
96C2×D29#13512yes—
97#1181—82no—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—41no—
101Dic29—21no—
102Dic29—21no—
103Dic29—41no—
104Dic29—41no—
105#525—291no—
106C2×C22⋊C8—291no—
107#381—291no—
108#328—292no—
109#327—292no—
110C2×C29—41no—
111C2×C29—81no—
112C2×C29C2×#9911yescharacteristic
113C2×C29#41611yescharacteristic
114C2×C29#42111yescharacteristic
115D29—22no—
116D29—22no—
117C2×#41—291no—
118C23×C4—291no—
119C22×C8—581no—
120#123—581no—
121C22⋊Q8—291no—
122C22⋊Q8—291no—
123#121—291no—
124#121#118111yescharacteristic, complemented
125#120—581no—
126C4×D4—581no—
127C4×D4—581no—
128#117—291no—
129C2×C22⋊C4—581no—
130C22⋊C8—292no—
131C22⋊C8—581no—
132#95—292no—
133#95—581no—
134C29#151611yescharacteristic, complemented, Sylow
135C24—291no—
136#41—1162no—
137C2×Q8—291no—
138C2×D4—21no—
139C2×D4—581no—
140C2×D4—581no—
141C2×D4C2×#118111yescharacteristic
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—291no—
146C22×C4—291no—
147C22×C4—581no—
148C22×C4—582no—
149C22×C4—1162no—
150C22×C4C2×#118111yescharacteristic
151C2×C8—582no—
152C2×C8—1162no—
153C4⋊C4—291no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4C2×#118111yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—581no—
159C22⋊C4—581no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—1162no—
163C42—581no—
164C23—21no—
165C23—291no—
166C23—291no—
167C23—582no—
168C23—582no—
169C23—1161no—
170C23C22⋊#118111yescharacteristic
171Q8—1161no—
172D4—41no—
173D4—42no—
174D4—1162no—
175D4—1162no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—291no—
179C2×C4—291no—
180C2×C4—582no—
181C2×C4—582no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—1161no—
185C2×C4—1161no—
186C2×C4—1161no—
187C2×C4—1162no—
188C2×C4—1162no—
189C2×C4—1162no—
190C2×C4—1162no—
191C2×C4C22⋊#118111yescharacteristic
192C2×C4C22×#118111yescharacteristic
193C8—1162no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—41no—
198C22—41no—
199C22—41no—
200C22—292no—
201C22—292no—
202C22—581no—
203C22—581no—
204C22—581no—
205C22—581no—
206C22—1164no—
207C22C2×C22⋊#118111yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—581no—
212C4—581no—
213C4—1161no—
214C4—1161no—
215C4—2322no—
216C2—41no—
217C2—81no—
218C2—582no—
219C2—582no—
220C2D29⋊#9911yescharacteristic
221C2#1427215311yescharacteristic
222C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#121C4
socleC22×C29C2×C22⋊C4
prime radical#14271673C2
cosocleC2×C4×D29C23
hypercenter#121#1181
hypocenterC29#1516
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. D29⋊(C22⋊C8)C2semidirect
2. #14272106C2semidirect
3. #14272016C2semidirect
4. #14272014C2semidirect
6. C2×#90807C4semidirect
10. C29×#121C4semidirect
14. #11745286C4semidirect
16. #11745254C4semidirect
124. #121#1181semidirect
134. C29#1516semidirect

Maximal subgroups

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

subgroupindex
D29⋊(C22⋊C8)2
#142721062
#142720162
#142720142
#142716732
#151629