Finite Group Databasebeta

← #16834870

Subgroups — #16834870

Order 3712.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#11745219C211yesmaximal, characteristic, complemented
2C4×C22⋊#1181C211yesmaximal, characteristic, complemented
3#14272017C212yesmaximal, complemented
4#14272015C212yesmaximal, complemented
5#14271676C211yesmaximal, characteristic
6C2×#90809C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C22×#6599—21no—
10C2×C4×#1181—21no—
11C29×C22⋊Q8C411yescharacteristic, complemented
12#11745308C2211yescharacteristic
13#11745292C411yescharacteristic, complemented
14#11745257C2211yescharacteristic
15#11745256—21no—
16#11745255—21no—
17#11745254C411yescharacteristic, complemented
18#11745244—21no—
19#11745243—21no—
20(C2×#1181)⋊C4C2212yes—
21#11745219—21no—
22#11745219C2212yes—
23C23×D29D411yescharacteristic
24C22×#1181—22no—
25C2×Q8×C29C2×C411yescharacteristic
26C22×C4×C29C2×C411yescharacteristic
27C2×C22⋊D29—21no—
28C22×Dic29D411yescharacteristic
29#90809—42no—
30C2×D116—21no—
31C2×D116—21no—
32C2×D116C2×C411yescharacteristic
33C2×C4×D29—21no—
34C2×C4×D29—42no—
35C2×C4×D29C2×C411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C4×D29C2311yescharacteristic
39C22⋊#1181—24no—
40C2×#6599—22no—
41C2×#6599—42no—
42C4×#1181—42no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29C2×C411yescharacteristic
45C22⋊C4×C29—21no—
46#90781—21no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50C4⋊Dic29C2×C411yescharacteristic
51#90779—21no—
52C4×Dic29—21no—
53C23×C29C22⋊C411yescharacteristic
54C22×D29—22no—
55C22×D29—22no—
56C22×D29—21no—
57C22×D29—41no—
58C22×D29C22⋊C411yescharacteristic
59C22×D29C2×D411yescharacteristic
60C2×#1181—24no—
61C2×#1181—42no—
62C2×#1181—42no—
63Q8×C29—41no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—41no—
67C2×C4×C29C22⋊C411yescharacteristic
68C2×C4×C29C22×C411yescharacteristic
69C22⋊D29—42no—
70C2×Dic29—22no—
71C2×Dic29—21no—
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C2×D411yescharacteristic
74D116—41no—
75D116—42no—
76D116—42no—
77C4×D29—22no—
78C4×D29—22no—
79C4×D29—41no—
80C4×D29—41no—
81C4×D29—42no—
82#6599—42no—
83#1501—291nomaximal, Sylow
84C22×C29—21no—
85C22×C29—21no—
86C22×C29#10412yes—
87C22×C29C2×C22⋊C411yescharacteristic
88C2×D29—21no—
89C2×D29—21no—
90C2×D29—21no—
91C2×D29—21no—
92C2×D29—21no—
93C2×D29—44no—
94C2×D29—41no—
95C2×D29—41no—
96C2×D29—41no—
97C2×D29#13512yes—
98#1181—44no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—41no—
102C4×C29—41no—
103Dic29—21no—
104Dic29—41no—
105Dic29#9912yes—
106#525—291no—
107C2×C22⋊C8—291no—
108C4×C22⋊C4—291no—
109#328—292no—
110#327—292no—
111C2×C29—22no—
112C2×C29C2×#9911yescharacteristic
113C2×C29#41611yescharacteristic
114C2×C29C2×#10411yescharacteristic
115D29—22no—
116D29—41no—
117D29—81no—
118C2×#41—291no—
119C23×C4—291no—
120C22×C8—581no—
121#123—581no—
122C22⋊Q8—291no—
123C22⋊Q8#118111yescharacteristic, complemented
124#121—291no—
125#121—291no—
126#120—581no—
127C4×D4—581no—
128C4×D4—581no—
129#117—291no—
130C2×C22⋊C4—581no—
131C2×C42—581no—
132C22⋊C8—292no—
133C22⋊C8—581no—
134#95—292no—
135C29#150111yescharacteristic, complemented, Sylow
136C24—291no—
137#41—1162no—
138C2×Q8C2×#118111yescharacteristic
139C2×D4—291no—
140C2×D4—581no—
141C2×D4—581no—
142C2×D4—581no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—291no—
146C22×C4—291no—
147C22×C4—291no—
148C22×C4—581no—
149C22×C4—582no—
150C22×C4—1162no—
151C22×C4C2×#118111yescharacteristic
152C2×C8—582no—
153C2×C8—1162no—
154C4⋊C4—21no—
155C4⋊C4—291no—
156C4⋊C4—581no—
157C4⋊C4C2×#118111yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—581no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—584no—
163C22⋊C4—581no—
164C42—581no—
165C42—1162no—
166C23—291no—
167C23—291no—
168C23—582no—
169C23—582no—
170C23—581no—
171C23—1161no—
172C23C22⋊#118111yescharacteristic
173Q8—41no—
174D4—1161no—
175D4—1162no—
176D4—1162no—
177D4—1162no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—291no—
182C2×C4—291no—
183C2×C4—582no—
184C2×C4—582no—
185C2×C4—582no—
186C2×C4—584no—
187C2×C4—581no—
188C2×C4—1161no—
189C2×C4—1161no—
190C2×C4—1162no—
191C2×C4—1162no—
192C2×C4—1162no—
193C2×C4C22⋊#118111yescharacteristic
194C2×C4C22×#118111yescharacteristic
195C8—1162no—
196C22—21no—
197C22—21no—
198C22—292no—
199C22—581no—
200C22—581no—
201C22—581no—
202C22—581no—
203C22—581no—
204C22—1164no—
205C22—1161no—
206C22—1161no—
207C22—1161no—
208C22#1174522612yes—
209C22C2×C22⋊#118111yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—292no—
215C4—581no—
216C4—1164no—
217C4—1161no—
218C2—22no—
219C2—582no—
220C2—1161no—
221C2—2321no—
222C2D29⋊#9911yescharacteristic
223C2#1427215311yescharacteristic
224C2C2×#1174522611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C22⋊Q8C4
socleC22×C29C2×C22⋊C4
prime radical#14271676C2
cosocleC2×C4×D29C23
hypercenterC22⋊Q8#1181
hypocenterC29#1501
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11745219C2semidirect
2. C4×C22⋊#1181C2semidirect
3. #14272017C2semidirect
4. #14272015C2semidirect
6. C2×#90809C4semidirect
11. C29×C22⋊Q8C4semidirect
13. #11745292C4semidirect
17. #11745254C4semidirect
123. C22⋊Q8#1181semidirect
135. C29#1501semidirect

Maximal subgroups

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

subgroupindex
C2×#117452192
C4×C22⋊#11812
#142720172
#142720152
#142716762
#150129