Finite Group Databasebeta

← #16834896

Subgroups — #16834896

Order 3712.

242 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 60 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#14272185C211yesmaximal, characteristic, complemented
2C4×C4⋊#1181C211yesmaximal, characteristic, complemented
3#14272017C212yesmaximal, complemented
4#14272015C212yesmaximal
5#14271700C211yesmaximal, characteristic
6C2×C4⋊#1181—21no—
7C2×C4×#1181—21no—
8C4×Q8×C29C411yescharacteristic, complemented
9#11745309C411yescharacteristic, complemented
10#11745308C2211yescharacteristic
11#11745260—21no—
12#11745257C2211yescharacteristic
13#11745256—21no—
14#11745252C411yescharacteristic, complemented
15C4×D116—21no—
16C4×D116C411yescharacteristic, complemented
17#11745234—21no—
18C42×D29C2211yescharacteristic
19(C2×#1181)⋊C4C2212yes—
20#11745219C2212yes—
21#11745218—21no—
22C4⋊#6599—21no—
23C22×#1181—22no—
24C2×Q8×C29C2×C411yescharacteristic
25C2×D116—21no—
26C2×D116C2×C411yescharacteristic
27C2×C4×D29—21no—
28C2×C4×D29D411yescharacteristic
29C2×C4×D29D411yescharacteristic
30C2×C4×D29C2311yescharacteristic
31C2×#6599—22no—
32C4⋊#1181—24no—
33C4×#1181—42no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29C2×C411yescharacteristic
36C42×C29—21no—
37C42×C29C2×C411yescharacteristic
38#90781—21no—
39#90781—21no—
40#90781—21no—
41#90781—21no—
42#90781—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29C2×C411yescharacteristic
45#90779—21no—
46#90779—21no—
47C4×Dic29C2×C411yescharacteristic
48C4×Dic29D411yescharacteristic
49C4×Dic29D411yescharacteristic
50C22×D29—21no—
51C22×D29C2×D411yescharacteristic
52C2×#1181—24no—
53C2×#1181—42no—
54C2×#1181—42no—
55Q8×C29—41no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22⋊C411yescharacteristic
60C2×C4×C29C22×C411yescharacteristic
61C2×Dic29—21no—
62C2×Dic29C22⋊C411yescharacteristic
63C2×Dic29C22⋊C411yescharacteristic
64C2×Dic29C2×D411yescharacteristic
65D116—41no—
66D116—41no—
67D116—41no—
68C4×D29—21no—
69C4×D29—21no—
70C4×D29—22no—
71C4×D29—41no—
72C4×D29—42no—
73#6599—42no—
74#1509—291nomaximal, Sylow
75C22×C29C2×C22⋊C411yescharacteristic
76C2×D29—21no—
77C2×D29—21no—
78C2×D29—41no—
79C2×D29—41no—
80C2×D29—41no—
81C2×D29AGL(1,ℤ/8)11yescharacteristic
82C2×D29#13711yescharacteristic
83#1181—44no—
84C4×C29—21no—
85C4×C29—21no—
86C4×C29—41no—
87C4×C29—41no—
88C4×C29#10412yes—
89Dic29—21no—
90Dic29—21no—
91Dic29—21no—
92Dic29—41no—
93#529—291no—
94#432—291no—
95C4×C4⋊C4—291no—
96#328—292no—
97#327—292no—
98C2×C29#41011yescharacteristic
99C2×C29#41711yescharacteristic
100C2×C29C2×#10411yescharacteristic
101D29—21no—
102D29—21no—
103D29—81no—
104#126—581no—
105#125—291no—
106#124—291no—
107#123—581no—
108C22⋊Q8—291no—
109#121—291no—
110C4×Q8#118111yescharacteristic, complemented
111C4×D4—291no—
112C4×D4—581no—
113#117—581no—
114C2×C4⋊C4—581no—
115C2×C42—291no—
116C2×C42—581no—
117C4⋊C8—581no—
118C22⋊C8—292no—
119#97—581no—
120#95—292no—
121C29#150911yescharacteristic, complemented, Sylow
122C2×Q8C2×#118111yescharacteristic
123C2×D4—291no—
124C2×D4—581no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—291no—
128C22×C4—582no—
129C22×C4—581no—
130C2×C8—582no—
131C4⋊C4—21no—
132C4⋊C4—291no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4—581no—
136C4⋊C4—584no—
137C4⋊C4C2×#118111yescharacteristic
138C22⋊C4—581no—
139C22⋊C4—581no—
140C22⋊C4—581no—
141C22⋊C4—581no—
142C22⋊C4—581no—
143C42—21no—
144C42—291no—
145C42—291no—
146C42—291no—
147C42—1162no—
148C42C2×#118111yescharacteristic
149C23—291no—
150C23—581no—
151Q8—41no—
152D4—1161no—
153D4—1161no—
154D4—1161no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—291no—
158C2×C4—291no—
159C2×C4—291no—
160C2×C4—581no—
161C2×C4—581no—
162C2×C4—582no—
163C2×C4—584no—
164C2×C4—581no—
165C2×C4—1161no—
166C2×C4—1162no—
167C2×C4—1162no—
168C2×C4—1162no—
169C2×C4C22⋊#118111yescharacteristic
170C2×C4C22⋊#118111yescharacteristic
171C2×C4C22×#118111yescharacteristic
172C8—1162no—
173C22—291no—
174C22—291no—
175C22—581no—
176C22—581no—
177C22—1161no—
178C22—1161no—
179C22—1161no—
180C22C2×C22⋊#118111yescharacteristic
181C4—21no—
182C4—21no—
183C4—41no—
184C4—41no—
185C4—581no—
186C4—581no—
187C4—581no—
188C4—1164no—
189C4—1161no—
190C4#1174522612yes—
191C2—581no—
192C2—581no—
193C2—2321no—
194C2#1427214211yescharacteristic
195C2#1427215411yescharacteristic
196C2C2×#1174522611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×Q8×C29C4
socleC22×C29C2×C22⋊C4
prime radical#11745257C22
cosocleC2×C4×D29C23
hypercenterC4×Q8#1181
hypocenterC29#1509
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14272185C2semidirect
2. C4×C4⋊#1181C2semidirect
3. #14272017C2semidirect
8. C4×Q8×C29C4semidirect
9. #11745309C4semidirect
14. #11745252C4semidirect
16. C4×D116C4semidirect
110. C4×Q8#1181semidirect
121. C29#1509semidirect

Maximal subgroups

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

subgroupindex
#142721852
C4×C4⋊#11812
#142720172
#142720152
#142717002
#150929