Finite Group Databasebeta

← #49174530

Subgroups — #49174530

Order 37504.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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×#22627683C212yesmaximal
2C4×C22⋊#11924078C212yesmaximal, complemented
3#34037007C212yesmaximal, complemented
4C2×#22627586C211yesmaximal, characteristic
5C2×C22⋊#11924078C2214yes—
6C2×C4×#11924078—22no—
7#22627683C418yescomplemented
8(C2×#11924078)⋊C4—22no—
9C22×D1172C2211yescharacteristic
10C22×C4×D293C411yescharacteristic, complemented
11C22×C4×D293C2211yescharacteristic
12#22627586—22no—
13#22627586—22no—
14C2×#17989779C411yescharacteristic, complemented
15C2×#17989779C2211yescharacteristic
16C2×C4×Dic293C411yescharacteristic, complemented
17C2×C4⋊C4×C293C411yescharacteristic, complemented
18C22×#11924078—24no—
19C22⋊#11924078—24no—
20C22⋊#11924078C2×C418yescomplemented
21C4×#11924078—44no—
22C23×D293C2×C411yescharacteristic
23C23×D293C2311yescharacteristic
24C2×D1172—22no—
25C2×D1172—22no—
26C2×D1172C2×C414yes—
27C22×Dic293C2×C411yescharacteristic
28C22×Dic293C2×C411yescharacteristic
29C2×C4×D293—21no—
30C2×C4×D293—21no—
31C2×C4×D293—42no—
32C2×C4×D293—42no—
33C2×C4×D293D412yes—
34C2×C4×D293D412yes—
35#17989779—22no—
36#17989779—22no—
37C4×Dic293—21no—
38C4×Dic293—21no—
39C22×C4×C293C2×C411yescharacteristic
40C22×C4×C293C2×C411yescharacteristic
41C22×C4×C293C2×C411yescharacteristic
42C4⋊C4×C293—22no—
43C2×#11924078—28no—
44C2×#11924078—44no—
45C2×#11924078—44no—
46C22×D293—21no—
47C22×D293—21no—
48C22×D293—41no—
49C22×D293—41no—
50C22×D293—41no—
51C22×D293—41no—
52C22×D293C4212yescomplemented
53C22×D293C22×C412yes—
54C22×D293C2×D412yes—
55C22×D293#4112yes—
56D1172—28no—
57C2×Dic293—22no—
58C2×Dic293—21no—
59C2×Dic293—41no—
60C2×Dic293C22⋊C411yescharacteristic
61C2×Dic293C22⋊C411yescharacteristic
62C4×D293—24no—
63C4×D293—42no—
64C4×D293—42no—
65C4×D293—42no—
66C23×C293C22×C411yescharacteristic
67C2×C4×C293—21no—
68C2×C4×C293—21no—
69C2×C4×C293—21no—
70C2×C4×C293—41no—
71C2×C4×C293—41no—
72C2×C4×C293C4212yescomplemented
73C2×C4×C293C22⋊C412yes—
74C22×C293—21no—
75C22×C293—21no—
76C22×C293C2×C4211yescharacteristic
77C22×C293C2×C22⋊C411yescharacteristic
78C22×C293#11711yescharacteristic
79C2×D293—22no—
80C2×D293—22no—
81C2×D293—22no—
82C2×D293—42no—
83C2×D293—42no—
84C2×D293—42no—
85C2×D293—41no—
86C2×D293—41no—
87C2×D293—42no—
88C2×D293C4×D414yes—
89#11924078—48no—
90C4×C293—22no—
91C4×C293—22no—
92C4×C293—41no—
93Dic293—21no—
94Dic293—41no—
95Dic293#9912yescomplemented
96C2×C293—21no—
97C2×C293—21no—
98C2×C293C4×C22⋊C411yescharacteristic
99C2×C293C2×#9911yescharacteristic
100C2×C293#41011yescharacteristic
101D293—24no—
102D293—42no—
103C293C4×#9911yescharacteristic, complemented, Sylow
104C4×#99—2931nomaximal, Sylow
105C2×C4×D4—2931no—
106C2×#99—2932no—
107C4×C22⋊C4—2932no—
108#342—2932no—
109C22×D4—2931no—
110C23×C4—2931no—
111C23×C4—2931no—
112C4×D4—5862no—
113C4×D4—5862no—
114C2×C4⋊C4#1192407811yescharacteristic, complemented
115C2×C22⋊C4—2934no—
116C2×C22⋊C4—2931no—
117C2×C22⋊C4—2931no—
118C2×C42—2931no—
119C2×C42—5862no—
120#99—2938no—
121#95—5862no—
122C24—2931no—
123C24—2931no—
124C2×D4—2934no—
125C2×D4—5862no—
126C2×D4—5862no—
127C22×C4—2931no—
128C22×C4—2932no—
129C22×C4—2932no—
130C22×C4—2931no—
131C22×C4—5861no—
132C22×C4—5861no—
133C22×C4—5864no—
134C22×C4—11722no—
135C22×C4—11722no—
136C22×C4C2×#1192407811yescharacteristic
137C22×C4C2×#1192407811yescharacteristic
138C22×C4C2×#1192407811yescharacteristic
139C4⋊C4—22no—
140C22⋊C4—2938no—
141C22⋊C4—5862no—
142C22⋊C4—5864no—
143C22⋊C4—5862no—
144C42—5861no—
145C42—5861no—
146C42—11724no—
147C23—2932no—
148C23—2932no—
149C23—2932no—
150C23—2932no—
151C23—5861no—
152C23—5861no—
153C23—11721no—
154C23—11721no—
155C23—11721no—
156C23—11721no—
157C23C22×#1192407811yescharacteristic
158D4—5868no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—2931no—
165C2×C4—2931no—
166C2×C4—5864no—
167C2×C4—5862no—
168C2×C4—5868no—
169C2×C4—5861no—
170C2×C4—11722no—
171C2×C4—11722no—
172C2×C4—11722no—
173C2×C4—11724no—
174C2×C4—11724no—
175C2×C4—11721no—
176C2×C4C4×#1192407812yescomplemented
177C2×C4C22⋊#1192407812yes—
178C22—21no—
179C22—21no—
180C22—2934no—
181C22—5862no—
182C22—5862no—
183C22—5862no—
184C22—11722no—
185C22—11722no—
186C22—11722no—
187C22—11722no—
188C22—11721no—
189C22—11721no—
190C22C2×C4×#1192407811yescharacteristic
191C22C2×C22⋊#1192407811yescharacteristic
192C22#2262770311yescharacteristic
193C4—22no—
194C4—22no—
195C4—41no—
196C4—2932no—
197C4—5861no—
198C4—11728no—
199C4—11721no—
200C2—21no—
201C2—21no—
202C2—5864no—
203C2—11722no—
204C2C4×C22⋊#1192407811yescharacteristic
205C2D293⋊#9911yescharacteristic
206C2#3403711011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC22×C293C2×C42
FrattiniC23C22×#11924078
FittingC2×C4⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC22×D1172C22
cosocleC23×D293C23
hypercenterC2×C4⋊C4#11924078
hypocenterC293C4×#99
LCSG ▷ C22×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#11924078C2semidirect
3. #34037007C2semidirect
7. #22627683C4semidirect
10. C22×C4×D293C4semidirect
14. C2×#17989779C4semidirect
16. C2×C4×Dic293C4semidirect
17. C2×C4⋊C4×C293C4semidirect
20. C22⋊#11924078C2×C4semidirect
52. C22×D293C42semidirect
72. C2×C4×C293C42semidirect
95. Dic293#99semidirect
103. C293C4×#99semidirect
114. C2×C4⋊C4#11924078semidirect
176. C2×C4C4×#11924078semidirect

Maximal subgroups

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

subgroupindex
C2×#226276832
C4×C22⋊#119240782
#340370072
C2×#226275862
C4×#99293