Finite Group Databasebeta

← C37×#1521 #17990339

Subgroups — C37×#1521 #17990339

Order 4736.

218 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C37×#529C211yesmaximal, characteristic
2C37×#431C211yesmaximal, characteristic, complemented
3C37×#383C211yesmaximal, characteristic, complemented
4C37×#328C212yesmaximal, complemented
5C37×#327C212yesmaximal
6#126×C37—21no—
7#125×C37C411yescharacteristic, complemented
8#124×C37C411yescharacteristic, complemented
9#123×C37—21no—
10C22⋊Q8×C37C2211yescharacteristic
11#121×C37C2211yescharacteristic
12C4×Q8×C37C411yescharacteristic, complemented
13C4×D4×C37—21no—
14C4×D4×C37C411yescharacteristic, complemented
15#117×C37—21no—
16C2×C42×C37C2211yescharacteristic
17C4⋊C8×C37—21no—
18C22⋊C8×C37C2212yes—
19C4×C8×C37—21no—
20#95×C37—21no—
21#95×C37—21no—
22#95×C37C2212yes—
23C2×Q8×C37C2×C411yescharacteristic
24C2×D4×C37—21no—
25C2×D4×C37C2×C411yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37—22no—
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C2×C8×C37—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C411yescharacteristic
37C4⋊C4×C37C2×C411yescharacteristic
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—21no—
43C42×C37—21no—
44C42×C37C2×C411yescharacteristic
45C42×C37C2×C411yescharacteristic
46C42×C37D411yescharacteristic
47C42×C37D411yescharacteristic
48C23×C37—21no—
49C23×C37C2×D411yescharacteristic
50Q8×C37—41no—
51D4×C37—41no—
52D4×C37—42no—
53C2×C4×C37—22no—
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37—42no—
60C2×C4×C37—42no—
61C2×C4×C37—42no—
62C2×C4×C37—42no—
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22⋊C411yescharacteristic
67C2×C4×C37C22×C411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C8×C37—42no—
70C22×C37—21no—
71C22×C37—21no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C22×C37#13512yes—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—21no—
83C4×C37—41no—
84C4×C37—41no—
85C4×C37—41no—
86C4×C37—82no—
87#1521C3711yesmaximal, characteristic, direct product factor, Sylow
88C2×C37—22no—
89C2×C37—81no—
90C2×C37#41011yescharacteristic
91C2×C37#41611yescharacteristic
92C2×C37#42111yescharacteristic
93#529C2×C3711yescharacteristic
94#431C2×C3711yescharacteristic, complemented
95#383C2×C3711yescharacteristic, complemented
96#328C2×C3712yescomplemented
97#327C2×C3712yes—
98C37#152111yescharacteristic, direct product factor, Sylow
99#126—21no—
100#125C4×C3711yescharacteristic, complemented
101#124C4×C3711yescharacteristic, complemented
102#123—21no—
103C22⋊Q8C22×C3711yescharacteristic
104#121C22×C3711yescharacteristic
105C4×Q8C4×C3711yescharacteristic, complemented
106C4×D4—21no—
107C4×D4C4×C3711yescharacteristic, complemented
108#117—21no—
109C2×C42C22×C3711yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C22×C3712yes—
112C4×C8—21no—
113#95—21no—
114#95—21no—
115#95C22×C3712yes—
116C2×Q8C2×C4×C3711yescharacteristic
117C2×D4—21no—
118C2×D4C2×C4×C3711yescharacteristic
119C22×C4—21no—
120C22×C4—22no—
121C22×C4D4×C3711yescharacteristic
122C22×C4D4×C3711yescharacteristic
123C22×C4C23×C3711yescharacteristic
124C2×C8—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4C2×C4×C3711yescharacteristic
130C4⋊C4C2×C4×C3711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42C2×C4×C3711yescharacteristic
138C42C2×C4×C3711yescharacteristic
139C42D4×C3711yescharacteristic
140C42D4×C3711yescharacteristic
141C23—21no—
142C23C2×D4×C3711yescharacteristic
143Q8—41no—
144D4—41no—
145D4—42no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4C22⋊C4×C3711yescharacteristic
157C2×C4C22⋊C4×C3711yescharacteristic
158C2×C4C22⋊C4×C3711yescharacteristic
159C2×C4C22⋊C4×C3711yescharacteristic
160C2×C4C22×C4×C3711yescharacteristic
161C2×C4C2×D4×C3711yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22C2×C22⋊C4×C3711yescharacteristic
169C22#135×C3712yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—82no—
180C2—22no—
181C2—81no—
182C2C37×#41011yescharacteristic
183C2C37×#41611yescharacteristic
184C2C37×#42111yescharacteristic
subgroupG/H
center, socleC22×C37C2×C22⋊C4
commutatorC2×C4C22×C4×C37
Frattini, cosocleC22×C4C23×C37
prime radical#121×C37C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#431C2semidirect
3. C37×#383C2semidirect
4. C37×#328C2semidirect
7. #125×C37C4semidirect
8. #124×C37C4semidirect
12. C4×Q8×C37C4semidirect
14. C4×D4×C37C4semidirect
87. #1521C37direct (N × H)
94. #431C2×C37semidirect
95. #383C2×C37semidirect
96. #328C2×C37semidirect
98. C37#1521direct (N × H)
100. #125C4×C37semidirect
101. #124C4×C37semidirect
105. C4×Q8C4×C37semidirect
107. C4×D4C4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#5292
C37×#4312
C37×#3832
C37×#3282
C37×#3272
#152137