Finite Group Databasebeta

← C37×#8335 #22629588

Subgroups — C37×#8335 #22629588

Order 9472.

826 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 182 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
1C22×#125×C37C211yesmaximal, characteristic
2C37×#1749C212yesmaximal
3C2×C37×#330C214yesmaximal, complemented
4C2×#125×C37—28no—
5C2×#125×C37—22no—
6C2×#125×C37C412yes—
7C2×#125×C37C2212yes—
8C22×C4⋊C4×C37—22no—
9C22×C4⋊C4×C37C412yes—
10C22×C42×C37C2211yescharacteristic
11C2×C22⋊C8×C37—22no—
12C2×#97×C37C2214yes—
13C37×#336—22no—
14C37×#330—28no—
15C23×C4×C37—22no—
16C23×C4×C37C2×C411yescharacteristic
17C23×C4×C37D412yes—
18C22×C8×C37—24no—
19#125×C37—216no—
20#125×C37—28no—
21#125×C37—24no—
22#125×C37D418yes—
23C2×C4⋊C4×C37—216no—
24C2×C4⋊C4×C37—22no—
25C2×C4⋊C4×C37—24no—
26C2×C4⋊C4×C37—24no—
27C2×C4⋊C4×C37—28no—
28C2×C4⋊C4×C37C2×C414yes—
29C2×C42×C37—24no—
30C2×C42×C37C2×C411yescharacteristic
31C2×C42×C37D412yes—
32C2×C42×C37C2311yescharacteristic
33C22⋊C8×C37—28no—
34#97×C37—28no—
35C24×C37C22⋊C411yescharacteristic
36C22×C4×C37—22no—
37C22×C4×C37—22no—
38C22×C4×C37—22no—
39C22×C4×C37—28no—
40C22×C4×C37—24no—
41C22×C4×C37—24no—
42C22×C4×C37—24no—
43C22×C4×C37—42no—
44C22×C4×C37—44no—
45C22×C4×C37—44no—
46C22×C4×C37C22⋊C412yes—
47C22×C4×C37C22⋊C411yescharacteristic
48C22×C4×C37C22×C411yescharacteristic
49C22×C4×C37C2×D412yes—
50C2×C8×C37—28no—
51C2×C8×C37—44no—
52C2×C8×C37—44no—
53C4⋊C4×C37—28no—
54C4⋊C4×C37—216no—
55C4⋊C4×C37—24no—
56C4⋊C4×C37—216no—
57C4⋊C4×C37C22⋊C418yes—
58C42×C37—22no—
59C42×C37—24no—
60C42×C37C2×D414yes—
61C23×C37—21no—
62C23×C37—21no—
63C23×C37—22no—
64C23×C37#10112yes—
65C23×C37#10414yes—
66C23×C37C2×C22⋊C411yescharacteristic
67C2×C4×C37—28no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—28no—
76C2×C4×C37—22no—
77C2×C4×C37—22no—
78C2×C4×C37—48no—
79C2×C4×C37—416no—
80C2×C4×C37—44no—
81C2×C4×C37—44no—
82C2×C4×C37#10112yes—
83C2×C4×C37C2×C22⋊C412yes—
84C2×C4×C37#12014yes—
85C8×C37—48no—
86#8335C3711yesmaximal, characteristic, direct product factor, Sylow
87C22×C37—24no—
88C22×C37—22no—
89C22×C37—24no—
90C22×C37—22no—
91C22×C37#33014yescomplemented
92C22×C37#37911yescharacteristic
93C22×C37C2×#10111yescharacteristic
94C22×C37C2×#10111yescharacteristic
95C22×C37C2×#10412yes—
96C22×C37#42112yes—
97C4×C37—22no—
98C4×C37—22no—
99C4×C37—24no—
100C4×C37—42no—
101C4×C37—48no—
102C22×#125C2×C3711yescharacteristic
103#1749C2×C3712yes—
104C2×#330C2×C3714yescomplemented
105C2×C37—24no—
106C2×C37C2×#33011yescharacteristic
107C2×C37#152812yes—
108C2×C37#153411yescharacteristic
109C2×C37#178411yescharacteristic
110C2×C37#178912yes—
111C2×#125—28no—
112C2×#125—22no—
113C2×#125C4×C3712yes—
114C2×#125C22×C3712yes—
115C22×C4⋊C4—22no—
116C22×C4⋊C4C4×C3712yes—
117C22×C42C22×C3711yescharacteristic
118C2×C22⋊C8—22no—
119C2×#97C22×C3714yes—
120#336—22no—
121#330—28no—
122C37#833511yescharacteristic, direct product factor, Sylow
123C23×C4—22no—
124C23×C4C2×C4×C3711yescharacteristic
125C23×C4D4×C3712yes—
126C22×C8—24no—
127#125—216no—
128#125—28no—
129#125—24no—
130#125D4×C3718yes—
131C2×C4⋊C4—216no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—28no—
136C2×C4⋊C4C2×C4×C3714yes—
137C2×C42—24no—
138C2×C42C2×C4×C3711yescharacteristic
139C2×C42D4×C3712yes—
140C2×C42C23×C3711yescharacteristic
141C22⋊C8—28no—
142#97—28no—
143C24C22⋊C4×C3711yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—28no—
148C22×C4—24no—
149C22×C4—24no—
150C22×C4—24no—
151C22×C4—42no—
152C22×C4—44no—
153C22×C4—44no—
154C22×C4C22⋊C4×C3712yes—
155C22×C4C22⋊C4×C3711yescharacteristic
156C22×C4C22×C4×C3711yescharacteristic
157C22×C4C2×D4×C3712yes—
158C2×C8—28no—
159C2×C8—44no—
160C2×C8—44no—
161C4⋊C4—28no—
162C4⋊C4—216no—
163C4⋊C4—24no—
164C4⋊C4—216no—
165C4⋊C4C22⋊C4×C3718yes—
166C42—22no—
167C42—24no—
168C42C2×D4×C3714yes—
169C23—21no—
170C23—21no—
171C23—22no—
172C23#101×C3712yes—
173C23#104×C3714yes—
174C23C2×C22⋊C4×C3711yescharacteristic
175C2×C4—28no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—28no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—48no—
187C2×C4—416no—
188C2×C4—44no—
189C2×C4—44no—
190C2×C4#101×C3712yes—
191C2×C4C2×C22⋊C4×C3712yes—
192C2×C4#120×C3714yes—
193C8—48no—
194C22—24no—
195C22—22no—
196C22—24no—
197C22—22no—
198C22C37×#33014yescomplemented
199C22C37×#37911yescharacteristic
200C22C2×#101×C3711yescharacteristic
201C22C2×#101×C3711yescharacteristic
202C22C2×#104×C3712yes—
203C22C37×#42112yes—
204C4—22no—
205C4—22no—
206C4—24no—
207C4—42no—
208C4—48no—
209C2—24no—
210C2C2×C37×#33011yescharacteristic
211C2C37×#152812yes—
212C2C37×#153411yescharacteristic
213C2C37×#178411yescharacteristic
214C2C37×#178912yes—
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC24×C37C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C37×#330C2semidirect
86. #8335C37direct (N × H)
91. C22×C37#330semidirect
104. C2×#330C2×C37semidirect
122. C37#8335direct (N × H)
198. C22C37×#330semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C372
C37×#17492
C2×C37×#3302
#833537