Finite Group Databasebeta

← C37×#9399 #22630652

Subgroups — C37×#9399 #22630652

Order 9472.

514 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2975C211yesmaximal, characteristic
2C37×#2563C211yesmaximal, characteristic
3C37×#1800C211yesmaximal, characteristic
4C37×#1548C212yesmaximal, complemented
5C37×#1303C212yesmaximal, complemented
6C2×C4⋊Q8×C37C2211yescharacteristic
7C2×C4×D4×C37C2211yescharacteristic
8C37×#436—24no—
9C37×#431C2212yes—
10C37×#423C2212yes—
11C2×#100×C37—21no—
12C37×#407—22no—
13C37×#393C414yes—
14C37×#390—21no—
15C37×#382—21no—
16C37×#380—22no—
17C4×C4⋊C4×C37C2211yescharacteristic
18C37×#343—21no—
19C37×#333—24no—
20C22×Q8×C37C2×C412yes—
21C22×D4×C37D411yescharacteristic
22C23×C4×C37D412yes—
23C2×M16×C37—24no—
24C2×M16×C37—22no—
25C4⋊Q8×C37—22no—
26C4⋊Q8×C37—22no—
27C4×D4×C37—22no—
28C4×D4×C37—22no—
29C2×C4⋊C4×C37—21no—
30C2×C4⋊C4×C37—21no—
31C2×C4⋊C4×C37—21no—
32C2×C4⋊C4×C37D411yescharacteristic
33C2×C22⋊C4×C37—24no—
34C2×C22⋊C4×C37C2×C412yes—
35C2×C42×C37—21no—
36C2×C42×C37C2311yescharacteristic
37C4⋊C8×C37—22no—
38C4⋊C8×C37—22no—
39C4⋊C8×C37D414yes—
40#100×C37—42no—
41C22⋊C8×C37—24no—
42C22⋊C8×C37—22no—
43C4×C8×C37—22no—
44#95×C37—24no—
45#95×C37C2×C412yes—
46C24×C37C22⋊C412yes—
47C2×Q8×C37—24no—
48C2×Q8×C37—82no—
49C2×D4×C37—22no—
50C2×D4×C37—21no—
51C2×D4×C37—22no—
52C2×D4×C37—21no—
53C22×C4×C37—22no—
54C22×C4×C37—22no—
55C22×C4×C37—22no—
56C22×C4×C37—22no—
57C22×C4×C37—44no—
58C22×C4×C37C22⋊C412yes—
59C22×C4×C37C22×C411yescharacteristic
60C22×C4×C37C2×D411yescharacteristic
61C22×C4×C37C2×D411yescharacteristic
62M16×C37—42no—
63M16×C37—42no—
64M16×C37—84no—
65C2×C8×C37—24no—
66C2×C8×C37—42no—
67C4⋊C4×C37—22no—
68C4⋊C4×C37—42no—
69C4⋊C4×C37—41no—
70C4⋊C4×C37—42no—
71C4⋊C4×C37—41no—
72C22⋊C4×C37—24no—
73C22⋊C4×C37—84no—
74C42×C37—41no—
75C42×C37—41no—
76C42×C37C2×D412yes—
77C42×C37#4112yes—
78C23×C37—22no—
79C23×C37—22no—
80C23×C37—22no—
81C23×C37—42no—
82C23×C37—42no—
83C23×C37C2×C22⋊C411yescharacteristic
84Q8×C37—84no—
85D4×C37—42no—
86D4×C37—42no—
87C2×C4×C37—22no—
88C2×C4×C37—22no—
89C2×C4×C37—41no—
90C2×C4×C37—44no—
91C2×C4×C37—42no—
92C2×C4×C37—42no—
93C2×C4×C37—44no—
94C2×C4×C37—42no—
95C2×C4×C37—42no—
96C2×C4×C37—42no—
97C2×C4×C37—82no—
98C2×C4×C37C4×D412yes—
99C2×C4×C37#12011yescharacteristic
100C2×C4×C37#12112yes—
101C2×C4×C37#12311yescharacteristic
102C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C37#13712yes—
104C2×C4×C37#13711yescharacteristic
105C8×C37—44no—
106C8×C37—82no—
107#9399C3711yesmaximal, characteristic, direct product factor, Sylow
108C22×C37—21no—
109C22×C37—21no—
110C22×C37—44no—
111C22×C37—42no—
112C22×C37—42no—
113C22×C37—42no—
114C22×C37—82no—
115C22×C37#38611yescharacteristic
116C22×C37#41711yescharacteristic
117C22×C37#41911yescharacteristic
118C4×C37—21no—
119C4×C37—22no—
120C4×C37—42no—
121C4×C37—82no—
122C4×C37—82no—
123C4×C37#45512yes—
124C4×C37#46812yes—
125C4×C37#47012yes—
126#2975C2×C3711yescharacteristic
127#2563C2×C3711yescharacteristic
128#1800C2×C3711yescharacteristic
129#1548C2×C3712yescomplemented
130#1303C2×C3712yescomplemented
131C2×C37—21no—
132C2×C37—21no—
133C2×C37—82no—
134C2×C37#188511yescharacteristic
135C2×C37#189411yescharacteristic
136C2×C37#191411yescharacteristic
137C2×C4⋊Q8C22×C3711yescharacteristic
138C2×C4×D4C22×C3711yescharacteristic
139#436—24no—
140#431C22×C3712yes—
141#423C22×C3712yes—
142C2×#100—21no—
143#407—22no—
144#393C4×C3714yes—
145#390—21no—
146#382—21no—
147#380—22no—
148C4×C4⋊C4C22×C3711yescharacteristic
149#343—21no—
150#333—24no—
151C37#939911yescharacteristic, direct product factor, Sylow
152C22×Q8C2×C4×C3712yes—
153C22×D4D4×C3711yescharacteristic
154C23×C4D4×C3712yes—
155C2×M16—24no—
156C2×M16—22no—
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4×D4—22no—
160C4×D4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4D4×C3711yescharacteristic
165C2×C22⋊C4—24no—
166C2×C22⋊C4C2×C4×C3712yes—
167C2×C42—21no—
168C2×C42C23×C3711yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8D4×C3714yes—
172#100—42no—
173C22⋊C8—24no—
174C22⋊C8—22no—
175C4×C8—22no—
176#95—24no—
177#95C2×C4×C3712yes—
178C24C22⋊C4×C3712yes—
179C2×Q8—24no—
180C2×Q8—82no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—44no—
190C22×C4C22⋊C4×C3712yes—
191C22×C4C22×C4×C3711yescharacteristic
192C22×C4C2×D4×C3711yescharacteristic
193C22×C4C2×D4×C3711yescharacteristic
194M16—42no—
195M16—42no—
196M16—84no—
197C2×C8—24no—
198C2×C8—42no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C22⋊C4—24no—
205C22⋊C4—84no—
206C42—41no—
207C42—41no—
208C42C2×D4×C3712yes—
209C42#41×C3712yes—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C22⋊C4×C3711yescharacteristic
216Q8—84no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4C4×D4×C3712yes—
231C2×C4#120×C3711yescharacteristic
232C2×C4#121×C3712yes—
233C2×C4#123×C3711yescharacteristic
234C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
235C2×C4#137×C3712yes—
236C2×C4#137×C3711yescharacteristic
237C8—44no—
238C8—82no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22C37×#38611yescharacteristic
247C22C37×#41711yescharacteristic
248C22C37×#41911yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—82no—
253C4—82no—
254C4C37×#45512yes—
255C4C37×#46812yes—
256C4C37×#47012yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2C37×#188511yescharacteristic
261C2C37×#189411yescharacteristic
262C2C37×#191411yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC22×D4×C37D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1548C2semidirect
5. C37×#1303C2semidirect
107. #9399C37direct (N × H)
129. #1548C2×C37semidirect
130. #1303C2×C37semidirect
151. C37#9399direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#29752
C37×#25632
C37×#18002
C37×#15482
C37×#13032
#939937