Finite Group Databasebeta

← C37×#9452 #22630705

Subgroups — C37×#9452 #22630705

Order 9472.

468 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2983C211yesmaximal, characteristic
2C37×#2546C211yesmaximal, characteristic
3C37×#1558C212yesmaximal
4C37×#1467C211yesmaximal, characteristic
5C37×#1285C212yesmaximal
6C2×C4⋊Q8×C37C412yes—
7C2×C4⋊Q8×C37C2211yescharacteristic
8C2×C4×Q8×C37C2211yescharacteristic
9C37×#446—24no—
10C37×#432—21no—
11C37×#432C2212yes—
12C37×#432C2212yes—
13C37×#431—21no—
14C37×#398—21no—
15C37×#398—21no—
16C37×#391C412yes—
17C37×#389—21no—
18C37×#389—21no—
19C4×C4⋊C4×C37C2211yescharacteristic
20C37×#333—24no—
21C37×#324—21no—
22C37×#324—21no—
23C22×Q8×C37C2×C412yes—
24C22×Q8×C37C2×C411yescharacteristic
25C4⋊Q8×C37—22no—
26C4⋊Q8×C37—22no—
27C4⋊Q8×C37—44no—
28C4×Q8×C37—22no—
29C4×Q8×C37—22no—
30C2×C4⋊C4×C37—21no—
31C2×C4⋊C4×C37—22no—
32C2×C4⋊C4×C37—22no—
33C2×C4⋊C4×C37—21no—
34C2×C4⋊C4×C37—21no—
35C2×C4⋊C4×C37C2×C411yescharacteristic
36C2×C4⋊C4×C37D411yescharacteristic
37C2×C4⋊C4×C37D411yescharacteristic
38C2×C42×C37C2×C412yes—
39C2×C42×C37D411yescharacteristic
40C2×C42×C37D411yescharacteristic
41C2×C42×C37C2311yescharacteristic
42C4⋊C8×C37—22no—
43C4⋊C8×C37—22no—
44C4⋊C8×C37—22no—
45C4⋊C8×C37D414yes—
46C22⋊C8×C37—22no—
47C22⋊C8×C37—22no—
48#97×C37—22no—
49#97×C37—22no—
50#97×C37—22no—
51C4×C8×C37—22no—
52#95×C37—22no—
53#95×C37—22no—
54#95×C37—21no—
55C2×Q8×C37—22no—
56C2×Q8×C37—22no—
57C2×Q8×C37—24no—
58C2×Q8×C37—41no—
59C2×Q8×C37—42no—
60C2×Q8×C37—42no—
61C22×C4×C37—22no—
62C22×C4×C37—22no—
63C22×C4×C37C22⋊C411yescharacteristic
64C22×C4×C37C22⋊C411yescharacteristic
65C22×C4×C37C22⋊C411yescharacteristic
66C22×C4×C37C22⋊C411yescharacteristic
67C22×C4×C37C22×C411yescharacteristic
68C22×C4×C37C2×D411yescharacteristic
69C22×C4×C37C2×D411yescharacteristic
70C2×C8×C37—24no—
71C2×C8×C37—42no—
72C4⋊C4×C37—24no—
73C4⋊C4×C37—22no—
74C4⋊C4×C37—22no—
75C4⋊C4×C37—22no—
76C4⋊C4×C37—44no—
77C4⋊C4×C37—44no—
78C4⋊C4×C37—41no—
79C4⋊C4×C37—42no—
80C4⋊C4×C37—41no—
81C42×C37—21no—
82C42×C37—21no—
83C42×C37—21no—
84C42×C37—21no—
85C42×C37—42no—
86C42×C37C2×D412yes—
87C42×C37#4112yes—
88C23×C37C2×C22⋊C411yescharacteristic
89Q8×C37—44no—
90Q8×C37—84no—
91C2×C4×C37—21no—
92C2×C4×C37—21no—
93C2×C4×C37—21no—
94C2×C4×C37—21no—
95C2×C4×C37—22no—
96C2×C4×C37—24no—
97C2×C4×C37—21no—
98C2×C4×C37—21no—
99C2×C4×C37—21no—
100C2×C4×C37—21no—
101C2×C4×C37—21no—
102C2×C4×C37—41no—
103C2×C4×C37—42no—
104C2×C4×C37—42no—
105C2×C4×C37—41no—
106C2×C4×C37—41no—
107C2×C4×C37—42no—
108C2×C4×C37—42no—
109C2×C4×C37—42no—
110C2×C4×C37#10012yes—
111C2×C4×C37C4×D412yes—
112C2×C4×C37#12011yescharacteristic
113C2×C4×C37#12112yes—
114C2×C4×C37#12311yescharacteristic
115C8×C37—44no—
116C8×C37—82no—
117#9452C3711yesmaximal, characteristic, direct product factor, Sylow
118C22×C37—21no—
119C22×C37—21no—
120C22×C37#38611yescharacteristic
121C22×C37C2×#10011yescharacteristic
122C22×C37#41311yescharacteristic
123C4×C37—21no—
124C4×C37—22no—
125C4×C37—22no—
126C4×C37—22no—
127C4×C37—44no—
128C4×C37—41no—
129C4×C37—41no—
130C4×C37—41no—
131C4×C37—82no—
132C4×C37#45612yes—
133#2983C2×C3711yescharacteristic
134#2546C2×C3711yescharacteristic
135#1558C2×C3712yes—
136#1467C2×C3711yescharacteristic
137#1285C2×C3712yes—
138C2×C37—21no—
139C2×C37—21no—
140C2×C37#188611yescharacteristic
141C2×C37#190011yescharacteristic
142C2×C37#190911yescharacteristic
143C2×C4⋊Q8C4×C3712yes—
144C2×C4⋊Q8C22×C3711yescharacteristic
145C2×C4×Q8C22×C3711yescharacteristic
146#446—24no—
147#432—21no—
148#432C22×C3712yes—
149#432C22×C3712yes—
150#431—21no—
151#398—21no—
152#398—21no—
153#391C4×C3712yes—
154#389—21no—
155#389—21no—
156C4×C4⋊C4C22×C3711yescharacteristic
157#333—24no—
158#324—21no—
159#324—21no—
160C37#945211yescharacteristic, direct product factor, Sylow
161C22×Q8C2×C4×C3712yes—
162C22×Q8C2×C4×C3711yescharacteristic
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×C4×C3711yescharacteristic
174C2×C4⋊C4D4×C3711yescharacteristic
175C2×C4⋊C4D4×C3711yescharacteristic
176C2×C42C2×C4×C3712yes—
177C2×C42D4×C3711yescharacteristic
178C2×C42D4×C3711yescharacteristic
179C2×C42C23×C3711yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8D4×C3714yes—
184C22⋊C8—22no—
185C22⋊C8—22no—
186#97—22no—
187#97—22no—
188#97—22no—
189C4×C8—22no—
190#95—22no—
191#95—22no—
192#95—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊C4×C3711yescharacteristic
202C22×C4C22⋊C4×C3711yescharacteristic
203C22×C4C22⋊C4×C3711yescharacteristic
204C22×C4C22⋊C4×C3711yescharacteristic
205C22×C4C22×C4×C3711yescharacteristic
206C22×C4C2×D4×C3711yescharacteristic
207C22×C4C2×D4×C3711yescharacteristic
208C2×C8—24no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—44no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42C2×D4×C3712yes—
225C42#41×C3712yes—
226C23C2×C22⋊C4×C3711yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#100×C3712yes—
249C2×C4C4×D4×C3712yes—
250C2×C4#120×C3711yescharacteristic
251C2×C4#121×C3712yes—
252C2×C4#123×C3711yescharacteristic
253C8—44no—
254C8—82no—
255C22—21no—
256C22—21no—
257C22C37×#38611yescharacteristic
258C22C2×#100×C3711yescharacteristic
259C22C37×#41311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4C37×#45612yes—
270C2—21no—
271C2—21no—
272C2C37×#188611yescharacteristic
273C2C37×#190011yescharacteristic
274C2C37×#190911yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC23×C37C2×C22⋊C4
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
117. #9452C37direct (N × H)
160. C37#9452direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#29832
C37×#25462
C37×#15582
C37×#14672
C37×#12852
#945237