Finite Group Databasebeta

← C37×#9202 #22630455

Subgroups — C37×#9202 #22630455

Order 9472.

516 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2627C211yesmaximal, characteristic
2C37×#2313C211yesmaximal, characteristic
3C37×#1520C212yesmaximal
4C2×C37×#324C211yesmaximal, characteristic
5C37×#1289C212yesmaximal
6C2×C22⋊Q8×C37C2211yescharacteristic
7C22×C4⋊C4×C37C2211yescharacteristic
8C2×C22⋊C8×C37C2212yes—
9C37×#400C412yescomplemented
10C37×#398—22no—
11C37×#395C412yescomplemented
12C37×#387—24no—
13C37×#385—21no—
14C37×#381—21no—
15C37×#381—21no—
16C37×#380C2211yescharacteristic
17C37×#380C2212yes—
18C4×C22⋊C4×C37—21no—
19C37×#328—24no—
20C37×#324—22no—
21C22×Q8×C37C2×C411yescharacteristic
22C23×C4×C37D411yescharacteristic
23C23×C4×C37D411yescharacteristic
24C23×C4×C37C2311yescharacteristic
25C22×C8×C37—22no—
26C22⋊Q8×C37—22no—
27C22⋊Q8×C37—22no—
28C2×C4⋊C4×C37—22no—
29C2×C4⋊C4×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×C37C2×C411yescharacteristic
35C2×C4⋊C4×C37C2×C412yes—
36C2×C4⋊C4×C37D412yes—
37C2×C22⋊C4×C37—21no—
38C2×C22⋊C4×C37—22no—
39C2×C22⋊C4×C37—21no—
40C2×C42×C37—22no—
41C22⋊C8×C37—22no—
42C22⋊C8×C37—22no—
43#95×C37—22no—
44#95×C37—24no—
45#95×C37—22no—
46#95×C37—22no—
47#95×C37—22no—
48#95×C37C2×C412yes—
49#95×C37D414yes—
50C24×C37C2×D411yescharacteristic
51C2×Q8×C37—22no—
52C2×Q8×C37—81no—
53C22×C4×C37—21no—
54C22×C4×C37—21no—
55C22×C4×C37—21no—
56C22×C4×C37—22no—
57C22×C4×C37—22no—
58C22×C4×C37—21no—
59C22×C4×C37—21no—
60C22×C4×C37—22no—
61C22×C4×C37—21no—
62C22×C4×C37—24no—
63C22×C4×C37—81no—
64C22×C4×C37—81no—
65C22×C4×C37C22⋊C412yes—
66C22×C4×C37C22⋊C412yes—
67C22×C4×C37C22×C411yescharacteristic
68C22×C4×C37C2×D412yes—
69C22×C4×C37C2×D411yescharacteristic
70C22×C4×C37#4112yes—
71C2×C8×C37—42no—
72C2×C8×C37—82no—
73C4⋊C4×C37—24no—
74C4⋊C4×C37—24no—
75C4⋊C4×C37—22no—
76C4⋊C4×C37—42no—
77C4⋊C4×C37—82no—
78C4⋊C4×C37—81no—
79C4⋊C4×C37—82no—
80C22⋊C4×C37—41no—
81C22⋊C4×C37—41no—
82C22⋊C4×C37—42no—
83C22⋊C4×C37—42no—
84C22⋊C4×C37—42no—
85C42×C37—82no—
86C23×C37—41no—
87C23×C37—41no—
88C23×C37C2×C22⋊C411yescharacteristic
89C23×C37#12011yescharacteristic
90C23×C37#12311yescharacteristic
91C23×C37#13512yes—
92C23×C37#13712yes—
93Q8×C37—82no—
94C2×C4×C37—22no—
95C2×C4×C37—22no—
96C2×C4×C37—22no—
97C2×C4×C37—22no—
98C2×C4×C37—41no—
99C2×C4×C37—42no—
100C2×C4×C37—42no—
101C2×C4×C37—41no—
102C2×C4×C37—42no—
103C2×C4×C37—42no—
104C2×C4×C37—42no—
105C2×C4×C37—42no—
106C2×C4×C37—44no—
107C2×C4×C37—42no—
108C2×C4×C37—42no—
109C2×C4×C37—42no—
110C2×C4×C37—44no—
111C2×C4×C37—42no—
112C2×C4×C37—41no—
113C2×C4×C37—41no—
114C2×C4×C37—42no—
115C2×C4×C37—44no—
116C2×C4×C37—81no—
117C2×C4×C37C4×D412yes—
118C2×C4×C37#12112yes—
119C8×C37—82no—
120#9202C3711yesmaximal, characteristic, direct product factor, Sylow
121C22×C37—21no—
122C22×C37—21no—
123C22×C37—21no—
124C22×C37—21no—
125C22×C37—21no—
126C22×C37—21no—
127C22×C37—42no—
128C22×C37—42no—
129C22×C37#38611yescharacteristic
130C22×C37#41611yescharacteristic
131C22×C37#41911yescharacteristic
132C22×C37#45212yes—
133C22×C37#48512yes—
134C4×C37—22no—
135C4×C37—22no—
136C4×C37—42no—
137C4×C37—42no—
138C4×C37—82no—
139C4×C37—84no—
140C4×C37—81no—
141C4×C37—81no—
142#2627C2×C3711yescharacteristic
143#2313C2×C3711yescharacteristic
144#1520C2×C3712yes—
145C2×#324C2×C3711yescharacteristic
146#1289C2×C3712yes—
147C2×C37—21no—
148C2×C37—22no—
149C2×C37—21no—
150C2×C37—22no—
151C2×C37#187311yescharacteristic
152C2×C37#191211yescharacteristic
153C2×C37#191311yescharacteristic
154C2×C22⋊Q8C22×C3711yescharacteristic
155C22×C4⋊C4C22×C3711yescharacteristic
156C2×C22⋊C8C22×C3712yes—
157#400C4×C3712yescomplemented
158#398—22no—
159#395C4×C3712yescomplemented
160#387—24no—
161#385—21no—
162#381—21no—
163#381—21no—
164#380C22×C3711yescharacteristic
165#380C22×C3712yes—
166C4×C22⋊C4—21no—
167#328—24no—
168#324—22no—
169C37#920211yescharacteristic, direct product factor, Sylow
170C22×Q8C2×C4×C3711yescharacteristic
171C23×C4D4×C3711yescharacteristic
172C23×C4D4×C3711yescharacteristic
173C23×C4C23×C3711yescharacteristic
174C22×C8—22no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C3711yescharacteristic
184C2×C4⋊C4C2×C4×C3712yes—
185C2×C4⋊C4D4×C3712yes—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C42—22no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192#95—22no—
193#95—24no—
194#95—22no—
195#95—22no—
196#95—22no—
197#95C2×C4×C3712yes—
198#95D4×C3714yes—
199C24C2×D4×C3711yescharacteristic
200C2×Q8—22no—
201C2×Q8—81no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—24no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4C22⋊C4×C3712yes—
215C22×C4C22⋊C4×C3712yes—
216C22×C4C22×C4×C3711yescharacteristic
217C22×C4C2×D4×C3712yes—
218C22×C4C2×D4×C3711yescharacteristic
219C22×C4#41×C3712yes—
220C2×C8—42no—
221C2×C8—82no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—42no—
226C4⋊C4—82no—
227C4⋊C4—81no—
228C4⋊C4—82no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C42—82no—
235C23—41no—
236C23—41no—
237C23C2×C22⋊C4×C3711yescharacteristic
238C23#120×C3711yescharacteristic
239C23#123×C3711yescharacteristic
240C23#135×C3712yes—
241C23#137×C3712yes—
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—81no—
266C2×C4C4×D4×C3712yes—
267C2×C4#121×C3712yes—
268C8—82no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22C37×#38611yescharacteristic
278C22C37×#41611yescharacteristic
279C22C37×#41911yescharacteristic
280C22C37×#45212yes—
281C22C37×#48512yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—82no—
287C4—84no—
288C4—81no—
289C4—81no—
290C2—21no—
291C2—22no—
292C2—21no—
293C2—22no—
294C2C37×#187311yescharacteristic
295C2C37×#191211yescharacteristic
296C2C37×#191311yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC24×C37C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
9. C37×#400C4semidirect
11. C37×#395C4semidirect
120. #9202C37direct (N × H)
157. #400C4×C37semidirect
159. #395C4×C37semidirect
169. C37#9202direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#26272
C37×#23132
C37×#15202
C2×C37×#3242
C37×#12892
#920237