Finite Group Databasebeta

← C37×#36691 #22657944

Subgroups — C37×#36691 #22657944

Order 9472.

1474 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2845C212yesmaximal, complemented
2C37×#2844C212yesmaximal, complemented
3C37×#2843C214yesmaximal, complemented
4C37×#2841C218yesmaximal
5C37×#2402C214yesmaximal, complemented
6C37×#2399C214yesmaximal, complemented
7C37×#2396C214yesmaximal
8C37×#2285C211yesmaximal, characteristic
9C37×#2283C212yesmaximal
10C2×C4×Q8×C37C2214yes—
11C2×#117×C37C2212yes—
12C22×C42×C37C2211yescharacteristic
13C37×#400C2214yes—
14C37×#400C2218yes—
15C37×#400C2218yes—
16C37×#399C2214yes—
17C37×#398C2218yes—
18C37×#398C2218yes—
19C37×#398C2218yes—
20C37×#398C2218yes—
21C37×#398C2218yes—
22C37×#396C2218yes—
23C37×#395C2214yes—
24C37×#395C2218yes—
25C37×#395C2218yes—
26C37×#393C2214yes—
27C37×#384C2212yes—
28C37×#383C2214yes—
29C37×#382C2214yes—
30C37×#382C2211yescharacteristic
31C37×#382C2211yescharacteristic
32C37×#381C2214yes—
33C37×#380C2214yes—
34C37×#380C2214yes—
35C4×C4⋊C4×C37C2218yes—
36C4×C4⋊C4×C37C2214yes—
37C4×C4⋊C4×C37C2212yes—
38C4×C4⋊C4×C37C2214yes—
39C4×C4⋊C4×C37C2212yes—
40C4×C22⋊C4×C37C2214yes—
41C37×#376C2214yes—
42C22×Q8×C37C2314yes—
43C23×C4×C37C2311yescharacteristic
44C23×C4×C37C2312yes—
45C4×Q8×C37—48no—
46#117×C37—44no—
47C2×C4⋊C4×C37C2314yes—
48C2×C4⋊C4×C37C2314yes—
49C2×C4⋊C4×C37C2318yes—
50C2×C4⋊C4×C37C2318yes—
51C2×C4⋊C4×C37C2318yes—
52C2×C4⋊C4×C37C2318yes—
53C2×C4⋊C4×C37C2312yes—
54C2×C4⋊C4×C37C2312yes—
55C2×C4⋊C4×C37C2314yes—
56C2×C4⋊C4×C37C2318yes—
57C2×C22⋊C4×C37C2318yes—
58C2×C22⋊C4×C37C2314yes—
59C2×C42×C37Q818yescomplemented
60C2×C42×C37C2314yes—
61C2×C42×C37C2314yes—
62C2×C42×C37C2314yes—
63C2×C42×C37C2311yescharacteristic
64C2×C42×C37C2311yescharacteristic
65C2×C42×C37C2312yes—
66#95×C37C2318yes—
67#95×C37C2318yes—
68#95×C37C2318yes—
69#95×C37C2314yes—
70#95×C37C2314yes—
71#95×C37C2314yes—
72#95×C37C2314yes—
73#95×C37C2318yes—
74#95×C37C2314yes—
75#95×C37C2318yes—
76#95×C37C2314yes—
77C24×C37C2411yescharacteristic
78C2×Q8×C37—44no—
79C2×Q8×C37—48no—
80C22×C4×C37—22no—
81C22×C4×C37—22no—
82C22×C4×C37—44no—
83C22×C4×C37C2×Q814yes—
84C22×C4×C37C2×Q818yes—
85C22×C4×C37C2418yes—
86C22×C4×C37C2414yes—
87C22×C4×C37C2418yes—
88C22×C4×C37C2414yes—
89C22×C4×C37C2411yescharacteristic
90C22×C4×C37C2412yes—
91C22×C4×C37C2412yes—
92C22×C4×C37C2411yescharacteristic
93C4⋊C4×C37—44no—
94C4⋊C4×C37—48no—
95C4⋊C4×C37—44no—
96C4⋊C4×C37—48no—
97C4⋊C4×C37—48no—
98C4⋊C4×C37—48no—
99C4⋊C4×C37—42no—
100C4⋊C4×C37—42no—
101C4⋊C4×C37—48no—
102C4⋊C4×C37—44no—
103C22⋊C4×C37—48no—
104C22⋊C4×C37—44no—
105C42×C37—28no—
106C42×C37—28no—
107C42×C37—28no—
108C42×C37C2×Q814yes—
109C42×C37C2×Q814yes—
110C42×C37C2×Q818yes—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—24no—
114C23×C37C22×Q812yes—
115C23×C37C2511yescharacteristic
116Q8×C37—416no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—24no—
120C2×C4×C37—24no—
121C2×C4×C37—28no—
122C2×C4×C37—24no—
123C2×C4×C37—24no—
124C2×C4×C37—28no—
125C2×C4×C37—28no—
126C2×C4×C37—28no—
127C2×C4×C37—28no—
128C2×C4×C37—28no—
129C2×C4×C37—28no—
130C2×C4×C37—28no—
131C2×C4×C37—28no—
132C2×C4×C37—48no—
133C2×C4×C37C22×Q812yes—
134C2×C4×C37C22×Q814yes—
135C2×C4×C37C22×Q814yes—
136C2×C4×C37C22×Q812yes—
137C2×C4×C37H(5,𝔽2)12yes—
138C2×C4×C372−1+412yes—
139#36691C3711yesmaximal, characteristic, direct product factor, Sylow
140C22×C37—22no—
141C22×C37—24no—
142C22×C37—42no—
143C22×C37—42no—
144C22×C37C23×Q811yescharacteristic
145C22×C37C2×H(5,𝔽2)11yescharacteristic
146C22×C37C2×2−1+411yescharacteristic
147C22×C37#58514yes—
148C4×C37—22no—
149C4×C37—24no—
150C4×C37—24no—
151C4×C37—44no—
152C4×C37—44no—
153C4×C37—48no—
154C4×C37—48no—
155C4×C37#54414yes—
156#2845C2×C3712yescomplemented
157#2844C2×C3712yescomplemented
158#2843C2×C3714yescomplemented
159#2841C2×C3718yes—
160#2402C2×C3714yescomplemented
161#2399C2×C3714yescomplemented
162#2396C2×C3714yes—
163#2285C2×C3711yescharacteristic
164#2283C2×C3712yes—
165C2×C37—42no—
166C2×C37C2×#54411yescharacteristic
167C2×C37#345812yes—
168C2×C37#352912yes—
169C2×C37#353112yes—
170C2×C4×Q8C22×C3714yes—
171C2×#117C22×C3712yes—
172C22×C42C22×C3711yescharacteristic
173#400C22×C3718yes—
174#400C22×C3718yes—
175#400C22×C3714yes—
176#399C22×C3714yes—
177#398C22×C3718yes—
178#398C22×C3718yes—
179#398C22×C3718yes—
180#398C22×C3718yes—
181#398C22×C3718yes—
182#396C22×C3718yes—
183#395C22×C3718yes—
184#395C22×C3718yes—
185#395C22×C3714yes—
186#393C22×C3714yes—
187#384C22×C3712yes—
188#383C22×C3714yes—
189#382C22×C3711yescharacteristic
190#382C22×C3714yes—
191#382C22×C3711yescharacteristic
192#381C22×C3714yes—
193#380C22×C3714yes—
194#380C22×C3714yes—
195C4×C4⋊C4C22×C3718yes—
196C4×C4⋊C4C22×C3714yes—
197C4×C4⋊C4C22×C3712yes—
198C4×C4⋊C4C22×C3714yes—
199C4×C4⋊C4C22×C3712yes—
200C4×C22⋊C4C22×C3714yes—
201#376C22×C3714yes—
202C37#3669111yescharacteristic, direct product factor, Sylow
203C22×Q8C23×C3714yes—
204C23×C4C23×C3711yescharacteristic
205C23×C4C23×C3712yes—
206C4×Q8—48no—
207#117—44no—
208C2×C4⋊C4C23×C3712yes—
209C2×C4⋊C4C23×C3712yes—
210C2×C4⋊C4C23×C3714yes—
211C2×C4⋊C4C23×C3718yes—
212C2×C4⋊C4C23×C3714yes—
213C2×C4⋊C4C23×C3714yes—
214C2×C4⋊C4C23×C3718yes—
215C2×C4⋊C4C23×C3718yes—
216C2×C4⋊C4C23×C3718yes—
217C2×C4⋊C4C23×C3718yes—
218C2×C22⋊C4C23×C3714yes—
219C2×C22⋊C4C23×C3718yes—
220C2×C42Q8×C3718yescomplemented
221C2×C42C23×C3714yes—
222C2×C42C23×C3714yes—
223C2×C42C23×C3714yes—
224C2×C42C23×C3712yes—
225C2×C42C23×C3711yescharacteristic
226C2×C42C23×C3711yescharacteristic
227#95C23×C3718yes—
228#95C23×C3718yes—
229#95C23×C3718yes—
230#95C23×C3714yes—
231#95C23×C3714yes—
232#95C23×C3714yes—
233#95C23×C3714yes—
234#95C23×C3718yes—
235#95C23×C3714yes—
236#95C23×C3718yes—
237#95C23×C3714yes—
238C24C24×C3711yescharacteristic
239C2×Q8—44no—
240C2×Q8—48no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—44no—
244C22×C4C2×Q8×C3714yes—
245C22×C4C2×Q8×C3718yes—
246C22×C4C24×C3718yes—
247C22×C4C24×C3714yes—
248C22×C4C24×C3718yes—
249C22×C4C24×C3714yes—
250C22×C4C24×C3711yescharacteristic
251C22×C4C24×C3712yes—
252C22×C4C24×C3712yes—
253C22×C4C24×C3711yescharacteristic
254C4⋊C4—44no—
255C4⋊C4—48no—
256C4⋊C4—44no—
257C4⋊C4—48no—
258C4⋊C4—48no—
259C4⋊C4—48no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—48no—
263C4⋊C4—44no—
264C22⋊C4—48no—
265C22⋊C4—44no—
266C42—28no—
267C42—28no—
268C42—28no—
269C42C2×Q8×C3714yes—
270C42C2×Q8×C3714yes—
271C42C2×Q8×C3718yes—
272C23—21no—
273C23—21no—
274C23—24no—
275C23C22×Q8×C3712yes—
276C23C25×C3711yescharacteristic
277Q8—416no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—28no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—28no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—48no—
294C2×C4C22×Q8×C3712yes—
295C2×C4C22×Q8×C3714yes—
296C2×C4C22×Q8×C3714yes—
297C2×C4C22×Q8×C3712yes—
298C2×C4H(5,𝔽2)×C3712yes—
299C2×C42−1+4×C3712yes—
300C22—22no—
301C22—24no—
302C22—42no—
303C22—42no—
304C22C23×Q8×C3711yescharacteristic
305C22C2×H(5,𝔽2)×C3711yescharacteristic
306C22C2×2−1+4×C3711yescharacteristic
307C22C37×#58514yes—
308C4—22no—
309C4—24no—
310C4—24no—
311C4—44no—
312C4—48no—
313C4—44no—
314C4—48no—
315C4C37×#54414yes—
316C2—42no—
317C2C2×C37×#54411yescharacteristic
318C2C37×#345812yes—
319C2C37×#352912yes—
320C2C37×#353112yes—
subgroupG/H
centerC22×C4×C37C24
commutator, Frattini, cosocleC23C25×C37
socleC23×C37C25
prime radicalC24×C37C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#2845C2semidirect
2. C37×#2844C2semidirect
3. C37×#2843C2semidirect
5. C37×#2402C2semidirect
6. C37×#2399C2semidirect
59. C2×C42×C37Q8semidirect
139. #36691C37direct (N × H)
156. #2845C2×C37semidirect
157. #2844C2×C37semidirect
158. #2843C2×C37semidirect
160. #2402C2×C37semidirect
161. #2399C2×C37semidirect
202. C37#36691direct (N × H)
220. C2×C42Q8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#28452
C37×#28442
C37×#28432
C37×#28412
C37×#24022
C37×#23992
C37×#23962
C37×#22852
C37×#22832
#3669137