Finite Group Databasebeta

← C37×#20532 #22641785

Subgroups — C37×#20532 #22641785

Order 9472.

1106 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#408C212yesmaximal
2C37×#2297C211yesmaximal, characteristic
3C37×#1753C214yesmaximal, complemented
4C37×#1752C214yesmaximal, complemented
5C37×#1750C212yesmaximal, complemented
6C37×#1749C212yesmaximal, complemented
7C22×#41×C37C2211yescharacteristic
8C22×M16×C37C2212yes—
9C23×C8×C37C2212yes—
10C2×#117×C37C2211yescharacteristic
11C22×C42×C37C2211yescharacteristic
12C37×#408C4116yescomplemented
13C2×C22⋊C8×C37C2214yes—
14C2×C22⋊C8×C37C2214yes—
15C2×#97×C37C2214yes—
16C2×#97×C37C2212yes—
17C2×C4×C8×C37C2212yes—
18C37×#391C412yes—
19C37×#390C412yes—
20C37×#386C414yes—
21C4×C22⋊C4×C37C2214yes—
22C37×#336C2212yes—
23C37×#336C2212yes—
24C37×#336C2214yes—
25C2×#41×C37—42no—
26C2×#41×C37—41no—
27C2×#41×C37—41no—
28C2×#41×C37C2×C418yes—
29C22×Q8×C37C2×C411yescharacteristic
30C22×D4×C37C2×C412yes—
31C22×D4×C37C2×C411yescharacteristic
32C23×C4×C37C2×C412yes—
33C23×C4×C37C2312yes—
34C23×C4×C37C2311yescharacteristic
35C2×M16×C37—42no—
36C2×M16×C37—42no—
37C2×M16×C37C2×C418yescomplemented
38C22×C8×C37—42no—
39C22×C8×C37—42no—
40C22×C8×C37C2×C418yescomplemented
41C22×C8×C37C2314yes—
42C22×C8×C37C2314yes—
43#117×C37—41no—
44#117×C37—41no—
45C2×C4⋊C4×C37C2×C412yes—
46C2×C22⋊C4×C37C2×C418yes—
47C2×C22⋊C4×C37C2×C412yes—
48C2×C42×C37—42no—
49C2×C42×C37C2×C412yes—
50C2×C42×C37C2312yes—
51C2×C42×C37C2312yes—
52C22⋊C8×C37C2×C4116yes—
53C22⋊C8×C37C2×C4116yescomplemented
54#97×C37—44no—
55#97×C37—42no—
56C4×C8×C37—42no—
57#95×C37C2×C418yes—
58C24×C37C22×C412yes—
59C24×C37C22×C411yescharacteristic
60#41×C37—48no—
61#41×C37—48no—
62C2×Q8×C37—41no—
63C2×Q8×C37—41no—
64C2×Q8×C37C4214yes—
65C2×D4×C37—41no—
66C2×D4×C37—41no—
67C2×D4×C37—42no—
68C2×D4×C37—42no—
69C2×D4×C37C4218yes—
70C2×D4×C37C4214yes—
71C22×C4×C37—22no—
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37—22no—
75C22×C4×C37—22no—
76C22×C4×C37—22no—
77C22×C4×C37—22no—
78C22×C4×C37—42no—
79C22×C4×C37—44no—
80C22×C4×C37C22×C414yes—
81C22×C4×C37C22×C414yes—
82C22×C4×C37C22×C412yes—
83C22×C4×C37C22×C411yescharacteristic
84C22×C4×C37C22×C414yes—
85C22×C4×C37C22×C414yes—
86C22×C4×C37C22×C414yes—
87C22×C4×C37C2411yescharacteristic
88M16×C37—48no—
89C2×C8×C37—24no—
90C2×C8×C37—24no—
91C2×C8×C37—24no—
92C2×C8×C37—24no—
93C2×C8×C37—48no—
94C2×C8×C37C22×C418yes—
95C2×C8×C37C22×C418yes—
96C4⋊C4×C37—42no—
97C22⋊C4×C37—48no—
98C22⋊C4×C37—42no—
99C42×C37—22no—
100C42×C37—24no—
101C42×C37—22no—
102C42×C37—42no—
103C23×C37—21no—
104C23×C37—21no—
105C23×C37—22no—
106C23×C37—22no—
107C23×C37—28no—
108C23×C37—24no—
109C23×C37C2×C4212yes—
110C23×C37C2×C4214yes—
111C23×C37C23×C411yescharacteristic
112Q8×C37—44no—
113D4×C37—44no—
114D4×C37—48no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—22no—
118C2×C4×C37—22no—
119C2×C4×C37—24no—
120C2×C4×C37—24no—
121C2×C4×C37—24no—
122C2×C4×C37—24no—
123C2×C4×C37—24no—
124C2×C4×C37—24no—
125C2×C4×C37—24no—
126C2×C4×C37—24no—
127C2×C4×C37—24no—
128C2×C4×C37—28no—
129C2×C4×C37—24no—
130C2×C4×C37—48no—
131C2×C4×C37C2×C4214yes—
132C2×C4×C37C2×C4212yes—
133C2×C4×C37C23×C412yes—
134C2×C4×C37H(5,𝔽2)12yes—
135C2×C4×C37H(5,𝔽2)11yescharacteristic
136C2×C4×C37H(5,𝔽2)11yescharacteristic
137C8×C37—28no—
138C8×C37—28no—
139#20532C3711yesmaximal, characteristic, direct product factor, Sylow
140C22×C37—28no—
141C22×C37—24no—
142C22×C37—24no—
143C22×C37—22no—
144C22×C37—42no—
145C22×C37—44no—
146C22×C37—42no—
147C22×C37—44no—
148C22×C37C22×C4211yescharacteristic
149C22×C37#51811yescharacteristic
150C22×C37#51811yescharacteristic
151C22×C37#56814yes—
152C4×C37—22no—
153C4×C37—24no—
154C4×C37—44no—
155C4×C37—44no—
156C4×C37#51812yes—
157C4×C37#51812yes—
158C2×#408C2×C3712yes—
159#2297C2×C3711yescharacteristic
160#1753C2×C3714yescomplemented
161#1752C2×C3714yescomplemented
162#1750C2×C3712yescomplemented
163#1749C2×C3712yescomplemented
164C2×C37—42no—
165C2×C37—44no—
166C2×C37#227311yescharacteristic
167C2×C37#287512yes—
168C2×C37#297812yes—
169C2×C37#298012yes—
170C22×#41C22×C3711yescharacteristic
171C22×M16C22×C3712yes—
172C23×C8C22×C3712yes—
173C2×#117C22×C3711yescharacteristic
174C22×C42C22×C3711yescharacteristic
175#408C4×C37116yescomplemented
176C2×C22⋊C8C22×C3714yes—
177C2×C22⋊C8C22×C3714yes—
178C2×#97C22×C3714yes—
179C2×#97C22×C3712yes—
180C2×C4×C8C22×C3712yes—
181#391C4×C3712yes—
182#390C4×C3712yes—
183#386C4×C3714yes—
184C4×C22⋊C4C22×C3714yes—
185#336C22×C3712yes—
186#336C22×C3712yes—
187#336C22×C3714yes—
188C37#2053211yescharacteristic, direct product factor, Sylow
189C2×#41—42no—
190C2×#41—41no—
191C2×#41—41no—
192C2×#41C2×C4×C3718yes—
193C22×Q8C2×C4×C3711yescharacteristic
194C22×D4C2×C4×C3712yes—
195C22×D4C2×C4×C3711yescharacteristic
196C23×C4C2×C4×C3712yes—
197C23×C4C23×C3711yescharacteristic
198C23×C4C23×C3712yes—
199C2×M16—42no—
200C2×M16—42no—
201C2×M16C2×C4×C3718yescomplemented
202C22×C8—42no—
203C22×C8—42no—
204C22×C8C2×C4×C3718yescomplemented
205C22×C8C23×C3714yes—
206C22×C8C23×C3714yes—
207#117—41no—
208#117—41no—
209C2×C4⋊C4C2×C4×C3712yes—
210C2×C22⋊C4C2×C4×C3712yes—
211C2×C22⋊C4C2×C4×C3718yes—
212C2×C42—42no—
213C2×C42C2×C4×C3712yes—
214C2×C42C23×C3712yes—
215C2×C42C23×C3712yes—
216C22⋊C8C2×C4×C37116yes—
217C22⋊C8C2×C4×C37116yescomplemented
218#97—44no—
219#97—42no—
220C4×C8—42no—
221#95C2×C4×C3718yes—
222C24C22×C4×C3712yes—
223C24C22×C4×C3711yescharacteristic
224#41—48no—
225#41—48no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8C42×C3714yes—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—42no—
232C2×D4—42no—
233C2×D4C42×C3718yes—
234C2×D4C42×C3714yes—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—44no—
244C22×C4C22×C4×C3714yes—
245C22×C4C22×C4×C3714yes—
246C22×C4C22×C4×C3712yes—
247C22×C4C22×C4×C3711yescharacteristic
248C22×C4C22×C4×C3714yes—
249C22×C4C22×C4×C3714yes—
250C22×C4C22×C4×C3714yes—
251C22×C4C24×C3711yescharacteristic
252M16—48no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8—24no—
256C2×C8—24no—
257C2×C8—48no—
258C2×C8C22×C4×C3718yes—
259C2×C8C22×C4×C3718yes—
260C4⋊C4—42no—
261C22⋊C4—48no—
262C22⋊C4—42no—
263C42—22no—
264C42—24no—
265C42—22no—
266C42—42no—
267C23—28no—
268C23—24no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—22no—
273C23C2×C42×C3712yes—
274C23C2×C42×C3714yes—
275C23C23×C4×C3711yescharacteristic
276Q8—44no—
277D4—44no—
278D4—48no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—28no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—48no—
295C2×C4C2×C42×C3714yes—
296C2×C4C2×C42×C3712yes—
297C2×C4C23×C4×C3712yes—
298C2×C4H(5,𝔽2)×C3712yes—
299C2×C4H(5,𝔽2)×C3711yescharacteristic
300C2×C4H(5,𝔽2)×C3711yescharacteristic
301C8—28no—
302C8—28no—
303C22—28no—
304C22—24no—
305C22—24no—
306C22—22no—
307C22—42no—
308C22—44no—
309C22—44no—
310C22—42no—
311C22C22×C42×C3711yescharacteristic
312C22C37×#51811yescharacteristic
313C22C37×#51811yescharacteristic
314C22C37×#56814yes—
315C4—22no—
316C4—24no—
317C4—44no—
318C4—44no—
319C4C37×#51812yes—
320C4C37×#51812yes—
321C2—42no—
322C2—44no—
323C2C37×#227311yescharacteristic
324C2C37×#287512yes—
325C2C37×#297812yes—
326C2C37×#298012yes—
subgroupG/H
centerC22×C4×C37C24
commutatorC22C22×C42×C37
Frattini, cosocleC22×C4C24×C37
socleC23×C37C23×C4
prime radicalC22×#41×C37C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1753C2semidirect
4. C37×#1752C2semidirect
5. C37×#1750C2semidirect
6. C37×#1749C2semidirect
12. C37×#408C4semidirect
37. C2×M16×C37C2×C4semidirect
40. C22×C8×C37C2×C4semidirect
53. C22⋊C8×C37C2×C4semidirect
139. #20532C37direct (N × H)
160. #1753C2×C37semidirect
161. #1752C2×C37semidirect
162. #1750C2×C37semidirect
163. #1749C2×C37semidirect
175. #408C4×C37semidirect
188. C37#20532direct (N × H)
201. C2×M16C2×C4×C37semidirect
204. C22×C8C2×C4×C37semidirect
217. C22⋊C8C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4082
C37×#22972
C37×#17532
C37×#17522
C37×#17502
C37×#17492
#2053237