Finite Group Databasebeta

← C2×C37×#1386 #22633819

Subgroups — C2×C37×#1386 #22633819

Order 9472.

630 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
1C22×M32×C37C211yesmaximal, characteristic
2C2×C37×#427C211yesmaximal, characteristic
3C22×#106×C37C211yesmaximal, characteristic
4C37×#1386C214yesmaximal, direct product factor
5C23×C8×C37C2211yescharacteristic
6C2×#117×C37—21no—
7C22×C4⋊C4×C37—21no—
8C2×M32×C37—22no—
9C2×M32×C37—21no—
10C2×M32×C37C414yescomplemented
11C2×M32×C37C2212yes—
12C22×C16×C37—21no—
13C37×#427—21no—
14C37×#427—21no—
15C37×#427C412yescomplemented
16C37×#427C2212yes—
17C2×#107×C37C412yescomplemented
18C2×#106×C37—21no—
19C2×#106×C37—22no—
20C2×#106×C37—21no—
21C2×#106×C37C414yescomplemented
22C2×#106×C37C2212yes—
23C23×C4×C37—41no—
24C23×C4×C37D411yescharacteristic
25C22×C8×C37C2×C412yes—
26C22×C8×C37C2×C412yes—
27C22×C8×C37C2×C411yescharacteristic
28C22×C8×C37C2×C411yescharacteristic
29C22×C8×C37D411yescharacteristic
30C22×C8×C37D411yescharacteristic
31C22×C8×C37D412yes—
32C22×C8×C37D411yescharacteristic
33C22×C8×C37Q812yes—
34C22×C8×C37C2311yescharacteristic
35#117×C37—22no—
36#117×C37—22no—
37#117×C37—41no—
38#117×C37—41no—
39C2×C4⋊C4×C37—24no—
40C2×C4⋊C4×C37—22no—
41C2×C4⋊C4×C37—22no—
42C2×C4⋊C4×C37—41no—
43C2×C4⋊C4×C37—42no—
44C2×C22⋊C4×C37—41no—
45C2×C42×C37—41no—
46M32×C37—24no—
47M32×C37—22no—
48M32×C37C2×C414yescomplemented
49C2×C16×C37—24no—
50C2×C16×C37—22no—
51#107×C37—22no—
52#107×C37C2×C414yescomplemented
53#106×C37—24no—
54#106×C37—22no—
55#106×C37—22no—
56#106×C37—22no—
57#106×C37C2×C414yescomplemented
58C24×C37D811yescharacteristic
59C22×C4×C37—44no—
60C22×C4×C37—42no—
61C22×C4×C37—42no—
62C22×C4×C37—84no—
63C22×C4×C37C22⋊C412yes—
64C22×C4×C37C22⋊C411yescharacteristic
65C22×C4×C37C22⋊C411yescharacteristic
66C22×C4×C37C4⋊C412yes—
67C22×C4×C37D811yescharacteristic
68C22×C4×C37SD1612yes—
69C22×C4×C37SD1611yescharacteristic
70C22×C4×C37SD1611yescharacteristic
71C22×C4×C37Q1612yes—
72C22×C4×C37C2×D411yescharacteristic
73C2×C8×C37C4212yes—
74C2×C8×C37C4212yes—
75C2×C8×C37C22⋊C412yes—
76C2×C8×C37C22⋊C411yescharacteristic
77C2×C8×C37C22⋊C411yescharacteristic
78C2×C8×C37C22⋊C412yes—
79C2×C8×C37C22⋊C412yes—
80C2×C8×C37C4⋊C412yes—
81C2×C8×C37C4⋊C412yes—
82C2×C8×C37C4⋊C412yes—
83C2×C8×C37C4⋊C412yes—
84C2×C8×C37C4⋊C412yes—
85C2×C8×C37C22×C411yescharacteristic
86C2×C8×C37C22×C411yescharacteristic
87C2×C8×C37C22×C411yescharacteristic
88C2×C8×C37C2×D411yescharacteristic
89C2×C8×C37C2×D411yescharacteristic
90C2×C8×C37C2×Q811yescharacteristic
91C4⋊C4×C37—24no—
92C4⋊C4×C37—24no—
93C4⋊C4×C37—44no—
94C4⋊C4×C37—42no—
95C4⋊C4×C37—42no—
96C22⋊C4×C37—42no—
97C22⋊C4×C37—42no—
98C42×C37—42no—
99C42×C37—42no—
100C16×C37—24no—
101C23×C37—24no—
102C23×C37#10211yescharacteristic
103C23×C37#10212yes—
104C23×C37#10211yescharacteristic
105C23×C37#10712yes—
106C23×C37C2×D811yescharacteristic
107C2×C4×C37—44no—
108C2×C4×C37—44no—
109C2×C4×C37—84no—
110C2×C4×C37—88no—
111C2×C4×C37—84no—
112C2×C4×C37#9512yes—
113C2×C4×C37#9512yes—
114C2×C4×C37#10211yescharacteristic
115C2×C4×C37#10212yes—
116C2×C4×C37#10211yescharacteristic
117C2×C4×C37#10312yes—
118C2×C4×C37#10312yes—
119C2×C4×C37#10312yes—
120C2×C4×C37#10312yes—
121C2×C4×C37#10612yes—
122C2×C4×C37#10612yes—
123C2×C4×C37#10712yes—
124C2×C4×C37C2×C22⋊C411yescharacteristic
125C2×C4×C37C2×C22⋊C411yescharacteristic
126C2×C4×C37C2×C4⋊C411yescharacteristic
127C2×C4×C37C2×SD1611yescharacteristic
128C2×C4×C37C2×SD1611yescharacteristic
129C2×C4×C37C2×Q1611yescharacteristic
130C8×C37#9512yes—
131C8×C37#9512yes—
132C8×C37C2×C4211yescharacteristic
133C8×C37C2×C22⋊C411yescharacteristic
134C8×C37C2×C4⋊C411yescharacteristic
135C8×C37C2×C4⋊C411yescharacteristic
136C2×#1386C3711yesmaximal, characteristic, direct product factor, Sylow
137C22×C37—22no—
138C22×C37—22no—
139C22×C37—24no—
140C22×C37—24no—
141C22×C37#34012yes—
142C22×C37#34012yes—
143C22×C37#36014yes—
144C22×C37C2×#10211yescharacteristic
145C22×C37C2×#10211yescharacteristic
146C22×C37C2×#10711yescharacteristic
147C4×C37—84no—
148C4×C37—84no—
149C4×C37#34012yes—
150C4×C37#34012yes—
151C4×C37C2×#9511yescharacteristic
152C4×C37C2×#10311yescharacteristic
153C4×C37C2×#10311yescharacteristic
154C4×C37C2×#10611yescharacteristic
155C22×M32C2×C3711yescharacteristic
156C2×#427C2×C3711yescharacteristic
157C22×#106C2×C3711yescharacteristic
158#1386C2×C3714yesdirect product factor
159C2×C37—21no—
160C2×C37—22no—
161C2×C37—21no—
162C2×C37#138614yesdirect product factor
163C2×C37C2×#34011yescharacteristic
164C2×C37C2×#36012yes—
165C23×C8C22×C3711yescharacteristic
166C2×#117—21no—
167C22×C4⋊C4—21no—
168C2×M32—22no—
169C2×M32—21no—
170C2×M32C4×C3714yescomplemented
171C2×M32C22×C3712yes—
172C22×C16—21no—
173#427—21no—
174#427—21no—
175#427C4×C3712yescomplemented
176#427C22×C3712yes—
177C2×#107C4×C3712yescomplemented
178C2×#106—21no—
179C2×#106—22no—
180C2×#106—21no—
181C2×#106C4×C3714yescomplemented
182C2×#106C22×C3712yes—
183C37C2×#138611yescharacteristic, direct product factor, Sylow
184C23×C4—41no—
185C23×C4D4×C3711yescharacteristic
186C22×C8C2×C4×C3712yes—
187C22×C8C2×C4×C3712yes—
188C22×C8C2×C4×C3711yescharacteristic
189C22×C8C2×C4×C3711yescharacteristic
190C22×C8D4×C3711yescharacteristic
191C22×C8D4×C3711yescharacteristic
192C22×C8D4×C3712yes—
193C22×C8D4×C3711yescharacteristic
194C22×C8Q8×C3712yes—
195C22×C8C23×C3711yescharacteristic
196#117—22no—
197#117—22no—
198#117—41no—
199#117—41no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—42no—
205C2×C22⋊C4—41no—
206C2×C42—41no—
207M32—24no—
208M32—22no—
209M32C2×C4×C3714yescomplemented
210C2×C16—24no—
211C2×C16—22no—
212#107—22no—
213#107C2×C4×C3714yescomplemented
214#106—24no—
215#106—22no—
216#106—22no—
217#106—22no—
218#106C2×C4×C3714yescomplemented
219C24D8×C3711yescharacteristic
220C22×C4—42no—
221C22×C4—44no—
222C22×C4—42no—
223C22×C4—84no—
224C22×C4C22⋊C4×C3712yes—
225C22×C4C22⋊C4×C3711yescharacteristic
226C22×C4C22⋊C4×C3711yescharacteristic
227C22×C4C4⋊C4×C3712yes—
228C22×C4D8×C3711yescharacteristic
229C22×C4SD16×C3711yescharacteristic
230C22×C4SD16×C3712yes—
231C22×C4SD16×C3711yescharacteristic
232C22×C4Q16×C3712yes—
233C22×C4C2×D4×C3711yescharacteristic
234C2×C8C42×C3712yes—
235C2×C8C42×C3712yes—
236C2×C8C22⋊C4×C3712yes—
237C2×C8C22⋊C4×C3711yescharacteristic
238C2×C8C22⋊C4×C3711yescharacteristic
239C2×C8C22⋊C4×C3712yes—
240C2×C8C22⋊C4×C3712yes—
241C2×C8C4⋊C4×C3712yes—
242C2×C8C4⋊C4×C3712yes—
243C2×C8C4⋊C4×C3712yes—
244C2×C8C4⋊C4×C3712yes—
245C2×C8C4⋊C4×C3712yes—
246C2×C8C22×C4×C3711yescharacteristic
247C2×C8C22×C4×C3711yescharacteristic
248C2×C8C22×C4×C3711yescharacteristic
249C2×C8C2×D4×C3711yescharacteristic
250C2×C8C2×D4×C3711yescharacteristic
251C2×C8C2×Q8×C3711yescharacteristic
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C42—42no—
260C42—42no—
261C16—24no—
262C23—24no—
263C23#102×C3711yescharacteristic
264C23#102×C3712yes—
265C23#102×C3711yescharacteristic
266C23#107×C3712yes—
267C23C2×D8×C3711yescharacteristic
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—84no—
271C2×C4—88no—
272C2×C4—84no—
273C2×C4#95×C3712yes—
274C2×C4#95×C3712yes—
275C2×C4#102×C3711yescharacteristic
276C2×C4#102×C3712yes—
277C2×C4#102×C3711yescharacteristic
278C2×C4#103×C3712yes—
279C2×C4#103×C3712yes—
280C2×C4#103×C3712yes—
281C2×C4#103×C3712yes—
282C2×C4#106×C3712yes—
283C2×C4#106×C3712yes—
284C2×C4#107×C3712yes—
285C2×C4C2×C22⋊C4×C3711yescharacteristic
286C2×C4C2×C22⋊C4×C3711yescharacteristic
287C2×C4C2×C4⋊C4×C3711yescharacteristic
288C2×C4C2×SD16×C3711yescharacteristic
289C2×C4C2×SD16×C3711yescharacteristic
290C2×C4C2×Q16×C3711yescharacteristic
291C8#95×C3712yes—
292C8#95×C3712yes—
293C8C2×C42×C3711yescharacteristic
294C8C2×C22⋊C4×C3711yescharacteristic
295C8C2×C4⋊C4×C3711yescharacteristic
296C8C2×C4⋊C4×C3711yescharacteristic
297C22—22no—
298C22—22no—
299C22—24no—
300C22—24no—
301C22C37×#34012yes—
302C22C37×#34012yes—
303C22C37×#36014yes—
304C22C2×#102×C3711yescharacteristic
305C22C2×#102×C3711yescharacteristic
306C22C2×#107×C3711yescharacteristic
307C4—84no—
308C4—84no—
309C4C37×#34012yes—
310C4C37×#34012yes—
311C4C2×#95×C3711yescharacteristic
312C4C2×#103×C3711yescharacteristic
313C4C2×#103×C3711yescharacteristic
314C4C2×#106×C3711yescharacteristic
315C2—21no—
316C2—22no—
317C2—21no—
318C2C37×#138614yesdirect product factor
319C2C2×C37×#34011yescharacteristic
320C2C2×C37×#36012yes—
subgroupG/H
center, socleC23×C37#102
commutatorC8C2×C42×C37
Frattini, cosocleC22×C8C23×C37
prime radicalC24×C37D8
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C23×C4×C37 ◁ C23×C8×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1386C2direct (N × H)
10. C2×M32×C37C4semidirect
15. C37×#427C4semidirect
17. C2×#107×C37C4semidirect
21. C2×#106×C37C4semidirect
48. M32×C37C2×C4semidirect
52. #107×C37C2×C4semidirect
57. #106×C37C2×C4semidirect
136. C2×#1386C37direct (N × H)
158. #1386C2×C37direct (N × H)
162. C2×C37#1386direct (N × H)
170. C2×M32C4×C37semidirect
175. #427C4×C37semidirect
177. C2×#107C4×C37semidirect
181. C2×#106C4×C37semidirect
183. C37C2×#1386direct (N × H)
209. M32C2×C4×C37semidirect
213. #107C2×C4×C37semidirect
218. #106C2×C4×C37semidirect
318. C2C37×#1386direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M32×C372
C2×C37×#4272
C22×#106×C372
C37×#13862
C2×#138637