Finite Group Databasebeta

← C37×#21989 #22643242

Subgroups — C37×#21989 #22643242

Order 9472.

786 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×#432C211yesmaximal, characteristic
2C37×#2285C211yesmaximal, characteristic
3C37×#2283C211yesmaximal, characteristic
4C37×#1949C214yesmaximal, complemented
5C37×#1854C214yesmaximal
6C37×#1847C212yesmaximal, complemented
7C37×#1836C212yesmaximal, complemented
8C2×#117×C37C2212yes—
9C22×C42×C37C2211yescharacteristic
10C37×#432C418yescomplemented
11C2×#107×C37C2214yes—
12C2×#106×C37C2214yes—
13C2×C4⋊C8×C37C2212yes—
14C2×C22⋊C8×C37C2212yes—
15C2×#97×C37C2212yes—
16C37×#384C2212yes—
17C37×#383—21no—
18C37×#382C2211yescharacteristic
19C37×#382C2212yes—
20C37×#382C2211yescharacteristic
21C37×#381—21no—
22C37×#380—21no—
23C37×#380—21no—
24C37×#380C2212yes—
25C4×C4⋊C4×C37—21no—
26C4×C4⋊C4×C37—21no—
27C4×C4⋊C4×C37C2212yes—
28C4×C22⋊C4×C37—21no—
29C37×#376—21no—
30C37×#340C2218yes—
31C23×C4×C37D411yescharacteristic
32C23×C4×C37D411yescharacteristic
33C23×C4×C37C2311yescharacteristic
34C22×C8×C37C2314yes—
35#117×C37—42no—
36#117×C37—42no—
37C2×C4⋊C4×C37—22no—
38C2×C4⋊C4×C37—22no—
39C2×C4⋊C4×C37C2312yes—
40C2×C4⋊C4×C37C2314yes—
41C2×C4⋊C4×C37C2312yes—
42C2×C22⋊C4×C37—22no—
43C2×C22⋊C4×C37—22no—
44C2×C42×C37—22no—
45C2×C42×C37—22no—
46C2×C42×C37C2×C414yes—
47C2×C42×C37D411yescharacteristic
48C2×C42×C37D411yescharacteristic
49C2×C42×C37Q814yes—
50C2×C42×C37C2311yescharacteristic
51C2×C42×C37C2311yescharacteristic
52#107×C37—44no—
53#106×C37—44no—
54C4⋊C8×C37C2×C418yes—
55C22⋊C8×C37C2×C418yes—
56#97×C37C2×C418yes—
57#95×C37—22no—
58#95×C37—21no—
59#95×C37—21no—
60#95×C37—21no—
61#95×C37—21no—
62#95×C37—22no—
63#95×C37—22no—
64#95×C37—22no—
65C24×C37C2×D411yescharacteristic
66C22×C4×C37—22no—
67C22×C4×C37—22no—
68C22×C4×C37—22no—
69C22×C4×C37—22no—
70C22×C4×C37—24no—
71C22×C4×C37—42no—
72C22×C4×C37—42no—
73C22×C4×C37C4⋊C414yes—
74C22×C4×C37C4⋊C414yes—
75C22×C4×C37C22×C412yes—
76C22×C4×C37C2×D411yescharacteristic
77C22×C4×C37C2×D411yescharacteristic
78C22×C4×C37C2×D411yescharacteristic
79C22×C4×C37C2×D411yescharacteristic
80C22×C4×C37C2×D411yescharacteristic
81C22×C4×C37C2×Q812yes—
82C22×C4×C37C2411yescharacteristic
83C2×C8×C37—24no—
84C2×C8×C37—24no—
85C2×C8×C37C22×C418yes—
86C4⋊C4×C37—24no—
87C4⋊C4×C37—24no—
88C4⋊C4×C37—24no—
89C4⋊C4×C37—24no—
90C4⋊C4×C37—44no—
91C4⋊C4×C37—44no—
92C22⋊C4×C37—44no—
93C22⋊C4×C37—44no—
94C42×C37—44no—
95C42×C37—44no—
96C42×C37C4⋊C414yes—
97C42×C37C4⋊C414yes—
98C42×C37C22×C412yes—
99C42×C37C22×C412yes—
100C42×C37C2×Q812yes—
101C42×C37C2×Q812yes—
102C23×C37—21no—
103C23×C37—21no—
104C23×C37—22no—
105C23×C37—22no—
106C23×C37C2×C4⋊C412yes—
107C23×C37C22×D411yescharacteristic
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—22no—
111C2×C4×C37—22no—
112C2×C4×C37—22no—
113C2×C4×C37—22no—
114C2×C4×C37—24no—
115C2×C4×C37—24no—
116C2×C4×C37—44no—
117C2×C4×C37—44no—
118C2×C4×C37—44no—
119C2×C4×C37—42no—
120C2×C4×C37—42no—
121C2×C4×C37—42no—
122C2×C4×C37—42no—
123C2×C4×C37—42no—
124C2×C4×C37—42no—
125C2×C4×C37—44no—
126C2×C4×C37—44no—
127C2×C4×C37C2×C4⋊C412yes—
128C2×C4×C37C2×C4⋊C412yes—
129C2×C4×C37C2×C4⋊C412yes—
130C2×C4×C37C2×C4⋊C412yes—
131C2×C4×C37C2×C4⋊C412yes—
132C2×C4×C37C23×C411yescharacteristic
133C2×C4×C37C22×Q811yescharacteristic
134C2×C4×C37H(5,𝔽2)12yes—
135C2×C4×C372−1+412yes—
136C8×C37—28no—
137#21989C3711yesmaximal, characteristic, direct product factor, Sylow
138C22×C37—22no—
139C22×C37—22no—
140C22×C37—22no—
141C22×C37—42no—
142C22×C37—42no—
143C22×C37C22×C4⋊C411yescharacteristic
144C22×C37#53511yescharacteristic
145C22×C37#53611yescharacteristic
146C22×C37#57512yes—
147C22×C37#57512yes—
148C4×C37—22no—
149C4×C37—22no—
150C4×C37—22no—
151C4×C37—22no—
152C4×C37—22no—
153C4×C37—84no—
154C4×C37—82no—
155C4×C37—82no—
156C4×C37#52012yes—
157C4×C37#54412yes—
158C2×#432C2×C3711yescharacteristic
159#2285C2×C3711yescharacteristic
160#2283C2×C3711yescharacteristic
161#1949C2×C3714yescomplemented
162#1854C2×C3714yes—
163#1847C2×C3712yescomplemented
164#1836C2×C3712yescomplemented
165C2×C37—42no—
166C2×C37#231711yescharacteristic
167C2×C37#291111yescharacteristic
168C2×C37#291111yescharacteristic
169C2×C37#321912yes—
170C2×C37#324012yes—
171C2×#117C22×C3712yes—
172C22×C42C22×C3711yescharacteristic
173#432C4×C3718yescomplemented
174C2×#107C22×C3714yes—
175C2×#106C22×C3714yes—
176C2×C4⋊C8C22×C3712yes—
177C2×C22⋊C8C22×C3712yes—
178C2×#97C22×C3712yes—
179#384C22×C3712yes—
180#383—21no—
181#382C22×C3711yescharacteristic
182#382C22×C3711yescharacteristic
183#382C22×C3712yes—
184#381—21no—
185#380—21no—
186#380—21no—
187#380C22×C3712yes—
188C4×C4⋊C4—21no—
189C4×C4⋊C4—21no—
190C4×C4⋊C4C22×C3712yes—
191C4×C22⋊C4—21no—
192#376—21no—
193#340C22×C3718yes—
194C37#2198911yescharacteristic, direct product factor, Sylow
195C23×C4D4×C3711yescharacteristic
196C23×C4D4×C3711yescharacteristic
197C23×C4C23×C3711yescharacteristic
198C22×C8C23×C3714yes—
199#117—42no—
200#117—42no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4C23×C3714yes—
204C2×C4⋊C4C23×C3712yes—
205C2×C4⋊C4C23×C3712yes—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42C2×C4×C3714yes—
211C2×C42D4×C3711yescharacteristic
212C2×C42D4×C3711yescharacteristic
213C2×C42Q8×C3714yes—
214C2×C42C23×C3711yescharacteristic
215C2×C42C23×C3711yescharacteristic
216#107—44no—
217#106—44no—
218C4⋊C8C2×C4×C3718yes—
219C22⋊C8C2×C4×C3718yes—
220#97C2×C4×C3718yes—
221#95—22no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—22no—
227#95—22no—
228#95—22no—
229C24C2×D4×C3711yescharacteristic
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C4⋊C4×C3714yes—
238C22×C4C4⋊C4×C3714yes—
239C22×C4C22×C4×C3712yes—
240C22×C4C2×D4×C3711yescharacteristic
241C22×C4C2×D4×C3711yescharacteristic
242C22×C4C2×D4×C3711yescharacteristic
243C22×C4C2×D4×C3711yescharacteristic
244C22×C4C2×D4×C3711yescharacteristic
245C22×C4C2×Q8×C3712yes—
246C22×C4C24×C3711yescharacteristic
247C2×C8—24no—
248C2×C8—24no—
249C2×C8C22×C4×C3718yes—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—44no—
255C4⋊C4—44no—
256C22⋊C4—44no—
257C22⋊C4—44no—
258C42—44no—
259C42—44no—
260C42C4⋊C4×C3714yes—
261C42C4⋊C4×C3714yes—
262C42C22×C4×C3712yes—
263C42C22×C4×C3712yes—
264C42C2×Q8×C3712yes—
265C42C2×Q8×C3712yes—
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23C2×C4⋊C4×C3712yes—
271C23C22×D4×C3711yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4C2×C4⋊C4×C3712yes—
292C2×C4C2×C4⋊C4×C3712yes—
293C2×C4C2×C4⋊C4×C3712yes—
294C2×C4C2×C4⋊C4×C3712yes—
295C2×C4C2×C4⋊C4×C3712yes—
296C2×C4C23×C4×C3711yescharacteristic
297C2×C4C22×Q8×C3711yescharacteristic
298C2×C4H(5,𝔽2)×C3712yes—
299C2×C42−1+4×C3712yes—
300C8—28no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22C22×C4⋊C4×C3711yescharacteristic
307C22C37×#53511yescharacteristic
308C22C37×#53611yescharacteristic
309C22C37×#57512yes—
310C22C37×#57512yes—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—84no—
317C4—82no—
318C4—82no—
319C4C37×#52012yes—
320C4C37×#54412yes—
321C2—42no—
322C2C37×#231711yescharacteristic
323C2C37×#291111yescharacteristic
324C2C37×#291111yescharacteristic
325C2C37×#321912yes—
326C2C37×#324012yes—
subgroupG/H
center, socleC23×C37C22×D4
commutatorC2×C4C23×C4×C37
Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1949C2semidirect
6. C37×#1847C2semidirect
7. C37×#1836C2semidirect
10. C37×#432C4semidirect
137. #21989C37direct (N × H)
161. #1949C2×C37semidirect
163. #1847C2×C37semidirect
164. #1836C2×C37semidirect
173. #432C4×C37semidirect
194. C37#21989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4322
C37×#22852
C37×#22832
C37×#19492
C37×#18542
C37×#18472
C37×#18362
#2198937