Finite Group Databasebeta

← C37×#10856 #22632109

Subgroups — C37×#10856 #22632109

Order 9472.

810 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#423C211yesmaximal, characteristic
2C2×C37×#423C211yesmaximal, characteristic
3C4×#117×C37C211yesmaximal, characteristic
4C2×C37×#344C214yesmaximal
5C22×M16×C37C2212yes—
6C22×M16×C37C2212yes—
7C2×#117×C37C2212yes—
8C22×C42×C37C2211yescharacteristic
9C37×#423—22no—
10C37×#423—22no—
11C37×#423—21no—
12C37×#423—21no—
13C37×#423C412yescomplemented
14C37×#423C412yescomplemented
15C2×C4⋊C8×C37—22no—
16C2×C4⋊C8×C37C414yescomplemented
17C4×C4⋊C4×C37—22no—
18C4×C22⋊C4×C37C414yes—
19C37×#376—21no—
20C43×C37—21no—
21C37×#344—28no—
22C23×C4×C37C2×C412yes—
23C23×C4×C37C2311yescharacteristic
24C2×M16×C37—24no—
25C2×M16×C37—22no—
26C2×M16×C37—22no—
27C2×M16×C37—22no—
28C2×M16×C37—24no—
29C2×M16×C37—24no—
30C2×M16×C37—24no—
31C2×M16×C37C2×C414yes—
32C22×C8×C37—22no—
33C22×C8×C37C2×C414yes—
34#117×C37—22no—
35#117×C37—22no—
36#117×C37D414yes—
37#117×C37Q814yes—
38C2×C4⋊C4×C37—22no—
39C2×C22⋊C4×C37C2×C414yes—
40C2×C42×C37—22no—
41C2×C42×C37—24no—
42C2×C42×C37C2×C412yes—
43C2×C42×C37C2×C411yescharacteristic
44C2×C42×C37C2×C411yescharacteristic
45C2×C42×C37D412yes—
46C2×C42×C37D411yescharacteristic
47C2×C42×C37D411yescharacteristic
48C2×C42×C37D412yes—
49C2×C42×C37Q811yescharacteristic
50C2×C42×C37Q811yescharacteristic
51C4⋊C8×C37—24no—
52C4⋊C8×C37—24no—
53C4⋊C8×C37—24no—
54C4⋊C8×C37—24no—
55#95×C37—24no—
56C24×C37C22×C411yescharacteristic
57C22×C4×C37—24no—
58C22×C4×C37—44no—
59C22×C4×C37C4212yes—
60C22×C4×C37C4212yes—
61C22×C4×C37C22⋊C412yes—
62C22×C4×C37C22⋊C412yes—
63C22×C4×C37C4⋊C412yes—
64C22×C4×C37C4⋊C412yes—
65C22×C4×C37C22×C411yescharacteristic
66C22×C4×C37C22×C411yescharacteristic
67C22×C4×C37C2×D411yescharacteristic
68C22×C4×C37C2×D411yescharacteristic
69C22×C4×C37C2×D411yescharacteristic
70C22×C4×C37C2×D412yes—
71C22×C4×C37C2×Q811yescharacteristic
72C22×C4×C37C2×Q812yes—
73C22×C4×C37#4112yes—
74C22×C4×C37#4112yes—
75M16×C37—28no—
76M16×C37—44no—
77M16×C37—44no—
78M16×C37—42no—
79M16×C37—42no—
80C2×C8×C37—24no—
81C2×C8×C37—24no—
82C2×C8×C37—28no—
83C2×C8×C37—42no—
84C2×C8×C37—42no—
85C4⋊C4×C37—24no—
86C4⋊C4×C37—24no—
87C22⋊C4×C37—24no—
88C22⋊C4×C37C4⋊C418yes—
89C42×C37—24no—
90C42×C37—24no—
91C42×C37—48no—
92C42×C37C22⋊C412yes—
93C42×C37C22⋊C412yes—
94C42×C37C22⋊C412yes—
95C42×C37C22⋊C412yes—
96C42×C37C4⋊C412yes—
97C42×C37C4⋊C411yescharacteristic
98C42×C37C4⋊C411yescharacteristic
99C42×C37C4⋊C411yescharacteristic
100C42×C37C4⋊C412yes—
101C42×C37C4⋊C411yescharacteristic
102C23×C37—42no—
103C23×C37C2×C4211yescharacteristic
104C23×C37C2×C22⋊C411yescharacteristic
105C23×C37C2×C4⋊C411yescharacteristic
106C23×C37C2×C4⋊C412yes—
107C23×C37#11712yes—
108C2×C4×C37—24no—
109C2×C4×C37—24no—
110C2×C4×C37—24no—
111C2×C4×C37—28no—
112C2×C4×C37—42no—
113C2×C4×C37—42no—
114C2×C4×C37—42no—
115C2×C4×C37—48no—
116C2×C4×C37#9512yes—
117C2×C4×C37#9512yes—
118C2×C4×C37#9512yes—
119C2×C4×C37#9512yes—
120C2×C4×C37C2×C22⋊C411yescharacteristic
121C2×C4×C37C2×C22⋊C411yescharacteristic
122C2×C4×C37C2×C4⋊C411yescharacteristic
123C2×C4×C37C2×C4⋊C411yescharacteristic
124C2×C4×C37C4×D412yes—
125C2×C4×C37C4×D412yes—
126C2×C4×C37C4×Q812yes—
127C2×C4×C37C4×Q812yes—
128C2×C4×C37#12112yes—
129C2×C4×C37#12112yes—
130C2×C4×C37C22⋊Q812yes—
131C2×C4×C37C22⋊Q812yes—
132C2×C4×C37#12411yescharacteristic
133C2×C4×C37#12411yescharacteristic
134C2×C4×C37#12512yes—
135C2×C4×C37#12711yescharacteristic
136C2×C4×C37C4⋊Q812yes—
137C2×C4×C37C4⋊Q811yescharacteristic
138C8×C37—44no—
139C8×C37—44no—
140#10856C3711yesmaximal, characteristic, direct product factor, Sylow
141C22×C37—22no—
142C22×C37—22no—
143C22×C37—22no—
144C22×C37—42no—
145C22×C37—42no—
146C22×C37C2×#9511yescharacteristic
147C22×C37C4×C4⋊C412yes—
148C22×C37#38012yes—
149C22×C37#38211yescharacteristic
150C22×C37#38411yescharacteristic
151C4×C37—22no—
152C4×C37—22no—
153C4×C37—22no—
154C4×C37—48no—
155C4×C37#34414yescomplemented
156C4×C37#38912yes—
157C4×C37#38912yes—
158C4×C37#39011yescharacteristic
159C4×C37#39011yescharacteristic
160C4×C37#39111yescharacteristic
161C4×C37#39111yescharacteristic
162C2×#423C2×C3711yescharacteristic
163C2×#423C2×C3711yescharacteristic
164C4×#117C2×C3711yescharacteristic
165C2×#344C2×C3714yes—
166C2×C37—22no—
167C2×C37—22no—
168C2×C37—21no—
169C2×C37—21no—
170C2×C37C4⋊#9511yescharacteristic
171C2×C37C2×#34412yes—
172C22×M16C22×C3712yes—
173C22×M16C22×C3712yes—
174C2×#117C22×C3712yes—
175C22×C42C22×C3711yescharacteristic
176#423—22no—
177#423—22no—
178#423—21no—
179#423—21no—
180#423C4×C3712yescomplemented
181#423C4×C3712yescomplemented
182C2×C4⋊C8—22no—
183C2×C4⋊C8C4×C3714yescomplemented
184C4×C4⋊C4—22no—
185C4×C22⋊C4C4×C3714yes—
186#376—21no—
187C43—21no—
188#344—28no—
189C37#1085611yescharacteristic, direct product factor, Sylow
190C23×C4C2×C4×C3712yes—
191C23×C4C23×C3711yescharacteristic
192C2×M16—24no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—24no—
197C2×M16—24no—
198C2×M16—24no—
199C2×M16C2×C4×C3714yes—
200C22×C8—22no—
201C22×C8C2×C4×C3714yes—
202#117—22no—
203#117—22no—
204#117D4×C3714yes—
205#117Q8×C3714yes—
206C2×C4⋊C4—22no—
207C2×C22⋊C4C2×C4×C3714yes—
208C2×C42—22no—
209C2×C42—24no—
210C2×C42C2×C4×C3712yes—
211C2×C42C2×C4×C3711yescharacteristic
212C2×C42C2×C4×C3711yescharacteristic
213C2×C42D4×C3712yes—
214C2×C42D4×C3711yescharacteristic
215C2×C42D4×C3711yescharacteristic
216C2×C42D4×C3712yes—
217C2×C42Q8×C3711yescharacteristic
218C2×C42Q8×C3711yescharacteristic
219C4⋊C8—24no—
220C4⋊C8—24no—
221C4⋊C8—24no—
222C4⋊C8—24no—
223#95—24no—
224C24C22×C4×C3711yescharacteristic
225C22×C4—24no—
226C22×C4—44no—
227C22×C4C42×C3712yes—
228C22×C4C42×C3712yes—
229C22×C4C22⋊C4×C3712yes—
230C22×C4C22⋊C4×C3712yes—
231C22×C4C4⋊C4×C3712yes—
232C22×C4C4⋊C4×C3712yes—
233C22×C4C22×C4×C3711yescharacteristic
234C22×C4C22×C4×C3711yescharacteristic
235C22×C4C2×D4×C3711yescharacteristic
236C22×C4C2×D4×C3711yescharacteristic
237C22×C4C2×D4×C3711yescharacteristic
238C22×C4C2×D4×C3712yes—
239C22×C4C2×Q8×C3711yescharacteristic
240C22×C4C2×Q8×C3712yes—
241C22×C4#41×C3712yes—
242C22×C4#41×C3712yes—
243M16—28no—
244M16—44no—
245M16—44no—
246M16—42no—
247M16—42no—
248C2×C8—24no—
249C2×C8—24no—
250C2×C8—28no—
251C2×C8—42no—
252C2×C8—42no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C22⋊C4—24no—
256C22⋊C4C4⋊C4×C3718yes—
257C42—24no—
258C42—24no—
259C42—48no—
260C42C22⋊C4×C3712yes—
261C42C22⋊C4×C3712yes—
262C42C22⋊C4×C3712yes—
263C42C22⋊C4×C3712yes—
264C42C4⋊C4×C3712yes—
265C42C4⋊C4×C3711yescharacteristic
266C42C4⋊C4×C3711yescharacteristic
267C42C4⋊C4×C3711yescharacteristic
268C42C4⋊C4×C3712yes—
269C42C4⋊C4×C3711yescharacteristic
270C23—42no—
271C23C2×C42×C3711yescharacteristic
272C23C2×C22⋊C4×C3711yescharacteristic
273C23C2×C4⋊C4×C3711yescharacteristic
274C23C2×C4⋊C4×C3712yes—
275C23#117×C3712yes—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—48no—
284C2×C4#95×C3712yes—
285C2×C4#95×C3712yes—
286C2×C4#95×C3712yes—
287C2×C4#95×C3712yes—
288C2×C4C2×C22⋊C4×C3711yescharacteristic
289C2×C4C2×C22⋊C4×C3711yescharacteristic
290C2×C4C2×C4⋊C4×C3711yescharacteristic
291C2×C4C2×C4⋊C4×C3711yescharacteristic
292C2×C4C4×D4×C3712yes—
293C2×C4C4×D4×C3712yes—
294C2×C4C4×Q8×C3712yes—
295C2×C4C4×Q8×C3712yes—
296C2×C4#121×C3712yes—
297C2×C4#121×C3712yes—
298C2×C4C22⋊Q8×C3712yes—
299C2×C4C22⋊Q8×C3712yes—
300C2×C4#124×C3711yescharacteristic
301C2×C4#124×C3711yescharacteristic
302C2×C4#125×C3712yes—
303C2×C4#127×C3711yescharacteristic
304C2×C4C4⋊Q8×C3712yes—
305C2×C4C4⋊Q8×C3711yescharacteristic
306C8—44no—
307C8—44no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—42no—
312C22—42no—
313C22C2×#95×C3711yescharacteristic
314C22C4×C4⋊C4×C3712yes—
315C22C37×#38012yes—
316C22C37×#38211yescharacteristic
317C22C37×#38411yescharacteristic
318C4—22no—
319C4—22no—
320C4—22no—
321C4—48no—
322C4C37×#34414yescomplemented
323C4C37×#38912yes—
324C4C37×#38912yes—
325C4C37×#39011yescharacteristic
326C4C37×#39011yescharacteristic
327C4C37×#39111yescharacteristic
328C4C37×#39111yescharacteristic
329C2—22no—
330C2—22no—
331C2—21no—
332C2—21no—
333C2C37×C4⋊#9511yescharacteristic
334C2C2×C37×#34412yes—
subgroupG/H
centerC2×C4×C37C2×C22⋊C4
commutatorC23C2×C42×C37
Frattini, cosocleC23×C4C23×C37
socleC22×C37C2×#95
prime radicalC24×C37C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
13. C37×#423C4semidirect
14. C37×#423C4semidirect
16. C2×C4⋊C8×C37C4semidirect
140. #10856C37direct (N × H)
155. C4×C37#344semidirect
180. #423C4×C37semidirect
181. #423C4×C37semidirect
183. C2×C4⋊C8C4×C37semidirect
189. C37#10856direct (N × H)
322. C4C37×#344semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4232
C4×#117×C372
C2×C37×#3442
#1085637