Finite Group Databasebeta

← C37×#19118 #22640371

Subgroups — C37×#19118 #22640371

Order 9472.

606 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3160C211yesmaximal, characteristic
2C37×#3104C212yesmaximal
3C2×C8×Q8×C37C211yesmaximal, characteristic
4C37×#1676C212yesmaximal, complemented
5C37×#1674C212yesmaximal, complemented
6C37×#1672C214yesmaximal, complemented
7C37×#1564C211yesmaximal, characteristic
8C37×#1542C212yesmaximal
9C37×#533C2212yes—
10C2×C4×Q8×C37C2211yescharacteristic
11C37×#500C2211yescharacteristic
12C37×#500C2211yescharacteristic
13C37×#499—21no—
14C37×#499—21no—
15C37×#498C2212yes—
16C37×#484—22no—
17C37×#477C2214yes—
18C37×#462C2214yes—
19C37×#451—22no—
20C8×Q8×C37—21no—
21C8×Q8×C37—21no—
22C8×Q8×C37C2212yes—
23C8×Q8×C37C2212yes—
24C4×Q16×C37—24no—
25C37×#431C2212yes—
26C37×#427—21no—
27C37×#427—21no—
28C2×C4⋊C8×C37—21no—
29C2×C4⋊C8×C37C2211yescharacteristic
30C2×C4×C8×C37—21no—
31C2×C4×C8×C37C2211yescharacteristic
32C37×#335C2212yes—
33C37×#334C2212yes—
34C37×#333C2214yes—
35C37×#332C2214yes—
36C22×Q8×C37D411yescharacteristic
37C2×Q16×C37—24no—
38C22×C8×C37—21no—
39C22×C8×C37D411yescharacteristic
40C22×C8×C37D411yescharacteristic
41C4⋊Q8×C37C2312yes—
42C4⋊Q8×C37C2312yes—
43#125×C37—22no—
44C22⋊Q8×C37—22no—
45C22⋊Q8×C37—22no—
46C4×Q8×C37—21no—
47C4×Q8×C37—21no—
48C4×Q8×C37—22no—
49C4×Q8×C37—22no—
50C4×Q8×C37D412yes—
51C4×Q8×C37C2312yes—
52#117×C37—22no—
53C2×C4⋊C4×C37—21no—
54C2×C4⋊C4×C37D411yescharacteristic
55C2×C42×C37—21no—
56C2×C42×C37C2311yescharacteristic
57#107×C37—21no—
58#107×C37—21no—
59#107×C37—21no—
60#107×C37—21no—
61#107×C37—24no—
62#106×C37—22no—
63#106×C37—22no—
64C4⋊C8×C37—22no—
65C4⋊C8×C37—22no—
66C4⋊C8×C37—21no—
67C4⋊C8×C37C2312yes—
68C4⋊C8×C37C2314yes—
69#103×C37—24no—
70#103×C37—24no—
71C22⋊C8×C37—22no—
72C4×C8×C37—22no—
73C4×C8×C37—22no—
74C4×C8×C37—22no—
75C4×C8×C37D411yescharacteristic
76C4×C8×C37D411yescharacteristic
77C4×C8×C37C2311yescharacteristic
78C4×C8×C37C2311yescharacteristic
79C2×Q8×C37—24no—
80C2×Q8×C37—21no—
81C2×Q8×C37—22no—
82C2×Q8×C37—22no—
83C2×Q8×C37C2×D412yes—
84C22×C4×C37—21no—
85C22×C4×C37—21no—
86C22×C4×C37C2×D411yescharacteristic
87C22×C4×C37C2×D411yescharacteristic
88C22×C4×C37#4111yescharacteristic
89Q16×C37—48no—
90C2×C8×C37—22no—
91C2×C8×C37—22no—
92C2×C8×C37—24no—
93C2×C8×C37—42no—
94C2×C8×C37Q1614yescomplemented
95C2×C8×C37C2×D411yescharacteristic
96C2×C8×C37C2×D411yescharacteristic
97C2×C8×C37C2×D411yescharacteristic
98C2×C8×C37C2×D411yescharacteristic
99C4⋊C4×C37—22no—
100C4⋊C4×C37—21no—
101C4⋊C4×C37—22no—
102C4⋊C4×C37—22no—
103C4⋊C4×C37—22no—
104C4⋊C4×C37—22no—
105C4⋊C4×C37—22no—
106C4⋊C4×C37—42no—
107C4⋊C4×C37—42no—
108C4⋊C4×C37C2×D412yes—
109C22⋊C4×C37—42no—
110C42×C37—22no—
111C42×C37—22no—
112C42×C37—42no—
113C42×C37C2×D411yescharacteristic
114C42×C37C2×D411yescharacteristic
115C42×C37#4111yescharacteristic
116C42×C37C2411yescharacteristic
117C23×C37#12111yescharacteristic
118Q8×C37—24no—
119Q8×C37—22no—
120Q8×C37—44no—
121Q8×C37—82no—
122Q8×C37#13514yes—
123C2×C4×C37—24no—
124C2×C4×C37—22no—
125C2×C4×C37—22no—
126C2×C4×C37—22no—
127C2×C4×C37—41no—
128C2×C4×C37—42no—
129C2×C4×C37—42no—
130C2×C4×C37—42no—
131C2×C4×C37#12111yescharacteristic
132C2×C4×C37#12111yescharacteristic
133C2×C4×C37#12111yescharacteristic
134C2×C4×C37C2×Q1612yes—
135C2×C4×C37#13712yes—
136C2×C4×C37C22×D411yescharacteristic
137C2×C4×C37C22×D411yescharacteristic
138C2×C4×C37C2×#4111yescharacteristic
139C8×C37—21no—
140C8×C37—21no—
141C8×C37—44no—
142C8×C37—42no—
143C8×C37C2×Q1612yes—
144C8×C37C2×Q1612yes—
145#19118C3711yesmaximal, characteristic, direct product factor, Sylow
146C22×C37—21no—
147C22×C37—21no—
148C22×C37#46212yes—
149C22×C37C2×#12111yescharacteristic
150C4×C37—24no—
151C4×C37—21no—
152C4×C37—21no—
153C4×C37—21no—
154C4×C37—42no—
155C4×C37—82no—
156C4×C37—82no—
157C4×C37#46212yes—
158C4×C37C22×Q1611yescharacteristic
159C4×C37C2×#13512yes—
160C4×C37C2×#13711yescharacteristic
161#3160C2×C3711yescharacteristic
162#3104C2×C3712yes—
163C2×C8×Q8C2×C3711yescharacteristic
164#1676C2×C3712yescomplemented
165#1674C2×C3712yescomplemented
166#1672C2×C3714yescomplemented
167#1564C2×C3711yescharacteristic
168#1542C2×C3712yes—
169C2×C37—22no—
170C2×C37C2×#46211yescharacteristic
171C2×C37#305011yescharacteristic
172C2×C37#306711yescharacteristic
173#533C22×C3712yes—
174C2×C4×Q8C22×C3711yescharacteristic
175#500C22×C3711yescharacteristic
176#500C22×C3711yescharacteristic
177#499—21no—
178#499—21no—
179#498C22×C3712yes—
180#484—22no—
181#477C22×C3714yes—
182#462C22×C3714yes—
183#451—22no—
184C8×Q8—21no—
185C8×Q8—21no—
186C8×Q8C22×C3712yes—
187C8×Q8C22×C3712yes—
188C4×Q16—24no—
189#431C22×C3712yes—
190#427—21no—
191#427—21no—
192C2×C4⋊C8—21no—
193C2×C4⋊C8C22×C3711yescharacteristic
194C2×C4×C8—21no—
195C2×C4×C8C22×C3711yescharacteristic
196#335C22×C3712yes—
197#334C22×C3712yes—
198#333C22×C3714yes—
199#332C22×C3714yes—
200C37#1911811yescharacteristic, direct product factor, Sylow
201C22×Q8D4×C3711yescharacteristic
202C2×Q16—24no—
203C22×C8—21no—
204C22×C8D4×C3711yescharacteristic
205C22×C8D4×C3711yescharacteristic
206C4⋊Q8C23×C3712yes—
207C4⋊Q8C23×C3712yes—
208#125—22no—
209C22⋊Q8—22no—
210C22⋊Q8—22no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×Q8D4×C3712yes—
216C4×Q8C23×C3712yes—
217#117—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4×C3711yescharacteristic
220C2×C42—21no—
221C2×C42C23×C3711yescharacteristic
222#107—21no—
223#107—21no—
224#107—21no—
225#107—21no—
226#107—24no—
227#106—22no—
228#106—22no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—21no—
232C4⋊C8C23×C3712yes—
233C4⋊C8C23×C3714yes—
234#103—24no—
235#103—24no—
236C22⋊C8—22no—
237C4×C8—22no—
238C4×C8—22no—
239C4×C8—22no—
240C4×C8D4×C3711yescharacteristic
241C4×C8D4×C3711yescharacteristic
242C4×C8C23×C3711yescharacteristic
243C4×C8C23×C3711yescharacteristic
244C2×Q8—24no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8C2×D4×C3712yes—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4C2×D4×C3711yescharacteristic
252C22×C4C2×D4×C3711yescharacteristic
253C22×C4#41×C3711yescharacteristic
254Q16—48no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—24no—
258C2×C8—42no—
259C2×C8Q16×C3714yescomplemented
260C2×C8C2×D4×C3711yescharacteristic
261C2×C8C2×D4×C3711yescharacteristic
262C2×C8C2×D4×C3711yescharacteristic
263C2×C8C2×D4×C3711yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4C2×D4×C3712yes—
274C22⋊C4—42no—
275C42—22no—
276C42—22no—
277C42—42no—
278C42C2×D4×C3711yescharacteristic
279C42C2×D4×C3711yescharacteristic
280C42#41×C3711yescharacteristic
281C42C24×C3711yescharacteristic
282C23#121×C3711yescharacteristic
283Q8—24no—
284Q8—22no—
285Q8—44no—
286Q8—82no—
287Q8#135×C3714yes—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4#121×C3711yescharacteristic
297C2×C4#121×C3711yescharacteristic
298C2×C4#121×C3711yescharacteristic
299C2×C4C2×Q16×C3712yes—
300C2×C4#137×C3712yes—
301C2×C4C22×D4×C3711yescharacteristic
302C2×C4C22×D4×C3711yescharacteristic
303C2×C4C2×#41×C3711yescharacteristic
304C8—21no—
305C8—21no—
306C8—44no—
307C8—42no—
308C8C2×Q16×C3712yes—
309C8C2×Q16×C3712yes—
310C22—21no—
311C22—21no—
312C22C37×#46212yes—
313C22C2×#121×C3711yescharacteristic
314C4—24no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—42no—
319C4—82no—
320C4—82no—
321C4C37×#46212yes—
322C4C22×Q16×C3711yescharacteristic
323C4C2×#135×C3712yes—
324C4C2×#137×C3711yescharacteristic
325C2—22no—
326C2C2×C37×#46211yescharacteristic
327C2C37×#305011yescharacteristic
328C2C37×#306711yescharacteristic
subgroupG/H
centerC2×C4×C37#121
commutator, Frattini, cosocleC42C24×C37
socleC22×C37C2×#121
prime radicalC23×C37#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1676C2semidirect
5. C37×#1674C2semidirect
6. C37×#1672C2semidirect
94. C2×C8×C37Q16semidirect
145. #19118C37direct (N × H)
164. #1676C2×C37semidirect
165. #1674C2×C37semidirect
166. #1672C2×C37semidirect
200. C37#19118direct (N × H)
259. C2×C8Q16×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#31602
C37×#31042
C2×C8×Q8×C372
C37×#16762
C37×#16742
C37×#16722
C37×#15642
C37×#15422
#1911837