Finite Group Databasebeta

← C37×#11806 #22633059

Subgroups — C37×#11806 #22633059

Order 9472.

488 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2619C211yesmaximal, characteristic
2C37×#1822C211yesmaximal, characteristic, complemented
3C37×#1464C211yesmaximal, characteristic, complemented
4C37×#1345C214yesmaximal, complemented
5C2×#127×C37C411yescharacteristic
6C2×#121×C37—21no—
7C2×#117×C37C2211yescharacteristic
8C37×#432—21no—
9C37×#407—21no—
10C37×#394—21no—
11C37×#394C2212yes—
12C37×#392—21no—
13C37×#392C412yes—
14C37×#390—21no—
15C37×#382C411yescharacteristic
16C37×#343—21no—
17C37×#343C2212yes—
18C37×#324C2212yes—
19C37×#323—21no—
20C22×D4×C37—22no—
21C22×D4×C37—21no—
22C22×D4×C37—21no—
23C22×D4×C37C2×C412yes—
24C23×C4×C37D411yescharacteristic
25C2×M16×C37—22no—
26#127×C37—41no—
27#127×C37—41no—
28#121×C37—44no—
29#117×C37—41no—
30#117×C37—41no—
31C2×C4⋊C4×C37—21no—
32C2×C4⋊C4×C37D411yescharacteristic
33C2×C4⋊C4×C37C2311yescharacteristic
34C2×C22⋊C4×C37—22no—
35C2×C22⋊C4×C37—22no—
36C2×C22⋊C4×C37—22no—
37C2×C22⋊C4×C37C2×C411yescharacteristic
38C2×C22⋊C4×C37D411yescharacteristic
39C2×C42×C37C2×C411yescharacteristic
40C2×C42×C37D411yescharacteristic
41C4⋊C8×C37—41no—
42C22⋊C8×C37—22no—
43C22⋊C8×C37—41no—
44C22⋊C8×C37—41no—
45#97×C37—41no—
46#95×C37—21no—
47#95×C37C2×C412yes—
48C24×C37—22no—
49C24×C37C22⋊C411yescharacteristic
50C2×D4×C37—42no—
51C2×D4×C37—42no—
52C2×D4×C37—42no—
53C2×D4×C37—42no—
54C2×D4×C37—44no—
55C2×D4×C37—41no—
56C2×D4×C37—41no—
57C2×D4×C37—82no—
58C2×D4×C37—82no—
59C2×D4×C37—82no—
60C2×D4×C37—82no—
61C22×C4×C37—21no—
62C22×C4×C37—21no—
63C22×C4×C37—22no—
64C22×C4×C37—22no—
65C22×C4×C37—41no—
66C22×C4×C37C22⋊C411yescharacteristic
67C22×C4×C37C22⋊C411yescharacteristic
68C22×C4×C37C22⋊C411yescharacteristic
69C22×C4×C37C22×C411yescharacteristic
70C22×C4×C37C2×D411yescharacteristic
71C22×C4×C37C2×D411yescharacteristic
72M16×C37—42no—
73M16×C37—42no—
74C2×C8×C37—42no—
75C2×C8×C37—42no—
76C4⋊C4×C37—41no—
77C4⋊C4×C37—41no—
78C4⋊C4×C37—42no—
79C22⋊C4×C37—41no—
80C22⋊C4×C37—41no—
81C22⋊C4×C37—44no—
82C22⋊C4×C37—82no—
83C22⋊C4×C37—82no—
84C42×C37—21no—
85C42×C37—21no—
86C42×C37—21no—
87C42×C37—21no—
88C23×C37—21no—
89C23×C37—21no—
90C23×C37—21no—
91C23×C37—41no—
92C23×C37—41no—
93C23×C37—42no—
94C23×C37—42no—
95C23×C37—42no—
96C23×C37—42no—
97C23×C37—42no—
98C23×C37—42no—
99C23×C37—42no—
100C23×C37C2×C22⋊C411yescharacteristic
101D4×C37—82no—
102D4×C37—82no—
103D4×C37—84no—
104D4×C37—84no—
105D4×C37—88no—
106C2×C4×C37—21no—
107C2×C4×C37—21no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—42no—
115C2×C4×C37—42no—
116C2×C4×C37—41no—
117C2×C4×C37—41no—
118C2×C4×C37—41no—
119C2×C4×C37—41no—
120C2×C4×C37—42no—
121C2×C4×C37—42no—
122C2×C4×C37—42no—
123C2×C4×C37#9911yescharacteristic
124C2×C4×C37#9911yescharacteristic
125C2×C4×C37AGL(1,ℤ/8)12yes—
126C8×C37—82no—
127C8×C37—82no—
128#11806C3711yesmaximal, characteristic, direct product factor, Sylow
129C22×C37—21no—
130C22×C37—21no—
131C22×C37—42no—
132C22×C37—41no—
133C22×C37—41no—
134C22×C37—41no—
135C22×C37—81no—
136C22×C37—82no—
137C22×C37—82no—
138C22×C37—82no—
139C22×C37—82no—
140C22×C37—82no—
141C22×C37—82no—
142C22×C37—82no—
143C22×C37C2×#9911yescharacteristic
144C22×C37#41811yescharacteristic
145C22×C37#42111yescharacteristic
146C4×C37—22no—
147C4×C37—21no—
148C4×C37—21no—
149C4×C37—41no—
150C4×C37—41no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37—82no—
154#2619C2×C3711yescharacteristic
155#1822C2×C3711yescharacteristic, complemented
156#1464C2×C3711yescharacteristic, complemented
157#1345C2×C3714yescomplemented
158C2×C37—21no—
159C2×C37—21no—
160C2×C37—81no—
161C2×C37—162no—
162C2×C37#151011yescharacteristic
163C2×C37#212211yescharacteristic
164C2×C37#213411yescharacteristic
165C2×#127C4×C3711yescharacteristic
166C2×#121—21no—
167C2×#117C22×C3711yescharacteristic
168#432—21no—
169#407—21no—
170#394—21no—
171#394C22×C3712yes—
172#392—21no—
173#392C4×C3712yes—
174#390—21no—
175#382C4×C3711yescharacteristic
176#343—21no—
177#343C22×C3712yes—
178#324C22×C3712yes—
179#323—21no—
180C37#1180611yescharacteristic, direct product factor, Sylow
181C22×D4—22no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4C2×C4×C3712yes—
185C23×C4D4×C3711yescharacteristic
186C2×M16—22no—
187#127—41no—
188#127—41no—
189#121—44no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4D4×C3711yescharacteristic
194C2×C4⋊C4C23×C3711yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4C2×C4×C3711yescharacteristic
199C2×C22⋊C4D4×C3711yescharacteristic
200C2×C42C2×C4×C3711yescharacteristic
201C2×C42D4×C3711yescharacteristic
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206#97—41no—
207#95—21no—
208#95C2×C4×C3712yes—
209C24—22no—
210C24C22⋊C4×C3711yescharacteristic
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—44no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4—82no—
221C2×D4—82no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4C22⋊C4×C3711yescharacteristic
228C22×C4C22⋊C4×C3711yescharacteristic
229C22×C4C22⋊C4×C3711yescharacteristic
230C22×C4C22×C4×C3711yescharacteristic
231C22×C4C2×D4×C3711yescharacteristic
232C22×C4C2×D4×C3711yescharacteristic
233M16—42no—
234M16—42no—
235C2×C8—42no—
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—44no—
243C22⋊C4—82no—
244C22⋊C4—82no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23C2×C22⋊C4×C3711yescharacteristic
262D4—82no—
263D4—82no—
264D4—84no—
265D4—84no—
266D4—88no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4#99×C3711yescharacteristic
285C2×C4#99×C3711yescharacteristic
286C2×C4AGL(1,ℤ/8)×C3712yes—
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—82no—
301C22—82no—
302C22—82no—
303C22C2×#99×C3711yescharacteristic
304C22C37×#41811yescharacteristic
305C22C37×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—82no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—162no—
318C2C37×#151011yescharacteristic
319C2C37×#212211yescharacteristic
320C2C37×#213411yescharacteristic
subgroupG/H
center, socleC22×C37C2×#99
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C4⋊C4C23×C37
prime radicalC37×#2619C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#1822C2semidirect
3. C37×#1464C2semidirect
4. C37×#1345C2semidirect
128. #11806C37direct (N × H)
155. #1822C2×C37semidirect
156. #1464C2×C37semidirect
157. #1345C2×C37semidirect
180. C37#11806direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#26192
C37×#18222
C37×#14642
C37×#13452
#1180637