Finite Group Databasebeta

← C37×#29658 #22650911

Subgroups — C37×#29658 #22650911

Order 9472.

1086 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1086 conjugacy classes of subgroups — too many to draw. Only its 238 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×#3458C211yesmaximal, characteristic, complemented
2C37×#2482C213yesmaximal
3C37×#2062C214yesmaximal, complemented
4C37×#2029C214yesmaximal
5C37×#1820C213yesmaximal, complemented
6C37×#544—23no—
7C37×#544—23no—
8C37×#543C2214yes—
9C37×#533—26no—
10C2×#117×C37C2213yes—
11C22×C22⋊C4×C37C2211yescharacteristic
12C37×#399—23no—
13C37×#397—23no—
14C37×#388—26no—
15C37×#385C2216yes—
16C37×#381C2213yes—
17C37×#379C2216yes—
18C37×#342C22112yes—
19C25×C37C2311yescharacteristic
20C23×C4×C37C2311yescharacteristic
21C23×C4×C37C2311yescharacteristic
22C4⋊Q8×C37—26no—
23C4⋊Q8×C37—26no—
24#125×C37—212no—
25C22⋊Q8×C37—212no—
26C22⋊Q8×C37—212no—
27C4×Q8×C37—24no—
28C4×Q8×C37—24no—
29#117×C37—26no—
30#117×C37—26no—
31C2×C4⋊C4×C37—26no—
32C2×C4⋊C4×C37D413yes—
33C2×C4⋊C4×C37D413yes—
34C2×C22⋊C4×C37—26no—
35C2×C22⋊C4×C37—23no—
36C2×C22⋊C4×C37—23no—
37C2×C22⋊C4×C37—26no—
38C2×C22⋊C4×C37C2316yes—
39C2×C22⋊C4×C37C2316yes—
40C2×C42×C37D416yes—
41#95×C37—23no—
42#95×C37—23no—
43#95×C37—26no—
44C24×C37—23no—
45C24×C37—24no—
46C24×C37—42no—
47C24×C37—81no—
48C24×C37C2411yescharacteristic
49C2×Q8×C37—24no—
50C2×Q8×C37—24no—
51C22×C4×C37—24no—
52C22×C4×C37—26no—
53C22×C4×C37—23no—
54C22×C4×C37—81no—
55C22×C4×C37C2×D413yes—
56C22×C4×C37C2×D413yes—
57C22×C4×C37C2×D416yes—
58C22×C4×C37C2×D416yes—
59C4⋊C4×C37—212no—
60C4⋊C4×C37—212no—
61C4⋊C4×C37—26no—
62C4⋊C4×C37—26no—
63C4⋊C4×C37—86no—
64C22⋊C4×C37—212no—
65C22⋊C4×C37—212no—
66C22⋊C4×C37—412no—
67C22⋊C4×C37—41no—
68C22⋊C4×C37—43no—
69C22⋊C4×C37—86no—
70C42×C37—26no—
71C42×C37—26no—
72C23×C37—26no—
73C23×C37—41no—
74C23×C37—41no—
75C23×C37—46no—
76C23×C37—43no—
77C23×C37—41no—
78C23×C37—46no—
79C23×C37—88no—
80C23×C37C22×D413yes—
81C23×C372−1+414yes—
82Q8×C37—84no—
83Q8×C37—84no—
84C2×C4×C37—26no—
85C2×C4×C37—26no—
86C2×C4×C37—26no—
87C2×C4×C37—26no—
88C2×C4×C37—46no—
89C2×C4×C37—46no—
90C2×C4×C37—46no—
91C2×C4×C37—46no—
92C2×C4×C37—46no—
93C2×C4×C37—41no—
94C2×C4×C37—46no—
95C2×C4×C37#12011yescharacteristic
96C2×C4×C37#12013yes—
97#29658C3711yesmaximal, characteristic, direct product factor, Sylow
98C22×C37—23no—
99C22×C37—23no—
100C22×C37—44no—
101C22×C37—412no—
102C22×C37—42no—
103C22×C37—86no—
104C22×C37—81no—
105C22×C37—81no—
106C22×C37C2×#12011yescharacteristic
107C22×C37#53616yes—
108C4×C37—21no—
109C4×C37—23no—
110C4×C37—46no—
111C4×C37—46no—
112C4×C37—86no—
113C4×C37—81no—
114#3458C2×C3711yescharacteristic, complemented
115#2482C2×C3713yes—
116#2062C2×C3714yescomplemented
117#2029C2×C3714yes—
118#1820C2×C3713yescomplemented
119C2×C37—26no—
120C2×C37—82no—
121C2×C37#261411yescharacteristic
122C2×C37#302511yescharacteristic
123C2×C37#302711yescharacteristic
124#544—23no—
125#544—23no—
126#543C22×C3714yes—
127#533—26no—
128C2×#117C22×C3713yes—
129C22×C22⋊C4C22×C3711yescharacteristic
130#399—23no—
131#397—23no—
132#388—26no—
133#385C22×C3716yes—
134#381C22×C3713yes—
135#379C22×C3716yes—
136#342C22×C37112yes—
137C37#2965811yescharacteristic, direct product factor, Sylow
138C25C23×C3711yescharacteristic
139C23×C4C23×C3711yescharacteristic
140C23×C4C23×C3711yescharacteristic
141C4⋊Q8—26no—
142C4⋊Q8—26no—
143#125—212no—
144C22⋊Q8—212no—
145C22⋊Q8—212no—
146C4×Q8—24no—
147C4×Q8—24no—
148#117—26no—
149#117—26no—
150C2×C4⋊C4—26no—
151C2×C4⋊C4D4×C3713yes—
152C2×C4⋊C4D4×C3713yes—
153C2×C22⋊C4—23no—
154C2×C22⋊C4—23no—
155C2×C22⋊C4—26no—
156C2×C22⋊C4—26no—
157C2×C22⋊C4C23×C3716yes—
158C2×C22⋊C4C23×C3716yes—
159C2×C42D4×C3716yes—
160#95—23no—
161#95—23no—
162#95—26no—
163C24—23no—
164C24—24no—
165C24—42no—
166C24—81no—
167C24C24×C3711yescharacteristic
168C2×Q8—24no—
169C2×Q8—24no—
170C22×C4—24no—
171C22×C4—26no—
172C22×C4—23no—
173C22×C4—81no—
174C22×C4C2×D4×C3713yes—
175C22×C4C2×D4×C3713yes—
176C22×C4C2×D4×C3716yes—
177C22×C4C2×D4×C3716yes—
178C4⋊C4—212no—
179C4⋊C4—212no—
180C4⋊C4—26no—
181C4⋊C4—26no—
182C4⋊C4—86no—
183C22⋊C4—212no—
184C22⋊C4—212no—
185C22⋊C4—412no—
186C22⋊C4—41no—
187C22⋊C4—43no—
188C22⋊C4—86no—
189C42—26no—
190C42—26no—
191C23—26no—
192C23—41no—
193C23—41no—
194C23—46no—
195C23—43no—
196C23—41no—
197C23—46no—
198C23—88no—
199C23C22×D4×C3713yes—
200C232−1+4×C3714yes—
201Q8—84no—
202Q8—84no—
203C2×C4—26no—
204C2×C4—26no—
205C2×C4—26no—
206C2×C4—26no—
207C2×C4—46no—
208C2×C4—46no—
209C2×C4—46no—
210C2×C4—46no—
211C2×C4—46no—
212C2×C4—41no—
213C2×C4—46no—
214C2×C4#120×C3711yescharacteristic
215C2×C4#120×C3713yes—
216C22—23no—
217C22—23no—
218C22—44no—
219C22—412no—
220C22—42no—
221C22—86no—
222C22—81no—
223C22—81no—
224C22C2×#120×C3711yescharacteristic
225C22C37×#53616yes—
226C4—21no—
227C4—23no—
228C4—46no—
229C4—46no—
230C4—86no—
231C4—81no—
232C2—26no—
233C2—82no—
234C2C37×#261411yescharacteristic
235C2C37×#302511yescharacteristic
236C2C37×#302711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC25×C37C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3458C2semidirect
3. C37×#2062C2semidirect
5. C37×#1820C2semidirect
97. #29658C37direct (N × H)
114. #3458C2×C37semidirect
116. #2062C2×C37semidirect
118. #1820C2×C37semidirect
137. C37#29658direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34582
C37×#24822
C37×#20622
C37×#20292
C37×#18202
#2965837