Finite Group Databasebeta

← C37×#7495 #22628748

Subgroups — C37×#7495 #22628748

Order 9472.

280 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×C37×#355C211yesmaximal, characteristic
2C37×#1885C211yesmaximal, characteristic
3C37×#1533C211yesmaximal, characteristic
4C2×#124×C37C2211yescharacteristic
5C37×#518C411yescharacteristic
6C37×#432—21no—
7C37×#419—21no—
8C2×#101×C37—21no—
9C2×#100×C37C411yescharacteristic
10C37×#355—21no—
11C37×#355C412yescomplemented
12C37×#339—21no—
13C37×#329—21no—
14C37×#329C412yescomplemented
15C22×Q8×C37D411yescharacteristic
16C22×D4×C37C2×C411yescharacteristic
17C2×M16×C37—21no—
18C2×M16×C37—41no—
19#124×C37—41no—
20#124×C37C2×C411yescharacteristic
21#124×C37C2×C411yescharacteristic
22#124×C37D411yescharacteristic
23#124×C37Q811yescharacteristic
24C4×D4×C37—42no—
25#117×C37—21no—
26C2×C22⋊C4×C37—41no—
27C2×C22⋊C4×C37—41no—
28C2×C42×C37D411yescharacteristic
29C4⋊C8×C37—41no—
30#103×C37—42no—
31#101×C37—22no—
32#101×C37—41no—
33#100×C37—41no—
34C22⋊C8×C37—41no—
35#97×C37—22no—
36C24×C37—21no—
37C2×Q8×C37—21no—
38C2×Q8×C37—41no—
39C2×Q8×C37—41no—
40C2×Q8×C37C22⋊C411yescharacteristic
41C2×Q8×C37C4⋊C411yescharacteristic
42C2×D4×C37—21no—
43C2×D4×C37—41no—
44C2×D4×C37—41no—
45C2×D4×C37C4211yescharacteristic
46C2×D4×C37C4⋊C411yescharacteristic
47C22×C4×C37—21no—
48C22×C4×C37—21no—
49C22×C4×C37—42no—
50C22×C4×C37C22⋊C411yescharacteristic
51M16×C37—42no—
52M16×C37—41no—
53M16×C37—41no—
54M16×C37—81no—
55C2×C8×C37—42no—
56C2×C8×C37—41no—
57C2×C8×C37—81no—
58C4⋊C4×C37—22no—
59C22⋊C4×C37—41no—
60C22⋊C4×C37—41no—
61C22⋊C4×C37—41no—
62C22⋊C4×C37—41no—
63C22⋊C4×C37—41no—
64C22⋊C4×C37—42no—
65C42×C37—21no—
66C42×C37—41no—
67C42×C37C22⋊C411yescharacteristic
68C42×C37C4⋊C411yescharacteristic
69C23×C37—21no—
70C23×C37—21no—
71C23×C37—41no—
72C23×C37—41no—
73C23×C37—82no—
74C23×C37#9911yescharacteristic
75Q8×C37—41no—
76Q8×C37—41no—
77Q8×C37—81no—
78D4×C37—41no—
79D4×C37—41no—
80D4×C37—42no—
81C2×C4×C37—21no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37—21no—
85C2×C4×C37—21no—
86C2×C4×C37—21no—
87C2×C4×C37—41no—
88C2×C4×C37—41no—
89C2×C4×C37—42no—
90C2×C4×C37—81no—
91C2×C4×C37—162no—
92C2×C4×C37#9511yescharacteristic
93C2×C4×C37#9911yescharacteristic
94C8×C37—81no—
95C8×C37—82no—
96C8×C37—82no—
97#7495C3711yesmaximal, characteristic, direct product factor, Sylow
98C22×C37—41no—
99C22×C37—41no—
100C22×C37—41no—
101C22×C37—81no—
102C22×C37—81no—
103C22×C37—82no—
104C22×C37—161no—
105C22×C37#34211yescharacteristic
106C22×C37AΣL(1,𝔽16)11yescharacteristic
107C22×C37#35211yescharacteristic
108C4×C37—21no—
109C4×C37—21no—
110C4×C37—41no—
111C4×C37—41no—
112C4×C37—41no—
113C4×C37—41no—
114C4×C37—82no—
115C2×#355C2×C3711yescharacteristic
116#1885C2×C3711yescharacteristic
117#1533C2×C3711yescharacteristic
118C2×C37—21no—
119C2×C37—21no—
120C2×C37—21no—
121C2×C37—81no—
122C2×C37—81no—
123C2×C37#139011yescharacteristic
124C2×#124C22×C3711yescharacteristic
125#518C4×C3711yescharacteristic
126#432—21no—
127#419—21no—
128C2×#101—21no—
129C2×#100C4×C3711yescharacteristic
130#355—21no—
131#355C4×C3712yescomplemented
132#339—21no—
133#329—21no—
134#329C4×C3712yescomplemented
135C37#749511yescharacteristic, direct product factor, Sylow
136C22×Q8D4×C3711yescharacteristic
137C22×D4C2×C4×C3711yescharacteristic
138C2×M16—21no—
139C2×M16—41no—
140#124—41no—
141#124C2×C4×C3711yescharacteristic
142#124C2×C4×C3711yescharacteristic
143#124D4×C3711yescharacteristic
144#124Q8×C3711yescharacteristic
145C4×D4—42no—
146#117—21no—
147C2×C22⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C42D4×C3711yescharacteristic
150C4⋊C8—41no—
151#103—42no—
152#101—22no—
153#101—41no—
154#100—41no—
155C22⋊C8—41no—
156#97—22no—
157C24—21no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8C22⋊C4×C3711yescharacteristic
162C2×Q8C4⋊C4×C3711yescharacteristic
163C2×D4—21no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C42×C3711yescharacteristic
167C2×D4C4⋊C4×C3711yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4C22⋊C4×C3711yescharacteristic
172M16—42no—
173M16—41no—
174M16—41no—
175M16—81no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—81no—
179C4⋊C4—22no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C42—21no—
187C42—41no—
188C42C22⋊C4×C3711yescharacteristic
189C42C4⋊C4×C3711yescharacteristic
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23—82no—
195C23#99×C3711yescharacteristic
196Q8—41no—
197Q8—41no—
198Q8—81no—
199D4—41no—
200D4—41no—
201D4—42no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—162no—
213C2×C4#95×C3711yescharacteristic
214C2×C4#99×C3711yescharacteristic
215C8—81no—
216C8—82no—
217C8—82no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—81no—
222C22—81no—
223C22—82no—
224C22—161no—
225C22C37×#34211yescharacteristic
226C22C37×AΣL(1,𝔽16)11yescharacteristic
227C22C37×#35211yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—82no—
235C2—21no—
236C2—21no—
237C2—21no—
238C2—81no—
239C2—81no—
240C2C37×#139011yescharacteristic
subgroupG/H
center, socleC2×C37#1390
commutatorC2×D4C42×C37
Frattini, cosocleC2×#124C22×C37
prime radicalC22×D4×C37C2×C4
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C23×C37 ◁ C22×C4×C37 ◁ C2×#124×C37 ◁ G

Complements

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

NH ≅ G/Ntype
11. C37×#355C4semidirect
14. C37×#329C4semidirect
97. #7495C37direct (N × H)
131. #355C4×C37semidirect
134. #329C4×C37semidirect
135. C37#7495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#3552
C37×#18852
C37×#15332
#749537