Finite Group Databasebeta

← C37×#7078 #22628331

Subgroups — C37×#7078 #22628331

Order 9472.

286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#2001C211yesmaximal, characteristic
2C37×#1314C211yesmaximal, characteristic
3C37×#1289C211yesmaximal, characteristic
4C22×Q16×C37C411yescharacteristic, complemented
5C2×C22⋊Q8×C37—21no—
6C2×#103×C37—21no—
7C2×C22⋊C8×C37C2211yescharacteristic
8C37×#380—21no—
9C37×C22⋊C16—21no—
10C37×#340C411yescharacteristic, complemented
11C22×Q8×C37—21no—
12C23×C4×C37D411yescharacteristic
13C2×Q16×C37—41no—
14C2×Q16×C37—42no—
15C22×C8×C37C2×C411yescharacteristic
16C22×C8×C37D411yescharacteristic
17C22⋊Q8×C37—42no—
18C22⋊Q8×C37—42no—
19C2×C4⋊C4×C37—21no—
20C2×C4⋊C4×C37—41no—
21C2×C4⋊C4×C37—41no—
22C2×C22⋊C4×C37—41no—
23C2×C22⋊C4×C37—41no—
24C2×C16×C37—41no—
25#103×C37—42no—
26C22⋊C8×C37—41no—
27#95×C37—22no—
28C24×C37D811yescharacteristic
29C2×Q8×C37—22no—
30C2×Q8×C37—41no—
31C2×Q8×C37—41no—
32C2×Q8×C37—41no—
33C2×Q8×C37—41no—
34C2×Q8×C37—41no—
35C22×C4×C37—21no—
36C22×C4×C37—21no—
37C22×C4×C37—41no—
38C22×C4×C37—41no—
39C22×C4×C37—41no—
40C22×C4×C37—41no—
41C22×C4×C37—42no—
42C22×C4×C37C22⋊C411yescharacteristic
43C22×C4×C37SD1611yescharacteristic
44Q16×C37—42no—
45Q16×C37—42no—
46C2×C8×C37—21no—
47C2×C8×C37—21no—
48C2×C8×C37—41no—
49C2×C8×C37—41no—
50C4⋊C4×C37—22no—
51C4⋊C4×C37—41no—
52C4⋊C4×C37—44no—
53C4⋊C4×C37—81no—
54C4⋊C4×C37—81no—
55C22⋊C4×C37—44no—
56C22⋊C4×C37—81no—
57C22⋊C4×C37—81no—
58C16×C37—81no—
59C23×C37—21no—
60C23×C37—21no—
61C23×C37—41no—
62C23×C37—41no—
63C23×C37#10211yescharacteristic
64C23×C37SD3211yescharacteristic
65C23×C37Q3211yescharacteristic
66Q8×C37—42no—
67Q8×C37—42no—
68Q8×C37—81no—
69Q8×C37—81no—
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—41no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37—42no—
77C2×C4×C37—42no—
78C2×C4×C37—81no—
79C2×C4×C37—81no—
80C2×C4×C37—81no—
81C2×C4×C37—81no—
82C2×C4×C37—81no—
83C2×C4×C37—82no—
84C2×C4×C37—82no—
85C2×C4×C37—82no—
86C2×C4×C37#9911yescharacteristic
87C2×C4×C37#10411yescharacteristic
88C8×C37—41no—
89C8×C37—41no—
90#7078C3711yesmaximal, characteristic, direct product factor, Sylow
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37—81no—
100C22×C37#32711yescharacteristic
101C22×C37#35811yescharacteristic
102C22×C37#36011yescharacteristic
103C4×C37—21no—
104C4×C37—41no—
105C4×C37—82no—
106C4×C37—82no—
107C4×C37—162no—
108C4×C37AΣL(1,𝔽16)11yescharacteristic
109C4×C37#35311yescharacteristic
110#2001C2×C3711yescharacteristic
111#1314C2×C3711yescharacteristic
112#1289C2×C3711yescharacteristic
113C2×C37—21no—
114C2×C37—21no—
115C2×C37—41no—
116C2×C37—41no—
117C2×C37#134011yescharacteristic
118C2×C37#134311yescharacteristic
119C2×C37#134811yescharacteristic
120C22×Q16C4×C3711yescharacteristic, complemented
121C2×C22⋊Q8—21no—
122C2×#103—21no—
123C2×C22⋊C8C22×C3711yescharacteristic
124#380—21no—
125C22⋊C16—21no—
126#340C4×C3711yescharacteristic, complemented
127C37#707811yescharacteristic, direct product factor, Sylow
128C22×Q8—21no—
129C23×C4D4×C3711yescharacteristic
130C2×Q16—41no—
131C2×Q16—42no—
132C22×C8C2×C4×C3711yescharacteristic
133C22×C8D4×C3711yescharacteristic
134C22⋊Q8—42no—
135C22⋊Q8—42no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—41no—
141C2×C16—41no—
142#103—42no—
143C22⋊C8—41no—
144#95—22no—
145C24D8×C3711yescharacteristic
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—42no—
159C22×C4C22⋊C4×C3711yescharacteristic
160C22×C4SD16×C3711yescharacteristic
161Q16—42no—
162Q16—42no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8—41no—
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—44no—
170C4⋊C4—81no—
171C4⋊C4—81no—
172C22⋊C4—44no—
173C22⋊C4—81no—
174C22⋊C4—81no—
175C16—81no—
176C23—21no—
177C23—21no—
178C23—41no—
179C23—41no—
180C23#102×C3711yescharacteristic
181C23SD32×C3711yescharacteristic
182C23Q32×C3711yescharacteristic
183Q8—42no—
184Q8—42no—
185Q8—81no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—82no—
201C2×C4—82no—
202C2×C4—82no—
203C2×C4#99×C3711yescharacteristic
204C2×C4#104×C3711yescharacteristic
205C8—41no—
206C8—41no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22—81no—
216C22C37×#32711yescharacteristic
217C22C37×#35811yescharacteristic
218C22C37×#36011yescharacteristic
219C4—21no—
220C4—41no—
221C4—82no—
222C4—82no—
223C4—162no—
224C4C37×AΣL(1,𝔽16)11yescharacteristic
225C4C37×#35311yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2C37×#134011yescharacteristic
231C2C37×#134311yescharacteristic
232C2C37×#134811yescharacteristic
subgroupG/H
center, socleC22×C37#327
commutatorC22×C8C2×C4×C37
Frattini, cosocleC2×C22⋊C8C22×C37
prime radicalC24×C37D8
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ C2×C22⋊C8×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×Q16×C37C4semidirect
10. C37×#340C4semidirect
90. #7078C37direct (N × H)
120. C22×Q16C4×C37semidirect
126. #340C4×C37semidirect
127. C37#7078direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#20012
C37×#13142
C37×#12892
#707837