Finite Group Databasebeta

← #324×D37 #17992904

Subgroups — #324×D37 #17992904

Order 4736.

328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊C4×D37C211yesmaximal, characteristic
2C22⋊C8×D37C212yesmaximal
3#14557259C211yesmaximal, characteristic, complemented
4#14557258C212yesmaximal, complemented
5C37×#324C211yesmaximal, characteristic, complemented
6C22×C4×D37C411yescharacteristic
7C22×C4×D37C411yescharacteristic
8C22×C4×D37C2211yescharacteristic
9C2×C8×D37—22no—
10C2×C4⋊Dic37C411yescharacteristic
11C2×#10596936C411yescharacteristic
12C2×#10596936C2211yescharacteristic
13C4⋊C4×D37—22no—
14C4⋊C4×D37—22no—
15C22⋊#64436C2212yes—
16#11924448—22no—
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C23×D37C2×C411yescharacteristic
20C22×C4×C37C2×C411yescharacteristic
21C22×C4×C37C2×C411yescharacteristic
22C22×C4×C37C2311yescharacteristic
23C22×Dic37C2×C411yescharacteristic
24C22×Dic37C2×C411yescharacteristic
25C22×Dic37C2×C411yescharacteristic
26C2×C4×D37—21no—
27C2×C4×D37—21no—
28C2×C4×D37—22no—
29C2×C4×D37—21no—
30C2×C4×D37—21no—
31C2×C4×D37—42no—
32C2×C4×D37—42no—
33C2×C4×D37C814yescomplemented
34C2×C4×D37D412yes—
35C2×C4×D37D412yes—
36C2×C8×C37—22no—
37C4⋊C4×C37—22no—
38C4⋊Dic37—22no—
39#10596936—22no—
40#10596936—22no—
41C2×#64436—22no—
42C8×D37—44no—
43C23×C37C22×C411yescharacteristic
44C22×D37—22no—
45C22×D37—22no—
46C22×D37C22⋊C411yescharacteristic
47C22×D37C22⋊C411yescharacteristic
48C22×D37C2×C812yes—
49C22×D37M1612yes—
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37C2×C812yescomplemented
56C2×C4×C37C2×D412yes—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—41no—
61C2×Dic37—41no—
62C2×Dic37C22⋊C412yes—
63C2×Dic37C2×C812yescomplemented
64C4×D37—24no—
65C4×D37—24no—
66C4×D37—24no—
67C4×D37—42no—
68C4×D37—42no—
69C4×D37—42no—
70C8×C37—42no—
71#64436—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37C2×C22⋊C411yescharacteristic
75C22×C37C22×C811yescharacteristic
76C22×C37C2×M1611yescharacteristic
77C2×D37—21no—
78C2×D37—21no—
79C2×D37—24no—
80C2×D37—24no—
81C2×D37C22⋊C812yes—
82C2×D37C22⋊C812yes—
83C2×D37#9912yes—
84C2×D37#10112yes—
85C4×C37—22no—
86C4×C37—22no—
87C4×C37—41no—
88Dic37—22no—
89Dic37—22no—
90Dic37—41no—
91C2×#324—371nomaximal, Sylow
92C2×C37—21no—
93C2×C37—21no—
94C2×C37C2×C22⋊C811yescharacteristic
95C2×C37C2×#9911yescharacteristic
96C2×C37C2×#10111yescharacteristic
97D37—22no—
98D37#32414yesdirect product factor
99C22×C4⋊C4—371no—
100C2×C22⋊C8—372no—
101#324—371no—
102#324—372no—
103#324D3711yescharacteristic, direct product factor
104C37C2×#32411yescharacteristic, complemented, Sylow
105C23×C4—371no—
106C23×C4—371no—
107C23×C4—371no—
108C22×C8—742no—
109C2×C4⋊C4—371no—
110C2×C4⋊C4—371no—
111C2×C4⋊C4—371no—
112C2×C4⋊C4—742no—
113C2×C4⋊C4—742no—
114C2×C4⋊C4C2×D3711yescharacteristic
115C22⋊C8—372no—
116C22⋊C8—742no—
117C22⋊C8C2×D3712yes—
118C24—371no—
119C22×C4—371no—
120C22×C4—371no—
121C22×C4—374no—
122C22×C4—372no—
123C22×C4—372no—
124C22×C4—371no—
125C22×C4—741no—
126C22×C4—741no—
127C22×C4—742no—
128C22×C4—741no—
129C22×C4—741no—
130C22×C4—1482no—
131C22×C4—1482no—
132C22×C4C4×D3711yescharacteristic
133C22×C4C4×D3711yescharacteristic
134C22×C4C22×D3711yescharacteristic
135C2×C8—22no—
136C2×C8—742no—
137C2×C8—1484no—
138C4⋊C4—22no—
139C4⋊C4—742no—
140C4⋊C4—742no—
141C4⋊C4—742no—
142C23—371no—
143C23—371no—
144C23—372no—
145C23—372no—
146C23—742no—
147C23—742no—
148C23C2×C4×D3711yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—372no—
155C2×C4—372no—
156C2×C4—744no—
157C2×C4—744no—
158C2×C4—744no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4—1482no—
163C2×C4—1482no—
164C2×C4—1482no—
165C2×C4—1481no—
166C2×C4—1481no—
167C2×C4C8×D3712yescomplemented
168C2×C4D4×D3712yes—
169C8—42no—
170C8—1482no—
171C22—21no—
172C22—21no—
173C22—372no—
174C22—372no—
175C22—372no—
176C22—372no—
177C22—744no—
178C22—744no—
179C22—741no—
180C22—741no—
181C22C22⋊C4×D3711yescharacteristic
182C22C2×C8×D3711yescharacteristic
183C22M16×D3711yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—742no—
188C4—742no—
189C4—1481no—
190C2—21no—
191C2—21no—
192C2—374no—
193C2—742no—
194C2C22⋊C8×D3711yescharacteristic
195C2#99×D3711yescharacteristic
196C2#101×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC22×C37C22×C8
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#324D37
hypocenterC37C2×#324
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #14557259C2semidirect
4. #14557258C2semidirect
5. C37×#324C2semidirect
33. C2×C4×D37C8semidirect
55. C2×C4×C37C2×C8semidirect
63. C2×Dic37C2×C8semidirect
98. D37#324direct (N × H)
103. #324D37direct (N × H)
104. C37C2×#324semidirect
167. C2×C4C8×D37semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D372
C22⋊C8×D372
#145572592
#145572582
C37×#3242
C2×#32437