Finite Group Databasebeta

← #18010758

Subgroups — #18010758

Order 4736.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D37⋊#108C211yesmaximal, characteristic
2#14558526C212yesmaximal
3D37⋊#101C212yesmaximal
4#14558496C211yesmaximal, characteristic
5C2×Q16×D37C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7D37⋊M16C2211yescharacteristic
8#11924615C2211yescharacteristic
9#11924607—21no—
10#11924606—21no—
11#11924599—24no—
12#11924597—24no—
13#11924590—21no—
14C8×#3866—21no—
15C2×Q8×D37C2212yes—
16C2×Dic148C411yescharacteristic, complemented
17C2×#10596942C412yescomplemented
18Q16×D37—21no—
19Q16×D37—21no—
20Q16×D37—21no—
21Q16×D37—21no—
22C2×C8×D37C2211yescharacteristic
23C2×Q16×C37C411yescharacteristic, complemented
24C2×Q8×C37C2×C412yes—
25Q8×D37—22no—
26Q8×D37—22no—
27Q8×D37—22no—
28Q8×D37—22no—
29C2×C4×D37—22no—
30C2×C4×D37C2311yescharacteristic
31C2×Dic74—22no—
32C2×Dic74C2×C412yes—
33C22⋊#3866—21no—
34#10596957—22no—
35#10596957D412yes—
36C4⋊#3866D412yes—
37C4×#3866—21no—
38#10596953—21no—
39#10596953—22no—
40D37⋊C8—21no—
41D37⋊C8—22no—
42Q16×C37—21no—
43Q16×C37—21no—
44C2×C8×C37C2×C411yescharacteristic
45#10596942—22no—
46#10596942—22no—
47C2×#64436C2×C411yescharacteristic
48Dic148—21no—
49Dic148—21no—
50C8×D37D411yescharacteristic
51C8×D37D411yescharacteristic
52C8×D37D411yescharacteristic
53C8×D37D411yescharacteristic
54C22×D37#4111yescharacteristic
55C2×#3866—22no—
56Q8×C37—22no—
57Q8×C37—22no—
58C2×C4×C37—22no—
59C2×C4×C37C22×C411yescharacteristic
60C2×Dic37—22no—
61C2×Dic37C2×D411yescharacteristic
62C4×D37—42no—
63C4×D37—42no—
64C4×D37C2×D411yescharacteristic
65C4×D37C2×D411yescharacteristic
66C4×D37C2×D411yescharacteristic
67C4×D37#4111yescharacteristic
68Dic74—22no—
69Dic74—22no—
70Dic74—42no—
71Dic74—42no—
72#64438—22no—
73#64438—42no—
74C8×C37C22⋊C411yescharacteristic
75C8×C37C22⋊C411yescharacteristic
76#64436C22⋊C411yescharacteristic
77#64436C22⋊C411yescharacteristic
78C22×C37C4×D411yescharacteristic
79C2×D37—22no—
80C2×D37#12111yescharacteristic
81C2×D37#12411yescharacteristic
82#3866—42no—
83C4×C37—42no—
84C4×C37C2×C22⋊C411yescharacteristic
85C4×C37C4×D411yescharacteristic
86Dic37—42no—
87Dic37#12111yescharacteristic
88Dic37#12711yescharacteristic
89#1979—371nomaximal, Sylow
90C2×C37—21no—
91C2×C37#39011yescharacteristic
92D37—21no—
93D37#47312yes—
94C22×Q16—371no—
95C2×#108—371no—
96#419—372no—
97C2×#101—372no—
98#405—371no—
99C37#197911yescharacteristic, complemented, Sylow
100C22×Q8—372no—
101C2×Q16—372no—
102C2×Q16—371no—
103C2×Q16—741no—
104C2×Q16—741no—
105C2×Q16—741no—
106C2×Q16—741no—
107C2×Q16#386611yescharacteristic, complemented
108C2×M16—371no—
109C2×M16—372no—
110C22×C8—371no—
111#117—371no—
112#108—741no—
113#108—741no—
114#103—744no—
115#101—744no—
116#97—741no—
117C4×C8—741no—
118C2×Q8—372no—
119C2×Q8—742no—
120C2×Q8—742no—
121C2×Q8—742no—
122C2×Q8—742no—
123C2×Q8—742no—
124C2×Q8C2×#386612yes—
125C22×C4—371no—
126C22×C4—742no—
127Q16—21no—
128Q16—21no—
129Q16—742no—
130Q16—742no—
131Q16—741no—
132Q16—741no—
133M16—372no—
134M16—741no—
135M16—742no—
136M16—742no—
137C2×C8—371no—
138C2×C8—371no—
139C2×C8—371no—
140C2×C8—371no—
141C2×C8—371no—
142C2×C8—741no—
143C2×C8—742no—
144C2×C8C2×#386611yescharacteristic
145C4⋊C4—372no—
146C22⋊C4—741no—
147C42—741no—
148C23—371no—
149Q8—22no—
150Q8—22no—
151Q8—742no—
152Q8—742no—
153Q8—1482no—
154Q8—1482no—
155C2×C4—22no—
156C2×C4—371no—
157C2×C4—371no—
158C2×C4—371no—
159C2×C4—371no—
160C2×C4—371no—
161C2×C4—742no—
162C2×C4—742no—
163C2×C4—1482no—
164C2×C4—1482no—
165C2×C4C22×#386611yescharacteristic
166C8—371no—
167C8—371no—
168C8—742no—
169C8—1482no—
170C8C22⋊#386611yescharacteristic
171C8C22⋊#386611yescharacteristic
172C22—371no—
173C22—371no—
174C22—742no—
175C22D4×#386611yescharacteristic
176C4—42no—
177C4—371no—
178C4—371no—
179C4—1482no—
180C4—1482no—
181C4C2×C22⋊#386611yescharacteristic
182C4D4×#386611yescharacteristic
183C2—21no—
184C2—372no—
185C2—741no—
186C2#1455848511yescharacteristic
subgroupG/H
centerC2#14558485
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×Q16×C37C4
socleC2×C37#390
prime radicalC22×D37#41
cosocleC2×C4×D37C23
hypercenterC2×Q16#3866
hypocenterC37#1979
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
16. C2×Dic148C4semidirect
17. C2×#10596942C4semidirect
23. C2×Q16×C37C4semidirect
99. C37#1979semidirect
107. C2×Q16#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1082
#145585262
D37⋊#1012
#145584962
C2×Q16×D372
#197937