Finite Group Databasebeta

← #18010757

Subgroups — #18010757

Order 4736.

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

normal subgroups only

This group has 316 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, complemented
2#14558525C212yesmaximal, complemented
3D37⋊#100C212yesmaximal, complemented
4#14558496C211yesmaximal, characteristic, complemented
5C2×D8×D37C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7D37⋊M16C2211yescharacteristic
8#11924615C2211yescharacteristic
9#11924607—21no—
10#11924606—21no—
11#11924598—24no—
12#11924596—24no—
13#11924590—21no—
14C8×#3866—21no—
15C2×D4×D37C2212yes—
16C2×D296C411yescharacteristic, complemented
17C2×#10596939C412yescomplemented
18D8×D37—21no—
19D8×D37—21no—
20D8×D37—21no—
21D8×D37—21no—
22C2×C8×D37C2211yescharacteristic
23C2×D8×C37C411yescharacteristic, complemented
24C23×D37—22no—
25C2×D4×C37C2×C412yes—
26C2×C22⋊D37—22no—
27D4×D37—22no—
28D4×D37—22no—
29D4×D37—22no—
30D4×D37—22no—
31C2×D148C2×C412yes—
32C2×C4×D37C2311yescharacteristic
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—
42D8×C37—21no—
43D8×C37—21no—
44C2×C8×C37C2×C411yescharacteristic
45#10596939—22no—
46#10596939—22no—
47C2×#64436C2×C411yescharacteristic
48D296—21no—
49D296—21no—
50C8×D37D411yescharacteristic
51C8×D37D411yescharacteristic
52C8×D37D411yescharacteristic
53C8×D37D411yescharacteristic
54C23×C37—22no—
55C22×D37—22no—
56C22×D37—42no—
57C22×D37—42no—
58C22×D37—84no—
59C22×D37#4111yescharacteristic
60C2×#3866—22no—
61D4×C37—22no—
62D4×C37—22no—
63C2×C4×C37C22×C411yescharacteristic
64C22⋊D37—42no—
65C22⋊D37—42no—
66C2×Dic37C2×D411yescharacteristic
67D148—22no—
68D148—22no—
69C4×D37C2×D411yescharacteristic
70C4×D37C2×D411yescharacteristic
71C4×D37C2×D411yescharacteristic
72C4×D37#4111yescharacteristic
73#64438—22no—
74#64438—42no—
75C8×C37C22⋊C411yescharacteristic
76C8×C37C22⋊C411yescharacteristic
77#64436C22⋊C411yescharacteristic
78#64436C22⋊C411yescharacteristic
79C22×C37—42no—
80C22×C37—82no—
81C22×C37C4×D411yescharacteristic
82C2×D37—22no—
83C2×D37—42no—
84C2×D37—84no—
85C2×D37—84no—
86C2×D37—82no—
87C2×D37#12111yescharacteristic
88C2×D37#12411yescharacteristic
89#3866—42no—
90C4×C37C2×C22⋊C411yescharacteristic
91C4×C37C4×D411yescharacteristic
92Dic37#12111yescharacteristic
93Dic37#12711yescharacteristic
94#1978—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—82no—
97C2×C37#39011yescharacteristic
98D37—21no—
99D37—82no—
100D37#47212yes—
101C22×D8—371no—
102C2×#108—371no—
103#418—372no—
104C2×#100—372no—
105#405—371no—
106C37#197811yescharacteristic, complemented, Sylow
107C22×D4—372no—
108C2×D8—372no—
109C2×D8—371no—
110C2×D8—741no—
111C2×D8—741no—
112C2×D8—741no—
113C2×D8—741no—
114C2×D8#386611yescharacteristic, complemented
115C2×M16—371no—
116C2×M16—372no—
117C22×C8—371no—
118#117—371no—
119#108—741no—
120#108—741no—
121#102—744no—
122#100—744no—
123#97—741no—
124C4×C8—741no—
125C24—742no—
126C2×D4—372no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—742no—
130C2×D4—742no—
131C2×D4—742no—
132C2×D4C2×#386612yes—
133C22×C4—371no—
134D8—21no—
135D8—21no—
136D8—742no—
137D8—742no—
138D8—741no—
139D8—741no—
140M16—372no—
141M16—741no—
142M16—742no—
143M16—742no—
144C2×C8—371no—
145C2×C8—371no—
146C2×C8—371no—
147C2×C8—371no—
148C2×C8—371no—
149C2×C8—741no—
150C2×C8—742no—
151C2×C8C2×#386611yescharacteristic
152C4⋊C4—372no—
153C22⋊C4—741no—
154C42—741no—
155C23—22no—
156C23—371no—
157C23—2964no—
158C23—742no—
159C23—1482no—
160C23—1482no—
161D4—22no—
162D4—22no—
163D4—742no—
164D4—742no—
165D4—1482no—
166D4—1482no—
167C2×C4—371no—
168C2×C4—371no—
169C2×C4—371no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—742no—
173C2×C4C22×#386611yescharacteristic
174C8—371no—
175C8—371no—
176C8—742no—
177C8—1482no—
178C8C22⋊#386611yescharacteristic
179C8C22⋊#386611yescharacteristic
180C22—42no—
181C22—82no—
182C22—371no—
183C22—371no—
184C22—2962no—
185C22—2964no—
186C22—2964no—
187C22—742no—
188C22—1482no—
189C22D4×#386611yescharacteristic
190C4—371no—
191C4—371no—
192C4—1482no—
193C4C2×C22⋊#386611yescharacteristic
194C4D4×#386611yescharacteristic
195C2—21no—
196C2—82no—
197C2—372no—
198C2—2962no—
199C2—741no—
200C2#1455848511yescharacteristic
subgroupG/H
centerC2#14558485
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×D8×C37C4
socleC2×C37#390
prime radicalC2×D8×D37C2
cosocleC2×C4×D37C23
hypercenterC2×D8#3866
hypocenterC37#1978
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D37⋊#108C2semidirect
2. #14558525C2semidirect
3. D37⋊#100C2semidirect
4. #14558496C2semidirect
16. C2×D296C4semidirect
17. C2×#10596939C4semidirect
23. C2×D8×C37C4semidirect
106. C37#1978semidirect
114. C2×D8#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1082
#145585252
D37⋊#1002
#145584962
C2×D8×D372
#197837