Finite Group Databasebeta

← D37⋊#353 #18010862

Subgroups — D37⋊#353 #18010862

Order 4736.

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

normal subgroups only

This group has 368 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
1D37⋊#99C212yesmaximal, complemented
2#14558438C212yesmaximal, complemented
3#14558437C212yesmaximal, complemented
4#127×D37C211yesmaximal, characteristic
5C2×C22⋊#3866—22no—
6#11924595C2214yescomplemented
7#11924594—22no—
8C2×D4×D37—22no—
9C2×D4×D37C411yescharacteristic, complemented
10C2×D4×D37C2211yescharacteristic
11#11924533C2211yescharacteristic
12#11924532—22no—
13#11924532C411yescharacteristic, complemented
14#11924532C2211yescharacteristic
15C42×D37C411yescharacteristic, complemented
16#127×C37C411yescharacteristic, complemented
17C23×D37—21no—
18C23×D37D412yes—
19C22×#3866—42no—
20C2×D4×C37—22no—
21C2×D4×C37C2×C411yescharacteristic
22C2×D4×C37C2×C411yescharacteristic, complemented
23C2×C22⋊D37—22no—
24C2×C22⋊D37—22no—
25C2×C22⋊D37—21no—
26C2×C22⋊D37D412yes—
27D4×D37—41no—
28D4×D37—41no—
29D4×D37—41no—
30D4×D37—41no—
31D4×D37—48no—
32C2×D148—22no—
33C2×D148C2×C411yescharacteristic, complemented
34C2×D148C2311yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37C2×C411yescharacteristic
37C22⋊#3866—24no—
38C22⋊#3866—42no—
39C42×C37C2×C411yescharacteristic, complemented
40C4×Dic37—21no—
41C4×Dic37C2×C411yescharacteristic, complemented
42C23×C37—21no—
43C23×C37C22⋊C412yes—
44C22×D37—22no—
45C22×D37—22no—
46C22×D37—21no—
47C22×D37—44no—
48C22×D37—44no—
49C22×D37—41no—
50C22×D37—41no—
51C22×D37C22⋊C411yescharacteristic
52C22×D37C2×D412yes—
53C2×#3866—44no—
54C2×#3866—84no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—44no—
58C2×C4×C37—21no—
59C2×C4×C37C22×C411yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—44no—
62C22⋊D37—44no—
63C22⋊D37—42no—
64C2×Dic37—21no—
65C2×Dic37C22⋊C411yescharacteristic
66D148—41no—
67D148—41no—
68D148—44no—
69C4×D37—24no—
70C4×D37—21no—
71C4×D37—21no—
72C22×C37—22no—
73C22×C37—42no—
74C22×C37—42no—
75C22×C37—41no—
76C22×C37C2×C22⋊C411yescharacteristic
77C2×D37—22no—
78C2×D37—22no—
79C2×D37—44no—
80C2×D37—42no—
81C2×D37—42no—
82C2×D37—41no—
83C2×D37—82no—
84C2×D37—82no—
85C2×D37—82no—
86C2×D37#9911yescharacteristic
87C2×D37#9911yescharacteristic
88#3866—84no—
89C4×C37—22no—
90C4×C37—21no—
91Dic37—22no—
92Dic37—21no—
93C2×#353—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—42no—
96C2×C37—81no—
97C2×C37C2×#9911yescharacteristic
98D37—21no—
99D37—42no—
100D37—81no—
101D37#35312yescomplemented
102C2×#127—371no—
103C2×#99—372no—
104#353—372no—
105#353—372no—
106C37C2×#35311yescharacteristic, complemented, Sylow
107C22×D4—371no—
108C22×D4—371no—
109C22×D4—742no—
110#127—371no—
111#127—371no—
112#127—371no—
113#127—742no—
114#127#386611yescharacteristic, complemented
115C2×C22⋊C4—742no—
116C2×C42—371no—
117#99—374no—
118#99—742no—
119C24—372no—
120C24—741no—
121C2×D4—22no—
122C2×D4—372no—
123C2×D4—371no—
124C2×D4—371no—
125C2×D4—742no—
126C2×D4—741no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—1481no—
130C2×D4—1481no—
131C2×D4—1481no—
132C2×D4—1481no—
133C2×D4—1488no—
134C2×D4C2×#386611yescharacteristic
135C2×D4C2×#386611yescharacteristic, complemented
136C22×C4—371no—
137C22×C4—741no—
138C22×C4—1482no—
139C22⋊C4—744no—
140C22⋊C4—1482no—
141C42—371no—
142C42—741no—
143C42C2×#386611yescharacteristic, complemented
144C23—21no—
145C23—371no—
146C23—372no—
147C23—742no—
148C23—742no—
149C23—741no—
150C23—1481no—
151C23—1481no—
152C23—1484no—
153C23—1484no—
154C23C22⋊#386612yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—1481no—
159D4—1481no—
160D4—1484no—
161D4—1482no—
162D4—1484no—
163D4—1484no—
164D4—1482no—
165C2×C4—21no—
166C2×C4—371no—
167C2×C4—2964no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—744no—
171C2×C4—741no—
172C2×C4—1484no—
173C2×C4C22×#386611yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—371no—
179C22—371no—
180C22—2962no—
181C22—2962no—
182C22—2962no—
183C22—742no—
184C22—742no—
185C22—1482no—
186C22—1482no—
187C22—1484no—
188C22—1481no—
189C22C2×C22⋊#386611yescharacteristic
190C4—22no—
191C4—21no—
192C4—2964no—
193C4—742no—
194C4—741no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—372no—
199C2—2961no—
200C2—741no—
201C2—1482no—
202C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC2×C37C2×#99
prime radical#127×D37C2
cosocleC2×D148C23
hypercenter#127#3866
hypocenterC37C2×#353
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D37⋊#99C2semidirect
2. #14558438C2semidirect
3. #14558437C2semidirect
6. #11924595C22semidirect
9. C2×D4×D37C4semidirect
13. #11924532C4semidirect
15. C42×D37C4semidirect
16. #127×C37C4semidirect
22. C2×D4×C37C2×C4semidirect
33. C2×D148C2×C4semidirect
39. C42×C37C2×C4semidirect
41. C4×Dic37C2×C4semidirect
101. D37#353semidirect
106. C37C2×#353semidirect
114. #127#3866semidirect
135. C2×D4C2×#3866semidirect
143. C42C2×#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#992
#145584382
#145584372
#127×D372
C2×#35337