Finite Group Databasebeta

← D37⋊#354 #18010865

Subgroups — D37⋊#354 #18010865

Order 4736.

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

normal subgroups only

This group has 284 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
2#14558440C212yesmaximal, complemented
3#14558439C212yesmaximal, complemented
4#124×D37C211yesmaximal, characteristic
5C2×C22⋊#3866—22no—
6#11924595C2214yes—
7#11924594—22no—
8C2×Q8×D37C411yescharacteristic, complemented
9C2×D4×D37C2211yescharacteristic
10#11924525C2211yescharacteristic
11#11924524C2211yescharacteristic
12#11924523C411yescharacteristic, complemented
13#11924522—22no—
14C22⋊C4×D37—22no—
15C42×D37C411yescharacteristic, complemented
16#124×C37C411yescharacteristic, complemented
17C23×D37D412yes—
18C22×#3866—42no—
19C2×Q8×C37C2×C411yescharacteristic, complemented
20C2×D4×C37C2×C411yescharacteristic
21C2×C22⋊D37D412yes—
22Q8×D37—41no—
23Q8×D37—41no—
24D4×D37—41no—
25D4×D37—41no—
26C2×D148C2311yescharacteristic
27C2×C4×D37—21no—
28C2×C4×D37—21no—
29C2×C4×D37C2×C411yescharacteristic
30C2×Dic74—21no—
31C2×Dic74C2×C411yescharacteristic, complemented
32C22⋊#3866—24no—
33C22⋊#3866—42no—
34C22⋊C4×C37—22no—
35C42×C37C2×C411yescharacteristic, complemented
36C22⋊Dic37—22no—
37#10596938—22no—
38#10596938—22no—
39C4×Dic37—21no—
40C4×Dic37C2×C411yescharacteristic, complemented
41C23×C37C22⋊C412yes—
42C22×D37—22no—
43C22×D37—22no—
44C22×D37—44no—
45C22×D37C22⋊C411yescharacteristic
46C22×D37C2×D412yes—
47C2×#3866—44no—
48C2×#3866—84no—
49Q8×C37—41no—
50D4×C37—41no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37C22×C411yescharacteristic
54C22⋊D37—42no—
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37C22⋊C411yescharacteristic
58D148—41no—
59C4×D37—21no—
60C4×D37—21no—
61C4×D37—42no—
62C4×D37—41no—
63C4×D37—41no—
64Dic74—42no—
65Dic74—41no—
66C22×C37—22no—
67C22×C37—42no—
68C22×C37C2×C22⋊C411yescharacteristic
69C2×D37—22no—
70C2×D37—22no—
71C2×D37—44no—
72C2×D37—42no—
73C2×D37—82no—
74C2×D37#9911yescharacteristic
75C2×D37#9911yescharacteristic
76#3866—84no—
77C4×C37—21no—
78C4×C37—41no—
79C4×C37—41no—
80Dic37—21no—
81Dic37—41no—
82Dic37—41no—
83C2×#354—371nomaximal, Sylow
84C2×C37—21no—
85C2×C37—42no—
86C2×C37C2×#9911yescharacteristic
87D37—21no—
88D37—42no—
89D37#35412yescomplemented
90C2×#124—371no—
91C2×#99—372no—
92#354—372no—
93#354—372no—
94C37C2×#35411yescharacteristic, complemented, Sylow
95C22×Q8—371no—
96C22×D4—371no—
97#124—371no—
98#124—371no—
99#124—371no—
100#124—742no—
101#124#386611yescharacteristic, complemented
102C2×C22⋊C4—742no—
103C2×C22⋊C4—742no—
104C2×C42—371no—
105#99—374no—
106#99—742no—
107C24—372no—
108C2×Q8—371no—
109C2×Q8—741no—
110C2×Q8—1481no—
111C2×Q8—1481no—
112C2×Q8C2×#386611yescharacteristic, complemented
113C2×D4—372no—
114C2×D4—371no—
115C2×D4—1481no—
116C2×D4—1481no—
117C2×D4C2×#386611yescharacteristic
118C22×C4—371no—
119C22×C4—741no—
120C22×C4—741no—
121C22×C4—1482no—
122C22⋊C4—22no—
123C22⋊C4—742no—
124C22⋊C4—742no—
125C22⋊C4—742no—
126C22⋊C4—744no—
127C22⋊C4—1482no—
128C42—371no—
129C42—741no—
130C42C2×#386611yescharacteristic, complemented
131C23—371no—
132C23—372no—
133C23—742no—
134C23—742no—
135C23—1484no—
136C23C22⋊#386612yes—
137Q8—41no—
138Q8—1481no—
139Q8—1482no—
140D4—41no—
141D4—1481no—
142D4—1482no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—371no—
146C2×C4—2964no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4—741no—
150C2×C4—741no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4—1482no—
154C2×C4—1484no—
155C2×C4C22×#386611yescharacteristic
156C22—22no—
157C22—42no—
158C22—371no—
159C22—371no—
160C22—2962no—
161C22—742no—
162C22—742no—
163C22—1482no—
164C22—1484no—
165C22C2×C22⋊#386611yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—2964no—
170C4—741no—
171C4—1481no—
172C4—1481no—
173C2—21no—
174C2—42no—
175C2—372no—
176C2—741no—
177C2—1482no—
178C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37C2×#99
prime radicalC2×D4×D37C22
cosocleC2×D148C23
hypercenter#124#3866
hypocenterC37C2×#354
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #14558440C2semidirect
3. #14558439C2semidirect
8. C2×Q8×D37C4semidirect
12. #11924523C4semidirect
15. C42×D37C4semidirect
16. #124×C37C4semidirect
19. C2×Q8×C37C2×C4semidirect
31. C2×Dic74C2×C4semidirect
35. C42×C37C2×C4semidirect
40. C4×Dic37C2×C4semidirect
89. D37#354semidirect
94. C37C2×#354semidirect
101. #124#3866semidirect
112. C2×Q8C2×#3866semidirect
130. C42C2×#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#992
#145584402
#145584392
#124×D372
C2×#35437