Finite Group Databasebeta

← D37⋊#355 #18010882

Subgroups — D37⋊#355 #18010882

Order 4736.

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

normal subgroups only

This group has 260 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⋊#101C212yesmaximal, complemented
2#14558442C212yesmaximal, complemented
3#14558441C212yesmaximal, complemented
4#124×D37C211yesmaximal, characteristic
5D37⋊M16—22no—
6#11924597—22no—
7#11924597C2214yescomplemented
8C2×Q8×D37C2211yescharacteristic
9C2×D4×D37C411yescharacteristic
10#11924525C411yescharacteristic
11#11924524C2211yescharacteristic
12#11924523C2211yescharacteristic
13#11924522—22no—
14C22⋊C4×D37—22no—
15C42×D37C411yescharacteristic
16#124×C37C411yescharacteristic
17C23×D37—21no—
18C2×Q8×C37C2×C411yescharacteristic
19C2×D4×C37C2×C411yescharacteristic
20C2×C22⋊D37—21no—
21Q8×D37—41no—
22Q8×D37—41no—
23D4×D37—41no—
24D4×D37—41no—
25C2×D148C2×C411yescharacteristic
26C2×C4×D37—21no—
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D412yes—
29C2×Dic74D412yes—
30C2×Dic74C2311yescharacteristic
31#10596957—24no—
32#10596953—42no—
33D37⋊C8—42no—
34C22⋊C4×C37—22no—
35C42×C37C2×C411yescharacteristic
36C22⋊Dic37—22no—
37#10596938—22no—
38#10596938—22no—
39C4×Dic37—21no—
40C4×Dic37C2×C411yescharacteristic
41C23×C37—21no—
42C22×D37—21no—
43C22×D37—44no—
44C22×D37—41no—
45C22×D37—41no—
46C22×D37C22⋊C411yescharacteristic
47Q8×C37—41no—
48D4×C37—41no—
49C2×C4×C37—21no—
50C2×C4×C37C22⋊C412yes—
51C2×C4×C37C22×C411yescharacteristic
52C22⋊D37—42no—
53C2×Dic37—21no—
54C2×Dic37C22⋊C411yescharacteristic
55C2×Dic37C2×D412yes—
56D148—41no—
57C4×D37—22no—
58C4×D37—22no—
59C4×D37—21no—
60C4×D37—21no—
61C4×D37—42no—
62Dic74—42no—
63Dic74—41no—
64#64438—44no—
65C22×C37—42no—
66C22×C37—41no—
67C22×C37C2×C22⋊C411yescharacteristic
68C2×D37—22no—
69C2×D37—42no—
70C2×D37—41no—
71C2×D37—82no—
72C2×D37—82no—
73C2×D37#9911yescharacteristic
74C2×D37#9911yescharacteristic
75C4×C37—21no—
76C4×C37—22no—
77C4×C37—41no—
78Dic37—22no—
79Dic37—21no—
80Dic37—41no—
81C2×#355—371nomaximal, Sylow
82C2×C37—21no—
83C2×C37—81no—
84C2×C37C2×#9911yescharacteristic
85D37—21no—
86D37—81no—
87D37#35512yescomplemented
88C2×#124—371no—
89C2×#101—372no—
90#355—372no—
91#355—372no—
92C37C2×#35511yescharacteristic, complemented, Sylow
93C22×Q8—371no—
94C22×D4—371no—
95C2×M16—742no—
96#124—371no—
97#124—371no—
98#124—371no—
99#124—742no—
100#124#386611yescharacteristic
101C2×C22⋊C4—742no—
102C2×C42—371no—
103#101—374no—
104#101—742no—
105C24—741no—
106C2×Q8—372no—
107C2×Q8—371no—
108C2×Q8—1481no—
109C2×Q8—1481no—
110C2×Q8C2×#386611yescharacteristic
111C2×D4—371no—
112C2×D4—741no—
113C2×D4—1481no—
114C2×D4—1481no—
115C2×D4C2×#386611yescharacteristic
116C22×C4—372no—
117C22×C4—371no—
118C22×C4—741no—
119M16—744no—
120M16—1482no—
121C2×C8—1482no—
122C22⋊C4—22no—
123C22⋊C4—742no—
124C22⋊C4—742no—
125C22⋊C4—742no—
126C42—371no—
127C42—741no—
128C42C2×#386611yescharacteristic
129C23—21no—
130C23—371no—
131C23—741no—
132C23—1481no—
133C23—1481no—
134C23—1484no—
135Q8—41no—
136Q8—1482no—
137Q8—1481no—
138D4—41no—
139D4—1481no—
140D4—1482no—
141C2×C4—21no—
142C2×C4—371no—
143C2×C4—372no—
144C2×C4—742no—
145C2×C4—742no—
146C2×C4—741no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4—1482no—
150C2×C4C22⋊#386612yes—
151C2×C4C22×#386611yescharacteristic
152C8—1484no—
153C22—42no—
154C22—41no—
155C22—371no—
156C22—371no—
157C22—2962no—
158C22—2962no—
159C22—742no—
160C22—1482no—
161C22—1481no—
162C22C2×C22⋊#386611yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—742no—
167C4—741no—
168C4—1481no—
169C2—21no—
170C2—81no—
171C2—372no—
172C2—2961no—
173C2—741no—
174C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37C2×#99
prime radicalC2×D4×D37C4
cosocleC2×Dic74C23
hypercenter#124#3866
hypocenterC37C2×#355
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D37⋊#101C2semidirect
2. #14558442C2semidirect
3. #14558441C2semidirect
7. #11924597C22semidirect
87. D37#355semidirect
92. C37C2×#355semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1012
#145584422
#145584412
#124×D372
C2×#35537