Finite Group Databasebeta

← D37⋊#356 #18010885

Subgroups — D37⋊#356 #18010885

Order 4736.

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

normal subgroups only

This group has 240 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
2#14558444C212yesmaximal, complemented
3#14558443C212yesmaximal, complemented
4C4⋊Q8×D37C211yesmaximal, characteristic
5D37⋊M16—22no—
6#11924597—22no—
7#11924597C2214yes—
8C2×Q8×D37C411yescharacteristic
9C2×Q8×D37C2211yescharacteristic
10#11924536C2211yescharacteristic
11#11924535—22no—
12#11924534C411yescharacteristic
13#11924534C2211yescharacteristic
14C4⋊C4×D37—22no—
15C42×D37C411yescharacteristic
16C4⋊Q8×C37C411yescharacteristic
17C2×Q8×C37C2×C411yescharacteristic
18C2×Q8×C37C2×C411yescharacteristic
19Q8×D37—41no—
20Q8×D37—41no—
21Q8×D37—41no—
22Q8×D37—41no—
23C2×C4×D37—21no—
24C2×C4×D37—21no—
25C2×C4×D37C2×C411yescharacteristic
26C2×C4×D37D412yes—
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29C2×Dic74D412yes—
30C2×Dic74C2311yescharacteristic
31#10596957—24no—
32#10596953—42no—
33D37⋊C8—42no—
34C4⋊C4×C37—22no—
35C42×C37C2×C411yescharacteristic
36C4⋊Dic37—22no—
37#10596936—22no—
38#10596936—22no—
39C4×Dic37—21no—
40C4×Dic37C2×C411yescharacteristic
41C22×D37C22⋊C411yescharacteristic
42Q8×C37—41no—
43Q8×C37—41no—
44C2×C4×C37—21no—
45C2×C4×C37—21no—
46C2×C4×C37C22⋊C412yes—
47C2×C4×C37C22×C411yescharacteristic
48C2×Dic37—21no—
49C2×Dic37—21no—
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C2×D412yes—
52C4×D37—24no—
53C4×D37—22no—
54C4×D37—22no—
55C4×D37—21no—
56C4×D37—21no—
57C4×D37—41no—
58C4×D37—41no—
59Dic74—42no—
60Dic74—41no—
61Dic74—42no—
62Dic74—41no—
63#64438—44no—
64C22×C37C2×C22⋊C411yescharacteristic
65C2×D37—22no—
66C2×D37#9911yescharacteristic
67C2×D37#9911yescharacteristic
68C4×C37—22no—
69C4×C37—21no—
70C4×C37—22no—
71C4×C37—41no—
72Dic37—22no—
73Dic37—22no—
74Dic37—21no—
75Dic37—41no—
76C2×#356—371nomaximal, Sylow
77C2×C37—21no—
78C2×C37C2×#9911yescharacteristic
79D37—21no—
80D37#35612yescomplemented
81C2×C4⋊Q8—371no—
82C2×#101—372no—
83#356—372no—
84#356—372no—
85C37C2×#35611yescharacteristic, complemented, Sylow
86C22×Q8—371no—
87C22×Q8—371no—
88C2×M16—742no—
89C4⋊Q8—371no—
90C4⋊Q8—371no—
91C4⋊Q8—371no—
92C4⋊Q8—742no—
93C4⋊Q8#386611yescharacteristic
94C2×C4⋊C4—742no—
95C2×C42—371no—
96#101—374no—
97#101—742no—
98C2×Q8—372no—
99C2×Q8—371no—
100C2×Q8—371no—
101C2×Q8—741no—
102C2×Q8—1481no—
103C2×Q8—1481no—
104C2×Q8—1481no—
105C2×Q8—1481no—
106C2×Q8C2×#386611yescharacteristic
107C2×Q8C2×#386611yescharacteristic
108C22×C4—372no—
109C22×C4—371no—
110C22×C4—741no—
111C22×C4—741no—
112M16—744no—
113M16—1482no—
114C2×C8—1482no—
115C4⋊C4—22no—
116C4⋊C4—742no—
117C4⋊C4—742no—
118C4⋊C4—742no—
119C42—371no—
120C42—741no—
121C42C2×#386611yescharacteristic
122C23—371no—
123Q8—41no—
124Q8—41no—
125Q8—1482no—
126Q8—1481no—
127Q8—1481no—
128Q8—1482no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—371no—
132C2×C4—372no—
133C2×C4—742no—
134C2×C4—742no—
135C2×C4—741no—
136C2×C4—741no—
137C2×C4—744no—
138C2×C4—741no—
139C2×C4—741no—
140C2×C4—1481no—
141C2×C4—1481no—
142C2×C4C22⋊#386612yes—
143C2×C4C22×#386611yescharacteristic
144C8—1484no—
145C22—371no—
146C22—371no—
147C22—742no—
148C22C2×C22⋊#386611yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—742no—
154C4—742no—
155C4—741no—
156C4—1481no—
157C2—21no—
158C2—372no—
159C2—741no—
160C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC2×C37C2×#99
prime radicalC22×D37C22⋊C4
cosocleC2×Dic74C23
hypercenterC4⋊Q8#3866
hypocenterC37C2×#356
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14558444C2semidirect
3. #14558443C2semidirect
80. D37#356semidirect
85. C37C2×#356semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1012
#145584442
#145584432
C4⋊Q8×D372
C2×#35637