Finite Group Databasebeta

← #17993266

Subgroups — #17993266

Order 4736.

240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4⋊Q8×D37C211yesmaximal, characteristic
2#14557585C211yesmaximal, characteristic
3#14557555C211yesmaximal, characteristic
4#14557280C211yesmaximal, characteristic, complemented
5#14557279C211yesmaximal, characteristic, complemented
6#14557278C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9C2×#10596929—21no—
10#11924536C2211yescharacteristic
11#11924535—21no—
12#11924535C412yes—
13#11924534—21no—
14C4⋊C4×D37—21no—
15C4⋊C4×D37C412yes—
16C42×D37C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21C8×Dic37—21no—
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26Q8×D37—42no—
27Q8×D37—42no—
28C2×C4×D37—22no—
29C2×C4×D37C2×C411yescharacteristic
30C2×C4×D37D411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×Dic74—21no—
33C2×Dic74—22no—
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37C2×C412yes—
38C42×C37C2311yescharacteristic
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C412yes—
41#10596936—22no—
42#10596936—22no—
43C4×Dic37C2×C411yescharacteristic
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C2×#64436—21no—
47C2×#64436—21no—
48#10596929—42no—
49C22×D37C22⋊C411yescharacteristic
50Q8×C37—41no—
51Q8×C37—41no—
52C2×C4×C37—22no—
53C2×C4×C37C22×C411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×Dic37—22no—
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C22⋊C411yescharacteristic
59C2×Dic37C22⋊C411yescharacteristic
60C4×D37—21no—
61C4×D37—21no—
62C4×D37—22no—
63C4×D37—44no—
64C4×D37D812yes—
65C4×D37SD1612yes—
66Dic74—41no—
67Dic74—41no—
68Dic74—44no—
69C8×C37—41no—
70C8×C37—41no—
71#64436—41no—
72#64436—41no—
73C22×C37C2×C22⋊C411yescharacteristic
74C2×D37—21no—
75C2×D37—21no—
76C2×D37#10212yes—
77C4×C37—21no—
78C4×C37—42no—
79C4×C37C2×D811yescharacteristic
80C4×C37C2×SD1611yescharacteristic
81C4×C37#13711yescharacteristic
82C4×C37#13711yescharacteristic
83Dic37—21no—
84Dic37—42no—
85Dic37#10112yes—
86Dic37#10212yes—
87#1546—371nomaximal, Sylow
88C2×C37C2×#10111yescharacteristic
89C2×C37C2×#10211yescharacteristic
90C2×C37#41911yescharacteristic
91D37—22no—
92C2×C4⋊Q8—371no—
93#431—371no—
94#423—371no—
95#332—371no—
96#332—371no—
97#332—371no—
98#332D3711yescharacteristic, complemented
99C37#154611yescharacteristic, complemented, Sylow
100C22×Q8—741no—
101C2×M16—741no—
102C4⋊Q8—372no—
103C4⋊Q8—371no—
104C4⋊Q8—741no—
105C4⋊Q8—741no—
106C4⋊Q8C2×D3711yescharacteristic
107C2×C4⋊C4—372no—
108C2×C4⋊C4—741no—
109C2×C42—371no—
110C4⋊C8—371no—
111C4⋊C8—371no—
112C4⋊C8—741no—
113C4⋊C8C2×D3711yescharacteristic
114C4⋊C8C2×D3711yescharacteristic
115C22⋊C8—741no—
116C4×C8—741no—
117C2×Q8—21no—
118C2×Q8—742no—
119C2×Q8—741no—
120C2×Q8—1482no—
121C2×Q8—1482no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4—742no—
126M16—1482no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—741no—
130C2×C8—741no—
131C4⋊C4—21no—
132C4⋊C4—372no—
133C4⋊C4—742no—
134C4⋊C4—742no—
135C4⋊C4—741no—
136C4⋊C4C4×D3712yes—
137C42—371no—
138C42—371no—
139C42—371no—
140C42C22×D3711yescharacteristic
141C23—371no—
142Q8—41no—
143Q8—41no—
144Q8—1484no—
145Q8—1481no—
146Q8—1481no—
147C2×C4—22no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—372no—
151C2×C4—372no—
152C2×C4—371no—
153C2×C4—742no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—742no—
157C2×C4—1484no—
158C2×C4C2×C4×D3711yescharacteristic
159C2×C4D4×D3711yescharacteristic
160C2×C4D4×D3711yescharacteristic
161C8—41no—
162C8—41no—
163C8—1481no—
164C8—1481no—
165C22—372no—
166C22—741no—
167C22—741no—
168C22C22⋊C4×D3711yescharacteristic
169C4—21no—
170C4—42no—
171C4—372no—
172C4—372no—
173C4—741no—
174C4—1482no—
175C4D8×D3711yescharacteristic
176C4SD16×D3711yescharacteristic
177C4#1192456511yescharacteristic
178C4#1192456811yescharacteristic
179C2—742no—
180C2#101×D3711yescharacteristic
181C2#102×D3711yescharacteristic
182C2#1455754011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenter#332D37
hypocenterC37#1546
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #14557280C2semidirect
5. #14557279C2semidirect
6. #14557278C2semidirect
7. C37×#332C2semidirect
98. #332D37semidirect
99. C37#1546semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D372
#145575852
#145575552
#145572802
#145572792
#145572782
C37×#3322
#154637