Finite Group Databasebeta

← #17993311

Subgroups — #17993311

Order 4736.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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#14557589C211yesmaximal, characteristic
3#14557589C211yesmaximal, characteristic
4#14557280C211yesmaximal, characteristic, complemented
5#14557279C211yesmaximal, characteristic, complemented
6#14557278C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9#11924536C2211yescharacteristic
10#11924535—21no—
11#11924535C412yes—
12#11924534—21no—
13C4⋊C4×D37—21no—
14C4⋊C4×D37C412yes—
15C42×D37C2211yescharacteristic
16C4⋊#64436C2211yescharacteristic
17C4⋊#64436C2211yescharacteristic
18#11924448—21no—
19#11924448—21no—
20#11924446—21no—
21#11924446—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—
48C22×D37C22⋊C411yescharacteristic
49Q8×C37—41no—
50Q8×C37—41no—
51C2×C4×C37—22no—
52C2×C4×C37C22×C411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37—22no—
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C22⋊C411yescharacteristic
59C4×D37—22no—
60C4×D37—21no—
61C4×D37—21no—
62C4×D37—21no—
63C4×D37—21no—
64C4×D37—44no—
65Dic74—44no—
66Dic74—41no—
67Dic74—41no—
68C8×C37—41no—
69C8×C37—41no—
70#64436—41no—
71#64436—41no—
72C22×C37C2×C22⋊C411yescharacteristic
73C2×D37—21no—
74C2×D37—21no—
75C2×D37#10112yes—
76C4×C37—21no—
77C4×C37—42no—
78C4×C37AGL(1,ℤ/8)11yescharacteristic
79C4×C37AGL(1,ℤ/8)11yescharacteristic
80C4×C37#13711yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—21no—
83Dic37—21no—
84Dic37—21no—
85Dic37—42no—
86#1556—371nomaximal, Sylow
87C2×C37C2×#10111yescharacteristic
88C2×C37#41811yescharacteristic
89C2×C37#41911yescharacteristic
90D37—22no—
91C2×C4⋊Q8—371no—
92#432—371no—
93#432—371no—
94#332—371no—
95#332—371no—
96#332—371no—
97#332D3711yescharacteristic, complemented
98C37#155611yescharacteristic, complemented, Sylow
99C22×Q8—741no—
100C4⋊Q8—372no—
101C4⋊Q8—371no—
102C4⋊Q8—741no—
103C4⋊Q8—741no—
104C4⋊Q8C2×D3711yescharacteristic
105C2×C4⋊C4—372no—
106C2×C4⋊C4—741no—
107C2×C42—371no—
108C4⋊C8—371no—
109C4⋊C8—371no—
110C4⋊C8C2×D3711yescharacteristic
111C4⋊C8C2×D3711yescharacteristic
112C22⋊C8—741no—
113C22⋊C8—741no—
114#97—741no—
115#97—741no—
116C2×Q8—21no—
117C2×Q8—742no—
118C2×Q8—741no—
119C2×Q8—1482no—
120C2×Q8—1482no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—742no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—741no—
128C2×C8—741no—
129C4⋊C4—21no—
130C4⋊C4—372no—
131C4⋊C4—742no—
132C4⋊C4—742no—
133C4⋊C4—741no—
134C4⋊C4C4×D3712yes—
135C42—371no—
136C42—371no—
137C42—371no—
138C42C22×D3711yescharacteristic
139C23—371no—
140Q8—41no—
141Q8—41no—
142Q8—1484no—
143Q8—1481no—
144Q8—1481no—
145C2×C4—22no—
146C2×C4—371no—
147C2×C4—371no—
148C2×C4—371no—
149C2×C4—742no—
150C2×C4—741no—
151C2×C4—741no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—742no—
155C2×C4—1484no—
156C2×C4C2×C4×D3711yescharacteristic
157C2×C4D4×D3711yescharacteristic
158C2×C4D4×D3711yescharacteristic
159C8—41no—
160C8—41no—
161C8—1481no—
162C8—1481no—
163C22—372no—
164C22—741no—
165C22—741no—
166C22C22⋊C4×D3711yescharacteristic
167C4—21no—
168C4—42no—
169C4—741no—
170C4—741no—
171C4—741no—
172C4—1482no—
173C4#1192456011yescharacteristic
174C4#1192456311yescharacteristic
175C4#1192456511yescharacteristic
176C4#1192456811yescharacteristic
177C2—742no—
178C2#101×D3711yescharacteristic
179C2#1455753611yescharacteristic
180C2#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#1556
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
97. #332D37semidirect
98. C37#1556semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D372
#145575892
#145572802
#145572792
#145572782
C37×#3322
#155637