Finite Group Databasebeta

← #18009899

Subgroups — #18009899

Order 4736.

248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#14558552C211yesmaximal, characteristic
2#14558551C211yesmaximal, characteristic
3#14558383C212yesmaximal, complemented
4Q8⋊#64438C212yesmaximal, complemented
5C4×Q8×D37C211yesmaximal, characteristic
6#11924603—21no—
7C4⋊#64438C2212yes—
8#11924593—21no—
9#11924593—21no—
10C4×#64438—21no—
11C4×#64438C2212yes—
12C2×Q8×D37C411yescharacteristic
13Q8×Dic37C2211yescharacteristic
14C4×Dic74—21no—
15C4×Dic74C411yescharacteristic
16#11924501—21no—
17#11924501C2211yescharacteristic
18C4⋊C4×D37—21no—
19C4⋊C4×D37C411yescharacteristic
20C42×D37—21no—
21C42×D37C2211yescharacteristic
22C4×Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24Q8×D37—22no—
25Q8×D37C814yescomplemented
26C2×C4×D37—21no—
27C2×C4×D37—21no—
28C2×C4×D37C2×C411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37D411yescharacteristic
31C2×Dic74—21no—
32C2×Dic74C2×C411yescharacteristic
33C2×#64438—22no—
34C2×#64438—22no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C411yescharacteristic
37C42×C37—21no—
38C42×C37C2×C411yescharacteristic
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C411yescharacteristic
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37—21no—
46C4×Dic37—21no—
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37C2311yescharacteristic
50C22×D37C22⋊C411yescharacteristic
51Q8×C37—21no—
52Q8×C37C2×C812yes—
53C2×C4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C2×D411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63C4×D37—24no—
64C4×D37—22no—
65C4×D37—41no—
66C4×D37—42no—
67C4×D37C2×C812yes—
68C4×D37M1612yes—
69Dic74—21no—
70Dic74—24no—
71Dic74C2×C812yes—
72#64438—42no—
73#64438—42no—
74C22×C37C2×C22⋊C411yescharacteristic
75C2×D37—21no—
76C2×D37—21no—
77C2×D37C22⋊C812yes—
78C4×C37—22no—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—41no—
82C4×C37C22×C811yescharacteristic
83C4×C37C2×M1611yescharacteristic
84Dic37—22no—
85Dic37—21no—
86Dic37—41no—
87Dic37C22⋊C812yes—
88Dic37#13712yes—
89#1479—371nomaximal, Sylow
90C2×C37C2×C22⋊C811yescharacteristic
91C2×C37#41911yescharacteristic
92C2×C37#42111yescharacteristic
93D37—22no—
94C2×C4×Q8—371no—
95#431—371no—
96#431—371no—
97Q8⋊C8—372no—
98Q8⋊C8—372no—
99C37#147911yescharacteristic, complemented, Sylow
100C22×Q8—371no—
101C4×Q8—371no—
102C4×Q8—371no—
103C4×Q8—371no—
104C4×Q8—741no—
105C4×Q8—741no—
106C4×Q8#386611yescharacteristic
107C2×C4⋊C4—371no—
108C2×C4⋊C4—741no—
109C2×C42—371no—
110C2×C42—741no—
111C4⋊C8—372no—
112C4⋊C8—741no—
113C22⋊C8—741no—
114C22⋊C8—741no—
115C4×C8—372no—
116C4×C8—741no—
117C2×Q8—374no—
118C2×Q8—371no—
119C2×Q8—741no—
120C2×Q8—742no—
121C2×Q8C2×#386611yescharacteristic
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4—741no—
126C22×C4—741no—
127C2×C8—742no—
128C2×C8—742no—
129C4⋊C4—21no—
130C4⋊C4—371no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4C2×#386611yescharacteristic
136C42—21no—
137C42—371no—
138C42—371no—
139C42—371no—
140C42—741no—
141C42—741no—
142C42—741no—
143C42C2×#386611yescharacteristic
144C23—371no—
145Q8—21no—
146Q8—372no—
147Q8—744no—
148Q8—741no—
149Q8D37⋊C812yes—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—371no—
153C2×C4—371no—
154C2×C4—372no—
155C2×C4—372no—
156C2×C4—371no—
157C2×C4—742no—
158C2×C4—744no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—1481no—
162C2×C4—1482no—
163C2×C4C22⋊#386611yescharacteristic
164C2×C4C22⋊#386611yescharacteristic
165C2×C4C22×#386611yescharacteristic
166C8—1482no—
167C8—1482no—
168C22—372no—
169C22—741no—
170C22—741no—
171C22C2×C22⋊#386611yescharacteristic
172C4—22no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—372no—
177C4—372no—
178C4—742no—
179C4—741no—
180C4—1481no—
181C4C2×D37⋊C811yescharacteristic
182C4D37⋊M1611yescharacteristic
183C2—742no—
184C2D37⋊(C22⋊C8)11yescharacteristic
185C2#1455852611yescharacteristic
186C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C22×C8
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC4×Dic37C23
hypercenterC4×Q8#3866
hypocenterC37#1479
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #14558383C2semidirect
4. Q8⋊#64438C2semidirect
25. Q8×D37C8semidirect
99. C37#1479semidirect

Maximal subgroups

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

subgroupindex
#145585522
#145585512
#145583832
Q8⋊#644382
C4×Q8×D372
#147937