Finite Group Databasebeta

← #18010759

Subgroups — #18010759

Order 4736.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#11924601C214yesmaximal, complemented
2C4×#10596953C211yesmaximal, characteristic, complemented
3C4×C4⋊#3866C211yesmaximal, characteristic, complemented
4#14558084C211yesmaximal, characteristic
5C2×#10596953C2212yes—
6C2×C4⋊#3866—21no—
7C2×C4×#3866C2212yes—
8#11924601—28no—
9#11924591—21no—
10C4×#64438—21no—
11(C2×#3866)⋊C4—21no—
12C2×#10596966C2212yes—
13#11924533C411yescharacteristic, complemented
14#11924525C412yescomplemented
15#11924511—21no—
16#11924511—21no—
17#11924498—21no—
18#11924498—21no—
19C42×D37C2211yescharacteristic
20C4⋊Q8×C37C411yescharacteristic, complemented
21C22×#3866—22no—
22C2×Q8×C37C2×C412yes—
23#10596966—24no—
24#10596966—24no—
25C2×D148—22no—
26C2×D148—21no—
27C2×D148—21no—
28C2×D148C2×C412yes—
29C2×C4×D37—22no—
30C2×C4×D37D411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37C2311yescharacteristic
33C2×#64438—22no—
34C4⋊#3866—24no—
35C4×#3866—24no—
36#10596953—22no—
37#10596953D414yescomplemented
38C4⋊C4×C37—21no—
39C4⋊C4×C37—21no—
40C42×C37C2×C411yescharacteristic
41#10596938—22no—
42#10596938—22no—
43C4×Dic37C2×C411yescharacteristic
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C22×D37—22no—
47C22×D37C2×D411yescharacteristic
48C2×#3866—24no—
49C2×#3866—42no—
50C2×#3866—42no—
51Q8×C37—24no—
52C2×C4×C37—22no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22×C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59D148—24no—
60D148—42no—
61D148—42no—
62D148—42no—
63D148—42no—
64C4×D37—22no—
65C4×D37—41no—
66C4×D37—44no—
67C4×D37C2×D412yes—
68C4×D37#4112yes—
69#64438—24no—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—21no—
73C2×D37—42no—
74C2×D37—42no—
75C2×D37—42no—
76C2×D37#12411yescharacteristic
77C2×D37#12711yescharacteristic
78#3866—44no—
79C4×C37—21no—
80C4×C37—42no—
81C4×C37#10412yescomplemented
82C4×C37C4×D412yes—
83Dic37—21no—
84Dic37—21no—
85Dic37#12112yes—
86#1980—371nomaximal, Sylow
87C2×C37#39011yescharacteristic
88C2×C37C2×#10411yescharacteristic
89C2×C37#42111yescharacteristic
90D37—21no—
91D37—21no—
92D37—82no—
93#532—371no—
94C2×#104—374no—
95C4×M16—371no—
96C4×C4⋊C4—371no—
97C37#198011yescharacteristic, complemented, Sylow
98C2×#41—372no—
99C2×M16—372no—
100C4⋊Q8#386611yescharacteristic, complemented
101#127—371no—
102#124—372no—
103#121—741no—
104#121—741no—
105C4×D4—741no—
106C4×D4—741no—
107C2×C4⋊C4—741no—
108C2×C42—371no—
109C2×C42—372no—
110#104—748no—
111#97—741no—
112C4×C8—741no—
113#95—741no—
114#41—744no—
115#41—744no—
116C2×Q8C2×#386612yes—
117C2×D4—372no—
118C2×D4—742no—
119C2×D4—741no—
120C2×D4—741no—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—742no—
125C22×C4—742no—
126M16—374no—
127M16—742no—
128C2×C8—742no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—744no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C42—371no—
135C42—371no—
136C42—371no—
137C42—744no—
138C42C2×#386611yescharacteristic
139C23—371no—
140C23—742no—
141Q8—24no—
142D4—744no—
143D4—1482no—
144D4—1482no—
145D4—1482no—
146D4—1482no—
147C2×C4—22no—
148C2×C4—371no—
149C2×C4—372no—
150C2×C4—372no—
151C2×C4—371no—
152C2×C4—371no—
153C2×C4—742no—
154C2×C4—744no—
155C2×C4—1481no—
156C2×C4—1484no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4C22⋊#386611yescharacteristic
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22×#386611yescharacteristic
162C8—744no—
163C22—371no—
164C22—371no—
165C22—741no—
166C22—741no—
167C22—1482no—
168C22—1482no—
169C22—1482no—
170C22C2×C22⋊#386611yescharacteristic
171C4—21no—
172C4—42no—
173C4—372no—
174C4—741no—
175C4—741no—
176C4—1484no—
177C4#1192460112yescomplemented
178C4D4×#386612yes—
179C2—2962no—
180C2—741no—
181C2—741no—
182C2#1455848511yescharacteristic
183C2C2×#1192460111yescharacteristic
184C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558084C2
cosocleC2×C4×D37C23
hypercenterC4⋊Q8#3866
hypocenterC37#1980
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11924601C2semidirect
2. C4×#10596953C2semidirect
3. C4×C4⋊#3866C2semidirect
13. #11924533C4semidirect
14. #11924525C4semidirect
20. C4⋊Q8×C37C4semidirect
37. #10596953D4semidirect
81. C4×C37#104semidirect
97. C37#1980semidirect
100. C4⋊Q8#3866semidirect
177. C4#11924601semidirect

Maximal subgroups

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

subgroupindex
C2×#119246012
C4×#105969532
C4×C4⋊#38662
#145580842
#198037