Finite Group Databasebeta

← #18009974

Subgroups — #18009974

Order 4736.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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×#11924593C211yesmaximal, characteristic, complemented
2C4×C22⋊#3866C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558385C212yesmaximal, complemented
5#14558046C211yesmaximal, characteristic
6C22×#64438—21no—
7C2×C22⋊#3866—21no—
8C2×C4×#3866—21no—
9#11924593—21no—
10#11924593C2212yes—
11(C2×#3866)⋊C4C2212yes—
12C2×#10596966C411yescharacteristic, complemented
13C22×C4×D37C2211yescharacteristic
14#11924521—21no—
15#11924512C2211yescharacteristic
16#11924511C2211yescharacteristic
17#11924510C411yescharacteristic, complemented
18#11924506—21no—
19#11924498—21no—
20#11924496—21no—
21#11924494C411yescharacteristic, complemented
22C22⋊Q8×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—22no—
25C2×Q8×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C2×C22⋊D37—21no—
28C22×Dic37D411yescharacteristic
29#10596966—42no—
30C2×D148—21no—
31C2×D148—21no—
32C2×D148C2×C411yescharacteristic
33C2×C4×D37—21no—
34C2×C4×D37—42no—
35C2×C4×D37C2×C411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37C2311yescharacteristic
39C22⋊#3866—24no—
40C2×#64438—22no—
41C2×#64438—42no—
42C4×#3866—42no—
43C4⋊C4×C37—21no—
44C4⋊C4×C37C2×C411yescharacteristic
45C22⋊C4×C37—21no—
46#10596938—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50C4⋊Dic37C2×C411yescharacteristic
51#10596936—21no—
52C4×Dic37—21no—
53C23×C37C22⋊C411yescharacteristic
54C22×D37—22no—
55C22×D37—22no—
56C22×D37—21no—
57C22×D37—41no—
58C22×D37C22⋊C411yescharacteristic
59C22×D37C2×D411yescharacteristic
60C2×#3866—24no—
61C2×#3866—42no—
62C2×#3866—42no—
63Q8×C37—41no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—41no—
67C2×C4×C37C22⋊C411yescharacteristic
68C2×C4×C37C22×C411yescharacteristic
69C22⋊D37—42no—
70C2×Dic37—22no—
71C2×Dic37—21no—
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74D148—41no—
75D148—42no—
76D148—42no—
77C4×D37—22no—
78C4×D37—22no—
79C4×D37—41no—
80C4×D37—41no—
81C4×D37—42no—
82#64438—42no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37#10412yes—
86C22×C37C2×C22⋊C411yescharacteristic
87C2×D37—21no—
88C2×D37—21no—
89C2×D37—21no—
90C2×D37—21no—
91C2×D37—21no—
92C2×D37—44no—
93C2×D37—41no—
94C2×D37—41no—
95C2×D37—41no—
96C2×D37#13512yes—
97#3866—44no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—41no—
101C4×C37—41no—
102Dic37—21no—
103Dic37—41no—
104Dic37#9912yes—
105#1501—371nomaximal, Sylow
106C2×C37—22no—
107C2×C37C2×#9911yescharacteristic
108C2×C37#41611yescharacteristic
109C2×C37C2×#10411yescharacteristic
110D37—22no—
111D37—41no—
112D37—81no—
113#525—371no—
114C2×C22⋊C8—371no—
115C4×C22⋊C4—371no—
116#328—372no—
117#327—372no—
118C37#150111yescharacteristic, complemented, Sylow
119C2×#41—371no—
120C23×C4—371no—
121C22×C8—741no—
122#123—741no—
123C22⋊Q8—371no—
124C22⋊Q8#386611yescharacteristic, complemented
125#121—371no—
126#121—371no—
127#120—741no—
128C4×D4—741no—
129C4×D4—741no—
130#117—371no—
131C2×C22⋊C4—741no—
132C2×C42—741no—
133C22⋊C8—372no—
134C22⋊C8—741no—
135#95—372no—
136C24—371no—
137#41—1482no—
138C2×Q8C2×#386611yescharacteristic
139C2×D4—371no—
140C2×D4—741no—
141C2×D4—741no—
142C2×D4—741no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—371no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—741no—
149C22×C4—742no—
150C22×C4—1482no—
151C22×C4C2×#386611yescharacteristic
152C2×C8—742no—
153C2×C8—1482no—
154C4⋊C4—21no—
155C4⋊C4—371no—
156C4⋊C4—741no—
157C4⋊C4C2×#386611yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—744no—
163C22⋊C4—741no—
164C42—741no—
165C42—1482no—
166C23—371no—
167C23—371no—
168C23—742no—
169C23—742no—
170C23—741no—
171C23—1481no—
172C23C22⋊#386611yescharacteristic
173Q8—41no—
174D4—1481no—
175D4—1482no—
176D4—1482no—
177D4—1482no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—371no—
182C2×C4—371no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4—742no—
186C2×C4—744no—
187C2×C4—741no—
188C2×C4—1481no—
189C2×C4—1481no—
190C2×C4—1482no—
191C2×C4—1482no—
192C2×C4—1482no—
193C2×C4C22⋊#386611yescharacteristic
194C2×C4C22×#386611yescharacteristic
195C8—1482no—
196C22—21no—
197C22—21no—
198C22—372no—
199C22—741no—
200C22—741no—
201C22—741no—
202C22—741no—
203C22—741no—
204C22—1484no—
205C22—1481no—
206C22—1481no—
207C22—1481no—
208C22#1192460112yes—
209C22C2×C22⋊#386611yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—372no—
215C4—741no—
216C4—1484no—
217C4—1481no—
218C2—22no—
219C2—2961no—
220C2—742no—
221C2—1481no—
222C2D37⋊#9911yescharacteristic
223C2#1455852311yescharacteristic
224C2C2×#1192460111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558046C2
cosocleC2×C4×D37C23
hypercenterC22⋊Q8#3866
hypocenterC37#1501
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11924593C2semidirect
2. C4×C22⋊#3866C2semidirect
3. #14558387C2semidirect
4. #14558385C2semidirect
12. C2×#10596966C4semidirect
17. #11924510C4semidirect
21. #11924494C4semidirect
22. C22⋊Q8×C37C4semidirect
118. C37#1501semidirect
124. C22⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245932
C4×C22⋊#38662
#145583872
#145583852
#145580462
#150137