Finite Group Databasebeta

← #18010022

Subgroups — #18010022

Order 4736.

284 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 60 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
2#14558476C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#14558040C211yesmaximal, characteristic
6C22×#64438—21no—
7C2×C22⋊#3866—21no—
8#11924593—21no—
9#11924593C2212yes—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4C2212yes—
12C22×C4×D37C2211yescharacteristic
13#11924517—21no—
14#11924512C411yescharacteristic, complemented
15#11924512C2211yescharacteristic
16#11924507C411yescharacteristic, complemented
17#11924507C2211yescharacteristic
18#11924504—21no—
19C4×C22⋊D37—21no—
20C4×C22⋊D37—21no—
21#11924495C411yescharacteristic, complemented
22C2×#41×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—22no—
25#41×C37—42no—
26C2×Q8×C37C2×C411yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2×C411yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C22×Dic37D411yescharacteristic
34C2×C4×D37—42no—
35C2×C4×D37C2×C411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37C2311yescharacteristic
39C22⋊#3866—42no—
40C2×#64438—22no—
41C2×#64438—42no—
42C22⋊Dic37—21no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37C2×C411yescharacteristic
48C4⋊Dic37C2×C411yescharacteristic
49#10596936—21no—
50#10596936—21no—
51C4×Dic37—21no—
52C23×C37—21no—
53C23×C37C22⋊C411yescharacteristic
54C22×D37—22no—
55C22×D37—22no—
56C22×D37—41no—
57C22×D37C22⋊C411yescharacteristic
58C22×D37C2×D411yescharacteristic
59C2×#3866—42no—
60C2×#3866—42no—
61C2×#3866—42no—
62Q8×C37—41no—
63D4×C37—41no—
64D4×C37—42no—
65C2×C4×C37—22no—
66C2×C4×C37—21no—
67C2×C4×C37—42no—
68C2×C4×C37C22⋊C411yescharacteristic
69C2×C4×C37C22×C411yescharacteristic
70C22⋊D37—42no—
71C22⋊D37—42no—
72C2×Dic37—22no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37C22⋊C411yescharacteristic
76C2×Dic37C2×D411yescharacteristic
77C4×D37—41no—
78C4×D37—41no—
79C4×D37—41no—
80C4×D37—41no—
81#64438—42no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37#9912yes—
88C22×C37C2×C22⋊C411yescharacteristic
89C2×D37—21no—
90C2×D37—21no—
91C2×D37—21no—
92C2×D37—21no—
93C2×D37—21no—
94C2×D37—44no—
95C2×D37#13512yes—
96#3866—82no—
97C4×C37—21no—
98C4×C37—21no—
99C4×C37—41no—
100Dic37—21no—
101Dic37—21no—
102Dic37—41no—
103Dic37—41no—
104#1516—371nomaximal, Sylow
105C2×C37—22no—
106C2×C37—81no—
107C2×C37C2×#9911yescharacteristic
108C2×C37#41611yescharacteristic
109C2×C37#42111yescharacteristic
110D37—22no—
111D37—41no—
112#525—371no—
113C2×C22⋊C8—371no—
114#381—371no—
115#328—372no—
116#327—372no—
117C37#151611yescharacteristic, complemented, Sylow
118C2×#41#386611yescharacteristic, complemented
119C23×C4—371no—
120C22×C8—741no—
121#123—741no—
122C22⋊Q8—371no—
123C22⋊Q8—371no—
124#121—371no—
125#121—371no—
126#120—741no—
127C4×D4—741no—
128C4×D4—741no—
129#117—371no—
130C2×C22⋊C4—741no—
131C22⋊C8—372no—
132C22⋊C8—741no—
133#95—372no—
134#95—741no—
135C24—371no—
136#41—42no—
137C2×Q8C2×#386611yescharacteristic
138C2×D4—21no—
139C2×D4—741no—
140C2×D4—741no—
141C2×D4C2×#386611yescharacteristic
142C22×C4—21no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—371no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—742no—
149C22×C4—1482no—
150C22×C4C2×#386611yescharacteristic
151C2×C8—742no—
152C2×C8—1482no—
153C4⋊C4—371no—
154C4⋊C4—371no—
155C4⋊C4—741no—
156C4⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—1482no—
163C42—741no—
164C23—21no—
165C23—371no—
166C23—371no—
167C23—742no—
168C23—742no—
169C23—1481no—
170C23C22⋊#386611yescharacteristic
171Q8—41no—
172D4—41no—
173D4—42no—
174D4—1482no—
175D4—1482no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—742no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—1481no—
185C2×C4—1481no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4—1482no—
189C2×C4—1482no—
190C2×C4—1482no—
191C2×C4C22⋊#386611yescharacteristic
192C2×C4C22×#386611yescharacteristic
193C8—1482no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—372no—
200C22—741no—
201C22—741no—
202C22—741no—
203C22—741no—
204C22—741no—
205C22—1484no—
206C22#1192459412yes—
207C22C2×C22⋊#386611yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2962no—
212C4—741no—
213C4—741no—
214C4—1481no—
215C4—1481no—
216C2—22no—
217C2—81no—
218C2—742no—
219C2—1481no—
220C2C2×#1192459411yescharacteristic
221C2#1455852311yescharacteristic
222C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558040C2
cosocleC2×C4×D37C23
hypercenterC2×#41#3866
hypocenterC37#1516
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11924593C2semidirect
2. #14558476C2semidirect
3. #14558387C2semidirect
4. #14558384C2semidirect
14. #11924512C4semidirect
16. #11924507C4semidirect
21. #11924495C4semidirect
22. C2×#41×C37C4semidirect
117. C37#1516semidirect
118. C2×#41#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245932
#145584762
#145583872
#145583842
#145580402
#151637