Finite Group Databasebeta

← #18010108

Subgroups — #18010108

Order 4736.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#14558536C211yesmaximal, characteristic, complemented
2C2×#11924603C211yesmaximal, characteristic, complemented
3#14558392C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558078C211yesmaximal, characteristic
6C2×#10596957—21no—
7C22×#64438—21no—
8#11924603—21no—
9#11924603C2212yes—
10#11924603C2212yes—
11C4⋊#64438—21no—
12C2×#10596964—21no—
13#11924535C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924522—21no—
16#11924510C411yescharacteristic
17#11924508—21no—
18D4×Dic37C411yescharacteristic
19#11924498C411yescharacteristic
20#11924496—21no—
21C2×C4×Dic37C2211yescharacteristic
22#121×C37C411yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29C22×Dic37—21no—
30C22×Dic37D411yescharacteristic
31C22×Dic37D411yescharacteristic
32#10596964—42no—
33#10596964—42no—
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×Dic74—21no—
37#10596957—42no—
38C2×#64438—22no—
39C2×#64438—22no—
40C2×#64438—42no—
41C4⋊C4×C37C2×C411yescharacteristic
42C22⋊C4×C37—21no—
43C22⋊Dic37—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48C4×Dic37C2×C411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37C2311yescharacteristic
52C23×C37—21no—
53C23×C37C22⋊C411yescharacteristic
54C22×D37—21no—
55D4×C37—41no—
56D4×C37—42no—
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C22⋊D37—42no—
62C22⋊D37—41no—
63C22⋊D37—41no—
64C22⋊D37—41no—
65C22⋊D37—41no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—42no—
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37D812yes—
73C2×Dic37SD1612yes—
74C2×Dic37C2×D411yescharacteristic
75C2×Dic37C2×D411yescharacteristic
76D148—41no—
77C4×D37—42no—
78Dic74—41no—
79Dic74—41no—
80#64438—42no—
81#64438—42no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37#10212yes—
88C22×C37C2×C22⋊C411yescharacteristic
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—41no—
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—41no—
95Dic37—21no—
96Dic37—41no—
97Dic37#10212yes—
98Dic37C2×D811yescharacteristic
99Dic37C2×SD1611yescharacteristic
100Dic37AGL(1,ℤ/8)11yescharacteristic
101Dic37#13711yescharacteristic
102#1547—371nomaximal, Sylow
103C2×C37—22no—
104C2×C37—81no—
105C2×C37#41311yescharacteristic
106C2×C37C2×#10211yescharacteristic
107C2×C37#41711yescharacteristic
108D37—81no—
109#532—371no—
110#423—371no—
111C2×C4⋊C8—371no—
112#332—372no—
113#331—372no—
114C37#154711yescharacteristic, complemented, Sylow
115C2×#41—741no—
116C2×M16—741no—
117C22×C8—741no—
118C4⋊Q8—371no—
119#127—371no—
120#124—741no—
121#121—371no—
122#121—741no—
123#121#386611yescharacteristic
124C4×D4—371no—
125C4×D4—371no—
126C4×D4—741no—
127C2×C42—371no—
128C4⋊C8—372no—
129C4⋊C8—372no—
130C4⋊C8—741no—
131C4⋊C8—741no—
132#41—1482no—
133#41—1482no—
134C2×Q8—741no—
135C2×D4—21no—
136C2×D4—371no—
137C2×D4—741no—
138C2×D4—741no—
139C2×D4—741no—
140C2×D4C2×#386611yescharacteristic
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—741no—
144C22×C4—741no—
145C22×C4C2×#386611yescharacteristic
146M16—1482no—
147C2×C8—742no—
148C2×C8—742no—
149C2×C8—1482no—
150C4⋊C4—371no—
151C4⋊C4—741no—
152C4⋊C4C2×#386611yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C42—371no—
158C42—371no—
159C42—371no—
160C42—371no—
161C23—21no—
162C23—741no—
163C23C22⋊#386611yescharacteristic
164Q8—1481no—
165Q8—1481no—
166D4—41no—
167D4—42no—
168D4—1481no—
169D4—1481no—
170D4—1481no—
171D4—1481no—
172D4—1481no—
173D4—1482no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—372no—
177C2×C4—372no—
178C2×C4—371no—
179C2×C4—371no—
180C2×C4—371no—
181C2×C4—371no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—1482no—
186C2×C4—1482no—
187C2×C4C22⋊#386611yescharacteristic
188C2×C4C22×#386611yescharacteristic
189C8—1482no—
190C8—1482no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—1481no—
197C22—1481no—
198C22—1481no—
199C22#1192459812yes—
200C22C2×C22⋊#386611yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—371no—
205C4—372no—
206C4—371no—
207C4—371no—
208C4—371no—
209C4—741no—
210C4—1481no—
211C2—22no—
212C2—81no—
213C2—2961no—
214C2#1455852011yescharacteristic
215C2C2×#1192459811yescharacteristic
216C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#121×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558078C2
cosocleC4×Dic37C23
hypercenter#121#3866
hypocenterC37#1547
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558536C2semidirect
2. C2×#11924603C2semidirect
3. #14558392C2semidirect
4. #14558391C2semidirect
114. C37#1547semidirect

Maximal subgroups

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

subgroupindex
#145585362
C2×#119246032
#145583922
#145583912
#145580782
#154737