Finite Group Databasebeta

← #17993153

Subgroups — #17993153

Order 4736.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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#14558044C211yesmaximal, characteristic
2#14557396C211yesmaximal, characteristic, complemented
3#14557271C212yesmaximal, complemented
4#14557268C212yesmaximal, complemented
5C2×C22⋊C8×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C411yescharacteristic, complemented
7#11924519—21no—
8#11924515C411yescharacteristic, complemented
9#11924515C2211yescharacteristic
10#11924510C411yescharacteristic, complemented
11#11924510C2211yescharacteristic
12#11924505—21no—
13C4×C22⋊D37—21no—
14C4×C22⋊D37—21no—
15#11924495C411yescharacteristic, complemented
16C2×C22⋊Dic37—21no—
17#11924443—21no—
18#11924443C2212yes—
19C23×C4×C37C2211yescharacteristic
20C22×C8×C37—21no—
21C22⋊C8×C37—21no—
22C22⋊C8×C37C2212yes—
23C24×C37D411yescharacteristic
24C22×C4×C37—42no—
25C22×C4×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—22no—
35#10596962—42no—
36C2×D148C2×C411yescharacteristic
37C2×C4×D37—21no—
38C2×Dic74C2×C411yescharacteristic
39C2×C8×C37—22no—
40C2×C8×C37—42no—
41C22⋊Dic37—21no—
42C22⋊Dic37—21no—
43C22⋊Dic37—21no—
44C22⋊Dic37—42no—
45#10596938—21no—
46#10596938—21no—
47C4⋊Dic37C2×C411yescharacteristic
48C4⋊Dic37C2×C411yescharacteristic
49#10596936—21no—
50#10596936—21no—
51C4×Dic37—21no—
52C23×C37—22no—
53C23×C37—22no—
54C23×C37—41no—
55C23×C37C22⋊C411yescharacteristic
56C23×C37C22⋊C411yescharacteristic
57C23×C37C2×D411yescharacteristic
58C22×D37—21no—
59C2×C4×C37—22no—
60C2×C4×C37—22no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22⋊C411yescharacteristic
67C2×C4×C37C22×C411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C22⋊D37—42no—
70C22⋊D37—42no—
71C22⋊D37—42no—
72C2×Dic37—21no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—42no—
76C2×Dic37—42no—
77C2×Dic37—42no—
78D148—41no—
79C4×D37—42no—
80Dic74—41no—
81C8×C37—42no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—44no—
90C22×C37#9912yes—
91C22×C37C2×C22⋊C411yescharacteristic
92C22×C37#13512yes—
93C2×D37—41no—
94C2×D37—41no—
95C2×D37—41no—
96C4×C37—21no—
97C4×C37—21no—
98C4×C37—21no—
99C4×C37—21no—
100Dic37—41no—
101Dic37—41no—
102Dic37—41no—
103Dic37—82no—
104#1516—371nomaximal, Sylow
105C2×C37—22no—
106C2×C37—22no—
107C2×C37—41no—
108C2×C37C2×#9911yescharacteristic
109C2×C37#41611yescharacteristic
110C2×C37#42111yescharacteristic
111D37—81no—
112#525—371no—
113C2×C22⋊C8D3711yescharacteristic, complemented
114#381—371no—
115#328—372no—
116#327—372no—
117C37#151611yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C23×C4C2×D3711yescharacteristic
120C22×C8—21no—
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—21no—
132C22⋊C8C2×D3712yes—
133#95—372no—
134#95—741no—
135C24D14811yescharacteristic
136#41—1482no—
137C2×Q8—371no—
138C2×D4—371no—
139C2×D4—741no—
140C2×D4—741no—
141C2×D4—741no—
142C22×C4—42no—
143C22×C4—741no—
144C22×C4—742no—
145C22×C4C4×D3711yescharacteristic
146C22×C4C4×D3711yescharacteristic
147C22×C4D14811yescharacteristic
148C22×C4C22⋊D3711yescharacteristic
149C22×C4C22⋊D3711yescharacteristic
150C22×C4C22×D3711yescharacteristic
151C2×C8—22no—
152C2×C8—42no—
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—22no—
165C23—22no—
166C23—41no—
167C23—741no—
168C23#1059693811yescharacteristic
169C23#1059693811yescharacteristic
170C23C2×D14811yescharacteristic
171Q8—1481no—
172D4—1481no—
173D4—1482no—
174D4—1482no—
175D4—1482no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—1482no—
186C2×C4—1482no—
187C2×C4—1482no—
188C2×C4—1482no—
189C2×C4#1059693811yescharacteristic
190C2×C4#1059693811yescharacteristic
191C2×C4C2×C4×D3711yescharacteristic
192C2×C4C2×C22⋊D3711yescharacteristic
193C8—42no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—1481no—
203C22—1481no—
204C22—1481no—
205C22#1192445012yes—
206C22C2×#1059693811yescharacteristic
207C22#1192455812yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—2962no—
213C4—1481no—
214C4—1481no—
215C4—1481no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—2961no—
220C2C2×#1192445011yescharacteristic
221C2#1455753011yescharacteristic
222C2#1455754911yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×C22⋊C8×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenterC2×C22⋊C8D37
hypocenterC37#1516
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557396C2semidirect
3. #14557271C2semidirect
4. #14557268C2semidirect
5. C2×C22⋊C8×C37C2semidirect
6. C2×#10596962C4semidirect
8. #11924515C4semidirect
10. #11924510C4semidirect
15. #11924495C4semidirect
113. C2×C22⋊C8D37semidirect
117. C37#1516semidirect

Maximal subgroups

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

subgroupindex
#145580442
#145573962
#145572712
#145572682
C2×C22⋊C8×C372
#151637