Finite Group Databasebeta

← #18010471

Subgroups — #18010471

Order 4736.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#14558538C211yesmaximal, characteristic, complemented
2C2×#11924601C212yesmaximal
3C4×C4⋊#3866C211yesmaximal, characteristic, complemented
4#14558403C212yesmaximal, complemented
5C4×#10596966C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×C4⋊#3866—21no—
8C2×C4×#3866C2212yes—
9#11924603—21no—
10#11924603—21no—
11#11924601—24no—
12(C2×#3866)⋊C4—21no—
13C2×#10596966C2211yescharacteristic
14Q8×Dic37C411yescharacteristic, complemented
15C4×D148—21no—
16C4×D148C411yescharacteristic, complemented
17#11924498—21no—
18#11924498C411yescharacteristic, complemented
19#11924494—21no—
20#11924494C2211yescharacteristic
21C42×D37—21no—
22C42×D37C2211yescharacteristic
23C4×Q8×C37C411yescharacteristic, complemented
24C22×#3866—22no—
25C2×Q8×C37C2×C411yescharacteristic
26#10596966—21no—
27#10596966—21no—
28#10596966D412yes—
29#10596966Q812yes—
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37C2311yescharacteristic
38C2×#64438—22no—
39C4⋊#3866—24no—
40C4×#3866—22no—
41C4×#3866—22no—
42#10596953—22no—
43#10596953—22no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic
46C42×C37—21no—
47C42×C37C2×C411yescharacteristic
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37—21no—
52C4⋊Dic37C2×C411yescharacteristic
53C4×Dic37—21no—
54C4×Dic37—21no—
55C4×Dic37C2×C411yescharacteristic
56C4×Dic37D411yescharacteristic
57C4×Dic37D411yescharacteristic
58C22×D37—21no—
59C22×D37C2×D411yescharacteristic
60C2×#3866—24no—
61C2×#3866—42no—
62C2×#3866—42no—
63Q8×C37—21no—
64Q8×C37C4⋊C412yescomplemented
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37C22⋊C411yescharacteristic
68C2×C4×C37C22⋊C411yescharacteristic
69C2×C4×C37C22×C411yescharacteristic
70C2×Dic37—21no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74D148—22no—
75D148—22no—
76D148—21no—
77D148C4⋊C412yescomplemented
78C4×D37—22no—
79C4×D37—22no—
80C4×D37—22no—
81C4×D37—41no—
82C4×D37—42no—
83C4×D37—42no—
84C4×D37C2×D411yescharacteristic
85C4×D37C2×Q811yescharacteristic
86C4×D37#4111yescharacteristic
87C4×D37#4111yescharacteristic
88#64438—42no—
89C22×C37C2×C22⋊C411yescharacteristic
90C2×D37—21no—
91C2×D37—21no—
92C2×D37—22no—
93C2×D37—41no—
94C2×D37—41no—
95C2×D37#12111yescharacteristic
96C2×D37C22⋊Q811yescharacteristic
97#3866—44no—
98C4×C37—22no—
99C4×C37—21no—
100C4×C37—21no—
101C4×C37—41no—
102C4×C37C2×C4⋊C411yescharacteristic
103C4×C37#11711yescharacteristic
104Dic37—21no—
105Dic37—41no—
106Dic37#10412yescomplemented
107Dic37#12111yescharacteristic
108Dic37C22⋊Q811yescharacteristic
109#1806—371nomaximal, Sylow
110C2×C37#38011yescharacteristic
111C2×C37C2×#10411yescharacteristic
112C2×C37#42111yescharacteristic
113D37—21no—
114D37—21no—
115D37—42no—
116C4×#41—371no—
117#423—371no—
118C2×#104—372no—
119C4×C4⋊C4—371no—
120#339—372no—
121C37#180611yescharacteristic, complemented, Sylow
122C2×#41—371no—
123C2×M16—372no—
124C4×Q8—371no—
125C4×Q8#386611yescharacteristic, complemented
126C4×D4—371no—
127C4×D4—371no—
128C4×D4—741no—
129C4×D4—741no—
130#117—371no—
131#117—741no—
132C2×C4⋊C4—741no—
133C2×C42—371no—
134C2×C42—372no—
135C2×C42—741no—
136C4⋊C8—741no—
137C4⋊C8—741no—
138#104—744no—
139#95—741no—
140#41—372no—
141#41—372no—
142#41—741no—
143#41—741no—
144C2×Q8C2×#386611yescharacteristic
145C2×D4—371no—
146C2×D4—741no—
147C22×C4—371no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—741no—
151C22×C4—741no—
152C22×C4—742no—
153C22×C4—741no—
154M16—742no—
155M16—742no—
156C2×C8—742no—
157C4⋊C4—21no—
158C4⋊C4—371no—
159C4⋊C4—741no—
160C4⋊C4—744no—
161C4⋊C4C2×#386611yescharacteristic
162C22⋊C4—741no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C42—21no—
166C42—371no—
167C42—371no—
168C42—371no—
169C42—741no—
170C42—741no—
171C42—742no—
172C42—742no—
173C42C2×#386611yescharacteristic
174C23—371no—
175C23—741no—
176Q8—21no—
177Q8C4⋊#386612yescomplemented
178D4—372no—
179D4—742no—
180D4—742no—
181D4—741no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—371no—
185C2×C4—371no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—371no—
191C2×C4—742no—
192C2×C4—742no—
193C2×C4—742no—
194C2×C4—744no—
195C2×C4—741no—
196C2×C4—1481no—
197C2×C4—1482no—
198C2×C4—1482no—
199C2×C4—1482no—
200C2×C4—1482no—
201C2×C4C22⋊#386611yescharacteristic
202C2×C4C22⋊#386611yescharacteristic
203C2×C4C22×#386611yescharacteristic
204C8—1482no—
205C22—371no—
206C22—371no—
207C22—741no—
208C22—741no—
209C22—742no—
210C22—1481no—
211C22—1481no—
212C22C2×C22⋊#386611yescharacteristic
213C4—22no—
214C4—21no—
215C4—21no—
216C4—41no—
217C4—371no—
218C4—371no—
219C4—372no—
220C4—741no—
221C4—1484no—
222C4—1481no—
223C4C2×C4⋊#386611yescharacteristic
224C4#1192461511yescharacteristic
225C2—741no—
226C2—741no—
227C2—1482no—
228C2#1455847511yescharacteristic
229C2D37⋊#10411yescharacteristic
230C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596966C22
cosocleC2×C4×D37C23
hypercenterC4×Q8#3866
hypocenterC37#1806
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. #14558538C2semidirect
3. C4×C4⋊#3866C2semidirect
4. #14558403C2semidirect
14. Q8×Dic37C4semidirect
16. C4×D148C4semidirect
18. #11924498C4semidirect
23. C4×Q8×C37C4semidirect
64. Q8×C37C4⋊C4semidirect
77. D148C4⋊C4semidirect
106. Dic37#104semidirect
121. C37#1806semidirect
125. C4×Q8#3866semidirect
177. Q8C4⋊#3866semidirect

Maximal subgroups

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

subgroupindex
#145585382
C2×#119246012
C4×C4⋊#38662
#145584032
C4×#105969662
#180637