Finite Group Databasebeta

← #18010613

Subgroups — #18010613

Order 4736.

442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C22×C4×#3866C211yesmaximal, characteristic, complemented
2C2×#11924601C212yesmaximal, complemented
3#14558504C211yesmaximal, characteristic, complemented
4#14558403C212yesmaximal, complemented
5#14558046C211yesmaximal, characteristic
6C23×#3866—21no—
7C2×#10596953C2212yes—
8C2×C4×#3866—21no—
9C2×C4×#3866—24no—
10C2×C4×#3866C2212yes—
11#11924601—24no—
12#11924593—21no—
13C22⋊#64438—21no—
14C2×#10596966C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16#11924521—21no—
17#11924512C411yescharacteristic, complemented
18#11924511C411yescharacteristic, complemented
19#11924510C411yescharacteristic, complemented
20#11924506—21no—
21#11924498—21no—
22#11924496—21no—
23#11924494C2211yescharacteristic
24C22⋊Q8×C37C411yescharacteristic, complemented
25C23×D37D411yescharacteristic
26C22×#3866—24no—
27C22×#3866—24no—
28C22×#3866—24no—
29C22×#3866—22no—
30C2×Q8×C37C2×C411yescharacteristic, complemented
31C22×C4×C37C2×C411yescharacteristic
32C2×C22⋊D37—21no—
33C22×Dic37D411yescharacteristic
34#10596966—22no—
35#10596966—22no—
36C2×D148—21no—
37C2×D148—21no—
38C2×D148C2×C411yescharacteristic, complemented
39C2×C4×D37—22no—
40C2×C4×D37—22no—
41C2×C4×D37—21no—
42C2×C4×D37C2×C411yescharacteristic
43C2×C4×D37D411yescharacteristic
44C2×C4×D37D411yescharacteristic
45C2×C4×D37C2311yescharacteristic
46C2×#64438—22no—
47C4×#3866—24no—
48C4×#3866—22no—
49C4×#3866D414yescomplemented
50#10596953—22no—
51#10596953—22no—
52C4⋊C4×C37—21no—
53C4⋊C4×C37C2×C411yescharacteristic, complemented
54C22⋊C4×C37—21no—
55#10596938—21no—
56#10596938—21no—
57#10596938—21no—
58#10596938—21no—
59C4⋊Dic37C2×C411yescharacteristic, complemented
60#10596936—21no—
61C4×Dic37—21no—
62C23×C37C22⋊C411yescharacteristic
63C22×D37—22no—
64C22×D37—22no—
65C22×D37—21no—
66C22×D37—21no—
67C22×D37—21no—
68C22×D37C22⋊C411yescharacteristic
69C22×D37C2×D411yescharacteristic
70C2×#3866—216no—
71C2×#3866—24no—
72C2×#3866—24no—
73C2×#3866—24no—
74Q8×C37—22no—
75C2×C4×C37—22no—
76C2×C4×C37—21no—
77C2×C4×C37—21no—
78C2×C4×C37C22⋊C411yescharacteristic
79C2×C4×C37C22×C411yescharacteristic
80C22⋊D37—42no—
81C2×Dic37—22no—
82C2×Dic37—21no—
83C2×Dic37C22⋊C411yescharacteristic
84C2×Dic37C2×D411yescharacteristic
85D148—22no—
86D148—42no—
87D148—41no—
88D148—41no—
89C4×D37—21no—
90C4×D37—21no—
91C4×D37—22no—
92C4×D37—22no—
93C4×D37—42no—
94C4×D37C2×D412yes—
95C4×D37#4112yes—
96#64438—42no—
97C22×C37—21no—
98C22×C37—21no—
99C22×C37#10412yescomplemented
100C22×C37C2×C22⋊C411yescharacteristic
101C2×D37—24no—
102C2×D37—24no—
103C2×D37—21no—
104C2×D37—21no—
105C2×D37—21no—
106C2×D37—21no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37#10412yescomplemented
111C2×D37#12011yescharacteristic
112C2×D37#12311yescharacteristic
113#3866—28no—
114C4×C37—21no—
115C4×C37—41no—
116C4×C37—41no—
117C4×C37C4×D412yes—
118Dic37—21no—
119Dic37—41no—
120Dic37#12112yes—
121#1896—371nomaximal, Sylow
122C2×C37—22no—
123C2×C37#38611yescharacteristic
124C2×C37C2×#10411yescharacteristic
125C2×C37C2×#10411yescharacteristic
126D37—21no—
127D37—22no—
128D37—21no—
129D37—81no—
130#525—371no—
131C22×C42—371no—
132C2×#104—372no—
133#407—371no—
134#339—372no—
135C37#189611yescharacteristic, complemented, Sylow
136C2×#41—371no—
137C23×C4—371no—
138C23×C4—741no—
139C2×M16—372no—
140#123—741no—
141C22⋊Q8—371no—
142C22⋊Q8#386611yescharacteristic, complemented
143#121—371no—
144#121—371no—
145#120—741no—
146C4×D4—741no—
147C4×D4—741no—
148#117—371no—
149C2×C42—372no—
150C2×C42—744no—
151C2×C42—741no—
152#104—744no—
153C22⋊C8—741no—
154C22⋊C8—741no—
155C24—371no—
156#41—742no—
157#41—742no—
158C2×Q8C2×#386611yescharacteristic, complemented
159C2×D4—371no—
160C2×D4—741no—
161C2×D4—741no—
162C2×D4—741no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—371no—
166C22×C4—371no—
167C22×C4—371no—
168C22×C4—742no—
169C22×C4—742no—
170C22×C4—741no—
171C22×C4—742no—
172C22×C4—744no—
173C22×C4—744no—
174C22×C4—744no—
175C22×C4C2×#386611yescharacteristic
176M16—742no—
177M16—742no—
178C2×C8—742no—
179C4⋊C4—21no—
180C4⋊C4—371no—
181C4⋊C4—741no—
182C4⋊C4C2×#386611yescharacteristic, complemented
183C22⋊C4—21no—
184C22⋊C4—741no—
185C22⋊C4—741no—
186C22⋊C4—741no—
187C22⋊C4—741no—
188C42—374no—
189C42—741no—
190C42—742no—
191C42—744no—
192C23—371no—
193C23—371no—
194C23—741no—
195C23—741no—
196C23—742no—
197C23—742no—
198C23—741no—
199C23C22⋊#386611yescharacteristic
200Q8—22no—
201D4—742no—
202D4—1481no—
203D4—1481no—
204D4—1482no—
205D4—1482no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—371no—
210C2×C4—372no—
211C2×C4—372no—
212C2×C4—371no—
213C2×C4—742no—
214C2×C4—741no—
215C2×C4—741no—
216C2×C4—742no—
217C2×C4—744no—
218C2×C4—7416no—
219C2×C4—744no—
220C2×C4—744no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—1482no—
224C2×C4C22⋊#386611yescharacteristic
225C2×C4C22×#386611yescharacteristic
226C8—1482no—
227C22—21no—
228C22—21no—
229C22—371no—
230C22—371no—
231C22—372no—
232C22—744no—
233C22—744no—
234C22—741no—
235C22—741no—
236C22—741no—
237C22—741no—
238C22—1481no—
239C22—1481no—
240C22—1481no—
241C22#1192460112yescomplemented
242C22C2×C22⋊#386611yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—372no—
247C4—748no—
248C4—741no—
249C4—1481no—
250C4D4×#386612yes—
251C2—22no—
252C2—2961no—
253C2—741no—
254C2—741no—
255C2—742no—
256C2#1455848111yescharacteristic
257C2D37⋊#10411yescharacteristic
258C2C2×#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#1896
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C4×#3866C2semidirect
2. C2×#11924601C2semidirect
3. #14558504C2semidirect
4. #14558403C2semidirect
17. #11924512C4semidirect
18. #11924511C4semidirect
19. #11924510C4semidirect
24. C22⋊Q8×C37C4semidirect
30. C2×Q8×C37C2×C4semidirect
38. C2×D148C2×C4semidirect
49. C4×#3866D4semidirect
53. C4⋊C4×C37C2×C4semidirect
59. C4⋊Dic37C2×C4semidirect
99. C22×C37#104semidirect
110. C2×D37#104semidirect
135. C37#1896semidirect
142. C22⋊Q8#3866semidirect
158. C2×Q8C2×#3866semidirect
182. C4⋊C4C2×#3866semidirect
241. C22#11924601semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#38662
C2×#119246012
#145585042
#145584032
#145580462
#189637