Finite Group Databasebeta

← #18010615

Subgroups — #18010615

Order 4736.

358 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 70 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×#11924615C211yesmaximal, characteristic, complemented
2C2×#11924601C212yesmaximal, complemented
3#14558504C211yesmaximal, characteristic, complemented
4#14558403C212yesmaximal, complemented
5#14558046C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7#11924615—24no—
8C2×C4⋊#3866—21no—
9C2×C22⋊#3866—21no—
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—22no—
27C2×Q8×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C22×Dic37D411yescharacteristic
31#10596966—22no—
32#10596966—22no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148C2×C411yescharacteristic
36C2×C4×D37—22no—
37C2×C4×D37—22no—
38C2×C4×D37—21no—
39C2×C4×D37C2×C411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37C2311yescharacteristic
43C22⋊#3866—24no—
44C2×#64438—22no—
45C4⋊#3866—24no—
46C4×#3866—22no—
47C4×#3866D414yescomplemented
48#10596953—22no—
49#10596953—22no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37C2×C411yescharacteristic
52C22⋊C4×C37—21no—
53#10596938—21no—
54#10596938—21no—
55#10596938—21no—
56#10596938—21no—
57C4⋊Dic37C2×C411yescharacteristic
58#10596936—21no—
59C4×Dic37—21no—
60C23×C37C22⋊C411yescharacteristic
61C22×D37—21no—
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—41no—
65C22×D37—41no—
66C22×D37C22⋊C411yescharacteristic
67C22×D37C2×D411yescharacteristic
68C2×#3866—24no—
69C2×#3866—42no—
70C2×#3866—42no—
71Q8×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37—21no—
74C2×C4×C37—21no—
75C2×C4×C37C22⋊C411yescharacteristic
76C2×C4×C37C22×C411yescharacteristic
77C22⋊D37—42no—
78C2×Dic37—22no—
79C2×Dic37—21no—
80C2×Dic37C22⋊C411yescharacteristic
81C2×Dic37C2×D411yescharacteristic
82D148—22no—
83D148—42no—
84D148—41no—
85D148—41no—
86C4×D37—21no—
87C4×D37—21no—
88C4×D37—22no—
89C4×D37—22no—
90C4×D37—42no—
91C4×D37C2×D412yes—
92C4×D37#4112yes—
93#64438—42no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37C2×C22⋊C411yescharacteristic
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—21no—
103C2×D37—42no—
104C2×D37—42no—
105C2×D37—41no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37#12011yescharacteristic
109C2×D37#12311yescharacteristic
110#3866—44no—
111C4×C37—21no—
112C4×C37—41no—
113C4×C37—41no—
114C4×C37C4×D412yes—
115Dic37—21no—
116Dic37—41no—
117Dic37#12112yes—
118#1897—371nomaximal, Sylow
119C2×C37—41no—
120C2×C37#38611yescharacteristic
121C2×C37#42111yescharacteristic
122C2×C37#42111yescharacteristic
123D37—21no—
124D37—21no—
125D37—41no—
126D37—81no—
127#525—371no—
128C2×#117—371no—
129C2×#104—372no—
130#407—371no—
131#339—372no—
132C37#189711yescharacteristic, complemented, Sylow
133C2×#41—371no—
134C23×C4—371no—
135C2×M16—372no—
136#123—741no—
137C22⋊Q8—371no—
138C22⋊Q8#386611yescharacteristic, complemented
139#121—371no—
140#121—371no—
141#120—741no—
142C4×D4—741no—
143C4×D4—741no—
144#117—371no—
145#117—744no—
146C2×C4⋊C4—741no—
147C2×C22⋊C4—741no—
148C2×C42—372no—
149#104—744no—
150C22⋊C8—741no—
151C22⋊C8—741no—
152C24—371no—
153#41—742no—
154#41—742no—
155C2×Q8C2×#386611yescharacteristic
156C2×D4—371no—
157C2×D4—741no—
158C2×D4—741no—
159C2×D4—741no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—742no—
166C22×C4—742no—
167C22×C4—741no—
168C22×C4—742no—
169C22×C4C2×#386611yescharacteristic
170M16—742no—
171M16—742no—
172C2×C8—742no—
173C4⋊C4—21no—
174C4⋊C4—371no—
175C4⋊C4—741no—
176C4⋊C4—744no—
177C4⋊C4C2×#386611yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—744no—
183C22⋊C4—741no—
184C42—374no—
185C42—741no—
186C42—742no—
187C23—371no—
188C23—371no—
189C23—741no—
190C23—741no—
191C23—741no—
192C23—1481no—
193C23—1481no—
194C23C22⋊#386611yescharacteristic
195Q8—22no—
196D4—742no—
197D4—1481no—
198D4—1481no—
199D4—1482no—
200D4—1482no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—371no—
205C2×C4—372no—
206C2×C4—372no—
207C2×C4—371no—
208C2×C4—742no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—742no—
212C2×C4—742no—
213C2×C4—744no—
214C2×C4—741no—
215C2×C4—1482no—
216C2×C4—1482no—
217C2×C4—1482no—
218C2×C4C22⋊#386611yescharacteristic
219C2×C4C22×#386611yescharacteristic
220C8—1482no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—371no—
225C22—371no—
226C22—741no—
227C22—741no—
228C22—741no—
229C22—741no—
230C22—741no—
231C22—1482no—
232C22—1482no—
233C22—1481no—
234C22—1481no—
235C22—1481no—
236C22C2×C22⋊#386611yescharacteristic
237C4—21no—
238C4—41no—
239C4—41no—
240C4—372no—
241C4—741no—
242C4—1484no—
243C4—1481no—
244C4D4×#386612yes—
245C2—41no—
246C2—2961no—
247C2—741no—
248C2—741no—
249C2—1481no—
250C2#1455848111yescharacteristic
251C2#1455853011yescharacteristic
252C2#1455853211yescharacteristic
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#1897
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. C2×#11924615C2semidirect
2. C2×#11924601C2semidirect
3. #14558504C2semidirect
4. #14558403C2semidirect
17. #11924512C4semidirect
18. #11924511C4semidirect
19. #11924510C4semidirect
24. C22⋊Q8×C37C4semidirect
47. C4×#3866D4semidirect
132. C37#1897semidirect
138. C22⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246152
C2×#119246012
#145585042
#145584032
#145580462
#189737