Finite Group Databasebeta

← #18010620

Subgroups — #18010620

Order 4736.

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

normal subgroups only

This group has 378 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×#11924595C212yesmaximal
3#14558476C211yesmaximal, characteristic, complemented
4#14558411C212yesmaximal, complemented
5C2×#11924521C211yesmaximal, characteristic
6#11924615—24no—
7C2×C4⋊#3866—21no—
8C2×C22⋊#3866C2212yes—
9C2×C22⋊#3866C2212yes—
10C2×C4×#3866—21no—
11#11924595—24no—
12(C2×#3866)⋊C4—21no—
13(C2×#3866)⋊C4—21no—
14C22×D148C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16#11924521—21no—
17#11924521—21no—
18#11924521—21no—
19#11924521—21no—
20C2×#10596936C411yescharacteristic, complemented
21C2×#10596938C411yescharacteristic, complemented
22C2×#10596938C411yescharacteristic, complemented
23C2×#10596938C2211yescharacteristic
24C2×C4⋊C4×C37C411yescharacteristic, complemented
25C23×D37C2×C411yescharacteristic
26C23×D37C2311yescharacteristic
27C22×#3866—22no—
28C22×#3866—22no—
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—22no—
37C2×D148—22no—
38C2×C4×D37—22no—
39C2×C4×D37—22no—
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C4×D37D411yescharacteristic
44C22⋊#3866—22no—
45C22⋊#3866—22no—
46C22⋊#3866—22no—
47C22⋊#3866D414yes—
48C4⋊#3866—24no—
49C4×#3866—24no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37—21no—
52#10596938—21no—
53#10596938—21no—
54#10596938—21no—
55#10596938—21no—
56#10596938—21no—
57#10596938—21no—
58#10596936—21no—
59#10596936—21no—
60C23×C37C22×C411yescharacteristic
61C22×D37—21no—
62C22×D37—22no—
63C22×D37—41no—
64C22×D37—41no—
65C22×D37—41no—
66C22×D37—41no—
67C22×D37C2×D411yescharacteristic
68C22×D37C2×D411yescharacteristic
69C22×D37C2×D412yes—
70C22×D37#4112yes—
71C2×#3866—24no—
72C2×#3866—42no—
73C2×#3866—42no—
74C2×#3866—42no—
75C2×#3866—42no—
76C2×#3866—42no—
77C2×C4×C37—22no—
78C2×C4×C37—21no—
79C2×C4×C37—21no—
80C2×C4×C37—22no—
81C2×C4×C37—41no—
82C2×C4×C37C22⋊C411yescharacteristic
83C2×C4×C37C22⋊C411yescharacteristic
84C2×Dic37—22no—
85C2×Dic37—21no—
86C2×Dic37—41no—
87C2×Dic37C22⋊C411yescharacteristic
88C2×Dic37C22⋊C411yescharacteristic
89D148—41no—
90D148—42no—
91D148—41no—
92C4×D37—21no—
93C4×D37—21no—
94C4×D37—22no—
95C4×D37—22no—
96C4×D37—21no—
97C4×D37—21no—
98C22×C37—21no—
99C22×C37—21no—
100C22×C37C2×C22⋊C411yescharacteristic
101C22×C37C4×D412yes—
102C2×D37—21no—
103C2×D37—21no—
104C2×D37—21no—
105C2×D37—21no—
106C2×D37—42no—
107C2×D37—42no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—82no—
112C2×D37#12011yescharacteristic
113C2×D37#12112yes—
114C2×D37#12311yescharacteristic
115#3866—44no—
116#3866—82no—
117C4×C37—21no—
118C4×C37—21no—
119C4×C37—41no—
120C4×C37—41no—
121Dic37—21no—
122Dic37—21no—
123Dic37—41no—
124#1899—371nomaximal, Sylow
125C2×C37—22no—
126C2×C37#38611yescharacteristic
127C2×C37#41011yescharacteristic
128C2×C37#41011yescharacteristic
129D37—21no—
130D37—22no—
131D37—21no—
132D37—81no—
133C2×#123—371no—
134C2×#117—371no—
135C2×#99—372no—
136#381—371no—
137#342—372no—
138C37#189911yescharacteristic, complemented, Sylow
139C22×D4—371no—
140C23×C4—371no—
141#123—741no—
142#123—741no—
143#123—741no—
144#123—741no—
145#117—744no—
146C2×C4⋊C4—371no—
147C2×C4⋊C4—741no—
148C2×C4⋊C4#386611yescharacteristic, complemented
149C2×C22⋊C4—372no—
150C2×C22⋊C4—371no—
151C2×C22⋊C4—371no—
152C2×C22⋊C4—371no—
153C2×C22⋊C4—372no—
154C2×C42—741no—
155#99—744no—
156#95—741no—
157#95—741no—
158C24—371no—
159C24—371no—
160C2×D4—742no—
161C2×D4—741no—
162C2×D4—741no—
163C2×D4—742no—
164C22×C4—371no—
165C22×C4—371no—
166C22×C4—371no—
167C22×C4—371no—
168C22×C4—371no—
169C22×C4—371no—
170C22×C4—742no—
171C22×C4—742no—
172C22×C4—742no—
173C22×C4—742no—
174C22×C4C2×#386611yescharacteristic
175C22×C4C2×#386611yescharacteristic
176C22×C4C2×#386611yescharacteristic
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—741no—
180C4⋊C4—741no—
181C4⋊C4—744no—
182C22⋊C4—374no—
183C22⋊C4—741no—
184C22⋊C4—741no—
185C22⋊C4—741no—
186C22⋊C4—741no—
187C22⋊C4—742no—
188C22⋊C4—741no—
189C22⋊C4—741no—
190C22⋊C4—742no—
191C22⋊C4—742no—
192C42—744no—
193C23—371no—
194C23—371no—
195C23—372no—
196C23—372no—
197C23—742no—
198C23—741no—
199C23—1481no—
200C23—1481no—
201C23—1481no—
202C23—1481no—
203C23C22×#386611yescharacteristic
204D4—1481no—
205D4—1482no—
206D4—1481no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—371no—
213C2×C4—371no—
214C2×C4—741no—
215C2×C4—741no—
216C2×C4—742no—
217C2×C4—742no—
218C2×C4—741no—
219C2×C4—741no—
220C2×C4—742no—
221C2×C4—744no—
222C2×C4—741no—
223C2×C4—1482no—
224C2×C4—1482no—
225C2×C4—1482no—
226C2×C4—1482no—
227C2×C4—1482no—
228C2×C4—1481no—
229C2×C4C22⋊#386611yescharacteristic
230C2×C4C22⋊#386611yescharacteristic
231C22—21no—
232C22—21no—
233C22—371no—
234C22—372no—
235C22—371no—
236C22—2962no—
237C22—741no—
238C22—741no—
239C22—741no—
240C22—741no—
241C22—1482no—
242C22—1482no—
243C22—1481no—
244C22—1481no—
245C22—1481no—
246C22C2×C22⋊#386611yescharacteristic
247C22D4×#386612yes—
248C4—21no—
249C4—21no—
250C4—41no—
251C4—41no—
252C4—2962no—
253C4—741no—
254C4—741no—
255C4—1484no—
256C4—1481no—
257C2—22no—
258C2—2961no—
259C2—742no—
260C2—741no—
261C2—741no—
262C2#1455848111yescharacteristic
263C2#1455851211yescharacteristic
264C2#1455851411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C22
cosocleC23×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1899
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11924615C2semidirect
3. #14558476C2semidirect
4. #14558411C2semidirect
20. C2×#10596936C4semidirect
21. C2×#10596938C4semidirect
22. C2×#10596938C4semidirect
24. C2×C4⋊C4×C37C4semidirect
138. C37#1899semidirect
148. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246152
C2×#119245952
#145584762
#145584112
C2×#119245212
#189937