Finite Group Databasebeta

← #18010646

Subgroups — #18010646

Order 4736.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558600C211yesmaximal, characteristic, complemented
2C2×#11924595C212yesmaximal, complemented
3D37⋊#99C211yesmaximal, characteristic, complemented
4#14558410C212yesmaximal, complemented
5#14558094C211yesmaximal, characteristic
6D4×#3866—24no—
7#11924615—21no—
8C2×C22⋊#3866—21no—
9C2×C22⋊#3866C2212yes—
10C2×C22⋊#3866C2212yes—
11#11924595—21no—
12#11924595—24no—
13#11924594—21no—
14C22×D148C2211yescharacteristic
15C2×D4×D37C2211yescharacteristic
16#11924521—21no—
17#11924519C411yescharacteristic, complemented
18#11924511—21no—
19#11924509—21no—
20#11924506—21no—
21#11924506C411yescharacteristic, complemented
22#11924504C411yescharacteristic, complemented
23C22⋊C4×D37C2211yescharacteristic
24#123×C37C411yescharacteristic, complemented
25C23×D37C2×C411yescharacteristic, complemented
26C23×D37D411yescharacteristic
27C23×D37C2311yescharacteristic
28C22×#3866—22no—
29C22×#3866—22no—
30C22×#3866—22no—
31C2×D4×C37C2×C411yescharacteristic
32C22×C4×C37C2×C411yescharacteristic, complemented
33C2×C22⋊D37—21no—
34C2×C22⋊D37C2×C411yescharacteristic
35C2×C22⋊D37D411yescharacteristic
36D4×D37—22no—
37D4×D37—22no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—22no—
41C2×D148—22no—
42C2×D148—21no—
43C2×D148D411yescharacteristic
44C2×C4×D37—21no—
45C2×C4×D37D411yescharacteristic
46C22⋊#3866—22no—
47C22⋊#3866—22no—
48C22⋊#3866—22no—
49C22⋊#3866—22no—
50C22⋊#3866D414yescomplemented
51C4⋊#3866—22no—
52C4×#3866—22no—
53C4⋊C4×C37—21no—
54C22⋊C4×C37—21no—
55C22⋊C4×C37C2×C411yescharacteristic, complemented
56C22⋊Dic37C2×C411yescharacteristic, complemented
57#10596938—21no—
58#10596938—21no—
59#10596938—21no—
60#10596938—21no—
61#10596936—21no—
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22×C411yescharacteristic
64C22×D37—21no—
65C22×D37—21no—
66C22×D37—21no—
67C22×D37—22no—
68C22×D37—81no—
69C22×D37—81no—
70C22×D37—81no—
71C22×D37C22⋊C411yescharacteristic
72C22×D37C2×D412yes—
73C22×D37C2×D411yescharacteristic
74C22×D37C2×D411yescharacteristic
75C22×D37#4112yes—
76C2×#3866—24no—
77C2×#3866—42no—
78C2×#3866—82no—
79C2×#3866—82no—
80C2×#3866—82no—
81D4×C37—22no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37—22no—
85C2×C4×C37C22⋊C411yescharacteristic
86C22⋊D37—22no—
87C22⋊D37—22no—
88C22⋊D37—81no—
89C2×Dic37—21no—
90C2×Dic37C22⋊C411yescharacteristic
91D148—22no—
92D148—41no—
93D148—42no—
94D148—41no—
95D148—81no—
96C4×D37—21no—
97C4×D37—21no—
98C4×D37—81no—
99C22×C37—21no—
100C22×C37—41no—
101C22×C37—41no—
102C22×C37C2×C22⋊C411yescharacteristic
103C22×C37C4×D412yes—
104C2×D37—21no—
105C2×D37—41no—
106C2×D37—42no—
107C2×D37—42no—
108C2×D37—41no—
109C2×D37—42no—
110C2×D37—41no—
111C2×D37—41no—
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—81no—
115C2×D37—82no—
116C2×D37#12011yescharacteristic
117C2×D37#12112yes—
118C2×D37#12311yescharacteristic
119#3866—44no—
120#3866—82no—
121C4×C37—21no—
122C4×C37—41no—
123C4×C37—41no—
124Dic37—21no—
125Dic37—41no—
126#1913—371nomaximal, Sylow
127C2×C37—21no—
128C2×C37—22no—
129C2×C37—41no—
130C2×C37#38611yescharacteristic
131D37—21no—
132D37—22no—
133D37—21no—
134D37—41no—
135D37—81no—
136#534—371no—
137#518—371no—
138C2×#99—371no—
139C2×#99—372no—
140#342—372no—
141C37#191311yescharacteristic, complemented, Sylow
142C22×D4—371no—
143C22×D4—371no—
144#123—371no—
145#123—741no—
146#123#386611yescharacteristic, complemented
147#121—741no—
148#121—741no—
149#120—371no—
150#120—371no—
151#120—741no—
152C4×D4—744no—
153#117—741no—
154C2×C22⋊C4—372no—
155C2×C22⋊C4—371no—
156C2×C22⋊C4—372no—
157C2×C22⋊C4—741no—
158#99—744no—
159#99—741no—
160#99—741no—
161C24—371no—
162C24—371no—
163C24—371no—
164C2×D4—371no—
165C2×D4—371no—
166C2×D4—371no—
167C2×D4—741no—
168C2×D4—742no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—742no—
172C2×D4—742no—
173C2×D4—742no—
174C2×D4—741no—
175C2×D4C2×#386611yescharacteristic
176C22×C4—371no—
177C22×C4—741no—
178C22×C4—742no—
179C22×C4—742no—
180C22×C4—742no—
181C22×C4C2×#386611yescharacteristic, complemented
182C4⋊C4—21no—
183C4⋊C4—741no—
184C4⋊C4—742no—
185C22⋊C4—21no—
186C22⋊C4—374no—
187C22⋊C4—371no—
188C22⋊C4—741no—
189C22⋊C4—741no—
190C22⋊C4—741no—
191C22⋊C4—742no—
192C22⋊C4—742no—
193C22⋊C4—741no—
194C22⋊C4—742no—
195C22⋊C4—742no—
196C22⋊C4C2×#386611yescharacteristic, complemented
197C42—742no—
198C23—371no—
199C23—371no—
200C23—372no—
201C23—372no—
202C23—371no—
203C23—2961no—
204C23—2961no—
205C23—2961no—
206C23—741no—
207C23—741no—
208C23—742no—
209C23—741no—
210C23C22⋊#386611yescharacteristic
211C23C22×#386611yescharacteristic
212D4—22no—
213D4—2961no—
214D4—2961no—
215D4—742no—
216D4—742no—
217D4—742no—
218D4—1481no—
219D4—1481no—
220D4—1482no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—371no—
225C2×C4—2961no—
226C2×C4—2962no—
227C2×C4—2962no—
228C2×C4—2962no—
229C2×C4—741no—
230C2×C4—741no—
231C2×C4—744no—
232C2×C4—741no—
233C2×C4—1482no—
234C2×C4C22⋊#386611yescharacteristic
235C22—21no—
236C22—41no—
237C22—41no—
238C22—371no—
239C22—371no—
240C22—372no—
241C22—2962no—
242C22—2961no—
243C22—741no—
244C22—1481no—
245C22—1481no—
246C22—1481no—
247C22—1482no—
248C22—1482no—
249C22—1481no—
250C22—1481no—
251C22—1482no—
252C22—1481no—
253C22C2×C22⋊#386611yescharacteristic
254C22D4×#386612yes—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—2962no—
259C4—741no—
260C4—1481no—
261C4—1484no—
262C2—21no—
263C2—22no—
264C2—41no—
265C2—2961no—
266C2—742no—
267C2—741no—
268C2—741no—
269C2—1481no—
270C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37#386
prime radical#14558094C2
cosocleC23×D37C23
hypercenter#123#3866
hypocenterC37#1913
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #14558600C2semidirect
2. C2×#11924595C2semidirect
3. D37⋊#99C2semidirect
4. #14558410C2semidirect
17. #11924519C4semidirect
21. #11924506C4semidirect
22. #11924504C4semidirect
24. #123×C37C4semidirect
25. C23×D37C2×C4semidirect
32. C22×C4×C37C2×C4semidirect
50. C22⋊#3866D4semidirect
55. C22⋊C4×C37C2×C4semidirect
56. C22⋊Dic37C2×C4semidirect
141. C37#1913semidirect
146. #123#3866semidirect
181. C22×C4C2×#3866semidirect
196. C22⋊C4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145586002
C2×#119245952
D37⋊#992
#145584102
#145580942
#191337