Finite Group Databasebeta

← #18010464

Subgroups — #18010464

Order 4736.

372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D37⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#11924598C212yesmaximal
3#14558479C211yesmaximal, characteristic, complemented
4#14558406C212yesmaximal, complemented
5C4×D4×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7C2×C4⋊#3866—21no—
8C2×C4⋊#3866—21no—
9C2×C4⋊#3866C2212yes—
10#11924603—21no—
11C4⋊#64438—21no—
12#11924598—24no—
13C2×D4×D37C2211yescharacteristic
14C22×C4×D37—21no—
15C4×D148C411yescharacteristic, complemented
16D4×Dic37C411yescharacteristic, complemented
17#11924498C411yescharacteristic, complemented
18C4×C22⋊D37—21no—
19#11924496—21no—
20C4⋊C4×D37C2211yescharacteristic
21C22⋊C4×D37—21no—
22C42×D37C2211yescharacteristic
23C4×D4×C37C411yescharacteristic, complemented
24C23×D37—21no—
25C22×#3866—22no—
26C2×D4×C37C2×C411yescharacteristic
27C22×C4×C37—21no—
28C2×C22⋊D37—21no—
29C22×Dic37—21no—
30D4×D37—21no—
31D4×D37—21no—
32D4×D37D412yes—
33D4×D37Q812yes—
34C2×D148C2×C411yescharacteristic
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37—42no—
39C2×C4×D37—42no—
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37C2311yescharacteristic
43C2×#64438—22no—
44C4⋊#3866—22no—
45C4⋊#3866—22no—
46C4⋊#3866—42no—
47C4⋊#3866—42no—
48D37⋊C8—22no—
49D37⋊C8—22no—
50C4⋊C4×C37C2×C411yescharacteristic
51C22⋊C4×C37—21no—
52C42×C37C2×C411yescharacteristic
53C22⋊Dic37—21no—
54#10596938—21no—
55#10596938—21no—
56C4⋊Dic37C2×C411yescharacteristic
57#10596936—21no—
58C4×Dic37C2×C411yescharacteristic
59C4×Dic37D411yescharacteristic
60C4×Dic37D411yescharacteristic
61C23×C37—21no—
62C22×D37—21no—
63C22×D37—22no—
64C22×D37—22no—
65C22×D37—41no—
66C22×D37—41no—
67C22×D37—41no—
68C22×D37—41no—
69C22×D37C2×D411yescharacteristic
70C2×#3866—42no—
71C2×#3866—42no—
72C2×#3866—42no—
73D4×C37—21no—
74D4×C37C4⋊C412yescomplemented
75C2×C4×C37—21no—
76C2×C4×C37—42no—
77C2×C4×C37C22⋊C411yescharacteristic
78C2×C4×C37C22⋊C411yescharacteristic
79C2×C4×C37C22×C411yescharacteristic
80C22⋊D37—22no—
81C22⋊D37—22no—
82C2×Dic37—21no—
83C2×Dic37—42no—
84C2×Dic37C22⋊C411yescharacteristic
85C2×Dic37C22⋊C411yescharacteristic
86C2×Dic37C2×D411yescharacteristic
87D148—21no—
88D148C4⋊C412yescomplemented
89C4×D37—21no—
90C4×D37—21no—
91C4×D37—41no—
92C4×D37—41no—
93C4×D37—42no—
94C4×D37—42no—
95C4×D37D812yes—
96C4×D37SD1612yes—
97C4×D37C2×D411yescharacteristic
98C4×D37C2×Q811yescharacteristic
99C4×D37#4111yescharacteristic
100C4×D37#4111yescharacteristic
101#64438—42no—
102C22×C37—22no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37C2×C22⋊C411yescharacteristic
106C2×D37—22no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—42no—
110C2×D37—42no—
111C2×D37—42no—
112C2×D37—42no—
113C2×D37#12111yescharacteristic
114C2×D37C22⋊Q811yescharacteristic
115C2×D37C2×D811yescharacteristic
116C2×D37C2×SD1611yescharacteristic
117C2×D37AGL(1,ℤ/8)11yescharacteristic
118C2×D37#13711yescharacteristic
119#3866—82no—
120C4×C37—21no—
121C4×C37—41no—
122C4×C37#10212yescomplemented
123C4×C37C2×C4⋊C411yescharacteristic
124C4×C37#11711yescharacteristic
125Dic37—21no—
126Dic37—41no—
127Dic37#10212yescomplemented
128Dic37#12111yescharacteristic
129Dic37C22⋊Q811yescharacteristic
130#1802—371nomaximal, Sylow
131C2×C37—42no—
132C2×C37#38011yescharacteristic
133C2×C37C2×#10211yescharacteristic
134C2×C37#41711yescharacteristic
135D37—42no—
136D37#45911yescharacteristic
137D37#46111yescharacteristic
138D37#47411yescharacteristic
139D37#47611yescharacteristic
140C2×C4×D4—371no—
141C2×C4⋊C8—371no—
142C2×#102—372no—
143#384—371no—
144#340—372no—
145C37#180211yescharacteristic, complemented, Sylow
146C22×D4—371no—
147C23×C4—741no—
148C22×C8—372no—
149C4×D4—371no—
150C4×D4—371no—
151C4×D4—371no—
152C4×D4—741no—
153C4×D4—741no—
154C4×D4#386611yescharacteristic, complemented
155C2×C4⋊C4—371no—
156C2×C4⋊C4—372no—
157C2×C4⋊C4—741no—
158C2×C4⋊C4—741no—
159C2×C22⋊C4—741no—
160C2×C42—371no—
161C4⋊C8—741no—
162C4⋊C8—741no—
163#102—744no—
164C24—741no—
165C2×D4—372no—
166C2×D4—372no—
167C2×D4—371no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4C2×#386611yescharacteristic
172C22×C4—21no—
173C22×C4—371no—
174C22×C4—371no—
175C22×C4—371no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180C22×C4—742no—
181C22×C4—1482no—
182C22×C4—1482no—
183C2×C8—742no—
184C2×C8—742no—
185C2×C8—742no—
186C4⋊C4—371no—
187C4⋊C4—741no—
188C4⋊C4—742no—
189C4⋊C4—742no—
190C4⋊C4—1482no—
191C4⋊C4—1482no—
192C4⋊C4C2×#386611yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—741no—
195C22⋊C4—741no—
196C22⋊C4—741no—
197C42—371no—
198C42—371no—
199C42—371no—
200C42C2×#386611yescharacteristic
201C23—21no—
202C23—371no—
203C23—742no—
204C23—742no—
205C23—741no—
206C23—1481no—
207C23—1481no—
208C23—1481no—
209C23—1481no—
210D4—21no—
211D4—372no—
212D4—742no—
213D4—742no—
214D4—741no—
215D4C4⋊#386612yescomplemented
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—371no—
219C2×C4—371no—
220C2×C4—372no—
221C2×C4—372no—
222C2×C4—371no—
223C2×C4—371no—
224C2×C4—371no—
225C2×C4—371no—
226C2×C4—371no—
227C2×C4—741no—
228C2×C4—741no—
229C2×C4—741no—
230C2×C4—1482no—
231C2×C4—1481no—
232C2×C4—1481no—
233C2×C4—1482no—
234C2×C4—1482no—
235C2×C4—1482no—
236C2×C4—1482no—
237C2×C4—1482no—
238C2×C4C22⋊#386611yescharacteristic
239C2×C4C22⋊#386611yescharacteristic
240C2×C4C22×#386611yescharacteristic
241C8—1482no—
242C22—22no—
243C22—41no—
244C22—41no—
245C22—371no—
246C22—371no—
247C22—371no—
248C22—371no—
249C22—371no—
250C22—371no—
251C22—742no—
252C22—1482no—
253C22—1482no—
254C22—1482no—
255C22—1482no—
256C22—1481no—
257C22—1481no—
258C22C2×C22⋊#386611yescharacteristic
259C4—21no—
260C4—41no—
261C4—371no—
262C4—371no—
263C4—372no—
264C4—2962no—
265C4—741no—
266C4—1481no—
267C4#1192459812yescomplemented
268C4C2×C4⋊#386611yescharacteristic
269C4#1192461511yescharacteristic
270C2—42no—
271C2—371no—
272C2—371no—
273C2—371no—
274C2—371no—
275C2—1482no—
276C2#1455847511yescharacteristic
277C2C2×#1192459811yescharacteristic
278C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C22
cosocleC2×C4×D37C23
hypercenterC4×D4#3866
hypocenterC37#1802
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D37⋊(C4⋊C8)C2semidirect
3. #14558479C2semidirect
4. #14558406C2semidirect
15. C4×D148C4semidirect
16. D4×Dic37C4semidirect
17. #11924498C4semidirect
23. C4×D4×C37C4semidirect
74. D4×C37C4⋊C4semidirect
88. D148C4⋊C4semidirect
122. C4×C37#102semidirect
127. Dic37#102semidirect
145. C37#1802semidirect
154. C4×D4#3866semidirect
215. D4C4⋊#3866semidirect
267. C4#11924598semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C4⋊C8)2
C2×#119245982
#145584792
#145584062
C4×D4×D372
#180237