Finite Group Databasebeta

← #18010466

Subgroups — #18010466

Order 4736.

356 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 84 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#14558477C211yesmaximal, characteristic, complemented
4#14558406C212yesmaximal, complemented
5C4×D4×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7C2×C4⋊#3866C2212yes—
8#11924603—21no—
9C4⋊#64438—21no—
10#11924598—24no—
11(C2×#3866)⋊C4—21no—
12(C2×#3866)⋊C4—21no—
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—44no—
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37C2311yescharacteristic
42C2×#64438—22no—
43C4⋊#3866—22no—
44C4⋊#3866—22no—
45D37⋊C8—22no—
46D37⋊C8—22no—
47C4⋊C4×C37C2×C411yescharacteristic
48C22⋊C4×C37—21no—
49C42×C37C2×C411yescharacteristic
50C22⋊Dic37—21no—
51#10596938—21no—
52#10596938—21no—
53C4⋊Dic37C2×C411yescharacteristic
54#10596936—21no—
55C4×Dic37C2×C411yescharacteristic
56C4×Dic37D411yescharacteristic
57C4×Dic37D411yescharacteristic
58C23×C37—21no—
59C22×D37—21no—
60C22×D37—22no—
61C22×D37—22no—
62C22×D37—42no—
63C22×D37—42no—
64C22×D37C2×D411yescharacteristic
65C2×#3866—42no—
66C2×#3866—42no—
67C2×#3866—42no—
68D4×C37—21no—
69D4×C37C4⋊C412yes—
70C2×C4×C37—21no—
71C2×C4×C37—42no—
72C2×C4×C37C22⋊C411yescharacteristic
73C2×C4×C37C22⋊C411yescharacteristic
74C2×C4×C37C22×C411yescharacteristic
75C22⋊D37—22no—
76C22⋊D37—22no—
77C2×Dic37—21no—
78C2×Dic37—42no—
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C22⋊C411yescharacteristic
81C2×Dic37C2×D411yescharacteristic
82D148—21no—
83D148C4⋊C412yes—
84C4×D37—22no—
85C4×D37—22no—
86C4×D37—42no—
87C4×D37—42no—
88C4×D37—42no—
89C4×D37C2×D411yescharacteristic
90C4×D37C2×Q811yescharacteristic
91C4×D37#4111yescharacteristic
92C4×D37#4111yescharacteristic
93#64438—42no—
94C22×C37—22no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37C2×C22⋊C411yescharacteristic
98C2×D37—22no—
99C2×D37—41no—
100C2×D37—41no—
101C2×D37—44no—
102C2×D37—44no—
103C2×D37#12111yescharacteristic
104C2×D37C22⋊Q811yescharacteristic
105C2×D37#13512yes—
106C2×D37AGL(1,ℤ/8)12yes—
107#3866—82no—
108C4×C37—21no—
109C4×C37—21no—
110C4×C37—41no—
111C4×C37C2×C4⋊C411yescharacteristic
112C4×C37#11711yescharacteristic
113Dic37—21no—
114Dic37—21no—
115Dic37—41no—
116Dic37#12111yescharacteristic
117Dic37C22⋊Q811yescharacteristic
118#1804—371nomaximal, Sylow
119C2×C37—42no—
120C2×C37#38011yescharacteristic
121C2×C37#41611yescharacteristic
122C2×C37#41811yescharacteristic
123D37—42no—
124D37#46312yes—
125D37#47812yes—
126C2×C4×D4—371no—
127C2×C4⋊C8—371no—
128C2×#102—372no—
129#382—371no—
130#340—372no—
131C37#180411yescharacteristic, complemented, Sylow
132C22×D4—371no—
133C23×C4—741no—
134C22×C8—372no—
135C4×D4—371no—
136C4×D4—371no—
137C4×D4—371no—
138C4×D4—741no—
139C4×D4—741no—
140C4×D4#386611yescharacteristic, complemented
141C2×C4⋊C4—371no—
142C2×C4⋊C4—372no—
143C2×C22⋊C4—741no—
144C2×C42—371no—
145C4⋊C8—741no—
146C4⋊C8—741no—
147#102—744no—
148#95—741no—
149#95—741no—
150C24—741no—
151C2×D4—372no—
152C2×D4—372no—
153C2×D4—371no—
154C2×D4—741no—
155C2×D4—741no—
156C2×D4—741no—
157C2×D4C2×#386611yescharacteristic
158C22×C4—21no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—741no—
163C22×C4—741no—
164C22×C4—741no—
165C22×C4—741no—
166C22×C4—742no—
167C22×C4—1484no—
168C2×C8—742no—
169C2×C8—742no—
170C2×C8—742no—
171C4⋊C4—371no—
172C4⋊C4—741no—
173C4⋊C4—742no—
174C4⋊C4—742no—
175C4⋊C4C2×#386611yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C42—371no—
181C42—371no—
182C42—371no—
183C42C2×#386611yescharacteristic
184C23—21no—
185C23—371no—
186C23—742no—
187C23—742no—
188C23—741no—
189C23—1482no—
190C23—1482no—
191D4—21no—
192D4—372no—
193D4—742no—
194D4—742no—
195D4—741no—
196D4C4⋊#386612yes—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—371no—
200C2×C4—371no—
201C2×C4—371no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—371no—
206C2×C4—742no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—1482no—
210C2×C4—1482no—
211C2×C4—1482no—
212C2×C4—1482no—
213C2×C4—1482no—
214C2×C4—1482no—
215C2×C4—1482no—
216C2×C4C22⋊#386611yescharacteristic
217C2×C4C22⋊#386611yescharacteristic
218C2×C4C22×#386611yescharacteristic
219C8—1482no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—371no—
224C22—371no—
225C22—372no—
226C22—372no—
227C22—742no—
228C22—1484no—
229C22—1484no—
230C22—1481no—
231C22—1481no—
232C22C2×C22⋊#386611yescharacteristic
233C4—21no—
234C4—21no—
235C4—41no—
236C4—371no—
237C4—371no—
238C4—2962no—
239C4—741no—
240C4—741no—
241C4—1481no—
242C4C2×C4⋊#386611yescharacteristic
243C4#1192461511yescharacteristic
244C2—42no—
245C2—372no—
246C2—372no—
247C2—1482no—
248C2#1455847511yescharacteristic
249C2#1455852311yescharacteristic
250C2#1455852511yescharacteristic
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#1804
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. #14558477C2semidirect
4. #14558406C2semidirect
15. C4×D148C4semidirect
16. D4×Dic37C4semidirect
17. #11924498C4semidirect
23. C4×D4×C37C4semidirect
131. C37#1804semidirect
140. C4×D4#3866semidirect

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
#145584772
#145584062
C4×D4×D372
#180437