Finite Group Databasebeta

← #18010609

Subgroups — #18010609

Order 4736.

380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×D37⋊C8C211yesmaximal, characteristic
2C2×#11924599C212yesmaximal, complemented
3#14558475C211yesmaximal, characteristic
4#14558406C212yesmaximal, complemented
5C22⋊Q8×D37C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7C2×D37⋊C8—24no—
8C2×D37⋊C8C2212yes—
9C22×#64438—21no—
10C2×C4⋊#3866C2212yes—
11C2×C22⋊#3866—21no—
12#11924599—24no—
13(C2×#3866)⋊C4—21no—
14C2×Q8×D37C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16#11924516C411yescharacteristic, complemented
17#11924515C411yescharacteristic, complemented
18#11924514—21no—
19#11924513—21no—
20#11924512C411yescharacteristic, complemented
21C4⋊C4×D37—21no—
22C4⋊C4×D37C2211yescharacteristic
23C22⋊C4×D37—21no—
24C22⋊Q8×C37C411yescharacteristic, complemented
25C23×D37D411yescharacteristic
26C22×#3866—22no—
27C2×Q8×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C22×Dic37D411yescharacteristic
30Q8×D37—22no—
31Q8×D37—22no—
32C2×C4×D37—22no—
33C2×C4×D37—22no—
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37C2×C411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×C4×D37C2311yescharacteristic
40C2×Dic74—21no—
41C2×Dic74C2×C411yescharacteristic
42C22⋊#3866—42no—
43C2×#64438—24no—
44C2×#64438—22no—
45C4⋊#3866—22no—
46C4⋊#3866—22no—
47D37⋊C8—24no—
48D37⋊C8—22no—
49D37⋊C8D414yes—
50C4⋊C4×C37—21no—
51C4⋊C4×C37C2×C411yescharacteristic
52C22⋊C4×C37—21no—
53C22⋊Dic37—21no—
54#10596938—21no—
55#10596938—21no—
56C4⋊Dic37—21no—
57C4⋊Dic37C2×C411yescharacteristic
58#10596936—21no—
59#10596936—21no—
60#10596936—21no—
61C23×C37C22⋊C411yescharacteristic
62C22×D37—22no—
63C22×D37—22no—
64C22×D37C22⋊C411yescharacteristic
65C22×D37SD1612yes—
66C22×D37Q1612yes—
67C22×D37C2×D411yescharacteristic
68C2×#3866—42no—
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
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C2×D411yescharacteristic
83C4×D37—22no—
84C4×D37—22no—
85C4×D37—21no—
86C4×D37—21no—
87C4×D37—42no—
88C4×D37—42no—
89C4×D37C2×D412yes—
90C4×D37#4112yes—
91Dic74—22no—
92Dic74—41no—
93Dic74—41no—
94#64438—24no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37#10312yescomplemented
98C22×C37C2×C22⋊C411yescharacteristic
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—24no—
102C2×D37—24no—
103C2×D37#10312yescomplemented
104C2×D37#12112yes—
105C2×D37C2×SD1611yescharacteristic
106C2×D37C2×Q1611yescharacteristic
107C2×D37#13512yes—
108#3866—82no—
109C4×C37—21no—
110C4×C37—41no—
111C4×C37—41no—
112C4×C37C4×D412yes—
113Dic37—21no—
114Dic37—41no—
115Dic37—41no—
116Dic37#12011yescharacteristic
117Dic37#12311yescharacteristic
118#1892—371nomaximal, Sylow
119C2×C37—22no—
120C2×C37#38611yescharacteristic
121C2×C37C2×#10311yescharacteristic
122C2×C37#41611yescharacteristic
123D37—22no—
124D37#46512yes—
125D37#46712yes—
126C23×C8—371no—
127C2×C22⋊Q8—371no—
128C2×#103—372no—
129#380—371no—
130#340—372no—
131C37#189211yescharacteristic, complemented, Sylow
132C22×Q8—371no—
133C23×C4—371no—
134C22×C8—372no—
135C22×C8—744no—
136C22×C8—741no—
137C22×C8—741no—
138C22⋊Q8—371no—
139C22⋊Q8—371no—
140C22⋊Q8—371no—
141C22⋊Q8—741no—
142C22⋊Q8—741no—
143C22⋊Q8#386611yescharacteristic, complemented
144C2×C4⋊C4—371no—
145C2×C4⋊C4—372no—
146C2×C4⋊C4—741no—
147C2×C22⋊C4—741no—
148C2×C22⋊C4—741no—
149#103—744no—
150#95—741no—
151C24—371no—
152C2×Q8—371no—
153C2×Q8—741no—
154C2×Q8—742no—
155C2×Q8—742no—
156C2×Q8C2×#386611yescharacteristic
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—742no—
163C22×C4—742no—
164C22×C4—741no—
165C22×C4—741no—
166C22×C4—742no—
167C22×C4C2×#386611yescharacteristic
168C2×C8—374no—
169C2×C8—742no—
170C2×C8—742no—
171C2×C8—744no—
172C2×C8—744no—
173C4⋊C4—21no—
174C4⋊C4—371no—
175C4⋊C4—741no—
176C4⋊C4—741no—
177C4⋊C4—741no—
178C4⋊C4—742no—
179C4⋊C4—742no—
180C4⋊C4—741no—
181C4⋊C4C2×#386611yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—741no—
184C22⋊C4—741no—
185C22⋊C4—741no—
186C22⋊C4—1482no—
187C23—371no—
188C23—372no—
189C23—372no—
190C23—371no—
191C23—742no—
192C23—742no—
193C23C22⋊#386611yescharacteristic
194Q8—22no—
195Q8—742no—
196Q8—1481no—
197Q8—1481no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—371no—
202C2×C4—372no—
203C2×C4—372no—
204C2×C4—371no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—742no—
211C2×C4—741no—
212C2×C4—741no—
213C2×C4—1482no—
214C2×C4—1482no—
215C2×C4—1482no—
216C2×C4—1482no—
217C2×C4—1482no—
218C2×C4C22⋊#386611yescharacteristic
219C2×C4C22×#386611yescharacteristic
220C8—744no—
221C22—21no—
222C22—21no—
223C22—372no—
224C22—371no—
225C22—371no—
226C22—372no—
227C22—372no—
228C22—744no—
229C22—744no—
230C22—741no—
231C22—741no—
232C22#1192459912yescomplemented
233C22C2×C22⋊#386611yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—371no—
238C4—371no—
239C4—2962no—
240C4—741no—
241C4—1481no—
242C4—1481no—
243C4D4×#386612yes—
244C2—22no—
245C2—372no—
246C2—372no—
247C2—742no—
248C2#1455848111yescharacteristic
249C2C2×#1192459911yescharacteristic
250C2#1455852311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC22⋊Q8#3866
hypocenterC37#1892
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
2. C2×#11924599C2semidirect
4. #14558406C2semidirect
16. #11924516C4semidirect
17. #11924515C4semidirect
20. #11924512C4semidirect
24. C22⋊Q8×C37C4semidirect
97. C22×C37#103semidirect
103. C2×D37#103semidirect
131. C37#1892semidirect
143. C22⋊Q8#3866semidirect
232. C22#11924599semidirect

Maximal subgroups

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

subgroupindex
C22×D37⋊C82
C2×#119245992
#145584752
#145584062
C22⋊Q8×D372
#189237