Finite Group Databasebeta

← #18010582

Subgroups — #18010582

Order 4736.

360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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
2C2×#11924599C212yesmaximal, complemented
3D37⋊(C22⋊C8)C211yesmaximal, characteristic
4#14558406C212yesmaximal, complemented
5C22⋊Q8×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7#11924615—24no—
8C2×C4⋊#3866C2212yes—
9C2×C22⋊#3866—21no—
10C2×C4×#3866—21no—
11#11924599—24no—
12#11924593—21no—
13C22⋊#64438—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—24no—
43C2×#64438—22no—
44C4⋊#3866—22no—
45C4⋊#3866D414yes—
46C4×#3866—24no—
47D37⋊C8—22no—
48D37⋊C8—22no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37C2×C411yescharacteristic
51C22⋊C4×C37—21no—
52C22⋊Dic37—21no—
53#10596938—21no—
54#10596938—21no—
55C4⋊Dic37—21no—
56C4⋊Dic37C2×C411yescharacteristic
57#10596936—21no—
58#10596936—21no—
59#10596936—21no—
60C23×C37C22⋊C411yescharacteristic
61C22×D37—21no—
62C22×D37—21no—
63C22×D37—22no—
64C22×D37—22no—
65C22×D37C22⋊C411yescharacteristic
66C22×D37C2×D411yescharacteristic
67C2×#3866—24no—
68C2×#3866—42no—
69C2×#3866—42no—
70Q8×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37C22⋊C411yescharacteristic
75C2×C4×C37C22×C411yescharacteristic
76C2×Dic37—22no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C2×D411yescharacteristic
81C4×D37—21no—
82C4×D37—21no—
83C4×D37—22no—
84C4×D37—22no—
85C4×D37—41no—
86C4×D37—41no—
87C4×D37—42no—
88C4×D37C2×D412yes—
89C4×D37#4112yes—
90Dic74—22no—
91Dic74—42no—
92#64438—42no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37C2×C22⋊C411yescharacteristic
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—42no—
101C2×D37—42no—
102C2×D37#12011yescharacteristic
103C2×D37#12311yescharacteristic
104C2×D37#13512yes—
105C2×D37#13712yes—
106#3866—44no—
107C4×C37—21no—
108C4×C37—41no—
109C4×C37—41no—
110C4×C37C4×D412yes—
111Dic37—21no—
112Dic37—41no—
113Dic37—41no—
114Dic37#12112yes—
115#1873—371nomaximal, Sylow
116C2×C37—41no—
117C2×C37#38611yescharacteristic
118C2×C37#41611yescharacteristic
119C2×C37#41911yescharacteristic
120D37—41no—
121D37#45212yes—
122D37#48512yes—
123C2×C22⋊Q8—371no—
124C2×#117—371no—
125C2×#103—372no—
126C2×C22⋊C8—371no—
127#340—372no—
128C37#187311yescharacteristic, complemented, Sylow
129C22×Q8—371no—
130C23×C4—371no—
131C22×C8—372no—
132C22⋊Q8—371no—
133C22⋊Q8—371no—
134C22⋊Q8—371no—
135C22⋊Q8—741no—
136C22⋊Q8—741no—
137C22⋊Q8#386611yescharacteristic, complemented
138#117—744no—
139C2×C4⋊C4—372no—
140C2×C4⋊C4—371no—
141C2×C4⋊C4—741no—
142C2×C22⋊C4—741no—
143C2×C22⋊C4—741no—
144C2×C42—741no—
145#103—744no—
146C22⋊C8—741no—
147C22⋊C8—741no—
148C24—371no—
149C2×Q8—371no—
150C2×Q8—741no—
151C2×Q8—742no—
152C2×Q8—742no—
153C2×Q8C2×#386611yescharacteristic
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—742no—
160C22×C4—742no—
161C22×C4—741no—
162C22×C4—741no—
163C22×C4—742no—
164C22×C4C2×#386611yescharacteristic
165C2×C8—742no—
166C2×C8—742no—
167C2×C8—742no—
168C4⋊C4—21no—
169C4⋊C4—374no—
170C4⋊C4—371no—
171C4⋊C4—741no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C4⋊C4—742no—
175C4⋊C4—741no—
176C4⋊C4C2×#386611yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—744no—
181C22⋊C4—741no—
182C42—744no—
183C23—371no—
184C23—371no—
185C23—741no—
186C23—741no—
187C23—742no—
188C23—742no—
189C23C22⋊#386611yescharacteristic
190Q8—22no—
191Q8—742no—
192Q8—1482no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—371no—
197C2×C4—372no—
198C2×C4—372no—
199C2×C4—371no—
200C2×C4—742no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—742no—
204C2×C4—742no—
205C2×C4—744no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—1481no—
209C2×C4—1481no—
210C2×C4—1482no—
211C2×C4—1482no—
212C2×C4—1482no—
213C2×C4C22⋊#386611yescharacteristic
214C2×C4C22×#386611yescharacteristic
215C8—1482no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—371no—
220C22—371no—
221C22—372no—
222C22—372no—
223C22—741no—
224C22—741no—
225C22—741no—
226C22—1482no—
227C22—1482no—
228C22C2×C22⋊#386611yescharacteristic
229C4—21no—
230C4—41no—
231C4—41no—
232C4—372no—
233C4—741no—
234C4—1484no—
235C4—1481no—
236C4—1481no—
237C4D4×#386612yes—
238C2—41no—
239C2—372no—
240C2—372no—
241C2—1481no—
242C2#1455848111yescharacteristic
243C2#1455852311yescharacteristic
244C2#1455852611yescharacteristic
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#1873
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
128. C37#1873semidirect
137. C22⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246152
C2×#119245992
D37⋊(C22⋊C8)2
#145584062
C22⋊Q8×D372
#187337