Finite Group Databasebeta

← #17994795

Subgroups — #17994795

Order 4736.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11924469C211yesmaximal, characteristic, complemented
2C2×#11924467C211yesmaximal, characteristic, complemented
3C2×C22⋊#64436C211yesmaximal, characteristic
4#14557393C211yesmaximal, characteristic
5#14557295C211yesmaximal, characteristic, complemented
6#14557295C211yesmaximal, characteristic, complemented
7C2×#117×C37C211yesmaximal, characteristic
8C22×#64436C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10C2×C4⋊Dic37C2211yescharacteristic
11C2×C4⋊Dic37C2211yescharacteristic
12C2×C22⋊Dic37—21no—
13#11924469—22no—
14#11924467—22no—
15C22⋊#64436C414yescomplemented
16#11924443—21no—
17C23×C4×C37C2211yescharacteristic
18#117×C37—22no—
19#117×C37—22no—
20C2×C4⋊C4×C37C2211yescharacteristic
21C2×C4⋊C4×C37C2211yescharacteristic
22C2×C22⋊C4×C37—21no—
23C2×C42×C37—21no—
24C24×C37D411yescharacteristic
25C22×C4×C37—21no—
26C22×C4×C37—21no—
27C22×C4×C37—21no—
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C22×C4×C37C2×C412yes—
32C22×C4×C37D411yescharacteristic
33C22×C4×C37Q812yes—
34C22×C4×C37C2311yescharacteristic
35C22×Dic37—21no—
36C22×Dic37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D412yes—
40C4⋊C4×C37D412yes—
41C22⋊C4×C37—24no—
42C42×C37—24no—
43C22⋊Dic37—42no—
44C4⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C2×#64436—21no—
51C2×#64436—21no—
52C2×#64436C2×C412yes—
53C2×#64436C2×C412yes—
54C23×C37—21no—
55C23×C37—21no—
56C23×C37—21no—
57C23×C37—21no—
58C23×C37—21no—
59C23×C37—21no—
60C23×C37C4⋊C412yes—
61C23×C37C2×D411yescharacteristic
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37—22no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—41no—
74C2×C4×C37C4⋊C412yes—
75C2×C4×C37C22×C411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×Q811yescharacteristic
79C2×C4×C37#4111yescharacteristic
80C2×C4×C37#4111yescharacteristic
81C2×Dic37—41no—
82C2×Dic37—41no—
83C2×Dic37—41no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37—41no—
87#64436—22no—
88#64436—22no—
89C22×C37—22no—
90C22×C37—22no—
91C22×C37—22no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37—41no—
95C22×C37—41no—
96C22×C37C2×C4⋊C411yescharacteristic
97C22×C37#12011yescharacteristic
98C22×C37#12311yescharacteristic
99C22×C37#13511yescharacteristic
100C22×C37#13511yescharacteristic
101C22×C37AGL(1,ℤ/8)11yescharacteristic
102C22×C37#13711yescharacteristic
103C4×C37—22no—
104C4×C37—42no—
105C4×C37—42no—
106C4×C37C4×D411yescharacteristic
107C4×C37C4×D411yescharacteristic
108C4×C37C22⋊Q811yescharacteristic
109C4×C37C22⋊Q811yescharacteristic
110Dic37—81no—
111Dic37—81no—
112#1854—371nomaximal, Sylow
113C2×C37—42no—
114C2×C37#38511yescharacteristic
115C2×C37#42711yescharacteristic
116C2×C37#42811yescharacteristic
117C2×C37#44911yescharacteristic
118C2×C37#45211yescharacteristic
119C2×C37#48211yescharacteristic
120C2×C37#48511yescharacteristic
121C2×#117D3711yescharacteristic
122C2×#107—371no—
123C2×#106—371no—
124C2×C22⋊C8—371no—
125#380—371no—
126#340—371no—
127#340—371no—
128C37#185411yescharacteristic, complemented, Sylow
129C23×C4C2×D3711yescharacteristic
130C22×C8—371no—
131C22×C8—371no—
132#117—22no—
133#117—22no—
134C2×C4⋊C4—371no—
135C2×C4⋊C4—371no—
136C2×C4⋊C4C2×D3711yescharacteristic
137C2×C4⋊C4C2×D3711yescharacteristic
138C2×C22⋊C4—21no—
139C2×C22⋊C4—741no—
140C2×C42—21no—
141#107—742no—
142#106—742no—
143C22⋊C8—374no—
144#95—741no—
145C24C22⋊D3711yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—741no—
153C22×C4—741no—
154C22×C4Dic7412yes—
155C22×C4C4×D3712yes—
156C22×C4C22⋊D3711yescharacteristic
157C22×C4C22×D3711yescharacteristic
158C2×C8—372no—
159C2×C8—372no—
160C2×C8—741no—
161C2×C8—741no—
162C2×C8—741no—
163C2×C8—741no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—741no—
167C4⋊C4—741no—
168C4⋊C4—741no—
169C4⋊C4—741no—
170C4⋊C4C22⋊D3712yes—
171C4⋊C4C22⋊D3712yes—
172C22⋊C4—24no—
173C22⋊C4—1482no—
174C42—24no—
175C23—21no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23#1059693612yes—
182C23C2×C22⋊D3711yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4—1481no—
200C2×C4—1481no—
201C2×C4#1059693612yes—
202C2×C4C2×Dic7411yescharacteristic
203C2×C4C2×C4×D3711yescharacteristic
204C2×C4#1059696211yescharacteristic
205C2×C4#1059696211yescharacteristic
206C2×C4C2×C22⋊D3711yescharacteristic
207C2×C4C2×C22⋊D3711yescharacteristic
208C8—742no—
209C8—742no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×#1059693611yescharacteristic
218C22#1192450511yescharacteristic
219C22#1192451911yescharacteristic
220C22#1192455611yescharacteristic
221C22#1192455611yescharacteristic
222C22#1192456111yescharacteristic
223C22#1192456611yescharacteristic
224C4—22no—
225C4—42no—
226C4—42no—
227C4—2961no—
228C4—2961no—
229C4C4×C22⋊D3711yescharacteristic
230C4C4×C22⋊D3711yescharacteristic
231C4#1192451511yescharacteristic
232C4#1192451511yescharacteristic
233C2—42no—
234C2#1455740611yescharacteristic
235C2#1455756911yescharacteristic
236C2#1455757611yescharacteristic
237C2#1455767811yescharacteristic
238C2#1455769511yescharacteristic
239C2#1455785711yescharacteristic
240C2#1455787411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#117×C37C2
socleC23×C37C2×D4
prime radicalC24×C37D4
cosocleC22×C4×C37C23
hypercenterC2×#117D37
hypocenterC37#1854
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#11924469C2semidirect
2. C2×#11924467C2semidirect
5. #14557295C2semidirect
6. #14557295C2semidirect
15. C22⋊#64436C4semidirect
128. C37#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#119244692
C2×#119244672
C2×C22⋊#644362
#145573932
#145572952
C2×#117×C372
#185437