Finite Group Databasebeta

← #17994792

Subgroups — #17994792

Order 4736.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#11924494C211yesmaximal, characteristic
2C2×#11924467C211yesmaximal, characteristic, complemented
3C2×#11924448C211yesmaximal, characteristic
4#14557390C211yesmaximal, characteristic
5#14557296C211yesmaximal, characteristic, complemented
6#14557295C211yesmaximal, characteristic, complemented
7C2×#107×C37C211yesmaximal, characteristic, complemented
8C22×C4×D37C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924494—22no—
11#11924494—22no—
12C2×C4⋊Dic37C2211yescharacteristic
13C2×C4⋊Dic37C2211yescharacteristic
14C2×#10596938—21no—
15C2×#10596938—21no—
16C2×C4×Dic37—21no—
17#11924467—22no—
18#11924448C414yescomplemented
19#11924443—21no—
20C22×C8×C37C2211yescharacteristic
21C2×C4⋊C4×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23#107×C37—22no—
24C23×D37D411yescharacteristic
25C22×C4×C37—21no—
26C22×C4×C37—21no—
27C22×C4×C37C2311yescharacteristic
28C22×Dic37—21no—
29C22×Dic37—21no—
30C22×Dic37D411yescharacteristic
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37C2×C412yes—
36C2×C4×D37Q812yes—
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C2×C8×C37C2×C412yes—
40C4⋊C4×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37D412yes—
44#10596938—24no—
45#10596938—42no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37—21no—
49C4⋊Dic37D412yes—
50C4×Dic37—24no—
51C2×#64436—21no—
52C2×#64436—21no—
53C2×#64436C2×C412yes—
54C23×C37C2×D411yescharacteristic
55C22×D37—21no—
56C22×D37—21no—
57C22×D37—21no—
58C22×D37—21no—
59C22×D37—21no—
60C22×D37—21no—
61C22×D37C4⋊C412yes—
62C2×C4×C37—22no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×Q811yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37C4⋊C412yes—
83C4×D37—22no—
84C4×D37—22no—
85C4×D37—22no—
86C4×D37—22no—
87C8×C37—22no—
88#64436—22no—
89C22×C37C2×C4⋊C411yescharacteristic
90C22×C37#12011yescharacteristic
91C22×C37#12311yescharacteristic
92C22×C37#13511yescharacteristic
93C22×C37#13511yescharacteristic
94C22×C37AGL(1,ℤ/8)11yescharacteristic
95C22×C37#13711yescharacteristic
96C2×D37—22no—
97C2×D37—22no—
98C2×D37—22no—
99C2×D37—41no—
100C2×D37—41no—
101C2×D37—41no—
102C2×D37—41no—
103C4×C37—42no—
104C4×C37—81no—
105C4×C37C4×D411yescharacteristic
106C4×C37C4×D411yescharacteristic
107C4×C37C22⋊Q811yescharacteristic
108C4×C37C22⋊Q811yescharacteristic
109Dic37—22no—
110Dic37—42no—
111Dic37—81no—
112#1854—371nomaximal, Sylow
113C2×C37#38511yescharacteristic
114C2×C37#42711yescharacteristic
115C2×C37#42811yescharacteristic
116C2×C37#44911yescharacteristic
117C2×C37#45211yescharacteristic
118C2×C37#48211yescharacteristic
119C2×C37#48511yescharacteristic
120D37—42no—
121C2×#117—371no—
122C2×#107D3711yescharacteristic, complemented
123C2×#106—371no—
124C2×C22⋊C8—371no—
125#380—371no—
126#340—371no—
127#340—371no—
128C37#185411yescharacteristic, complemented, Sylow
129C23×C4—371no—
130C22×C8—371no—
131C22×C8C2×D3711yescharacteristic
132#117—742no—
133#117—742no—
134C2×C4⋊C4—371no—
135C2×C4⋊C4—371no—
136C2×C4⋊C4C2×D3711yescharacteristic
137C2×C4⋊C4C2×D3711yescharacteristic
138C2×C22⋊C4—741no—
139C2×C22⋊C4—741no—
140C2×C42—741no—
141#107—22no—
142#106—742no—
143C22⋊C8—374no—
144#95—741no—
145C24—371no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—371no—
149C22×C4—372no—
150C22×C4—372no—
151C22×C4—741no—
152C22×C4—741no—
153C22×C4—741no—
154C22×C4—741no—
155C22×C4—741no—
156C22×C4—741no—
157C22×C4C22×D3711yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—372no—
161C2×C8—741no—
162C2×C8—741no—
163C2×C8C4×D3712yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—372no—
168C4⋊C4—741no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C4⋊C4C22⋊D3712yes—
172C22⋊C4—744no—
173C22⋊C4—1482no—
174C42—744no—
175C23—372no—
176C23—741no—
177C23—741no—
178C23—741no—
179C23—741no—
180C23—741no—
181C23—741no—
182C23D4×D3711yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—372no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—742no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4—1481no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4C2×C4×D3711yescharacteristic
203C2×C4#1059696211yescharacteristic
204C2×C4D4×D3711yescharacteristic
205C2×C4Q8×D3711yescharacteristic
206C2×C4#1059696611yescharacteristic
207C2×C4C2×C22⋊D3711yescharacteristic
208C8—22no—
209C8—742no—
210C22—742no—
211C22—742no—
212C22—742no—
213C22—1481no—
214C22—1481no—
215C22—1481no—
216C22—1481no—
217C22C4⋊C4×D3711yescharacteristic
218C22#1192450411yescharacteristic
219C22#1192452111yescharacteristic
220C22#1192455511yescharacteristic
221C22#1192455911yescharacteristic
222C22#1192456011yescharacteristic
223C22#1192456811yescharacteristic
224C4—42no—
225C4—81no—
226C4—2961no—
227C4—742no—
228C4—1482no—
229C4C4×C22⋊D3711yescharacteristic
230C4#1192449811yescharacteristic
231C4#1192451211yescharacteristic
232C4#1192451411yescharacteristic
233C2—1482no—
234C2#1455740411yescharacteristic
235C2#1455757011yescharacteristic
236C2#1455757411yescharacteristic
237C2#1455767511yescharacteristic
238C2#1455769411yescharacteristic
239C2#1455786011yescharacteristic
240C2#1455787611yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#107×C37C2
socleC23×C37C2×D4
prime radicalC23×D37D4
cosocleC22×C4×C37C23
hypercenterC2×#107D37
hypocenterC37#1854
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#11924467C2semidirect
5. #14557296C2semidirect
6. #14557295C2semidirect
7. C2×#107×C37C2semidirect
18. #11924448C4semidirect
122. C2×#107D37semidirect
128. C37#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#119244942
C2×#119244672
C2×#119244482
#145573902
#145572962
#145572952
C2×#107×C372
#185437