Finite Group Databasebeta

← #17994628

Subgroups — #17994628

Order 4736.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10596929C211yesmaximal, characteristic
2C2×#11924469C211yesmaximal, characteristic, complemented
3C2×#11924467C211yesmaximal, characteristic, complemented
4#14557390C211yesmaximal, characteristic
5#14557390C211yesmaximal, characteristic
6#14557296C211yesmaximal, characteristic, complemented
7C37×#340C211yesmaximal, characteristic, complemented
8C22×C4×D37C2211yescharacteristic
9C2×#10596929—22no—
10C2×#10596929—22no—
11C2×#10596929C414yescomplemented
12C22×#64436C2211yescharacteristic
13C2×C4⋊Dic37C2211yescharacteristic
14C2×C4⋊Dic37C2211yescharacteristic
15C2×#10596938—21no—
16C2×#10596938—21no—
17#11924469—22no—
18#11924467—22no—
19#11924443—21no—
20#11924443—21no—
21C22×C8×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
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×C37—21no—
44#10596938—42no—
45#10596938—42no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37—21no—
49C4⋊Dic37—21no—
50C2×#64436C2×C412yes—
51C2×#64436D412yes—
52C2×#64436D412yes—
53#10596929—28no—
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—41no—
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—41no—
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#64436C22⋊C414yescomplemented
89C22×C37C2×C4⋊C411yescharacteristic
90C22×C37#12111yescharacteristic
91C22×C37#12111yescharacteristic
92C22×C37AGL(1,ℤ/8)11yescharacteristic
93C22×C37AGL(1,ℤ/8)11yescharacteristic
94C22×C37#13711yescharacteristic
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—81no—
104C4×C37—81no—
105C4×C37C2×C22⋊C411yescharacteristic
106C4×C37#11711yescharacteristic
107C4×C37C22⋊Q811yescharacteristic
108C4×C37C22⋊Q811yescharacteristic
109Dic37—22no—
110Dic37—81no—
111Dic37—81no—
112#1809—371nomaximal, Sylow
113C2×C37#38011yescharacteristic
114C2×C37#42811yescharacteristic
115C2×C37#42811yescharacteristic
116C2×C37#46811yescharacteristic
117C2×C37#46811yescharacteristic
118C2×C37#46911yescharacteristic
119C2×C37#47011yescharacteristic
120D37—42no—
121C22×M16—371no—
122C2×#107—371no—
123C2×#106—371no—
124#380—371no—
125#380—371no—
126#340—371no—
127#340D3711yescharacteristic, complemented
128C37#180911yescharacteristic, complemented, Sylow
129C23×C4—371no—
130C2×M16—374no—
131C2×M16—742no—
132C2×M16—742no—
133C22×C8—371no—
134C22×C8C2×D3711yescharacteristic
135C2×C4⋊C4—371no—
136C2×C4⋊C4—371no—
137C2×C4⋊C4C2×D3711yescharacteristic
138C2×C4⋊C4C2×D3711yescharacteristic
139C2×C22⋊C4—741no—
140C2×C22⋊C4—741no—
141#107—742no—
142#106—742no—
143#95—741no—
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
158M16—748no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—372no—
162C2×C8—372no—
163C2×C8—372no—
164C2×C8C4×D3712yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C4⋊C4—741no—
172C4⋊C4—741no—
173C22⋊C4—1482no—
174C22⋊C4—1482no—
175C23—372no—
176C23—741no—
177C23—741no—
178C23—741no—
179C23—741no—
180C23—741no—
181C23—741no—
182C23D4×D3711yescharacteristic
183C2×C4—41no—
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—1481no—
197C2×C4—1481no—
198C2×C4—1481no—
199C2×C4—1481no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4C2×C4×D3711yescharacteristic
203C2×C4#1059696211yescharacteristic
204C2×C4#1059696211yescharacteristic
205C2×C4D4×D3711yescharacteristic
206C2×C4D4×D3711yescharacteristic
207C2×C4Q8×D3711yescharacteristic
208C8—22no—
209C8—374no—
210C22—742no—
211C22—742no—
212C22—742no—
213C22—1481no—
214C22—1481no—
215C22—1481no—
216C22—1481no—
217C22C4⋊C4×D3711yescharacteristic
218C22#1192450911yescharacteristic
219C22#1192450911yescharacteristic
220C22#1192456011yescharacteristic
221C22#1192456311yescharacteristic
222C22#1192456511yescharacteristic
223C22#1192456811yescharacteristic
224C4—81no—
225C4—81no—
226C4—2961no—
227C4—2961no—
228C4—742no—
229C4C22⋊C4×D3711yescharacteristic
230C4#1192449311yescharacteristic
231C4#1192451411yescharacteristic
232C4#1192451411yescharacteristic
233C2—1482no—
234C2#1455739211yescharacteristic
235C2#1455757211yescharacteristic
236C2#1455757411yescharacteristic
237C2#1455777811yescharacteristic
238C2#1455778211yescharacteristic
239C2#1455778511yescharacteristic
240C2#1455779011yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#340C2
socleC23×C37C2×D4
prime radicalC23×D37D4
cosocleC22×C4×C37C23
hypercenter#340D37
hypocenterC37#1809
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#11924469C2semidirect
3. C2×#11924467C2semidirect
6. #14557296C2semidirect
7. C37×#340C2semidirect
11. C2×#10596929C4semidirect
88. #64436C22⋊C4semidirect
127. #340D37semidirect
128. C37#1809semidirect

Maximal subgroups

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

subgroupindex
C22×#105969292
C2×#119244692
C2×#119244672
#145573902
#145572962
C37×#3402
#180937