Finite Group Databasebeta

← #17994905

Subgroups — #17994905

Order 4736.

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

normal subgroups only

This group has 360 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×#11924512C211yesmaximal, characteristic
2C2×#11924494C211yesmaximal, characteristic
3C2×#11924460C211yesmaximal, characteristic, complemented
4C2×#11924448C211yesmaximal, characteristic
5#14557296C211yesmaximal, characteristic, complemented
6#14557295C211yesmaximal, characteristic, complemented
7C2×#103×C37C211yesmaximal, characteristic, complemented
8C22×C4×D37C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924512—22no—
11#11924512C414yescomplemented
12#11924494—22no—
13#11924494—22no—
14C2×C4⋊Dic37C2211yescharacteristic
15C2×C4⋊Dic37C2211yescharacteristic
16C2×#10596936—21no—
17C2×#10596938—21no—
18C2×#10596938—21no—
19C2×C4×Dic37—21no—
20#11924460—22no—
21#11924448—22no—
22C22×Q8×C37C2211yescharacteristic
23C22×C8×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25#103×C37—22no—
26C23×D37D411yescharacteristic
27C2×Q8×C37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37C2×C412yes—
33C22×C4×C37—21no—
34C22×C4×C37—21no—
35C22×C4×C37C2311yescharacteristic
36C22×Dic37—21no—
37C22×Dic37—21no—
38C22×Dic37D411yescharacteristic
39C2×C4×D37—21no—
40C2×C4×D37—21no—
41C2×C4×D37—21no—
42C2×C4×D37—21no—
43C2×C4×D37C2×C412yes—
44C2×C4×D37D412yes—
45C2×C8×C37—21no—
46C2×C8×C37—21no—
47C2×C8×C37—21no—
48C4⋊C4×C37—21no—
49C4⋊C4×C37D412yes—
50#10596938—24no—
51#10596938—24no—
52C4⋊Dic37—21no—
53C4⋊Dic37—21no—
54C4⋊Dic37C2×C412yes—
55C4⋊Dic37D412yes—
56#10596936—24no—
57C4×Dic37—24no—
58C2×#64436—21no—
59C2×#64436—21no—
60C2×#64436—21no—
61C23×C37C2×D411yescharacteristic
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—21no—
66C22×D37—21no—
67C22×D37—21no—
68C22×D37C22⋊C412yes—
69Q8×C37—22no—
70Q8×C37—22no—
71Q8×C37—41no—
72Q8×C37—41no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—41no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37C22×C411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—41no—
90C2×Dic37—41no—
91C2×Dic37—41no—
92C2×Dic37—41no—
93C2×Dic37C22⋊C412yes—
94C4×D37—22no—
95C4×D37—22no—
96C4×D37—22no—
97C4×D37—22no—
98C8×C37—41no—
99#64436—41no—
100C22×C37C2×C22⋊C411yescharacteristic
101C22×C37#12011yescharacteristic
102C22×C37#12311yescharacteristic
103C22×C37#13511yescharacteristic
104C22×C37#13511yescharacteristic
105C22×C37#13711yescharacteristic
106C22×C37#13711yescharacteristic
107C2×D37—22no—
108C2×D37—22no—
109C2×D37—22no—
110C2×D37—41no—
111C2×D37—41no—
112C2×D37—41no—
113C2×D37—41no—
114C4×C37—42no—
115C4×C37—42no—
116C4×C37C4×D411yescharacteristic
117C4×C37C4×D411yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12111yescharacteristic
120Dic37—22no—
121Dic37—42no—
122Dic37—42no—
123#1873—371nomaximal, Sylow
124C2×C37#38611yescharacteristic
125C2×C37#41611yescharacteristic
126C2×C37#41911yescharacteristic
127C2×C37#45211yescharacteristic
128C2×C37#45211yescharacteristic
129C2×C37#48511yescharacteristic
130C2×C37#48511yescharacteristic
131D37—42no—
132C2×C22⋊Q8—371no—
133C2×#117—371no—
134C2×#103—371no—
135C2×#103D3711yescharacteristic, complemented
136C2×C22⋊C8—371no—
137#340—371no—
138#340—371no—
139C37#187311yescharacteristic, complemented, Sylow
140C22×Q8C2×D3711yescharacteristic
141C23×C4—371no—
142C22×C8—371no—
143C22×C8C2×D3711yescharacteristic
144C22⋊Q8—374no—
145C22⋊Q8—742no—
146#117—742no—
147#117—742no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4—371no—
150C2×C4⋊C4—741no—
151C2×C4⋊C4C2×D3711yescharacteristic
152C2×C22⋊C4—741no—
153C2×C22⋊C4—741no—
154C2×C42—741no—
155#103—22no—
156#103—742no—
157C22⋊C8—742no—
158C24—371no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8C4×D3712yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—371no—
168C22×C4—372no—
169C22×C4—372no—
170C22×C4—741no—
171C22×C4—741no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4—741no—
176C22×C4C22×D3711yescharacteristic
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—741no—
181C2×C8—741no—
182C2×C8—741no—
183C4⋊C4—21no—
184C4⋊C4—372no—
185C4⋊C4—372no—
186C4⋊C4—744no—
187C4⋊C4—741no—
188C4⋊C4—741no—
189C4⋊C4C22⋊D3712yes—
190C22⋊C4—744no—
191C22⋊C4—744no—
192C42—744no—
193C23—372no—
194C23—741no—
195C23—741no—
196C23—741no—
197C23—741no—
198C23—741no—
199C23—741no—
200C23D4×D3711yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—372no—
212C2×C4—741no—
213C2×C4—741no—
214C2×C4—742no—
215C2×C4—742no—
216C2×C4—742no—
217C2×C4—742no—
218C2×C4—742no—
219C2×C4—742no—
220C2×C4—1481no—
221C2×C4—1481no—
222C2×C4—1481no—
223C2×C4—1481no—
224C2×C4C2×C4×D3711yescharacteristic
225C2×C4#1059696211yescharacteristic
226C2×C4D4×D3711yescharacteristic
227C2×C4D4×D3711yescharacteristic
228C2×C4#1059696411yescharacteristic
229C2×C4C2×C22⋊D3711yescharacteristic
230C8—41no—
231C8—1481no—
232C22—742no—
233C22—742no—
234C22—742no—
235C22—1481no—
236C22—1481no—
237C22—1481no—
238C22—1481no—
239C22C22⋊C4×D3711yescharacteristic
240C22#1192450411yescharacteristic
241C22#1192451811yescharacteristic
242C22#1192455711yescharacteristic
243C22#1192455911yescharacteristic
244C22#1192456511yescharacteristic
245C22#1192456811yescharacteristic
246C4—42no—
247C4—42no—
248C4—742no—
249C4—1482no—
250C4—1482no—
251C4#1192449611yescharacteristic
252C4C4×C22⋊D3711yescharacteristic
253C4#1192450711yescharacteristic
254C4#1192450911yescharacteristic
255C2—1482no—
256C2#1455740911yescharacteristic
257C2#1455752811yescharacteristic
258C2#1455754011yescharacteristic
259C2#1455769211yescharacteristic
260C2#1455769411yescharacteristic
261C2#1455787211yescharacteristic
262C2#1455787311yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#103×C37C2
socleC23×C37C2×D4
prime radicalC23×D37D4
cosocleC22×C4×C37C23
hypercenterC2×#103D37
hypocenterC37#1873
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#11924460C2semidirect
5. #14557296C2semidirect
6. #14557295C2semidirect
7. C2×#103×C37C2semidirect
11. #11924512C4semidirect
135. C2×#103D37semidirect
139. C37#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#119245122
C2×#119244942
C2×#119244602
C2×#119244482
#145572962
#145572952
C2×#103×C372
#187337