Finite Group Databasebeta

← #18010584

Subgroups — #18010584

Order 4736.

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

normal subgroups only

This group has 412 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, complemented
2C2×#11924598C212yesmaximal, complemented
3D37⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#14558406C212yesmaximal, complemented
5#121×D37C211yesmaximal, characteristic
6C2×D37⋊C8C2212yes—
7#11924615—24no—
8C2×C4⋊#3866C2212yes—
9C2×C22⋊#3866—21no—
10C2×C4×#3866—21no—
11#11924598—24no—
12#11924593—21no—
13C22⋊#64438—21no—
14C2×D4×D37—21no—
15C2×D4×D37C2211yescharacteristic
16C22×C4×D37C2211yescharacteristic
17#11924511C411yescharacteristic, complemented
18#11924510C411yescharacteristic, complemented
19#11924509—21no—
20#11924508—21no—
21#11924507C411yescharacteristic, complemented
22C4⋊C4×D37C2211yescharacteristic
23C22⋊C4×D37—21no—
24#121×C37C411yescharacteristic, complemented
25C23×D37—21no—
26C23×D37D411yescharacteristic
27C22×#3866—22no—
28C2×D4×C37—21no—
29C2×D4×C37C2×C411yescharacteristic
30C22×C4×C37C2×C411yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37D411yescharacteristic
35D4×D37—22no—
36D4×D37—22no—
37D4×D37—44no—
38C2×D148—21no—
39C2×D148C2×C411yescharacteristic
40C2×C4×D37—22no—
41C2×C4×D37—22no—
42C2×C4×D37—21no—
43C2×C4×D37C2×C411yescharacteristic
44C2×C4×D37D411yescharacteristic
45C2×C4×D37D411yescharacteristic
46C2×C4×D37C2311yescharacteristic
47C22⋊#3866—24no—
48C2×#64438—22no—
49C4⋊#3866—22no—
50C4⋊#3866D414yescomplemented
51C4×#3866—24no—
52D37⋊C8—22no—
53D37⋊C8—22no—
54C4⋊C4×C37C2×C411yescharacteristic
55C22⋊C4×C37—21no—
56C22⋊Dic37—21no—
57#10596938—21no—
58#10596938—21no—
59C4⋊Dic37C2×C411yescharacteristic
60#10596936—21no—
61C23×C37—21no—
62C23×C37C22⋊C411yescharacteristic
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—22no—
66C22×D37—22no—
67C22×D37—21no—
68C22×D37—41no—
69C22×D37—41no—
70C22×D37—42no—
71C22×D37—42no—
72C22×D37C22⋊C411yescharacteristic
73C22×D37C2×D411yescharacteristic
74C2×#3866—24no—
75C2×#3866—42no—
76C2×#3866—42no—
77D4×C37—22no—
78D4×C37—42no—
79C2×C4×C37—22no—
80C2×C4×C37—21no—
81C2×C4×C37C22⋊C411yescharacteristic
82C2×C4×C37C22×C411yescharacteristic
83C22⋊D37—42no—
84C22⋊D37—42no—
85C22⋊D37—42no—
86C2×Dic37—22no—
87C2×Dic37—21no—
88C2×Dic37C22⋊C411yescharacteristic
89C2×Dic37C2×D411yescharacteristic
90D148—22no—
91D148—42no—
92C4×D37—21no—
93C4×D37—21no—
94C4×D37—22no—
95C4×D37—22no—
96C4×D37—42no—
97C4×D37C2×D412yes—
98C4×D37#4112yes—
99#64438—42no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37C2×C22⋊C411yescharacteristic
107C2×D37—21no—
108C2×D37—21no—
109C2×D37—21no—
110C2×D37—42no—
111C2×D37—42no—
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—41no—
115C2×D37—82no—
116C2×D37—82no—
117C2×D37#12011yescharacteristic
118C2×D37#12311yescharacteristic
119C2×D37#13512yes—
120C2×D37AGL(1,ℤ/8)12yes—
121#3866—44no—
122C4×C37—21no—
123C4×C37—41no—
124C4×C37C4×D412yes—
125Dic37—21no—
126Dic37—41no—
127Dic37#12112yes—
128#1875—371nomaximal, Sylow
129C2×C37—41no—
130C2×C37—81no—
131C2×C37#38611yescharacteristic
132C2×C37#41611yescharacteristic
133C2×C37#41811yescharacteristic
134D37—41no—
135D37—81no—
136D37#44912yes—
137D37#48212yes—
138C2×#121—371no—
139C2×#117—371no—
140C2×#102—372no—
141C2×C22⋊C8—371no—
142#340—372no—
143C37#187511yescharacteristic, complemented, Sylow
144C22×D4—371no—
145C22×D4—741no—
146C23×C4—371no—
147C22×C8—372no—
148#121—371no—
149#121—371no—
150#121—371no—
151#121—741no—
152#121—741no—
153#121#386611yescharacteristic, complemented
154#117—744no—
155C2×C4⋊C4—372no—
156C2×C4⋊C4—371no—
157C2×C22⋊C4—741no—
158C2×C22⋊C4—741no—
159C2×C42—741no—
160#102—744no—
161C22⋊C8—741no—
162C22⋊C8—741no—
163C24—371no—
164C24—741no—
165C2×D4—21no—
166C2×D4—371no—
167C2×D4—741no—
168C2×D4—742no—
169C2×D4—742no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—1484no—
174C2×D4C2×#386611yescharacteristic
175C22×C4—371no—
176C22×C4—371no—
177C22×C4—371no—
178C22×C4—371no—
179C22×C4—371no—
180C22×C4—742no—
181C22×C4—742no—
182C22×C4—741no—
183C22×C4—742no—
184C22×C4C2×#386611yescharacteristic
185C2×C8—742no—
186C2×C8—742no—
187C2×C8—742no—
188C4⋊C4—374no—
189C4⋊C4—371no—
190C4⋊C4—741no—
191C4⋊C4—742no—
192C4⋊C4C2×#386611yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—741no—
195C22⋊C4—741no—
196C22⋊C4—744no—
197C22⋊C4—741no—
198C42—744no—
199C23—21no—
200C23—371no—
201C23—371no—
202C23—741no—
203C23—741no—
204C23—742no—
205C23—742no—
206C23—741no—
207C23—1481no—
208C23—1481no—
209C23—1482no—
210C23—1482no—
211C23C22⋊#386611yescharacteristic
212D4—22no—
213D4—42no—
214D4—742no—
215D4—1482no—
216D4—1482no—
217D4—1482no—
218D4—1482no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—371no—
222C2×C4—372no—
223C2×C4—372no—
224C2×C4—371no—
225C2×C4—742no—
226C2×C4—741no—
227C2×C4—741no—
228C2×C4—742no—
229C2×C4—742no—
230C2×C4—744no—
231C2×C4—741no—
232C2×C4—1482no—
233C2×C4—1482no—
234C2×C4—1482no—
235C2×C4C22⋊#386611yescharacteristic
236C2×C4C22×#386611yescharacteristic
237C8—1482no—
238C22—21no—
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—371no—
245C22—371no—
246C22—372no—
247C22—372no—
248C22—2962no—
249C22—2962no—
250C22—741no—
251C22—741no—
252C22—741no—
253C22—1482no—
254C22—1482no—
255C22—1481no—
256C22—1481no—
257C22—1481no—
258C22C2×C22⋊#386611yescharacteristic
259C4—21no—
260C4—41no—
261C4—372no—
262C4—741no—
263C4—1484no—
264C4—1481no—
265C4D4×#386612yes—
266C2—41no—
267C2—81no—
268C2—372no—
269C2—372no—
270C2—2961no—
271C2—1481no—
272C2#1455848111yescharacteristic
273C2#1455852311yescharacteristic
274C2#1455852511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#121×C37C4
socleC22×C37C2×C22⋊C4
prime radical#121×D37C2
cosocleC2×C4×D37C23
hypercenter#121#3866
hypocenterC37#1875
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#11924615C2semidirect
2. C2×#11924598C2semidirect
3. D37⋊(C22⋊C8)C2semidirect
4. #14558406C2semidirect
17. #11924511C4semidirect
18. #11924510C4semidirect
21. #11924507C4semidirect
24. #121×C37C4semidirect
50. C4⋊#3866D4semidirect
143. C37#1875semidirect
153. #121#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246152
C2×#119245982
D37⋊(C22⋊C8)2
#145584062
#121×D372
#187537