Finite Group Databasebeta

← #17993127

Subgroups — #17993127

Order 4736.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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⋊Q8×D37C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic
3#14557395C211yesmaximal, characteristic
4#14557271C211yesmaximal, characteristic, complemented
5#14557270C211yesmaximal, characteristic, complemented
6#14557269C211yesmaximal, characteristic, complemented
7C37×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D37C411yescharacteristic, complemented
9C22×C4×D37C2211yescharacteristic
10C2×#10596929—21no—
11#11924516C411yescharacteristic, complemented
12#11924515C2211yescharacteristic
13#11924514—21no—
14#11924513—21no—
15#11924512C411yescharacteristic, complemented
16C4⋊C4×D37—21no—
17C4⋊C4×D37C411yescharacteristic, complemented
18C2×#10596938—21no—
19C22⋊C4×D37—21no—
20C22⋊#64436C2211yescharacteristic
21#11924448—21no—
22#11924443—21no—
23#11924443C2211yescharacteristic
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C2×Q8×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33Q8×D37—42no—
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—42no—
37C2×C4×D37C2×C411yescharacteristic
38C2×C4×D37C2×C411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×Dic74—21no—
42C2×Dic74C2×C411yescharacteristic
43C2×C8×C37—21no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37C2×C411yescharacteristic
46C22⋊C4×C37—21no—
47C22⋊Dic37—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—42no—
51C4⋊Dic37—21no—
52C4⋊Dic37C2×C411yescharacteristic
53#10596936—21no—
54#10596936—21no—
55#10596936—21no—
56C2×#64436—21no—
57#10596929—42no—
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—22no—
62C22×D37—41no—
63C22×D37C22⋊C411yescharacteristic
64C22×D37C22⋊C411yescharacteristic
65Q8×C37—41no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37C22×C411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—41no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37C22⋊C411yescharacteristic
81C2×Dic37C22⋊C411yescharacteristic
82C4×D37—22no—
83C4×D37—22no—
84C4×D37—41no—
85C4×D37—41no—
86C4×D37—42no—
87C4×D37—42no—
88Dic74—42no—
89Dic74—41no—
90C8×C37—41no—
91#64436—41no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37C2×C22⋊C411yescharacteristic
95C22×C37#13711yescharacteristic
96C22×C37#13711yescharacteristic
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—42no—
103C2×D37—42no—
104C2×D37#9912yes—
105C4×C37—21no—
106C4×C37—21no—
107C4×C37—41no—
108C4×C37—41no—
109C4×C37—81no—
110Dic37—21no—
111Dic37—21no—
112Dic37—41no—
113Dic37—41no—
114Dic37—81no—
115#1511—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—21no—
118C2×C37C2×#9911yescharacteristic
119C2×C37#41911yescharacteristic
120C2×C37#42111yescharacteristic
121D37—22no—
122D37—41no—
123C2×C22⋊Q8—371no—
124#407—371no—
125#381—371no—
126#328—371no—
127#328—371no—
128#328—371no—
129#328D3711yescharacteristic, complemented
130C37#151111yescharacteristic, complemented, Sylow
131C22×Q8—371no—
132C23×C4—371no—
133C2×M16—741no—
134C22⋊Q8—371no—
135C22⋊Q8—371no—
136C22⋊Q8—371no—
137C22⋊Q8—741no—
138C22⋊Q8—741no—
139C22⋊Q8C2×D3711yescharacteristic
140C2×C4⋊C4—371no—
141C2×C4⋊C4—741no—
142C2×C22⋊C4—741no—
143C2×C22⋊C4—741no—
144C22⋊C8—371no—
145C22⋊C8—741no—
146C22⋊C8C2×D3711yescharacteristic
147#95—371no—
148#95—741no—
149#95C2×D3711yescharacteristic
150C24—371no—
151C2×Q8—371no—
152C2×Q8—741no—
153C2×Q8—1482no—
154C2×Q8C4×D3711yescharacteristic
155C22×C4—21no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—741no—
162C22×C4—741no—
163C22×C4—741no—
164C22×C4—1482no—
165C22×C4C22×D3711yescharacteristic
166M16—1482no—
167C2×C8—21no—
168C2×C8—741no—
169C4⋊C4—21no—
170C4⋊C4—371no—
171C4⋊C4—741no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C4⋊C4C4×D3711yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—1482no—
181C23—371no—
182C23—371no—
183C23—742no—
184C23—741no—
185C23—741no—
186C23—1481no—
187C23D4×D3711yescharacteristic
188Q8—41no—
189Q8—1481no—
190Q8—1482no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—371no—
198C2×C4—371no—
199C2×C4—742no—
200C2×C4—742no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4—1482no—
206C2×C4—1482no—
207C2×C4—1481no—
208C2×C4—1481no—
209C2×C4—1481no—
210C2×C4—1481no—
211C2×C4C2×C4×D3711yescharacteristic
212C2×C4D4×D3711yescharacteristic
213C8—41no—
214C8—1481no—
215C22—21no—
216C22—21no—
217C22—372no—
218C22—741no—
219C22—741no—
220C22—741no—
221C22—741no—
222C22—741no—
223C22—1482no—
224C22—1482no—
225C22C22⋊C4×D3711yescharacteristic
226C22#1192456511yescharacteristic
227C22#1192456811yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—81no—
233C4—2961no—
234C4—741no—
235C4—741no—
236C4—1481no—
237C4—1481no—
238C2—21no—
239C2—21no—
240C2—742no—
241C2—1481no—
242C2#99×D3711yescharacteristic
243C2#1455754011yescharacteristic
244C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC22×C4×C37C23
hypercenter#328D37
hypocenterC37#1511
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #14557271C2semidirect
5. #14557270C2semidirect
6. #14557269C2semidirect
7. C37×#328C2semidirect
8. C2×Q8×D37C4semidirect
11. #11924516C4semidirect
15. #11924512C4semidirect
17. C4⋊C4×D37C4semidirect
129. #328D37semidirect
130. C37#1511semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D372
#145574952
#145573952
#145572712
#145572702
#145572692
C37×#3282
#151137