Finite Group Databasebeta

← #17995053

Subgroups — #17995053

Order 4736.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11924520C211yesmaximal, characteristic
2C2×#11924492C211yesmaximal, characteristic, complemented
3C2×#11924450C211yesmaximal, characteristic
4C2×#11924450C211yesmaximal, characteristic
5#14557394C211yesmaximal, characteristic, complemented
6#14557300C211yesmaximal, characteristic, complemented
7C37×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C2211yescharacteristic
9C23×Dic37C2211yescharacteristic
10#11924520—21no—
11#11924520—21no—
12#11924520—22no—
13#11924492—22no—
14#11924492—22no—
15C2×C4⋊Dic37C412yescomplemented
16C2×#10596936—21no—
17C2×C22⋊Dic37C2211yescharacteristic
18C2×C22⋊Dic37C2211yescharacteristic
19C2×#10596938C412yescomplemented
20C2×C4×Dic37—21no—
21#11924450—22no—
22#11924450—22no—
23#11924443—22no—
24C2×C22⋊C4×C37C2211yescharacteristic
25C2×C22⋊C4×C37C2211yescharacteristic
26C2×C22⋊C4×C37C2211yescharacteristic
27C24×C37C2311yescharacteristic
28C23×D37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C22×C4×C37C2×C412yes—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C2×C22⋊D37—21no—
37C2×C22⋊D37—21no—
38C22×Dic37—21no—
39C22×Dic37—21no—
40C22×Dic37—21no—
41C22×Dic37—21no—
42C22×Dic37—21no—
43C22×Dic37—21no—
44C22×Dic37C2×C411yescharacteristic
45C22×Dic37C2×C412yes—
46C22×Dic37D411yescharacteristic
47C22×Dic37D411yescharacteristic
48C22×Dic37D412yes—
49C22⋊C4×C37—21no—
50C22⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C22⋊C4×C37—21no—
53C22⋊C4×C37—21no—
54C22⋊C4×C37D412yes—
55C22⋊Dic37—21no—
56C22⋊Dic37—21no—
57C22⋊Dic37—21no—
58C22⋊Dic37D412yes—
59#10596938—22no—
60#10596938—22no—
61C4⋊Dic37—22no—
62C4⋊Dic37—22no—
63#10596936—24no—
64C4×Dic37—24no—
65C23×C37—42no—
66C23×C37C22×C411yescharacteristic
67C23×C37C2×D411yescharacteristic
68C23×C37C2×D411yescharacteristic
69C23×C37C2×D411yescharacteristic
70C23×C37C2×D411yescharacteristic
71C23×C37#4111yescharacteristic
72C23×C37#4111yescharacteristic
73C22×D37—21no—
74C22×D37—21no—
75C22×D37—21no—
76C22×D37—42no—
77C2×C4×C37—22no—
78C2×C4×C37—22no—
79C2×C4×C37—42no—
80C2×C4×C37—42no—
81C2×C4×C37—42no—
82C2×C4×C37—41no—
83C22⋊D37—41no—
84C22⋊D37—41no—
85C22⋊D37—41no—
86C22⋊D37—41no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37—21no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—21no—
97C2×Dic37—21no—
98C2×Dic37—22no—
99C2×Dic37—42no—
100C2×Dic37—42no—
101C2×Dic37—41no—
102C2×Dic37C22⋊C412yes—
103C2×Dic37C22⋊C412yes—
104C22×C37—22no—
105C22×C37—22no—
106C22×C37—22no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37—41no—
110C22×C37—41no—
111C22×C37C2×C22⋊C411yescharacteristic
112C22×C37C4×D411yescharacteristic
113C22×C37C4×D411yescharacteristic
114C22×C37#12011yescharacteristic
115C22×C37#12111yescharacteristic
116C22×C37#12111yescharacteristic
117C22×C37#12311yescharacteristic
118C2×D37—41no—
119C2×D37—42no—
120C2×D37—81no—
121C2×D37—81no—
122C4×C37—42no—
123C4×C37—42no—
124C4×C37—81no—
125Dic37—22no—
126Dic37—22no—
127Dic37—42no—
128Dic37—41no—
129Dic37—81no—
130#1899—371nomaximal, Sylow
131C2×C37—21no—
132C2×C37—21no—
133C2×C37—21no—
134C2×C37—21no—
135C2×C37—21no—
136C2×C37—21no—
137C2×C37#38611yescharacteristic
138C2×C37#41012yes—
139D37—81no—
140C2×#123—371no—
141C2×#117—371no—
142C2×#99—371no—
143C2×#99—371no—
144#381—371no—
145#342—371no—
146#342D3711yescharacteristic, complemented
147C37#189911yescharacteristic, complemented, Sylow
148C22×D4—371no—
149C23×C4—371no—
150#123—742no—
151#123—741no—
152#123—741no—
153#117—742no—
154#117—742no—
155C2×C4⋊C4—372no—
156C2×C4⋊C4—741no—
157C2×C22⋊C4—371no—
158C2×C22⋊C4—372no—
159C2×C22⋊C4—371no—
160C2×C22⋊C4C2×D3711yescharacteristic
161C2×C22⋊C4C2×D3711yescharacteristic
162C2×C22⋊C4C2×D3711yescharacteristic
163C2×C42—741no—
164#99—742no—
165#99—742no—
166#95—742no—
167C24—371no—
168C24C22×D3711yescharacteristic
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—741no—
174C2×D4—741no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—372no—
178C22×C4—372no—
179C22×C4—371no—
180C22×C4—371no—
181C22×C4—371no—
182C22×C4—741no—
183C22×C4—741no—
184C22×C4—741no—
185C22×C4—741no—
186C22×C4—741no—
187C22×C4—741no—
188C22×C4C4×D3712yes—
189C4⋊C4—742no—
190C4⋊C4—742no—
191C4⋊C4—744no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—372no—
198C22⋊C4—742no—
199C22⋊C4—742no—
200C22⋊C4—741no—
201C22⋊C4—741no—
202C22⋊C4—741no—
203C22⋊C4D14812yes—
204C42—744no—
205C23—42no—
206C23—741no—
207C23—741no—
208C23—741no—
209C23—1482no—
210C23C2×C4×D3711yescharacteristic
211C23C2×D14811yescharacteristic
212C23#1059696211yescharacteristic
213C23D4×D3711yescharacteristic
214C23D4×D3711yescharacteristic
215C23D4×D3711yescharacteristic
216C23#1059696611yescharacteristic
217D4—1481no—
218D4—1481no—
219D4—1481no—
220D4—1481no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—372no—
228C2×C4—372no—
229C2×C4—742no—
230C2×C4—742no—
231C2×C4—741no—
232C2×C4—741no—
233C2×C4—742no—
234C2×C4—742no—
235C2×C4—741no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—741no—
240C2×C4—742no—
241C2×C4—1482no—
242C2×C4—1481no—
243C2×C4—1482no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—2961no—
252C22—2961no—
253C22—1482no—
254C22—1481no—
255C22C22⋊C4×D3711yescharacteristic
256C22#1192449811yescharacteristic
257C22C4×D14811yescharacteristic
258C22#1192450611yescharacteristic
259C22#1192450911yescharacteristic
260C22#1192451111yescharacteristic
261C22#1192452111yescharacteristic
262C4—42no—
263C4—42no—
264C4—81no—
265C4—2961no—
266C4—742no—
267C4—742no—
268C4—1482no—
269C4—1481no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—2961no—
277C2#1455741111yescharacteristic
278C2#1455750512yes—
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC24×C37C23
hypercenter#342D37
hypocenterC37#1899
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#11924492C2semidirect
5. #14557394C2semidirect
6. #14557300C2semidirect
7. C37×#342C2semidirect
15. C2×C4⋊Dic37C4semidirect
19. C2×#10596938C4semidirect
146. #342D37semidirect
147. C37#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#119245202
C2×#119244922
C2×#119244502
#145573942
#145573002
C37×#3422
#189937