Finite Group Databasebeta

← #17995008

Subgroups — #17995008

Order 4736.

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

normal subgroups only

This group has 386 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
2#14558006C211yesmaximal, characteristic
3C2×#11924450C211yesmaximal, characteristic
4#14557394C211yesmaximal, characteristic, complemented
5#14557394C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C37×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C2211yescharacteristic
9C23×Dic37C2211yescharacteristic
10#11924520—22no—
11#11924520C414yescomplemented
12C4×C22⋊D37—22no—
13#11924496—22no—
14#11924492—21no—
15C2×C4⋊Dic37—21no—
16C2×C22⋊Dic37C2211yescharacteristic
17C2×C22⋊Dic37C2211yescharacteristic
18C2×#10596938—21no—
19C22⋊C4×D37—21no—
20#11924450—22no—
21#11924443—22no—
22#11924443—22no—
23C2×C22⋊C4×C37C2211yescharacteristic
24C2×C22⋊C4×C37C2211yescharacteristic
25C2×C22⋊C4×C37C2211yescharacteristic
26C24×C37C2311yescharacteristic
27C23×D37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37—21no—
30C22×C4×C37D412yes—
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37C2×C412yes—
36C2×C22⋊D37D412yes—
37C22×Dic37—21no—
38C22×Dic37—21no—
39C22×Dic37—21no—
40C22×Dic37—21no—
41C22×Dic37—21no—
42C22×Dic37—21no—
43C22×Dic37—21no—
44C22×Dic37C2×C412yescomplemented
45C22×Dic37D411yescharacteristic
46C22×Dic37D412yes—
47C2×C4×D37—22no—
48C22⋊C4×C37—21no—
49C22⋊C4×C37—21no—
50C22⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C22⋊C4×C37—21no—
53C22⋊C4×C37C2×C412yescomplemented
54C22⋊Dic37—21no—
55C22⋊Dic37—21no—
56C22⋊Dic37—21no—
57C22⋊Dic37—21no—
58#10596938—22no—
59#10596938—24no—
60C4⋊Dic37—24no—
61#10596936—22no—
62C4×Dic37—22no—
63C23×C37—42no—
64C23×C37C22×C411yescharacteristic
65C23×C37C2×D411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C23×C37C2×D411yescharacteristic
68C23×C37C2×D411yescharacteristic
69C23×C37#4111yescharacteristic
70C23×C37#4111yescharacteristic
71C22×D37—21no—
72C22×D37—21no—
73C22×D37—42no—
74C22×D37C22⋊C412yes—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—42no—
78C2×C4×C37—42no—
79C2×C4×C37—42no—
80C2×C4×C37—41no—
81C22⋊D37—22no—
82C22⋊D37—22no—
83C22⋊D37—22no—
84C22⋊D37—22no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—41no—
92C2×Dic37—41no—
93C2×Dic37—41no—
94C2×Dic37—41no—
95C2×Dic37—42no—
96C2×Dic37—42no—
97C2×Dic37—41no—
98C2×Dic37C22⋊C412yes—
99C4×D37—82no—
100C22×C37—22no—
101C22×C37—22no—
102C22×C37—22no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37—41no—
107C22×C37C2×C22⋊C411yescharacteristic
108C22×C37C4×D411yescharacteristic
109C22×C37C4×D411yescharacteristic
110C22×C37#12011yescharacteristic
111C22×C37#12111yescharacteristic
112C22×C37#12111yescharacteristic
113C22×C37#12311yescharacteristic
114C2×D37—22no—
115C2×D37—42no—
116C2×D37—42no—
117C2×D37—81no—
118C4×C37—42no—
119C4×C37—42no—
120C4×C37—81no—
121Dic37—22no—
122Dic37—42no—
123Dic37—42no—
124Dic37—81no—
125#1890—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—21no—
129C2×C37—21no—
130C2×C37—21no—
131C2×C37—21no—
132C2×C37#38611yescharacteristic
133C2×C37#45812yes—
134D37—42no—
135C2×#123—371no—
136#518—371no—
137C2×#99—371no—
138#381—371no—
139#381—371no—
140#342—371no—
141#342D3711yescharacteristic, complemented
142C37#189011yescharacteristic, complemented, Sylow
143C22×D4—371no—
144C23×C4—371no—
145#123—374no—
146#123—742no—
147C4×D4—742no—
148C4×D4—742no—
149#117—741no—
150C2×C4⋊C4—741no—
151C2×C22⋊C4—371no—
152C2×C22⋊C4—371no—
153C2×C22⋊C4—741no—
154C2×C22⋊C4—741no—
155C2×C22⋊C4C2×D3711yescharacteristic
156C2×C22⋊C4C2×D3711yescharacteristic
157C2×C22⋊C4C2×D3711yescharacteristic
158#99—742no—
159#95—742no—
160#95—742no—
161C24—371no—
162C24C22×D3711yescharacteristic
163C2×D4—372no—
164C2×D4—372no—
165C2×D4—741no—
166C2×D4—741no—
167C2×D4—741no—
168C2×D4—741no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—371no—
172C22×C4—372no—
173C22×C4—372no—
174C22×C4—742no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180C22×C4—741no—
181C22×C4—741no—
182C22×C4D14812yes—
183C4⋊C4—744no—
184C4⋊C4—742no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—744no—
191C22⋊C4—742no—
192C22⋊C4—741no—
193C22⋊C4—741no—
194C22⋊C4—741no—
195C22⋊C4—741no—
196C22⋊C4C4×D3712yescomplemented
197C42—742no—
198C23—42no—
199C23—372no—
200C23—741no—
201C23—741no—
202C23—1482no—
203C23C2×C4×D3711yescharacteristic
204C23C2×D14811yescharacteristic
205C23#1059696211yescharacteristic
206C23D4×D3711yescharacteristic
207C23D4×D3711yescharacteristic
208C23D4×D3711yescharacteristic
209C23#1059696611yescharacteristic
210D4—742no—
211D4—742no—
212D4—742no—
213D4—742no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—372no—
221C2×C4—2962no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—742no—
227C2×C4—742no—
228C2×C4—1482no—
229C2×C4—1481no—
230C2×C4—1481no—
231C2×C4—1481no—
232C2×C4—1481no—
233C2×C4—1481no—
234C2×C4—1482no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—2961no—
243C22—742no—
244C22—1482no—
245C22—1482no—
246C22C22⋊C4×D3711yescharacteristic
247C22#1192449811yescharacteristic
248C22C4×D14811yescharacteristic
249C22#1192450611yescharacteristic
250C22#1192450911yescharacteristic
251C22#1192451111yescharacteristic
252C22#1192452111yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—2961no—
257C4—742no—
258C4—1482no—
259C4—1482no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—1482no—
267C2#1455741111yescharacteristic
268C2#1455772412yes—
subgroupG/H
centerC22#11924506
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37#120
prime radicalC22×C22⋊D37C22
cosocleC24×C37C23
hypercenter#342D37
hypocenterC37#1890
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #14557394C2semidirect
5. #14557394C2semidirect
6. #14557299C2semidirect
7. C37×#342C2semidirect
11. #11924520C4semidirect
44. C22×Dic37C2×C4semidirect
53. C22⋊C4×C37C2×C4semidirect
141. #342D37semidirect
142. C37#1890semidirect
196. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245202
#145580062
C2×#119244502
#145573942
#145572992
C37×#3422
#189037