Finite Group Databasebeta

← #17995051

Subgroups — #17995051

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×#11924517C211yesmaximal, characteristic
2C2×#11924492C211yesmaximal, characteristic, complemented
3C2×#11924451C211yesmaximal, characteristic
4#14557394C211yesmaximal, characteristic, complemented
5#14557299C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C2×#99×C37C211yesmaximal, characteristic
8C23×Dic37C2211yescharacteristic
9#11924517—21no—
10#11924517—21no—
11#11924517—22no—
12#11924492—22no—
13#11924492—22no—
14C2×#10596936—21no—
15C2×#10596936C412yescomplemented
16C2×C22⋊Dic37C412yescomplemented
17C2×C22⋊Dic37C2211yescharacteristic
18C2×C22⋊Dic37C2211yescharacteristic
19C2×C22⋊Dic37C2211yescharacteristic
20C2×C4×Dic37—21no—
21#11924451—22no—
22#11924443—22no—
23C22×D4×C37C2211yescharacteristic
24C2×C22⋊C4×C37C2211yescharacteristic
25C2×C22⋊C4×C37C2211yescharacteristic
26#99×C37—22no—
27C24×C37C2×C411yescharacteristic
28C24×C37C2311yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—21no—
35C22×C4×C37—21no—
36C22×C4×C37—21no—
37C22×C4×C37C2×C411yescharacteristic
38C22×Dic37—21no—
39C22×Dic37—21no—
40C22×Dic37—21no—
41C22×Dic37—21no—
42C22×Dic37—21no—
43C22×Dic37—21no—
44C22×Dic37C2×C412yes—
45C22×Dic37C2×C412yes—
46C22×Dic37D411yescharacteristic
47C22×Dic37D411yescharacteristic
48C22×Dic37D412yes—
49C22⋊C4×C37—21no—
50C22⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C22⋊C4×C37D412yes—
53C22⋊Dic37—21no—
54C22⋊Dic37—21no—
55C22⋊Dic37—21no—
56C22⋊Dic37—22no—
57C22⋊Dic37—22no—
58C22⋊Dic37—21no—
59C22⋊Dic37—21no—
60C22⋊Dic37D412yes—
61#10596936—24no—
62#10596936—22no—
63#10596936—22no—
64C4×Dic37—24no—
65C23×C37—21no—
66C23×C37—21no—
67C23×C37—21no—
68C23×C37—42no—
69C23×C37—42no—
70C23×C37C22×C411yescharacteristic
71C23×C37C2×D411yescharacteristic
72C23×C37C2×D411yescharacteristic
73C23×C37C2×D411yescharacteristic
74C23×C37C2×D411yescharacteristic
75C23×C37#4111yescharacteristic
76C23×C37#4111yescharacteristic
77D4×C37—41no—
78D4×C37—41no—
79D4×C37—41no—
80D4×C37—41no—
81C2×C4×C37—21no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37—22no—
85C2×C4×C37—42no—
86C2×C4×C37—42no—
87C2×C4×C37—41no—
88C2×Dic37—22no—
89C2×Dic37—22no—
90C2×Dic37—21no—
91C2×Dic37—21no—
92C2×Dic37—22no—
93C2×Dic37—22no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37—42no—
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×C37—41no—
112C22×C37—42no—
113C22×C37—81no—
114C22×C37—81no—
115C22×C37C2×C22⋊C411yescharacteristic
116C22×C37C4×D411yescharacteristic
117C22×C37C4×D411yescharacteristic
118C22×C37#12011yescharacteristic
119C22×C37#12111yescharacteristic
120C22×C37#12111yescharacteristic
121C22×C37#12311yescharacteristic
122C4×C37—42no—
123C4×C37—41no—
124C4×C37—81no—
125Dic37—22no—
126Dic37—22no—
127Dic37—42no—
128Dic37—42no—
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—81no—
138C2×C37#38611yescharacteristic
139C2×C37#41012yes—
140C2×#123—371no—
141C2×#117—371no—
142C2×#99—371no—
143C2×#99D3711yescharacteristic
144#381—371no—
145#342—371no—
146#342—371no—
147C37#189911yescharacteristic, complemented, Sylow
148C22×D4C2×D3711yescharacteristic
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⋊C4—371no—
161C2×C22⋊C4C2×D3711yescharacteristic
162C2×C22⋊C4C2×D3711yescharacteristic
163C2×C42—741no—
164#99—22no—
165#99—742no—
166#95—742no—
167C24C4×D3711yescharacteristic
168C24C22×D3711yescharacteristic
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—372no—
178C22×C4—372no—
179C22×C4—371no—
180C22×C4—371no—
181C22×C4—372no—
182C22×C4—741no—
183C22×C4—741no—
184C22×C4—741no—
185C22×C4—741no—
186C22×C4—741no—
187C22×C4—741no—
188C22×C4C4×D3711yescharacteristic
189C4⋊C4—742no—
190C4⋊C4—742no—
191C4⋊C4—744no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—372no—
196C22⋊C4—742no—
197C22⋊C4—742no—
198C22⋊C4—741no—
199C22⋊C4—741no—
200C22⋊C4—741no—
201C22⋊C4—741no—
202C22⋊C4—741no—
203C22⋊C4C22⋊D3712yes—
204C42—744no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—42no—
209C23—42no—
210C23C2×C4×D3711yescharacteristic
211C23#1059696211yescharacteristic
212C23D4×D3711yescharacteristic
213C23D4×D3711yescharacteristic
214C23D4×D3711yescharacteristic
215C23#1059696411yescharacteristic
216C23C2×C22⋊D3711yescharacteristic
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—372no—
229C2×C4—372no—
230C2×C4—742no—
231C2×C4—742no—
232C2×C4—741no—
233C2×C4—741no—
234C2×C4—742no—
235C2×C4—742no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—742no—
239C2×C4—742no—
240C2×C4—1482no—
241C2×C4—1481no—
242C2×C4—1482no—
243C2×C4—1482no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—81no—
254C22—81no—
255C22C22⋊C4×D3711yescharacteristic
256C22#1192449611yescharacteristic
257C22C4×C22⋊D3711yescharacteristic
258C22#1192450411yescharacteristic
259C22#1192450711yescharacteristic
260C22#1192450911yescharacteristic
261C22#1192451811yescharacteristic
262C4—42no—
263C4—41no—
264C4—81no—
265C4—2961no—
266C4—742no—
267C4—742no—
268C4—1482no—
269C4—1482no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—81no—
277C2#1455740911yescharacteristic
278C2#1455750512yes—
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC2×#99×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D4×C37C22
cosocleC24×C37C23
hypercenterC2×#99D37
hypocenterC37#1899
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#11924492C2semidirect
4. #14557394C2semidirect
5. #14557299C2semidirect
6. #14557299C2semidirect
15. C2×#10596936C4semidirect
16. C2×C22⋊Dic37C4semidirect
147. C37#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#119245172
C2×#119244922
C2×#119244512
#145573942
#145572992
C2×#99×C372
#189937