Finite Group Databasebeta

← #18010610

Subgroups — #18010610

Order 4736.

432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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×D37⋊C8C211yesmaximal, characteristic, complemented
2C2×#11924598C212yesmaximal, complemented
3#14558475C211yesmaximal, characteristic, complemented
4#14558406C212yesmaximal, complemented
5#121×D37C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7C2×D37⋊C8—24no—
8C2×D37⋊C8C2212yes—
9C22×#64438—21no—
10C2×C4⋊#3866C2212yes—
11C2×C22⋊#3866—21no—
12#11924598—24no—
13(C2×#3866)⋊C4—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—42no—
38D4×D37—42no—
39C2×D148—21no—
40C2×D148C2×C411yescharacteristic
41C2×C4×D37—22no—
42C2×C4×D37—22no—
43C2×C4×D37—21no—
44C2×C4×D37C2×C411yescharacteristic
45C2×C4×D37D411yescharacteristic
46C2×C4×D37D411yescharacteristic
47C2×C4×D37C2311yescharacteristic
48C22⋊#3866—42no—
49C2×#64438—24no—
50C2×#64438—22no—
51C4⋊#3866—22no—
52C4⋊#3866—22no—
53D37⋊C8—24no—
54D37⋊C8—22no—
55D37⋊C8D414yescomplemented
56C4⋊C4×C37C2×C411yescharacteristic
57C22⋊C4×C37—21no—
58C22⋊Dic37—21no—
59#10596938—21no—
60#10596938—21no—
61C4⋊Dic37C2×C411yescharacteristic
62#10596936—21no—
63C23×C37—21no—
64C23×C37C22⋊C411yescharacteristic
65C22×D37—22no—
66C22×D37—22no—
67C22×D37—21no—
68C22×D37—42no—
69C22×D37—41no—
70C22×D37—41no—
71C22×D37—42no—
72C22×D37C22⋊C411yescharacteristic
73C22×D37D812yes—
74C22×D37SD1612yes—
75C22×D37C2×D411yescharacteristic
76C2×#3866—42no—
77C2×#3866—42no—
78C2×#3866—42no—
79D4×C37—22no—
80D4×C37—42no—
81C2×C4×C37—22no—
82C2×C4×C37—21no—
83C2×C4×C37C22⋊C411yescharacteristic
84C2×C4×C37C22×C411yescharacteristic
85C22⋊D37—42no—
86C22⋊D37—42no—
87C22⋊D37—41no—
88C22⋊D37—41no—
89C2×Dic37—21no—
90C2×Dic37—21no—
91C2×Dic37—21no—
92C2×Dic37C22⋊C411yescharacteristic
93C2×Dic37C2×D411yescharacteristic
94D148—22no—
95D148—42no—
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—21no—
99C4×D37—21no—
100C4×D37—41no—
101C4×D37—41no—
102C4×D37C2×D412yes—
103C4×D37#4112yes—
104#64438—24no—
105C22×C37—21no—
106C22×C37—21no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37—41no—
110C22×C37#10212yescomplemented
111C22×C37C2×C22⋊C411yescharacteristic
112C2×D37—21no—
113C2×D37—21no—
114C2×D37—24no—
115C2×D37—24no—
116C2×D37—41no—
117C2×D37—41no—
118C2×D37—41no—
119C2×D37—82no—
120C2×D37—82no—
121C2×D37#10212yescomplemented
122C2×D37#12112yes—
123C2×D37C2×D811yescharacteristic
124C2×D37C2×SD1611yescharacteristic
125C2×D37#13512yes—
126#3866—82no—
127C4×C37—21no—
128C4×C37—41no—
129C4×C37C4×D412yes—
130Dic37—21no—
131Dic37—41no—
132Dic37#12011yescharacteristic
133Dic37#12311yescharacteristic
134#1893—371nomaximal, Sylow
135C2×C37—22no—
136C2×C37—81no—
137C2×C37#38611yescharacteristic
138C2×C37C2×#10211yescharacteristic
139C2×C37#41611yescharacteristic
140D37—22no—
141D37—81no—
142D37#46512yes—
143D37#46612yes—
144C23×C8—371no—
145C2×#121—371no—
146C2×#102—372no—
147#380—371no—
148#340—372no—
149C37#189311yescharacteristic, complemented, Sylow
150C22×D4—371no—
151C22×D4—741no—
152C23×C4—371no—
153C22×C8—372no—
154C22×C8—744no—
155C22×C8—741no—
156C22×C8—741no—
157#121—371no—
158#121—371no—
159#121—371no—
160#121—741no—
161#121—741no—
162#121#386611yescharacteristic, complemented
163C2×C4⋊C4—371no—
164C2×C4⋊C4—372no—
165C2×C22⋊C4—741no—
166C2×C22⋊C4—741no—
167#102—744no—
168#95—741no—
169C24—371no—
170C24—741no—
171C2×D4—21no—
172C2×D4—371no—
173C2×D4—741no—
174C2×D4—742no—
175C2×D4—742no—
176C2×D4—741no—
177C2×D4—741no—
178C2×D4—741no—
179C2×D4—1482no—
180C2×D4—1482no—
181C2×D4C2×#386611yescharacteristic
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—371no—
185C22×C4—371no—
186C22×C4—371no—
187C22×C4—742no—
188C22×C4—742no—
189C22×C4—741no—
190C22×C4—742no—
191C22×C4C2×#386611yescharacteristic
192C2×C8—374no—
193C2×C8—742no—
194C2×C8—742no—
195C2×C8—744no—
196C2×C8—744no—
197C4⋊C4—371no—
198C4⋊C4—741no—
199C4⋊C4—742no—
200C4⋊C4—742no—
201C4⋊C4C2×#386611yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—741no—
204C22⋊C4—741no—
205C22⋊C4—741no—
206C22⋊C4—1482no—
207C23—21no—
208C23—371no—
209C23—372no—
210C23—372no—
211C23—371no—
212C23—742no—
213C23—742no—
214C23—741no—
215C23—1482no—
216C23—1481no—
217C23—1481no—
218C23—1482no—
219C23C22⋊#386611yescharacteristic
220D4—22no—
221D4—42no—
222D4—742no—
223D4—1482no—
224D4—1481no—
225D4—1481no—
226D4—1482no—
227D4—1482no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—371no—
231C2×C4—372no—
232C2×C4—372no—
233C2×C4—371no—
234C2×C4—741no—
235C2×C4—741no—
236C2×C4—742no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—742no—
240C2×C4—741no—
241C2×C4—1481no—
242C2×C4—1481no—
243C2×C4—1482no—
244C2×C4—1482no—
245C2×C4—1482no—
246C2×C4C22⋊#386611yescharacteristic
247C2×C4C22×#386611yescharacteristic
248C8—744no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—372no—
255C22—371no—
256C22—371no—
257C22—372no—
258C22—372no—
259C22—2962no—
260C22—2962no—
261C22—744no—
262C22—744no—
263C22—741no—
264C22—741no—
265C22—1481no—
266C22—1481no—
267C22—1481no—
268C22#1192459812yescomplemented
269C22C2×C22⋊#386611yescharacteristic
270C4—21no—
271C4—41no—
272C4—371no—
273C4—371no—
274C4—2962no—
275C4—741no—
276C4—1481no—
277C4D4×#386612yes—
278C2—22no—
279C2—81no—
280C2—372no—
281C2—372no—
282C2—2961no—
283C2—742no—
284C2#1455848111yescharacteristic
285C2C2×#1192459811yescharacteristic
286C2#1455852311yescharacteristic
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#1893
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. C22×D37⋊C8C2semidirect
2. C2×#11924598C2semidirect
3. #14558475C2semidirect
4. #14558406C2semidirect
17. #11924511C4semidirect
18. #11924510C4semidirect
21. #11924507C4semidirect
24. #121×C37C4semidirect
55. D37⋊C8D4semidirect
110. C22×C37#102semidirect
121. C2×D37#102semidirect
149. C37#1893semidirect
162. #121#3866semidirect
268. C22#11924598semidirect

Maximal subgroups

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

subgroupindex
C22×D37⋊C82
C2×#119245982
#145584752
#145584062
#121×D372
#189337