Finite Group Databasebeta

← #18010737

Subgroups — #18010737

Order 4736.

408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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×#11924595C212yesmaximal, complemented
2C2×#11924594C212yesmaximal, complemented
3#14558475C211yesmaximal, characteristic, complemented
4C4×C22⋊#3866C211yesmaximal, characteristic, complemented
5C2×#11924509C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C2×C22⋊#3866C2212yes—
8C2×C22⋊#3866C2212yes—
9C2×C4×#3866—21no—
10#11924595—24no—
11#11924594—24no—
12(C2×#3866)⋊C4—21no—
13(C2×#3866)⋊C4—21no—
14C22×D148C2211yescharacteristic
15C22×C22⋊D37C411yescharacteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18#11924509—21no—
19#11924509—21no—
20#11924509—21no—
21#11924509—21no—
22C2×#10596936C411yescharacteristic, complemented
23C2×#10596938C411yescharacteristic, complemented
24C2×C22⋊C4×C37C411yescharacteristic, complemented
25C24×C37C2×C411yescharacteristic
26C23×D37C2×C411yescharacteristic
27C23×D37C2311yescharacteristic
28C22×#3866—22no—
29C22×#3866—22no—
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37C2×C411yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—22no—
35C2×C22⋊D37—22no—
36C2×C22⋊D37—21no—
37C2×C22⋊D37—21no—
38C2×C22⋊D37—42no—
39C22×Dic37C2×C411yescharacteristic
40C22×Dic37C2×C411yescharacteristic
41C2×D148—21no—
42C2×D148—21no—
43C2×D148—22no—
44C2×D148—22no—
45C2×C4×D37—42no—
46C2×C4×D37D411yescharacteristic
47C2×C4×D37D411yescharacteristic
48C2×C4×D37D411yescharacteristic
49C2×C4×D37D411yescharacteristic
50C22⋊#3866—22no—
51C22⋊#3866—22no—
52C22⋊#3866—22no—
53C22⋊#3866D414yescomplemented
54C4⋊#3866—42no—
55C4×#3866—42no—
56C22⋊C4×C37—21no—
57C22⋊C4×C37—21no—
58#10596938—21no—
59#10596938—21no—
60#10596936—21no—
61#10596936—21no—
62C23×C37—21no—
63C23×C37—22no—
64C23×C37—41no—
65C23×C37—41no—
66C23×C37C22×C411yescharacteristic
67C22×D37—21no—
68C22×D37—22no—
69C22×D37—41no—
70C22×D37—41no—
71C22×D37—41no—
72C22×D37—41no—
73C22×D37C2×D411yescharacteristic
74C22×D37C2×D411yescharacteristic
75C22×D37C2×D412yes—
76C22×D37#4112yes—
77C2×#3866—24no—
78C2×#3866—42no—
79C2×#3866—42no—
80C2×#3866—42no—
81C2×#3866—42no—
82C2×#3866—42no—
83C2×C4×C37—21no—
84C2×C4×C37—22no—
85C2×C4×C37—41no—
86C2×C4×C37C22⋊C411yescharacteristic
87C2×C4×C37C22⋊C411yescharacteristic
88C22⋊D37—42no—
89C22⋊D37—42no—
90C22⋊D37—41no—
91C22⋊D37—41no—
92C22⋊D37—42no—
93C2×Dic37—22no—
94C2×Dic37—21no—
95C2×Dic37—22no—
96C2×Dic37C22⋊C411yescharacteristic
97C2×Dic37C22⋊C411yescharacteristic
98D148—42no—
99D148—41no—
100D148—41no—
101C4×D37—22no—
102C4×D37—22no—
103C4×D37—41no—
104C4×D37—41no—
105C22×C37—21no—
106C22×C37—21no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37—41no—
110C22×C37—82no—
111C22×C37C2×C22⋊C411yescharacteristic
112C22×C37C4×D412yes—
113C2×D37—21no—
114C2×D37—21no—
115C2×D37—21no—
116C2×D37—21no—
117C2×D37—42no—
118C2×D37—42no—
119C2×D37—41no—
120C2×D37—41no—
121C2×D37—41no—
122C2×D37—82no—
123C2×D37#12112yes—
124C2×D37#12411yescharacteristic
125C2×D37#12711yescharacteristic
126#3866—44no—
127#3866—82no—
128C4×C37—21no—
129C4×C37—21no—
130C4×C37—41no—
131Dic37—21no—
132Dic37—41no—
133Dic37#9912yescomplemented
134#1964—371nomaximal, Sylow
135C2×C37—22no—
136C2×C37—81no—
137C2×C37#39011yescharacteristic
138C2×C37C2×#9911yescharacteristic
139C2×C37#41011yescharacteristic
140D37—22no—
141D37—21no—
142D37—21no—
143D37—81no—
144C2×#121—371no—
145C2×#99—372no—
146C2×#99—372no—
147#380—371no—
148C4×C22⋊C4—371no—
149C37#196411yescharacteristic, complemented, Sylow
150C22×D4—371no—
151C22×D4—371no—
152C22×D4—371no—
153C23×C4—371no—
154#121—741no—
155#121—741no—
156#121—741no—
157#121—741no—
158C2×C4⋊C4—371no—
159C2×C4⋊C4—741no—
160C2×C22⋊C4—372no—
161C2×C22⋊C4—371no—
162C2×C22⋊C4—372no—
163C2×C22⋊C4#386611yescharacteristic, complemented
164C2×C42—741no—
165#99—744no—
166#99—744no—
167#95—741no—
168#95—741no—
169C24—371no—
170C24—371no—
171C24C2×#386611yescharacteristic
172C2×D4—742no—
173C2×D4—741no—
174C2×D4—741no—
175C2×D4—742no—
176C2×D4—741no—
177C2×D4—741no—
178C2×D4—742no—
179C2×D4—741no—
180C2×D4—741no—
181C2×D4—742no—
182C2×D4—1482no—
183C22×C4—371no—
184C22×C4—371no—
185C22×C4—371no—
186C22×C4—371no—
187C22×C4—371no—
188C22×C4—371no—
189C22×C4—742no—
190C22×C4—742no—
191C22×C4—1482no—
192C22×C4C2×#386611yescharacteristic
193C22×C4C2×#386611yescharacteristic
194C4⋊C4—741no—
195C4⋊C4—741no—
196C4⋊C4—1482no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—374no—
200C22⋊C4—742no—
201C22⋊C4—741no—
202C22⋊C4—741no—
203C22⋊C4—742no—
204C22⋊C4—742no—
205C42—1482no—
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—371no—
211C23—371no—
212C23—372no—
213C23—372no—
214C23—742no—
215C23—741no—
216C23—1481no—
217C23—1481no—
218C23—1481no—
219C23—1481no—
220C23C22×#386611yescharacteristic
221D4—1482no—
222D4—1481no—
223D4—1481no—
224D4—1482no—
225D4—1482no—
226D4—1482no—
227D4—1481no—
228D4—1481no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—371no—
233C2×C4—371no—
234C2×C4—742no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—744no—
238C2×C4—741no—
239C2×C4—742no—
240C2×C4—1481no—
241C2×C4—1481no—
242C2×C4—1482no—
243C2×C4—1482no—
244C2×C4—1482no—
245C2×C4—1482no—
246C2×C4—1482no—
247C2×C4C22⋊#386611yescharacteristic
248C2×C4C22⋊#386611yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—372no—
256C22—371no—
257C22—371no—
258C22—2962no—
259C22—741no—
260C22—741no—
261C22—741no—
262C22—741no—
263C22—1482no—
264C22—1482no—
265C22—1481no—
266C22—1481no—
267C22—1481no—
268C22C2×C22⋊#386611yescharacteristic
269C22D4×#386612yes—
270C4—21no—
271C4—21no—
272C4—41no—
273C4—372no—
274C4—2962no—
275C4—741no—
276C4—1484no—
277C4—1481no—
278C2—22no—
279C2—81no—
280C2—2961no—
281C2—741no—
282C2—742no—
283C2—741no—
284C2#1455848511yescharacteristic
285C2D37⋊#9911yescharacteristic
286C2#1455851211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924509C2
cosocleC23×D37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1964
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11924595C2semidirect
2. C2×#11924594C2semidirect
3. #14558475C2semidirect
4. C4×C22⋊#3866C2semidirect
15. C22×C22⋊D37C4semidirect
22. C2×#10596936C4semidirect
23. C2×#10596938C4semidirect
24. C2×C22⋊C4×C37C4semidirect
53. C22⋊#3866D4semidirect
133. Dic37#99semidirect
149. C37#1964semidirect
163. C2×C22⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245952
C2×#119245942
#145584752
C4×C22⋊#38662
C2×#119245092
#196437