Finite Group Databasebeta

← #17995795

Subgroups — #17995795

Order 4736.

316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11924516C211yesmaximal, characteristic
2C2×#11924467C211yesmaximal, characteristic, complemented
3C2×#11924461C211yesmaximal, characteristic, complemented
4C2×#11924459C211yesmaximal, characteristic, complemented
5C2×#11924448C211yesmaximal, characteristic
6#14557390C211yesmaximal, characteristic
7C37×#340C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×C4×D37C2211yescharacteristic
10C22×#64436C2211yescharacteristic
11#11924516—22no—
12#11924516—22no—
13C2×C4⋊Dic37—21no—
14C2×C4⋊Dic37C2211yescharacteristic
15C2×#10596938—21no—
16C2×#10596938—21no—
17#11924467—22no—
18#11924461—22no—
19#11924459—22no—
20#11924448—22no—
21#11924443—21no—
22C22×C8×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25C23×D37D411yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37—21no—
28C22×C4×C37C2311yescharacteristic
29C22×Dic37—21no—
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74—21no—
42C2×Dic74—21no—
43C2×Dic74D412yes—
44C2×C8×C37—21no—
45C2×C8×C37—21no—
46C2×C8×C37—21no—
47C4⋊C4×C37—21no—
48C4⋊C4×C37—21no—
49C4⋊C4×C37—21no—
50C4⋊C4×C37D412yes—
51#10596938—24no—
52#10596938—42no—
53C4⋊Dic37—24no—
54C4⋊Dic37—21no—
55C4⋊Dic37—21no—
56C2×#64436—21no—
57C2×#64436—21no—
58C2×#64436D412yes—
59C23×C37C2×D411yescharacteristic
60C22×D37—21no—
61C22×D37—21no—
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—21no—
66C22×D37SD1612yes—
67C2×C4×C37—22no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C2×C4×C37#4111yescharacteristic
78C2×C4×C37#4111yescharacteristic
79C2×Dic37—21no—
80C2×Dic37—22no—
81C2×Dic37—21no—
82C2×Dic37—21no—
83C2×Dic37—41no—
84C2×Dic37—41no—
85C2×Dic37—41no—
86C2×Dic37—41no—
87C2×Dic37—41no—
88C4×D37—41no—
89C4×D37—41no—
90C4×D37—41no—
91C4×D37—41no—
92Dic74—22no—
93Dic74—22no—
94Dic74—41no—
95Dic74—41no—
96C8×C37—41no—
97#64436—22no—
98C22×C37#12011yescharacteristic
99C22×C37#12111yescharacteristic
100C22×C37#12311yescharacteristic
101C22×C37C2×SD1611yescharacteristic
102C22×C37#13511yescharacteristic
103C22×C37#13711yescharacteristic
104C22×C37#13711yescharacteristic
105C2×D37—22no—
106C2×D37—22no—
107C2×D37—22no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—41no—
112C4×C37—42no—
113C4×C37—81no—
114C4×C37#12111yescharacteristic
115C4×C37#12111yescharacteristic
116C4×C37#12311yescharacteristic
117C4×C37#12411yescharacteristic
118Dic37—42no—
119Dic37—41no—
120Dic37—81no—
121#2035—371nomaximal, Sylow
122C2×C37#39411yescharacteristic
123C2×C37#44811yescharacteristic
124C2×C37#45211yescharacteristic
125C2×C37#46511yescharacteristic
126C2×C37#47011yescharacteristic
127C2×C37#48311yescharacteristic
128C2×C37#48511yescharacteristic
129D37—42no—
130C2×C22⋊Q8—371no—
131C2×#106—371no—
132C2×#103—371no—
133C2×#103—371no—
134C2×C22⋊C8—371no—
135#380—371no—
136#340D3711yescharacteristic, complemented
137C37#203511yescharacteristic, complemented, Sylow
138C22×Q8—371no—
139C23×C4—371no—
140C22×C8—371no—
141C22×C8C2×D3711yescharacteristic
142C22⋊Q8—742no—
143C22⋊Q8—742no—
144C2×C4⋊C4—371no—
145C2×C4⋊C4—741no—
146C2×C4⋊C4C2×D3711yescharacteristic
147C2×C4⋊C4C2×D3711yescharacteristic
148C2×C22⋊C4—741no—
149C2×C22⋊C4—741no—
150#106—742no—
151#103—742no—
152#103—742no—
153C22⋊C8—742no—
154#95—741no—
155C24—371no—
156C2×Q8—372no—
157C2×Q8—741no—
158C2×Q8—741no—
159C2×Q8—741no—
160C2×Q8—741no—
161C2×Q8—741no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—371no—
165C22×C4—741no—
166C22×C4—741no—
167C22×C4—741no—
168C22×C4—741no—
169C22×C4—741no—
170C22×C4—741no—
171C22×C4—741no—
172C22×C4—741no—
173C22×C4C22×D3711yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—372no—
178C2×C8—741no—
179C2×C8—741no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—744no—
184C4⋊C4—741no—
185C4⋊C4—741no—
186C4⋊C4D14812yes—
187C22⋊C4—744no—
188C22⋊C4—1482no—
189C23—372no—
190C23—741no—
191C23—741no—
192C23—741no—
193C23—741no—
194C23—741no—
195C23—741no—
196C23D4×D3711yescharacteristic
197Q8—742no—
198Q8—742no—
199Q8—1481no—
200Q8—1481no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—1481no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4—1481no—
217C2×C4—1481no—
218C2×C4—1481no—
219C2×C4—1481no—
220C2×C4C2×D14811yescharacteristic
221C2×C4#1059696211yescharacteristic
222C2×C4#1059696211yescharacteristic
223C2×C4D4×D3711yescharacteristic
224C2×C4D4×D3711yescharacteristic
225C2×C4#1059696611yescharacteristic
226C8—41no—
227C8—742no—
228C22—742no—
229C22—742no—
230C22—742no—
231C22—1481no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22#1192450611yescharacteristic
236C22#1192450911yescharacteristic
237C22#1192452111yescharacteristic
238C22SD16×D3711yescharacteristic
239C22#1192455511yescharacteristic
240C22#1192456511yescharacteristic
241C22#1192456811yescharacteristic
242C4—42no—
243C4—81no—
244C4—2961no—
245C4—1481no—
246C4—1482no—
247C4#1192450911yescharacteristic
248C4#1192451111yescharacteristic
249C4#1192452111yescharacteristic
250C4#1192452411yescharacteristic
251C2—1482no—
252C2#1455745111yescharacteristic
253C2#1455767311yescharacteristic
254C2#1455769611yescharacteristic
255C2#1455776111yescharacteristic
256C2#1455779011yescharacteristic
257C2#1455786511yescharacteristic
258C2#1455787611yescharacteristic
subgroupG/H
centerC23D4×D37
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#340C2
socleC23×C37C2×D4
prime radicalC23×D37D4
hypercenter#340D37
hypocenterC37#2035
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#11924467C2semidirect
3. C2×#11924461C2semidirect
4. C2×#11924459C2semidirect
7. C37×#340C2semidirect
136. #340D37semidirect
137. C37#2035semidirect

Maximal subgroups

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

subgroupindex
C2×#119245162
C2×#119244672
C2×#119244612
C2×#119244592
C2×#119244482
#145573902
C37×#3402
#203537