Finite Group Databasebeta

← #17994896

Subgroups — #17994896

Order 4736.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10596934C211yesmaximal, characteristic, complemented
2#14558044C211yesmaximal, characteristic
3C2×#11924464C212yesmaximal, complemented
4#14557293C212yesmaximal, complemented
5C4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7C2×#10596934—21no—
8C2×#10596934—24no—
9C2×#10596934C2212yes—
10C22×#64436—21no—
11#11924519—21no—
12#11924515C411yescharacteristic, complemented
13#11924515C411yescharacteristic, complemented
14#11924510C411yescharacteristic, complemented
15#11924510C411yescharacteristic, complemented
16#11924505—21no—
17C4×C22⋊D37—21no—
18C4×C22⋊D37—21no—
19#11924495C2211yescharacteristic
20#11924464—24no—
21C23×C4×C37C2211yescharacteristic
22C2×C22⋊C4×C37—21no—
23C2×C42×C37C2212yes—
24#95×C37—21no—
25C24×C37D411yescharacteristic
26C22×C4×C37—22no—
27C22×C4×C37—22no—
28C22×C4×C37—22no—
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37D411yescharacteristic
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D411yescharacteristic
34C22×C4×C37C2311yescharacteristic
35C2×C22⋊D37—21no—
36C2×C22⋊D37—21no—
37C2×C22⋊D37—21no—
38#10596962—22no—
39#10596962—22no—
40C2×D148C2×C411yescharacteristic
41C2×C4×D37—21no—
42C2×Dic74C2×C411yescharacteristic
43C22⋊C4×C37—24no—
44C42×C37—22no—
45C42×C37—22no—
46C22⋊Dic37—21no—
47C22⋊Dic37—21no—
48C22⋊Dic37—21no—
49#10596938—21no—
50#10596938—21no—
51C4⋊Dic37C2×C411yescharacteristic
52C4⋊Dic37C2×C411yescharacteristic
53#10596936—21no—
54#10596936—21no—
55C4×Dic37—21no—
56#10596934—24no—
57#10596934—22no—
58#10596934D414yescomplemented
59C2×#64436—24no—
60C2×#64436—22no—
61C23×C37—22no—
62C23×C37—22no—
63C23×C37—41no—
64C23×C37C22⋊C411yescharacteristic
65C23×C37C22⋊C411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—21no—
75C2×C4×C37—24no—
76C2×C4×C37—42no—
77C2×C4×C37—42no—
78C2×C4×C37C22⋊C411yescharacteristic
79C2×C4×C37C22⋊C411yescharacteristic
80C2×C4×C37C22×C411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D412yes—
83C2×C4×C37#4112yes—
84C22⋊D37—42no—
85C22⋊D37—42no—
86C22⋊D37—42no—
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—21no—
90D148—22no—
91C4×D37—41no—
92C4×D37—41no—
93Dic74—22no—
94#64436—24no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37—21no—
99C22×C37—21no—
100C22×C37—21no—
101C22×C37—21no—
102C22×C37—44no—
103C22×C37#10412yescomplemented
104C22×C37C2×C22⋊C411yescharacteristic
105C22×C37#12112yes—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—41no—
109C4×C37—21no—
110C4×C37—21no—
111C4×C37—44no—
112C4×C37C4×D412yes—
113C4×C37#12011yescharacteristic
114C4×C37#12311yescharacteristic
115Dic37—41no—
116Dic37—41no—
117Dic37—41no—
118#1871—371nomaximal, Sylow
119C2×C37—22no—
120C2×C37—22no—
121C2×C37—41no—
122C2×C37#38611yescharacteristic
123C2×C37C2×#10411yescharacteristic
124C2×C37#42111yescharacteristic
125D37—81no—
126C22×M16—371no—
127#525—371no—
128C2×#104—372no—
129C4×C22⋊C4D3711yescharacteristic, complemented
130#339—372no—
131C37#187111yescharacteristic, complemented, Sylow
132C2×#41—371no—
133C23×C4C2×D3711yescharacteristic
134C2×M16—372no—
135C2×M16—744no—
136C2×M16—741no—
137C22×C8—741no—
138#123—741no—
139C22⋊Q8—371no—
140C22⋊Q8—371no—
141#121—371no—
142#121—371no—
143#120—741no—
144C4×D4—741no—
145C4×D4—741no—
146#117—371no—
147C2×C22⋊C4—21no—
148C2×C42C2×D3712yes—
149#104—744no—
150#95—21no—
151C24C22⋊D3711yescharacteristic
152#41—742no—
153#41—742no—
154C2×Q8—371no—
155C2×D4—371no—
156C2×D4—741no—
157C2×D4—741no—
158C2×D4—741no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—741no—
163C22×C4C4×D3711yescharacteristic
164C22×C4C4×D3711yescharacteristic
165C22×C4D14811yescharacteristic
166C22×C4D14811yescharacteristic
167C22×C4C22⋊D3711yescharacteristic
168C22×C4C22×D3711yescharacteristic
169M16—374no—
170M16—744no—
171M16—742no—
172C2×C8—744no—
173C2×C8—742no—
174C4⋊C4—371no—
175C4⋊C4—371no—
176C4⋊C4—741no—
177C4⋊C4—741no—
178C22⋊C4—24no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C42—22no—
185C42—22no—
186C42—741no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—741no—
191C23#1059693811yescharacteristic
192C23#1059693811yescharacteristic
193C23C2×C22⋊D3711yescharacteristic
194Q8—742no—
195D4—742no—
196D4—1482no—
197D4—1482no—
198D4—1482no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—741no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4#1059693811yescharacteristic
215C2×C4#1059693811yescharacteristic
216C2×C4C2×C4×D3711yescharacteristic
217C2×C4C2×D14811yescharacteristic
218C2×C4D4×D3712yes—
219C2×C4#1059696412yes—
220C8—744no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—1481no—
230C22—1481no—
231C22—1481no—
232C22#1192446412yescomplemented
233C22C2×#1059693811yescharacteristic
234C22#1192450812yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—1481no—
239C4—1481no—
240C4—1481no—
241C4#1192449612yes—
242C4#1192450611yescharacteristic
243C4#1192452011yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—2961no—
248C2#1455741011yescharacteristic
249C2C2×#1192446411yescharacteristic
250C2#1455755111yescharacteristic
subgroupG/H
centerC2×C4C2×D148
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC4×C22⋊C4×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenterC4×C22⋊C4D37
hypocenterC37#1871
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#10596934C2semidirect
3. C2×#11924464C2semidirect
4. #14557293C2semidirect
5. C4×C22⋊C4×C37C2semidirect
12. #11924515C4semidirect
13. #11924515C4semidirect
14. #11924510C4semidirect
15. #11924510C4semidirect
58. #10596934D4semidirect
103. C22×C37#104semidirect
129. C4×C22⋊C4D37semidirect
131. C37#1871semidirect
232. C22#11924464semidirect

Maximal subgroups

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

subgroupindex
C22×#105969342
#145580442
C2×#119244642
#145572932
C4×C22⋊C4×C372
#187137