Finite Group Databasebeta

← #17995625

Subgroups — #17995625

Order 4736.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11924567C211yesmaximal, characteristic, complemented
2#14558100C211yesmaximal, characteristic
3C2×#11924464C211yesmaximal, characteristic, complemented
4#14557542C211yesmaximal, characteristic, complemented
5C2×#11924453C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#124×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—22no—
10#11924567—22no—
11C2×#10596942—21no—
12C2×#10596941—21no—
13C2×#10596934C2211yescharacteristic
14C2×#10596934C2211yescharacteristic
15#11924532—21no—
16#11924523—21no—
17#11924507—22no—
18#11924505—22no—
19#11924495C2211yescharacteristic
20#11924464—22no—
21#11924460—22no—
22#11924453—22no—
23C22×Q8×C37C2211yescharacteristic
24C22×D4×C37C2211yescharacteristic
25#124×C37—22no—
26#124×C37—22no—
27C2×C22⋊C4×C37—22no—
28C2×C42×C37C2211yescharacteristic
29C24×C37D412yes—
30C2×Q8×C37—21no—
31C2×Q8×C37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37—21no—
34C2×Q8×C37—21no—
35C2×Q8×C37D412yescomplemented
36C2×D4×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37—21no—
39C2×D4×C37—21no—
40C2×D4×C37—21no—
41C2×D4×C37—21no—
42C22×C4×C37—21no—
43C22×C4×C37—21no—
44C22×C4×C37C2311yescharacteristic
45C2×C22⋊D37—21no—
46C2×C22⋊D37—24no—
47#10596962—21no—
48#10596962—21no—
49#10596962—21no—
50#10596962—21no—
51C2×D148D411yescharacteristic
52C2×C4×D37—21no—
53C2×Dic74D411yescharacteristic
54C22⋊C4×C37—28no—
55C42×C37—21no—
56C42×C37D412yescomplemented
57C22⋊Dic37—24no—
58C22⋊Dic37—21no—
59#10596942—24no—
60#10596941—24no—
61C4⋊Dic37D412yes—
62C4×Dic37—21no—
63#10596934—21no—
64#10596934—21no—
65#10596934—21no—
66#10596934D412yescomplemented
67C2×#64436—21no—
68C2×#64436—21no—
69C23×C37—22no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—44no—
73C23×C37C2×D411yescharacteristic
74C22×D37—21no—
75Q8×C37—22no—
76Q8×C37—22no—
77Q8×C37—41no—
78Q8×C37—41no—
79D4×C37—41no—
80D4×C37—41no—
81D4×C37—41no—
82D4×C37—41no—
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—42no—
86C2×C4×C37—41no—
87C2×C4×C37—41no—
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37#4111yescharacteristic
94C22⋊D37—41no—
95C22⋊D37—41no—
96C22⋊D37—84no—
97C2×Dic37—22no—
98C2×Dic37—21no—
99D148—21no—
100D148—21no—
101C4×D37—41no—
102C4×D37—41no—
103Dic74—21no—
104Dic74—21no—
105#64436—22no—
106#64436—41no—
107C22×C37—22no—
108C22×C37—44no—
109C22×C37—42no—
110C22×C37—44no—
111C22×C37—82no—
112C22×C37#12011yescharacteristic
113C22×C37#12011yescharacteristic
114C22×C37#12111yescharacteristic
115C2×D37—41no—
116C2×D37—42no—
117C4×C37—42no—
118C4×C37—42no—
119C4×C37#12011yescharacteristic
120C4×C37#12111yescharacteristic
121C4×C37#12111yescharacteristic
122C4×C37#12711yescharacteristic
123Dic37—41no—
124Dic37—42no—
125#2004—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—82no—
129C2×C37#39211yescharacteristic
130C2×C37#45512yes—
131D37—81no—
132C2×#137—371no—
133#535—371no—
134C2×#124D3711yescharacteristic, complemented
135C2×#104—371no—
136#419—371no—
137C2×#100—371no—
138#339—371no—
139C37#200411yescharacteristic, complemented, Sylow
140C2×#41—371no—
141C22×Q8C2×D3711yescharacteristic
142C22×D4C2×D3711yescharacteristic
143#137—742no—
144#137—742no—
145C2×Q16—741no—
146C2×SD16—741no—
147C2×M16—371no—
148C2×M16—371no—
149#127—741no—
150#124—22no—
151#124—22no—
152#124—741no—
153#121—742no—
154#120—742no—
155#117—371no—
156C2×C22⋊C4—22no—
157C2×C42C2×D3711yescharacteristic
158#104—742no—
159#103—742no—
160#100—742no—
161C24C22⋊D3712yes—
162#41—741no—
163#41—741no—
164#41—741no—
165#41—741no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—371no—
172C2×Q8C22⋊D3712yescomplemented
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—371no—
180C2×D4—744no—
181C2×D4—741no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—741no—
185C22×C4C22×D3711yescharacteristic
186Q16—744no—
187SD16—744no—
188M16—372no—
189M16—741no—
190M16—741no—
191M16—741no—
192C2×C8—741no—
193C2×C8—741no—
194C4⋊C4—372no—
195C22⋊C4—28no—
196C22⋊C4—744no—
197C22⋊C4—741no—
198C42—21no—
199C42—741no—
200C42C22⋊D3712yescomplemented
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—741no—
206C23C2×C22⋊D3711yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—741no—
212Q8—741no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2964no—
218D4—741no—
219D4—741no—
220D4—1481no—
221D4—1481no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—742no—
228C2×C4—741no—
229C2×C4—1481no—
230C2×C4—1481no—
231C2×C4D4×D3711yescharacteristic
232C2×C4D4×D3711yescharacteristic
233C2×C4D4×D3711yescharacteristic
234C2×C4#1059696411yescharacteristic
235C2×C4C2×C22⋊D3711yescharacteristic
236C2×C4C2×C22⋊D3711yescharacteristic
237C8—742no—
238C8—1481no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—1481no—
245C22—1482no—
246C22#1192450411yescharacteristic
247C22#1192450511yescharacteristic
248C22#1192450811yescharacteristic
249C4—42no—
250C4—42no—
251C4—1481no—
252C4—1482no—
253C4#1192450411yescharacteristic
254C4#1192450711yescharacteristic
255C4#1192450811yescharacteristic
256C4#1192453211yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—2961no—
261C2#1455744111yescharacteristic
262C2#1455771012yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#124×C37C2
socleC22×C37#120
prime radical#14558100C2
hypercenterC2×#124D37
hypocenterC37#2004
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
3. C2×#11924464C2semidirect
4. #14557542C2semidirect
5. C2×#11924453C2semidirect
6. #14557293C2semidirect
7. C2×#124×C37C2semidirect
35. C2×Q8×C37D4semidirect
56. C42×C37D4semidirect
66. #10596934D4semidirect
134. C2×#124D37semidirect
139. C37#2004semidirect
172. C2×Q8C22⋊D37semidirect
200. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
#145581002
C2×#119244642
#145575422
C2×#119244532
#145572932
C2×#124×C372
#200437