Finite Group Databasebeta

← #18003960

Subgroups — #18003960

Order 4736.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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
1#14558331C212yesmaximal, complemented
2#14558107C211yesmaximal, characteristic, complemented
3#14557716C214yesmaximal, complemented
4#14557706C214yesmaximal, complemented
5#14557550C212yesmaximal, complemented
6C2×#11924455C211yesmaximal, characteristic, complemented
7C2×2−1+4×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—22no—
10#11924566C2214yescomplemented
11#11924562—22no—
12#11924561C2214yescomplemented
13#11924556—24no—
14C2×#10596934C2212yes—
15#11924534C2212yescomplemented
16#11924525C2212yescomplemented
17#11924519—22no—
18#11924512—22no—
19#11924495C2211yescharacteristic
20#11924463C2218yescomplemented
21#11924455C2214yescomplemented
222−1+4×C37—24no—
232−1+4×C37—22no—
242−1+4×C37C2214yes—
25C2×#41×C37—22no—
26C2×#41×C37—22no—
27C2×#41×C37C2212yes—
28C22×Q8×C37—22no—
29C22×Q8×C37C2211yescharacteristic
30#41×C37—28no—
31#41×C37—28no—
32#41×C37—28no—
33#41×C37—28no—
34#41×C37—22no—
35#41×C37—22no—
36#41×C37D414yes—
37#41×C37C2314yes—
38C2×Q8×C37—22no—
39C2×Q8×C37—28no—
40C2×Q8×C37—28no—
41C2×Q8×C37—22no—
42C2×Q8×C37—22no—
43C2×Q8×C37D412yes—
44C2×Q8×C37D412yes—
45C2×Q8×C37C2312yes—
46C2×D4×C37—22no—
47C2×D4×C37—22no—
48C2×D4×C37D412yes—
49C22×C4×C37—24no—
50C22×C4×C37—22no—
51C22×C4×C37D412yes—
52C22×C4×C37C2311yescharacteristic
53C2×C22⋊D37—21no—
54#10596962—22no—
55#10596962—22no—
56C2×D148C2311yescharacteristic
57C2×C4×D37—21no—
58C2×Dic74C2311yescharacteristic
59C22⋊Dic37—21no—
60#10596942—24no—
61#10596941—24no—
62#10596940—24no—
63#10596939—24no—
64#10596938—24no—
65C4⋊Dic37—21no—
66#10596936—24no—
67C4×Dic37C2312yes—
68#10596934—22no—
69#10596934C2314yes—
70C2×#64436—22no—
71C23×C37—22no—
72C23×C37C2×D411yescharacteristic
73C22×D37—21no—
74Q8×C37—28no—
75Q8×C37—22no—
76Q8×C37—24no—
77Q8×C37—24no—
78Q8×C37C2×D414yes—
79D4×C37—28no—
80D4×C37—24no—
81D4×C37—24no—
82D4×C37—22no—
83D4×C37C2×D414yes—
84C2×C4×C37—216no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37—24no—
89C2×C4×C37—24no—
90C2×C4×C37C2×D414yes—
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D412yes—
93C2×C4×C37C2×D412yes—
94C2×C4×C37C2411yescharacteristic
95C22⋊D37—41no—
96C22⋊D37—41no—
97C2×Dic37—22no—
98C2×Dic37—21no—
99D148—22no—
100C4×D37—42no—
101Dic74—22no—
102#64436—24no—
103C22×C37—24no—
104C22×C37—41no—
105C22×C37—44no—
106C22×C37#12011yescharacteristic
107C22×C37#12011yescharacteristic
108C22×C37C22×D411yescharacteristic
109C2×D37—42no—
110C2×D37—41no—
111C4×C37—24no—
112C4×C37—24no—
113C4×C37#12012yes—
114C4×C37C22×D412yes—
115Dic37—42no—
116Dic37—41no—
117#3020—371nomaximal, Sylow
118C2×C37—21no—
119C2×C37—21no—
120C2×C37—21no—
121C2×C37—44no—
122C2×C37C2×#12011yescharacteristic
123D37—81no—
124C2×2−1+4D3711yescharacteristic, complemented
125#575—372no—
126#536—371no—
127#456—374no—
128#454—374no—
129#421—372no—
130C2×#101—371no—
131C37#302011yescharacteristic, complemented, Sylow
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D3714yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—371no—
138C2×#41C2×D3712yes—
139C22×Q8—22no—
140C22×Q8C2×D3711yescharacteristic
141#137—374no—
142#137—742no—
143AGL(1,ℤ/8)—374no—
144AGL(1,ℤ/8)—742no—
145#135—744no—
146C2×M16—372no—
147C4⋊Q8—372no—
148#124—372no—
149#123—742no—
150C22⋊Q8—742no—
151#117—371no—
152#104—378no—
153#101—374no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—742no—
161#41—742no—
162#41C22⋊D3714yes—
163#41C22×D3714yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—371no—
170C2×Q8C22⋊D3712yes—
171C2×Q8C22⋊D3712yes—
172C2×Q8C22×D3712yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—371no—
176C2×D4—741no—
177C2×D4C22⋊D3712yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—741no—
181C22×C4C22⋊D3712yes—
182C22×C4C22×D3711yescharacteristic
183Q16—744no—
184SD16—744no—
185SD16—744no—
186D8—744no—
187M16—374no—
188M16—742no—
189C2×C8—742no—
190C4⋊C4—744no—
191C4⋊C4—741no—
192C22⋊C4—741no—
193C22⋊C4—744no—
194C42—372no—
195C23—22no—
196C23—741no—
197C23C2×C22⋊D3711yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—742no—
203Q8C2×C22⋊D3714yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—742no—
209D4—1481no—
210D4—1481no—
211D4C2×C22⋊D3714yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—742no—
219C2×C4—741no—
220C2×C4—1482no—
221C2×C4C2×C22⋊D3714yes—
222C2×C4C2×C22⋊D3711yescharacteristic
223C2×C4C2×C22⋊D3712yes—
224C2×C4C2×C22⋊D3712yes—
225C2×C4C23×D3711yescharacteristic
226C8—744no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—1482no—
231C22—1481no—
232C22#1192450511yescharacteristic
233C22#1192450511yescharacteristic
234C22C22×C22⋊D3711yescharacteristic
235C4—24no—
236C4—24no—
237C4—1482no—
238C4—1481no—
239C4#1192450512yes—
240C4C22×C22⋊D3712yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—2961no—
246C2C2×#1192450511yescharacteristic
subgroupG/H
centerC2C2×#11924505
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×2−1+4×C37C2
socleC2×C37C2×#120
hypercenterC2×2−1+4D37
hypocenterC37#3020
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. #14558107C2semidirect
3. #14557716C2semidirect
4. #14557706C2semidirect
5. #14557550C2semidirect
6. C2×#11924455C2semidirect
7. C2×2−1+4×C37C2semidirect
10. #11924566C22semidirect
12. #11924561C22semidirect
15. #11924534C22semidirect
16. #11924525C22semidirect
20. #11924463C22semidirect
21. #11924455C22semidirect
124. C2×2−1+4D37semidirect
131. C37#3020semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145581072
#145577162
#145577062
#145575502
C2×#119244552
C2×2−1+4×C372
#302037