Finite Group Databasebeta

← #18005064

Subgroups — #18005064

Order 4736.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924566C212yesmaximal, complemented
2C2×#11924561C212yesmaximal, complemented
3C2×#11924524C211yesmaximal, characteristic, complemented
4#14557925C212yesmaximal, complemented
5#14557920C212yesmaximal, complemented
6#14557915C214yesmaximal, complemented
7C4×#10596934C211yesmaximal, characteristic, complemented
8C37×#532C211yesmaximal, characteristic, complemented
9C22×Dic74C2211yescharacteristic
10C22×D148C2211yescharacteristic
11#11924566—28no—
12#11924561—28no—
13C2×#10596942C2214yescomplemented
14C2×#10596940C2214yescomplemented
15C2×#10596941C2214yes—
16C2×#10596939C2214yes—
17C2×#10596934C2212yes—
18#11924524—22no—
19#11924524C2212yes—
20#11924524C2212yes—
21C2×#10596938—22no—
22#11924447C2212yescomplemented
23C4×#64436C2212yescomplemented
24C2×#41×C37C2212yes—
25C4⋊Q8×C37C2211yescharacteristic, complemented
26#127×C37C2211yescharacteristic, complemented
27#124×C37C2212yescomplemented
28#121×C37—22no—
29C4×D4×C37—22no—
30C2×C42×C37C2211yescharacteristic
31C23×D37—21no—
32#41×C37—24no—
33#41×C37—24no—
34C2×Q8×C37C2312yes—
35C2×D4×C37—22no—
36C2×D4×C37—22no—
37C2×D4×C37C2312yes—
38C22×C4×C37—22no—
39C22×C4×C37D412yes—
40C22×C4×C37C2311yescharacteristic
41C22×Dic37—21no—
42C2×D148—24no—
43C2×D148—21no—
44C2×D148C2312yes—
45C2×Dic74—24no—
46C2×Dic74—21no—
47C2×Dic74C2312yes—
48C4⋊C4×C37—22no—
49C22⋊C4×C37—24no—
50C42×C37D412yes—
51C42×C37C2311yescharacteristic
52C42×C37C2311yescharacteristic
53#10596942—28no—
54#10596941—28no—
55#10596940—28no—
56#10596939—28no—
57#10596938—24no—
58#10596938—24no—
59#10596934D418yescomplemented
60C2×#64436C2314yes—
61C23×C37—22no—
62C23×C37C2×D411yescharacteristic
63C22×D37—22no—
64C22×D37—44no—
65C22×D37—42no—
66Q8×C37—22no—
67Q8×C37—22no—
68D4×C37—22no—
69D4×C37—22no—
70D4×C37—44no—
71D4×C37—44no—
72C2×C4×C37—22no—
73C2×C4×C37—42no—
74C2×C4×C37—44no—
75C2×C4×C37C2×D414yes—
76C2×C4×C37C2×D412yes—
77C2×C4×C37C2×D412yes—
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2411yescharacteristic
80C2×Dic37—22no—
81C2×Dic37—42no—
82D148—24no—
83D148—42no—
84Dic74—24no—
85Dic74—42no—
86#64436C2×D418yes—
87C22×C37—22no—
88C22×C37—42no—
89C22×C37—44no—
90C22×C37#12712yes—
91C22×C37C22×D411yescharacteristic
92C2×D37—42no—
93C2×D37—44no—
94C2×D37—84no—
95C4×C37—22no—
96C4×C37—22no—
97C4×C37—42no—
98C4×C37#12712yes—
99C4×C37C22×D412yes—
100Dic37—42no—
101#3153—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37—82no—
104C2×C37C2×#12711yescharacteristic
105C2×C37#57512yes—
106D37—82no—
107C2×#137—372no—
108C2×AGL(1,ℤ/8)—372no—
109#532D3711yescharacteristic, complemented
110C2×#124—371no—
111#497—372no—
112#496—372no—
113#495—374no—
114C4×M16—371no—
115C37#315311yescharacteristic, complemented, Sylow
116C2×#41C2×D3712yes—
117C22×Q8—371no—
118C22×D4—371no—
119#137—748no—
120AGL(1,ℤ/8)—748no—
121C2×Q16—374no—
122C2×SD16—374no—
123C2×SD16—374no—
124C2×D8—374no—
125C2×M16—372no—
126C4⋊Q8C2×D3711yescharacteristic, complemented
127#127C2×D3711yescharacteristic, complemented
128#124—372no—
129#124—372no—
130#124—742no—
131#124C2×D3712yescomplemented
132#121—22no—
133C4×D4—22no—
134C2×C22⋊C4—742no—
135C2×C42C2×D3711yescharacteristic
136#97—372no—
137C4×C8—372no—
138C24—741no—
139#41—24no—
140#41—24no—
141C2×Q8—372no—
142C2×Q8—741no—
143C2×Q8—744no—
144C2×Q8C22×D3712yes—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—372no—
148C2×D4—744no—
149C2×D4—741no—
150C2×D4C22×D3712yes—
151C22×C4—22no—
152C22×C4—741no—
153C22×C4C22⋊D3712yes—
154C22×C4C22×D3711yescharacteristic
155Q16—748no—
156SD16—748no—
157SD16—748no—
158D8—748no—
159M16—378no—
160C2×C8—374no—
161C4⋊C4—22no—
162C22⋊C4—24no—
163C22⋊C4—744no—
164C22⋊C4—744no—
165C42C22⋊D3712yes—
166C42C22×D3711yescharacteristic
167C42C22×D3711yescharacteristic
168C23—22no—
169C23—742no—
170C23—1484no—
171C23—1482no—
172C23C2×C22⋊D3711yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—744no—
176Q8—1482no—
177D4—22no—
178D4—22no—
179D4—44no—
180D4—44no—
181D4—744no—
182D4—1482no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—44no—
186C2×C4—742no—
187C2×C4—1482no—
188C2×C4D4×D3714yes—
189C2×C4C2×C22⋊D3712yes—
190C2×C4C2×C22⋊D3712yes—
191C2×C4C2×C22⋊D3711yescharacteristic
192C2×C4C23×D3711yescharacteristic
193C8—378no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—2964no—
198C22—1482no—
199C22—1484no—
200C22#1192453212yes—
201C22C22×C22⋊D3711yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—1482no—
206C4#1192453212yes—
207C4C2×D4×D3712yes—
208C2—22no—
209C2—82no—
210C2—2962no—
211C2C2×#1192453211yescharacteristic
212C2#1455833112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#532C2
socleC22×C37C22×D4
hypercenter#532D37
hypocenterC37#3153
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#11924566C2semidirect
2. C2×#11924561C2semidirect
3. C2×#11924524C2semidirect
4. #14557925C2semidirect
5. #14557920C2semidirect
6. #14557915C2semidirect
7. C4×#10596934C2semidirect
8. C37×#532C2semidirect
13. C2×#10596942C22semidirect
14. C2×#10596940C22semidirect
22. #11924447C22semidirect
23. C4×#64436C22semidirect
25. C4⋊Q8×C37C22semidirect
26. #127×C37C22semidirect
27. #124×C37C22semidirect
59. #10596934D4semidirect
109. #532D37semidirect
115. C37#3153semidirect
126. C4⋊Q8C2×D37semidirect
127. #127C2×D37semidirect
131. #124C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
C2×#119245612
C2×#119245242
#145579252
#145579202
#145579152
C4×#105969342
C37×#5322
#315337