Finite Group Databasebeta

← #22592616

Subgroups — #22592616

Order 9088.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14556087C211yesmaximal, characteristic, complemented
2C22×(C2×D71)⋊C4C211yesmaximal, characteristic
3#17985936C212yesmaximal, complemented
4#17985926C212yesmaximal, complemented
5#17985891C214yesmaximal, complemented
6#17985874C212yesmaximal, complemented
7#17985854C212yesmaximal
8#381×C71C211yesmaximal, characteristic, complemented
9C24×D71C2211yescharacteristic
10C23×Dic71C2211yescharacteristic
11#14556087—24no—
12C2×C4⋊Dic71C2211yescharacteristic, complemented
13C2×C4⋊Dic71C2211yescharacteristic, complemented
14C2×C4⋊Dic71C2214yescomplemented
15C2×C22⋊Dic71C2212yes—
16C2×(C2×D71)⋊C4—24no—
17C2×(C2×D71)⋊C4C2214yes—
18C2×(C2×D71)⋊C4C2212yes—
19C2×(C2×D71)⋊C4C2212yes—
20C2×(C2×D71)⋊C4C2214yes—
21C2×C4×Dic71C2212yescomplemented
22C71⋊#95C2214yescomplemented
23C23×C4×C71C2211yescharacteristic
24C2×C22⋊C4×C71C2212yes—
25#95×C71C2212yescomplemented
26#95×C71C2212yescomplemented
27C23×D71—22no—
28C23×D71—24no—
29C23×D71—24no—
30C23×D71—42no—
31C23×D71C2312yes—
32C22×Dic71—22no—
33C22×Dic71—42no—
34C22×Dic71C2312yes—
35C22×Dic71C2312yes—
36C22×Dic71C2312yes—
37C4⋊Dic71—22no—
38C4⋊Dic71—22no—
39C4⋊Dic71—44no—
40C22⋊Dic71—24no—
41(C2×D71)⋊C4—28no—
42(C2×D71)⋊C4—24no—
43(C2×D71)⋊C4—24no—
44(C2×D71)⋊C4—44no—
45C4×Dic71—24no—
46C24×C71C2311yescharacteristic
47C22×C4×C71—24no—
48C22×C4×C71D414yes—
49C22×C4×C71C2314yes—
50C22×C4×C71C2311yescharacteristic
51C22×C4×C71C2311yescharacteristic
52C22⋊C4×C71—24no—
53C23×C71—22no—
54C23×C71—22no—
55C23×C71C2×D412yes—
56C23×C71#4114yes—
57C23×C71C2411yescharacteristic
58C22×D71—28no—
59C22×D71—22no—
60C22×D71—22no—
61C22×D71—24no—
62C22×D71—24no—
63C22×D71—416no—
64C22×D71—44no—
65C22×D71—44no—
66C22×D71#4114yes—
67C2×C4×C71—28no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—24no—
71C2×C4×C71—24no—
72C2×C4×C71—24no—
73C2×C4×C71C2×D412yes—
74C2×C4×C71C2×D412yes—
75C2×Dic71—22no—
76C2×Dic71—22no—
77C2×Dic71—22no—
78C2×Dic71—24no—
79C2×Dic71—24no—
80C2×Dic71—24no—
81C2×Dic71—44no—
82C22×C71—22no—
83C22×C71—22no—
84C22×C71—28no—
85C22×C71#12314yes—
86C22×C71C22×D411yescharacteristic
87C22×C71C2×#4112yes—
88C22×C71C2×#4112yes—
89C22×C71H(5,𝔽2)12yes—
90C2×D71—24no—
91C2×D71—28no—
92C2×D71—416no—
93C2×D71—42no—
94C2×D71—42no—
95C2×D71—44no—
96C4×C71—22no—
97C4×C71—22no—
98C4×C71—44no—
99Dic71—42no—
100Dic71—42no—
101Dic71—42no—
102C2×C71—24no—
103C2×C71C2×#12311yescharacteristic
104C2×C71#52511yescharacteristic
105C2×C71#53511yescharacteristic
106C2×C71#55114yes—
107D71—44no—
108#2482—711nomaximal, Sylow
109C71#248211yescharacteristic, complemented, Sylow
110C2×#117—711no—
111C22×C22⋊C4—711no—
112#399—712no—
113#397—712no—
114#388—714no—
115#385—712no—
116#381D7111yescharacteristic, complemented
117#379—712no—
118C25—711no—
119C23×C4—711no—
120C23×C4C2×D7111yescharacteristic
121#117—1424no—
122C2×C4⋊C4—714no—
123C2×C4⋊C4—711no—
124C2×C4⋊C4—711no—
125C2×C22⋊C4—714no—
126C2×C22⋊C4—712no—
127C2×C22⋊C4—712no—
128C2×C22⋊C4—712no—
129C2×C22⋊C4—714no—
130C2×C22⋊C4—1424no—
131C2×C22⋊C4C2×D7112yes—
132C2×C42—712no—
133#95—714no—
134#95C2×D7112yescomplemented
135#95C2×D7112yescomplemented
136C24—2842no—
137C24—712no—
138C24—1424no—
139C24—1424no—
140C24—1422no—
141C24C22×D7111yescharacteristic
142C22×C4—24no—
143C22×C4—2842no—
144C22×C4—712no—
145C22×C4—712no—
146C22×C4—712no—
147C22×C4—1422no—
148C22×C4D28414yes—
149C22×C4C22×D7114yes—
150C22×C4C22×D7111yescharacteristic
151C22×C4C22×D7111yescharacteristic
152C4⋊C4—2844no—
153C4⋊C4—1422no—
154C4⋊C4—1422no—
155C22⋊C4—24no—
156C22⋊C4—2844no—
157C22⋊C4—1428no—
158C22⋊C4—1424no—
159C22⋊C4—1424no—
160C22⋊C4—1424no—
161C42—1424no—
162C23—22no—
163C23—22no—
164C23—2844no—
165C23—28416no—
166C23—2844no—
167C23—714no—
168C23—1428no—
169C23—1422no—
170C23—1422no—
171C23—1424no—
172C23—1424no—
173C23C2×D28412yes—
174C23#1176586414yes—
175C23C23×D7111yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—28no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—2844no—
183C2×C4—1422no—
184C2×C4—1422no—
185C2×C4—1422no—
186C2×C4—1424no—
187C2×C4—1424no—
188C2×C4—1424no—
189C2×C4C2×D28412yes—
190C2×C4C2×D28412yes—
191C22—22no—
192C22—28no—
193C22—22no—
194C22—28416no—
195C22—2842no—
196C22—2844no—
197C22—2842no—
198C22—1428no—
199C22—1424no—
200C22#1455611214yes—
201C22C22×D28411yescharacteristic
202C22#41×D7112yes—
203C22C2×#1176586412yes—
204C22#1455617412yes—
205C4—22no—
206C4—22no—
207C4—44no—
208C4—2842no—
209C4—2842no—
210C4—2842no—
211C2—24no—
212C2—2844no—
213C2C2×#1455611211yescharacteristic
214C2#1798651111yescharacteristic
215C2#1798656811yescharacteristic
216C2#1798667214yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#381×C71C2
hypercenter#381D71
hypocenterC71#2482
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#14556087C2semidirect
3. #17985936C2semidirect
4. #17985926C2semidirect
5. #17985891C2semidirect
6. #17985874C2semidirect
8. #381×C71C2semidirect
12. C2×C4⋊Dic71C22semidirect
13. C2×C4⋊Dic71C22semidirect
14. C2×C4⋊Dic71C22semidirect
21. C2×C4×Dic71C22semidirect
22. C71⋊#95C22semidirect
25. #95×C71C22semidirect
26. #95×C71C22semidirect
109. C71#2482semidirect
116. #381D71semidirect
134. #95C2×D71semidirect
135. #95C2×D71semidirect