Finite Group Databasebeta

← #22595860

Subgroups — #22595860

Order 9088.

392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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#17985938C212yesmaximal, complemented
2#17985937C212yesmaximal, complemented
3#17985924C211yesmaximal, characteristic
4#17985898C212yesmaximal, complemented
5#17985893C212yesmaximal
6#17985886C212yesmaximal, complemented
7#17985874C212yesmaximal
8#17985860C211yesmaximal, characteristic
9#399×C71C211yesmaximal, characteristic
10C23×Dic71C2211yescharacteristic
11C2×C4⋊Dic71C2212yes—
12C2×C4⋊Dic71C2212yes—
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4C2212yes—
15C2×C22⋊Dic71C2212yes—
16C2×C22⋊Dic71C2211yescharacteristic
17C2×C4×Dic71C2212yes—
18C71⋊#95C2212yes—
19C71⋊#95C2212yes—
20C71⋊#95C2212yes—
21C71⋊#95C2212yes—
22C71⋊#95C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2212yes—
25C71⋊#95C2211yescharacteristic
26C2×C4⋊C4×C71C2212yes—
27C2×C4⋊C4×C71C2211yescharacteristic
28C2×C22⋊C4×C71C2212yes—
29C2×C22⋊C4×C71C2211yescharacteristic
30#95×C71C2211yescharacteristic
31C22×Dic71—22no—
32C22×Dic71—41no—
33C22×Dic71—41no—
34C22×Dic71C2312yes—
35C22×Dic71C2312yes—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C4⋊Dic71—42no—
39C4⋊Dic71—41no—
40C4⋊Dic71—42no—
41Dic71⋊C4—24no—
42C22⋊Dic71—24no—
43C22⋊Dic71—41no—
44C4×Dic71—42no—
45C24×C71C2311yescharacteristic
46C22×C4×C71C2311yescharacteristic
47C22×C4×C71C2312yes—
48C22×C4×C71C2311yescharacteristic
49C22×C4×C71C2312yes—
50C4⋊C4×C71—24no—
51C4⋊C4×C71—41no—
52C22⋊C4×C71—24no—
53C22⋊C4×C71—41no—
54C23×C71—22no—
55C23×C71—21no—
56C23×C71—21no—
57C23×C71—22no—
58C23×C71#4112yes—
59C23×C71C2411yescharacteristic
60C2×C4×C71—22no—
61C2×C4×C71—22no—
62C2×C4×C71—22no—
63C2×C4×C71—22no—
64C2×C4×C71—22no—
65C2×C4×C71—21no—
66C2×C4×C71—21no—
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71#4114yes—
70C2×Dic71—22no—
71C2×Dic71—22no—
72C2×Dic71—22no—
73C2×Dic71—22no—
74C2×Dic71—22no—
75C2×Dic71—22no—
76C2×Dic71—22no—
77C2×Dic71—22no—
78C2×Dic71—22no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—44no—
83C22×C71—22no—
84C22×C71—24no—
85C22×C71—42no—
86C22×C71—41no—
87C22×C71—41no—
88C22×C71C2×#4112yes—
89C22×C71C2×#4111yescharacteristic
90C22×C71H(5,𝔽2)11yescharacteristic
91C22×C71H(5,𝔽2)11yescharacteristic
92C22×C712−1+412yes—
93C4×C71—24no—
94C4×C71—42no—
95C4×C71—41no—
96C4×C71—41no—
97Dic71—42no—
98Dic71—42no—
99Dic71—42no—
100Dic71—42no—
101C2×C71—42no—
102C2×C71#53811yescharacteristic
103C2×C71#53912yes—
104C2×C71#55212yes—
105C2×C71#55911yescharacteristic
106C2×C71#56311yescharacteristic
107#2771—711nomaximal, Sylow
108C71#277111yescharacteristic, complemented, Sylow
109#400—712no—
110#400—712no—
111#399D7111yescharacteristic
112#397—711no—
113#389—712no—
114#388—712no—
115#387—712no—
116#385—712no—
117#381—711no—
118C23×C4—711no—
119C2×C4⋊C4—712no—
120C2×C4⋊C4—712no—
121C2×C4⋊C4—711no—
122C2×C4⋊C4—712no—
123C2×C4⋊C4C2×D7112yes—
124C2×C4⋊C4C2×D7111yescharacteristic
125C2×C22⋊C4—711no—
126C2×C22⋊C4—712no—
127C2×C22⋊C4C2×D7112yes—
128C2×C22⋊C4C2×D7111yescharacteristic
129C2×C42—712no—
130#95—712no—
131#95—712no—
132#95—712no—
133#95—712no—
134#95—712no—
135#95—712no—
136#95—712no—
137#95—711no—
138#95C2×D7111yescharacteristic
139C24C22×D7111yescharacteristic
140C22×C4—2841no—
141C22×C4—2841no—
142C22×C4—712no—
143C22×C4—712no—
144C22×C4—712no—
145C22×C4—712no—
146C22×C4—1422no—
147C22×C4C22×D7111yescharacteristic
148C22×C4C22×D7112yes—
149C22×C4C22×D7111yescharacteristic
150C22×C4C22×D7112yes—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—2842no—
154C4⋊C4—2841no—
155C4⋊C4—2842no—
156C4⋊C4—1424no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—2841no—
160C22⋊C4—1424no—
161C42—2842no—
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23#1176586612yes—
167C23C23×D7111yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—2844no—
178C2×C4—1422no—
179C2×C4—1422no—
180C2×C4—1422no—
181C2×C4—1422no—
182C2×C4—1422no—
183C2×C4—1422no—
184C2×C4—1422no—
185C2×C4—1422no—
186C2×C4—1422no—
187C2×C4—1422no—
188C2×C4—1422no—
189C2×C4—1422no—
190C2×C4#1176586414yes—
191C22—22no—
192C22—24no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22C2×#1176586412yes—
197C22C2×#1176586611yescharacteristic
198C22#1455617311yescharacteristic
199C22#1455617411yescharacteristic
200C22#1455617512yes—
201C4—24no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—2842no—
206C4—2842no—
207C4—2842no—
208C4—2842no—
209C2—42no—
210C2#1798658911yescharacteristic
211C2#1798659312yes—
212C2#1798669112yes—
213C2#1798673511yescharacteristic
214C2#1798675211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#399×C71C2
hypercenter#399D71
hypocenterC71#2771
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #17985938C2semidirect
2. #17985937C2semidirect
4. #17985898C2semidirect
6. #17985886C2semidirect
108. C71#2771semidirect