Finite Group Databasebeta

← #22596311

Subgroups — #22596311

Order 9088.

408 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 133 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#17985937C212yesmaximal, complemented
2#17985935C211yesmaximal, characteristic
3#17985929C212yesmaximal, complemented
4#17985898C212yesmaximal, complemented
5#17985896C212yesmaximal, complemented
6#17985893C212yesmaximal
7#17985874C212yesmaximal
8#17985871C211yesmaximal, characteristic
9#399×C71C211yesmaximal, characteristic
10C23×Dic71C2211yescharacteristic
11C2×C4⋊Dic71C2212yes—
12C2×C4⋊Dic71C2212yes—
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4C2212yes—
15C2×Dic71⋊C4C2212yes—
16C2×Dic71⋊C4C2212yes—
17C2×C22⋊Dic71C2212yes—
18C2×C22⋊Dic71C2211yescharacteristic
19C2×C4×Dic71C2212yes—
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—42no—
32C22×Dic71—41no—
33C22×Dic71C2312yes—
34C22×Dic71C2312yes—
35C22×Dic71C2312yes—
36C22×Dic71C2312yes—
37C4⋊Dic71—42no—
38C4⋊Dic71—41no—
39C4⋊Dic71—42no—
40Dic71⋊C4—24no—
41Dic71⋊C4—42no—
42Dic71⋊C4—42no—
43C22⋊Dic71—42no—
44C22⋊Dic71Q814yes—
45C4×Dic71—42no—
46C24×C71C2311yescharacteristic
47C22×C4×C71C2311yescharacteristic
48C22×C4×C71C2312yes—
49C22×C4×C71C2311yescharacteristic
50C22×C4×C71C2312yes—
51C4⋊C4×C71—24no—
52C4⋊C4×C71—41no—
53C22⋊C4×C71—24no—
54C22⋊C4×C71—41no—
55C23×C71—22no—
56C23×C71—21no—
57C23×C71—22no—
58C23×C71—21no—
59C23×C71C2×Q812yes—
60C23×C71C2411yescharacteristic
61C2×C4×C71—22no—
62C2×C4×C71—22no—
63C2×C4×C71—22no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—21no—
67C2×C4×C71—21no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71#4114yes—
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—
83C2×Dic71C2×Q814yes—
84C22×C71—22no—
85C22×C71—24no—
86C22×C71—42no—
87C22×C71—41no—
88C22×C71—41no—
89C22×C71C22×Q811yescharacteristic
90C22×C71C2×#4112yes—
91C22×C71H(5,𝔽2)11yescharacteristic
92C22×C71H(5,𝔽2)12yes—
93C22×C712−1+411yescharacteristic
94C4×C71—24no—
95C4×C71—42no—
96C4×C71—41no—
97C4×C71—41no—
98Dic71—24no—
99Dic71—42no—
100Dic71—42no—
101Dic71—42no—
102C2×C71—42no—
103C2×C71#53912yes—
104C2×C71#54411yescharacteristic
105C2×C71#55412yes—
106C2×C71#55911yescharacteristic
107C2×C71#56011yescharacteristic
108#2807—711nomaximal, Sylow
109C71#280711yescharacteristic, complemented, Sylow
110#400—712no—
111#399—711no—
112#399D7111yescharacteristic
113#398—712no—
114#389—712no—
115#389—712no—
116#388—712no—
117#385—711no—
118#385—712no—
119C23×C4—711no—
120C2×C4⋊C4—712no—
121C2×C4⋊C4—712no—
122C2×C4⋊C4—712no—
123C2×C4⋊C4—711no—
124C2×C4⋊C4—712no—
125C2×C4⋊C4—712no—
126C2×C4⋊C4C2×D7112yes—
127C2×C4⋊C4C2×D7111yescharacteristic
128C2×C22⋊C4—712no—
129C2×C22⋊C4—711no—
130C2×C22⋊C4C2×D7112yes—
131C2×C22⋊C4C2×D7111yescharacteristic
132C2×C42—712no—
133#95—712no—
134#95—712no—
135#95—712no—
136#95—712no—
137#95—712no—
138#95—711no—
139#95C2×D7111yescharacteristic
140C24C22×D7111yescharacteristic
141C22×C4—2841no—
142C22×C4—2842no—
143C22×C4—712no—
144C22×C4—712no—
145C22×C4—712no—
146C22×C4—712no—
147C22×C4C22×D7112yes—
148C22×C4C22×D7111yescharacteristic
149C22×C4C22×D7111yescharacteristic
150C22×C4C22×D7112yes—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—2842no—
154C4⋊C4—2842no—
155C4⋊C4—2842no—
156C4⋊C4—2841no—
157C4⋊C4—2842no—
158C4⋊C4—1424no—
159C22⋊C4—24no—
160C22⋊C4—41no—
161C22⋊C4—2842no—
162C22⋊C4—714no—
163C42—2842no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—21no—
168C23Q8×D7112yes—
169C23C23×D7111yescharacteristic
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2844no—
180C2×C4—714no—
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—1422no—
191C2×C4—1422no—
192C2×C4#1176586414yes—
193C22—22no—
194C22—24no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22C2×Q8×D7111yescharacteristic
199C22C2×#1176586412yes—
200C22#1455617311yescharacteristic
201C22#1455617412yes—
202C22#1455617511yescharacteristic
203C4—24no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—2842no—
208C4—2842no—
209C4—2842no—
210C4—1424no—
211C2—42no—
212C2#1798659312yes—
213C2#1798662811yescharacteristic
214C2#1798670712yes—
215C2#1798673511yescharacteristic
216C2#1798673911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#399×C71C2
hypercenter#399D71
hypocenterC71#2807
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #17985937C2semidirect
3. #17985929C2semidirect
4. #17985898C2semidirect
5. #17985896C2semidirect
109. C71#2807semidirect