Finite Group Databasebeta

← #22591508

Subgroups — #22591508

Order 9088.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14556107C211yesmaximal, characteristic
2#17985903C212yesmaximal, complemented
3#17985896C212yesmaximal, complemented
4#17985893C212yesmaximal
5#17985887C212yesmaximal
6#17985886C212yesmaximal, complemented
7#17985884C212yesmaximal, complemented
8#17985859C211yesmaximal, characteristic
9#381×C71C211yesmaximal, characteristic
10C22×Dic142C2211yescharacteristic
11#14556107C418yescomplemented
12C2×C4⋊Dic71C2212yes—
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4C2212yes—
15C2×Dic71⋊C4C2212yes—
16C2×Dic71⋊C4C2212yes—
17C2×C22⋊Dic71C2211yescharacteristic
18C2×C22⋊Dic71C2211yescharacteristic
19C2×C22⋊Dic71C2212yes—
20C2×C4×Dic71C2212yes—
21C2×C4×Dic71C2212yes—
22C71⋊#95C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C23×C4×C71C2211yescharacteristic
28C2×C22⋊C4×C71C2212yes—
29#95×C71C2212yes—
30#95×C71C2211yescharacteristic
31#95×C71C2211yescharacteristic
32C2×Dic142—42no—
33C2×Dic142C2×C414yes—
34C22×Dic71C2312yes—
35C22×Dic71C2312yes—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C4⋊Dic71—42no—
39C4⋊Dic71C2×C414yes—
40Dic71⋊C4—42no—
41Dic71⋊C4—42no—
42Dic71⋊C4C2×C418yes—
43C22⋊Dic71—41no—
44C22⋊Dic71—41no—
45C22⋊Dic71C2×C418yes—
46C4×Dic71—42no—
47C4×Dic71—42no—
48C24×C71C2311yescharacteristic
49C22×C4×C71—42no—
50C22×C4×C71C2×C414yes—
51C22×C4×C71C2312yes—
52C22×C4×C71C2312yes—
53C22×C4×C71C2311yescharacteristic
54C22×C4×C71C2311yescharacteristic
55C22⋊C4×C71—42no—
56C23×C71—22no—
57C23×C71—21no—
58C23×C71—22no—
59C23×C71—21no—
60C23×C71C22×C412yes—
61C23×C71C2411yescharacteristic
62C2×C4×C71—22no—
63C2×C4×C71—22no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—44no—
71C2×C4×C71C22×C412yes—
72C2×C4×C71C22×C412yes—
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—22no—
83C2×Dic71C22×C414yes—
84C2×Dic71C22×C414yes—
85Dic142—44no—
86C22×C71—22no—
87C22×C71—22no—
88C22×C71—22no—
89C22×C71—42no—
90C22×C71—42no—
91C22×C71C23×C411yescharacteristic
92C22×C71H(5,𝔽2)12yes—
93C22×C71H(5,𝔽2)11yescharacteristic
94C22×C712−1+412yes—
95C22×C712−1+411yescharacteristic
96C4×C71—22no—
97C4×C71—22no—
98C4×C71—42no—
99C4×C71—42no—
100Dic71—24no—
101Dic71—24no—
102Dic71—42no—
103Dic71—42no—
104C2×C71—42no—
105C2×C71#51811yescharacteristic
106C2×C71#51911yescharacteristic
107C2×C71#52011yescharacteristic
108C2×C71#56212yes—
109C2×C71#56312yes—
110#2378—711nomaximal, Sylow
111C71#237811yescharacteristic, complemented, Sylow
112C2×C22⋊Q8—711no—
113#391—712no—
114#389—712no—
115#388—712no—
116#388—712no—
117#387—712no—
118#387—712no—
119#381D7111yescharacteristic
120#380—711no—
121C22×Q8—711no—
122C23×C4C2×D7111yescharacteristic
123C22⋊Q8—718no—
124C2×C4⋊C4—712no—
125C2×C4⋊C4—712no—
126C2×C4⋊C4—712no—
127C2×C4⋊C4—711no—
128C2×C4⋊C4—712no—
129C2×C22⋊C4—711no—
130C2×C22⋊C4—711no—
131C2×C22⋊C4—712no—
132C2×C22⋊C4C2×D7112yes—
133C2×C42—712no—
134C2×C42—712no—
135#95—712no—
136#95—712no—
137#95—712no—
138#95—712no—
139#95—712no—
140#95C2×D7111yescharacteristic
141#95C2×D7112yes—
142#95C2×D7111yescharacteristic
143C24C22×D7111yescharacteristic
144C2×Q8—2842no—
145C2×Q8—714no—
146C22×C4—42no—
147C22×C4—712no—
148C22×C4—712no—
149C22×C4—712no—
150C22×C4—712no—
151C22×C4C4×D7114yes—
152C22×C4C22×D7112yes—
153C22×C4C22×D7112yes—
154C22×C4C22×D7111yescharacteristic
155C22×C4C22×D7111yescharacteristic
156C4⋊C4—2842no—
157C4⋊C4—2842no—
158C4⋊C4—2842no—
159C4⋊C4—718no—
160C4⋊C4—714no—
161C22⋊C4—42no—
162C22⋊C4—2841no—
163C22⋊C4—2841no—
164C22⋊C4—718no—
165C42—2842no—
166C42—2842no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D7112yes—
172C23C23×D7111yescharacteristic
173Q8—2844no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—714no—
184C2×C4—714no—
185C2×C4—1422no—
186C2×C4—1422no—
187C2×C4—1422no—
188C2×C4—1422no—
189C2×C4—1422no—
190C2×C4—1422no—
191C2×C4—1422no—
192C2×C4—1422no—
193C2×C4—1422no—
194C2×C4—1422no—
195C2×C4C2×C4×D7112yes—
196C2×C4C2×C4×D7112yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D7111yescharacteristic
203C22#1455617312yes—
204C22#1455617411yescharacteristic
205C22#1455617512yes—
206C22#1455617511yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—2842no—
212C4—2842no—
213C4—1424no—
214C4—1424no—
215C2—42no—
216C2#1798647211yescharacteristic
217C2#1798647611yescharacteristic
218C2#1798647911yescharacteristic
219C2#1798674612yes—
220C2#1798675212yes—
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
Fitting#381×C71C2
socleC23×C71C24
hypercenter#381D71
hypocenterC71#2378
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #17985903C2semidirect
3. #17985896C2semidirect
6. #17985886C2semidirect
7. #17985884C2semidirect
11. #14556107C4semidirect
111. C71#2378semidirect