Finite Group Databasebeta

← #22594222

Subgroups — #22594222

Order 9088.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14556119C211yesmaximal, characteristic
2C2×#14556093C211yesmaximal, characteristic
3#17985941C212yesmaximal
4#17985937C211yesmaximal, characteristic
5#17985931C211yesmaximal, characteristic
6#17985929C211yesmaximal, characteristic
7#17985920C212yesmaximal
8#17985882C212yesmaximal
9#17985881C212yesmaximal
10#17985866C211yesmaximal, characteristic
11#400×C71C211yesmaximal, characteristic
12C22×Dic142C2211yescharacteristic
13#14556119—24no—
14#14556093—24no—
15C2×C4⋊Dic71C2212yes—
16C2×C4⋊Dic71C2212yes—
17C2×C4⋊Dic71C2211yescharacteristic
18C2×Dic71⋊C4C2212yes—
19C2×Dic71⋊C4C2212yes—
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×C4×Dic71C2211yescharacteristic
23C2×C4×Dic71C2211yescharacteristic
24C2×C4×Dic71C2211yescharacteristic
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C71⋊#95C2211yescharacteristic
28C71⋊#95C2212yes—
29C71⋊#95C2212yes—
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C2×C4⋊C4×C71C2211yescharacteristic
33C2×C4⋊C4×C71C2211yescharacteristic
34#95×C71C2211yescharacteristic
35#95×C71C2212yes—
36#95×C71C2212yes—
37C2×Dic142—22no—
38C2×Dic142—22no—
39C2×Dic142—22no—
40C22×Dic71C2312yes—
41C22×Dic71C2311yescharacteristic
42C22×Dic71C2312yes—
43C22×Dic71C2311yescharacteristic
44C22×Dic71C2311yescharacteristic
45C22×Dic71C2311yescharacteristic
46C4⋊Dic71—22no—
47C4⋊Dic71—24no—
48C4⋊Dic71—24no—
49Dic71⋊C4—22no—
50Dic71⋊C4—24no—
51Dic71⋊C4—22no—
52Dic71⋊C4—24no—
53C4×Dic71—22no—
54C4×Dic71—22no—
55C4×Dic71D414yes—
56C22×C4×C71C2312yes—
57C22×C4×C71C2311yescharacteristic
58C22×C4×C71C2312yes—
59C22×C4×C71C2311yescharacteristic
60C22×C4×C71C2311yescharacteristic
61C4⋊C4×C71—22no—
62C4⋊C4×C71—22no—
63C23×C71C2411yescharacteristic
64C2×C4×C71—21no—
65C2×C4×C71—21no—
66C2×C4×C71—22no—
67C2×C4×C71—21no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—24no—
72C2×C4×C71—22no—
73C2×C4×C71—22no—
74C2×C4×C71C2×D412yes—
75C2×C4×C71#4112yes—
76C2×Dic71—21no—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—22no—
81C2×Dic71—21no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—22no—
89C2×Dic71C2×D412yes—
90C2×Dic71C2×D412yes—
91C2×Dic71#4112yes—
92Dic142—28no—
93C22×C71C22×D411yescharacteristic
94C22×C71C2×#4111yescharacteristic
95C22×C71C2×#4111yescharacteristic
96C22×C712−1+412yes—
97C22×C712−1+412yes—
98C4×C71—22no—
99C4×C71—22no—
100C4×C71—42no—
101C4×C71—41no—
102C4×C71—42no—
103Dic71—22no—
104Dic71—22no—
105Dic71—22no—
106Dic71—42no—
107Dic71—41no—
108Dic71—42no—
109C2×C71#52511yescharacteristic
110C2×C71#53611yescharacteristic
111C2×C71#53611yescharacteristic
112C2×C71#54112yes—
113C2×C71#54112yes—
114#2634—711nomaximal, Sylow
115C71#263411yescharacteristic, complemented, Sylow
116C2×#125—711no—
117C2×C4×Q8—711no—
118#400—711no—
119#400—712no—
120#400D7111yescharacteristic
121#398—711no—
122#398—711no—
123#395—712no—
124#387—712no—
125#387—712no—
126#383—711no—
127C22×Q8—711no—
128#125—1424no—
129C4×Q8—1424no—
130C2×C4⋊C4—711no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—712no—
133C2×C4⋊C4—712no—
134C2×C4⋊C4—711no—
135C2×C4⋊C4—712no—
136C2×C4⋊C4—712no—
137C2×C4⋊C4C2×D7111yescharacteristic
138C2×C4⋊C4C2×D7111yescharacteristic
139C2×C42—711no—
140C2×C42—711no—
141C2×C42—711no—
142#95—712no—
143#95—712no—
144#95—711no—
145#95—712no—
146#95—712no—
147#95—712no—
148#95—712no—
149#95C2×D7111yescharacteristic
150#95C2×D7112yes—
151#95C2×D7112yes—
152C2×Q8—1422no—
153C2×Q8—1422no—
154C2×Q8—1422no—
155C22×C4—711no—
156C22×C4—711no—
157C22×C4—711no—
158C22×C4—712no—
159C22×C4—711no—
160C22×C4—712no—
161C22×C4C22×D7112yes—
162C22×C4C22×D7111yescharacteristic
163C22×C4C22×D7112yes—
164C22×C4C22×D7111yescharacteristic
165C22×C4C22×D7111yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—1422no—
169C4⋊C4—1424no—
170C4⋊C4—1424no—
171C4⋊C4—1424no—
172C4⋊C4—1422no—
173C4⋊C4—1422no—
174C4⋊C4—1424no—
175C42—714no—
176C42—1422no—
177C42—1422no—
178C23C23×D7111yescharacteristic
179Q8—1428no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—712no—
191C2×C4—712no—
192C2×C4—712no—
193C2×C4—1421no—
194C2×C4—1422no—
195C2×C4—1422no—
196C2×C4—1422no—
197C2×C4—1422no—
198C2×C4—1422no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4—1421no—
202C2×C4—1421no—
203C2×C4—1421no—
204C2×C4—1421no—
205C2×C4—1422no—
206C2×C4D4×D7112yes—
207C2×C4#1176586612yes—
208C22C2×D4×D7111yescharacteristic
209C22#41×D7111yescharacteristic
210C22C2×#1176586611yescharacteristic
211C22#1455617512yes—
212C22#1455617512yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—41no—
217C4—42no—
218C4—2841no—
219C4—2842no—
220C4—2842no—
221C4—1422no—
222C4—1422no—
223C4—1422no—
224C2#1798651211yescharacteristic
225C2#1798656911yescharacteristic
226C2#1798657111yescharacteristic
227C2#1798660612yes—
228C2#1798661212yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#400×C71C2
hypercenter#400D71
hypocenterC71#2634
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
115. C71#2634semidirect