Finite Group Databasebeta

← #22594215

Subgroups — #22594215

Order 9088.

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

normal subgroups only

This group has 416 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
1C2×#14556118C211yesmaximal, characteristic
2C2×Q8×Dic71C211yesmaximal, characteristic
3#17985941C212yesmaximal
4#17985939C211yesmaximal, characteristic
5#17985938C211yesmaximal, characteristic
6#17985932C212yesmaximal
7#17985918C211yesmaximal, characteristic
8#17985885C212yesmaximal
9#17985881C212yesmaximal
10#17985866C211yesmaximal, characteristic
11#395×C71C211yesmaximal, characteristic
12#14556118—24no—
13Q8×Dic71—24no—
14C2×C4⋊Dic71C2211yescharacteristic
15C2×C4⋊Dic71C2212yes—
16C2×C4⋊Dic71C2211yescharacteristic
17C2×Dic71⋊C4C2211yescharacteristic
18C2×Dic71⋊C4C2212yes—
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×C4×Dic71C2212yes—
23C2×C4×Dic71C2211yescharacteristic
24C71⋊#95C2212yes—
25C71⋊#95C2211yescharacteristic
26C71⋊#95C2212yes—
27C71⋊#95C2212yes—
28C71⋊#95C2212yes—
29C71⋊#95C2212yes—
30C71⋊#95C2212yes—
31C71⋊#95C2212yes—
32C22×Q8×C71C2211yescharacteristic
33C2×C4⋊C4×C71C2212yes—
34C2×C4⋊C4×C71C2211yescharacteristic
35#95×C71C2211yescharacteristic
36#95×C71C2212yes—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C22×Dic71C2311yescharacteristic
40C22×Dic71C2311yescharacteristic
41C22×Dic71C2311yescharacteristic
42C22×Dic71C2311yescharacteristic
43C4⋊Dic71—22no—
44C4⋊Dic71—24no—
45C4⋊Dic71—22no—
46Dic71⋊C4—22no—
47Dic71⋊C4—24no—
48Dic71⋊C4—22no—
49Dic71⋊C4—22no—
50Dic71⋊C4—22no—
51C4×Dic71—24no—
52C4×Dic71D414yes—
53C2×Q8×C71—22no—
54C2×Q8×C71—24no—
55C22×C4×C71C2312yes—
56C22×C4×C71C2311yescharacteristic
57C22×C4×C71C2311yescharacteristic
58C22×C4×C71C2311yescharacteristic
59C22×C4×C71C2312yes—
60C4⋊C4×C71—22no—
61C4⋊C4×C71—24no—
62C23×C71C2411yescharacteristic
63Q8×C71—28no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—21no—
68C2×C4×C71—21no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—21no—
72C2×C4×C71—22no—
73C2×C4×C71—21no—
74C2×C4×C71—22no—
75C2×C4×C71C2×D412yes—
76C2×C4×C71#4114yes—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—21no—
82C2×Dic71—21no—
83C2×Dic71—22no—
84C2×Dic71—22no—
85C2×Dic71—21no—
86C2×Dic71—24no—
87C2×Dic71—21no—
88C2×Dic71—22no—
89C2×Dic71—22no—
90C2×Dic71C2×D412yes—
91C2×Dic71C2×D412yes—
92C22×C71C22×D411yescharacteristic
93C22×C71C2×#4112yes—
94C22×C712−1+411yescharacteristic
95C22×C712−1+411yescharacteristic
96C22×C712−1+412yes—
97C4×C71—22no—
98C4×C71—24no—
99C4×C71—41no—
100C4×C71—41no—
101C4×C71—42no—
102Dic71—22no—
103Dic71—22no—
104Dic71—41no—
105Dic71—41no—
106Dic71—42no—
107Dic71—42no—
108C2×C71#52511yescharacteristic
109C2×C71#53611yescharacteristic
110C2×C71#53611yescharacteristic
111C2×C71#54112yes—
112C2×C71#54112yes—
113#2634—711nomaximal, Sylow
114C71#263411yescharacteristic, complemented, Sylow
115C2×#125—711no—
116C2×C4×Q8—711no—
117#400—711no—
118#400—711no—
119#400—712no—
120#398—712no—
121#395—711no—
122#395D7111yescharacteristic
123#387—712no—
124#387—712no—
125#383—711no—
126C22×Q8C2×D7111yescharacteristic
127#125—1424no—
128C4×Q8—1424no—
129C2×C4⋊C4—712no—
130C2×C4⋊C4—711no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—711no—
133C2×C4⋊C4—711no—
134C2×C4⋊C4—711no—
135C2×C4⋊C4—711no—
136C2×C4⋊C4—712no—
137C2×C4⋊C4C2×D7111yescharacteristic
138C2×C4⋊C4C2×D7112yes—
139C2×C42—711no—
140C2×C42—712no—
141#95—712no—
142#95—711no—
143#95—712no—
144#95—712no—
145#95—712no—
146#95—712no—
147#95—712no—
148#95—712no—
149#95C2×D7111yescharacteristic
150#95C2×D7112yes—
151C2×Q8—22no—
152C2×Q8—24no—
153C22×C4—711no—
154C22×C4—711no—
155C22×C4—712no—
156C22×C4—712no—
157C22×C4—711no—
158C22×C4—711no—
159C22×C4C22×D7112yes—
160C22×C4C22×D7111yescharacteristic
161C22×C4C22×D7111yescharacteristic
162C22×C4C22×D7111yescharacteristic
163C22×C4C22×D7112yes—
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—1422no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4—1424no—
170C4⋊C4—1422no—
171C4⋊C4—1422no—
172C4⋊C4—1422no—
173C4⋊C4—1424no—
174C42—714no—
175C42—1424no—
176C23C23×D7111yescharacteristic
177Q8—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—712no—
190C2×C4—712no—
191C2×C4—1422no—
192C2×C4—1421no—
193C2×C4—1421no—
194C2×C4—1422no—
195C2×C4—1422no—
196C2×C4—1421no—
197C2×C4—1421no—
198C2×C4—1424no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4—1421no—
202C2×C4—1421no—
203C2×C4—1422no—
204C2×C4D4×D7112yes—
205C2×C4#1176586414yes—
206C22C2×D4×D7111yescharacteristic
207C22C2×#1176586412yes—
208C22#1455617511yescharacteristic
209C22#1455617611yescharacteristic
210C22#1455617612yes—
211C4—22no—
212C4—24no—
213C4—41no—
214C4—42no—
215C4—41no—
216C4—2841no—
217C4—2842no—
218C4—2842no—
219C4—2841no—
220C4—1422no—
221C4—1422no—
222C2#1798650511yescharacteristic
223C2#1798657211yescharacteristic
224C2#1798657411yescharacteristic
225C2#1798660912yes—
226C2#1798661012yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#395×C71C2
hypercenter#395D71
hypocenterC71#2634
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
114. C71#2634semidirect