Finite Group Databasebeta

← #22593701

Subgroups — #22593701

Order 9088.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q8×Dic71C211yesmaximal, characteristic
2C2×#14556093C211yesmaximal, characteristic
3#17985939C211yesmaximal, characteristic
4#17985938C211yesmaximal, characteristic
5#17985918C211yesmaximal, characteristic
6#17985903C212yesmaximal
7#17985894C212yesmaximal
8#17985886C212yesmaximal
9#17985885C212yesmaximal
10#17985863C211yesmaximal, characteristic
11#395×C71C211yesmaximal, characteristic
12C22×Dic142C2211yescharacteristic
13Q8×Dic71—24no—
14#14556093—24no—
15C2×C4⋊Dic71C2212yes—
16C2×C4⋊Dic71C2211yescharacteristic
17C2×Dic71⋊C4C2212yes—
18C2×Dic71⋊C4C2212yes—
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×C4×Dic71C2211yescharacteristic
22C2×C4×Dic71C2211yescharacteristic
23C2×C4×Dic71C2212yes—
24C2×C4×Dic71C2211yescharacteristic
25C71⋊#95C2212yes—
26C71⋊#95C2211yescharacteristic
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—
37C2×Dic142—22no—
38C2×Dic142—22no—
39C2×Dic142Q814yescomplemented
40C22×Dic71C2312yes—
41C22×Dic71C2312yes—
42C22×Dic71C2311yescharacteristic
43C22×Dic71C2311yescharacteristic
44C22×Dic71C2311yescharacteristic
45C22×Dic71C2311yescharacteristic
46C4⋊Dic71—22no—
47C4⋊Dic71—24no—
48Dic71⋊C4—22no—
49Dic71⋊C4—24no—
50Dic71⋊C4—22no—
51Dic71⋊C4—24no—
52C4×Dic71—22no—
53C4×Dic71—22no—
54C4×Dic71—24no—
55C4×Dic71D414yes—
56C2×Q8×C71—22no—
57C2×Q8×C71—24no—
58C22×C4×C71C2312yes—
59C22×C4×C71C2311yescharacteristic
60C22×C4×C71C2311yescharacteristic
61C22×C4×C71C2311yescharacteristic
62C22×C4×C71C2312yes—
63C4⋊C4×C71—22no—
64C4⋊C4×C71—24no—
65C23×C71C2411yescharacteristic
66Q8×C71—28no—
67C2×C4×C71—21no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—21no—
72C2×C4×C71—21no—
73C2×C4×C71—22no—
74C2×C4×C71—22no—
75C2×C4×C71—22no—
76C2×C4×C71—22no—
77C2×C4×C71C2×D412yes—
78C2×C4×C71C2×Q812yes—
79C2×C4×C71#4114yes—
80C2×Dic71—21no—
81C2×Dic71—21no—
82C2×Dic71—22no—
83C2×Dic71—21no—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—24no—
89C2×Dic71—22no—
90C2×Dic71C2×D412yes—
91C2×Dic71C2×D412yes—
92C2×Dic71C2×Q812yes—
93C2×Dic71C2×Q812yes—
94C2×Dic71#4112yes—
95Dic142—28no—
96C22×C71C22×D411yescharacteristic
97C22×C71C22×Q811yescharacteristic
98C22×C71C2×#4111yescharacteristic
99C22×C71C2×#4112yes—
100C22×C712−1+412yes—
101C4×C71—22no—
102C4×C71—22no—
103C4×C71—24no—
104C4×C71—41no—
105C4×C71—42no—
106Dic71—22no—
107Dic71—22no—
108Dic71—41no—
109Dic71—42no—
110Dic71—42no—
111Dic71C22⋊Q814yes—
112C2×C71C2×C22⋊Q811yescharacteristic
113C2×C71#52511yescharacteristic
114C2×C71#53611yescharacteristic
115C2×C71#55612yes—
116C2×C71#55712yes—
117#2581—711nomaximal, Sylow
118C71#258111yescharacteristic, complemented, Sylow
119C2×C4×Q8—711no—
120C2×C4×Q8—711no—
121#400—711no—
122#400—711no—
123#395—711no—
124#395D7111yescharacteristic
125#391—712no—
126#389—712no—
127#387—712no—
128#387—712no—
129#382—711no—
130C22×Q8—711no—
131C22×Q8C2×D7111yescharacteristic
132C4×Q8—1424no—
133C4×Q8—1424no—
134C2×C4⋊C4—712no—
135C2×C4⋊C4—711no—
136C2×C4⋊C4—711no—
137C2×C4⋊C4—711no—
138C2×C4⋊C4—712no—
139C2×C4⋊C4—712no—
140C2×C4⋊C4C2×D7111yescharacteristic
141C2×C4⋊C4C2×D7112yes—
142C2×C42—711no—
143C2×C42—711no—
144C2×C42—711no—
145C2×C42—712no—
146#95—712no—
147#95—711no—
148#95—712no—
149#95—712no—
150#95—712no—
151#95—712no—
152#95—712no—
153#95C2×D7111yescharacteristic
154#95C2×D7112yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C2×Q8—714no—
158C2×Q8—1422no—
159C2×Q8—1422no—
160C22×C4—711no—
161C22×C4—711no—
162C22×C4—711no—
163C22×C4—712no—
164C22×C4—712no—
165C22×C4—711no—
166C22×C4C22×D7112yes—
167C22×C4C22×D7111yescharacteristic
168C22×C4C22×D7111yescharacteristic
169C22×C4C22×D7111yescharacteristic
170C22×C4C22×D7112yes—
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—1424no—
174C4⋊C4—1422no—
175C4⋊C4—1424no—
176C4⋊C4—1422no—
177C4⋊C4—1422no—
178C4⋊C4—1424no—
179C42—714no—
180C42—1422no—
181C42—1424no—
182C42—1422no—
183C23C23×D7111yescharacteristic
184Q8—28no—
185Q8—1428no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—712no—
197C2×C4—712no—
198C2×C4—712no—
199C2×C4—712no—
200C2×C4—712no—
201C2×C4—1422no—
202C2×C4—1421no—
203C2×C4—1422no—
204C2×C4—1422no—
205C2×C4—1422no—
206C2×C4—1424no—
207C2×C4—1422no—
208C2×C4—1421no—
209C2×C4—1421no—
210C2×C4—1422no—
211C2×C4D4×D7112yes—
212C2×C4Q8×D7112yes—
213C2×C4#1176586414yes—
214C22C2×D4×D7111yescharacteristic
215C22C2×Q8×D7111yescharacteristic
216C22#41×D7111yescharacteristic
217C22C2×#1176586412yes—
218C22#1455617612yes—
219C4—22no—
220C4—22no—
221C4—24no—
222C4—42no—
223C4—41no—
224C4—2842no—
225C4—2842no—
226C4—2841no—
227C4—714no—
228C4—1422no—
229C4—1422no—
230C2C22⋊Q8×D7111yescharacteristic
231C2#1798650511yescharacteristic
232C2#1798657411yescharacteristic
233C2#1798672012yes—
234C2#1798672412yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#395×C71C2
hypercenter#395D71
hypocenterC71#2581
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
39. C2×Dic142Q8semidirect
118. C71#2581semidirect