Finite Group Databasebeta

← #22593365

Subgroups — #22593365

Order 9088.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14556127C212yesmaximal
2C2×#14556126C212yesmaximal
3#17985920C212yesmaximal
4#17985919C211yesmaximal, characteristic
5#17985896C212yesmaximal
6#17985894C212yesmaximal
7#17985868C211yesmaximal, characteristic
8#17985850C212yesmaximal
9#395×C71C211yesmaximal, characteristic
10C22×Dic142C2211yescharacteristic
11C22×Dic142C2212yes—
12#14556127—28no—
13#14556126—28no—
14C2×C4⋊Dic71C2212yes—
15C2×C4⋊Dic71C2211yescharacteristic
16C2×Dic71⋊C4C2212yes—
17C2×Dic71⋊C4C2212yes—
18C2×Dic71⋊C4C2212yes—
19C2×Dic71⋊C4C2212yes—
20C2×Dic71⋊C4C2212yes—
21C2×Dic71⋊C4C2212yes—
22C2×C4×Dic71C2212yes—
23C2×C4×Dic71C2212yes—
24C2×C4×Dic71C2211yescharacteristic
25C71⋊#95C2212yes—
26C71⋊#95C2211yescharacteristic
27C71⋊#95C2212yes—
28C22×Q8×C71C2211yescharacteristic
29C2×C4⋊C4×C71C2212yes—
30C2×C4⋊C4×C71C2211yescharacteristic
31#95×C71C2212yes—
32#95×C71C2211yescharacteristic
33C2×Dic142—24no—
34C2×Dic142—24no—
35C2×Dic142—24no—
36C2×Dic142—41no—
37C2×Dic142—42no—
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C22×Dic71C2312yes—
41C22×Dic71C2312yes—
42C4⋊Dic71—24no—
43C4⋊Dic71—41no—
44Dic71⋊C4—24no—
45Dic71⋊C4—24no—
46Dic71⋊C4—24no—
47Dic71⋊C4—24no—
48Dic71⋊C4D418yes—
49Dic71⋊C4Q818yescomplemented
50C4×Dic71—24no—
51C4×Dic71—24no—
52C4×Dic71Q814yescomplemented
53C2×Q8×C71—24no—
54C2×Q8×C71—41no—
55C22×C4×C71C2311yescharacteristic
56C22×C4×C71C2311yescharacteristic
57C22×C4×C71C2312yes—
58C22×C4×C71C2311yescharacteristic
59C22×C4×C71C2312yes—
60C4⋊C4×C71—24no—
61C4⋊C4×C71—41no—
62C23×C71C2411yescharacteristic
63Q8×C71—44no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—21no—
67C2×C4×C71—22no—
68C2×C4×C71—21no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—21no—
73C2×C4×C71—21no—
74C2×C4×C71C2×D414yes—
75C2×C4×C71C2×Q812yes—
76C2×C4×C71C2×Q814yes—
77C2×Dic71—22no—
78C2×Dic71—22no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71C2×D414yes—
85C2×Dic71C2×D414yes—
86C2×Dic71C2×Q814yes—
87C2×Dic71C2×Q814yes—
88C2×Dic71C2×Q814yes—
89Dic142—44no—
90Dic142—48no—
91C22×C71C22×D412yes—
92C22×C71C22×Q811yescharacteristic
93C22×C71C22×Q812yes—
94C22×C71H(5,𝔽2)11yescharacteristic
95C22×C712−1+411yescharacteristic
96C4×C71—22no—
97C4×C71—24no—
98C4×C71—24no—
99C4×C71—41no—
100C4×C71—41no—
101Dic71—24no—
102Dic71—24no—
103Dic71—42no—
104Dic71C4⋊Q818yescomplemented
105C2×C71C2×C4⋊Q812yes—
106C2×C71#54411yescharacteristic
107C2×C71D4211yescharacteristic
108C2×C71D4×Q812yes—
109C2×C71Q8211yescharacteristic
110#2551—711nomaximal, Sylow
111C71#255111yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—712no—
113C2×C4⋊Q8—712no—
114#395—711no—
115#395—712no—
116#395D7111yescharacteristic
117#389—712no—
118#389—712no—
119#384—711no—
120C4×C4⋊C4—712no—
121C22×Q8—711no—
122C22×Q8—712no—
123C22×Q8C2×D7111yescharacteristic
124C4⋊Q8—1428no—
125C4⋊Q8—1428no—
126C2×C4⋊C4—711no—
127C2×C4⋊C4—712no—
128C2×C4⋊C4—712no—
129C2×C4⋊C4—712no—
130C2×C4⋊C4—712no—
131C2×C4⋊C4—712no—
132C2×C4⋊C4—712no—
133C2×C4⋊C4—712no—
134C2×C4⋊C4C2×D7112yes—
135C2×C4⋊C4C2×D7111yescharacteristic
136C2×C42—711no—
137C2×C42—712no—
138C2×C42—712no—
139#95—712no—
140#95—711no—
141#95—712no—
142#95C2×D7112yes—
143#95C2×D7111yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—2842no—
147C2×Q8—2841no—
148C2×Q8—1424no—
149C2×Q8—1424no—
150C2×Q8—1424no—
151C22×C4—712no—
152C22×C4—712no—
153C22×C4—712no—
154C22×C4—712no—
155C22×C4C22×D7111yescharacteristic
156C22×C4C22×D7111yescharacteristic
157C22×C4C22×D7112yes—
158C22×C4C22×D7111yescharacteristic
159C22×C4C22×D7112yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—2841no—
163C4⋊C4—718no—
164C4⋊C4—718no—
165C4⋊C4—1424no—
166C4⋊C4—1424no—
167C4⋊C4—1424no—
168C4⋊C4—1424no—
169C4⋊C4—1424no—
170C42—714no—
171C42—1424no—
172C42—1424no—
173C23C23×D7111yescharacteristic
174Q8—44no—
175Q8—2848no—
176Q8—2844no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—714no—
188C2×C4—714no—
189C2×C4—714no—
190C2×C4—714no—
191C2×C4—714no—
192C2×C4—1422no—
193C2×C4—1422no—
194C2×C4—1422no—
195C2×C4—1422no—
196C2×C4—1422no—
197C2×C4—1422no—
198C2×C4—1422no—
199C2×C4D4×D7114yes—
200C2×C4Q8×D7112yes—
201C2×C4Q8×D7114yes—
202C22C2×D4×D7112yes—
203C22C2×Q8×D7111yescharacteristic
204C22C2×Q8×D7112yes—
205C22#1455617311yescharacteristic
206C22#1455617511yescharacteristic
207C4—22no—
208C4—24no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—2842no—
213C4—718no—
214C4—1424no—
215C4—1424no—
216C2C4⋊Q8×D7112yes—
217C2#1798662811yescharacteristic
218C2#1798663111yescharacteristic
219C2#1798666212yes—
220C2#1798672911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#395×C71C2
hypercenter#395D71
hypocenterC71#2551
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
49. Dic71⋊C4Q8semidirect
52. C4×Dic71Q8semidirect
104. Dic71C4⋊Q8semidirect
111. C71#2551semidirect