Finite Group Databasebeta

← #22596409

Subgroups — #22596409

Order 9088.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556118C211yesmaximal, characteristic
3#17985940C212yesmaximal
4#17985937C211yesmaximal, characteristic
5#17985933C212yesmaximal
6#17985933C212yesmaximal
7#17985931C211yesmaximal, characteristic
8#17985931C212yesmaximal
9#17985929C211yesmaximal, characteristic
10#17985863C211yesmaximal, characteristic
11#400×C71C211yesmaximal, characteristic
12#14556119—24no—
13#14556118—24no—
14C2×C4⋊Dic71C2211yescharacteristic
15C2×C4⋊Dic71C2211yescharacteristic
16C2×C4⋊Dic71C2212yes—
17C2×C4⋊Dic71C2212yes—
18C2×Dic71⋊C4C2211yescharacteristic
19C2×Dic71⋊C4C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×Dic71⋊C4C2212yes—
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2212yes—
24C2×Dic71⋊C4C2212yes—
25C2×C4×Dic71C2211yescharacteristic
26C71⋊#95C2211yescharacteristic
27C71⋊#95C2212yes—
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—
37C22×Dic71C2312yes—
38C22×Dic71C2311yescharacteristic
39C22×Dic71C2311yescharacteristic
40C22×Dic71C2312yes—
41C22×Dic71C2311yescharacteristic
42C22×Dic71C2311yescharacteristic
43C4⋊Dic71—22no—
44C4⋊Dic71—22no—
45C4⋊Dic71—24no—
46C4⋊Dic71—42no—
47Dic71⋊C4—22no—
48Dic71⋊C4—22no—
49Dic71⋊C4—22no—
50Dic71⋊C4—22no—
51Dic71⋊C4—24no—
52Dic71⋊C4—42no—
53Dic71⋊C4—42no—
54C4×Dic71D414yes—
55C22×C4×C71C2312yes—
56C22×C4×C71C2311yescharacteristic
57C22×C4×C71C2312yes—
58C22×C4×C71C2311yescharacteristic
59C22×C4×C71C2311yescharacteristic
60C4⋊C4×C71—22no—
61C4⋊C4×C71—22no—
62C23×C71C2411yescharacteristic
63C2×C4×C71—22no—
64C2×C4×C71—21no—
65C2×C4×C71—21no—
66C2×C4×C71—22no—
67C2×C4×C71—21no—
68C2×C4×C71—22no—
69C2×C4×C71—24no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—22no—
73C2×C4×C71—21no—
74C2×C4×C71C2×D412yes—
75C2×Dic71—21no—
76C2×Dic71—22no—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—21no—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71—22no—
87C2×Dic71—21no—
88C2×Dic71—22no—
89C2×Dic71C2×D412yes—
90C2×Dic71C2×D412yes—
91C22×C71C22×D411yescharacteristic
92C22×C71H(5,𝔽2)11yescharacteristic
93C22×C712−1+412yes—
94C22×C712−1+412yes—
95C22×C712−1+411yescharacteristic
96C4×C71—22no—
97C4×C71—42no—
98C4×C71—41no—
99C4×C71—41no—
100C4×C71—42no—
101Dic71—22no—
102Dic71—22no—
103Dic71—41no—
104Dic71—41no—
105Dic71—42no—
106Dic71—42no—
107C2×C71#53611yescharacteristic
108C2×C71#53611yescharacteristic
109C2×C71#53711yescharacteristic
110C2×C71#56312yes—
111C2×C71#56412yes—
112#2822—711nomaximal, Sylow
113C71#282211yescharacteristic, complemented, Sylow
114C2×#125—711no—
115C2×#125—711no—
116#400—711no—
117#400—712no—
118#400D7111yescharacteristic
119#398—711no—
120#398—711no—
121#398—712no—
122#398—712no—
123#398—712no—
124#382—711no—
125#125—1424no—
126#125—1424no—
127C2×C4⋊C4—712no—
128C2×C4⋊C4—712no—
129C2×C4⋊C4—712no—
130C2×C4⋊C4—711no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—711no—
133C2×C4⋊C4—712no—
134C2×C4⋊C4—711no—
135C2×C4⋊C4—712no—
136C2×C4⋊C4—711no—
137C2×C4⋊C4—711no—
138C2×C4⋊C4C2×D7111yescharacteristic
139C2×C4⋊C4C2×D7111yescharacteristic
140C2×C42—711no—
141#95—712no—
142#95—711no—
143#95—712no—
144#95—712no—
145#95—712no—
146#95—712no—
147#95C2×D7111yescharacteristic
148#95C2×D7112yes—
149#95C2×D7112yes—
150C22×C4—711no—
151C22×C4—711no—
152C22×C4—712no—
153C22×C4—711no—
154C22×C4—712no—
155C22×C4—711no—
156C22×C4C22×D7112yes—
157C22×C4C22×D7111yescharacteristic
158C22×C4C22×D7112yes—
159C22×C4C22×D7111yescharacteristic
160C22×C4C22×D7111yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—2842no—
164C4⋊C4—2842no—
165C4⋊C4—2842no—
166C4⋊C4—1422no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4—1424no—
170C4⋊C4—1422no—
171C4⋊C4—1424no—
172C4⋊C4—1422no—
173C4⋊C4—1422no—
174C42—714no—
175C23C23×D7111yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—712no—
188C2×C4—712no—
189C2×C4—1421no—
190C2×C4—1421no—
191C2×C4—1422no—
192C2×C4—1422no—
193C2×C4—1421no—
194C2×C4—1422no—
195C2×C4—1422no—
196C2×C4—1422no—
197C2×C4—1422no—
198C2×C4—1422no—
199C2×C4—1421no—
200C2×C4—1421no—
201C2×C4—1422no—
202C2×C4—1421no—
203C2×C4D4×D7112yes—
204C22C2×D4×D7111yescharacteristic
205C22#1455617411yescharacteristic
206C22#1455617512yes—
207C22#1455617512yes—
208C22#1455617611yescharacteristic
209C4—22no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—42no—
214C4—2841no—
215C4—2841no—
216C4—2842no—
217C4—2842no—
218C4—1422no—
219C4—1422no—
220C2#1798656911yescharacteristic
221C2#1798657111yescharacteristic
222C2#1798657911yescharacteristic
223C2#1798675112yes—
224C2C71⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#400×C71C2
hypercenter#400D71
hypocenterC71#2822
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
113. C71#2822semidirect