Finite Group Databasebeta

← #22593590

Subgroups — #22593590

Order 9088.

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

normal subgroups only

This group has 476 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
1#17985916C211yesmaximal, characteristic
2#17985912C212yesmaximal, complemented
3#17985904C211yesmaximal, characteristic, complemented
4#17985889C212yesmaximal, complemented
5#17985877C212yesmaximal
6#17985866C212yesmaximal, complemented
7#17985861C212yesmaximal, complemented
8#17985846C212yesmaximal, complemented
9#400×C71C211yesmaximal, characteristic, complemented
10C22×Dic142C2211yescharacteristic
11C22×D284C2211yescharacteristic
12C22×C4×D71C2212yes—
13C2×(C2×D71)⋊C4C2212yes—
14C2×(C2×D71)⋊C4C2212yes—
15C2×(C2×D71)⋊C4C2212yes—
16C2×(C2×D71)⋊C4C2212yes—
17C2×(C2×D71)⋊C4C2212yes—
18C2×C4×Dic71C2212yes—
19C2×C4×Dic71C2211yescharacteristic
20C71⋊#95C2212yes—
21C71⋊#95C2212yes—
22C71⋊#95C2212yes—
23C71⋊#95C2211yescharacteristic
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C2×C4⋊C4×C71C2211yescharacteristic
27C2×C4⋊C4×C71C2211yescharacteristic
28#95×C71C2212yes—
29#95×C71C2211yescharacteristic
30#95×C71C2212yes—
31C23×D71C2312yes—
32C2×Dic142—22no—
33C2×Dic142—41no—
34C2×Dic142—41no—
35C2×D284—24no—
36C2×D284—41no—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C2×C4×D71—24no—
41C2×C4×D71—24no—
42C2×C4×D71—42no—
43(C2×D71)⋊C4—24no—
44(C2×D71)⋊C4—24no—
45(C2×D71)⋊C4—24no—
46(C2×D71)⋊C4—42no—
47(C2×D71)⋊C4—42no—
48C4×Dic71—24no—
49C4×Dic71—41no—
50C22×C4×C71C2312yes—
51C22×C4×C71C2311yescharacteristic
52C22×C4×C71C2312yes—
53C22×C4×C71C2311yescharacteristic
54C22×C4×C71C2311yescharacteristic
55C4⋊C4×C71—41no—
56C4⋊C4×C71—41no—
57C23×C71C2411yescharacteristic
58C22×D71—22no—
59C22×D71—22no—
60C22×D71—22no—
61C22×D71—22no—
62C22×D71—22no—
63C22×D71—22no—
64C22×D71#4114yes—
65C2×C4×C71—21no—
66C2×C4×C71—21no—
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—22no—
73C2×C4×C71—21no—
74C2×C4×C71—22no—
75C2×C4×C71—21no—
76C2×C4×C71—22no—
77C2×C4×C71#4112yes—
78C2×Dic71—22no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71#4114yes—
87D284—44no—
88C4×D71—48no—
89Dic142—44no—
90C22×C71C2×#4112yes—
91C22×C71C2×#4112yes—
92C22×C71C2×#4111yescharacteristic
93C22×C71H(5,𝔽2)11yescharacteristic
94C22×C71H(5,𝔽2)11yescharacteristic
95C2×D71—24no—
96C2×D71—24no—
97C2×D71—24no—
98C2×D71—42no—
99C2×D71—42no—
100C2×D71—42no—
101C2×D71—42no—
102C4×C71—22no—
103C4×C71—42no—
104C4×C71—41no—
105C4×C71—41no—
106C4×C71—42no—
107Dic71—24no—
108Dic71—42no—
109Dic71—42no—
110C2×C71#52912yes—
111C2×C71#53811yescharacteristic
112C2×C71#55112yes—
113C2×C71#55111yescharacteristic
114C2×C71#55511yescharacteristic
115D71—44no—
116#2572—711nomaximal, Sylow
117C71#257211yescharacteristic, complemented, Sylow
118#400D7111yescharacteristic, complemented
119#394—711no—
120#393—712no—
121#391—711no—
122#388—712no—
123#386—712no—
124#383—712no—
125#381—712no—
126C4×C22⋊C4—712no—
127C22×Q8—711no—
128C22×D4—711no—
129C23×C4—712no—
130C2×C4⋊C4C2×D7111yescharacteristic
131C2×C4⋊C4C2×D7111yescharacteristic
132C2×C22⋊C4—712no—
133C2×C22⋊C4—712no—
134C2×C22⋊C4—712no—
135C2×C22⋊C4—712no—
136C2×C22⋊C4—712no—
137C2×C42—711no—
138C2×C42—712no—
139#95—712no—
140#95—712no—
141#95—712no—
142#95—711no—
143#95—712no—
144#95—712no—
145#95C2×D7112yes—
146#95C2×D7111yescharacteristic
147#95C2×D7112yes—
148C24—712no—
149C2×Q8—2841no—
150C2×Q8—2841no—
151C2×Q8—1422no—
152C2×D4—2841no—
153C2×D4—1424no—
154C22×C4—2842no—
155C22×C4—712no—
156C22×C4—712no—
157C22×C4—712no—
158C22×C4—1424no—
159C22×C4—1424no—
160C22×C4C22×D7111yescharacteristic
161C22×C4C22×D7112yes—
162C22×C4C22×D7111yescharacteristic
163C22×C4C22×D7112yes—
164C22×C4C22×D7111yescharacteristic
165C4⋊C4—41no—
166C4⋊C4—41no—
167C22⋊C4—2842no—
168C22⋊C4—2842no—
169C22⋊C4—1424no—
170C22⋊C4—1424no—
171C22⋊C4—1424no—
172C42—2841no—
173C42—1424no—
174C23—714no—
175C23—1422no—
176C23—1422no—
177C23—1422no—
178C23—1422no—
179C23—1422no—
180C23—1422no—
181C23C23×D7111yescharacteristic
182Q8—2844no—
183D4—2844no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—2848no—
197C2×C4—714no—
198C2×C4—1422no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4—1422no—
202C2×C4—1422no—
203C2×C4—1422no—
204C2×C4—1422no—
205C2×C4—1422no—
206C2×C4#1176586612yes—
207C22—2842no—
208C22—2842no—
209C22—2842no—
210C22—2842no—
211C22—1424no—
212C22—1424no—
213C22—1424no—
214C22#41×D7112yes—
215C22#41×D7112yes—
216C22C2×#1176586611yescharacteristic
217C22#1455617311yescharacteristic
218C22#1455617411yescharacteristic
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—2842no—
225C4—2842no—
226C4—1424no—
227C2—2844no—
228C2#1798653412yes—
229C2#1798658911yescharacteristic
230C2#1798667412yes—
231C2#1798667711yescharacteristic
232C2#1798671111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#400×C71C2
hypercenter#400D71
hypocenterC71#2572
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #17985912C2semidirect
3. #17985904C2semidirect
4. #17985889C2semidirect
6. #17985866C2semidirect
7. #17985861C2semidirect
8. #17985846C2semidirect
9. #400×C71C2semidirect
117. C71#2572semidirect
118. #400D71semidirect