Finite Group Databasebeta

← #22589177

Subgroups — #22589177

Order 9088.

408 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556043C214yesmaximal, complemented
2#17985859C211yesmaximal, characteristic, complemented
3C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
4C2×#121×C71C211yesmaximal, characteristic
5C2×C4⋊Dic71—21no—
6C2×C22⋊Dic71C2212yes—
7C2×C22⋊Dic71C2212yes—
8C2×C4×Dic71—21no—
9#14556043—28no—
10C71⋊#95—21no—
11C71⋊#95—21no—
12C22×D4×C71C411yescharacteristic, complemented
13C22×D4×C71C2212yes—
14C23×C4×C71C2211yescharacteristic
15#121×C71—21no—
16#121×C71—21no—
17#121×C71—21no—
18#121×C71—21no—
19C2×C4⋊C4×C71C411yescharacteristic, complemented
20C2×C22⋊C4×C71C412yescomplemented
21C22×Dic71—22no—
22C22×Dic71—22no—
23C4⋊Dic71—42no—
24C22⋊Dic71—22no—
25C22⋊Dic71—24no—
26C22⋊Dic71D414yescomplemented
27C4×Dic71—42no—
28C24×C71C2×C412yes—
29C24×C71C2311yescharacteristic
30C2×D4×C71—22no—
31C2×D4×C71—22no—
32C2×D4×C71—24no—
33C2×D4×C71—24no—
34C2×D4×C71—21no—
35C2×D4×C71—21no—
36C2×D4×C71—42no—
37C22×C4×C71—42no—
38C22×C4×C71C2×C412yes—
39C22×C4×C71C2×C411yescharacteristic
40C22×C4×C71C2×C411yescharacteristic
41C22×C4×C71D411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71D411yescharacteristic
44C22×C4×C71D411yescharacteristic
45C4⋊C4×C71—21no—
46C4⋊C4×C71—21no—
47C22⋊C4×C71—22no—
48C22⋊C4×C71—22no—
49C23×C71—22no—
50C23×C71—24no—
51C23×C71—41no—
52C23×C71—41no—
53C23×C71—42no—
54C23×C71—42no—
55C23×C71C22×C411yescharacteristic
56C23×C71C2×D412yes—
57C23×C71C2×D411yescharacteristic
58C23×C71C2×D411yescharacteristic
59C23×C71#4112yes—
60D4×C71—42no—
61D4×C71—44no—
62D4×C71—42no—
63D4×C71—42no—
64D4×C71—42no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71—24no—
70C2×C4×C71—41no—
71C2×C4×C71—41no—
72C2×C4×C71—41no—
73C2×C4×C71C22⋊C411yescharacteristic
74C2×C4×C71C22⋊C411yescharacteristic
75C2×C4×C71C22⋊C411yescharacteristic
76C2×C4×C71C22⋊C411yescharacteristic
77C2×Dic71—24no—
78C2×Dic71—42no—
79C2×Dic71—42no—
80C2×Dic71—42no—
81C2×Dic71—42no—
82C2×Dic71—42no—
83C22×C71—21no—
84C22×C71—21no—
85C22×C71—21no—
86C22×C71—21no—
87C22×C71—21no—
88C22×C71—21no—
89C22×C71—42no—
90C22×C71—42no—
91C22×C71—42no—
92C22×C71—42no—
93C22×C71—42no—
94C22×C71—84no—
95C22×C71C2×C22⋊C411yescharacteristic
96C22×C71C4×D412yes—
97C22×C71#12112yes—
98C22×C71#12411yescharacteristic
99C22×C71#12711yescharacteristic
100C4×C71—21no—
101C4×C71—21no—
102C4×C71—21no—
103C4×C71—42no—
104C4×C71#9912yescomplemented
105Dic71—44no—
106Dic71—82no—
107C2×C71—22no—
108C2×C71—21no—
109C2×C71—22no—
110C2×C71—21no—
111C2×C71—82no—
112C2×C71#39011yescharacteristic
113C2×C71C2×#9911yescharacteristic
114C2×C71#41011yescharacteristic
115#1964—711nomaximal, Sylow
116C71#196411yescharacteristic, complemented, Sylow
117C2×#121D7111yescharacteristic
118C2×#99—714no—
119#380—711no—
120C4×C22⋊C4—711no—
121C22×D4Dic7111yescharacteristic, complemented
122C22×D4C2×D7112yes—
123C23×C4C2×D7111yescharacteristic
124#121—21no—
125#121—21no—
126#121—21no—
127#121—21no—
128C2×C4⋊C4—1421no—
129C2×C4⋊C4Dic7111yescharacteristic, complemented
130C2×C22⋊C4—712no—
131C2×C22⋊C4—712no—
132C2×C22⋊C4Dic7112yescomplemented
133C2×C42—1421no—
134#99—1428no—
135#95—1421no—
136#95—1421no—
137C24C2×Dic7112yes—
138C24C22×D7111yescharacteristic
139C2×D4—24no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—24no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—42no—
146C22×C4—42no—
147C22×C4—1422no—
148C22×C4—1422no—
149C22×C4C2×Dic7112yes—
150C22×C4C2×Dic7111yescharacteristic
151C22×C4C2×Dic7111yescharacteristic
152C22×C4C22⋊D7111yescharacteristic
153C22×C4C22⋊D7111yescharacteristic
154C22×C4C22⋊D7111yescharacteristic
155C22×C4C22⋊D7111yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—2842no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—714no—
162C22⋊C4—1424no—
163C22⋊C4—1422no—
164C42—2842no—
165C23—22no—
166C23—24no—
167C23—41no—
168C23—41no—
169C23—42no—
170C23—42no—
171C23C22×Dic7111yescharacteristic
172C23D4×D7112yes—
173C23C2×C22⋊D7111yescharacteristic
174C23C2×C22⋊D7111yescharacteristic
175C23#1176586412yes—
176D4—42no—
177D4—44no—
178D4—42no—
179D4—42no—
180D4—42no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2842no—
190C2×C4—2842no—
191C2×C4—2842no—
192C2×C4—2842no—
193C2×C4—2842no—
194C2×C4—1424no—
195C2×C4C22⋊Dic7111yescharacteristic
196C2×C4C22⋊Dic7111yescharacteristic
197C2×C4C22⋊Dic7111yescharacteristic
198C2×C4C22⋊Dic7111yescharacteristic
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22C2×C22⋊Dic7111yescharacteristic
212C22D4×Dic7112yes—
213C22#1455609912yes—
214C22#1455611511yescharacteristic
215C22#1455612411yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—2844no—
221C4—5682no—
222C4#1455604312yescomplemented
223C2—22no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—82no—
228C2#1798590211yescharacteristic
229C2C2×#1455604311yescharacteristic
230C2#1798597311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic71
commutatorC23×C71C22×C4
FrattiniC24C22×D71
FittingC2×#121×C71C2
socleC22×C71C2×C22⋊C4
hypercenterC2×#121D71
hypocenterC71#1964
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14556043C2semidirect
2. #17985859C2semidirect
3. C4×C22⋊Dic71C2semidirect
12. C22×D4×C71C4semidirect
19. C2×C4⋊C4×C71C4semidirect
20. C2×C22⋊C4×C71C4semidirect
26. C22⋊Dic71D4semidirect
104. C4×C71#99semidirect
116. C71#1964semidirect
121. C22×D4Dic71semidirect
129. C2×C4⋊C4Dic71semidirect
132. C2×C22⋊C4Dic71semidirect
222. C4#14556043semidirect