Finite Group Databasebeta

← #22586845

Subgroups — #22586845

Order 9088.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#17986510C211yesmaximal, characteristic
2C2×C71⋊#95C211yesmaximal, characteristic, complemented
3#17985737C212yesmaximal, complemented
4#17985734C212yesmaximal, complemented
5#407×C71C211yesmaximal, characteristic, complemented
6C2×#11765865C411yescharacteristic, complemented
7C23×Dic71—21no—
8#14556111—21no—
9#14556107C411yescharacteristic, complemented
10#14556107C2211yescharacteristic
11#14556102C411yescharacteristic, complemented
12#14556102C2211yescharacteristic
13#14556097—21no—
14C4×C22⋊D71—21no—
15C4×C22⋊D71—21no—
16#14556087C411yescharacteristic, complemented
17C71⋊#95—21no—
18C71⋊#95C2212yes—
19C23×C4×C71C2211yescharacteristic
20C2×M16×C71—21no—
21C22⋊C8×C71—21no—
22C22⋊C8×C71C2212yes—
23#11765865—42no—
24C2×Dic142C2×C411yescharacteristic, complemented
25C2×D284C2×C411yescharacteristic, complemented
26C2×C22⋊D71—21no—
27C2×C22⋊D71—21no—
28C2×C22⋊D71—21no—
29C22×Dic71—24no—
30C22×Dic71—22no—
31C22×Dic71—42no—
32C22×Dic71—42no—
33C2×C4×D71—21no—
34C4⋊Dic71C2×C411yescharacteristic, complemented
35C4⋊Dic71C2×C411yescharacteristic, complemented
36Dic71⋊C4—21no—
37Dic71⋊C4—21no—
38C22⋊Dic71—21no—
39C22⋊Dic71—21no—
40C22⋊Dic71—21no—
41(C2×D71)⋊C4—21no—
42(C2×D71)⋊C4—21no—
43C4×Dic71—21no—
44C24×C71D411yescharacteristic
45C22×C4×C71—42no—
46C22×C4×C71C2×C411yescharacteristic
47C22×C4×C71C2×C411yescharacteristic
48C22×C4×C71D411yescharacteristic
49C22×C4×C71D411yescharacteristic
50C22×C4×C71D411yescharacteristic
51C22×C4×C71C2311yescharacteristic
52M16×C71—42no—
53C2×C8×C71—22no—
54C23×C71—22no—
55C23×C71—22no—
56C23×C71—21no—
57C23×C71—21no—
58C23×C71C22⋊C411yescharacteristic
59C23×C71C22⋊C411yescharacteristic
60C23×C71C2×D411yescharacteristic
61C22×D71—21no—
62C2×C4×C71—22no—
63C2×C4×C71—22no—
64C2×C4×C71—41no—
65C2×C4×C71—41no—
66C2×C4×C71—41no—
67C2×C4×C71—41no—
68C2×C4×C71C22⋊C411yescharacteristic
69C2×C4×C71C22⋊C411yescharacteristic
70C2×C4×C71C22×C411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C22⋊D71—42no—
73C22⋊D71—42no—
74C22⋊D71—41no—
75C22⋊D71—41no—
76C2×Dic71—24no—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—48no—
81C2×Dic71—42no—
82C2×Dic71—42no—
83D284—41no—
84C4×D71—42no—
85Dic142—41no—
86C8×C71—42no—
87C22×C71—24no—
88C22×C71—24no—
89C22×C71—21no—
90C22×C71—21no—
91C22×C71—21no—
92C22×C71—21no—
93C22×C71—21no—
94C22×C71—21no—
95C22×C71#9912yes—
96C22×C71#10412yes—
97C22×C71C2×C22⋊C411yescharacteristic
98C22×C71AGL(1,ℤ/8)11yescharacteristic
99C22×C71#13711yescharacteristic
100C2×D71—41no—
101C2×D71—41no—
102C2×D71—41no—
103C4×C71—21no—
104C4×C71—21no—
105C4×C71—21no—
106C4×C71—21no—
107Dic71—44no—
108Dic71—41no—
109Dic71—41no—
110Dic71—41no—
111C2×C71—21no—
112C2×C71—22no—
113C2×C71—22no—
114C2×C71—21no—
115C2×C71C2×#9911yescharacteristic
116C2×C71#41711yescharacteristic
117C2×C71C2×#10411yescharacteristic
118D71—81no—
119#1504—711nomaximal, Sylow
120C71#150411yescharacteristic, complemented, Sylow
121#525—711no—
122#407D7111yescharacteristic, complemented
123C2×#95—711no—
124#328—712no—
125#327—712no—
126C2×#41—711no—
127C23×C4—1421no—
128C23×C4C2×D7111yescharacteristic
129C2×M16—21no—
130#123—1421no—
131C22⋊Q8—711no—
132C22⋊Q8—711no—
133#121—711no—
134#121—711no—
135#120—1421no—
136C4×D4—1421no—
137C4×D4—1421no—
138#117—711no—
139C22⋊C8—21no—
140C22⋊C8C2×D7112yes—
141#95—712no—
142#95—1421no—
143C24D28411yescharacteristic
144#41—2842no—
145C2×Q8—711no—
146C2×D4—711no—
147C2×D4—1421no—
148C2×D4—1421no—
149C2×D4—1421no—
150C22×C4—42no—
151C22×C4—2842no—
152C22×C4—2842no—
153C22×C4—1424no—
154C22×C4—1422no—
155C22×C4—1421no—
156C22×C4C4×D7111yescharacteristic
157C22×C4C4×D7111yescharacteristic
158C22×C4D28411yescharacteristic
159C22×C4C22⋊D7111yescharacteristic
160C22×C4C22⋊D7111yescharacteristic
161C22×C4C22×D7111yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—711no—
165C4⋊C4—711no—
166C4⋊C4—1421no—
167C4⋊C4—1421no—
168C22⋊C4—1421no—
169C22⋊C4—1421no—
170C22⋊C4—1421no—
171C22⋊C4—1421no—
172C22⋊C4—1421no—
173C42—1421no—
174C23—21no—
175C23—22no—
176C23—22no—
177C23—21no—
178C23—1421no—
179C23(C2×D71)⋊C411yescharacteristic
180C23(C2×D71)⋊C411yescharacteristic
181C23C2×D28411yescharacteristic
182Q8—2841no—
183D4—2841no—
184D4—2841no—
185D4—2842no—
186D4—2842no—
187D4—2841no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2842no—
195C2×C4—2848no—
196C2×C4—2842no—
197C2×C4—2842no—
198C2×C4—1424no—
199C2×C4—1421no—
200C2×C4—1421no—
201C2×C4—1421no—
202C2×C4(C2×D71)⋊C411yescharacteristic
203C2×C4(C2×D71)⋊C411yescharacteristic
204C2×C4C2×C4×D7111yescharacteristic
205C2×C4C2×C22⋊D7111yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—2841no—
216C22—2841no—
217C22—2841no—
218C22#1455604212yes—
219C22#1455605412yes—
220C22C2×(C2×D71)⋊C411yescharacteristic
221C22#1455615611yescharacteristic
222C22#1455616111yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—2844no—
228C4—2841no—
229C4—2841no—
230C4—2841no—
231C2—21no—
232C2—21no—
233C2—22no—
234C2—22no—
235C2—5681no—
236C2C2×#1455604211yescharacteristic
237C2#1798600111yescharacteristic
238C2C2×#1455605411yescharacteristic
subgroupG/H
centerC22C2×(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#407×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#407D71
hypocenterC71#1504
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C71⋊#95C2semidirect
3. #17985737C2semidirect
4. #17985734C2semidirect
5. #407×C71C2semidirect
6. C2×#11765865C4semidirect
9. #14556107C4semidirect
11. #14556102C4semidirect
16. #14556087C4semidirect
24. C2×Dic142C2×C4semidirect
25. C2×D284C2×C4semidirect
34. C4⋊Dic71C2×C4semidirect
35. C4⋊Dic71C2×C4semidirect
120. C71#1504semidirect
122. #407D71semidirect