Finite Group Databasebeta

← #22589984

Subgroups — #22589984

Order 9088.

280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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#17986558C211yesmaximal, characteristic
2C2×#14556045C211yesmaximal, characteristic, complemented
3#17985788C212yesmaximal, complemented
4#17985785C212yesmaximal, complemented
5C2×#99×C71C211yesmaximal, characteristic, complemented
6C22×C22⋊D71C411yescharacteristic, complemented
7C2×#11765849—21no—
8#14556111—21no—
9#14556109C411yescharacteristic, complemented
10#14556109C2211yescharacteristic
11#14556100—21no—
12#14556100—21no—
13#14556097—21no—
14#14556096C411yescharacteristic, complemented
15#14556096C2211yescharacteristic
16C2×C22⋊Dic71C411yescharacteristic, complemented
17#14556045—21no—
18#14556045C2212yes—
19C22×D4×C71C2211yescharacteristic
20C2×C22⋊C4×C71—21no—
21#99×C71—21no—
22#99×C71C2212yes—
23C23×D71C2×C411yescharacteristic, complemented
24C2×C22⋊D71—21no—
25C2×C22⋊D71—21no—
26C2×C22⋊D71—21no—
27C2×C22⋊D71—21no—
28C2×C22⋊D71—41no—
29C2×C22⋊D71—41no—
30C22×Dic71—21no—
31C22×Dic71C2×C411yescharacteristic, complemented
32#11765849—22no—
33#11765849—41no—
34C2×C71⋊C8—41no—
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37C22⋊Dic71—21no—
38C22⋊Dic71—21no—
39C22⋊Dic71—21no—
40C22⋊Dic71C2×C411yescharacteristic, complemented
41C22⋊Dic71C2×C411yescharacteristic, complemented
42(C2×D71)⋊C4—21no—
43(C2×D71)⋊C4—21no—
44C24×C71C2×C411yescharacteristic
45C24×C71D411yescharacteristic
46C2×D4×C71—41no—
47C2×D4×C71—41no—
48C2×D4×C71C2×C411yescharacteristic
49C2×D4×C71D411yescharacteristic
50C2×D4×C71D411yescharacteristic
51C2×D4×C71C2311yescharacteristic
52C22×C4×C71—41no—
53C22×C4×C71D411yescharacteristic
54C22⋊C4×C71—22no—
55C22⋊C4×C71—41no—
56C23×C71—21no—
57C23×C71—21no—
58C23×C71—21no—
59C23×C71—21no—
60C23×C71—81no—
61C23×C71—81no—
62C23×C71C22⋊C411yescharacteristic
63C23×C71C22⋊C411yescharacteristic
64C23×C71C22⋊C411yescharacteristic
65C23×C71C22×C411yescharacteristic
66C23×C71C2×D411yescharacteristic
67C22×D71—21no—
68C22×D71—41no—
69C22×D71—81no—
70D4×C71—41no—
71D4×C71—41no—
72D4×C71—41no—
73D4×C71—41no—
74C2×C4×C71—21no—
75C2×C4×C71—21no—
76C2×C4×C71—42no—
77C2×C4×C71—82no—
78C2×C4×C71C22⋊C411yescharacteristic
79C2×C4×C71C2×D411yescharacteristic
80C22⋊D71—42no—
81C22⋊D71—41no—
82C22⋊D71—41no—
83C22⋊D71—81no—
84C22⋊D71—81no—
85C2×Dic71—21no—
86C2×Dic71—21no—
87C2×Dic71—21no—
88C2×Dic71—41no—
89C2×Dic71—81no—
90C71⋊C8—42no—
91C22×C71—21no—
92C22×C71—21no—
93C22×C71—21no—
94C22×C71—21no—
95C22×C71—41no—
96C22×C71—41no—
97C22×C71—41no—
98C22×C71—41no—
99C22×C71—41no—
100C22×C71—42no—
101C22×C71—81no—
102C22×C71—81no—
103C22×C71—81no—
104C22×C71#9911yescharacteristic
105C22×C71#9911yescharacteristic
106C22×C71C2×C22⋊C411yescharacteristic
107C2×D71—41no—
108C2×D71—41no—
109C2×D71—41no—
110C2×D71—82no—
111C4×C71—21no—
112C4×C71—21no—
113C4×C71—82no—
114Dic71—41no—
115Dic71—41no—
116Dic71—41no—
117C2×C71—21no—
118C2×C71—21no—
119C2×C71—21no—
120C2×C71—41no—
121C2×C71—41no—
122C2×C71—41no—
123C2×C71—41no—
124C2×C71C2×#9911yescharacteristic
125D71—81no—
126#2121—711nomaximal, Sylow
127C71#212111yescharacteristic, complemented, Sylow
128#534—711no—
129C2×#100—711no—
130C2×#99D7111yescharacteristic, complemented
131#352—712no—
132AΣL(1,𝔽16)—712no—
133C22×D4—711no—
134C22×D4C2×D7111yescharacteristic
135C2×M16—1421no—
136#123—711no—
137#123—711no—
138#123—1421no—
139#121—1421no—
140#121—1421no—
141#120—711no—
142#120—711no—
143#120—1421no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—711no—
146#100—712no—
147#100—1421no—
148#99—21no—
149#99C2×D7112yes—
150C24—711no—
151C24C4×D7111yescharacteristic
152C24C22⋊D7111yescharacteristic
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—2841no—
156C2×D4—2841no—
157C2×D4—1421no—
158C2×D4—1421no—
159C2×D4—1421no—
160C2×D4—1421no—
161C2×D4C4×D7111yescharacteristic
162C2×D4D28411yescharacteristic
163C2×D4C22⋊D7111yescharacteristic
164C2×D4C22×D7111yescharacteristic
165C22×C4—41no—
166C22×C4—711no—
167C22×C4—1421no—
168C22×C4D28411yescharacteristic
169M16—2841no—
170M16—1422no—
171C2×C8—2841no—
172C4⋊C4—1421no—
173C4⋊C4—1421no—
174C22⋊C4—22no—
175C22⋊C4—41no—
176C22⋊C4—711no—
177C22⋊C4—711no—
178C22⋊C4—1421no—
179C22⋊C4—1421no—
180C22⋊C4—1421no—
181C22⋊C4—1421no—
182C22⋊C4—1421no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—81no—
188C23—81no—
189C23—2841no—
190C23—5681no—
191C23—1421no—
192C23(C2×D71)⋊C411yescharacteristic
193C23(C2×D71)⋊C411yescharacteristic
194C23(C2×D71)⋊C411yescharacteristic
195C23C2×C4×D7111yescharacteristic
196C23C2×C22⋊D7111yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—2842no—
202D4—2841no—
203D4—2841no—
204D4—5681no—
205D4—5681no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—42no—
209C2×C4—82no—
210C2×C4—2841no—
211C2×C4—5681no—
212C2×C4—1421no—
213C2×C4—1421no—
214C2×C4—1421no—
215C2×C4(C2×D71)⋊C411yescharacteristic
216C2×C4C2×D28411yescharacteristic
217C8—2842no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—81no—
229C22—81no—
230C22—81no—
231C22—2841no—
232C22—2841no—
233C22—2841no—
234C22—5682no—
235C22#1455604211yescharacteristic
236C22#1455604211yescharacteristic
237C22C2×(C2×D71)⋊C411yescharacteristic
238C4—21no—
239C4—21no—
240C4—82no—
241C4—2841no—
242C4—2841no—
243C4—2841no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—5681no—
252C2C2×#1455604211yescharacteristic
subgroupG/H
centerC2C2×#14556042
commutatorC23×C71C22×C4
FrattiniC2×D4C22×D71
FittingC2×#99×C71C2
socleC2×C71C2×#99
hypercenterC2×#99D71
hypocenterC71#2121
LCSG ▷ C23×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#14556045C2semidirect
3. #17985788C2semidirect
4. #17985785C2semidirect
5. C2×#99×C71C2semidirect
6. C22×C22⋊D71C4semidirect
9. #14556109C4semidirect
14. #14556096C4semidirect
16. C2×C22⋊Dic71C4semidirect
23. C23×D71C2×C4semidirect
31. C22×Dic71C2×C4semidirect
40. C22⋊Dic71C2×C4semidirect
41. C22⋊Dic71C2×C4semidirect
127. C71#2121semidirect
130. C2×#99D71semidirect