Finite Group Databasebeta

← #22589474

Subgroups — #22589474

Order 9088.

326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556127C211yesmaximal, characteristic, complemented
2C2×#14556049C211yesmaximal, characteristic
3#17985902C211yesmaximal, characteristic
4#17985762C211yesmaximal, characteristic, complemented
5#17985761C211yesmaximal, characteristic, complemented
6#17985753C211yesmaximal, characteristic, complemented
7C2×#102×C71C211yesmaximal, characteristic
8C22×Dic142—21no—
9C22×C71⋊C8C2211yescharacteristic
10#14556127—22no—
11#14556127—22no—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×C4⋊Dic71C2211yescharacteristic
14C2×Dic71⋊C4—21no—
15C2×C22⋊Dic71—21no—
16C2×C22⋊Dic71—21no—
17C2×C4×Dic71C2211yescharacteristic
18#14556049—22no—
19C22×D4×C71C2211yescharacteristic
20C22×C8×C71C2211yescharacteristic
21C2×C4⋊C4×C71C2211yescharacteristic
22#102×C71—22no—
23C2×Dic142—24no—
24C2×Dic142—42no—
25C2×Dic142—42no—
26C22×Dic71—21no—
27C22×Dic71—21no—
28C22×Dic71D411yescharacteristic
29C22×Dic71D411yescharacteristic
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71D412yes—
37Dic71⋊C4—24no—
38C22⋊Dic71—42no—
39C22⋊Dic71—42no—
40C4×Dic71—21no—
41C4×Dic71—21no—
42C24×C71—21no—
43C2×D4×C71—21no—
44C2×D4×C71—21no—
45C2×D4×C71—21no—
46C2×D4×C71—21no—
47C2×D4×C71—21no—
48C2×D4×C71Q812yescomplemented
49C22×C4×C71—21no—
50C22×C4×C71C2311yescharacteristic
51C2×C8×C71—21no—
52C2×C8×C71—21no—
53C2×C8×C71—21no—
54C4⋊C4×C71—21no—
55C4⋊C4×C71D412yes—
56C23×C71—22no—
57C23×C71—41no—
58C23×C71—41no—
59C23×C71—41no—
60C23×C71—41no—
61C23×C71—41no—
62C23×C71—41no—
63C23×C71C2×D411yescharacteristic
64D4×C71—22no—
65D4×C71—22no—
66D4×C71—41no—
67D4×C71—41no—
68C2×C4×C71—22no—
69C2×C4×C71—41no—
70C2×C4×C71—41no—
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×Q811yescharacteristic
74C2×C4×C71#4111yescharacteristic
75C2×C4×C71#4111yescharacteristic
76C2×C4×C71#4111yescharacteristic
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—21no—
81C2×Dic71—22no—
82C2×Dic71—41no—
83C2×Dic71—41no—
84C2×Dic71—41no—
85C2×Dic71—41no—
86C2×Dic71—41no—
87C2×Dic71D812yes—
88C2×Dic71SD1612yes—
89Dic142—48no—
90C8×C71—41no—
91C71⋊C8—41no—
92C22×C71—42no—
93C22×C71—42no—
94C22×C71—42no—
95C22×C71—81no—
96C22×C71—81no—
97C22×C71—81no—
98C22×C71—81no—
99C22×C71#12011yescharacteristic
100C22×C71C22⋊Q811yescharacteristic
101C22×C71#12411yescharacteristic
102C22×C71C2×D811yescharacteristic
103C22×C71C2×SD1611yescharacteristic
104C22×C71AGL(1,ℤ/8)11yescharacteristic
105C22×C71#13711yescharacteristic
106C4×C71—42no—
107C4×C71C22⋊Q811yescharacteristic
108C4×C71C22⋊Q811yescharacteristic
109C4×C71#12411yescharacteristic
110C4×C71#12411yescharacteristic
111Dic71—22no—
112Dic71—22no—
113Dic71—42no—
114Dic71—81no—
115C2×C71—82no—
116C2×C71#39311yescharacteristic
117C2×C71#44711yescharacteristic
118C2×C71#44811yescharacteristic
119C2×C71#47411yescharacteristic
120C2×C71#47611yescharacteristic
121C2×C71#48611yescharacteristic
122C2×C71#48911yescharacteristic
123#2023—711nomaximal, Sylow
124C71#202311yescharacteristic, complemented, Sylow
125C2×C4⋊Q8—711no—
126C2×#102—711no—
127C2×#102D7111yescharacteristic
128#390—711no—
129#340—711no—
130#340—711no—
131#336—711no—
132C22×Q8—1421no—
133C22×D4C2×D7111yescharacteristic
134C22×C8—711no—
135C22×C8C2×D7111yescharacteristic
136C4⋊Q8—1422no—
137C4⋊Q8—1422no—
138C2×C4⋊C4—711no—
139C2×C4⋊C4—711no—
140C2×C4⋊C4—1421no—
141C2×C4⋊C4C2×D7111yescharacteristic
142C2×C22⋊C4—1421no—
143C2×C22⋊C4—1421no—
144C2×C42—711no—
145#102—22no—
146#102—1422no—
147C24—21no—
148C2×Q8—2842no—
149C2×Q8—2842no—
150C2×Q8—1424no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4Dic14212yescomplemented
157C22×C4—21no—
158C22×C4—711no—
159C22×C4—711no—
160C22×C4—1421no—
161C22×C4—1421no—
162C22×C4C22×D7111yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1421no—
167C2×C8—1421no—
168C2×C8—1421no—
169C4⋊C4—21no—
170C4⋊C4—712no—
171C4⋊C4—1424no—
172C4⋊C4—1421no—
173C4⋊C4—1421no—
174C4⋊C4—1421no—
175C4⋊C4C22⋊D7112yes—
176C22⋊C4—2842no—
177C22⋊C4—2842no—
178C42—1421no—
179C42—1421no—
180C23—22no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23D4×D7111yescharacteristic
188Q8—2848no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2841no—
197C2×C4—2841no—
198C2×C4—2841no—
199C2×C4—2841no—
200C2×C4—2841no—
201C2×C4—712no—
202C2×C4—712no—
203C2×C4—1422no—
204C2×C4—1421no—
205C2×C4—1421no—
206C2×C4—1421no—
207C2×C4—1421no—
208C2×C4D4×D7111yescharacteristic
209C2×C4C2×C22⋊D7111yescharacteristic
210C2×C4C2×Dic14211yescharacteristic
211C2×C4#1176586411yescharacteristic
212C2×C4#1176586411yescharacteristic
213C2×C4#1176586511yescharacteristic
214C8—41no—
215C8—2841no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22—81no—
223C22#1455609611yescharacteristic
224C22#1455610511yescharacteristic
225C22#1455611411yescharacteristic
226C22D8×D7111yescharacteristic
227C22SD16×D7111yescharacteristic
228C22#1455615211yescharacteristic
229C22#1455615711yescharacteristic
230C4—42no—
231C4—2842no—
232C4—5681no—
233C4—1422no—
234C4—1422no—
235C4#1455610511yescharacteristic
236C4#1455610711yescharacteristic
237C4#1455611411yescharacteristic
238C4#1455611511yescharacteristic
239C2—82no—
240C2#1798591111yescharacteristic
241C2#1798613111yescharacteristic
242C2#1798613611yescharacteristic
243C2#1798627711yescharacteristic
244C2#1798628711yescharacteristic
245C2#1798634411yescharacteristic
246C2#1798635711yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#102×C71C2
socleC23×C71C2×D4
hypercenterC2×#102D71
hypocenterC71#2023
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14556127C2semidirect
4. #17985762C2semidirect
5. #17985761C2semidirect
6. #17985753C2semidirect
48. C2×D4×C71Q8semidirect
124. C71#2023semidirect
156. C2×D4Dic142semidirect