Finite Group Databasebeta

← #22588869

Subgroups — #22588869

Order 9088.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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#17986563C211yesmaximal, characteristic
2#17986473C211yesmaximal, characteristic, complemented
3#17986016C211yesmaximal, characteristic, complemented
4C2×#14556044C211yesmaximal, characteristic, complemented
5#17985756C211yesmaximal, characteristic, complemented
6#17985755C211yesmaximal, characteristic, complemented
7#421×C71C211yesmaximal, characteristic, complemented
8C22×D284C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10#14556124C412yescomplemented
11#14556117C412yescomplemented
12#14556102—22no—
13#14556096—22no—
14C4×D284—22no—
15#14556090—22no—
16#14556087C2211yescharacteristic
17#14556087C2211yescharacteristic
18C22⋊C4×D71—22no—
19#14556055—22no—
20#14556044—22no—
21C2×#41×C71C2211yescharacteristic
22C2×M16×C71C2211yescharacteristic
23#117×C71C2211yescharacteristic
24#104×C71—22no—
25C23×D71D412yes—
26C2×D284—21no—
27C2×D284—21no—
28C2×D284—21no—
29C2×D284—21no—
30C2×D284C2×C412yes—
31C2×D284D412yes—
32C2×C22⋊D71—24no—
33C2×C4×D71—24no—
34#11765849—21no—
35#11765849—21no—
36C2×C71⋊C8—21no—
37C4⋊Dic71—21no—
38C4⋊Dic71—21no—
39C22⋊Dic71—21no—
40C22⋊Dic71—21no—
41(C2×D71)⋊C4—24no—
42(C2×D71)⋊C4—24no—
43C4×Dic71C2×C412yescomplemented
44C4×Dic71D412yescomplemented
45#41×C71—21no—
46#41×C71—21no—
47#41×C71—21no—
48#41×C71—21no—
49C2×Q8×C71C2×C411yescharacteristic, complemented
50C2×D4×C71—21no—
51C2×D4×C71C2×C411yescharacteristic, complemented
52C22×C4×C71—21no—
53C22×C4×C71C2311yescharacteristic
54M16×C71—21no—
55M16×C71—21no—
56C2×C8×C71—21no—
57C4⋊C4×C71—21no—
58C22⋊C4×C71—21no—
59C42×C71D412yescomplemented
60C23×C71—21no—
61C23×C71C2×D411yescharacteristic
62C22×D71—22no—
63C22×D71—22no—
64C22×D71—82no—
65C22×D71C22⋊C414yes—
66Q8×C71—21no—
67Q8×C71—21no—
68D4×C71—21no—
69D4×C71—21no—
70D4×C71—41no—
71D4×C71—41no—
72C2×C4×C71—21no—
73C2×C4×C71—22no—
74C2×C4×C71—41no—
75C2×C4×C71—41no—
76C2×C4×C71C22×C411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2×D411yescharacteristic
80C2×C4×C71#4111yescharacteristic
81C2×C4×C71#4111yescharacteristic
82C22⋊D71—84no—
83C2×Dic71—22no—
84C2×Dic71—22no—
85D284—22no—
86D284—22no—
87D284—22no—
88D284—22no—
89C4×D71—84no—
90C8×C71—41no—
91C71⋊C8—41no—
92C22×C71—41no—
93C22×C71—42no—
94C22×C71—41no—
95C22×C71C2×C22⋊C411yescharacteristic
96C22×C71#12011yescharacteristic
97C22×C71#12311yescharacteristic
98C2×D71—24no—
99C2×D71—44no—
100C2×D71—44no—
101C2×D71—82no—
102C4×C71—42no—
103C4×C71—41no—
104C4×C71C4×D411yescharacteristic
105C4×C71C4×D411yescharacteristic
106C4×C71#12111yescharacteristic
107C4×C71#12111yescharacteristic
108Dic71—42no—
109Dic71—42no—
110C2×C71—21no—
111C2×C71—21no—
112C2×C71—21no—
113C2×C71—81no—
114C2×C71#38611yescharacteristic
115D71—44no—
116#1911—711nomaximal, Sylow
117C71#191111yescharacteristic, complemented, Sylow
118#535—711no—
119#518—711no—
120#421—711no—
121#421D7111yescharacteristic, complemented
122C2×#100—711no—
123H(3,ℤ/4)—711no—
124H(3,ℤ/4)—711no—
125C2×#41C2×D7111yescharacteristic
126C22×D4—711no—
127C2×M16—711no—
128C2×M16C2×D7111yescharacteristic
129#127—712no—
130#124—712no—
131#121—1422no—
132#120—1422no—
133C4×D4—1422no—
134C4×D4—1422no—
135#117—711no—
136#117—711no—
137#117C2×D7111yescharacteristic
138C2×C22⋊C4—1422no—
139#104—22no—
140#104—1422no—
141#100—1422no—
142C24—712no—
143#41—21no—
144#41—21no—
145#41—21no—
146#41—21no—
147C2×Q8C4×D7111yescharacteristic, complemented
148C2×D4—21no—
149C2×D4—712no—
150C2×D4—712no—
151C2×D4—1424no—
152C2×D4—1421no—
153C2×D4—1421no—
154C2×D4—1421no—
155C2×D4—1421no—
156C2×D4C4×D7111yescharacteristic, complemented
157C22×C4—21no—
158C22×C4—1424no—
159C22×C4C22×D7111yescharacteristic
160M16—21no—
161M16—21no—
162M16—1421no—
163M16—1421no—
164C2×C8—21no—
165C2×C8—1421no—
166C4⋊C4—21no—
167C4⋊C4—1421no—
168C4⋊C4—1421no—
169C22⋊C4—21no—
170C22⋊C4—1424no—
171C22⋊C4—1424no—
172C22⋊C4—1421no—
173C22⋊C4—1421no—
174C42—712no—
175C42—712no—
176C42C22⋊D7112yescomplemented
177C23—21no—
178C23—5682no—
179C23—714no—
180C23—1422no—
181C23—1422no—
182C23D4×D7111yescharacteristic
183Q8—21no—
184Q8—21no—
185D4—21no—
186D4—21no—
187D4—41no—
188D4—41no—
189D4—5684no—
190D4—1422no—
191D4—1422no—
192D4—1422no—
193D4—1422no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—5684no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4C2×C4×D7111yescharacteristic
202C2×C4D4×D7111yescharacteristic
203C2×C4D4×D7111yescharacteristic
204C2×C4C2×C22⋊D7111yescharacteristic
205C2×C4#1176586411yescharacteristic
206C2×C4#1176586511yescharacteristic
207C8—41no—
208C8—2841no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—2844no—
213C22—2844no—
214C22—5682no—
215C22—1424no—
216C22C22⋊C4×D7111yescharacteristic
217C22#1455609611yescharacteristic
218C22#1455611011yescharacteristic
219C4—42no—
220C4—41no—
221C4—2842no—
222C4—2842no—
223C4(C22⋊D71)⋊C411yescharacteristic
224C4C4×C22⋊D7111yescharacteristic
225C4#1455609911yescharacteristic
226C4#1455610111yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—81no—
231C2—2844no—
232C2#1798587511yescharacteristic
subgroupG/H
centerC2#17985875
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#421×C71C2
socleC2×C71#386
hypercenter#421D71
hypocenterC71#1911
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #17986473C2semidirect
3. #17986016C2semidirect
4. C2×#14556044C2semidirect
5. #17985756C2semidirect
6. #17985755C2semidirect
7. #421×C71C2semidirect
10. #14556124C4semidirect
11. #14556117C4semidirect
43. C4×Dic71C2×C4semidirect
44. C4×Dic71D4semidirect
49. C2×Q8×C71C2×C4semidirect
51. C2×D4×C71C2×C4semidirect
59. C42×C71D4semidirect
117. C71#1911semidirect
121. #421D71semidirect
147. C2×Q8C4×D71semidirect
156. C2×D4C4×D71semidirect
176. C42C22⋊D71semidirect