Finite Group Databasebeta

← #22598989

Subgroups — #22598989

Order 9088.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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#17986605C211yesmaximal, characteristic, complemented
2#17986603C211yesmaximal, characteristic, complemented
3#17986398C211yesmaximal, characteristic, complemented
4#17986375C211yesmaximal, characteristic, complemented
5#17986364C211yesmaximal, characteristic, complemented
6#17986251C212yesmaximal, complemented
7#17986234C212yesmaximal, complemented
8#17986108C212yesmaximal, complemented
9#17986079C212yesmaximal, complemented
10#17985956C211yesmaximal, characteristic, complemented
11#490×C71C211yesmaximal, characteristic, complemented
12C2×#11765850C2212yes—
13C2×#11765850C2212yes—
14C2×#11765848C2211yescharacteristic
15C2×C8×D71C2211yescharacteristic
16#14556125C2211yescharacteristic
17#14556120C2211yescharacteristic
18#14556113—22no—
19#14556109—22no—
20#14556103—22no—
21#14556103C2212yes—
22#14556100—22no—
23#14556099C2212yes—
24D4×Dic71C2212yes—
25#14556090C2212yes—
26#14556085C2211yescharacteristic
27#14556061C2212yes—
28#14556059C2212yes—
29#14556050C2212yes—
30#14556050C2212yes—
31#14556038C2211yescharacteristic
32C4×C71⋊C8C2211yescharacteristic
33C8×Dic71C2211yescharacteristic
34#127×C71C2211yescharacteristic
35#125×C71C2211yescharacteristic
36#102×C71C2212yes—
37#102×C71C2212yes—
38#97×C71C2211yescharacteristic
39C2×D284—22no—
40C2×D284—22no—
41C2×D284C2312yes—
42C2×C22⋊D71—22no—
43C22×Dic71—22no—
44C2×C4×D71—22no—
45C2×C4×D71C2311yescharacteristic
46#11765850—24no—
47#11765850—24no—
48#11765848—22no—
49C2×C71⋊C8C2311yescharacteristic
50C2×C71⋊C8C2311yescharacteristic
51C8×D71—22no—
52C4⋊Dic71C2312yes—
53Dic71⋊C4—22no—
54Dic71⋊C4D412yes—
55C22⋊Dic71—22no—
56C22⋊Dic71—22no—
57(C2×D71)⋊C4—22no—
58(C2×D71)⋊C4—22no—
59(C2×D71)⋊C4D412yes—
60C4×Dic71C2311yescharacteristic
61C2×D4×C71—22no—
62C2×D4×C71C2312yes—
63C2×C8×C71C2311yescharacteristic
64C2×C8×C71C2311yescharacteristic
65C4⋊C4×C71—22no—
66C4⋊C4×C71C2312yes—
67C42×C71C2311yescharacteristic
68C23×C71—22no—
69C22×D71—22no—
70C22×D71C2×D411yescharacteristic
71D4×C71—22no—
72D4×C71—22no—
73D4×C71—82no—
74C2×C4×C71—22no—
75C2×C4×C71C2×D412yes—
76C2×C4×C71C2411yescharacteristic
77C22⋊D71—82no—
78C2×Dic71—22no—
79C2×Dic71—82no—
80C2×Dic71C2×D412yes—
81C2×Dic71C2×D411yescharacteristic
82D284—22no—
83D284—22no—
84D284—82no—
85D284—82no—
86C4×D71—21no—
87C4×D71—21no—
88C4×D71—82no—
89C8×C71—21no—
90C8×C71—21no—
91C71⋊C8#4112yes—
92C71⋊C8#4112yes—
93C22×C71—42no—
94C22×C71—42no—
95C22×C71—42no—
96C22×C71C22×D411yescharacteristic
97C2×D71—21no—
98C2×D71—22no—
99C2×D71—42no—
100C2×D71—42no—
101C2×D71—42no—
102C4×C71—22no—
103C4×C71—42no—
104C4×C71C2×#4111yescharacteristic
105C4×C71C2×#4111yescharacteristic
106Dic71—21no—
107Dic71—22no—
108Dic71—42no—
109C2×C71—82no—
110C2×C71#53211yescharacteristic
111C2×C71#57612yes—
112D71—41no—
113D71—82no—
114#3176—711nomaximal, Sylow
115C71#317611yescharacteristic, complemented, Sylow
116#540—711no—
117#540—711no—
118#499—711no—
119#493—711no—
120#490—711no—
121#490D7111yescharacteristic, complemented
122#469—712no—
123#466—712no—
124#442—712no—
125C4×D8—712no—
126#405—711no—
127C2×D8—712no—
128C2×D8—712no—
129C2×M16—711no—
130C22×C8—711no—
131#127—711no—
132#127C2×D7111yescharacteristic
133#125—711no—
134#125C2×D7111yescharacteristic
135#123—1422no—
136#123—1422no—
137#121—712no—
138#121—712no—
139#121—1422no—
140#121—1422no—
141C4×D4—712no—
142C4×D4—712no—
143#117—711no—
144#107—712no—
145#106—712no—
146#102—712no—
147#102—712no—
148#102C2×D7112yes—
149#102C2×D7112yes—
150#97—711no—
151#97C2×D7111yescharacteristic
152C4×C8—711no—
153C4×C8—711no—
154C2×D4—22no—
155C2×D4—712no—
156C2×D4—1422no—
157C2×D4—1422no—
158C2×D4—1422no—
159C2×D4C22×D7112yes—
160C22×C4—711no—
161C22×C4—1422no—
162C22×C4—1422no—
163D8—1424no—
164D8—1424no—
165M16—1422no—
166C2×C8—711no—
167C2×C8—711no—
168C2×C8—1422no—
169C2×C8C22×D7111yescharacteristic
170C2×C8C22×D7111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—712no—
173C4⋊C4—712no—
174C4⋊C4—1422no—
175C4⋊C4C22×D7112yes—
176C22⋊C4—712no—
177C22⋊C4—1422no—
178C22⋊C4—1422no—
179C22⋊C4—1422no—
180C22⋊C4—1422no—
181C42—711no—
182C42C22×D7111yescharacteristic
183C23—22no—
184C23—711no—
185C23—1422no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—5682no—
190D4—5682no—
191D4—5682no—
192D4—1422no—
193D4—1422no—
194C2×C4—22no—
195C2×C4—5682no—
196C2×C4—5682no—
197C2×C4—712no—
198C2×C4—711no—
199C2×C4—1422no—
200C2×C4—1421no—
201C2×C4—1421no—
202C2×C4D4×D7112yes—
203C2×C4C23×D7111yescharacteristic
204C8—21no—
205C8—21no—
206C8—712no—
207C8—712no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—2842no—
212C22—2842no—
213C22—2842no—
214C22—1422no—
215C22—1421no—
216C22C2×D4×D7111yescharacteristic
217C4—22no—
218C4—42no—
219C4—2842no—
220C4—1422no—
221C4—1421no—
222C4#41×D7111yescharacteristic
223C4#41×D7111yescharacteristic
224C2—82no—
225C2—2841no—
226C2—5682no—
227C2#1798654811yescharacteristic
228C2#1798680312yes—
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#490×C71C2
socleC22×C71C22×D4
hypercenter#490D71
hypocenterC71#3176
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17986605C2semidirect
2. #17986603C2semidirect
3. #17986398C2semidirect
4. #17986375C2semidirect
5. #17986364C2semidirect
6. #17986251C2semidirect
7. #17986234C2semidirect
8. #17986108C2semidirect
9. #17986079C2semidirect
10. #17985956C2semidirect
11. #490×C71C2semidirect
115. C71#3176semidirect
121. #490D71semidirect