Finite Group Databasebeta

← #22599403

Subgroups — #22599403

Order 9088.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#17986604C211yesmaximal, characteristic, complemented
2#17986575C211yesmaximal, characteristic, complemented
3#17986388C211yesmaximal, characteristic, complemented
4#17986372C211yesmaximal, characteristic, complemented
5#17986368C211yesmaximal, characteristic, complemented
6#17986354C211yesmaximal, characteristic, complemented
7#17986215C212yesmaximal, complemented
8#17986205C212yesmaximal, complemented
9#17986146C212yesmaximal, complemented
10#17986140C212yesmaximal, complemented
11#433×C71C211yesmaximal, characteristic, complemented
12C2×#11765865C2211yescharacteristic
13C22×Dic142C2211yescharacteristic
14C2×#11765854C2212yes—
15C2×#11765854C2212yes—
16C2×#11765854C2212yes—
17C2×D568C2212yes—
18#14556128C2211yescharacteristic
19#14556128C2211yescharacteristic
20#14556125C2211yescharacteristic
21#14556120C2211yescharacteristic
22#14556116C2211yescharacteristic
23#14556116C2211yescharacteristic
24#14556113—22no—
25#14556112—22no—
26#14556108—22no—
27#14556102C2212yes—
28#14556101—22no—
29C4×D284C2212yes—
30#14556053C2212yes—
31#14556053C2212yes—
32#14556053C2212yes—
33#14556050C2212yes—
34#117×C71C2211yescharacteristic
35C4⋊C8×C71C2212yes—
36C22⋊C8×C71C2212yes—
37#97×C71C2211yescharacteristic
38C4×C8×C71C2211yescharacteristic
39#11765865—42no—
40C2×Dic142—21no—
41C2×Dic142—42no—
42C2×Dic142C2311yescharacteristic
43C2×Dic142C2311yescharacteristic
44C2×Dic142C2311yescharacteristic
45C2×D284—22no—
46C2×D284C2311yescharacteristic
47C2×D284C2312yes—
48C2×C22⋊D71—21no—
49C2×C22⋊D71—22no—
50C22×Dic71—21no—
51C2×C4×D71—21no—
52C2×C4×D71—22no—
53#11765854—42no—
54#11765854—42no—
55#11765854—42no—
56D568—42no—
57C4⋊Dic71—22no—
58C4⋊Dic71—22no—
59C4⋊Dic71C2312yes—
60Dic71⋊C4—22no—
61(C2×D71)⋊C4—22no—
62(C2×D71)⋊C4—22no—
63(C2×D71)⋊C4—22no—
64(C2×D71)⋊C4—22no—
65C22×C4×C71C2311yescharacteristic
66C2×C8×C71C2312yes—
67C2×C8×C71C2312yes—
68C4⋊C4×C71D412yes—
69C22⋊C4×C71D412yes—
70C42×C71C2311yescharacteristic
71C42×C71C2311yescharacteristic
72C23×C71C2×D411yescharacteristic
73C22×D71—21no—
74C22×D71—22no—
75C2×C4×C71—22no—
76C2×C4×C71C2×D412yes—
77C2×C4×C71C2×D412yes—
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2411yescharacteristic
80C22⋊D71—42no—
81C22⋊D71—82no—
82C2×Dic71—22no—
83C2×Dic71—21no—
84C2×Dic71—21no—
85C2×Dic71—21no—
86C2×Dic71—42no—
87D284—22no—
88D284—22no—
89D284—22no—
90D284—82no—
91C4×D71—42no—
92C4×D71—82no—
93Dic142—22no—
94Dic142—22no—
95Dic142—22no—
96Dic142—42no—
97C8×C71—22no—
98C8×C71—22no—
99C22×C71—21no—
100C22×C71—22no—
101C22×C71C22×D411yescharacteristic
102C2×D71—41no—
103C2×D71—42no—
104C2×D71—42no—
105C2×D71—42no—
106C2×D71—42no—
107C4×C71—21no—
108C4×C71—22no—
109C4×C71—22no—
110C4×C71H(5,𝔽2)12yes—
111Dic71—41no—
112Dic71—41no—
113Dic71—41no—
114Dic71—42no—
115C2×C71—41no—
116C2×C71#53511yescharacteristic
117C2×C71#57712yes—
118D71—81no—
119D71—82no—
120#3221—711nomaximal, Sylow
121C71#322111yescharacteristic, complemented, Sylow
122#540—711no—
123#536—711no—
124#496—711no—
125#492—711no—
126#491—711no—
127#488—711no—
128#463—712no—
129#461—712no—
130#449—712no—
131#448—712no—
132#433D7111yescharacteristic, complemented
133C2×#41—711no—
134C22×Q8—711no—
135C2×SD16—712no—
136C2×SD16—712no—
137C2×SD16—712no—
138C2×D8—712no—
139C4⋊Q8—711no—
140C4⋊Q8—711no—
141#127—711no—
142#125—711no—
143#124—711no—
144#124—711no—
145#123—1422no—
146#123—1422no—
147C22⋊Q8—1422no—
148#121—712no—
149#121—1422no—
150C4×D4—712no—
151#117C2×D7111yescharacteristic
152C4⋊C8C2×D7112yes—
153#103—712no—
154#103—712no—
155#103—712no—
156#102—712no—
157C22⋊C8C2×D7112yes—
158#97C2×D7111yescharacteristic
159C4×C8C2×D7111yescharacteristic
160#41—2842no—
161C2×Q8—2842no—
162C2×Q8—711no—
163C2×Q8—711no—
164C2×Q8—711no—
165C2×Q8—1421no—
166C2×D4—711no—
167C2×D4—712no—
168C2×D4—1421no—
169C2×D4—1422no—
170C2×D4—1422no—
171C22×C4—1421no—
172C22×C4—1421no—
173C22×C4—1422no—
174C22×C4C22×D7111yescharacteristic
175SD16—2842no—
176SD16—2842no—
177SD16—2842no—
178D8—2842no—
179C2×C8C22×D7112yes—
180C2×C8C22×D7112yes—
181C4⋊C4—712no—
182C4⋊C4—1422no—
183C4⋊C4—1422no—
184C4⋊C4—1422no—
185C4⋊C4D28412yes—
186C22⋊C4—1422no—
187C22⋊C4—1422no—
188C22⋊C4—1422no—
189C22⋊C4—1422no—
190C22⋊C4D28412yes—
191C42C22×D7111yescharacteristic
192C42C22×D7111yescharacteristic
193C23—1421no—
194C23—1422no—
195C23C2×D28411yescharacteristic
196Q8—2842no—
197Q8—1422no—
198Q8—1422no—
199Q8—1422no—
200D4—2842no—
201D4—5682no—
202D4—5682no—
203D4—1422no—
204D4—1422no—
205D4—1422no—
206C2×C4—22no—
207C2×C4—2842no—
208C2×C4—2842no—
209C2×C4—5682no—
210C2×C4—1422no—
211C2×C4—1421no—
212C2×C4—1421no—
213C2×C4—1421no—
214C2×C4C2×D28412yes—
215C2×C4C2×D28412yes—
216C2×C4C2×D28411yescharacteristic
217C2×C4C23×D7111yescharacteristic
218C8—22no—
219C8—22no—
220C22—21no—
221C22—22no—
222C22—2841no—
223C22—2842no—
224C22—2842no—
225C22—2842no—
226C22—2842no—
227C22C22×D28411yescharacteristic
228C4—21no—
229C4—22no—
230C4—22no—
231C4—2841no—
232C4—2841no—
233C4—2841no—
234C4—2842no—
235C4#1455617412yes—
236C2—41no—
237C2—5681no—
238C2—5682no—
239C2#1798656811yescharacteristic
240C2#1798681112yes—
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#433×C71C2
socleC22×C71C22×D4
hypercenter#433D71
hypocenterC71#3221
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #17986604C2semidirect
2. #17986575C2semidirect
3. #17986388C2semidirect
4. #17986372C2semidirect
5. #17986368C2semidirect
6. #17986354C2semidirect
7. #17986215C2semidirect
8. #17986205C2semidirect
9. #17986146C2semidirect
10. #17986140C2semidirect
11. #433×C71C2semidirect
121. C71#3221semidirect
132. #433D71semidirect