Finite Group Databasebeta

← #22599066

Subgroups — #22599066

Order 9088.

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

normal subgroups only

This group has 370 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#17986528C212yesmaximal, complemented
2#17986401C211yesmaximal, characteristic, complemented
3#17986353C212yesmaximal, complemented
4#17986254C211yesmaximal, characteristic, complemented
5#17986249C211yesmaximal, characteristic
6#17986242C212yesmaximal, complemented
7#17986111C211yesmaximal, characteristic, complemented
8#17986106C211yesmaximal, characteristic, complemented
9#17986100C212yesmaximal, complemented
10C4×#11765848C211yesmaximal, characteristic, complemented
11#495×C71C211yesmaximal, characteristic, complemented
12C2×#11765848C2211yescharacteristic
13C2×#11765848C2211yescharacteristic
14#14556121—22no—
15#14556120C2212yes—
16#14556110—22no—
17#14556104C2212yes—
18#14556099C2212yes—
19Q8×Dic71C2212yes—
20D4×Dic71C2212yes—
21(C22⋊D71)⋊C4—22no—
22#14556084—22no—
23C42×D71C2211yescharacteristic
24#14556062C2212yes—
25#14556060C2211yescharacteristic
26#14556060C2211yescharacteristic
27#14556052C2212yes—
28#14556052C2212yes—
29#14556049C2212yes—
30#14556049C2212yes—
31#14556038C2211yescharacteristic
32#14556038C2211yescharacteristic
33C4×C71⋊C8C2211yescharacteristic
34C2×Q16×C71C2211yescharacteristic
35C2×SD16×C71C2212yes—
36C2×D8×C71C2211yescharacteristic
37#124×C71C2212yes—
38C4×C8×C71C2211yescharacteristic
39C2×C22⋊D71—22no—
40C22×Dic71—22no—
41C2×C4×D71D412yes—
42C2×C4×D71C2311yescharacteristic
43#11765848—22no—
44#11765848—22no—
45C2×C71⋊C8C2311yescharacteristic
46C2×C71⋊C8C2311yescharacteristic
47C4⋊Dic71—22no—
48C4⋊Dic71C2312yes—
49C4⋊Dic71C2312yes—
50Dic71⋊C4—22no—
51Dic71⋊C4—22no—
52Dic71⋊C4—22no—
53C22⋊Dic71—22no—
54C22⋊Dic71—22no—
55(C2×D71)⋊C4—22no—
56C4×Dic71—22no—
57C4×Dic71D412yes—
58C4×Dic71C2311yescharacteristic
59C2×Q8×C71C2312yes—
60C2×D4×C71C2312yes—
61Q16×C71—22no—
62SD16×C71—24no—
63D8×C71—22no—
64C2×C8×C71C2311yescharacteristic
65C2×C8×C71C2311yescharacteristic
66C22⋊C4×C71—22no—
67C22⋊C4×C71—22no—
68C42×C71C2311yescharacteristic
69C23×C71—22no—
70C22×D71C2×D411yescharacteristic
71Q8×C71—22no—
72Q8×C71—22no—
73D4×C71—22no—
74D4×C71—22no—
75C2×C4×C71—22no—
76C2×C4×C71C2×D412yes—
77C2×C4×C71C2411yescharacteristic
78C22⋊D71—44no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—44no—
82C2×Dic71C2×D412yes—
83C2×Dic71C2×D411yescharacteristic
84C4×D71—21no—
85C4×D71—21no—
86C4×D71—42no—
87C8×C71#4112yes—
88C8×C71#4112yes—
89C71⋊C8—21no—
90C71⋊C8—21no—
91C22×C71—42no—
92C22×C71—42no—
93C22×C71—42no—
94C22×C71C22×D411yescharacteristic
95C2×D71—21no—
96C2×D71—22no—
97C4×C71—22no—
98C4×C71—42no—
99C4×C71C2×#4111yescharacteristic
100C4×C71C2×#4111yescharacteristic
101Dic71—21no—
102Dic71—22no—
103Dic71—42no—
104Dic71—42no—
105C2×C71—82no—
106C2×C71#53211yescharacteristic
107C2×C71#57512yes—
108D71—41no—
109#3183—711nomaximal, Sylow
110C71#318311yescharacteristic, complemented, Sylow
111#529—712no—
112#499—711no—
113#495D7111yescharacteristic, complemented
114#488—712no—
115#470—711no—
116#469—711no—
117#468—712no—
118#442—711no—
119#441—711no—
120#440—712no—
121C4×M16—711no—
122C2×Q16C2×D7111yescharacteristic
123C2×SD16C2×D7112yes—
124C2×D8C2×D7111yescharacteristic
125C2×M16—711no—
126C2×M16—711no—
127#126—1422no—
128#125—712no—
129#124C2×D7112yes—
130#123—1422no—
131C22⋊Q8—712no—
132#121—712no—
133C4×Q8—712no—
134C4×D4—712no—
135C4×D4—1422no—
136#117—1422no—
137C2×C42—711no—
138#107—712no—
139#106—711no—
140#106—711no—
141#103—712no—
142#103—712no—
143#102—712no—
144#102—712no—
145#97—711no—
146#97—711no—
147C4×C8—711no—
148C4×C8C2×D7111yescharacteristic
149C2×Q8C22×D7112yes—
150C2×D4—1422no—
151C2×D4C22×D7112yes—
152C22×C4—712no—
153C22×C4—711no—
154C22×C4—1422no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—1422no—
159M16—1422no—
160C2×C8—711no—
161C2×C8—711no—
162C2×C8C22×D7111yescharacteristic
163C2×C8C22×D7111yescharacteristic
164C4⋊C4—712no—
165C4⋊C4—712no—
166C4⋊C4—1422no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4—1422no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—1422no—
173C22⋊C4—1422no—
174C22⋊C4—1422no—
175C42—712no—
176C42—711no—
177C42—1422no—
178C42C22×D7111yescharacteristic
179C23—22no—
180C23—711no—
181Q8—22no—
182Q8—22no—
183D4—22no—
184D4—22no—
185D4—2844no—
186C2×C4—22no—
187C2×C4—2842no—
188C2×C4—2844no—
189C2×C4—712no—
190C2×C4—711no—
191C2×C4—1422no—
192C2×C4—1422no—
193C2×C4—1421no—
194C2×C4—1421no—
195C2×C4D4×D7112yes—
196C2×C4C23×D7111yescharacteristic
197C8—1421no—
198C8—1421no—
199C8#1176586412yes—
200C8#1176586412yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1422no—
205C22—1421no—
206C22C2×D4×D7111yescharacteristic
207C4—22no—
208C4—42no—
209C4—2842no—
210C4—2842no—
211C4—1422no—
212C4—1421no—
213C4C2×#1176586411yescharacteristic
214C4C2×#1176586411yescharacteristic
215C2—82no—
216C2—2841no—
217C2#1798654711yescharacteristic
218C2#1798679612yes—
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#495×C71C2
socleC22×C71C22×D4
hypercenter#495D71
hypocenterC71#3183
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #17986528C2semidirect
2. #17986401C2semidirect
3. #17986353C2semidirect
4. #17986254C2semidirect
6. #17986242C2semidirect
7. #17986111C2semidirect
8. #17986106C2semidirect
9. #17986100C2semidirect
10. C4×#11765848C2semidirect
11. #495×C71C2semidirect
110. C71#3183semidirect
113. #495D71semidirect