Finite Group Databasebeta

← #22598954

Subgroups — #22598954

Order 9088.

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

normal subgroups only

This group has 362 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#17986618C212yesmaximal, complemented
2#17986397C211yesmaximal, characteristic, complemented
3#17986358C212yesmaximal, complemented
4#17986254C211yesmaximal, characteristic, complemented
5#17986249C211yesmaximal, characteristic
6#17986225C212yesmaximal, complemented
7#17986111C211yesmaximal, characteristic, complemented
8#17986106C211yesmaximal, characteristic, complemented
9SD16×Dic71C212yesmaximal, complemented
10#17985953C211yesmaximal, characteristic, complemented
11#495×C71C211yesmaximal, characteristic, complemented
12C2×#11765848C2211yescharacteristic
13C2×C8×D71C2211yescharacteristic
14#14556128C2212yes—
15#14556121—22no—
16#14556114—22no—
17#14556112—22no—
18#14556105—22no—
19#14556104C2212yes—
20#14556099C2212yes—
21Q8×Dic71C2212yes—
22D4×Dic71C2212yes—
23#14556085C2211yescharacteristic
24#14556060C2212yes—
25#14556060C2211yescharacteristic
26#14556060C2211yescharacteristic
27#14556052C2212yes—
28#14556052C2212yes—
29#14556049C2212yes—
30#14556049C2212yes—
31#14556039C2211yescharacteristic
32#14556038C2211yescharacteristic
33C8×Dic71C2211yescharacteristic
34C2×Q16×C71C2211yescharacteristic
35C2×SD16×C71C2212yes—
36C2×D8×C71C2211yescharacteristic
37#124×C71C2212yes—
38C4×C8×C71C2211yescharacteristic
39C2×Dic142—22no—
40C2×C22⋊D71—22no—
41C22×Dic71—22no—
42C2×C4×D71C2311yescharacteristic
43#11765848—22no—
44C2×C71⋊C8C2311yescharacteristic
45C2×C71⋊C8C2311yescharacteristic
46C8×D71—22no—
47C4⋊Dic71—22no—
48C4⋊Dic71—22no—
49C4⋊Dic71C2312yes—
50C4⋊Dic71C2312yes—
51Dic71⋊C4—22no—
52Dic71⋊C4D412yes—
53C22⋊Dic71—22no—
54C22⋊Dic71—22no—
55(C2×D71)⋊C4—22no—
56(C2×D71)⋊C4D412yes—
57C4×Dic71—22no—
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—82no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81C2×Dic71—82no—
82C2×Dic71C2×D412yes—
83C2×Dic71C2×D411yescharacteristic
84C4×D71—21no—
85C4×D71—21no—
86Dic142—82no—
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#57712yes—
108D71—41no—
109#3173—711nomaximal, Sylow
110C71#317311yescharacteristic, complemented, Sylow
111#542—712no—
112#498—711no—
113#495D7111yescharacteristic, complemented
114#489—712no—
115#470—711no—
116#469—711no—
117#465—712no—
118#442—711no—
119#441—711no—
120C4×SD16—712no—
121#405—711no—
122C2×Q16C2×D7111yescharacteristic
123C2×SD16C2×D7112yes—
124C2×D8C2×D7111yescharacteristic
125C2×M16—711no—
126C22×C8—711no—
127C4⋊Q8—712no—
128#126—1422no—
129#124—1422no—
130#124C2×D7112yes—
131#123—1422no—
132C22⋊Q8—712no—
133C22⋊Q8—1422no—
134#121—712no—
135C4×Q8—712no—
136C4×D4—712no—
137#117—711no—
138#106—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×Q8—1422no—
150C2×Q8C22×D7112yes—
151C2×D4—1422no—
152C2×D4C22×D7112yes—
153C22×C4—711no—
154C22×C4—1422no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—1422no—
159C2×C8—711no—
160C2×C8—711no—
161C2×C8—1422no—
162C2×C8C22×D7111yescharacteristic
163C2×C8C22×D7111yescharacteristic
164C4⋊C4—712no—
165C4⋊C4—712no—
166C4⋊C4—712no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4—1422no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—712no—
173C22⋊C4—1422no—
174C22⋊C4—1422no—
175C22⋊C4—1422no—
176C42—711no—
177C42—1422no—
178C42C22×D7111yescharacteristic
179C23—22no—
180C23—711no—
181Q8—22no—
182Q8—22no—
183Q8—5682no—
184D4—22no—
185D4—22no—
186D4—5682no—
187C2×C4—22no—
188C2×C4—5682no—
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—1421no—
205C22—1422no—
206C22C2×D4×D7111yescharacteristic
207C4—22no—
208C4—42no—
209C4—2842no—
210C4—2842no—
211C4—1421no—
212C4—1422no—
213C4C2×#1176586411yescharacteristic
214C4C2×#1176586411yescharacteristic
215C2—82no—
216C2—2841no—
217C2#1798654711yescharacteristic
218C2#1798680612yes—
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#495×C71C2
socleC22×C71C22×D4
hypercenter#495D71
hypocenterC71#3173
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. #17986618C2semidirect
2. #17986397C2semidirect
3. #17986358C2semidirect
4. #17986254C2semidirect
6. #17986225C2semidirect
7. #17986111C2semidirect
8. #17986106C2semidirect
9. SD16×Dic71C2semidirect
10. #17985953C2semidirect
11. #495×C71C2semidirect
110. C71#3173semidirect
113. #495D71semidirect