Finite Group Databasebeta

← #22598958

Subgroups — #22598958

Order 9088.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#17986622C212yesmaximal, complemented
2#17986396C211yesmaximal, characteristic, complemented
3#17986384C211yesmaximal, characteristic, complemented
4#17986360C212yesmaximal, complemented
5#17986252C211yesmaximal, characteristic
6#17986230C212yesmaximal, complemented
7#17986110C211yesmaximal, characteristic, complemented
8#17986106C211yesmaximal, characteristic, complemented
9#17986084C212yesmaximal, complemented
10#17985957C211yesmaximal, characteristic, complemented
11#470×C71C211yesmaximal, characteristic, complemented
12C2×#11765852C2212yes—
13C2×D568C2211yescharacteristic
14C22×C71⋊C8C2211yescharacteristic
15#14556127C2212yes—
16#14556123—22no—
17#14556117C2212yes—
18#14556114—22no—
19#14556110—22no—
20#14556108—22no—
21#14556102C2212yes—
22Q8×Dic71C2212yes—
23#14556090C2212yes—
24#14556087C2211yescharacteristic
25#14556060C2211yescharacteristic
26#14556059C2212yes—
27#14556052C2212yes—
28#14556050C2212yes—
29#14556048C2212yes—
30#14556038C2211yescharacteristic
31#14556038C2211yescharacteristic
32C8×Dic71C2211yescharacteristic
33C8×Dic71C2211yescharacteristic
34C2×Q16×C71C2211yescharacteristic
35C2×M16×C71C2211yescharacteristic
36C22⋊Q8×C71C2212yes—
37#106×C71C2211yescharacteristic
38#103×C71C2212yes—
39C2×Dic142—22no—
40C2×D284C2312yes—
41C2×C22⋊D71—22no—
42C2×C4×D71—22no—
43#11765852—24no—
44D568—22no—
45C2×C71⋊C8—22no—
46C2×C71⋊C8C2311yescharacteristic
47C2×C71⋊C8C2311yescharacteristic
48C4⋊Dic71—22no—
49C4⋊Dic71D412yes—
50C4⋊Dic71C2312yes—
51Dic71⋊C4—22no—
52C22⋊Dic71D412yes—
53(C2×D71)⋊C4—22no—
54(C2×D71)⋊C4—22no—
55(C2×D71)⋊C4—22no—
56(C2×D71)⋊C4—22no—
57C4×Dic71—22no—
58C4×Dic71C2311yescharacteristic
59C4×Dic71C2311yescharacteristic
60C2×Q8×C71C2312yes—
61C22×C4×C71C2311yescharacteristic
62Q16×C71—22no—
63M16×C71—22no—
64C2×C8×C71C2311yescharacteristic
65C2×C8×C71C2311yescharacteristic
66C4⋊C4×C71—22no—
67C4⋊C4×C71C2312yes—
68C22⋊C4×C71—22no—
69C23×C71C2×D411yescharacteristic
70C22×D71—22no—
71Q8×C71—22no—
72Q8×C71—22no—
73C2×C4×C71—21no—
74C2×C4×C71—21no—
75C2×C4×C71—22no—
76C2×C4×C71—22no—
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2411yescharacteristic
79C22⋊D71—82no—
80C2×Dic71—22no—
81C2×Dic71C2×D412yes—
82C2×Dic71C2×D412yes—
83D284—22no—
84D284—22no—
85C4×D71—82no—
86Dic142—82no—
87C8×C71—21no—
88C8×C71#4112yes—
89C71⋊C8—21no—
90C71⋊C8#4112yes—
91C22×C71—21no—
92C22×C71—22no—
93C22×C71C22×D411yescharacteristic
94C2×D71—42no—
95C2×D71—42no—
96C2×D71—42no—
97C4×C71—21no—
98C4×C71—42no—
99C4×C71—42no—
100C4×C71C2×#4111yescharacteristic
101C4×C71C2×#4111yescharacteristic
102Dic71—22no—
103Dic71—22no—
104Dic71—42no—
105C2×C71—41no—
106C2×C71#53211yescharacteristic
107C2×C71#57712yes—
108D71—82no—
109#3173—711nomaximal, Sylow
110C71#317311yescharacteristic, complemented, Sylow
111#542—712no—
112#498—711no—
113#495—711no—
114#489—712no—
115#470D7111yescharacteristic, complemented
116#469—711no—
117#465—712no—
118#442—711no—
119#441—711no—
120C4×SD16—712no—
121#405—711no—
122C2×Q16C2×D7111yescharacteristic
123C2×SD16—712no—
124C2×D8—711no—
125C2×M16C2×D7111yescharacteristic
126C22×C8—711no—
127C4⋊Q8—712no—
128#126—1422no—
129#124—712no—
130#124—1422no—
131#123—1422no—
132C22⋊Q8—1422no—
133C22⋊Q8C2×D7112yes—
134#121—712no—
135C4×Q8—712no—
136C4×D4—712no—
137#117—711no—
138#106—711no—
139#106—712no—
140#106C2×D7111yescharacteristic
141#103—712no—
142#103C2×D7112yes—
143#102—712no—
144#102—712no—
145#97—711no—
146#97—711no—
147C4×C8—711no—
148C4×C8—711no—
149C2×Q8—1422no—
150C2×Q8C22×D7112yes—
151C2×D4—712no—
152C2×D4—1422no—
153C22×C4—1422no—
154C22×C4C22×D7111yescharacteristic
155Q16—22no—
156SD16—1424no—
157D8—1422no—
158M16—22no—
159C2×C8—711no—
160C2×C8—711no—
161C2×C8—1422no—
162C2×C8C22×D7111yescharacteristic
163C2×C8C22×D7111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—712no—
166C4⋊C4—712no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4C22×D7112yes—
170C22⋊C4—22no—
171C22⋊C4—712no—
172C22⋊C4—1422no—
173C22⋊C4—1422no—
174C22⋊C4—1422no—
175C22⋊C4—1422no—
176C42—711no—
177C42—711no—
178C42—1422no—
179C23—1422no—
180C23D4×D7111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—5682no—
184D4—5682no—
185D4—1422no—
186D4—1422no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—5682no—
192C2×C4—712no—
193C2×C4—712no—
194C2×C4—1422no—
195C2×C4D4×D7111yescharacteristic
196C2×C4C23×D7111yescharacteristic
197C8—21no—
198C8—712no—
199C8—1421no—
200C8#1176586412yes—
201C22—21no—
202C22—22no—
203C22—2842no—
204C22—2842no—
205C22—2842no—
206C22C2×D4×D7111yescharacteristic
207C4—21no—
208C4—42no—
209C4—42no—
210C4—2842no—
211C4—1422no—
212C4—1422no—
213C4#41×D7111yescharacteristic
214C4C2×#1176586411yescharacteristic
215C2—41no—
216C2—5682no—
217C2#1798654411yescharacteristic
218C2#1798680812yes—
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#470×C71C2
socleC22×C71C22×D4
hypercenter#470D71
hypocenterC71#3173
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #17986622C2semidirect
2. #17986396C2semidirect
3. #17986384C2semidirect
4. #17986360C2semidirect
6. #17986230C2semidirect
7. #17986110C2semidirect
8. #17986106C2semidirect
9. #17986084C2semidirect
10. #17985957C2semidirect
11. #470×C71C2semidirect
110. C71#3173semidirect
115. #470D71semidirect