Finite Group Databasebeta

← #22587638

Subgroups — #22587638

Order 9088.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#17986389C211yesmaximal, characteristic
2#17986365C212yesmaximal, complemented
3#17985741C212yesmaximal, complemented
4#17985739C211yesmaximal, characteristic, complemented
5#563×C71C211yesmaximal, characteristic, complemented
6C2×#11765852—21no—
7C2×#11765850—21no—
8#14556125C2211yescharacteristic
9#14556048—22no—
10#14556048—22no—
11#14556039C2212yes—
12#14556039C2211yescharacteristic
13C4⋊Q8×C71—21no—
14#126×C71—22no—
15#125×C71C2212yes—
16#124×C71C2211yescharacteristic
17#123×C71—21no—
18C22⋊Q8×C71—22no—
19C2×D284—22no—
20C2×D284—21no—
21#11765852—42no—
22#11765850—42no—
23C2×C71⋊C8—21no—
24C2×C71⋊C8—22no—
25C2×Q8×C71—21no—
26C2×Q8×C71D411yescharacteristic
27C2×D4×C71D411yescharacteristic
28C22×C4×C71—21no—
29C4⋊C4×C71—22no—
30C4⋊C4×C71—22no—
31C4⋊C4×C71—22no—
32C4⋊C4×C71D412yes—
33C4⋊C4×C71D412yes—
34C22⋊C4×C71—22no—
35C22⋊C4×C71—21no—
36C22⋊C4×C71—22no—
37C42×C71—21no—
38C42×C71C2311yescharacteristic
39C23×C71—21no—
40C22×D71—41no—
41Q8×C71—41no—
42Q8×C71—81no—
43D4×C71—41no—
44C2×C4×C71—22no—
45C2×C4×C71—21no—
46C2×C4×C71—22no—
47C2×C4×C71—81no—
48C2×C4×C71C2×D412yes—
49C2×C4×C71C2×D411yescharacteristic
50D284—41no—
51D284—41no—
52D284—44no—
53C71⋊C8—22no—
54C71⋊C8—42no—
55C22×C71—41no—
56C22×C71—42no—
57C22×C71#12011yescharacteristic
58C2×D71—81no—
59C2×D71—82no—
60C4×C71—21no—
61C4×C71—22no—
62C4×C71—42no—
63C4×C71—41no—
64C4×C71—42no—
65C2×C71—81no—
66C2×C71#45311yescharacteristic
67C2×C71#45412yes—
68D71—161no—
69#1657—711nomaximal, Sylow
70C71#165711yescharacteristic, complemented, Sylow
71#563D7111yescharacteristic, complemented
72#496—711no—
73#490—712no—
74#330—712no—
75#329—711no—
76C2×SD16—1421no—
77C2×D8—1421no—
78C4⋊Q8—21no—
79#127—711no—
80#126—22no—
81#125C2×D7112yes—
82#124C2×D7111yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—1422no—
86#102—1422no—
87#97—712no—
88#97—711no—
89C2×Q8—21no—
90C2×Q8C22⋊D7111yescharacteristic
91C2×D4—1422no—
92C2×D4—1421no—
93C2×D4C22⋊D7111yescharacteristic
94C22×C4—21no—
95SD16—2842no—
96D8—2842no—
97C2×C8—1422no—
98C2×C8—1421no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D7112yes—
103C4⋊C4C22⋊D7112yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D7111yescharacteristic
109C23—21no—
110C23—2841no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—2841no—
115D4—2841no—
116D4—2844no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D7112yes—
122C2×C4C2×C22⋊D7111yescharacteristic
123C8—2842no—
124C8—1422no—
125C22—41no—
126C22—42no—
127C22—5681no—
128C22—5682no—
129C22#1455609711yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—11361no—
137C2#1798616711yescharacteristic
138C2#1798617212yes—
subgroupG/H
centerC22#14556097
commutatorC42×C71C23
FrattiniC42C22×D71
Fitting#563×C71C2
socleC22×C71#120
hypercenter#563D71
hypocenterC71#1657
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #17986365C2semidirect
3. #17985741C2semidirect
4. #17985739C2semidirect
5. #563×C71C2semidirect
70. C71#1657semidirect
71. #563D71semidirect