Finite Group Databasebeta

← #22590049

Subgroups — #22590049

Order 9088.

232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#14556147C211yesmaximal, characteristic
2C2×#14556067C211yesmaximal, characteristic, complemented
3#107×D71C211yesmaximal, characteristic, complemented
4#17985804C211yesmaximal, characteristic, complemented
5#17985802C211yesmaximal, characteristic, complemented
6#17985800C211yesmaximal, characteristic, complemented
7#357×C71C211yesmaximal, characteristic, complemented
8C2×#11765864—21no—
9#14556147—22no—
10#14556147C414yescomplemented
11C2×Dic284C2211yescharacteristic
12C2×#11765853—21no—
13C2×C8×D71C2211yescharacteristic
14C4⋊C4×D71—21no—
15#14556067—22no—
16C2×C71⋊C16C2211yescharacteristic
17#14556062C2211yescharacteristic
18#14556061—21no—
19C2×D8×C71C2211yescharacteristic
20C2×C16×C71C2211yescharacteristic
21#107×C71C2211yescharacteristic
22#11765864—24no—
23#11765864—42no—
24C2×Dic142—21no—
25C2×C22⋊D71—41no—
26C22×Dic71—41no—
27C2×C4×D71—41no—
28C2×C4×D71D411yescharacteristic
29Dic284—21no—
30Dic284C2×C412yescomplemented
31#11765853—24no—
32C2×C71⋊C8D411yescharacteristic
33C8×D71C2×C412yes—
34C8×D71D412yes—
35C4⋊Dic71—21no—
36Dic71⋊C4—41no—
37C71⋊C16—21no—
38C2×D4×C71—21no—
39D8×C71—21no—
40D8×C71C2×C412yescomplemented
41C2×C8×C71C2311yescharacteristic
42C4⋊C4×C71—21no—
43C16×C71—21no—
44C23×C71—41no—
45C22×D71D811yescharacteristic
46D4×C71—22no—
47D4×C71—41no—
48C2×C4×C71—41no—
49C2×C4×C71C2×D411yescharacteristic
50C22⋊D71—44no—
51C2×Dic71—41no—
52C2×Dic71—44no—
53C2×Dic71—41no—
54C2×Dic71D811yescharacteristic
55C4×D71—82no—
56C4×D71C22⋊C412yes—
57C4×D71SD1612yes—
58Dic142—22no—
59Dic142—41no—
60C8×C71C22×C411yescharacteristic
61C8×C71C2×D411yescharacteristic
62C71⋊C8C22⋊C412yes—
63C22×C71—42no—
64C22×C71—81no—
65C22×C71—81no—
66C22×C71C2×D811yescharacteristic
67C2×D71—21no—
68C2×D71—21no—
69C2×D71#10212yes—
70C4×C71—81no—
71C4×C71C2×C22⋊C411yescharacteristic
72C4×C71C2×SD1611yescharacteristic
73Dic71—42no—
74Dic71—81no—
75Dic71#10212yes—
76C2×C71—82no—
77C2×C71C2×#10211yescharacteristic
78C2×C71#50911yescharacteristic
79C2×C71#51011yescharacteristic
80D71—22no—
81#2139—711nomaximal, Sylow
82C71#213911yescharacteristic, complemented, Sylow
83C2×#135—711no—
84C2×M32—711no—
85C2×#107—711no—
86#358—711no—
87#358—711no—
88#357—711no—
89#357D7111yescharacteristic, complemented
90C2×#41—1421no—
91#135—714no—
92#135—1422no—
93C2×Q16—711no—
94C2×SD16—1421no—
95C2×D8C2×D7111yescharacteristic
96C22×C8—711no—
97C2×C4⋊C4—1421no—
98M32—1422no—
99C2×C16—711no—
100C2×C16C2×D7111yescharacteristic
101#107—711no—
102#107—1421no—
103#107C2×D7111yescharacteristic
104#41—2842no—
105#41—1424no—
106C2×Q8—1421no—
107C2×D4—21no—
108C2×D4—2841no—
109C22×C4—2841no—
110C22×C4—2841no—
111C22×C4—711no—
112Q16—712no—
113Q16—1421no—
114SD16—1424no—
115D8—21no—
116D8C4×D7112yescomplemented
117C2×C8—711no—
118C2×C8—712no—
119C2×C8—712no—
120C2×C8C22×D7111yescharacteristic
121C4⋊C4—21no—
122C4⋊C4—2841no—
123C4⋊C4—1421no—
124C16—21no—
125C16—1421no—
126C23—41no—
127C23—711no—
128Q8—2841no—
129Q8—1422no—
130D4—22no—
131D4—41no—
132D4—2844no—
133C2×C4—41no—
134C2×C4—2841no—
135C2×C4—2844no—
136C2×C4—2841no—
137C2×C4—5682no—
138C2×C4—711no—
139C2×C4—712no—
140C2×C4—712no—
141C2×C4D4×D7111yescharacteristic
142C8—712no—
143C8C2×C4×D7111yescharacteristic
144C8D4×D7111yescharacteristic
145C22—42no—
146C22—81no—
147C22—81no—
148C22—712no—
149C22—1421no—
150C22—1421no—
151C22D8×D7111yescharacteristic
152C4—81no—
153C4—2842no—
154C4—5681no—
155C4—712no—
156C4C22⋊C4×D7111yescharacteristic
157C4SD16×D7111yescharacteristic
158C2—82no—
159C2—1422no—
160C2#102×D7111yescharacteristic
161C2#1798643311yescharacteristic
162C2#1798643811yescharacteristic
subgroupG/H
centerC22D8×D71
commutatorC8×C71C22×C4
FrattiniC2×C8C22×D71
Fitting#357×C71C2
socleC22×C71C2×D8
hypercenter#357D71
hypocenterC71#2139
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#14556067C2semidirect
3. #107×D71C2semidirect
4. #17985804C2semidirect
5. #17985802C2semidirect
6. #17985800C2semidirect
7. #357×C71C2semidirect
10. #14556147C4semidirect
30. Dic284C2×C4semidirect
40. D8×C71C2×C4semidirect
82. C71#2139semidirect
89. #357D71semidirect
116. D8C4×D71semidirect