Finite Group Databasebeta

← #22587613

Subgroups — #22587613

Order 9088.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#17986719C211yesmaximal, characteristic
2#17986397C211yesmaximal, characteristic, complemented
3#17986279C211yesmaximal, characteristic
4#17986210C211yesmaximal, characteristic, complemented
5#17985744C211yesmaximal, characteristic, complemented
6#17985731C211yesmaximal, characteristic, complemented
7D4⋊C8×C71C211yesmaximal, characteristic
8C2×Dic284—21no—
9#14556128C2211yescharacteristic
10#14556128C2211yescharacteristic
11#14556121—22no—
12#14556115—21no—
13#14556107—21no—
14C4×Dic142C2211yescharacteristic
15#14556093—21no—
16#14556087—21no—
17#14556061—21no—
18#14556060—22no—
19C4⋊(C71⋊C8)C2211yescharacteristic
20#14556053—21no—
21#14556049—21no—
22C4×D4×C71C2211yescharacteristic
23C4⋊C8×C71C2211yescharacteristic
24C4×C8×C71C2211yescharacteristic
25C2×Dic142—21no—
26C2×Dic142—21no—
27C2×Dic142D411yescharacteristic
28Dic284—42no—
29C2×C71⋊C8—21no—
30C4⋊Dic71—21no—
31C4⋊Dic71—21no—
32C4⋊Dic71—21no—
33C4⋊Dic71D411yescharacteristic
34C4⋊Dic71D412yes—
35Dic71⋊C4—22no—
36Dic71⋊C4—21no—
37C22⋊Dic71—22no—
38C22⋊Dic71—22no—
39C4×Dic71—22no—
40C4×Dic71—21no—
41C2×D4×C71D411yescharacteristic
42C22×C4×C71—21no—
43C2×C8×C71—21no—
44C2×C8×C71—21no—
45C4⋊C4×C71D411yescharacteristic
46C22⋊C4×C71—21no—
47C42×C71C2311yescharacteristic
48C23×C71—21no—
49D4×C71—21no—
50D4×C71—21no—
51C2×C4×C71—21no—
52C2×C4×C71—41no—
53C2×C4×C71—41no—
54C2×C4×C71C2×D411yescharacteristic
55C2×C4×C71C2×D411yescharacteristic
56C2×C4×C71C2×D411yescharacteristic
57C2×Dic71—21no—
58C2×Dic71—21no—
59C2×Dic71—22no—
60C2×Dic71—41no—
61Dic142—21no—
62Dic142—21no—
63Dic142—41no—
64Dic142—41no—
65Dic142—41no—
66Dic142—41no—
67C8×C71—22no—
68C8×C71—41no—
69C71⋊C8—41no—
70C22×C71—41no—
71C22×C71—41no—
72C22×C71—41no—
73C22×C71#12011yescharacteristic
74C4×C71—21no—
75C4×C71—41no—
76C4×C71#13511yescharacteristic
77C4×C71#13511yescharacteristic
78C4×C71AGL(1,ℤ/8)11yescharacteristic
79C4×C71#13711yescharacteristic
80Dic71—41no—
81Dic71—42no—
82Dic71—41no—
83Dic71—81no—
84C2×C71—81no—
85C2×C71#44911yescharacteristic
86C2×C71#45211yescharacteristic
87C2×C71#45611yescharacteristic
88#1652—711nomaximal, Sylow
89C71#165211yescharacteristic, complemented, Sylow
90#556—711no—
91#498—711no—
92#474—711no—
93#462—711no—
94#332—711no—
95Q8⋊C8—711no—
96D4⋊C8D7111yescharacteristic
97C2×Q16—1421no—
98C4⋊Q8—711no—
99C4⋊Q8—711no—
100#126—1422no—
101#124—1421no—
102C22⋊Q8—1421no—
103C4×Q8—711no—
104C4×Q8—1421no—
105C4×D4C2×D7111yescharacteristic
106#117—1421no—
107#107—1421no—
108#106—1422no—
109C4⋊C8—711no—
110C4⋊C8C2×D7111yescharacteristic
111#103—1421no—
112#102—1421no—
113C4×C8C2×D7111yescharacteristic
114C2×Q8—711no—
115C2×Q8—1421no—
116C2×Q8—1421no—
117C2×D4D28411yescharacteristic
118C22×C4—21no—
119Q16—2842no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1421no—
123C4⋊C4—711no—
124C4⋊C4—712no—
125C4⋊C4—1422no—
126C4⋊C4—1421no—
127C4⋊C4—1421no—
128C4⋊C4—1421no—
129C4⋊C4—1421no—
130C4⋊C4D28411yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—1422no—
133C22⋊C4—1422no—
134C42—1422no—
135C42—1421no—
136C42C22×D7111yescharacteristic
137C23—21no—
138Q8—2841no—
139Q8—2841no—
140Q8—2841no—
141Q8—2841no—
142Q8—1421no—
143Q8—1421no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2841no—
150C2×C4—1421no—
151C2×C4—1422no—
152C2×C4—1421no—
153C2×C4D4×D7111yescharacteristic
154C2×C4D4×D7111yescharacteristic
155C2×C4C2×D28411yescharacteristic
156C8—22no—
157C8—41no—
158C8—2841no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1455609811yescharacteristic
163C4—21no—
164C4—41no—
165C4—2841no—
166C4—2842no—
167C4—2841no—
168C4—5681no—
169C4#1455614911yescharacteristic
170C4#1455615011yescharacteristic
171C4#1455615211yescharacteristic
172C4#1455616111yescharacteristic
173C2—81no—
174C2#1798614511yescharacteristic
175C2#1798616311yescharacteristic
176C2#1798618311yescharacteristic
subgroupG/H
centerC22#14556098
commutatorC42×C71C23
FrattiniC42C22×D71
FittingD4⋊C8×C71C2
socleC22×C71#120
hypercenterD4⋊C8D71
hypocenterC71#1652
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17986397C2semidirect
4. #17986210C2semidirect
5. #17985744C2semidirect
6. #17985731C2semidirect
89. C71#1652semidirect