Finite Group Databasebeta

← #22587460

Subgroups — #22587460

Order 9088.

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

normal subgroups only

This group has 218 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#17986734C211yesmaximal, characteristic
2#17986373C211yesmaximal, characteristic
3#17986291C211yesmaximal, characteristic, complemented
4#17985742C211yesmaximal, characteristic
5Q8⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
6#17985729C211yesmaximal, characteristic, complemented
7#477×C71C211yesmaximal, characteristic, complemented
8C2×#11765852—22no—
9#14556125C2211yescharacteristic
10#14556117—21no—
11#14556116—21no—
12#14556113—22no—
13C4×Dic142C2211yescharacteristic
14C4×D284—21no—
15#14556090—21no—
16#14556061—21no—
17C4⋊(C71⋊C8)C2211yescharacteristic
18#14556051—21no—
19C4×C71⋊C8C2211yescharacteristic
20C4⋊Q8×C71C2211yescharacteristic
21C4×Q8×C71C2211yescharacteristic
22#107×C71—21no—
23C4⋊C8×C71C2211yescharacteristic
24#103×C71—21no—
25C2×Dic142D411yescharacteristic
26C2×D284—21no—
27C2×D284—21no—
28C2×D284D412yes—
29C2×C4×D71—22no—
30#11765852—44no—
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C4⋊Dic71D411yescharacteristic
34Dic71⋊C4—21no—
35(C2×D71)⋊C4—22no—
36(C2×D71)⋊C4—22no—
37(C2×D71)⋊C4—22no—
38C4×Dic71—21no—
39C2×Q8×C71—21no—
40C2×Q8×C71D411yescharacteristic
41C2×C8×C71—21no—
42C4⋊C4×C71—21no—
43C4⋊C4×C71—21no—
44C4⋊C4×C71—21no—
45C4⋊C4×C71D411yescharacteristic
46C42×C71—21no—
47C42×C71C2311yescharacteristic
48C22×D71—22no—
49Q8×C71—21no—
50Q8×C71—21no—
51Q8×C71—42no—
52C2×C4×C71—21no—
53C2×C4×C71—21no—
54C2×C4×C71—41no—
55C2×C4×C71C2×D411yescharacteristic
56C2×C4×C71C2×D411yescharacteristic
57C2×C4×C71C2×D411yescharacteristic
58C2×Dic71—21no—
59C2×Dic71—21no—
60D284—42no—
61D284—41no—
62D284—41no—
63D284—41no—
64D284—41no—
65C4×D71—82no—
66Dic142—21no—
67Dic142—21no—
68C8×C71—41no—
69C71⋊C8—22no—
70C71⋊C8—41no—
71C22×C71#12011yescharacteristic
72C2×D71—42no—
73C2×D71—42no—
74C2×D71—42no—
75C4×C71—21no—
76C4×C71—41no—
77C4×C71—41no—
78C4×C71—81no—
79C4×C71#13511yescharacteristic
80C4×C71#13511yescharacteristic
81C4×C71#13711yescharacteristic
82C4×C71#13711yescharacteristic
83Dic71—41no—
84Dic71—41no—
85C2×C71#45211yescharacteristic
86C2×C71#45211yescharacteristic
87C2×C71#45311yescharacteristic
88D71—82no—
89#1630—711nomaximal, Sylow
90C71#163011yescharacteristic, complemented, Sylow
91#559—711no—
92#492—711no—
93#477—711no—
94#477D7111yescharacteristic, complemented
95#331—711no—
96Q8⋊C8—711no—
97Q8⋊C8—711no—
98C2×SD16—1422no—
99C4⋊Q8C2×D7111yescharacteristic
100#127—711no—
101#124—1421no—
102#124—1421no—
103#123—1422no—
104C4×Q8—711no—
105C4×Q8C2×D7111yescharacteristic
106C4×D4—1421no—
107C4×D4—1421no—
108#107—21no—
109#107—1421no—
110C4⋊C8—711no—
111C4⋊C8C2×D7111yescharacteristic
112#103—21no—
113#103—1421no—
114C4×C8—711no—
115C2×Q8—21no—
116C2×Q8—711no—
117C2×Q8C22⋊D7111yescharacteristic
118C2×D4—712no—
119C2×D4—1421no—
120C2×D4—1421no—
121C22×C4—1422no—
122SD16—2844no—
123C2×C8—21no—
124C2×C8—1421no—
125C2×C8—1421no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—711no—
130C4⋊C4—1421no—
131C4⋊C4C22⋊D7111yescharacteristic
132C22⋊C4—1422no—
133C22⋊C4—1422no—
134C22⋊C4—1422no—
135C42—21no—
136C42—1421no—
137C42C22×D7111yescharacteristic
138C23—1422no—
139Q8—21no—
140Q8—21no—
141Q8—42no—
142Q8—1421no—
143Q8—1421no—
144D4—2842no—
145D4—2841no—
146D4—2841no—
147D4—2841no—
148D4—2841no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—5682no—
153C2×C4—1421no—
154C2×C4—1421no—
155C2×C4D4×D7111yescharacteristic
156C2×C4D4×D7111yescharacteristic
157C2×C4C2×C22⋊D7111yescharacteristic
158C8—41no—
159C8—2841no—
160C8—1422no—
161C22—2842no—
162C22—2842no—
163C22—2842no—
164C22#1455609611yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—2841no—
170C4—2841no—
171C4#1455614811yescharacteristic
172C4#1455615111yescharacteristic
173C4#1455615911yescharacteristic
174C4#1455616011yescharacteristic
175C2—5682no—
176C2#1798615911yescharacteristic
177C2#1798616011yescharacteristic
178C2#1798616511yescharacteristic
subgroupG/H
centerC22#14556096
commutatorC42×C71C23
FrattiniC42C22×D71
Fitting#477×C71C2
socleC22×C71#120
hypercenter#477D71
hypocenterC71#1630
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #17986291C2semidirect
5. Q8⋊(C71⋊C8)C2semidirect
6. #17985729C2semidirect
7. #477×C71C2semidirect
90. C71#1630semidirect
94. #477D71semidirect