Finite Group Databasebeta

← #22586929

Subgroups — #22586929

Order 9088.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#17986533C211yesmaximal, characteristic
2C2×#14556039C211yesmaximal, characteristic, complemented
3#17985740C212yesmaximal, complemented
4#17985738C212yesmaximal, complemented
5C4×M16×C71C211yesmaximal, characteristic, complemented
6C22×C71⋊C8—21no—
7#14556122—21no—
8#14556120C2211yescharacteristic
9#14556116C2211yescharacteristic
10#14556111—21no—
11#14556107C411yescharacteristic
12#14556102C411yescharacteristic
13C4×Dic142C411yescharacteristic
14C4×D284C411yescharacteristic
15C4×C22⋊D71—21no—
16#14556085—21no—
17#14556039—21no—
18#14556039C2212yes—
19C2×M16×C71—21no—
20C2×C42×C71C2211yescharacteristic
21#97×C71C2212yes—
22C4×C8×C71—21no—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—21no—
26C2×C4×D71—21no—
27C2×C71⋊C8—24no—
28C2×C71⋊C8—22no—
29C4⋊Dic71C2×C411yescharacteristic
30C4⋊Dic71C2×C411yescharacteristic
31Dic71⋊C4—21no—
32Dic71⋊C4—21no—
33Dic71⋊C4—21no—
34Dic71⋊C4—21no—
35C22⋊Dic71—21no—
36(C2×D71)⋊C4—21no—
37(C2×D71)⋊C4—21no—
38(C2×D71)⋊C4—21no—
39(C2×D71)⋊C4—21no—
40C4×Dic71—21no—
41C22×C4×C71C2×C411yescharacteristic
42C22×C4×C71D411yescharacteristic
43C22×C4×C71D411yescharacteristic
44M16×C71—24no—
45C2×C8×C71—22no—
46C42×C71C2×C411yescharacteristic
47C42×C71D411yescharacteristic
48C42×C71D411yescharacteristic
49C42×C71C2311yescharacteristic
50C23×C71C22⋊C411yescharacteristic
51C22×D71—21no—
52C2×C4×C71—22no—
53C2×C4×C71—22no—
54C2×C4×C71—41no—
55C2×C4×C71C22⋊C411yescharacteristic
56C2×C4×C71C22⋊C411yescharacteristic
57C2×C4×C71C22⋊C411yescharacteristic
58C2×C4×C71C22×C411yescharacteristic
59C2×C4×C71C2×D411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C22⋊D71—42no—
62C2×Dic71—21no—
63C2×Dic71—21no—
64C2×Dic71—21no—
65D284—41no—
66C4×D71—42no—
67Dic142—41no—
68C8×C71—24no—
69C71⋊C8—24no—
70C22×C71—21no—
71C22×C71—21no—
72C22×C71#10412yes—
73C22×C71C2×C22⋊C411yescharacteristic
74C2×D71—41no—
75C2×D71—41no—
76C2×D71—41no—
77C4×C71—21no—
78C4×C71—21no—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71#10412yes—
83Dic71—41no—
84Dic71—41no—
85Dic71—41no—
86C2×C71—22no—
87C2×C71#41311yescharacteristic
88C2×C71C2×#10411yescharacteristic
89C2×C71C2×#10411yescharacteristic
90D71—81no—
91#1524—711nomaximal, Sylow
92C71#152411yescharacteristic, complemented, Sylow
93#529—711no—
94C4×M16D7111yescharacteristic, complemented
95C2×#97—711no—
96#330—712no—
97#329—712no—
98C2×M16—21no—
99C22×C8—1421no—
100#126—1421no—
101#125—711no—
102#124—711no—
103#123—1421no—
104C22⋊Q8—711no—
105#121—711no—
106C4×Q8—711no—
107C4×D4—711no—
108C4×D4—1421no—
109#117—1421no—
110C2×C42C2×D7111yescharacteristic
111#97—712no—
112#97—1421no—
113#97C2×D7112yes—
114C4×C8—21no—
115C2×Q8—711no—
116C2×D4—711no—
117C2×D4—1421no—
118C22×C4—1421no—
119C22×C4C4×D7111yescharacteristic
120C22×C4D28411yescharacteristic
121C22×C4C22⋊D7111yescharacteristic
122M16—24no—
123C2×C8—22no—
124C2×C8—1424no—
125C2×C8—1422no—
126C4⋊C4—711no—
127C4⋊C4—711no—
128C4⋊C4—1421no—
129C4⋊C4—1421no—
130C4⋊C4—1421no—
131C4⋊C4—1421no—
132C22⋊C4—1421no—
133C22⋊C4—1421no—
134C22⋊C4—1421no—
135C22⋊C4—1421no—
136C22⋊C4—1421no—
137C42—1421no—
138C42C4×D7111yescharacteristic
139C42D28411yescharacteristic
140C42C22⋊D7111yescharacteristic
141C42C22×D7111yescharacteristic
142C23—1421no—
143C23(C2×D71)⋊C411yescharacteristic
144Q8—2841no—
145D4—2841no—
146D4—2842no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—2842no—
151C2×C4—1421no—
152C2×C4—1421no—
153C2×C4—1421no—
154C2×C4(C2×D71)⋊C411yescharacteristic
155C2×C4(C2×D71)⋊C411yescharacteristic
156C2×C4(C2×D71)⋊C411yescharacteristic
157C2×C4C2×C4×D7111yescharacteristic
158C2×C4C2×C22⋊D7111yescharacteristic
159C2×C4C2×D28411yescharacteristic
160C8—24no—
161C8—1424no—
162C22—21no—
163C22—21no—
164C22—2841no—
165C22—2841no—
166C22—2841no—
167C22#1455605612yes—
168C22C2×(C2×D71)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—2841no—
175C4—2841no—
176C4—2841no—
177C4#1455605412yes—
178C2—22no—
179C2—5681no—
180C2#1798598111yescharacteristic
181C2C2×#1455605411yescharacteristic
182C2C2×#1455605611yescharacteristic
subgroupG/H
centerC2×C4(C2×D71)⋊C4
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
FittingC4×M16×C71C2
socleC22×C71C2×C22⋊C4
hypercenterC4×M16D71
hypocenterC71#1524
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#14556039C2semidirect
3. #17985740C2semidirect
4. #17985738C2semidirect
5. C4×M16×C71C2semidirect
92. C71#1524semidirect
94. C4×M16D71semidirect