Finite Group Databasebeta

← #22586751

Subgroups — #22586751

Order 9088.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×#11765849C211yesmaximal, characteristic, complemented
3#17985729C212yesmaximal, complemented
4#17985726C212yesmaximal, complemented
5C2×C4⋊C8×C71C211yesmaximal, characteristic, complemented
6C2×#11765849—21no—
7#14556122—21no—
8#14556120C411yescharacteristic
9#14556116C411yescharacteristic
10#14556111—21no—
11#14556107C411yescharacteristic
12#14556102C411yescharacteristic
13C4×Dic142C2211yescharacteristic
14C4×D284C2211yescharacteristic
15C4×C22⋊D71—21no—
16#14556085—21no—
17#14556039—21no—
18C4×C71⋊C8C2212yes—
19C22×C8×C71—21no—
20C2×C42×C71C2211yescharacteristic
21C4⋊C8×C71—21no—
22C4⋊C8×C71C2212yes—
23C2×Dic142C2×C411yescharacteristic
24C2×D284C2×C411yescharacteristic
25C2×C22⋊D71—21no—
26C2×C4×D71—21no—
27#11765849—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
44C2×C8×C71—22no—
45C2×C8×C71—42no—
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—21no—
55C2×C4×C71—21no—
56C2×C4×C71C22⋊C411yescharacteristic
57C2×C4×C71C22⋊C411yescharacteristic
58C2×C4×C71C22⋊C411yescharacteristic
59C2×C4×C71C22×C411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C2×C4×C71C2×D411yescharacteristic
62C22⋊D71—42no—
63C2×Dic71—21no—
64C2×Dic71—21no—
65C2×Dic71—21no—
66D284—22no—
67C4×D71—41no—
68C4×D71—41no—
69Dic142—22no—
70C8×C71—42no—
71C71⋊C8—24no—
72C22×C71—21no—
73C22×C71—21no—
74C22×C71#10412yes—
75C22×C71C2×C22⋊C411yescharacteristic
76C2×D71—41no—
77C2×D71—41no—
78C2×D71—41no—
79C4×C71—21no—
80C4×C71—21no—
81C4×C71—21no—
82C4×C71—21no—
83C4×C71#13112yes—
84C4×C71AGL(1,ℤ/8)11yescharacteristic
85C4×C71#13711yescharacteristic
86Dic71—41no—
87Dic71—41no—
88Dic71—41no—
89C2×C71—22no—
90C2×C71#40811yescharacteristic
91C2×C71#41711yescharacteristic
92C2×C71C2×#10411yescharacteristic
93D71—81no—
94#1483—711nomaximal, Sylow
95C71#148311yescharacteristic, complemented, Sylow
96#529—711no—
97C2×C4⋊C8D7111yescharacteristic, complemented
98C4×M16—711no—
99Q8⋊C8—712no—
100D4⋊C8—712no—
101C2×M16—1421no—
102C22×C8—21no—
103#126—1421no—
104#125—711no—
105#124—711no—
106#123—1421no—
107C22⋊Q8—711no—
108#121—711no—
109C4×Q8—711no—
110C4×D4—711no—
111C4×D4—1421no—
112#117—1421no—
113C2×C42C2×D7111yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D7112yes—
116#97—1421no—
117C4×C8—712no—
118C2×Q8—711no—
119C2×D4—711no—
120C2×D4—1421no—
121C22×C4—1421no—
122C22×C4C4×D7111yescharacteristic
123C22×C4D28411yescharacteristic
124C22×C4C22⋊D7111yescharacteristic
125M16—1424no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—1422no—
129C4⋊C4—711no—
130C4⋊C4—711no—
131C4⋊C4—1421no—
132C4⋊C4—1421no—
133C4⋊C4—1421no—
134C4⋊C4—1421no—
135C22⋊C4—1421no—
136C22⋊C4—1421no—
137C22⋊C4—1421no—
138C22⋊C4—1421no—
139C22⋊C4—1421no—
140C42—1421no—
141C42C4×D7111yescharacteristic
142C42D28411yescharacteristic
143C42C22⋊D7111yescharacteristic
144C42C22×D7111yescharacteristic
145C23—1421no—
146C23(C2×D71)⋊C411yescharacteristic
147Q8—1422no—
148D4—2842no—
149D4—1422no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—2841no—
155C2×C4—2841no—
156C2×C4—1421no—
157C2×C4—1421no—
158C2×C4—1421no—
159C2×C4(C2×D71)⋊C411yescharacteristic
160C2×C4(C2×D71)⋊C411yescharacteristic
161C2×C4(C2×D71)⋊C411yescharacteristic
162C2×C4C2×C4×D7111yescharacteristic
163C2×C4C2×C22⋊D7111yescharacteristic
164C2×C4C2×D28411yescharacteristic
165C8—42no—
166C8—1424no—
167C22—21no—
168C22—21no—
169C22—2841no—
170C22—2841no—
171C22—2841no—
172C22#1455605412yes—
173C22C2×(C2×D71)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—2841no—
179C4—2841no—
180C4—2841no—
181C4#1455613412yes—
182C4#1455615411yescharacteristic
183C4#1455615911yescharacteristic
184C2—22no—
185C2—5681no—
186C2#1798596511yescharacteristic
187C2#1798599811yescharacteristic
188C2C2×#1455605411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
FittingC2×C4⋊C8×C71C2
socleC22×C71C2×C22⋊C4
hypercenterC2×C4⋊C8D71
hypocenterC71#1483
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#11765849C2semidirect
3. #17985729C2semidirect
4. #17985726C2semidirect
5. C2×C4⋊C8×C71C2semidirect
95. C71#1483semidirect
97. C2×C4⋊C8D71semidirect