Finite Group Databasebeta

← #22590027

Subgroups — #22590027

Order 9088.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#17986573C211yesmaximal, characteristic
2C2×#14556047C211yesmaximal, characteristic, complemented
3#17985797C212yesmaximal, complemented
4#17985795C212yesmaximal, complemented
5C2×#101×C71C211yesmaximal, characteristic, complemented
6C2×#11765865C411yescharacteristic
7C2×#11765849—21no—
8#14556126C411yescharacteristic
9#14556126C2211yescharacteristic
10#14556117C411yescharacteristic
11#14556117C2211yescharacteristic
12#14556111—21no—
13#14556111—21no—
14#14556104—21no—
15#14556104—21no—
16#14556087C411yescharacteristic
17#14556047—21no—
18#14556047C2212yes—
19C22×Q8×C71C2211yescharacteristic
20C2×M16×C71—21no—
21#101×C71—21no—
22#101×C71C2212yes—
23#11765865—41no—
24#11765865—41no—
25C2×Dic142C2×C411yescharacteristic
26C2×D284C2×C411yescharacteristic
27C2×C22⋊D71—21no—
28C2×C4×D71—21no—
29#11765849—22no—
30#11765849—41no—
31C2×C71⋊C8—41no—
32C4⋊Dic71—21no—
33Dic71⋊C4—21no—
34Dic71⋊C4—21no—
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37C22⋊Dic71—21no—
38(C2×D71)⋊C4—21no—
39(C2×D71)⋊C4—21no—
40(C2×D71)⋊C4—21no—
41(C2×D71)⋊C4—21no—
42C4×Dic71C2×C411yescharacteristic
43C4×Dic71C2×C411yescharacteristic
44C2×Q8×C71—41no—
45C2×Q8×C71—41no—
46C2×Q8×C71C2×C411yescharacteristic
47C2×Q8×C71D411yescharacteristic
48C2×Q8×C71D411yescharacteristic
49C2×Q8×C71C2311yescharacteristic
50C22×C4×C71C2×C411yescharacteristic
51C22×C4×C71D411yescharacteristic
52C22×C4×C71D411yescharacteristic
53M16×C71—22no—
54M16×C71—41no—
55C2×C8×C71—41no—
56C23×C71C22⋊C411yescharacteristic
57C22×D71—21no—
58Q8×C71—41no—
59Q8×C71—41no—
60Q8×C71—41no—
61Q8×C71—41no—
62C2×C4×C71—21no—
63C2×C4×C71—21no—
64C2×C4×C71—21no—
65C2×C4×C71—21no—
66C2×C4×C71—21no—
67C2×C4×C71—21no—
68C2×C4×C71C22⋊C411yescharacteristic
69C2×C4×C71C22⋊C411yescharacteristic
70C2×C4×C71C22⋊C411yescharacteristic
71C2×C4×C71C22×C411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C22⋊D71—41no—
75C22⋊D71—41no—
76C2×Dic71—21no—
77C2×Dic71—21no—
78C2×Dic71—21no—
79D284—41no—
80C4×D71—42no—
81Dic142—41no—
82C8×C71—42no—
83C71⋊C8—42no—
84C22×C71—41no—
85C22×C71#9911yescharacteristic
86C22×C71#9911yescharacteristic
87C22×C71C2×C22⋊C411yescharacteristic
88C2×D71—42no—
89C2×D71—41no—
90C4×C71—21no—
91C4×C71—21no—
92C4×C71—21no—
93C4×C71—21no—
94C4×C71—21no—
95C4×C71—21no—
96Dic71—41no—
97Dic71—41no—
98Dic71—41no—
99C2×C71—21no—
100C2×C71—21no—
101C2×C71—21no—
102C2×C71C2×#9911yescharacteristic
103D71—81no—
104#2133—711nomaximal, Sylow
105C71#213311yescharacteristic, complemented, Sylow
106#536—711no—
107C2×#101—711no—
108C2×#101D7111yescharacteristic, complemented
109#356—712no—
110#355—712no—
111C2×#41—711no—
112C22×Q8C2×D7111yescharacteristic
113C2×M16—21no—
114C2×M16—1421no—
115C4⋊Q8—711no—
116C4⋊Q8—711no—
117#124—711no—
118#124—711no—
119#123—1421no—
120#123—1421no—
121C22⋊Q8—1421no—
122C22⋊Q8—1421no—
123#117—711no—
124#101—21no—
125#101—712no—
126#101—1421no—
127#101C2×D7112yes—
128#41—2841no—
129#41—2841no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—711no—
133C2×Q8C4×D7111yescharacteristic
134C2×Q8D28411yescharacteristic
135C2×Q8C22⋊D7111yescharacteristic
136C2×Q8C22×D7111yescharacteristic
137C2×D4—711no—
138C2×D4—1421no—
139C22×C4—1421no—
140C22×C4C4×D7111yescharacteristic
141C22×C4D28411yescharacteristic
142C22×C4C22⋊D7111yescharacteristic
143M16—22no—
144M16—41no—
145M16—2841no—
146M16—1422no—
147C2×C8—41no—
148C2×C8—2841no—
149C4⋊C4—1421no—
150C4⋊C4—1421no—
151C4⋊C4—1421no—
152C4⋊C4—1421no—
153C4⋊C4—1421no—
154C22⋊C4—1421no—
155C22⋊C4—1421no—
156C22⋊C4—1421no—
157C22⋊C4—1421no—
158C22⋊C4—1421no—
159C42—711no—
160C42—711no—
161C23—1421no—
162C23(C2×D71)⋊C411yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—2841no—
168D4—2841no—
169D4—2841no—
170D4—2841no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—2842no—
178C2×C4—1421no—
179C2×C4—1421no—
180C2×C4—1421no—
181C2×C4(C2×D71)⋊C411yescharacteristic
182C2×C4(C2×D71)⋊C411yescharacteristic
183C2×C4(C2×D71)⋊C411yescharacteristic
184C2×C4C2×C4×D7111yescharacteristic
185C2×C4C2×C22⋊D7111yescharacteristic
186C2×C4C2×D28411yescharacteristic
187C8—42no—
188C8—2842no—
189C22—41no—
190C22—2842no—
191C22—2841no—
192C22#1455604211yescharacteristic
193C22#1455604211yescharacteristic
194C22C2×(C2×D71)⋊C411yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—2841no—
202C4—2841no—
203C4—2841no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—5681no—
208C2C2×#1455604211yescharacteristic
subgroupG/H
centerC2C2×#14556042
commutatorC2×C4×C71C22×C4
FrattiniC2×Q8C22×D71
FittingC2×#101×C71C2
socleC2×C71C2×#99
hypercenterC2×#101D71
hypocenterC71#2133
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14556047C2semidirect
3. #17985797C2semidirect
4. #17985795C2semidirect
5. C2×#101×C71C2semidirect
105. C71#2133semidirect
108. C2×#101D71semidirect