Finite Group Databasebeta

← #22589182

Subgroups — #22589182

Order 9088.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#14556126C211yesmaximal, characteristic
2#17986022C211yesmaximal, characteristic
3C2×#14556047C211yesmaximal, characteristic
4C2×#14556046C211yesmaximal, characteristic
5C2×#14556046C211yesmaximal, characteristic
6M16×Dic71C211yesmaximal, characteristic
7C2×#101×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C2×#11765849C2211yescharacteristic
11#14556126—21no—
12#14556126—21no—
13#14556126—22no—
14C2×Dic71⋊C4C414yes—
15C2×C4×Dic71C2211yescharacteristic
16Dic71⋊C8—22no—
17#14556047—22no—
18#14556046—22no—
19#14556046—22no—
20#14556038—21no—
21C8×Dic71—21no—
22C22×Q8×C71C2211yescharacteristic
23C2×M16×C71C2211yescharacteristic
24C2×M16×C71C2211yescharacteristic
25#101×C71—22no—
26C2×Dic142—21no—
27C2×Dic142—21no—
28C2×Dic142—21no—
29C2×Dic142—21no—
30C2×Dic142—21no—
31C2×Dic142—21no—
32C22×Dic71C2×C412yes—
33C22×Dic71C2×C412yes—
34#11765849—21no—
35#11765849—21no—
36#11765849—21no—
37#11765849D412yes—
38C2×C71⋊C8—21no—
39C2×C71⋊C8—21no—
40Dic71⋊C4—24no—
41Dic71⋊C4—24no—
42C4×Dic71D411yescharacteristic
43C4×Dic71D411yescharacteristic
44C4×Dic71D412yes—
45C2×Q8×C71—21no—
46C2×Q8×C71—21no—
47C2×Q8×C71—21no—
48C2×Q8×C71—21no—
49C2×Q8×C71—21no—
50C2×Q8×C71—21no—
51C22×C4×C71C2×C412yes—
52C22×C4×C71C2311yescharacteristic
53M16×C71—21no—
54M16×C71—21no—
55M16×C71—21no—
56M16×C71D412yes—
57C2×C8×C71—21no—
58C2×C8×C71—21no—
59C23×C71C22×C411yescharacteristic
60Q8×C71—41no—
61Q8×C71—41no—
62Q8×C71—41no—
63Q8×C71—41no—
64C2×C4×C71—22no—
65C2×C4×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71C2×D411yescharacteristic
68C2×C4×C71C2×D411yescharacteristic
69C2×C4×C71C2×D411yescharacteristic
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71#4111yescharacteristic
72C2×C4×C71#4111yescharacteristic
73C2×Dic71—24no—
74C2×Dic71—22no—
75C2×Dic71—22no—
76C2×Dic71—22no—
77C2×Dic71C22⋊C412yes—
78C2×Dic71C22⋊C412yes—
79Dic142—41no—
80Dic142—41no—
81Dic142—41no—
82Dic142—41no—
83C8×C71—22no—
84C8×C71—41no—
85C71⋊C8—22no—
86C71⋊C8—41no—
87C22×C71—22no—
88C22×C71C2×C22⋊C411yescharacteristic
89C22×C71C4×D411yescharacteristic
90C22×C71C4×D411yescharacteristic
91C4×C71—42no—
92C4×C71#12111yescharacteristic
93C4×C71#12111yescharacteristic
94C4×C71#12411yescharacteristic
95C4×C71#12711yescharacteristic
96Dic71—22no—
97Dic71—42no—
98Dic71#10114yescomplemented
99C2×C71—21no—
100C2×C71—21no—
101C2×C71#39011yescharacteristic
102C2×C71C2×#10112yes—
103#1966—711nomaximal, Sylow
104C71#196611yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—711no—
106#423—711no—
107C2×#101—711no—
108C2×#101—711no—
109C2×#101—711no—
110C2×#101D7111yescharacteristic
111C4×M16—711no—
112C22×Q8—711no—
113C22×Q8C2×D7111yescharacteristic
114C2×M16—711no—
115C2×M16—711no—
116C2×M16C2×D7111yescharacteristic
117C2×M16C2×D7111yescharacteristic
118C4⋊Q8—1421no—
119C4⋊Q8—1421no—
120C4⋊Q8—1422no—
121C2×C4⋊C4—714no—
122C2×C42—711no—
123C4⋊C8—1422no—
124#101—22no—
125#101—1422no—
126#101—1422no—
127#101—1422no—
128#97—1421no—
129C4×C8—1421no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—1421no—
137C2×Q8—1421no—
138C2×Q8—1421no—
139C2×Q8—1421no—
140C2×Q8—1421no—
141C2×Q8—1421no—
142C22×C4—712no—
143C22×C4—712no—
144C22×C4C4×D7112yes—
145C22×C4C22×D7111yescharacteristic
146M16—21no—
147M16—21no—
148M16—21no—
149M16—712no—
150M16—1421no—
151M16—1421no—
152M16—1421no—
153M16C22⋊D7112yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1421no—
157C2×C8—1421no—
158C4⋊C4—1424no—
159C4⋊C4—1424no—
160C42—711no—
161C42—711no—
162C42—712no—
163C23C2×C4×D7111yescharacteristic
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—41no—
168Q8—2841no—
169Q8—2841no—
170Q8—2841no—
171Q8—2841no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—712no—
176C2×C4—712no—
177C2×C4—1422no—
178C2×C4—1422no—
179C2×C4—1422no—
180C2×C4—1424no—
181C2×C4D4×D7111yescharacteristic
182C2×C4D4×D7111yescharacteristic
183C2×C4D4×D7111yescharacteristic
184C2×C4C2×C22⋊D7111yescharacteristic
185C2×C4#1176586411yescharacteristic
186C2×C4#1176586511yescharacteristic
187C8—22no—
188C8—41no—
189C8—2841no—
190C8—1422no—
191C22—22no—
192C22C22⋊C4×D7111yescharacteristic
193C22(C22⋊D71)⋊C411yescharacteristic
194C22C4×C22⋊D7111yescharacteristic
195C4—42no—
196C4—2842no—
197C4—714no—
198C4—1422no—
199C4#1455610011yescharacteristic
200C4#1455610111yescharacteristic
201C4#1455611411yescharacteristic
202C4#1455612411yescharacteristic
203C2—21no—
204C2—21no—
205C2#1798589911yescharacteristic
206C2#101×D7112yes—
subgroupG/H
centerC22C22⋊C4×D71
commutatorC23×C71C22×C4
FrattiniC22×C4C22×D71
FittingC2×#101×C71C2
socleC22×C71C2×C22⋊C4
hypercenterC2×#101D71
hypocenterC71#1966
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
98. Dic71#101semidirect
104. C71#1966semidirect