Finite Group Databasebeta

← #22589773

Subgroups — #22589773

Order 9088.

256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556060C211yesmaximal, characteristic, complemented
2#17985859C211yesmaximal, characteristic
3#17985859C211yesmaximal, characteristic
4#17985762C211yesmaximal, characteristic, complemented
5#17985762C211yesmaximal, characteristic, complemented
6#17985762C211yesmaximal, characteristic, complemented
7C2×C22⋊C8×C71C211yesmaximal, characteristic
8C2×C4⋊Dic71C2211yescharacteristic
9C2×C4⋊Dic71C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12C2×C22⋊Dic71—21no—
13C2×C22⋊Dic71—21no—
14#14556060—22no—
15C71⋊#95—21no—
16C71⋊#95—21no—
17C23×C4×C71C2211yescharacteristic
18C22×C8×C71C2211yescharacteristic
19C22×C8×C71C2211yescharacteristic
20C22⋊C8×C71—22no—
21C22×Dic71—21no—
22C22×Dic71—21no—
23C22×Dic71—21no—
24C22×Dic71—21no—
25C4⋊Dic71—21no—
26C4⋊Dic71—21no—
27C4⋊Dic71—21no—
28C4⋊Dic71—21no—
29C4⋊Dic71—21no—
30C4⋊Dic71—21no—
31C4⋊Dic71—21no—
32C4⋊Dic71—21no—
33C22⋊Dic71—42no—
34C22⋊Dic71—42no—
35C24×C71D411yescharacteristic
36C22×C4×C71—21no—
37C22×C4×C71—21no—
38C22×C4×C71—21no—
39C22×C4×C71—21no—
40C22×C4×C71—21no—
41C22×C4×C71—21no—
42C22×C4×C71D411yescharacteristic
43C22×C4×C71C2311yescharacteristic
44C2×C8×C71—21no—
45C2×C8×C71—21no—
46C2×C8×C71—21no—
47C2×C8×C71—21no—
48C2×C8×C71—21no—
49C2×C8×C71D412yes—
50C23×C71—21no—
51C23×C71—21no—
52C23×C71—21no—
53C23×C71—21no—
54C23×C71—21no—
55C23×C71—21no—
56C23×C71SD1612yes—
57C23×C71C2×D411yescharacteristic
58C2×C4×C71—21no—
59C2×C4×C71—21no—
60C2×C4×C71—21no—
61C2×C4×C71—41no—
62C2×C4×C71—41no—
63C2×C4×C71—41no—
64C2×C4×C71—41no—
65C2×C4×C71C2×D411yescharacteristic
66C2×C4×C71#4111yescharacteristic
67C2×C4×C71#4111yescharacteristic
68C2×C4×C71#4111yescharacteristic
69C2×C4×C71#4111yescharacteristic
70C2×C4×C71#4111yescharacteristic
71C2×Dic71—41no—
72C2×Dic71—41no—
73C2×Dic71—41no—
74C2×Dic71—41no—
75C2×Dic71—41no—
76C2×Dic71—41no—
77C2×Dic71—41no—
78C2×Dic71—41no—
79C2×Dic71—41no—
80C2×Dic71—41no—
81C2×Dic71—41no—
82C2×Dic71—41no—
83C8×C71—22no—
84C8×C71—41no—
85C22×C71—22no—
86C22×C71—22no—
87C22×C71—22no—
88C22×C71—41no—
89C22×C71—41no—
90C22×C71—41no—
91C22×C71—41no—
92C22×C71#12111yescharacteristic
93C22×C71#12311yescharacteristic
94C22×C71#12311yescharacteristic
95C22×C71C2×SD1611yescharacteristic
96C22×C71#13511yescharacteristic
97C22×C71AGL(1,ℤ/8)11yescharacteristic
98C22×C71#13711yescharacteristic
99C4×C71—41no—
100C4×C71#12311yescharacteristic
101C4×C71#12411yescharacteristic
102C4×C71#12611yescharacteristic
103C4×C71#12611yescharacteristic
104Dic71—81no—
105Dic71—81no—
106Dic71—81no—
107Dic71—81no—
108C2×C71—42no—
109C2×C71#39711yescharacteristic
110C2×C71#46511yescharacteristic
111C2×C71#46811yescharacteristic
112C2×C71#48111yescharacteristic
113C2×C71#48211yescharacteristic
114C2×C71#48311yescharacteristic
115C2×C71#48511yescharacteristic
116#2077—711nomaximal, Sylow
117C71#207711yescharacteristic, complemented, Sylow
118C2×#106—711no—
119C2×C22⋊C8D7111yescharacteristic
120#380—711no—
121#380—711no—
122#340—711no—
123#340—711no—
124#340—711no—
125C23×C4C2×D7111yescharacteristic
126C22×C8C2×D7111yescharacteristic
127C22×C8C2×D7111yescharacteristic
128C2×C4⋊C4—711no—
129C2×C4⋊C4—711no—
130C2×C4⋊C4—711no—
131C2×C4⋊C4—711no—
132C2×C22⋊C4—1421no—
133C2×C22⋊C4—1421no—
134#106—1422no—
135C22⋊C8—22no—
136#95—1421no—
137#95—1421no—
138C24D28411yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1421no—
146C22×C4—1421no—
147C22×C4—1421no—
148C22×C4—1421no—
149C22×C4D28411yescharacteristic
150C22×C4C22×D7111yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8C22⋊D7112yes—
157C4⋊C4—1421no—
158C4⋊C4—1421no—
159C4⋊C4—1421no—
160C4⋊C4—1421no—
161C4⋊C4—1421no—
162C4⋊C4—1421no—
163C4⋊C4—1421no—
164C4⋊C4—1421no—
165C22⋊C4—2842no—
166C22⋊C4—2842no—
167C23—21no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#1176585412yes—
174C23C2×D28411yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—2841no—
183C2×C4—2841no—
184C2×C4—2841no—
185C2×C4—2841no—
186C2×C4—2841no—
187C2×C4—2841no—
188C2×C4—2841no—
189C2×C4—2841no—
190C2×C4—2841no—
191C2×C4—2841no—
192C2×C4—2841no—
193C2×C4—2841no—
194C2×C4C2×C22⋊D7111yescharacteristic
195C2×C4#1176586411yescharacteristic
196C2×C4#1176586411yescharacteristic
197C2×C4#1176586411yescharacteristic
198C2×C4#1176586411yescharacteristic
199C2×C4#1176586511yescharacteristic
200C8—22no—
201C8—41no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#1455610211yescharacteristic
210C22#1455611211yescharacteristic
211C22#1455611211yescharacteristic
212C22C2×#1176585411yescharacteristic
213C22#1455615011yescharacteristic
214C22#1455615611yescharacteristic
215C22#1455616111yescharacteristic
216C4—41no—
217C4—5681no—
218C4—5681no—
219C4—5681no—
220C4—5681no—
221C4#1455610911yescharacteristic
222C4#1455611511yescharacteristic
223C4#1455612111yescharacteristic
224C4#1455612111yescharacteristic
225C2—42no—
226C2#1798592411yescharacteristic
227C2#1798622811yescharacteristic
228C2#1798624511yescharacteristic
229C2#1798631811yescharacteristic
230C2#1798632411yescharacteristic
231C2#1798633011yescharacteristic
232C2#1798634111yescharacteristic
subgroupG/H
centerC23C2×D284
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×C22⋊C8×C71C2
socleC23×C71C2×D4
hypercenterC2×C22⋊C8D71
hypocenterC71#2077
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14556060C2semidirect
4. #17985762C2semidirect
5. #17985762C2semidirect
6. #17985762C2semidirect
117. C71#2077semidirect