Finite Group Databasebeta

← #22589746

Subgroups — #22589746

Order 9088.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556049C211yesmaximal, characteristic
2#17985902C211yesmaximal, characteristic
3#17985868C211yesmaximal, characteristic, complemented
4#17985762C211yesmaximal, characteristic, complemented
5#17985761C211yesmaximal, characteristic, complemented
6#17985753C211yesmaximal, characteristic, complemented
7C2×#102×C71C211yesmaximal, characteristic
8C22×C71⋊C8C2211yescharacteristic
9C2×C4⋊Dic71C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×Dic71⋊C4—21no—
12C2×Dic71⋊C4—21no—
13C2×C22⋊Dic71—21no—
14C2×C22⋊Dic71—21no—
15C2×C4×Dic71C2211yescharacteristic
16#14556049—22no—
17C22×D4×C71C2211yescharacteristic
18C22×C8×C71C2211yescharacteristic
19C2×C4⋊C4×C71C2211yescharacteristic
20#102×C71—22no—
21C22×Dic71—21no—
22C22×Dic71—21no—
23C22×Dic71D411yescharacteristic
24C22×Dic71D411yescharacteristic
25C2×C71⋊C8—21no—
26C2×C71⋊C8—21no—
27C2×C71⋊C8—21no—
28C4⋊Dic71—21no—
29C4⋊Dic71—21no—
30C4⋊Dic71—21no—
31C4⋊Dic71—21no—
32Dic71⋊C4—42no—
33Dic71⋊C4—42no—
34C22⋊Dic71—42no—
35C22⋊Dic71—42no—
36C4×Dic71—21no—
37C4×Dic71—21no—
38C24×C71—21no—
39C2×D4×C71—21no—
40C2×D4×C71—21no—
41C2×D4×C71—21no—
42C2×D4×C71—21no—
43C2×D4×C71—21no—
44C2×D4×C71D412yes—
45C22×C4×C71—21no—
46C22×C4×C71C2311yescharacteristic
47C2×C8×C71—21no—
48C2×C8×C71—21no—
49C2×C8×C71—21no—
50C4⋊C4×C71—21no—
51C4⋊C4×C71—21no—
52C23×C71—22no—
53C23×C71—41no—
54C23×C71—41no—
55C23×C71—41no—
56C23×C71—41no—
57C23×C71—41no—
58C23×C71—41no—
59C23×C71C2×D411yescharacteristic
60D4×C71—22no—
61D4×C71—22no—
62D4×C71—41no—
63D4×C71—41no—
64C2×C4×C71—41no—
65C2×C4×C71—41no—
66C2×C4×C71—41no—
67C2×C4×C71C2×D411yescharacteristic
68C2×C4×C71#4111yescharacteristic
69C2×C4×C71#4111yescharacteristic
70C2×C4×C71#4111yescharacteristic
71C2×C4×C71#4111yescharacteristic
72C2×C4×C71#4111yescharacteristic
73C2×Dic71—21no—
74C2×Dic71—21no—
75C2×Dic71—21no—
76C2×Dic71—21no—
77C2×Dic71—41no—
78C2×Dic71—41no—
79C2×Dic71—41no—
80C2×Dic71—41no—
81C2×Dic71—41no—
82C2×Dic71—41no—
83C2×Dic71D812yes—
84C2×Dic71SD1612yes—
85C8×C71—41no—
86C71⋊C8—41no—
87C22×C71—42no—
88C22×C71—42no—
89C22×C71—42no—
90C22×C71—81no—
91C22×C71—81no—
92C22×C71—81no—
93C22×C71—81no—
94C22×C71#12111yescharacteristic
95C22×C71#12311yescharacteristic
96C22×C71#12411yescharacteristic
97C22×C71C2×D811yescharacteristic
98C22×C71C2×SD1611yescharacteristic
99C22×C71AGL(1,ℤ/8)11yescharacteristic
100C22×C71#13711yescharacteristic
101C4×C71—81no—
102C4×C71#12311yescharacteristic
103C4×C71#12311yescharacteristic
104C4×C71#12611yescharacteristic
105C4×C71#12611yescharacteristic
106Dic71—22no—
107Dic71—22no—
108Dic71—81no—
109Dic71—81no—
110C2×C71—82no—
111C2×C71#39711yescharacteristic
112C2×C71#45911yescharacteristic
113C2×C71#46111yescharacteristic
114C2×C71#48011yescharacteristic
115C2×C71#48111yescharacteristic
116C2×C71#48611yescharacteristic
117C2×C71#48911yescharacteristic
118#2071—711nomaximal, Sylow
119C71#207111yescharacteristic, complemented, Sylow
120C2×#102—711no—
121C2×#102D7111yescharacteristic
122#390—711no—
123#384—711no—
124#340—711no—
125#340—711no—
126#336—711no—
127C22×D4C2×D7111yescharacteristic
128C22×C8—711no—
129C22×C8C2×D7111yescharacteristic
130C2×C4⋊C4—711no—
131C2×C4⋊C4—711no—
132C2×C4⋊C4—1421no—
133C2×C4⋊C4—1421no—
134C2×C4⋊C4C2×D7111yescharacteristic
135C2×C22⋊C4—1421no—
136C2×C22⋊C4—1421no—
137C2×C42—711no—
138#102—22no—
139#102—1422no—
140C24—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D7112yes—
147C22×C4—21no—
148C22×C4—711no—
149C22×C4—711no—
150C22×C4—1421no—
151C22×C4—1421no—
152C22×C4C22×D7111yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1421no—
157C2×C8—1421no—
158C2×C8—1421no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2842no—
162C4⋊C4—2842no—
163C4⋊C4—1421no—
164C4⋊C4—1421no—
165C4⋊C4—1421no—
166C4⋊C4—1421no—
167C22⋊C4—2842no—
168C22⋊C4—2842no—
169C42—1421no—
170C42—1421no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23D4×D7111yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2841no—
187C2×C4—2841no—
188C2×C4—2841no—
189C2×C4—2841no—
190C2×C4—2841no—
191C2×C4—2841no—
192C2×C4—712no—
193C2×C4—712no—
194C2×C4—1421no—
195C2×C4—1421no—
196C2×C4—1421no—
197C2×C4—1421no—
198C2×C4C2×C22⋊D7111yescharacteristic
199C2×C4#1176586411yescharacteristic
200C2×C4#1176586411yescharacteristic
201C2×C4#1176586411yescharacteristic
202C2×C4#1176586511yescharacteristic
203C2×C4#1176586511yescharacteristic
204C8—41no—
205C8—2841no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22#1455610011yescharacteristic
214C22#1455611011yescharacteristic
215C22#1455611411yescharacteristic
216C22D8×D7111yescharacteristic
217C22SD16×D7111yescharacteristic
218C22#1455615211yescharacteristic
219C22#1455615711yescharacteristic
220C4—81no—
221C4—5681no—
222C4—5681no—
223C4—1422no—
224C4—1422no—
225C4#1455610911yescharacteristic
226C4#1455611111yescharacteristic
227C4#1455612111yescharacteristic
228C4#1455612111yescharacteristic
229C2—82no—
230C2#1798592711yescharacteristic
231C2#1798619211yescharacteristic
232C2#1798620211yescharacteristic
233C2#1798631111yescharacteristic
234C2#1798631611yescharacteristic
235C2#1798634411yescharacteristic
236C2#1798635711yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#102×C71C2
socleC23×C71C2×D4
hypercenterC2×#102D71
hypocenterC71#2071
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
3. #17985868C2semidirect
4. #17985762C2semidirect
5. #17985761C2semidirect
6. #17985753C2semidirect
119. C71#2071semidirect