Finite Group Databasebeta

← #22589579

Subgroups — #22589579

Order 9088.

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

normal subgroups only

This group has 318 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×#14556115C211yesmaximal, characteristic
2C2×#14556053C211yesmaximal, characteristic, complemented
3C2×#14556051C211yesmaximal, characteristic, complemented
4C2×#14556049C211yesmaximal, characteristic
5#17985895C211yesmaximal, characteristic, complemented
6#17985753C211yesmaximal, characteristic, complemented
7C2×#102×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10#14556115—22no—
11#14556115—22no—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×Dic71⋊C4—21no—
14C2×C22⋊Dic71—21no—
15C2×C22⋊Dic71—21no—
16C2×C4×Dic71C2211yescharacteristic
17#14556053—22no—
18#14556051—22no—
19#14556049—22no—
20C71⋊#95—21no—
21C22×D4×C71C2211yescharacteristic
22C22×C8×C71C2211yescharacteristic
23C2×C4⋊C4×C71C2211yescharacteristic
24#102×C71—22no—
25C2×Dic142—21no—
26C2×Dic142—21no—
27C2×Dic142—21no—
28C2×Dic142—21no—
29C2×Dic142—21no—
30C2×Dic142D412yes—
31C22×Dic71—21no—
32C22×Dic71—21no—
33C22×Dic71D411yescharacteristic
34C22×Dic71D411yescharacteristic
35C2×C71⋊C8—21no—
36C2×C71⋊C8—21no—
37C2×C71⋊C8—21no—
38C4⋊Dic71—21no—
39C4⋊Dic71D412yes—
40Dic71⋊C4—42no—
41C22⋊Dic71—24no—
42C22⋊Dic71—24no—
43C4×Dic71—21no—
44C4×Dic71—21no—
45C24×C71—21no—
46C2×D4×C71—21no—
47C2×D4×C71—21no—
48C2×D4×C71—21no—
49C2×D4×C71—21no—
50C2×D4×C71—21no—
51C2×D4×C71D412yes—
52C22×C4×C71—21no—
53C22×C4×C71C2311yescharacteristic
54C2×C8×C71—21no—
55C2×C8×C71—21no—
56C2×C8×C71—21no—
57C4⋊C4×C71—21no—
58C4⋊C4×C71—21no—
59C23×C71—22no—
60C23×C71—41no—
61C23×C71—41no—
62C23×C71—41no—
63C23×C71—41no—
64C23×C71—41no—
65C23×C71—41no—
66C23×C71C2×D411yescharacteristic
67D4×C71—22no—
68D4×C71—22no—
69D4×C71—41no—
70D4×C71—41no—
71C2×C4×C71—41no—
72C2×C4×C71—41no—
73C2×C4×C71—41no—
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71#4111yescharacteristic
78C2×C4×C71#4111yescharacteristic
79C2×C4×C71#4111yescharacteristic
80C2×Dic71—21no—
81C2×Dic71—21no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71—21no—
85C2×Dic71—21no—
86C2×Dic71—21no—
87C2×Dic71—21no—
88C2×Dic71—41no—
89C2×Dic71—41no—
90C2×Dic71—41no—
91C2×Dic71—41no—
92Dic142—22no—
93Dic142—22no—
94Dic142—41no—
95Dic142—41no—
96C8×C71—41no—
97C71⋊C8—41no—
98C22×C71—42no—
99C22×C71—42no—
100C22×C71—42no—
101C22×C71—81no—
102C22×C71—81no—
103C22×C71—81no—
104C22×C71—81no—
105C22×C71#12011yescharacteristic
106C22×C71#12111yescharacteristic
107C22×C71#12411yescharacteristic
108C22×C71#13511yescharacteristic
109C22×C71#13511yescharacteristic
110C22×C71AGL(1,ℤ/8)11yescharacteristic
111C22×C71#13711yescharacteristic
112C4×C71—81no—
113C4×C71#12111yescharacteristic
114C4×C71#12111yescharacteristic
115C4×C71#12311yescharacteristic
116C4×C71#12311yescharacteristic
117Dic71—42no—
118Dic71—41no—
119Dic71—41no—
120Dic71—42no—
121C2×C71—82no—
122C2×C71#39411yescharacteristic
123C2×C71#44911yescharacteristic
124C2×C71#45211yescharacteristic
125C2×C71#46311yescharacteristic
126C2×C71#46411yescharacteristic
127C2×C71#48811yescharacteristic
128C2×C71#48911yescharacteristic
129#2042—711nomaximal, Sylow
130C71#204211yescharacteristic, complemented, Sylow
131C2×#124—711no—
132C2×#103—711no—
133C2×#103—711no—
134C2×#102—711no—
135C2×#102D7111yescharacteristic
136#389—711no—
137#336—711no—
138C22×Q8—711no—
139C22×D4C2×D7111yescharacteristic
140C22×C8—711no—
141C22×C8C2×D7111yescharacteristic
142#124—1422no—
143#124—1422no—
144C2×C4⋊C4—711no—
145C2×C4⋊C4—1421no—
146C2×C4⋊C4C2×D7111yescharacteristic
147C2×C22⋊C4—1421no—
148C2×C22⋊C4—1421no—
149C2×C42—711no—
150#103—1422no—
151#103—1422no—
152#102—22no—
153#102—1422no—
154#95—1421no—
155C24—21no—
156C2×Q8—712no—
157C2×Q8—1421no—
158C2×Q8—1421no—
159C2×Q8—1421no—
160C2×Q8—1421no—
161C2×Q8—1421no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22⋊D7112yes—
168C22×C4—21no—
169C22×C4—711no—
170C22×C4—711no—
171C22×C4—1421no—
172C22×C4—1421no—
173C22×C4C22×D7111yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—1421no—
178C2×C8—1421no—
179C2×C8—1421no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—2842no—
183C4⋊C4—712no—
184C4⋊C4—1421no—
185C22⋊C4—1424no—
186C22⋊C4—1424no—
187C42—1421no—
188C42—1421no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23D4×D7111yescharacteristic
197Q8—2841no—
198Q8—2841no—
199Q8—1422no—
200Q8—1422no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2841no—
209C2×C4—2841no—
210C2×C4—2841no—
211C2×C4—2841no—
212C2×C4—1421no—
213C2×C4—1421no—
214C2×C4—1422no—
215C2×C4—1422no—
216C2×C4—1421no—
217C2×C4—1421no—
218C2×C4—1421no—
219C2×C4—1421no—
220C2×C4D4×D7111yescharacteristic
221C2×C4D4×D7111yescharacteristic
222C2×C4C2×C22⋊D7111yescharacteristic
223C2×C4#1176586411yescharacteristic
224C2×C4#1176586511yescharacteristic
225C2×C4#1176586511yescharacteristic
226C8—41no—
227C8—2841no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1455609611yescharacteristic
236C22#1455610111yescharacteristic
237C22#1455611411yescharacteristic
238C22#1455614711yescharacteristic
239C22#1455614911yescharacteristic
240C22#1455615211yescharacteristic
241C22#1455615711yescharacteristic
242C4—81no—
243C4—2841no—
244C4—2841no—
245C4—2842no—
246C4—2842no—
247C4#1455610011yescharacteristic
248C4#1455610111yescharacteristic
249C4#1455611011yescharacteristic
250C4#1455611111yescharacteristic
251C2—82no—
252C2#1798591411yescharacteristic
253C2#1798614111yescharacteristic
254C2#1798615811yescharacteristic
255C2#1798621311yescharacteristic
256C2#1798622011yescharacteristic
257C2#1798635211yescharacteristic
258C2#1798635711yescharacteristic
subgroupG/H
centerC23D4×D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#102×C71C2
socleC23×C71C2×D4
hypercenterC2×#102D71
hypocenterC71#2042
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
2. C2×#14556053C2semidirect
3. C2×#14556051C2semidirect
5. #17985895C2semidirect
6. #17985753C2semidirect
130. C71#2042semidirect