Finite Group Databasebeta

← #22589576

Subgroups — #22589576

Order 9088.

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

normal subgroups only

This group has 318 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×#14556052C211yesmaximal, characteristic, complemented
2C2×#14556052C211yesmaximal, characteristic, complemented
3C2×#14556049C211yesmaximal, characteristic
4C2×#14556049C211yesmaximal, characteristic
5#17985897C211yesmaximal, characteristic, complemented
6#17985754C211yesmaximal, characteristic, complemented
7C2×#124×C71C211yesmaximal, characteristic
8C22×C71⋊C8C2211yescharacteristic
9C22×C71⋊C8C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12C2×Dic71⋊C4—21no—
13#14556052—22no—
14#14556052—22no—
15#14556049—22no—
16#14556049—22no—
17C71⋊#95—21no—
18C22×Q8×C71C2211yescharacteristic
19C22×D4×C71C2211yescharacteristic
20#124×C71—22no—
21#124×C71—22no—
22C2×C22⋊C4×C71—21no—
23C2×C22⋊C4×C71—21no—
24C2×C42×C71C2211yescharacteristic
25C22×Dic71—21no—
26C22×Dic71—21no—
27C2×C71⋊C8—21no—
28C2×C71⋊C8—21no—
29C2×C71⋊C8—21no—
30C2×C71⋊C8—21no—
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71D412yes—
37Dic71⋊C4—42no—
38C24×C71—21no—
39C2×Q8×C71—21no—
40C2×Q8×C71—21no—
41C2×Q8×C71—21no—
42C2×Q8×C71—21no—
43C2×Q8×C71—21no—
44C2×Q8×C71D412yes—
45C2×D4×C71—21no—
46C2×D4×C71—21no—
47C2×D4×C71—21no—
48C2×D4×C71—21no—
49C2×D4×C71—21no—
50C2×D4×C71D412yes—
51C22×C4×C71—21no—
52C22×C4×C71D411yescharacteristic
53C22×C4×C71D411yescharacteristic
54C22×C4×C71C2311yescharacteristic
55C22⋊C4×C71—24no—
56C22⋊C4×C71—24no—
57C42×C71—21no—
58C42×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
67Q8×C71—22no—
68Q8×C71—22no—
69Q8×C71—41no—
70Q8×C71—41no—
71D4×C71—22no—
72D4×C71—22no—
73D4×C71—41no—
74D4×C71—41no—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71—21no—
79C2×C4×C71—21no—
80C2×C4×C71—21no—
81C2×C4×C71—21no—
82C2×C4×C71—41no—
83C2×C4×C71—41no—
84C2×C4×C71C2×D411yescharacteristic
85C2×C4×C71C2×D411yescharacteristic
86C2×C4×C71C2×D411yescharacteristic
87C2×C4×C71#4111yescharacteristic
88C2×C4×C71#4111yescharacteristic
89C2×C4×C71#4111yescharacteristic
90C2×Dic71—22no—
91C2×Dic71—41no—
92C2×Dic71—41no—
93C2×Dic71—41no—
94C2×Dic71—41no—
95C2×Dic71—41no—
96C71⋊C8—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—42no—
113C4×C71—41no—
114C4×C71—41no—
115C4×C71#12111yescharacteristic
116C4×C71#12111yescharacteristic
117C4×C71#12311yescharacteristic
118C4×C71#12311yescharacteristic
119Dic71—42no—
120Dic71—81no—
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×#124D7111yescharacteristic
132C2×#103—711no—
133C2×#103—711no—
134C2×#102—711no—
135C2×#102—711no—
136#389—711no—
137#336—711no—
138C22×Q8C2×D7111yescharacteristic
139C22×D4C2×D7111yescharacteristic
140C22×C8—711no—
141C22×C8—711no—
142#124—22no—
143#124—22no—
144C2×C4⋊C4—711no—
145C2×C4⋊C4—711no—
146C2×C4⋊C4—1421no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C42C2×D7111yescharacteristic
150#103—1422no—
151#103—1422no—
152#102—1422no—
153#102—1422no—
154#95—1421no—
155C24—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D7112yes—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22⋊D7112yes—
168C22×C4—21no—
169C22×C4—1421no—
170C22×C4—1421no—
171C22×C4C22⋊D7111yescharacteristic
172C22×C4C22⋊D7111yescharacteristic
173C22×C4C22×D7111yescharacteristic
174C2×C8—1421no—
175C2×C8—1421no—
176C2×C8—1421no—
177C2×C8—1421no—
178C2×C8—1421no—
179C2×C8—1421no—
180C4⋊C4—2842no—
181C4⋊C4—712no—
182C4⋊C4—1421no—
183C4⋊C4—1421no—
184C4⋊C4—1421no—
185C22⋊C4—24no—
186C22⋊C4—24no—
187C42—21no—
188C42—21no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×C22⋊D7111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2841no—
215C2×C4—2841no—
216C2×C4—2841no—
217C2×C4—2841no—
218C2×C4—2841no—
219C2×C4—1422no—
220C2×C4D4×D7111yescharacteristic
221C2×C4C2×C22⋊D7111yescharacteristic
222C2×C4C2×C22⋊D7111yescharacteristic
223C2×C4#1176586411yescharacteristic
224C2×C4#1176586411yescharacteristic
225C2×C4#1176586411yescharacteristic
226C8—2841no—
227C8—2841no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1455609711yescharacteristic
236C22#1455609911yescharacteristic
237C22#1455611511yescharacteristic
238C22#1455614811yescharacteristic
239C22#1455614811yescharacteristic
240C22#1455615311yescharacteristic
241C22#1455615811yescharacteristic
242C4—41no—
243C4—41no—
244C4—42no—
245C4—2842no—
246C4—5681no—
247C4#1455610011yescharacteristic
248C4#1455610011yescharacteristic
249C4#1455610911yescharacteristic
250C4#1455610911yescharacteristic
251C2—82no—
252C2#1798591311yescharacteristic
253C2#1798614411yescharacteristic
254C2#1798616111yescharacteristic
255C2#1798621111yescharacteristic
256C2#1798621811yescharacteristic
257C2#1798635311yescharacteristic
258C2#1798635811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D71
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#124×C71C2
socleC23×C71C2×D4
hypercenterC2×#124D71
hypocenterC71#2042
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14556052C2semidirect
2. C2×#14556052C2semidirect
5. #17985897C2semidirect
6. #17985754C2semidirect
130. C71#2042semidirect