Finite Group Databasebeta

← #22597808

Subgroups — #22597808

Order 9088.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556158C212yesmaximal, complemented
2C2×C4×Dic142C211yesmaximal, characteristic, complemented
3#17986218C214yesmaximal, complemented
4#17986206C212yesmaximal, complemented
5#17986196C212yesmaximal, complemented
6#17986023C211yesmaximal, characteristic, complemented
7#17986000C212yesmaximal, complemented
8#532×C71C211yesmaximal, characteristic
9C22×Dic142C2211yescharacteristic
10#14556158—28no—
11C2×#11765855C2214yes—
12C2×#11765853C2214yes—
13C2×#11765849C2212yes—
14C4×Dic142—21no—
15C4×Dic142—21no—
16C4×Dic142C2212yes—
17C4×Dic142C2212yes—
18C2×C4⋊Dic71C2211yescharacteristic
19C2×Dic71⋊C4—21no—
20C2×C4×Dic71—21no—
21C4⋊(C71⋊C8)C2212yes—
22C4⋊(C71⋊C8)C2212yes—
23#14556052C2214yes—
24#14556049C2214yes—
25C2×#41×C71C2212yes—
26C4⋊Q8×C71C2211yescharacteristic
27#127×C71C2211yescharacteristic
28#124×C71C2212yes—
29#121×C71—21no—
30#121×C71—21no—
31C4×D4×C71—21no—
32C4×D4×C71—21no—
33C2×C42×C71C2211yescharacteristic
34C2×Dic142—21no—
35C2×Dic142—22no—
36C2×Dic142D414yescomplemented
37C2×Dic142C2312yes—
38C22×Dic71—21no—
39C22×Dic71—21no—
40#11765855—28no—
41#11765853—28no—
42#11765849—24no—
43C2×C71⋊C8C2314yes—
44C4⋊Dic71—21no—
45C4⋊Dic71C2312yes—
46Dic71⋊C4—22no—
47Dic71⋊C4—22no—
48C4×Dic71—22no—
49C4×Dic71—22no—
50#41×C71—24no—
51#41×C71—24no—
52C2×Q8×C71C2312yes—
53C2×D4×C71—22no—
54C2×D4×C71—21no—
55C2×D4×C71—21no—
56C2×D4×C71C2312yes—
57C22×C4×C71—22no—
58C22×C4×C71D411yescharacteristic
59C22×C4×C71D411yescharacteristic
60C22×C4×C71C2311yescharacteristic
61C4⋊C4×C71—21no—
62C4⋊C4×C71—21no—
63C22⋊C4×C71—22no—
64C22⋊C4×C71—22no—
65C42×C71D411yescharacteristic
66C42×C71D411yescharacteristic
67C42×C71C2311yescharacteristic
68C42×C71C2311yescharacteristic
69C23×C71—22no—
70C23×C71C2×D411yescharacteristic
71Q8×C71—22no—
72Q8×C71—22no—
73D4×C71—22no—
74D4×C71—22no—
75D4×C71—42no—
76D4×C71—44no—
77D4×C71—42no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71—41no—
81C2×C4×C71—44no—
82C2×C4×C71C2×D412yes—
83C2×C4×C71C2×D411yescharacteristic
84C2×C4×C71C2×D411yescharacteristic
85C2×C4×C71C2×D411yescharacteristic
86C2×C4×C71C2×D411yescharacteristic
87C2×C4×C71C2×D411yescharacteristic
88C2×C4×C71#4112yes—
89C2×C4×C71C2411yescharacteristic
90C2×Dic71—24no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71—42no—
94Dic142—24no—
95Dic142—22no—
96Dic142C2×D414yes—
97C71⋊C8—24no—
98C22×C71—21no—
99C22×C71—21no—
100C22×C71—42no—
101C22×C71—42no—
102C22×C71—42no—
103C22×C71#12112yes—
104C22×C71C22×D411yescharacteristic
105C4×C71—21no—
106C4×C71—21no—
107C4×C71—21no—
108C4×C71—42no—
109C4×C71#12112yes—
110C4×C71#13712yescomplemented
111C4×C71C22×D411yescharacteristic
112C4×C71C2×#4111yescharacteristic
113Dic71—24no—
114Dic71—42no—
115C2×C71—22no—
116C2×C71—82no—
117C2×C71C2×#12111yescharacteristic
118C2×C71C2×#13711yescharacteristic
119C2×C71#57511yescharacteristic
120#3037—711nomaximal, Sylow
121C71#303711yescharacteristic, complemented, Sylow
122C2×#137—712no—
123#532D7111yescharacteristic
124C2×C4×Q8—711no—
125#464—714no—
126#462—712no—
127#460—712no—
128#423—711no—
129#417—712no—
130C2×#41C2×D7112yes—
131C22×Q8—711no—
132#137—1428no—
133C2×Q16—714no—
134C2×SD16—714no—
135C2×M16—712no—
136C4⋊Q8C2×D7111yescharacteristic
137#127C2×D7111yescharacteristic
138#124C2×D7112yes—
139#121—21no—
140#121—21no—
141C4×Q8—712no—
142C4×Q8—712no—
143C4×Q8—1421no—
144C4×Q8—1421no—
145C4×D4—21no—
146C4×D4—21no—
147C2×C4⋊C4—711no—
148C2×C4⋊C4—1421no—
149C2×C42—1421no—
150C2×C42C2×D7111yescharacteristic
151C4⋊C8—712no—
152C4⋊C8—712no—
153#103—714no—
154#102—714no—
155#41—24no—
156#41—24no—
157C2×Q8—714no—
158C2×Q8—712no—
159C2×Q8—1421no—
160C2×Q8—1422no—
161C2×Q8C22×D7112yes—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D7112yes—
166C22×C4—22no—
167C22×C4—1421no—
168C22×C4—1421no—
169C22×C4C22⋊D7111yescharacteristic
170C22×C4C22⋊D7111yescharacteristic
171C22×C4C22×D7111yescharacteristic
172Q16—1428no—
173SD16—1428no—
174M16—1424no—
175C2×C8—714no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—712no—
179C4⋊C4—1422no—
180C4⋊C4—1422no—
181C4⋊C4—1421no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C42—1422no—
185C42—1422no—
186C42C22⋊D7111yescharacteristic
187C42C22⋊D7111yescharacteristic
188C42C22×D7111yescharacteristic
189C42C22×D7111yescharacteristic
190C23—22no—
191C23C2×C22⋊D7111yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—714no—
195Q8—1422no—
196Q8—1424no—
197D4—22no—
198D4—22no—
199D4—42no—
200D4—44no—
201D4—42no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—44no—
206C2×C4—2842no—
207C2×C4—1422no—
208C2×C4—1422no—
209C2×C4—1424no—
210C2×C4D4×D7112yes—
211C2×C4C2×C22⋊D7111yescharacteristic
212C2×C4C2×C22⋊D7111yescharacteristic
213C2×C4C2×C22⋊D7111yescharacteristic
214C2×C4C2×C22⋊D7111yescharacteristic
215C2×C4C2×C22⋊D7111yescharacteristic
216C2×C4#1176586412yes—
217C2×C4C23×D7111yescharacteristic
218C8—1424no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1455609912yes—
225C22C22×C22⋊D7111yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—42no—
230C4—2842no—
231C4—1424no—
232C4#1455609912yes—
233C4#1455615812yescomplemented
234C4C2×D4×D7111yescharacteristic
235C4C2×#1176586411yescharacteristic
236C2—22no—
237C2—82no—
238C2C2×#1455609911yescharacteristic
239C2C2×#1455615811yescharacteristic
240C2#1798679711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#532×C71C2
socleC22×C71C22×D4
hypercenter#532D71
hypocenterC71#3037
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14556158C2semidirect
2. C2×C4×Dic142C2semidirect
3. #17986218C2semidirect
4. #17986206C2semidirect
5. #17986196C2semidirect
6. #17986023C2semidirect
7. #17986000C2semidirect
36. C2×Dic142D4semidirect
110. C4×C71#137semidirect
121. C71#3037semidirect
233. C4#14556158semidirect