Finite Group Databasebeta

← #22599337

Subgroups — #22599337

Order 9088.

434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#17986549C211yesmaximal, characteristic, complemented
2#17986549C211yesmaximal, characteristic, complemented
3#17986388C212yesmaximal, complemented
4#17986359C212yesmaximal, complemented
5#17986205C212yesmaximal, complemented
6#17986195C212yesmaximal, complemented
7#17986146C214yesmaximal, complemented
8#432×C71C211yesmaximal, characteristic, complemented
9C2×#11765865—21no—
10C2×#11765865C2212yes—
11C2×#11765854C2214yes—
12C2×D568C2214yes—
13#14556128C2211yescharacteristic
14#14556128C2211yescharacteristic
15#14556125C2211yescharacteristic
16#14556125C2211yescharacteristic
17#14556116—21no—
18#14556116C2212yes—
19#14556102—21no—
20#14556102—21no—
21#14556102—21no—
22#14556102C2212yes—
23C4×D284—21no—
24C4×D284—21no—
25C4×D284—21no—
26C4×D284C2212yes—
27#14556053C2214yes—
28#14556050C2214yes—
29C2×C42×C71C2211yescharacteristic
30C4⋊C8×C71C2212yes—
31C22⋊C8×C71C2212yes—
32#97×C71C2212yes—
33#11765865—44no—
34#11765865—44no—
35C2×Dic142—21no—
36C2×Dic142C2312yes—
37C2×D284—21no—
38C2×D284—21no—
39C2×D284—21no—
40C2×D284—21no—
41C2×D284C2312yes—
42C2×D284C2312yes—
43C2×C22⋊D71—22no—
44C2×C22⋊D71—22no—
45C2×C4×D71—22no—
46C2×C4×D71—22no—
47#11765854—44no—
48D568—44no—
49C4⋊Dic71—21no—
50C4⋊Dic71—21no—
51C4⋊Dic71—21no—
52C4⋊Dic71C2312yes—
53(C2×D71)⋊C4—22no—
54(C2×D71)⋊C4—22no—
55(C2×D71)⋊C4—22no—
56(C2×D71)⋊C4—22no—
57C22×C4×C71D411yescharacteristic
58C22×C4×C71D411yescharacteristic
59C22×C4×C71C2311yescharacteristic
60C2×C8×C71C2314yes—
61C42×C71D411yescharacteristic
62C42×C71D411yescharacteristic
63C42×C71C2311yescharacteristic
64C42×C71C2311yescharacteristic
65C23×C71C2×D411yescharacteristic
66C22×D71—22no—
67C22×D71—22no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—41no—
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2411yescharacteristic
77C22⋊D71—44no—
78C22⋊D71—44no—
79C2×Dic71—22no—
80C2×Dic71—22no—
81D284—22no—
82D284—24no—
83D284—22no—
84D284—42no—
85D284—42no—
86D284—42no—
87D284—42no—
88C4×D71—44no—
89C4×D71—44no—
90Dic142—24no—
91Dic142—42no—
92C8×C71—24no—
93C22×C71—21no—
94C22×C71—21no—
95C22×C71—21no—
96C22×C71C22×D411yescharacteristic
97C2×D71—42no—
98C2×D71—42no—
99C2×D71—42no—
100C2×D71—42no—
101C2×D71—42no—
102C2×D71—42no—
103C4×C71—21no—
104C4×C71—21no—
105C4×C71—21no—
106C4×C71—21no—
107C4×C71AGL(1,ℤ/8)12yes—
108C4×C71H(5,𝔽2)12yes—
109Dic71—42no—
110Dic71—42no—
111C2×C71—41no—
112C2×C71#53511yescharacteristic
113C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
114C2×C71#57511yescharacteristic
115D71—82no—
116D71—82no—
117#3214—711nomaximal, Sylow
118C71#321411yescharacteristic, complemented, Sylow
119#532—711no—
120#532—711no—
121#496—712no—
122#489—712no—
123#461—712no—
124#459—712no—
125#449—714no—
126#432D7111yescharacteristic, complemented
127C2×#41—712no—
128C2×#41—1421no—
129C2×SD16—714no—
130C2×D8—714no—
131C4⋊Q8—711no—
132C4⋊Q8—711no—
133#127—711no—
134#127—711no—
135#124—712no—
136#124—1421no—
137#121—712no—
138#121—1421no—
139#121—1421no—
140#121—1421no—
141C4×D4—712no—
142C4×D4—1421no—
143C4×D4—1421no—
144C4×D4—1421no—
145C2×C42C2×D7111yescharacteristic
146C4⋊C8C2×D7112yes—
147#103—714no—
148#102—714no—
149C22⋊C8C2×D7112yes—
150#97C2×D7112yes—
151#41—2844no—
152#41—2844no—
153C2×Q8—712no—
154C2×Q8—1421no—
155C2×D4—712no—
156C2×D4—712no—
157C2×D4—1422no—
158C2×D4—1422no—
159C2×D4—1421no—
160C2×D4—1421no—
161C2×D4—1421no—
162C2×D4—1421no—
163C22×C4—1422no—
164C22×C4—1422no—
165C22×C4D28411yescharacteristic
166C22×C4D28411yescharacteristic
167C22×C4C22×D7111yescharacteristic
168SD16—2844no—
169D8—2844no—
170C2×C8C22×D7114yes—
171C4⋊C4—712no—
172C4⋊C4—1421no—
173C4⋊C4—1421no—
174C4⋊C4—1421no—
175C22⋊C4—1422no—
176C22⋊C4—1422no—
177C22⋊C4—1422no—
178C22⋊C4—1422no—
179C42D28411yescharacteristic
180C42D28411yescharacteristic
181C42C22×D7111yescharacteristic
182C42C22×D7111yescharacteristic
183C23—1422no—
184C23—1422no—
185C23C2×D28411yescharacteristic
186Q8—2842no—
187Q8—1424no—
188D4—2842no—
189D4—2842no—
190D4—2842no—
191D4—2844no—
192D4—2844no—
193D4—2842no—
194D4—1422no—
195D4—1424no—
196D4—1422no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—2844no—
201C2×C4—2844no—
202C2×C4—1422no—
203C2×C4—1422no—
204C2×C4C2×D28411yescharacteristic
205C2×C4C2×D28411yescharacteristic
206C2×C4C2×D28411yescharacteristic
207C2×C4C2×D28411yescharacteristic
208C2×C4C2×D28411yescharacteristic
209C2×C4C23×D7111yescharacteristic
210C8—24no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—2842no—
215C22—2842no—
216C22—2842no—
217C22—2842no—
218C22—2842no—
219C22—2842no—
220C22C22×D28411yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—2842no—
226C4—2842no—
227C4#1455615612yes—
228C4#1455617412yes—
229C2—41no—
230C2—5682no—
231C2—5682no—
232C2#1798656811yescharacteristic
233C2C2×#1455615611yescharacteristic
234C2#1798679911yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#432×C71C2
socleC22×C71C22×D4
hypercenter#432D71
hypocenterC71#3214
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #17986549C2semidirect
2. #17986549C2semidirect
3. #17986388C2semidirect
4. #17986359C2semidirect
5. #17986205C2semidirect
6. #17986195C2semidirect
7. #17986146C2semidirect
8. #432×C71C2semidirect
118. C71#3214semidirect
126. #432D71semidirect