Finite Group Databasebeta

← #22598289

Subgroups — #22598289

Order 9088.

410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556107C211yesmaximal, characteristic
2C2×#14556087C211yesmaximal, characteristic
3#17986341C214yesmaximal, complemented
4#17986335C212yesmaximal, complemented
5#17986330C212yesmaximal, complemented
6#17986041C212yesmaximal, complemented
7#17986009C212yesmaximal, complemented
8#407×C71C211yesmaximal, characteristic
9C22×Dic142C2211yescharacteristic
10#14556107—21no—
11#14556107—21no—
12#14556107C2212yes—
13#14556107C2212yes—
14#14556087—21no—
15#14556087—21no—
16#14556087C2212yes—
17#14556087C2212yes—
18C2×C4⋊Dic71C2211yescharacteristic
19C2×C4⋊Dic71C2211yescharacteristic
20C2×C4⋊Dic71C2211yescharacteristic
21C2×Dic71⋊C4—21no—
22C2×C22⋊Dic71—21no—
23C2×C22⋊Dic71—21no—
24C2×C4×Dic71—21no—
25#14556062C2214yescomplemented
26#14556060C2214yescomplemented
27#14556053C2214yescomplemented
28#14556053C2214yescomplemented
29C23×C4×C71C2211yescharacteristic
30C2×M16×C71C2212yes—
31C22⋊C8×C71C2212yes—
32C22⋊C8×C71C2212yes—
33C2×Dic142—24no—
34C2×Dic142—21no—
35C2×Dic142C2312yes—
36C22×Dic71—21no—
37C22×Dic71—21no—
38C22×Dic71—21no—
39C22×Dic71—21no—
40C4⋊Dic71—21no—
41C4⋊Dic71—21no—
42C4⋊Dic71—21no—
43C4⋊Dic71C2312yes—
44C4⋊Dic71C2312yes—
45C4⋊Dic71C2312yes—
46Dic71⋊C4—22no—
47Dic71⋊C4—22no—
48C22⋊Dic71—22no—
49C22⋊Dic71—22no—
50C22⋊Dic71—22no—
51C22⋊Dic71—22no—
52C4×Dic71—22no—
53C4×Dic71—22no—
54C24×C71D411yescharacteristic
55C22×C4×C71—24no—
56C22×C4×C71D411yescharacteristic
57C22×C4×C71D411yescharacteristic
58C22×C4×C71D411yescharacteristic
59C22×C4×C71C2311yescharacteristic
60C22×C4×C71C2311yescharacteristic
61C22×C4×C71C2311yescharacteristic
62M16×C71—24no—
63C2×C8×C71C2314yes—
64C23×C71—22no—
65C23×C71—22no—
66C23×C71—41no—
67C23×C71C2×D411yescharacteristic
68C23×C71C2×D411yescharacteristic
69C23×C71C2×D411yescharacteristic
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—22no—
73C2×C4×C71—22no—
74C2×C4×C71—22no—
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71#4114yes—
79C2×C4×C71C2411yescharacteristic
80C2×Dic71—22no—
81C2×Dic71—22no—
82C2×Dic71—22no—
83C2×Dic71—22no—
84C2×Dic71—42no—
85C2×Dic71—42no—
86C2×Dic71—42no—
87C2×Dic71—42no—
88Dic142—24no—
89Dic142—42no—
90C8×C71—24no—
91C22×C71—21no—
92C22×C71—21no—
93C22×C71—21no—
94C22×C71—21no—
95C22×C71—21no—
96C22×C71—21no—
97C22×C71—21no—
98C22×C71—44no—
99C22×C71#12312yes—
100C22×C71#13712yes—
101C22×C71C22×D411yescharacteristic
102C4×C71—21no—
103C4×C71—21no—
104C4×C71#12312yes—
105C4×C71C2×#4112yes—
106Dic71—42no—
107Dic71—42no—
108Dic71—42no—
109Dic71—42no—
110C2×C71—22no—
111C2×C71—22no—
112C2×C71—41no—
113C2×C71C2×#12311yescharacteristic
114C2×C71C2×#13711yescharacteristic
115C2×C71#57511yescharacteristic
116#3095—711nomaximal, Sylow
117C71#309511yescharacteristic, complemented, Sylow
118C2×C22⋊Q8—711no—
119C2×#117—711no—
120#485—714no—
121#484—712no—
122#483—712no—
123#428—712no—
124#419—712no—
125#407D7111yescharacteristic
126C22×Q8—711no—
127C23×C4C2×D7111yescharacteristic
128C2×M16C2×D7112yes—
129C22⋊Q8—712no—
130C22⋊Q8—712no—
131C22⋊Q8—1421no—
132C22⋊Q8—1421no—
133#117—712no—
134#117—712no—
135#117—1421no—
136#117—1421no—
137C2×C4⋊C4—711no—
138C2×C4⋊C4—711no—
139C2×C4⋊C4—711no—
140C2×C4⋊C4—1421no—
141C2×C22⋊C4—1421no—
142C2×C22⋊C4—1421no—
143C2×C42—1421no—
144#107—714no—
145#106—714no—
146#103—714no—
147#103—714no—
148C22⋊C8C2×D7112yes—
149C22⋊C8C2×D7112yes—
150C24D28411yescharacteristic
151C2×Q8—712no—
152C2×Q8—1424no—
153C2×Q8—1421no—
154C22×C4—24no—
155C22×C4—1421no—
156C22×C4—1421no—
157C22×C4—1421no—
158C22×C4—1421no—
159C22×C4D28411yescharacteristic
160C22×C4D28411yescharacteristic
161C22×C4D28411yescharacteristic
162C22×C4C22×D7111yescharacteristic
163C22×C4C22×D7111yescharacteristic
164C22×C4C22×D7111yescharacteristic
165M16—24no—
166C2×C8C22×D7114yes—
167C4⋊C4—712no—
168C4⋊C4—712no—
169C4⋊C4—712no—
170C4⋊C4—1422no—
171C4⋊C4—1422no—
172C4⋊C4—1421no—
173C4⋊C4—1421no—
174C4⋊C4—1421no—
175C22⋊C4—1422no—
176C22⋊C4—1422no—
177C22⋊C4—1422no—
178C22⋊C4—1422no—
179C42—1422no—
180C42—1422no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×D28411yescharacteristic
185C23C2×D28411yescharacteristic
186C23C2×D28411yescharacteristic
187Q8—2842no—
188Q8—1424no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—2842no—
195C2×C4—2842no—
196C2×C4—2842no—
197C2×C4—2842no—
198C2×C4—1422no—
199C2×C4—1422no—
200C2×C4—1422no—
201C2×C4—1422no—
202C2×C4C2×D28411yescharacteristic
203C2×C4C2×D28411yescharacteristic
204C2×C4C2×D28411yescharacteristic
205C2×C4#1176586414yes—
206C2×C4C23×D7111yescharacteristic
207C8—24no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#1455611212yes—
217C22#1455616112yes—
218C22C22×D28411yescharacteristic
219C4—21no—
220C4—21no—
221C4—2842no—
222C4—2842no—
223C4—2842no—
224C4—2842no—
225C4#1455611212yes—
226C4C2×#1176586412yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#1455611211yescharacteristic
231C2C2×#1455616111yescharacteristic
232C2#1798679911yescharacteristic
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#407×C71C2
socleC22×C71C22×D4
hypercenter#407D71
hypocenterC71#3095
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #17986341C2semidirect
4. #17986335C2semidirect
5. #17986330C2semidirect
6. #17986041C2semidirect
7. #17986009C2semidirect
25. #14556062C22semidirect
26. #14556060C22semidirect
27. #14556053C22semidirect
28. #14556053C22semidirect
117. C71#3095semidirect