Finite Group Databasebeta

← #25005988

Subgroups — #25005988

Order 11008.

670 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 99 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#19132929C212yesmaximal, complemented
2#19132527C214yesmaximal, complemented
3C43×#2309C211yesmaximal, characteristic
4#14582956—22no—
5#14582625C2214yescomplemented
6#14582623—22no—
7C23×D4×C43C411yescharacteristic
8C2×#117×C43C411yescharacteristic
9C2×#117×C43C2211yescharacteristic
10C43×#390—22no—
11C43×#390C412yes—
12C43×#390C2212yes—
13C43×#379—22no—
14C4⋊(C43⋊C8)—42no—
15C22⋊(C43⋊C8)—24no—
16#13063236—42no—
17C25×C43—21no—
18C22×D4×C43—24no—
19C22×D4×C43—21no—
20C22×D4×C43—42no—
21C22×D4×C43—42no—
22C22×D4×C43C2×C412yes—
23C23×C4×C43C2×C411yescharacteristic
24#117×C43—42no—
25#117×C43—42no—
26C2×C4⋊C4×C43—21no—
27C2×C4⋊C4×C43C2×C411yescharacteristic
28C2×C4⋊C4×C43C2311yescharacteristic
29C2×C22⋊C4×C43—21no—
30C2×C22⋊C4×C43—24no—
31C2×C22⋊C4×C43—24no—
32C2×C22⋊C4×C43D412yes—
33C2×C42×C43C2×C412yes—
34C2×C42×C43D412yes—
35C24×C43—24no—
36C24×C43—22no—
37C24×C43—42no—
38C24×C43—42no—
39C24×C43—82no—
40C24×C43—82no—
41C24×C43C22⋊C411yescharacteristic
42C2×D4×C43—24no—
43C2×D4×C43—22no—
44C2×D4×C43—416no—
45C2×D4×C43—42no—
46C2×D4×C43—42no—
47C2×D4×C43—42no—
48C2×D4×C43—42no—
49C2×D4×C43M1614yes—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43C22⋊C412yes—
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22×C411yescharacteristic
57C22×C4×C43C2×D412yes—
58C4⋊C4×C43—41no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—42no—
61C22⋊C4×C43—42no—
62C22⋊C4×C43—42no—
63C22⋊C4×C43—84no—
64C22⋊C4×C43—84no—
65C42×C43—22no—
66C42×C43—22no—
67C42×C43—42no—
68C2×C43⋊C8—44no—
69C23×C43—21no—
70C23×C43—21no—
71C23×C43—24no—
72C23×C43—41no—
73C23×C43—41no—
74C23×C43—44no—
75C23×C43—44no—
76C23×C43—48no—
77C23×C43—42no—
78C23×C43—42no—
79C23×C43—88no—
80C23×C43—88no—
81C23×C43—84no—
82C23×C43—84no—
83C23×C43#10012yes—
84C23×C43C2×C22⋊C411yescharacteristic
85D4×C43—44no—
86D4×C43—48no—
87D4×C43—44no—
88C2×C4×C43—28no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43#9912yes—
101C2×C4×C43C2×M1612yes—
102C43⋊C8—84no—
103#11509—431nomaximal, Sylow
104C22×C43—21no—
105C22×C43—21no—
106C22×C43—22no—
107C22×C43—42no—
108C22×C43—42no—
109C22×C43—48no—
110C22×C43—41no—
111C22×C43—41no—
112C22×C43—44no—
113C22×C43—84no—
114C22×C43—816no—
115C22×C43—82no—
116C22×C43—82no—
117C22×C43#40711yescharacteristic
118C22×C43C2×#9911yescharacteristic
119C22×C43C2×#10011yescharacteristic
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43—42no—
124C4×C43—82no—
125#2309D4311yescharacteristic
126#1464—432no—
127#1318—434no—
128C2×C43—21no—
129C2×C43—21no—
130C2×C43—42no—
131C2×C43—84no—
132C2×C43#146211yescharacteristic
133C2×C43#212811yescharacteristic
134C2×C43#213411yescharacteristic
135C23×D4Dic4311yescharacteristic
136C2×#117Dic4311yescharacteristic
137C2×#117C2×D4311yescharacteristic
138#432—862no—
139#390—22no—
140#390Dic4312yes—
141#390C2×D4312yes—
142#379—22no—
143#324—434no—
144#323—862no—
145C43#1150911yescharacteristic, complemented, Sylow
146C25—21no—
147C22×D4—24no—
148C22×D4—21no—
149C22×D4—42no—
150C22×D4—42no—
151C22×D4C2×Dic4312yes—
152C23×C4C2×Dic4311yescharacteristic
153#117—42no—
154#117—42no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×Dic4311yescharacteristic
157C2×C4⋊C4C22×D4311yescharacteristic
158C2×C22⋊C4—21no—
159C2×C22⋊C4—24no—
160C2×C22⋊C4—24no—
161C2×C22⋊C4C22⋊D4312yes—
162C2×C42C2×Dic4312yes—
163C2×C42C22⋊D4312yes—
164C4⋊C8—1722no—
165C22⋊C8—864no—
166#97—1722no—
167C24—24no—
168C24—22no—
169C24—42no—
170C24—42no—
171C24—82no—
172C24—82no—
173C24C22⋊Dic4311yescharacteristic
174C2×D4—24no—
175C2×D4—22no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—416no—
179C2×D4—42no—
180C2×D4—42no—
181C2×D4#1062187714yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic4312yes—
187C22×C4C22⋊Dic4311yescharacteristic
188C22×C4C22×Dic4311yescharacteristic
189C22×C4C2×C22⋊D4312yes—
190C2×C8—1724no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—84no—
197C22⋊C4—84no—
198C42—22no—
199C42—22no—
200C42—42no—
201C23—21no—
202C23—21no—
203C23—24no—
204C23—41no—
205C23—41no—
206C23—44no—
207C23—44no—
208C23—48no—
209C23—42no—
210C23—42no—
211C23—88no—
212C23—88no—
213C23—84no—
214C23—84no—
215C23#1306324212yes—
216C23C2×C22⋊Dic4311yescharacteristic
217D4—44no—
218D4—48no—
219D4—44no—
220C2×C4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4#1306324012yes—
233C2×C4C2×#1062187712yes—
234C8—3444no—
235C22—21no—
236C22—21no—
237C22—22no—
238C22—42no—
239C22—42no—
240C22—48no—
241C22—41no—
242C22—41no—
243C22—44no—
244C22—84no—
245C22—816no—
246C22—82no—
247C22—82no—
248C22#1458286311yescharacteristic
249C22C2×#1306324011yescharacteristic
250C22C2×#1306324211yescharacteristic
251C4—22no—
252C4—22no—
253C4—42no—
254C4—42no—
255C4—82no—
256C2—21no—
257C2—21no—
258C2—42no—
259C2—84no—
260C2#1913292211yescharacteristic
261C2#1913626711yescharacteristic
262C2#1913628711yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2309C2
socleC22×C43C2×#99
prime radicalC23×D4×C43C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2309D43
hypocenterC43#11509
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
1. #19132929C2semidirect
2. #19132527C2semidirect
5. #14582625C22semidirect
145. C43#11509semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191329292
#191325272
C43×#23092
#1150943