Finite Group Databasebeta

← #25005891

Subgroups — #25005891

Order 11008.

460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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#19132913C212yesmaximal
2#19132541C212yesmaximal, complemented
3#19132529C212yesmaximal, complemented
4C43×#2326C211yesmaximal, characteristic
5C2×C22⋊(C43⋊C8)—22no—
6#14582625C2214yes—
7#14582623—22no—
8C2×#124×C43C411yescharacteristic
9C2×C4×Q8×C43C411yescharacteristic
10C2×C4×D4×C43C2211yescharacteristic
11C43×#391C2211yescharacteristic
12C43×#390C411yescharacteristic
13C43×#388—22no—
14C43×#385—22no—
15C43×#384C2211yescharacteristic
16C43×#376C411yescharacteristic
17C22×C43⋊C8—42no—
18C22⋊(C43⋊C8)—24no—
19C22⋊(C43⋊C8)—42no—
20C22×Q8×C43C2×C411yescharacteristic
21C22×D4×C43C2×C411yescharacteristic
22C23×C4×C43D412yes—
23#124×C43—22no—
24#124×C43C814yescomplemented
25C4×Q8×C43—42no—
26C4×D4×C43—42no—
27C2×C4⋊C4×C43—21no—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43C2×C411yescharacteristic
30C2×C4⋊C4×C43C2311yescharacteristic
31C2×C22⋊C4×C43—22no—
32C2×C22⋊C4×C43—22no—
33C2×C22⋊C4×C43D412yes—
34C2×C42×C43—21no—
35C2×C42×C43C2×C411yescharacteristic
36C2×C42×C43C2×C411yescharacteristic
37C2×C42×C43C2×C411yescharacteristic
38#95×C43—21no—
39#95×C43—21no—
40#95×C43—22no—
41C24×C43C22⋊C412yes—
42C2×Q8×C43—21no—
43C2×Q8×C43—41no—
44C2×Q8×C43—41no—
45C2×Q8×C43C2×C812yescomplemented
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43C2×C812yes—
49C2×D4×C43M1612yes—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—82no—
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22⋊C411yescharacteristic
59C22×C4×C43C22×C411yescharacteristic
60C22×C4×C43C2×D412yes—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—82no—
65C22⋊C4×C43—28no—
66C22⋊C4×C43—42no—
67C22⋊C4×C43—82no—
68C42×C43—22no—
69C42×C43—21no—
70C42×C43—41no—
71C42×C43—42no—
72C42×C43C2×C812yescomplemented
73C2×C43⋊C8—44no—
74C2×C43⋊C8—84no—
75C23×C43—22no—
76C23×C43—22no—
77C23×C43—42no—
78C23×C43—42no—
79C23×C43C22⋊C814yes—
80C23×C43C2×C22⋊C411yescharacteristic
81Q8×C43—42no—
82Q8×C43—42no—
83D4×C43—42no—
84D4×C43—42no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—21no—
91C2×C4×C43—41no—
92C2×C4×C43—44no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—82no—
105C2×C4×C43#9912yes—
106C2×C4×C43C22×C811yescharacteristic
107C2×C4×C43C2×M1611yescharacteristic
108C43⋊C8—84no—
109#11481—431nomaximal, Sylow
110C22×C43—21no—
111C22×C43—21no—
112C22×C43—24no—
113C22×C43—44no—
114C22×C43—42no—
115C22×C43—42no—
116C22×C43—82no—
117C22×C43C2×C22⋊C811yescharacteristic
118C22×C43C2×#9911yescharacteristic
119C22×C43#41311yescharacteristic
120C4×C43—22no—
121C4×C43—21no—
122C4×C43—21no—
123C4×C43—42no—
124C4×C43—42no—
125C4×C43—41no—
126C4×C43—42no—
127C4×C43—81no—
128C4×C43—81no—
129#2326D4311yescharacteristic
130#1459—432no—
131#1325—432no—
132#1319—432no—
133C2×C43—21no—
134C2×C43—21no—
135C2×C43—44no—
136C2×C43#145911yescharacteristic
137C2×C43#212711yescharacteristic
138C2×C43#213511yescharacteristic
139C2×#124Dic4311yescharacteristic
140C2×C4×Q8Dic4311yescharacteristic
141C2×C4×D4C2×D4311yescharacteristic
142C2×C22⋊C8—862no—
143#391C2×D4311yescharacteristic
144#390Dic4311yescharacteristic
145#388—22no—
146#385—22no—
147#384C2×D4311yescharacteristic
148#376Dic4311yescharacteristic
149#324—434no—
150#323—862no—
151C43#1148111yescharacteristic, complemented, Sylow
152C22×Q8C2×Dic4311yescharacteristic
153C22×D4C2×Dic4311yescharacteristic
154C23×C4C22⋊D4312yes—
155C22×C8—1722no—
156#124—22no—
157#124C43⋊C814yescomplemented
158C4×Q8—42no—
159C4×D4—42no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4C2×Dic4311yescharacteristic
163C2×C4⋊C4C22×D4311yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4C22⋊D4312yes—
167C2×C42—21no—
168C2×C42C2×Dic4311yescharacteristic
169C2×C42C2×Dic4311yescharacteristic
170C2×C42C2×Dic4311yescharacteristic
171C22⋊C8—864no—
172C22⋊C8—1722no—
173#95—21no—
174#95—21no—
175#95—22no—
176C24C22⋊Dic4312yes—
177C2×Q8—21no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8C2×C43⋊C812yescomplemented
181C2×D4—41no—
182C2×D4—41no—
183C2×D4C2×C43⋊C812yes—
184C2×D4#1062187712yes—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—82no—
192C22×C4C22⋊Dic4311yescharacteristic
193C22×C4C22⋊Dic4311yescharacteristic
194C22×C4C22×Dic4311yescharacteristic
195C22×C4C2×C22⋊D4312yes—
196C2×C8—3444no—
197C2×C8—1724no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—82no—
202C22⋊C4—28no—
203C22⋊C4—42no—
204C22⋊C4—82no—
205C42—22no—
206C42—21no—
207C42—41no—
208C42—42no—
209C42C2×C43⋊C812yescomplemented
210C23—22no—
211C23—22no—
212C23—42no—
213C23—42no—
214C23C22⋊(C43⋊C8)14yes—
215C23C2×C22⋊Dic4311yescharacteristic
216Q8—42no—
217Q8—42no—
218D4—42no—
219D4—42no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4#1306324012yes—
241C2×C4C22×C43⋊C811yescharacteristic
242C2×C4C2×#1062187711yescharacteristic
243C8—3444no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—82no—
251C22C2×C22⋊(C43⋊C8)11yescharacteristic
252C22C2×#1306324011yescharacteristic
253C22#1458288311yescharacteristic
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—81no—
262C4—81no—
263C2—21no—
264C2—21no—
265C2—44no—
266C2#1913291311yescharacteristic
267C2#1913626411yescharacteristic
268C2#1913629011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2326C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2326D43
hypocenterC43#11481
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #19132541C2semidirect
3. #19132529C2semidirect
24. #124×C43C8semidirect
45. C2×Q8×C43C2×C8semidirect
72. C42×C43C2×C8semidirect
151. C43#11481semidirect
157. #124C43⋊C8semidirect
180. C2×Q8C2×C43⋊C8semidirect
209. C42C2×C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
#191329132
#191325412
#191325292
C43×#23262
#1148143