Finite Group Databasebeta

← #25012600

Subgroups — #25012600

Order 11008.

468 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 123 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×#14582698C212yesmaximal
2#19134591C212yesmaximal
3#19132722C212yesmaximal
4C4×C4⋊Q8×C43C211yesmaximal, characteristic
5#14582923—22no—
6C2×#13063244C2214yes—
7#14582698—24no—
8#14582668—22no—
9C2×C4⋊Q8×C43C2211yescharacteristic
10C2×C4×Q8×C43C411yescharacteristic
11C2×C4×Q8×C43C2211yescharacteristic
12C43×#391C411yescharacteristic
13C43×#391C2211yescharacteristic
14C43×#389—22no—
15C43×#384C411yescharacteristic
16C4×C4⋊C4×C43—22no—
17C43×C43C411yescharacteristic
18C2×#10621877—24no—
19C4⋊(C43⋊C8)—42no—
20C4⋊(C43⋊C8)—42no—
21#13063244—24no—
22#13063244—24no—
23C22×Q8×C43C2×C411yescharacteristic
24C22×Q8×C43C2311yescharacteristic
25C4⋊Q8×C43—22no—
26C4⋊Q8×C43D412yes—
27C4⋊Q8×C43Q812yes—
28C4×Q8×C43—41no—
29C4×Q8×C43—41no—
30C4×Q8×C43—41no—
31C4×Q8×C43—41no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C4⋊C4×C43D412yes—
38C2×C42×C43—21no—
39C2×C42×C43—21no—
40C2×C42×C43—21no—
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D412yes—
45#95×C43—22no—
46#95×C43—22no—
47C2×Q8×C43—21no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43C4⋊C412yes—
53C2×Q8×C43C2×D411yescharacteristic
54C2×Q8×C43C2×Q811yescharacteristic
55C2×Q8×C43#4112yes—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D412yes—
65C4⋊C4×C43—24no—
66C4⋊C4×C43—24no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—42no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—44no—
71C4⋊C4×C43—42no—
72C42×C43—24no—
73C42×C43—21no—
74C42×C43—21no—
75C42×C43—22no—
76C42×C43—22no—
77C42×C43—21no—
78C42×C43—41no—
79C42×C43—42no—
80C42×C43—41no—
81C42×C43—41no—
82C42×C43C4⋊C412yes—
83#10621877—44no—
84#10621877—44no—
85C2×C43⋊C8—44no—
86C23×C43C2×C22⋊C411yescharacteristic
87Q8×C43—41no—
88Q8×C43—41no—
89Q8×C43—42no—
90Q8×C43—42no—
91Q8×C43—42no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43—22no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—41no—
112C2×C4×C43#9911yescharacteristic
113C2×C4×C43#9911yescharacteristic
114C2×C4×C43C2×C4⋊C411yescharacteristic
115C2×C4×C43#11711yescharacteristic
116C2×C4×C43#12112yes—
117C2×C4×C43C22⋊Q812yes—
118C43⋊C8—84no—
119#12802—431nomaximal, Sylow
120C22×C43—21no—
121C22×C43—21no—
122C22×C43#38011yescharacteristic
123C22×C43C2×#9911yescharacteristic
124C22×C43#41011yescharacteristic
125C4×C43—24no—
126C4×C43—22no—
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—22no—
130C4×C43—21no—
131C4×C43—42no—
132C4×C43—42no—
133C4×C43—41no—
134C4×C43—42no—
135C4×C43—81no—
136C4×C43#35612yescomplemented
137C4×C4⋊Q8D4311yescharacteristic
138C2×#356—432no—
139#1801—432no—
140#1394—432no—
141C2×C43—21no—
142C2×C43—21no—
143C2×C43#179911yescharacteristic
144C2×C43C2×#35611yescharacteristic
145C2×C43#213211yescharacteristic
146C2×C4⋊Q8C2×D4311yescharacteristic
147C2×C4×Q8Dic4311yescharacteristic
148C2×C4×Q8C2×D4311yescharacteristic
149#423—862no—
150C2×#101—434no—
151#391Dic4311yescharacteristic
152#391C2×D4311yescharacteristic
153#389—22no—
154#384Dic4311yescharacteristic
155C4×C4⋊C4—22no—
156C43Dic4311yescharacteristic
157#356—864no—
158#343—862no—
159C43#1280211yescharacteristic, complemented, Sylow
160C22×Q8C2×Dic4311yescharacteristic
161C22×Q8C22×D4311yescharacteristic
162C2×M16—864no—
163C4⋊Q8—22no—
164C4⋊Q8Dic8612yes—
165C4⋊Q8D17212yes—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4C2×Dic4311yescharacteristic
174C2×C4⋊C4C2×Dic4311yescharacteristic
175C2×C4⋊C4C22⋊D4312yes—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42C2×Dic4311yescharacteristic
180C2×C42C2×Dic4311yescharacteristic
181C2×C42C2×Dic4311yescharacteristic
182C2×C42C22⋊D4312yes—
183C4⋊C8—1722no—
184C4⋊C8—1722no—
185#101—864no—
186#101—864no—
187#95—22no—
188#95—22no—
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8C4⋊Dic4312yes—
195C2×Q8C2×Dic8611yescharacteristic
196C2×Q8C2×D17211yescharacteristic
197C2×Q8#1062189812yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4C22⋊Dic4312yes—
203C22×C4C22⋊Dic4311yescharacteristic
204C22×C4C22⋊Dic4311yescharacteristic
205C22×C4C22×Dic4311yescharacteristic
206C22×C4C2×C22⋊D4312yes—
207M16—1724no—
208M16—1724no—
209C2×C8—1724no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—44no—
217C42—24no—
218C42—22no—
219C42—22no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—41no—
224C42—42no—
225C42—41no—
226C42—41no—
227C42C4⋊Dic4312yes—
228C23C2×C22⋊Dic4311yescharacteristic
229Q8—41no—
230Q8—41no—
231Q8—42no—
232Q8—42no—
233Q8—42no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4#1306324011yescharacteristic
255C2×C4#1306324011yescharacteristic
256C2×C4C2×C4⋊Dic4311yescharacteristic
257C2×C4#1306328411yescharacteristic
258C2×C4#1306329912yes—
259C2×C4#1306330412yes—
260C8—3444no—
261C22—21no—
262C22—21no—
263C22#1458275911yescharacteristic
264C22C2×#1306324011yescharacteristic
265C22#1458287311yescharacteristic
266C4—24no—
267C4—21no—
268C4—22no—
269C4—21no—
270C4—21no—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—42no—
276C4—81no—
277C4#1458269812yescomplemented
278C2—21no—
279C2—21no—
280C2#1913458311yescharacteristic
281C2C2×#1458269811yescharacteristic
282C2#1913628011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC4×C4⋊Q8×C43C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC22×Q8×C43C23
hypercenterC4×C4⋊Q8D43
hypocenterC43#12802
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
136. C4×C43#356semidirect
159. C43#12802semidirect
277. C4#14582698semidirect

Maximal subgroups

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

subgroupindex
C2×#145826982
#191345912
#191327222
C4×C4⋊Q8×C432
#1280243