Finite Group Databasebeta

← #25002211

Subgroups — #25002211

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C43⋊C8C211yesmaximal, characteristic
2C2×#14582654C212yesmaximal
3C2×#14582654C212yesmaximal
4C2×#14582654C211yesmaximal, characteristic
5C4×#95×C43C211yesmaximal, characteristic
6C23×C43⋊C8C2212yes—
7C23×C43⋊C8C2211yescharacteristic
8C23×C43⋊C8C2211yescharacteristic
9C2×C4×C43⋊C8—24no—
10C2×C4×C43⋊C8C414yescomplemented
11#14582654—24no—
12#14582654—24no—
13#14582654C414yescomplemented
14C22×C42×C43C2212yes—
15C22×C42×C43C2211yescharacteristic
16C2×#95×C43C412yes—
17C2×#95×C43C412yes—
18C22×C43⋊C8—22no—
19C22×C43⋊C8—22no—
20C22×C43⋊C8—22no—
21C22×C43⋊C8—21no—
22C22×C43⋊C8—21no—
23C22×C43⋊C8—22no—
24C22×C43⋊C8—22no—
25C22×C43⋊C8—22no—
26C22×C43⋊C8—22no—
27C22×C43⋊C8—22no—
28C22×C43⋊C8—22no—
29C22×C43⋊C8C2×C414yes—
30C22×C43⋊C8C2×C412yes—
31C22×C43⋊C8C2×C412yes—
32C22×C43⋊C8D414yes—
33C22×C43⋊C8D412yes—
34C22×C43⋊C8Q812yes—
35C4×C43⋊C8—28no—
36C23×C4×C43C2×C414yes—
37C23×C4×C43C2×C411yescharacteristic
38C23×C4×C43C2×C411yescharacteristic
39C23×C4×C43C2311yescharacteristic
40C2×C42×C43—22no—
41C2×C42×C43—22no—
42C2×C42×C43—22no—
43C2×C42×C43—22no—
44C2×C42×C43—22no—
45C2×C42×C43—22no—
46C2×C42×C43—22no—
47C2×C42×C43—22no—
48C2×C42×C43C2×C412yes—
49C2×C42×C43C2×C412yes—
50#95×C43—24no—
51#95×C43C818yescomplemented
52C24×C43C22×C411yescharacteristic
53C22×C4×C43—24no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—24no—
57C22×C4×C43—24no—
58C22×C4×C43—24no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—24no—
62C22×C4×C43—24no—
63C22×C4×C43C4212yes—
64C22×C4×C43C4212yes—
65C22×C4×C43C2×C818yes—
66C22×C4×C43C2×C814yes—
67C22×C4×C43M1614yes—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D412yes—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×Q811yescharacteristic
73C22×C4×C43#4112yes—
74C22×C4×C43#4112yes—
75C22×C4×C43#4112yes—
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C42×C43—22no—
79C42×C43—22no—
80C42×C43—24no—
81C42×C43—42no—
82C42×C43—42no—
83C42×C43—42no—
84C42×C43—42no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—22no—
87C2×C43⋊C8—22no—
88C2×C43⋊C8—22no—
89C2×C43⋊C8—24no—
90C2×C43⋊C8—24no—
91C2×C43⋊C8—24no—
92C2×C43⋊C8—24no—
93C2×C43⋊C8—24no—
94C2×C43⋊C8—24no—
95C2×C43⋊C8—24no—
96C2×C43⋊C8—42no—
97C2×C43⋊C8—42no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—42no—
100C2×C43⋊C8C22⋊C414yes—
101C2×C43⋊C8C4⋊C414yes—
102C23×C43C2×C4211yescharacteristic
103C23×C43#11712yes—
104C23×C43C4×D412yes—
105C23×C43C4×D411yescharacteristic
106C23×C43C4×Q811yescharacteristic
107C23×C43C22×C812yes—
108C23×C43C2×M1612yes—
109C23×C43#13112yes—
110C23×C43#13112yes—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—28no—
116C2×C4×C43—28no—
117C2×C4×C43—28no—
118C2×C4×C43—28no—
119C2×C4×C43—28no—
120C2×C4×C43—44no—
121C2×C4×C43—44no—
122C2×C4×C43—44no—
123C2×C4×C43—44no—
124C2×C4×C43C4×C814yes—
125C2×C4×C43#9714yes—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43#11711yescharacteristic
129C2×C4×C43#11711yescharacteristic
130C2×C4×C43#11711yescharacteristic
131C2×C4×C43#11712yes—
132C2×C4×C43#11711yescharacteristic
133C2×C4×C43C4×D412yes—
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C4×Q811yescharacteristic
136C2×C4×C43#12112yes—
137C2×C4×C43C22⋊Q812yes—
138C2×C4×C43#12312yes—
139C2×C4×C43#12312yes—
140C2×C4×C43#12412yes—
141C2×C4×C43#12512yes—
142C2×C4×C43#12612yes—
143C2×C4×C43#12612yes—
144C43⋊C8—24no—
145C43⋊C8—24no—
146C43⋊C8—44no—
147#10797—431nomaximal, Sylow
148C22×C43#37611yescharacteristic
149C22×C43C4×C22⋊C411yescharacteristic
150C22×C43C4×C4⋊C411yescharacteristic
151C22×C43#38712yes—
152C22×C43#38812yes—
153C22×C43C2×C4×C811yescharacteristic
154C22×C43C2×#9711yescharacteristic
155C22×C43#40511yescharacteristic
156C22×C43#40511yescharacteristic
157C22×C43#43114yes—
158C22×C43#43314yes—
159C22×C43C8×D414yes—
160C22×C43C8×D412yes—
161C22×C43#43514yes—
162C22×C43#43612yes—
163C22×C43C8×Q812yes—
164C22×C43#44612yes—
165C4×C43—24no—
166C4×C43—24no—
167C4×C43—48no—
168C4×C43#38011yescharacteristic
169C4×C43#38111yescharacteristic
170C4×C43#38211yescharacteristic
171C4×C43#38311yescharacteristic
172C4×C43#38712yes—
173C4×C43#38812yes—
174C22×C4×C8—431no—
175C2×#336—431no—
176C2×#336—432no—
177C2×#336—432no—
178C4×#95D4311yescharacteristic
179C2×C43#143411yescharacteristic
180C2×C43#174411yescharacteristic
181C2×C43#174611yescharacteristic
182C2×C43C8×C22⋊C411yescharacteristic
183C2×C43#175211yescharacteristic
184C2×C43C8×C4⋊C411yescharacteristic
185C2×C43#177011yescharacteristic
186C2×C43#191614yes—
187C2×C43#192314yes—
188C23×C8—431no—
189C23×C8—431no—
190C23×C8—432no—
191C22×C42C2×D4312yes—
192C22×C42C2×D4311yescharacteristic
193C2×C4×C8—434no—
194C2×C4×C8—864no—
195C2×#95Dic4312yes—
196C2×#95Dic4312yes—
197#336—434no—
198#336—864no—
199#336—864no—
200C43#1079711yescharacteristic, complemented, Sylow
201C23×C4C2×Dic4314yes—
202C23×C4C2×Dic4311yescharacteristic
203C23×C4C2×Dic4311yescharacteristic
204C23×C4C22×D4311yescharacteristic
205C22×C8—432no—
206C22×C8—432no—
207C22×C8—432no—
208C22×C8—434no—
209C22×C8—432no—
210C22×C8—434no—
211C22×C8—862no—
212C22×C8—862no—
213C22×C8—862no—
214C22×C8—861no—
215C22×C8—861no—
216C22×C8—862no—
217C22×C8—862no—
218C22×C8—862no—
219C22×C8—862no—
220C22×C8—862no—
221C22×C8—862no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42C4×D4312yes—
231C2×C42C4×D4312yes—
232C4×C8—868no—
233#95—24no—
234#95C43⋊C818yescomplemented
235C24C22×Dic4311yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4C2×C43⋊C818yes—
247C22×C4C2×C43⋊C814yes—
248C22×C4#1062187714yes—
249C22×C4C4×Dic4312yes—
250C22×C4C4×Dic4312yes—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4#1062189812yes—
254C22×C4#1062189812yes—
255C22×C4D4×D4312yes—
256C22×C4D4×D4311yescharacteristic
257C22×C4#1062190012yes—
258C22×C4#1062190011yescharacteristic
259C22×C4Q8×D4311yescharacteristic
260C22×C4#1062190211yescharacteristic
261C2×C8—434no—
262C2×C8—434no—
263C2×C8—862no—
264C2×C8—862no—
265C2×C8—862no—
266C2×C8—862no—
267C2×C8—864no—
268C2×C8—864no—
269C2×C8—864no—
270C2×C8—864no—
271C2×C8—864no—
272C2×C8—864no—
273C2×C8—864no—
274C2×C8—1722no—
275C2×C8—1722no—
276C2×C8—1722no—
277C2×C8—1722no—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—42no—
285C23C2×C4×Dic4311yescharacteristic
286C23#1306328412yes—
287C23D4×Dic4312yes—
288C23D4×Dic4311yescharacteristic
289C23Q8×Dic4311yescharacteristic
290C23C22×C43⋊C812yes—
291C23C2×#1062187712yes—
292C23#1306333212yes—
293C23#1306333212yes—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—28no—
297C2×C4—28no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4C4×C43⋊C814yes—
308C2×C4#1306323614yes—
309C2×C4C22⋊C4×D4311yescharacteristic
310C2×C4C4⋊C4×D4311yescharacteristic
311C2×C4#1306328111yescharacteristic
312C2×C4#1306328212yes—
313C2×C4#1306328211yescharacteristic
314C2×C4#1306328211yescharacteristic
315C2×C4#1306328311yescharacteristic
316C2×C4(C22⋊D43)⋊C412yes—
317C2×C4#1306328711yescharacteristic
318C2×C4#1306329011yescharacteristic
319C2×C4#1306329812yes—
320C2×C4#1306330312yes—
321C2×C4#1306330712yes—
322C2×C4#1306331012yes—
323C2×C4#1306331112yes—
324C2×C4#1306331512yes—
325C2×C4#1306331812yes—
326C2×C4#1306332012yes—
327C8—864no—
328C8—864no—
329C8—1724no—
330C22#1458274511yescharacteristic
331C22C22⋊C4×Dic4311yescharacteristic
332C22C4⋊C4×Dic4311yescharacteristic
333C22#1458278512yes—
334C22#1458279212yes—
335C22C2×C4×C43⋊C811yescharacteristic
336C22C2×#1306323611yescharacteristic
337C22#1458285511yescharacteristic
338C22#1458285511yescharacteristic
339C22#1458295214yes—
340C22#1458296014yes—
341C22D4×C43⋊C814yes—
342C22D4×C43⋊C812yes—
343C22#1458297114yes—
344C22#1458297712yes—
345C22Q8×C43⋊C812yes—
346C22#1458303012yes—
347C4—24no—
348C4—24no—
349C4—48no—
350C4#1458275811yescharacteristic
351C4#1458276111yescharacteristic
352C4#1458276311yescharacteristic
353C4#1458276611yescharacteristic
354C4#1458278112yes—
355C4#1458278812yes—
356C2#1913282011yescharacteristic
357C2#1913434111yescharacteristic
358C2#1913434711yescharacteristic
359C2C22⋊C4×C43⋊C811yescharacteristic
360C2#1913437311yescharacteristic
361C2C4⋊C4×C43⋊C811yescharacteristic
362C2#1913446411yescharacteristic
363C2#1913515414yes—
364C2#1913520314yes—
subgroupG/H
center, FrattiniC23×C4C22×D43
commutatorC22×C43C2×C4×C8
FittingC4×#95×C43C2
socle, prime radicalC24×C43C22×C4
cosocleC23×C4×C43C23
hypercenterC4×#95D43
hypocenterC43#10797
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
10. C2×C4×C43⋊C8C4semidirect
13. #14582654C4semidirect
51. #95×C43C8semidirect
200. C43#10797semidirect
234. #95C43⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C43⋊C82
C2×#145826542
C4×#95×C432
#1079743