Finite Group Databasebeta

← #25002210

Subgroups — #25002210

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
1C2×#14582654C211yesmaximal, characteristic
2C2×#14582653C212yesmaximal
3C2×#14582653C212yesmaximal
4C4×C43⋊#95C211yesmaximal, characteristic
5C22×C4×C8×C43C211yesmaximal, characteristic
6C23×C43⋊C8C2212yes—
7C22×C4×Dic43C2212yes—
8C2×C43⋊#95C412yes—
9C2×C43⋊#95C412yes—
10#14582654C414yescomplemented
11#14582653—24no—
12#14582653—24no—
13C23×C8×C43C2211yescharacteristic
14C23×C8×C43C2211yescharacteristic
15C22×C42×C43C2211yescharacteristic
16C2×C4×C8×C43—24no—
17C2×C4×C8×C43C414yescomplemented
18C23×Dic43C2×C414yes—
19C22×C43⋊C8—22no—
20C22×C43⋊C8—22no—
21C22×C43⋊C8—22no—
22C22×C43⋊C8—22no—
23C22×C43⋊C8—22no—
24C22×C43⋊C8—22no—
25C22×C43⋊C8C2×C414yes—
26C2×C4×Dic43—22no—
27C2×C4×Dic43—22no—
28C2×C4×Dic43—22no—
29C2×C4×Dic43—22no—
30C2×C4×Dic43—22no—
31C2×C4×Dic43—22no—
32C43⋊#95—24no—
33C43⋊#95C818yescomplemented
34C23×C4×C43C2×C411yescharacteristic
35C23×C4×C43C2×C411yescharacteristic
36C23×C4×C43C2311yescharacteristic
37C22×C8×C43—22no—
38C22×C8×C43—22no—
39C22×C8×C43—22no—
40C22×C8×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43C2×C412yes—
43C22×C8×C43C2×C412yes—
44C22×C8×C43D412yes—
45C22×C8×C43D414yes—
46C22×C8×C43Q812yes—
47C2×C42×C43—22no—
48C2×C42×C43—22no—
49C2×C42×C43C2×C412yes—
50C2×C42×C43C2×C412yes—
51C4×C8×C43—28no—
52C24×C43C22×C411yescharacteristic
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43C4212yes—
58C22×C4×C43C4212yes—
59C22×C4×C43C2×C814yes—
60C22×C4×C43M1614yes—
61C22×C4×C43C22×C411yescharacteristic
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D412yes—
65C22×C4×C43C2×Q811yescharacteristic
66C22×C4×C43#4112yes—
67C22×C4×C43#4112yes—
68C22×C4×C43#4112yes—
69C22×C4×C43#4111yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C22×Dic43—24no—
72C22×Dic43—24no—
73C22×Dic43—24no—
74C22×Dic43—24no—
75C22×Dic43—24no—
76C22×Dic43—24no—
77C22×Dic43C2×C818yes—
78C2×C8×C43—22no—
79C2×C8×C43—22no—
80C2×C8×C43—22no—
81C2×C8×C43—22no—
82C2×C8×C43—24no—
83C2×C8×C43—24no—
84C2×C8×C43—24no—
85C2×C8×C43—24no—
86C2×C8×C43C22⋊C414yes—
87C2×C8×C43C4⋊C414yes—
88C42×C43—22no—
89C42×C43—22no—
90C42×C43—24no—
91C4×Dic43—42no—
92C4×Dic43—42no—
93C4×Dic43—42no—
94C4×Dic43—42no—
95C2×C43⋊C8—24no—
96C2×C43⋊C8—24no—
97C2×C43⋊C8—24no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—42no—
100C2×C43⋊C8—42no—
101C2×C43⋊C8—42no—
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×C43C4×C814yes—
118C2×C4×C43#9714yes—
119C2×C4×C43C2×C22⋊C411yescharacteristic
120C2×C4×C43C2×C4⋊C411yescharacteristic
121C2×C4×C43#11712yes—
122C2×C4×C43#11711yescharacteristic
123C2×C4×C43#11711yescharacteristic
124C2×C4×C43#11711yescharacteristic
125C2×C4×C43#11711yescharacteristic
126C2×C4×C43C4×D412yes—
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×Q811yescharacteristic
129C2×C4×C43#12112yes—
130C2×C4×C43C22⋊Q812yes—
131C2×C4×C43#12312yes—
132C2×C4×C43#12312yes—
133C2×C4×C43#12412yes—
134C2×C4×C43#12512yes—
135C2×C4×C43#12612yes—
136C2×C4×C43#12612yes—
137C2×Dic43—28no—
138C2×Dic43—28no—
139C2×Dic43—28no—
140C2×Dic43—44no—
141C2×Dic43—44no—
142C2×Dic43—44no—
143C2×Dic43—44no—
144C8×C43—24no—
145C8×C43—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#38011yescharacteristic
168C4×C43#38111yescharacteristic
169C4×C43#38211yescharacteristic
170C4×C43#38311yescharacteristic
171C4×C43#38712yes—
172C4×C43#38812yes—
173Dic43—48no—
174C22×C4×C8D4311yescharacteristic
175C2×#336—431no—
176C2×#336—432no—
177C2×#336—432no—
178C4×#95—431no—
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—432no—
189C23×C8C2×D4311yescharacteristic
190C23×C8C2×D4311yescharacteristic
191C22×C42—432no—
192C22×C42C2×D4311yescharacteristic
193C2×C4×C8—24no—
194C2×C4×C8Dic4314yescomplemented
195C2×#95—432no—
196C2×#95—432no—
197#336—434no—
198#336—864no—
199#336—864no—
200C43#1079711yescharacteristic, complemented, Sylow
201C23×C4—434no—
202C23×C4C4×D4311yescharacteristic
203C23×C4C4×D4311yescharacteristic
204C23×C4C22×D4311yescharacteristic
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—22no—
210C22×C8—434no—
211C22×C8—862no—
212C22×C8—862no—
213C22×C8—862no—
214C22×C8—862no—
215C22×C8—862no—
216C22×C8—862no—
217C22×C8Dic8612yes—
218C22×C8D17212yes—
219C22×C8C2×Dic4312yes—
220C22×C8C2×Dic4312yes—
221C22×C8C22⋊D4314yes—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—862no—
225C2×C42—862no—
226C2×C42—862no—
227C2×C42—862no—
228C2×C42—862no—
229C2×C42—862no—
230C2×C42C4×D4312yes—
231C2×C42C2×Dic4312yes—
232C4×C8—28no—
233#95—438no—
234#95—864no—
235C24C2×C4×D4311yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—438no—
241C22×C4—864no—
242C22×C4—864no—
243C22×C4—864no—
244C22×C4—864no—
245C22×C4—864no—
246C22×C4—864no—
247C22×C4C8×D4314yes—
248C22×C4#1062187214yes—
249C22×C4C4×Dic4312yes—
250C22×C4C4×Dic4312yes—
251C22×C4C2×Dic8611yescharacteristic
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4C2×D17211yescharacteristic
254C22×C4#1062189812yes—
255C22×C4#1062189812yes—
256C22×C4#1062189812yes—
257C22×C4#1062189811yescharacteristic
258C22×C4#1062189811yescharacteristic
259C22×C4C22×Dic4311yescharacteristic
260C22×C4C2×C22⋊D4312yes—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—24no—
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—864no—
270C2×C8—864no—
271C2×C8—864no—
272C2×C8—1722no—
273C2×C8—1722no—
274C2×C8—1722no—
275C2×C8—1722no—
276C2×C8C4⋊Dic4314yes—
277C2×C8C22⋊Dic4314yes—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—1722no—
282C42—1722no—
283C42—1722no—
284C42—1722no—
285C23C2×C4×Dic4311yescharacteristic
286C23#1306328212yes—
287C23C4×C22⋊D4312yes—
288C23C4×D17211yescharacteristic
289C23C4×Dic8611yescharacteristic
290C23C2×C8×D4312yes—
291C23C2×#1062187212yes—
292C23#1306333112yes—
293C23#1306333112yes—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—28no—
297C2×C4—28no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—868no—
301C2×C4—868no—
302C2×C4—868no—
303C2×C4—1724no—
304C2×C4—1724no—
305C2×C4—1724no—
306C2×C4—1724no—
307C2×C4C8×Dic4314yes—
308C2×C4#1306323514yes—
309C2×C4C2×C22⋊Dic4311yescharacteristic
310C2×C4C2×C4⋊Dic4311yescharacteristic
311C2×C4#1306328212yes—
312C2×C4#1306328411yescharacteristic
313C2×C4#1306328411yescharacteristic
314C2×C4#1306328411yescharacteristic
315C2×C4#1306328411yescharacteristic
316C2×C4C4×C22⋊D4312yes—
317C2×C4C4×D17211yescharacteristic
318C2×C4C4×Dic8611yescharacteristic
319C2×C4#1306329912yes—
320C2×C4#1306330412yes—
321C2×C4#1306330812yes—
322C2×C4#1306330812yes—
323C2×C4#1306331312yes—
324C2×C4#1306331712yes—
325C2×C4#1306331912yes—
326C2×C4#1306331912yes—
327C8—24no—
328C8—24no—
329C8—1724no—
330C22#1458274511yescharacteristic
331C22C4×C22⋊Dic4311yescharacteristic
332C22C4×C4⋊Dic4311yescharacteristic
333C22#1458278312yes—
334C22#1458279012yes—
335C22C2×C8×Dic4311yescharacteristic
336C22C2×#1306323511yescharacteristic
337C22#1458285411yescharacteristic
338C22#1458285411yescharacteristic
339C22#1458295014yes—
340C22#1458295814yes—
341C22C8×C22⋊D4314yes—
342C22C8×D17212yes—
343C22#1458297014yes—
344C22#1458297812yes—
345C22C8×Dic8612yes—
346C22#1458302912yes—
347C4—24no—
348C4—24no—
349C4—1728no—
350C4#1458275911yescharacteristic
351C4#1458276211yescharacteristic
352C4#1458276511yescharacteristic
353C4#1458276711yescharacteristic
354C4#1458278312yes—
355C4#1458279012yes—
356C2#1913282211yescharacteristic
357C2#1913434011yescharacteristic
358C2#1913434611yescharacteristic
359C2C8×C22⋊Dic4311yescharacteristic
360C2#1913437111yescharacteristic
361C2C8×C4⋊Dic4311yescharacteristic
362C2#1913446211yescharacteristic
363C2#1913515214yes—
364C2#1913520114yes—
subgroupG/H
center, FrattiniC23×C4C22×D43
commutatorC22×C43C2×C4×C8
FittingC22×C4×C8×C43C2
socle, prime radicalC24×C43C22×C4
cosocleC23×C4×C43C23
hypercenterC22×C4×C8D43
hypocenterC43#10797
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

Complements

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

NH ≅ G/Ntype
10. #14582654C4semidirect
17. C2×C4×C8×C43C4semidirect
33. C43⋊#95C8semidirect
194. C2×C4×C8Dic43semidirect
200. C43#10797semidirect

Maximal subgroups

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

subgroupindex
C2×#145826542
C2×#145826532
C4×C43⋊#952
C22×C4×C8×C432
#1079743