Finite Group Databasebeta

← #25016200

Subgroups — #25016200

Order 11008.

446 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×#13063270C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
3C2×#14582702C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic
5#19135459C211yesmaximal, characteristic
6#19135454C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×D344C2211yescharacteristic
10C2×#13063270—22no—
11C2×#13063270—22no—
12C2×#13063270—22no—
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063248—21no—
15C2×#13063245—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582804—21no—
18#14582800—21no—
19Dic43⋊C16—22no—
20#14582702—22no—
21#14582699—22no—
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C22×Dic86—21no—
26C22×D172—21no—
27C2×Dic172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172D412yes—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344—21no—
37C2×D344—21no—
38C2×D344D412yes—
39C22×C43⋊C8D411yescharacteristic
40C2×(C2×D43)⋊C4—41no—
41C2×(C2×D43)⋊C4—41no—
42C2×C4×Dic43D411yescharacteristic
43#13063270—28no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47#13063248—42no—
48#13063245—42no—
49C8×Dic43—21no—
50C8×Dic43—21no—
51C43⋊#95—41no—
52C43⋊#95—41no—
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C16×C43—21no—
57C2×C16×C43—21no—
58C2×C16×C43D412yes—
59#107×C43—21no—
60#107×C43—21no—
61#107×C43—21no—
62#107×C43—21no—
63C23×D43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—41no—
68C22×Dic43D811yescharacteristic
69C22×Dic43D811yescharacteristic
70C2×D172—22no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—41no—
76C2×Dic86—22no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×C8×C43C2×D411yescharacteristic
83C2×C8×C43C2×D411yescharacteristic
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43#4111yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C2×C8×C43#4111yescharacteristic
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92(C2×D43)⋊C4—82no—
93(C2×D43)⋊C4—82no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99Dic172—22no—
100Dic172—22no—
101Dic172—41no—
102Dic172—41no—
103D344—22no—
104D344—22no—
105D344—41no—
106D344—41no—
107C16×C43—22no—
108C43⋊C16—41no—
109C23×C43C2×D811yescharacteristic
110C22×D43—42no—
111C22×D43—81no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43—81no—
115C22×D43—81no—
116C22×D43—81no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43#12111yescharacteristic
124C2×C4×C43#12111yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43SD3212yescomplemented
138D172—42no—
139D172—42no—
140D172—81no—
141D172—81no—
142Dic86—42no—
143Dic86—42no—
144Dic86—81no—
145Dic86—81no—
146C8×C43#12011yescharacteristic
147C8×C43#12311yescharacteristic
148C8×C43#12311yescharacteristic
149C8×C43#12411yescharacteristic
150C43⋊C8—41no—
151#13449—431nomaximal, Sylow
152C22×C43#45911yescharacteristic
153C22×C43#45911yescharacteristic
154C22×C43#46611yescharacteristic
155C22×C43C2×SD3211yescharacteristic
156C22×C43#50811yescharacteristic
157C22×C43#50911yescharacteristic
158C22×C43#51011yescharacteristic
159C2×D43—82no—
160C2×D43—82no—
161C2×D43—82no—
162C2×D43—161no—
163C2×D43—161no—
164C2×D43—161no—
165C2×D43—161no—
166C4×C43—161no—
167C4×C43—161no—
168C4×C43#39411yescharacteristic
169C4×C43#46311yescharacteristic
170C4×C43#46311yescharacteristic
171C4×C43#46911yescharacteristic
172Dic43—22no—
173Dic43—41no—
174Dic43—82no—
175C22×SD32—431no—
176C2×C4⋊C16—431no—
177C2×#358—431no—
178C2×#357—431no—
179#1970—431no—
180#1969—431no—
181#1380D4311yescharacteristic, complemented
182C2×C43#205411yescharacteristic
183C2×C43#220711yescharacteristic
184C2×C43#220811yescharacteristic
185C2×C43#221011yescharacteristic
186C2×C43#221111yescharacteristic
187C2×C43#221711yescharacteristic
188C2×C43#222011yescharacteristic
189D43—162no—
190C22×Q16—431no—
191C22×D8—431no—
192C2×SD32—862no—
193C2×SD32—862no—
194C2×SD32—862no—
195C22×C16—431no—
196C22×C16C2×D4311yescharacteristic
197C2×#107C2×D4311yescharacteristic
198C2×#107C2×D4311yescharacteristic
199C2×#103—861no—
200C2×#102—861no—
201C2×C4×C8—431no—
202#391—861no—
203#390—861no—
204C4⋊C16—862no—
205#358—862no—
206#357—862no—
207C43#1344911yescharacteristic, complemented, Sylow
208C22×Q8—861no—
209C22×D4—861no—
210C2×Q16—432no—
211C2×Q16—861no—
212C2×Q16—861no—
213C2×Q16—861no—
214C2×Q16—861no—
215C2×Q16—861no—
216C2×D8—432no—
217C2×D8—861no—
218C2×D8—861no—
219C2×D8—861no—
220C2×D8—861no—
221C2×D8—861no—
222C22×C8—431no—
223C22×C8C22×D4311yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C22⋊C4—1721no—
227C2×C22⋊C4—1721no—
228C2×C42—431no—
229SD32—868no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—861no—
233C2×C16—861no—
234C2×C16—861no—
235C2×C16D17212yes—
236#107—21no—
237#107—21no—
238#107—21no—
239#107—21no—
240#103—1722no—
241#102—1722no—
242C4×C8—861no—
243C4×C8—861no—
244#95—1721no—
245#95—1721no—
246C24—1721no—
247C2×Q8—862no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×D4—862no—
254C2×D4—1721no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—1721no—
264C22×C4D4×D4311yescharacteristic
265Q16—862no—
266Q16—862no—
267Q16—1721no—
268Q16—1721no—
269D8—862no—
270D8—862no—
271D8—1721no—
272D8—1721no—
273C2×C8—861no—
274C2×C8—861no—
275C2×C8—861no—
276C2×C8C2×D17211yescharacteristic
277C2×C8#1062189811yescharacteristic
278C2×C8#1062189811yescharacteristic
279C2×C8D4×D4311yescharacteristic
280C2×C8D4×D4311yescharacteristic
281C2×C8#1062190211yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—3442no—
287C22⋊C4—3442no—
288C42—861no—
289C42—861no—
290C16—22no—
291C16—1721no—
292C23—3441no—
293C23—3441no—
294C23—3441no—
295C23—3441no—
296C23—3441no—
297C23—3441no—
298C23—1722no—
299C23D8×D4311yescharacteristic
300Q8—3441no—
301Q8—3441no—
302Q8—1722no—
303Q8—1722no—
304D4—3441no—
305D4—3441no—
306D4—1722no—
307D4—1722no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—432no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1722no—
323C2×C4#1306329811yescharacteristic
324C2×C4#1306329811yescharacteristic
325C2×C4#1306330011yescharacteristic
326C2×C4#1306334811yescharacteristic
327C2×C4#1306335211yescharacteristic
328C2×C4#1306335211yescharacteristic
329C8—1721no—
330C8#1306329511yescharacteristic
331C8#1306331011yescharacteristic
332C8#1306331011yescharacteristic
333C8#1306331311yescharacteristic
334C22—3442no—
335C22—3442no—
336C22—3442no—
337C22—6881no—
338C22—6881no—
339C22—6881no—
340C22—6881no—
341C22#1458309311yescharacteristic
342C22#1458309311yescharacteristic
343C22#1458313611yescharacteristic
344C22SD32×D4311yescharacteristic
345C22#1458333011yescharacteristic
346C22#1458333311yescharacteristic
347C22#1458334111yescharacteristic
348C4—161no—
349C4—161no—
350C4—862no—
351C4—3442no—
352C4—1721no—
353C4#1458281711yescharacteristic
354C4#1458311711yescharacteristic
355C4#1458311711yescharacteristic
356C4#1458315311yescharacteristic
357C2—6882no—
358C2#1913590711yescharacteristic
359C2#1913663411yescharacteristic
360C2#1913663911yescharacteristic
361C2#1913664911yescharacteristic
362C2#1913666011yescharacteristic
363C2#1913669211yescharacteristic
364C2#1913670911yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenter#1380D43
hypocenterC43#13449
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×Dic43⋊C16C2semidirect
3. C2×#14582702C2semidirect
6. #19135454C2semidirect
7. C43×#1380C2semidirect
137. C2×Dic43SD32semidirect
181. #1380D43semidirect
207. C43#13449semidirect

Maximal subgroups

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

subgroupindex
C22×#130632702
C2×Dic43⋊C162
C2×#145827022
C2×#145826992
#191354592
#191354542
C43×#13802
#1344943