Finite Group Databasebeta

← #25094846

Subgroups — #25094846

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582954C211yesmaximal, characteristic
2C2×C4×C8×D43C211yesmaximal, characteristic
3#19136987C211yesmaximal, characteristic
4#19134463C212yesmaximal, complemented
5C8×Dic43⋊C4C212yesmaximal, complemented
6#19134372C212yesmaximal
7C8×(C2×D43)⋊C4C212yesmaximal
8#19134348C211yesmaximal, characteristic, complemented
9#19134347C211yesmaximal, characteristic, complemented
10#19134281C211yesmaximal, characteristic, complemented
11C43×#1726C211yesmaximal, characteristic, complemented
12C22×C8×D43C2211yescharacteristic
13C22×C8×D43C2211yescharacteristic
14C2×C42×D43C2211yescharacteristic
15#14582954C418yescomplemented
16C2×Dic43⋊C8C2212yes—
17C2×(C2×D43)⋊C8C2212yes—
18C2×#13063236C2211yescharacteristic
19C2×#13063235C2212yes—
20C2×C4×C43⋊C8C2211yescharacteristic
21C2×C8×Dic43C2212yes—
22C2×C8×Dic43C2211yescharacteristic
23C2×C8×Dic43C2211yescharacteristic
24C4×C8×D43C418yescomplemented
25#14582766C412yes—
26#14582763C412yes—
27#14582761C412yes—
28#14582758C412yes—
29C4×Dic43⋊C4C2212yes—
30C4×(C2×D43)⋊C4C2212yes—
31#14582745C2211yescharacteristic
32#14582654C2212yes—
33#14582654C2212yes—
34#14582653C2212yes—
35#14582653C2212yes—
36C2×#97×C43C2212yes—
37C2×#97×C43C2211yescharacteristic
38C2×C4×C8×C43C2212yes—
39C2×C4×C8×C43C2211yescharacteristic
40C43×#376C2211yescharacteristic
41C22×C4×D43C2×C411yescharacteristic
42C22×C4×D43C2×C411yescharacteristic
43C22×C4×D43C2311yescharacteristic
44C22×C43⋊C8C2311yescharacteristic
45C22×C43⋊C8C2311yescharacteristic
46C22×C43⋊C8C2312yes—
47C2×C8×D43—24no—
48C2×C8×D43—24no—
49C2×C8×D43C2×C414yes—
50C2×C8×D43C2×C414yes—
51C2×Dic43⋊C4C2×C414yes—
52C2×(C2×D43)⋊C4C2×C414yes—
53C2×C4×Dic43C2×C411yescharacteristic
54C2×C4×Dic43C2×C411yescharacteristic
55C2×C4×Dic43C2312yes—
56C2×C4×Dic43C2311yescharacteristic
57C42×D43C2×C414yes—
58C42×D43C2×C414yes—
59Dic43⋊C8C2×C418yes—
60(C2×D43)⋊C8C2×C418yes—
61#13063236C2×C414yes—
62#13063235—24no—
63C4×C43⋊C8C2×C414yes—
64C8×Dic43—24no—
65C8×Dic43C2×C414yes—
66C8×Dic43C2×C414yes—
67C43⋊#95C2×C412yes—
68C43⋊#95C2×C412yes—
69C43⋊#95C2×C414yes—
70C43⋊#95C2×C414yes—
71C22×C8×C43C2312yes—
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C2×C42×C43C2312yes—
75C2×C42×C43C2311yescharacteristic
76#97×C43—24no—
77#97×C43C2×C414yes—
78C4×C8×C43—24no—
79C4×C8×C43C2×C414yes—
80#95×C43C2×C412yes—
81#95×C43C2×C412yes—
82C23×D43C22×C411yescharacteristic
83C22×C4×C43C22×C414yes—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2411yescharacteristic
87C22×Dic43C22×C414yes—
88C22×Dic43C22×C411yescharacteristic
89C22×Dic43C22×C411yescharacteristic
90C22×Dic43C22×C411yescharacteristic
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—24no—
94C2×C4×D43—24no—
95C2×C4×D43C4214yes—
96C2×C4×D43C4214yes—
97C2×C4×D43C22×C412yes—
98C2×C4×D43C22×C412yes—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43C22×C414yes—
102C2×C8×C43C22×C412yes—
103C2×C8×C43C22×C412yes—
104C2×C8×C43#4114yes—
105C2×C8×C43#4114yes—
106C42×C43—22no—
107C42×C43—22no—
108C42×C43C22×C412yes—
109C42×C43C22×C412yes—
110(C2×D43)⋊C4—28no—
111Dic43⋊C4—28no—
112C4×Dic43—22no—
113C4×Dic43—22no—
114C4×Dic43C4214yes—
115C4×Dic43C4214yes—
116C4×Dic43C22×C412yes—
117C4×Dic43C22×C412yes—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8C22×C412yes—
123C2×C43⋊C8C22×C412yes—
124C2×C43⋊C8C22×C414yes—
125C8×D43—28no—
126C8×D43—28no—
127C23×C43C23×C411yescharacteristic
128C22×D43—22no—
129C22×D43—22no—
130C22×D43C2×C4212yes—
131C22×D43#13114yes—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—24no—
135C2×C4×C43—24no—
136C2×C4×C43—24no—
137C2×C4×C43C2×C4212yes—
138C2×C4×C43C2×C4212yes—
139C2×C4×C43C23×C411yescharacteristic
140C2×C4×C43C23×C411yescharacteristic
141C2×C4×C43C2×#4112yes—
142C2×C4×C43C2×#4112yes—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—24no—
146C2×Dic43—24no—
147C2×Dic43—24no—
148C2×Dic43C2×C4212yes—
149C2×Dic43C2×C4212yes—
150C2×Dic43C2×C4212yes—
151C2×Dic43#13114yes—
152C4×D43—28no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—24no—
156C4×D43—28no—
157C8×C43—24no—
158C8×C43#11714yes—
159C8×C43#11714yes—
160C43⋊C8—22no—
161C43⋊C8—22no—
162C43⋊C8—24no—
163#20476—431nomaximal, Sylow
164C22×C43C22×C4211yescharacteristic
165C22×C43C4×#4112yes—
166C22×C43C2×#13112yes—
167C22×C43C2×#13112yes—
168C2×D43—22no—
169C2×D43—28no—
170C2×D43—22no—
171C2×D43#40514yes—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—44no—
175C4×C43C2×#11711yescharacteristic
176C4×C43C2×#11711yescharacteristic
177C4×C43C4×#4112yes—
178Dic43—22no—
179Dic43—22no—
180Dic43—44no—
181Dic43#40514yes—
182C2×#432—431no—
183C22×C4×C8—431no—
184#2283—431no—
185#1770—432no—
186C8×C4⋊C4—432no—
187#1752—432no—
188C8×C22⋊C4—432no—
189#1746—431no—
190#1746—431no—
191#1726—431no—
192#1726D4311yescharacteristic, complemented
193C2×C43C4×#11711yescharacteristic
194C2×C43C2×#40511yescharacteristic
195C2×C43C2×#40511yescharacteristic
196C2×C43#296614yes—
197D43—24no—
198C23×C8—431no—
199C23×C8—431no—
200C22×C42—431no—
201#432—438no—
202C2×C4⋊C8—432no—
203C2×C22⋊C8—432no—
204C2×#97—431no—
205C2×#97—432no—
206C2×#97C2×D4312yes—
207C2×#97C2×D4311yescharacteristic
208C2×C4×C8—431no—
209C2×C4×C8—431no—
210C2×C4×C8—431no—
211C2×C4×C8—438no—
212C2×C4×C8—432no—
213C2×C4×C8C2×D4312yes—
214C2×C4×C8C2×D4311yescharacteristic
215#383—432no—
216#382—432no—
217#381—432no—
218#380—432no—
219C4×C4⋊C4—432no—
220C4×C22⋊C4—432no—
221#376—431no—
222#376C2×D4311yescharacteristic
223#336—432no—
224#336—432no—
225#336—432no—
226#336—432no—
227C43#2047611yescharacteristic, complemented, Sylow
228C23×C4—431no—
229C23×C4—431no—
230C23×C4—431no—
231C22×C8—431no—
232C22×C8—431no—
233C22×C8—432no—
234C22×C8—434no—
235C22×C8—434no—
236C22×C8—864no—
237C22×C8—864no—
238C22×C8C22×D4312yes—
239C22×C8C22×D4311yescharacteristic
240C22×C8C22×D4311yescharacteristic
241C2×C4⋊C4—434no—
242C2×C22⋊C4—434no—
243C2×C42—431no—
244C2×C42—431no—
245C2×C42—431no—
246C2×C42—434no—
247C2×C42—434no—
248C2×C42—432no—
249C2×C42C22×D4312yes—
250C2×C42C22×D4311yescharacteristic
251C4⋊C8—438no—
252C22⋊C8—438no—
253#97—24no—
254#97—434no—
255#97—864no—
256#97C4×D4314yes—
257C4×C8—24no—
258C4×C8—434no—
259C4×C8—434no—
260C4×C8—434no—
261C4×C8—864no—
262C4×C8C4×D4314yes—
263#95—432no—
264#95—432no—
265#95—434no—
266#95—434no—
267#95C4×D4312yes—
268#95C4×D4312yes—
269C24—431no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—434no—
274C22×C4—434no—
275C22×C4—432no—
276C22×C4—432no—
277C22×C4—434no—
278C22×C4—864no—
279C22×C4—864no—
280C22×C4—862no—
281C22×C4—862no—
282C22×C4C2×C4×D4314yes—
283C22×C4C2×C4×D4311yescharacteristic
284C22×C4C2×C4×D4311yescharacteristic
285C22×C4C23×D4311yescharacteristic
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—432no—
289C2×C8—432no—
290C2×C8—434no—
291C2×C8—862no—
292C2×C8—862no—
293C2×C8—862no—
294C2×C8—862no—
295C2×C8—868no—
296C2×C8—868no—
297C2×C8C2×C4×D4314yes—
298C2×C8C2×C4×D4312yes—
299C2×C8C2×C4×D4312yes—
300C2×C8#1062189814yes—
301C2×C8#1062189814yes—
302C4⋊C4—868no—
303C22⋊C4—868no—
304C42—22no—
305C42—22no—
306C42—434no—
307C42—434no—
308C42—432no—
309C42—432no—
310C42—862no—
311C42—862no—
312C42C2×C4×D4312yes—
313C42C2×C4×D4312yes—
314C23—432no—
315C23—434no—
316C23—862no—
317C23—862no—
318C23C22×C4×D4311yescharacteristic
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—432no—
325C2×C4—434no—
326C2×C4—432no—
327C2×C4—432no—
328C2×C4—868no—
329C2×C4—868no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—864no—
335C2×C4—864no—
336C2×C4—864no—
337C2×C4—864no—
338C2×C4C42×D4312yes—
339C2×C4C42×D4312yes—
340C2×C4C22×C4×D4311yescharacteristic
341C2×C4C22×C4×D4311yescharacteristic
342C2×C4C2×#1062189812yes—
343C2×C4C2×#1062189812yes—
344C8—24no—
345C8—862no—
346C8—862no—
347C8—864no—
348C8#1306328214yes—
349C8#1306328214yes—
350C22—434no—
351C22—862no—
352C22—868no—
353C22—862no—
354C22C2×C42×D4311yescharacteristic
355C22C4×#1062189812yes—
356C22#131×D4312yes—
357C22#131×D4312yes—
358C4—22no—
359C4—22no—
360C4—44no—
361C4—434no—
362C4—862no—
363C4—862no—
364C4—1724no—
365C4C2×#1306328211yescharacteristic
366C4C2×#1306328211yescharacteristic
367C4C4×#1062189812yes—
368C2—864no—
369C2C4×#1306328211yescharacteristic
370C2#405×D4311yescharacteristic
371C2#405×D4311yescharacteristic
372C2#1914356614yes—
subgroupG/H
centerC22×C8C22×D43
commutatorC22×C43C22×C42
FrattiniC22×C4C23×D43
FittingC43×#1726C2
socleC23×C43C23×C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1726D43
hypocenterC43#20476
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ #1726

Complements

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

NH ≅ G/Ntype
4. #19134463C2semidirect
5. C8×Dic43⋊C4C2semidirect
8. #19134348C2semidirect
9. #19134347C2semidirect
10. #19134281C2semidirect
11. C43×#1726C2semidirect
15. #14582954C4semidirect
24. C4×C8×D43C4semidirect
192. #1726D43semidirect
227. C43#20476semidirect

Maximal subgroups

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

subgroupindex
C2×#145829542
C2×C4×C8×D432
#191369872
#191344632
C8×Dic43⋊C42
#191343722
C8×(C2×D43)⋊C42
#191343482
#191343472
#191342812
C43×#17262
#2047643