Finite Group Databasebeta

← #25094786

Subgroups — #25094786

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582954C211yesmaximal, characteristic
2C2×#14582950C211yesmaximal, characteristic
3#376×D43C211yesmaximal, characteristic
4#19134455C212yesmaximal, complemented
5#19134453C212yesmaximal, complemented
6#19134358C212yesmaximal
7C4×(C2×D43)⋊C8C212yesmaximal
8#19134348C211yesmaximal, characteristic, complemented
9#19134346C211yesmaximal, characteristic, complemented
10#19134282C211yesmaximal, characteristic, complemented
11C43×#1726C211yesmaximal, characteristic, complemented
12C2×C42×D43C2212yes—
13C2×C42×D43C2211yescharacteristic
14#14582954C418yescomplemented
15#14582950C418yescomplemented
16C2×Dic43⋊C8C2211yescharacteristic
17C2×Dic43⋊C8C2211yescharacteristic
18C2×Dic43⋊C8C2212yes—
19C2×(C2×D43)⋊C8C2211yescharacteristic
20C2×(C2×D43)⋊C8C2211yescharacteristic
21C2×(C2×D43)⋊C8C2212yes—
22C2×#13063236C2212yes—
23C2×#13063236C2211yescharacteristic
24C2×C4×C43⋊C8C2212yes—
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582745C2211yescharacteristic
27#14582745C2212yes—
28#14582744C412yes—
29#14582744C412yes—
30#95×D43C412yes—
31#95×D43C412yes—
32#14582653C2212yes—
33#14582653C2212yes—
34#14582653C2212yes—
35#14582653C2212yes—
36C2×#97×C43C2212yes—
37C2×#97×C43C2211yescharacteristic
38C2×C4×C8×C43C2212yes—
39C2×C4×C8×C43C2211yescharacteristic
40C43×#376C2211yescharacteristic
41C22×C4×D43C2×C414yes—
42C22×C4×D43C2×C411yescharacteristic
43C22×C4×D43C2×C411yescharacteristic
44C22×C4×D43C2311yescharacteristic
45C22×C43⋊C8C2311yescharacteristic
46C22×C43⋊C8C2312yes—
47C22×C43⋊C8C2311yescharacteristic
48C2×C4×Dic43C2×C414yes—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43C2×C411yescharacteristic
51C2×C4×Dic43C2312yes—
52C2×C4×Dic43C2311yescharacteristic
53C42×D43—24no—
54C42×D43—24no—
55C42×D43C2×C414yes—
56C42×D43C2×C414yes—
57Dic43⋊C8C2×C414yescomplemented
58Dic43⋊C8C2×C414yescomplemented
59Dic43⋊C8C2×C418yescomplemented
60(C2×D43)⋊C8C2×C414yes—
61(C2×D43)⋊C8C2×C414yes—
62(C2×D43)⋊C8C2×C418yes—
63#13063236—24no—
64#13063236C2×C414yescomplemented
65C4×C43⋊C8—24no—
66C4×C43⋊C8C2×C414yescomplemented
67C43⋊#95C2×C412yes—
68C43⋊#95C2×C412yes—
69C43⋊#95C2×C414yes—
70C43⋊#95C2×C414yes—
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2312yes—
73C22×C8×C43C2311yescharacteristic
74C2×C42×C43C2311yescharacteristic
75C2×C42×C43C2312yes—
76#97×C43—24no—
77#97×C43C2×C414yescomplemented
78C4×C8×C43—24no—
79C4×C8×C43C2×C414yescomplemented
80#95×C43C2×C412yes—
81#95×C43C2×C412yes—
82C23×D43C22×C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C22×C414yes—
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—28no—
94C2×C4×D43—24no—
95C2×C4×D43—28no—
96C2×C4×D43—42no—
97C2×C4×D43—44no—
98C2×C4×D43C4214yes—
99C2×C4×D43C4214yes—
100C2×C4×D43C22×C412yes—
101C2×C4×D43C22×C412yes—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43C22×C412yes—
107C2×C8×C43C22×C412yes—
108C2×C8×C43C22×C414yes—
109C42×C43C22×C412yes—
110C42×C43C22×C412yes—
111C42×C43#4114yes—
112C42×C43#4114yes—
113C4×Dic43—28no—
114C4×Dic43—22no—
115C4×Dic43—22no—
116C4×Dic43C4214yes—
117C4×Dic43C4214yes—
118C4×Dic43C22×C412yes—
119C4×Dic43C22×C412yes—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8C22×C412yes—
125C2×C43⋊C8C22×C412yes—
126C2×C43⋊C8C22×C414yes—
127C23×C43C23×C411yescharacteristic
128C22×D43—22no—
129C22×D43—22no—
130C22×D43C2×C4212yes—
131C22×D43#13114yes—
132C2×C4×C43—22no—
133C2×C4×C43—24no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43C2×C4212yes—
137C2×C4×C43C2×C4212yes—
138C2×C4×C43#11718yes—
139C2×C4×C43C23×C411yescharacteristic
140C2×C4×C43C23×C411yescharacteristic
141C2×C4×C43C2×#4112yes—
142C2×C4×C43C2×#4112yes—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—24no—
147C2×Dic43—24no—
148C2×Dic43—24no—
149C2×Dic43C2×C4212yes—
150C2×Dic43C2×C4212yes—
151C2×Dic43C2×C4212yes—
152C4×D43—28no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—24no—
156C4×D43—44no—
157C4×D43—416no—
158C8×C43—22no—
159C8×C43—24no—
160C8×C43—22no—
161C43⋊C8—22no—
162C43⋊C8—24no—
163C43⋊C8—22no—
164#20469—431nomaximal, Sylow
165C22×C43C22×C4211yescharacteristic
166C22×C43C2×#11712yes—
167C22×C43C2×#13112yes—
168C22×C43#56812yes—
169C2×D43—22no—
170C2×D43—28no—
171C2×D43—22no—
172C2×D43#40514yes—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—28no—
176C4×C43C4×#4111yescharacteristic
177C4×C43C4×#4112yes—
178C4×C43C4×#4111yescharacteristic
179Dic43—22no—
180Dic43—22no—
181Dic43—22no—
182Dic43—44no—
183C2×#432—431no—
184C2×#431—431no—
185C2×#376—431no—
186#1768—432no—
187#1768—432no—
188#1749—432no—
189C4×C22⋊C8—432no—
190#1746—431no—
191#1746—431no—
192#1726—431no—
193#1726D4311yescharacteristic, complemented
194C2×C43C4×#11711yescharacteristic
195C2×C43C2×#40511yescharacteristic
196C2×C43#287311yescharacteristic
197C2×C43#292414yes—
198D43—24no—
199C22×C42—431no—
200C22×C42—432no—
201#432—438no—
202#431—438no—
203C2×C4⋊C8—431no—
204C2×C4⋊C8—431no—
205C2×C4⋊C8—432no—
206C2×C22⋊C8—431no—
207C2×C22⋊C8—431no—
208C2×C22⋊C8—432no—
209C2×#97—431no—
210C2×#97—432no—
211C2×#97C2×D4312yes—
212C2×#97C2×D4311yescharacteristic
213C2×C4×C8—431no—
214C2×C4×C8—432no—
215C2×C4×C8C2×D4312yes—
216C2×C4×C8C2×D4311yescharacteristic
217#376—431no—
218#376—432no—
219#376—432no—
220#376—432no—
221#376C2×D4311yescharacteristic
222C2×#95—432no—
223C2×#95—432no—
224#336—432no—
225#336—432no—
226#336—432no—
227#336—432no—
228C43#2046911yescharacteristic, complemented, Sylow
229C23×C4—431no—
230C23×C4—431no—
231C23×C4—431no—
232C23×C4—434no—
233C22×C8—431no—
234C22×C8—431no—
235C22×C8—432no—
236C22×C8C22×D4311yescharacteristic
237C22×C8C22×D4312yes—
238C22×C8C22×D4311yescharacteristic
239C2×C42—431no—
240C2×C42—431no—
241C2×C42—431no—
242C2×C42—434no—
243C2×C42—434no—
244C2×C42—434no—
245C2×C42—432no—
246C2×C42—864no—
247C2×C42—864no—
248C2×C42C22×D4311yescharacteristic
249C2×C42C22×D4312yes—
250C4⋊C8—434no—
251C4⋊C8—434no—
252C4⋊C8—438no—
253C22⋊C8—434no—
254C22⋊C8—434no—
255C22⋊C8—438no—
256#97—24no—
257#97—434no—
258#97—864no—
259#97C4×D4314yescomplemented
260C4×C8—24no—
261C4×C8—434no—
262C4×C8—864no—
263C4×C8C4×D4314yescomplemented
264#95—434no—
265#95—434no—
266#95—432no—
267#95—432no—
268#95C4×D4312yes—
269#95C4×D4312yes—
270C24—431no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—434no—
275C22×C4—432no—
276C22×C4—432no—
277C22×C4—434no—
278C22×C4—434no—
279C22×C4—864no—
280C22×C4—868no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4—868no—
284C22×C4—1722no—
285C22×C4—1724no—
286C22×C4C2×C4×D4311yescharacteristic
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4C2×C4×D4314yes—
289C22×C4C23×D4311yescharacteristic
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—432no—
295C2×C8—432no—
296C2×C8—434no—
297C2×C8—862no—
298C2×C8—862no—
299C2×C8—862no—
300C2×C8—862no—
301C2×C8C2×C4×D4312yes—
302C2×C8C2×C4×D4312yes—
303C2×C8C2×C4×D4314yes—
304C42—434no—
305C42—434no—
306C42—432no—
307C42—432no—
308C42—868no—
309C42—862no—
310C42—862no—
311C42C2×C4×D4312yes—
312C42C2×C4×D4312yes—
313C42#1062189814yes—
314C42#1062189814yes—
315C23—432no—
316C23—434no—
317C23—862no—
318C23—862no—
319C23C22×C4×D4311yescharacteristic
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—432no—
325C2×C4—432no—
326C2×C4—432no—
327C2×C4—868no—
328C2×C4—862no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—864no—
334C2×C4—864no—
335C2×C4—864no—
336C2×C4—864no—
337C2×C4—1724no—
338C2×C4—17216no—
339C2×C4C42×D4312yes—
340C2×C4C42×D4312yes—
341C2×C4#1306328218yes—
342C2×C4C22×C4×D4311yescharacteristic
343C2×C4C22×C4×D4311yescharacteristic
344C2×C4C2×#1062189812yes—
345C2×C4C2×#1062189812yes—
346C8—22no—
347C8—24no—
348C8—22no—
349C8—862no—
350C8—862no—
351C8—864no—
352C22—434no—
353C22—868no—
354C22—862no—
355C22—862no—
356C22C2×C42×D4311yescharacteristic
357C22C2×#1306328212yes—
358C22#131×D4312yes—
359C22#1458366412yes—
360C4—28no—
361C4—22no—
362C4—22no—
363C4—862no—
364C4—862no—
365C4—862no—
366C4—1724no—
367C4C4×#1062189811yescharacteristic
368C4C4×#1062189812yes—
369C4C4×#1062189811yescharacteristic
370C2—864no—
371C2C4×#1306328211yescharacteristic
372C2#405×D4311yescharacteristic
373C2#1914301111yescharacteristic
374C2#1914325014yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC43×#1726C2
socleC23×C43C23×C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1726D43
hypocenterC43#20469
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1726

Complements

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

NH ≅ G/Ntype
4. #19134455C2semidirect
5. #19134453C2semidirect
8. #19134348C2semidirect
9. #19134346C2semidirect
10. #19134282C2semidirect
11. C43×#1726C2semidirect
14. #14582954C4semidirect
15. #14582950C4semidirect
57. Dic43⋊C8C2×C4semidirect
58. Dic43⋊C8C2×C4semidirect
59. Dic43⋊C8C2×C4semidirect
64. #13063236C2×C4semidirect
66. C4×C43⋊C8C2×C4semidirect
77. #97×C43C2×C4semidirect
79. C4×C8×C43C2×C4semidirect
193. #1726D43semidirect
228. C43#20469semidirect
259. #97C4×D43semidirect
263. C4×C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829542
C2×#145829502
#376×D432
#191344552
#191344532
#191343582
C4×(C2×D43)⋊C82
#191343482
#191343462
#191342822
C43×#17262
#2046943