Finite Group Databasebeta

← #25107198

Subgroups — #25107198

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582960C211yesmaximal, characteristic
2#19137204C211yesmaximal, characteristic
3#19135361C212yesmaximal, complemented
4#19135351C212yesmaximal, complemented
5#19134794C212yesmaximal
6#19134783C212yesmaximal
7#19134764C211yesmaximal, characteristic, complemented
8#19134754C211yesmaximal, characteristic, complemented
9#19134730C211yesmaximal, characteristic, complemented
10#19134725C211yesmaximal, characteristic, complemented
11C43×#2317C211yesmaximal, characteristic
12#14582960C418yescomplemented
13C2×#13063258C2212yes—
14C2×#13063258C2212yes—
15C2×#13063258C2212yes—
16C2×#13063256C2212yes—
17C2×C4⋊(C43⋊C8)C2212yes—
18C2×C22⋊(C43⋊C8)C2212yes—
19C2×#13063236C2211yescharacteristic
20C2×C4×C43⋊C8C2211yescharacteristic
21#14582792—22no—
22#14582785—22no—
23#14582769C2211yescharacteristic
24#14582765C2211yescharacteristic
25#14582759C2212yes—
26C4×C4⋊Dic43C2212yes—
27#14582661C2212yes—
28#14582661C2212yes—
29#14582661C2212yes—
30#14582661C2212yes—
31C2×#117×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#389—22no—
35C43×#385—22no—
36C43×#384C2211yescharacteristic
37C43×#384C2211yescharacteristic
38C43×#382C2211yescharacteristic
39C43×#382C2211yescharacteristic
40C22×C43⋊C8C2312yes—
41C22×C43⋊C8C2312yes—
42C2×C4⋊Dic43—22no—
43C2×C4⋊Dic43C2312yes—
44C2×C4⋊Dic43C2312yes—
45C2×C22⋊Dic43—22no—
46C2×C4×Dic43—22no—
47#13063258—42no—
48#13063258—42no—
49#13063258—42no—
50#13063256—42no—
51C4⋊(C43⋊C8)C2×C418yescomplemented
52C22⋊(C43⋊C8)C2×C418yes—
53#13063236C2×C414yescomplemented
54C4×C43⋊C8C2×C414yescomplemented
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—22no—
58C23×C4×C43—21no—
59C23×C4×C43C2311yescharacteristic
60#117×C43—42no—
61#117×C43C2×C414yes—
62#117×C43Q814yes—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43—42no—
67C2×C4⋊C4×C43D412yes—
68C2×C4⋊C4×C43C2311yescharacteristic
69C2×C4⋊C4×C43C2311yescharacteristic
70C2×C4⋊C4×C43C2311yescharacteristic
71C2×C4⋊C4×C43C2311yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43D412yes—
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C2×C42×C43C2311yescharacteristic
77#95×C43—22no—
78#95×C43—22no—
79C24×C43C2×D411yescharacteristic
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—42no—
87C22×C4×C43—82no—
88C22×C4×C43C22×C412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×Q812yes—
93C22×C4×C43C2411yescharacteristic
94C22×Dic43—22no—
95C22×Dic43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—42no—
101C4⋊C4×C43—82no—
102C4⋊C4×C43—82no—
103C4⋊C4×C43C4⋊C418yes—
104C22⋊C4×C43—42no—
105C22⋊C4×C43C4⋊C418yes—
106C42×C43—42no—
107C42×C43C22×C412yes—
108C42×C43C22×C412yes—
109C42×C43C2×Q812yes—
110C42×C43C2×Q812yes—
111C22⋊Dic43—82no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—24no—
115C4⋊Dic43—82no—
116C4×Dic43—82no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8C22×C414yes—
122C2×C43⋊C8C22×C414yes—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43C2×C4⋊C412yes—
128C23×C43C22×D411yescharacteristic
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43—24no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—84no—
146C2×C4×C43C2×C4⋊C414yes—
147C2×C4×C43C2×C4⋊C414yes—
148C2×C4×C43C2×C4⋊C412yes—
149C2×C4×C43C23×C411yescharacteristic
150C2×C4×C43C22×Q811yescharacteristic
151C2×C4×C43H(5,𝔽2)12yes—
152C2×C4×C432−1+412yes—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C43⋊C8—24no—
160C43⋊C8—24no—
161#21991—431nomaximal, Sylow
162C22×C43—22no—
163C22×C43—24no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—42no—
167C22×C43C22×C4⋊C411yescharacteristic
168C22×C43#53511yescharacteristic
169C22×C43#53611yescharacteristic
170C22×C43#57612yes—
171C22×C43#57812yes—
172C4×C43—22no—
173C4×C43—24no—
174C4×C43—24no—
175C4×C43—81no—
176C4×C43—81no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43#52012yes—
180C4×C43#54412yes—
181Dic43—82no—
182Dic43—82no—
183C2×#433—431no—
184#2317D4311yescharacteristic
185#2314—431no—
186#1949—432no—
187#1947—432no—
188#1854—432no—
189#1852—432no—
190#1847—431no—
191#1845—431no—
192#1836—431no—
193#1835—431no—
194C2×C43—42no—
195C2×C43#231711yescharacteristic
196C2×C43#291312yes—
197C2×C43#322011yescharacteristic
198C2×C43#322311yescharacteristic
199C2×C43#324312yes—
200C2×#117C2×D4311yescharacteristic
201C2×#117C2×D4311yescharacteristic
202C22×C4⋊C4C2×D4311yescharacteristic
203#433—438no—
204C2×#107—432no—
205C2×#107—432no—
206C2×#107—432no—
207C2×#106—432no—
208C2×C4⋊C8—432no—
209C2×C22⋊C8—432no—
210C2×#97—431no—
211C2×C4×C8—431no—
212#389—22no—
213#388—862no—
214#387—862no—
215#385—22no—
216#384—431no—
217#384C2×D4311yescharacteristic
218#384C2×D4311yescharacteristic
219#382—431no—
220#382C2×D4311yescharacteristic
221#382C2×D4311yescharacteristic
222#380—432no—
223C4×C4⋊C4—432no—
224#340—432no—
225#340—432no—
226#340—432no—
227#340—432no—
228C43#2199111yescharacteristic, complemented, Sylow
229C23×C4—21no—
230C23×C4C22×D4311yescharacteristic
231C22×C8—432no—
232C22×C8—432no—
233#117—42no—
234#117Dic8614yes—
235#117C4×D4314yes—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—432no—
241C2×C4⋊C4—432no—
242C2×C4⋊C4—862no—
243C2×C4⋊C4C22⋊D4312yes—
244C2×C4⋊C4C22×D4311yescharacteristic
245C2×C4⋊C4C22×D4311yescharacteristic
246C2×C4⋊C4C22×D4311yescharacteristic
247C2×C4⋊C4C22×D4311yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—862no—
250C2×C22⋊C4C22⋊D4312yes—
251C2×C42—21no—
252C2×C42—862no—
253C2×C42C22×D4311yescharacteristic
254C2×C42C22×D4311yescharacteristic
255#107—1722no—
256#107—1722no—
257#107—1722no—
258#106—1722no—
259C4⋊C8—438no—
260C22⋊C8—438no—
261#97—434no—
262C4×C8—434no—
263#95—22no—
264#95—22no—
265#95—862no—
266#95—862no—
267#95—862no—
268C24C2×C22⋊D4311yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—82no—
277C22×C4—862no—
278C22×C4—862no—
279C22×C4C2×Dic8612yes—
280C22×C4C2×C4×D4312yes—
281C22×C4C2×C22⋊D4312yes—
282C22×C4C2×C22⋊D4312yes—
283C22×C4C2×C22⋊D4311yescharacteristic
284C22×C4C23×D4311yescharacteristic
285C2×C8—434no—
286C2×C8—434no—
287C2×C8—862no—
288C2×C8—862no—
289C2×C8—862no—
290C2×C8—862no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—82no—
297C4⋊C4—82no—
298C4⋊C4—862no—
299C4⋊C4—862no—
300C4⋊C4—864no—
301C4⋊C4—3442no—
302C4⋊C4Dic43⋊C418yes—
303C22⋊C4—42no—
304C22⋊C4—3442no—
305C22⋊C4Dic43⋊C418yes—
306C42—42no—
307C42—3442no—
308C42C2×Dic8612yes—
309C42C2×Dic8612yes—
310C42C2×C4×D4312yes—
311C42C2×C4×D4312yes—
312C23—22no—
313C23—22no—
314C23—21no—
315C23—21no—
316C23C2×Dic43⋊C412yes—
317C23C22×C22⋊D4311yescharacteristic
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—84no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4C2×Dic43⋊C414yes—
342C2×C4C2×Dic43⋊C414yes—
343C2×C4C2×Dic43⋊C412yes—
344C2×C4C22×C4×D4311yescharacteristic
345C2×C4C22×Dic8611yescharacteristic
346C2×C4#1306337012yes—
347C2×C4#1306337312yes—
348C8—864no—
349C8—864no—
350C22—24no—
351C22—22no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22C22×Dic43⋊C411yescharacteristic
356C22#1458346611yescharacteristic
357C22#1458347311yescharacteristic
358C22#1458370212yes—
359C22#1458371412yes—
360C4—24no—
361C4—24no—
362C4—22no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4—3442no—
368C4—3442no—
369C4#1458338012yes—
370C4#1458353012yes—
371C2—42no—
372C2#1913721911yescharacteristic
373C2#1914319312yes—
374C2#1914564511yescharacteristic
375C2#1914567811yescharacteristic
376C2#1914587812yes—
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2317C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#2317D43
hypocenterC43#21991
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. #19135361C2semidirect
4. #19135351C2semidirect
7. #19134764C2semidirect
8. #19134754C2semidirect
9. #19134730C2semidirect
10. #19134725C2semidirect
12. #14582960C4semidirect
51. C4⋊(C43⋊C8)C2×C4semidirect
53. #13063236C2×C4semidirect
54. C4×C43⋊C8C2×C4semidirect
228. C43#21991semidirect

Maximal subgroups

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

subgroupindex
C2×#145829602
#191372042
#191353612
#191353512
#191347942
#191347832
#191347642
#191347542
#191347302
#191347252
C43×#23172
#2199143