Finite Group Databasebeta

← #25254739

Subgroups — #25254739

Order 11008.

466 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583328C211yesmaximal, characteristic, complemented
2#508×D43C211yesmaximal, characteristic, complemented
3#19136915C211yesmaximal, characteristic, complemented
4#19136912C211yesmaximal, characteristic, complemented
5#19136911C212yesmaximal, complemented
6#19136908C211yesmaximal, characteristic, complemented
7#19136906C212yesmaximal, complemented
8#19136903C212yesmaximal, complemented
9#19136901C212yesmaximal, complemented
10M64×D43C211yesmaximal, characteristic, complemented
11C43×#2263C211yesmaximal, characteristic, complemented
12C2×#13063344—21no—
13#135×D43—21no—
14#14583332C2211yescharacteristic, complemented
15#14583331C2211yescharacteristic
16#14583330—21no—
17#14583329—21no—
18#14583328—21no—
19#14583328—21no—
20#14583328C2212yes—
21#14583328C2211yescharacteristic, complemented
22#14583328C2212yescomplemented
23C2×Dic344C2211yescharacteristic, complemented
24Q32×D43C2211yescharacteristic, complemented
25C2×#13063269—21no—
26SD32×D43—21no—
27D16×D43C2211yescharacteristic, complemented
28C2×C16×D43C2211yescharacteristic
29Dic688C2212yescomplemented
30#14582739C2212yescomplemented
31#14582738C2212yescomplemented
32#14582737C2212yescomplemented
33#14582737C2212yescomplemented
34#14582734C2212yescomplemented
35#14582733C2211yescharacteristic, complemented
36#14582732C2212yescomplemented
37C32×D43C2212yescomplemented
38C43×#508C2211yescharacteristic
39C2×D16×C43C2211yescharacteristic, complemented
40C43×SD64C2212yescomplemented
41C43×D32C2212yescomplemented
42C43×M64C2211yescharacteristic, complemented
43C2×#10621900—41no—
44#41×D43—41no—
45#13063348—21no—
46#13063347—21no—
47#13063346—41no—
48#13063345—41no—
49#13063344—22no—
50#13063344—22no—
51#13063344—21no—
52#13063344—41no—
53#13063344—41no—
54C2×Dic172—21no—
55Q16×D43—21no—
56C2×#10621883—41no—
57SD16×D43—41no—
58D8×D43—21no—
59C2×C8×D43D411yescharacteristic
60Dic344—21no—
61Dic344C2311yescharacteristic
62Dic344C2312yes—
63#13063271—21no—
64#13063270—21no—
65#13063269—21no—
66#13063269—22no—
67#13063269—22no—
68#13063268—21no—
69D688C2311yescharacteristic
70#13063266—21no—
71C2×C43⋊C16D411yescharacteristic
72C16×D43D411yescharacteristic
73C16×D43D411yescharacteristic
74C16×D43C2311yescharacteristic
75C16×D43C2311yescharacteristic
76C43⋊C32C2312yes—
77#135×C43—21no—
78C2×D8×C43—21no—
79Q32×C43C2311yescharacteristic
80SD32×C43—21no—
81D16×C43—21no—
82D16×C43C2312yes—
83D16×C43C2311yescharacteristic
84C2×C16×C43C2311yescharacteristic
85C32×C43C2312yes—
86#41×C43—41no—
87C2×D4×C43—41no—
88C2×C22⋊D43—81no—
89C22×Dic43—81no—
90#10621902—41no—
91Q8×D43—41no—
92#10621900—42no—
93#10621900—42no—
94#10621900—41no—
95#10621900—81no—
96#10621900—81no—
97#10621900—81no—
98D4×D43—41no—
99D4×D43—81no—
100#10621898—41no—
101#10621898—81no—
102C2×C4×D43—81no—
103C2×C4×D43D811yescharacteristic
104C2×Dic86—41no—
105Q16×C43—21no—
106SD16×C43—41no—
107D8×C43—22no—
108D8×C43—21no—
109D8×C43—41no—
110C2×C8×C43C2×D411yescharacteristic
111#10621885—41no—
112#10621884—41no—
113#10621883—41no—
114#10621883—42no—
115#10621883—42no—
116#10621882—41no—
117C2×C43⋊C8D811yescharacteristic
118Dic172—22no—
119Dic172—21no—
120Dic172—41no—
121D344—21no—
122#10621873—41no—
123C8×D43D811yescharacteristic
124C8×D43D811yescharacteristic
125C8×D43C2×D411yescharacteristic
126C8×D43C2×D411yescharacteristic
127C16×C43C2×D411yescharacteristic
128C16×C43C2411yescharacteristic
129C43⋊C16C2×D411yescharacteristic
130C43⋊C16C2×D411yescharacteristic
131C23×C43—81no—
132C22×D43—81no—
133C22×D43D1611yescharacteristic
134Q8×C43—41no—
135D4×C43—41no—
136D4×C43—42no—
137D4×C43—81no—
138D4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43C2×D811yescharacteristic
141C22⋊D43—81no—
142C22⋊D43—81no—
143C22⋊D43—82no—
144C22⋊D43—82no—
145C22⋊D43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148C2×Dic43—82no—
149C2×Dic43—82no—
150C2×Dic43D1611yescharacteristic
151D172—41no—
152D172—81no—
153C4×D43—81no—
154C4×D43—81no—
155C4×D43—81no—
156C4×D43D1611yescharacteristic
157C4×D43D1611yescharacteristic
158C4×D43C2×D811yescharacteristic
159C4×D43C2×D811yescharacteristic
160Dic86—41no—
161Dic86—42no—
162Dic86—81no—
163Dic86—81no—
164C8×C43C2×D811yescharacteristic
165C8×C43C22×D411yescharacteristic
166C43⋊C8C2×D811yescharacteristic
167C43⋊C8C2×D811yescharacteristic
168#33981—431nomaximal, Sylow
169C22×C43—81no—
170C22×C43—82no—
171C22×C43—162no—
172C22×C43C2×D1611yescharacteristic
173C2×D43—41no—
174C2×D43—81no—
175C2×D43—162no—
176C2×D43C2×D1611yescharacteristic
177C2×D43C2×D1611yescharacteristic
178C4×C43—81no—
179C4×C43C2×D1611yescharacteristic
180C4×C43C22×D811yescharacteristic
181Dic43—81no—
182Dic43—82no—
183Dic43C2×D1611yescharacteristic
184Dic43C2×D1611yescharacteristic
185C2×#508—431no—
186C2×#508—431no—
187#2264—431no—
188#2264—432no—
189#2264—431no—
190#2263—431no—
191#2263—432no—
192#2263D4311yescharacteristic, complemented
193#2262—432no—
194#2262—432no—
195C2×M64—431no—
196C2×C43—21no—
197C2×C43—161no—
198C2×C43—162no—
199C2×C43C22×D1611yescharacteristic
200D43—21no—
201D43—21no—
202D43—161no—
203C2×#135—861no—
204C2×#135—861no—
205#508—431no—
206#508—432no—
207#508—432no—
208#508—431no—
209#508—431no—
210#508—861no—
211#508—861no—
212#508—861no—
213#508—861no—
214#508C2×D4311yescharacteristic
215C2×Q32—431no—
216C2×Q32—431no—
217C2×SD32—861no—
218C2×SD32—861no—
219C2×D16—431no—
220C2×D16C2×D4311yescharacteristic, complemented
221C22×C16—431no—
222Q64—432no—
223Q64—432no—
224SD64—432no—
225SD64—432no—
226SD64—432no—
227SD64C2×D4312yescomplemented
228D32—432no—
229D32C2×D4312yescomplemented
230M64—431no—
231M64—432no—
232M64C2×D4311yescharacteristic, complemented
233C2×C32—432no—
234C43#3398111yescharacteristic, complemented, Sylow
235C2×#41—1721no—
236C2×#41—1721no—
237#135—21no—
238#135—862no—
239#135—862no—
240#135—861no—
241#135—861no—
242#135—861no—
243#135—1721no—
244#135—1721no—
245#135—1721no—
246#135—1721no—
247C2×Q16—861no—
248C2×Q16—861no—
249C2×SD16—1721no—
250C2×SD16—1721no—
251C2×D8—21no—
252C2×D8—861no—
253C22×C8—431no—
254Q32—431no—
255Q32—432no—
256Q32—861no—
257Q32—861no—
258Q32C22×D4311yescharacteristic
259SD32—21no—
260SD32—862no—
261SD32—862no—
262SD32—861no—
263SD32—861no—
264SD32—861no—
265D16—21no—
266D16—431no—
267D16—861no—
268D16C22×D4312yes—
269D16C22×D4311yescharacteristic
270C2×C16—431no—
271C2×C16—431no—
272C2×C16—431no—
273C2×C16—431no—
274C2×C16—431no—
275C2×C16C22×D4311yescharacteristic
276C32—432no—
277C32C22×D4312yes—
278#41—41no—
279#41—3441no—
280#41—3441no—
281#41—3441no—
282#41—3441no—
283#41—1722no—
284#41—1722no—
285#41—1721no—
286#41—1721no—
287#41—1721no—
288C2×Q8—1721no—
289C2×Q8—1721no—
290C2×D4—41no—
291C2×D4—3441no—
292C2×D4—3441no—
293C2×D4—1721no—
294C22×C4—431no—
295C22×C4—3441no—
296C22×C4—3441no—
297Q16—21no—
298Q16—862no—
299Q16—861no—
300Q16—1721no—
301Q16—1721no—
302SD16—41no—
303SD16—1722no—
304SD16—1722no—
305SD16—1721no—
306SD16—1721no—
307SD16—1721no—
308D8—22no—
309D8—21no—
310D8—41no—
311D8—861no—
312D8—1721no—
313C2×C8—431no—
314C2×C8—431no—
315C2×C8—431no—
316C2×C8—431no—
317C2×C8—431no—
318C2×C8D4×D4311yescharacteristic
319C16—431no—
320C16—431no—
321C16D4×D4311yescharacteristic
322C16C23×D4311yescharacteristic
323C23—81no—
324C23—431no—
325C23—3441no—
326Q8—41no—
327Q8—3441no—
328Q8—3441no—
329Q8—1722no—
330Q8—1721no—
331D4—42no—
332D4—41no—
333D4—81no—
334D4—81no—
335D4—3441no—
336D4—3441no—
337D4—3441no—
338D4—3442no—
339D4—3442no—
340D4—3441no—
341D4—1721no—
342C2×C4—81no—
343C2×C4—431no—
344C2×C4—431no—
345C2×C4—431no—
346C2×C4—431no—
347C2×C4—431no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—3442no—
352C2×C4—3442no—
353C2×C4—3441no—
354C2×C4—3441no—
355C2×C4D8×D4311yescharacteristic
356C8—431no—
357C8—431no—
358C8D8×D4311yescharacteristic
359C8C2×D4×D4311yescharacteristic
360C22—81no—
361C22—82no—
362C22—162no—
363C22—431no—
364C22—431no—
365C22—3441no—
366C22—1721no—
367C22—6882no—
368C22D16×D4311yescharacteristic
369C4—81no—
370C4—431no—
371C4—431no—
372C4—3441no—
373C4—3442no—
374C4D16×D4311yescharacteristic
375C4C2×D8×D4311yescharacteristic
376C2—21no—
377C2—162no—
378C2—161no—
379C2—861no—
380C2—861no—
381C2—6881no—
382C2C2×D16×D4311yescharacteristic
subgroupG/H
centerC2C2×D16×D43
commutator, cosocleC16×C43C24
FrattiniC16C23×D43
FittingC43×#2263C2
socleC2×C43C22×D16
hypercenter#2263D43
hypocenterC43#33981
LCSG ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. C2×#14583328C2semidirect
2. #508×D43C2semidirect
3. #19136915C2semidirect
4. #19136912C2semidirect
5. #19136911C2semidirect
6. #19136908C2semidirect
7. #19136906C2semidirect
8. #19136903C2semidirect
9. #19136901C2semidirect
10. M64×D43C2semidirect
11. C43×#2263C2semidirect
14. #14583332C22semidirect
21. #14583328C22semidirect
22. #14583328C22semidirect
23. C2×Dic344C22semidirect
24. Q32×D43C22semidirect
27. D16×D43C22semidirect
29. Dic688C22semidirect
30. #14582739C22semidirect
31. #14582738C22semidirect
32. #14582737C22semidirect
33. #14582737C22semidirect
34. #14582734C22semidirect
35. #14582733C22semidirect
36. #14582732C22semidirect
37. C32×D43C22semidirect
39. C2×D16×C43C22semidirect
40. C43×SD64C22semidirect
41. C43×D32C22semidirect
42. C43×M64C22semidirect
192. #2263D43semidirect
220. C2×D16C2×D43semidirect
227. SD64C2×D43semidirect
229. D32C2×D43semidirect
232. M64C2×D43semidirect
234. C43#33981semidirect

Maximal subgroups

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

subgroupindex
C2×#145833282
#508×D432
#191369152
#191369122
#191369112
#191369082
#191369062
#191369032
#191369012
M64×D432
C43×#22632
#3398143