Finite Group Databasebeta

← #25253420

Subgroups — #25253420

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146943C211yesmaximal, characteristic, complemented
2#19136818C211yesmaximal, characteristic, complemented
3#19136773C212yesmaximal, complemented
4#19136732C211yesmaximal, characteristic, complemented
5#19136679C212yesmaximal, complemented
6#19136627C211yesmaximal, characteristic, complemented
7#19136507C212yesmaximal, complemented
8C4×#13063266C211yesmaximal, characteristic, complemented
9D4×C43⋊C16C211yesmaximal, characteristic, complemented
10C2×#14582700C212yesmaximal, complemented
11D4×D8×C43C211yesmaximal, characteristic, complemented
12#14583553—21no—
13C2×#13063266C2211yescharacteristic
14C2×#13063266C2212yescomplemented
15C22×C43⋊C16C2212yescomplemented
16#14583304C2211yescharacteristic, complemented
17#14583213—22no—
18#14583180—21no—
19#14583135C2212yescomplemented
20C4×D344C2211yescharacteristic, complemented
21C2×#13063259C2212yescomplemented
22#14582724C2211yescharacteristic, complemented
23#14582724C2212yescomplemented
24C4⋊(C43⋊C16)C2211yescharacteristic, complemented
25#14582700C2211yescharacteristic
26#14582700C2212yes—
27#14582700C2212yescomplemented
28#14582700C2212yescomplemented
29#14582700C2212yescomplemented
30#14582699C2211yescharacteristic, complemented
31C22⋊(C43⋊C16)C2212yescomplemented
32C4×C43⋊C16C2211yescharacteristic, complemented
33C22×D8×C43C2212yes—
34D42×C43—21no—
35C43×#493C2211yescharacteristic
36C43×#466C2212yes—
37C43×#459—21no—
38C43×#447—22no—
39C4×D8×C43C2211yescharacteristic
40C8×D4×C43C2211yescharacteristic
41C2×#10621900—41no—
42C2×D344C2311yescharacteristic
43#13063325—21no—
44#13063309—42no—
45#13063305—41no—
46#13063299—22no—
47C4×D172—21no—
48C2×C4⋊Dic43—22no—
49#13063266—22no—
50#13063266—42no—
51C2×C43⋊C16—42no—
52C2×C43⋊C16C2311yescharacteristic
53C2×C43⋊C16C2312yes—
54C2×C43⋊C16C2311yescharacteristic
55#13063259—21no—
56#13063259—22no—
57#13063259C2312yes—
58#13063259C2311yescharacteristic
59#13063247—22no—
60#13063247—21no—
61C22×D4×C43—22no—
62C22×D4×C43—41no—
63C2×D8×C43—24no—
64C2×D8×C43—22no—
65C2×D8×C43—21no—
66C2×D8×C43—42no—
67C2×D8×C43C2312yes—
68C2×D8×C43C2311yescharacteristic
69C22×C8×C43C2312yes—
70#127×C43—21no—
71#121×C43—22no—
72#121×C43—41no—
73#120×C43—42no—
74C4×D4×C43—21no—
75C4×D4×C43D411yescharacteristic
76#107×C43C2311yescharacteristic
77C4⋊C8×C43D411yescharacteristic
78#102×C43—21no—
79#102×C43—22no—
80C22⋊C8×C43D412yes—
81C4×C8×C43C2311yescharacteristic
82C24×C43—42no—
83C2×D4×C43—21no—
84C2×D4×C43—22no—
85C2×D4×C43—42no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—42no—
89C2×D4×C43—44no—
90C2×D4×C43—82no—
91C2×D4×C43—84no—
92C2×D4×C43D811yescharacteristic
93C22×C4×C43—41no—
94C22×C4×C43C2×D412yes—
95C2×C22⋊D43—42no—
96C22×Dic43—42no—
97#10621900—84no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—41no—
101D8×C43—22no—
102D8×C43—21no—
103D8×C43—22no—
104D8×C43—44no—
105D8×C43—81no—
106D8×C43#4112yescomplemented
107C2×C8×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D412yes—
111C2×C8×C43C2411yescharacteristic
112C4⋊C4×C43—21no—
113C4⋊C4×C43D811yescharacteristic
114C22⋊C4×C43—41no—
115C22⋊C4×C43—42no—
116C22⋊C4×C43D812yes—
117C42×C43C2×D411yescharacteristic
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—42no—
120C4⋊Dic43—21no—
121C4⋊Dic43—22no—
122C4⋊Dic43—42no—
123C4⋊Dic43—41no—
124D344—21no—
125D344—21no—
126C43⋊C16—21no—
127C43⋊C16—21no—
128C43⋊C16—22no—
129C23×C43—41no—
130C23×C43—42no—
131C23×C43—84no—
132C23×C43—84no—
133C23×C43—162no—
134C23×C43C2×D812yes—
135C22×D43—41no—
136D4×C43—22no—
137D4×C43—42no—
138D4×C43—41no—
139D4×C43—42no—
140D4×C43—84no—
141D4×C43—84no—
142D4×C43—82no—
143D4×C43—161no—
144D4×C43D1614yescomplemented
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—82no—
149C2×C4×C43C2×D811yescharacteristic
150C2×C4×C43C2×D812yes—
151C2×C4×C43C2×D811yescharacteristic
152C2×C4×C43C22×D411yescharacteristic
153C22⋊D43—84no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—84no—
157D172—41no—
158D172—41no—
159C4×D43—82no—
160Dic86—82no—
161C8×C43—22no—
162C8×C43—21no—
163C8×C43C2×#4111yescharacteristic
164C8×C43H(5,𝔽2)11yescharacteristic
165#33861—431nomaximal, Sylow
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—42no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43—82no—
172C22×C43—82no—
173C22×C43—82no—
174C22×C43—168no—
175C22×C43C2×D1614yes—
176C22×C43C22×D811yescharacteristic
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—81no—
180C4×C43—21no—
181C4×C43—22no—
182C4×C43—81no—
183C4×C43C2×D1612yes—
184C4×C43#54611yescharacteristic
185C4×C43#57711yescharacteristic
186Dic43—82no—
187Dic43—81no—
188#3334—431no—
189D4×D8D4311yescharacteristic, complemented
190#2240—431no—
191#2232—432no—
192#2224—431no—
193#2215—432no—
194#2206—431no—
195#2184—432no—
196C4×D16—431no—
197D4×C16—431no—
198C2×#357—432no—
199C2×C43—24no—
200C2×C43—82no—
201C2×C43—162no—
202C2×C43#329411yescharacteristic
203C2×C43C22×D1611yescharacteristic
204C2×C43#341611yescharacteristic
205D43—161no—
206C22×D8C2×D4312yes—
207#547—861no—
208D42—21no—
209C2×D16—431no—
210C2×D16—432no—
211C22×C16—432no—
212#500—431no—
213#493C2×D4311yescharacteristic
214#480—862no—
215#474—861no—
216#466—432no—
217#466C2×D4312yes—
218#459—21no—
219#447—22no—
220C4×D8—431no—
221C4×D8C2×D4311yescharacteristic
222C8×D4C2×D4311yescharacteristic
223C2×#107—432no—
224#366—431no—
225#366—432no—
226C4⋊C16—431no—
227#357—431no—
228#357—432no—
229#357—432no—
230#357—432no—
231#357—432no—
232#357—431no—
233C22⋊C16—432no—
234C4×C16—431no—
235C43#3386111yescharacteristic, complemented, Sylow
236C2×#41—1721no—
237C22×D4—22no—
238C22×D4—41no—
239C2×D8—24no—
240C2×D8—22no—
241C2×D8—21no—
242C2×D8—42no—
243C2×D8—431no—
244C2×D8C22×D4312yes—
245C2×D8C22×D4311yescharacteristic
246C22×C8C22×D4312yes—
247C4⋊Q8—861no—
248#127—21no—
249#123—1722no—
250C22⋊Q8—1721no—
251#121—22no—
252#121—41no—
253#121—862no—
254#120—42no—
255C4×D4—21no—
256C4×D4—861no—
257C4×D4C22⋊D4311yescharacteristic
258C2×C4⋊C4—862no—
259D16—862no—
260D16—1722no—
261C2×C16—431no—
262C2×C16—431no—
263C2×C16—432no—
264C2×C16—1722no—
265#107—431no—
266#107—432no—
267#107—862no—
268#107—861no—
269#107C22×D4311yescharacteristic
270C4⋊C8C22⋊D4311yescharacteristic
271#102—21no—
272#102—22no—
273#102—861no—
274#102—862no—
275C22⋊C8C22⋊D4312yes—
276C4×C8C22×D4311yescharacteristic
277C24—42no—
278#41—3444no—
279C2×Q8—1721no—
280C2×D4—21no—
281C2×D4—22no—
282C2×D4—44no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—82no—
288C2×D4—84no—
289C2×D4—861no—
290C2×D4—1722no—
291C2×D4#1062188211yescharacteristic
292C22×C4—41no—
293C22×C4—1722no—
294C22×C4—1721no—
295C22×C4C2×C22⋊D4312yes—
296D8—22no—
297D8—21no—
298D8—22no—
299D8—44no—
300D8—81no—
301D8—861no—
302D8—861no—
303D8#1062190012yescomplemented
304C2×C8—22no—
305C2×C8—22no—
306C2×C8C2×C22⋊D4311yescharacteristic
307C2×C8C2×C22⋊D4312yes—
308C2×C8C23×D4311yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—861no—
311C4⋊C4—862no—
312C4⋊C4—1722no—
313C4⋊C4—1721no—
314C4⋊C4#1062188211yescharacteristic
315C22⋊C4—41no—
316C22⋊C4—42no—
317C22⋊C4—1721no—
318C22⋊C4—1722no—
319C22⋊C4#1062188212yes—
320C42C2×C22⋊D4311yescharacteristic
321C16—861no—
322C16—861no—
323C16—862no—
324C23—41no—
325C23—42no—
326C23—84no—
327C23—84no—
328C23—162no—
329C23—1721no—
330C23C2×#1062188212yes—
331Q8—3442no—
332D4—22no—
333D4—41no—
334D4—42no—
335D4—42no—
336D4—84no—
337D4—84no—
338D4—82no—
339D4—161no—
340D4—3444no—
341D4—1721no—
342D4—1721no—
343D4#1306326614yescomplemented
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—82no—
348C2×C4—3444no—
349C2×C4—3442no—
350C2×C4—1721no—
351C2×C4—1722no—
352C2×C4C2×#1062188211yescharacteristic
353C2×C4C2×#1062188212yes—
354C2×C4C2×#1062188211yescharacteristic
355C2×C4C22×C22⋊D4311yescharacteristic
356C8—21no—
357C8—22no—
358C8C2×#1062190011yescharacteristic
359C8#1306337011yescharacteristic
360C22—22no—
361C22—22no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—168no—
369C22—3441no—
370C22—3441no—
371C22—3441no—
372C22C2×#1306326614yes—
373C22C22×#1062188211yescharacteristic
374C4—22no—
375C4—21no—
376C4—81no—
377C4—3441no—
378C4—3442no—
379C4C2×#1306326612yes—
380C4#1458354311yescharacteristic
381C4#1458371011yescharacteristic
382C2—24no—
383C2—82no—
384C2—162no—
385C2—6881no—
386C2#1914640811yescharacteristic
387C2C22×#1306326611yescharacteristic
388C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingD4×D8×C43C2
socleC22×C43C22×D8
hypercenterD4×D8D43
hypocenterC43#33861
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #19146943C2semidirect
2. #19136818C2semidirect
3. #19136773C2semidirect
4. #19136732C2semidirect
5. #19136679C2semidirect
6. #19136627C2semidirect
7. #19136507C2semidirect
8. C4×#13063266C2semidirect
9. D4×C43⋊C16C2semidirect
10. C2×#14582700C2semidirect
11. D4×D8×C43C2semidirect
14. C2×#13063266C22semidirect
15. C22×C43⋊C16C22semidirect
16. #14583304C22semidirect
19. #14583135C22semidirect
20. C4×D344C22semidirect
21. C2×#13063259C22semidirect
22. #14582724C22semidirect
23. #14582724C22semidirect
24. C4⋊(C43⋊C16)C22semidirect
27. #14582700C22semidirect
28. #14582700C22semidirect
29. #14582700C22semidirect
30. #14582699C22semidirect
31. C22⋊(C43⋊C16)C22semidirect
32. C4×C43⋊C16C22semidirect
106. D8×C43#41semidirect
144. D4×C43D16semidirect
189. D4×D8D43semidirect
235. C43#33861semidirect
303. D8#10621900semidirect
343. D4#13063266semidirect

Maximal subgroups

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

subgroupindex
#191469432
#191368182
#191367732
#191367322
#191366792
#191366272
#191365072
C4×#130632662
D4×C43⋊C162
C2×#145827002
D4×D8×C432
#3386143