Finite Group Databasebeta

← #25251660

Subgroups — #25251660

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145166C211yesmaximal, characteristic, complemented
2C2×D8×Dic43C211yesmaximal, characteristic, complemented
3#19136790C211yesmaximal, characteristic, complemented
4#19136776C211yesmaximal, characteristic, complemented
5#19136750C212yesmaximal, complemented
6#19136652C212yesmaximal, complemented
7#19136507C211yesmaximal, characteristic
8#19136468C212yesmaximal, complemented
9#19136460C212yesmaximal, complemented
10#19136395C211yesmaximal, characteristic, complemented
11C43×#2187C211yesmaximal, characteristic, complemented
12#14583435—21no—
13C2×D4×Dic43—21no—
14C2×#13063266C2212yes—
15#14583300C2211yescharacteristic, complemented
16#14583284C2211yescharacteristic, complemented
17#14583255—21no—
18#14583135C2211yescharacteristic
19#14583130—21no—
20Q16×Dic43C2211yescharacteristic, complemented
21#14582984—21no—
22D8×Dic43—21no—
23D8×Dic43—21no—
24D8×Dic43C2212yes—
25D8×Dic43C2212yes—
26#14582981C2211yescharacteristic, complemented
27C2×#13063259C2211yescharacteristic
28C2×#13063246—21no—
29C2×C8×Dic43C2211yescharacteristic
30#14582726C2212yescomplemented
31#14582725C2212yescomplemented
32Dic43⋊C16C2212yescomplemented
33#14582703C2212yescomplemented
34#14582701C2212yescomplemented
35#14582700C2212yes—
36C22⋊(C43⋊C16)C2211yescharacteristic
37#14582674C2212yescomplemented
38C22×D8×C43C2211yescharacteristic
39C2×SD32×C43C2212yes—
40C43×#467C2211yescharacteristic
41C43×#357C2212yes—
42C43×C22⋊C16C2211yescharacteristic
43C23×Dic43—41no—
44C2×#10621884—21no—
45C2×D344C2311yescharacteristic
46C22×C43⋊C8D411yescharacteristic
47#13063320—41no—
48#13063316—21no—
49#13063314—21no—
50#13063309—41no—
51#13063299—21no—
52Q8×Dic43—21no—
53D4×Dic43—22no—
54D4×Dic43—22no—
55D4×Dic43—41no—
56D4×Dic43—41no—
57#13063287—21no—
58(C22⋊D43)⋊C4—41no—
59#13063283—41no—
60C2×C4⋊Dic43—21no—
61C2×C22⋊Dic43—41no—
62C2×C4×Dic43D411yescharacteristic
63#13063266—24no—
64C2×C43⋊C16C2312yes—
65#13063259—21no—
66#13063259C2311yescharacteristic
67#13063259C2312yes—
68#13063256—21no—
69#13063249—21no—
70#13063247—21no—
71#13063246—22no—
72#13063246—22no—
73#13063245—21no—
74C8×Dic43D411yescharacteristic
75C8×Dic43D411yescharacteristic
76C8×Dic43C2311yescharacteristic
77C8×Dic43C2311yescharacteristic
78C22×D4×C43—21no—
79C2×Q16×C43C2311yescharacteristic
80C2×D8×C43—24no—
81C2×D8×C43—21no—
82C2×D8×C43C2312yes—
83C22×C8×C43C2311yescharacteristic
84C22⋊Q8×C43—21no—
85SD32×C43—24no—
86C2×C16×C43C2312yes—
87#107×C43C2311yescharacteristic
88#103×C43—21no—
89C24×C43—41no—
90C2×Q8×C43—21no—
91C2×D4×C43—24no—
92C2×D4×C43—22no—
93C2×D4×C43—42no—
94C2×D4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C2×C22⋊D43—41no—
97C22×Dic43—42no—
98C22×Dic43—42no—
99C22×Dic43—41no—
100C22×Dic43—84no—
101C22×Dic43D811yescharacteristic
102C22×Dic43D811yescharacteristic
103C2×D172—21no—
104C2×C4×D43—41no—
105Q16×C43—22no—
106D8×C43—24no—
107D8×C43—22no—
108D8×C43#4114yes—
109C2×C8×C43—22no—
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2411yescharacteristic
112C4⋊C4×C43—21no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊Dic43—42no—
116C22⋊Dic43—42no—
117#10621884—42no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—41no—
122C4⋊Dic43—22no—
123C4⋊Dic43—21no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126C4⋊Dic43—41no—
127Dic43⋊C4—41no—
128C4×Dic43—41no—
129C4×Dic43D811yescharacteristic
130C4×Dic43D811yescharacteristic
131C4×Dic43C2×D411yescharacteristic
132C4×Dic43C2×D411yescharacteristic
133C2×C43⋊C8—41no—
134C2×C43⋊C8C2×D411yescharacteristic
135C2×C43⋊C8C2×D411yescharacteristic
136D344—22no—
137C16×C43—22no—
138C43⋊C16—22no—
139C23×C43—44no—
140C23×C43—42no—
141C23×C43—82no—
142C23×C43—82no—
143C23×C43C2×D811yescharacteristic
144C22×D43—41no—
145Q8×C43—41no—
146Q8×C43—41no—
147D4×C43—24no—
148D4×C43—44no—
149D4×C43—42no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C22⋊D43—82no—
157C2×Dic43—22no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—42no—
161C2×Dic43—84no—
162C2×Dic43—84no—
163C2×Dic43—82no—
164C2×Dic43C2×D811yescharacteristic
165C2×Dic43C2×D811yescharacteristic
166C2×Dic43C2×D811yescharacteristic
167C2×Dic43C2×D811yescharacteristic
168D172—41no—
169D172—41no—
170C4×D43—82no—
171C8×C43—21no—
172C8×C43C2×#4112yes—
173C43⋊C8—21no—
174C43⋊C8—21no—
175#33674—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—44no—
179C22×C43—88no—
180C22×C43—82no—
181C22×C43—82no—
182C22×C43#50912yes—
183C22×C43C22×D811yescharacteristic
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C4×C43—21no—
188C4×C43—81no—
189C4×C43—81no—
190C4×C43#52511yescharacteristic
191C4×C43#57511yescharacteristic
192Dic43—21no—
193Dic43—21no—
194Dic43—21no—
195Dic43—21no—
196Dic43—82no—
197Dic43—81no—
198#3168—431no—
199C2×C4×D8—431no—
200#2235—431no—
201#2232—431no—
202#2228—432no—
203#2210—432no—
204#2187D4311yescharacteristic, complemented
205#2184—431no—
206#2177—432no—
207#2175—432no—
208#2163—431no—
209C2×C43—22no—
210C2×C43—84no—
211C2×C43#310011yescharacteristic
212C2×C43C2×#50911yescharacteristic
213C2×C43#341411yescharacteristic
214D43—161no—
215C22×D8C2×D4311yescharacteristic
216#529—861no—
217C2×C4×D4—861no—
218C2×SD32C2×D4312yes—
219C2×D16—432no—
220#499—431no—
221#495—431no—
222#488—861no—
223#467C2×D4311yescharacteristic
224#466—431no—
225#465—861no—
226C4×Q16—431no—
227C4×SD16—861no—
228C4×D8—432no—
229C4×D8—432no—
230C4×D8—431no—
231C4×D8—861no—
232C4×D8—861no—
233C2×#107—431no—
234C2×#102—861no—
235C2×C4×C8—431no—
236#367—432no—
237#366—432no—
238C4⋊C16—432no—
239#358—432no—
240#357—432no—
241#357—432no—
242#357C2×D4312yes—
243C22⋊C16—431no—
244C22⋊C16C2×D4311yescharacteristic
245#346—432no—
246C43#3367411yescharacteristic, complemented, Sylow
247C22×D4—21no—
248C23×C4—1721no—
249C2×Q16C22×D4311yescharacteristic
250C2×SD16—861no—
251C2×D8—24no—
252C2×D8—21no—
253C2×D8—431no—
254C2×D8C22×D4312yes—
255C22×C8—431no—
256C22×C8C22×D4311yescharacteristic
257#126—1721no—
258#125—861no—
259#124—861no—
260#123—1721no—
261C22⋊Q8—21no—
262#121—861no—
263C4×Q8—861no—
264C4×D4—861no—
265C4×D4—862no—
266C4×D4—862no—
267C4×D4—1721no—
268C4×D4—1721no—
269C4×D4—1721no—
270#117—1721no—
271C2×C4⋊C4—861no—
272C2×C22⋊C4—1721no—
273C2×C42—431no—
274SD32—24no—
275D16—864no—
276C2×C16—432no—
277C2×C16C22×D4312yes—
278#107—431no—
279#107—432no—
280#107—861no—
281#107C22×D4311yescharacteristic
282#106—861no—
283#103—21no—
284#103—861no—
285#102—861no—
286#102—862no—
287#102—862no—
288#102—861no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—431no—
292C4×C8—431no—
293C24—41no—
294C2×Q8—21no—
295C2×D4—24no—
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—861no—
300C2×D4—1721no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—3444no—
304C22×C4—1721no—
305C22×C4—1722no—
306C22×C4—1722no—
307C22×C4—1721no—
308C22×C4D4×D4311yescharacteristic
309Q16—22no—
310SD16—1722no—
311D8—24no—
312D8—22no—
313D8—862no—
314D8#1062190014yes—
315C2×C8—22no—
316C2×C8—431no—
317C2×C8—431no—
318C2×C8—1721no—
319C2×C8D4×D4311yescharacteristic
320C2×C8C23×D4311yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—862no—
324C4⋊C4—861no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C22⋊C4—41no—
330C22⋊C4—1721no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1722no—
334C22⋊C4—1722no—
335C22⋊C4—1721no—
336C42—431no—
337C42—431no—
338C42—431no—
339C42—431no—
340C42—1721no—
341C16—22no—
342C16—862no—
343C23—44no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—1721no—
348C23D8×D4311yescharacteristic
349Q8—41no—
350Q8—41no—
351D4—24no—
352D4—44no—
353D4—42no—
354D4—3442no—
355D4—1721no—
356D4—1721no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—431no—
362C2×C4—431no—
363C2×C4—431no—
364C2×C4—431no—
365C2×C4—862no—
366C2×C4—3442no—
367C2×C4—3444no—
368C2×C4—3444no—
369C2×C4—3442no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1722no—
373C2×C4D8×D4311yescharacteristic
374C2×C4C2×D4×D4311yescharacteristic
375C8—21no—
376C8—861no—
377C8—861no—
378C8C2×#1062190012yes—
379C22—21no—
380C22—21no—
381C22—44no—
382C22—88no—
383C22—82no—
384C22—82no—
385C22—3441no—
386C22—3441no—
387C22—3441no—
388C22#1458333612yes—
389C22C2×D8×D4311yescharacteristic
390C4—21no—
391C4—81no—
392C4—81no—
393C4—861no—
394C4—861no—
395C4—861no—
396C4—861no—
397C4—3442no—
398C4—3441no—
399C4#1458340511yescharacteristic
400C4#1458369511yescharacteristic
401C2—22no—
402C2—84no—
403C2—6881no—
404C2#1914459011yescharacteristic
405C2C2×#1458333611yescharacteristic
406C2#1914772711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2187C2
socleC22×C43C22×D8
prime radical#19136507C2
hypercenter#2187D43
hypocenterC43#33674
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #19145166C2semidirect
2. C2×D8×Dic43C2semidirect
3. #19136790C2semidirect
4. #19136776C2semidirect
5. #19136750C2semidirect
6. #19136652C2semidirect
8. #19136468C2semidirect
9. #19136460C2semidirect
10. #19136395C2semidirect
11. C43×#2187C2semidirect
15. #14583300C22semidirect
16. #14583284C22semidirect
20. Q16×Dic43C22semidirect
26. #14582981C22semidirect
30. #14582726C22semidirect
31. #14582725C22semidirect
32. Dic43⋊C16C22semidirect
33. #14582703C22semidirect
34. #14582701C22semidirect
37. #14582674C22semidirect
204. #2187D43semidirect
246. C43#33674semidirect

Maximal subgroups

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

subgroupindex
#191451662
C2×D8×Dic432
#191367902
#191367762
#191367502
#191366522
#191365072
#191364682
#191364602
#191363952
C43×#21872
#3367443