Finite Group Databasebeta

← #11886838

Subgroups — #11886838

Order 1152.

1380 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596308C212yesmaximal, complemented
2#10596249C212yesmaximal, complemented
3C32×#456C211yesmaximal, characteristic, complemented
4#10592902C212yesmaximal, complemented
5#10592794C211yesmaximal, characteristic, complemented
6#10592784C211yesmaximal, characteristic, complemented
7#10592523C212yesmaximal, complemented
8#10592521C212yesmaximal, complemented
9#10592453C212yesmaximal, complemented
10#80302—34nomaximal
11C32×2−1+4C2211yescharacteristic
12#64366C2212yescomplemented
13#64364C2211yescharacteristic
14C32×#137C2212yescomplemented
15C32×C4⋊Q8C2211yescharacteristic, complemented
16#64159—22no—
17#64159C2212yes—
18#64158—22no—
19#64158C2212yes—
20#64157C2212yescomplemented
21#64151—22no—
22#64151C2212yescomplemented
23C2×#3755—22no—
24C2×#3755C2212yescomplemented
25C2×#3755C2212yescomplemented
26#64128—22no—
27#64127—22no—
28#64123—22no—
29SD16×C3⋊D3—22no—
30#64117C2212yes—
31#64116C2212yescomplemented
32#64083C2211yescharacteristic
33C32×#104C2212yescomplemented
34C32×#101C2211yescharacteristic, complemented
35#63663C2211yescharacteristic, complemented
36#63650C2212yescomplemented
37#63649C2212yescomplemented
38#63632C2212yescomplemented
39C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
40#5837—38no—
41#5778—38no—
42C3×#456D314yescomplemented
43#5203—38no—
44#5095—34no—
45#5085—34no—
46#4824—38no—
47#4822—38no—
48#4754—38no—
49C32×#41—22no—
50C32×#41—41no—
51C32×#41C2312yes—
52C2×C32×Q8—22no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×Q8C2311yescharacteristic
55#3832—22no—
56#3832—22no—
57Q8×C3⋊D3—22no—
58D4×C3⋊D3—22no—
59D4×C3⋊D3—42no—
60#3828—22no—
61#3828—41no—
62#3828C2312yes—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)—41no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C32×Q16—22no—
67C32×SD16—22no—
68C32×M16C2312yes—
69C32×C4⋊C4—41no—
70C32×C42C2311yescharacteristic
71#3756—22no—
72#3756D412yescomplemented
73#3755—22no—
74#3755—22no—
75#3755—22no—
76#3755—22no—
77#3755—22no—
78#3755—22no—
79#3755D412yescomplemented
80#3754D412yescomplemented
81#3753—22no—
82#3753D412yescomplemented
83#3748—22no—
84#3748C2312yes—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87#3745—22no—
88#3744—22no—
89#3743—22no—
90C8×C3⋊D3—22no—
91#3291—91noSylow
92C3×2−1+4C2×D314yes—
93#1009—38no—
94#1007—34no—
95C3×#137C2×D318yescomplemented
96C3×C4⋊Q8C2×D314yescomplemented
97#950—38no—
98#950—68no—
99#949—38no—
100#949—68no—
101#948—38no—
102#942—38no—
103#942—68no—
104C2×#215—38no—
105C2×#215—38no—
106C2×#215—68no—
107#919—68no—
108#918—68no—
109#914—68no—
110D3×SD16—68no—
111#908—38no—
112#907—38no—
113#874—34no—
114C3×#104C2×D318yescomplemented
115C3×#101C2×D314yescomplemented
116#836—34no—
117#823—38no—
118#822—38no—
119#805—38no—
120C4×C3⋊C8—34no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—42no—
123C32×Q8—22no—
124C32×Q8—22no—
125C32×Q8—41no—
126C32×Q8C2×D412yes—
127C32×D4—22no—
128C32×D4—41no—
129C32×D4C2×D412yes—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—42no—
135C2×C32×C4C2411yescharacteristic
136#638—22no—
137#638—42no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—42no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—82no—
143C4⋊(C3⋊D3)C2×D412yes—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—42no—
146C4×C3⋊D3—42no—
147#634—41no—
148#634C2×D412yes—
149C32×C8—22no—
150C3⋊(C3⋊C8)—22no—
151C3⋊(C3⋊C8)C2×D412yes—
152C3⋊(C3⋊C8)C2×D412yes—
153#577—92no—
154#577—92no—
155#492—91no—
156#471—92no—
157#471—92no—
158#456—91no—
159#456C3⋊D311yescharacteristic, complemented
160#453—92no—
161#443—92no—
162C3×#41—28no—
163C3×#41—44no—
164C3×#41C22×D318yes—
165C2×C3×Q8—28no—
166C2×C3×Q8C22×D314yes—
167C2×C3×Q8C22×D314yes—
168#239—68no—
169#239—68no—
170D3×Q8—68no—
171D3×D4—68no—
172D3×D4—128no—
173#235—38no—
174#235—68no—
175#235—124no—
176C2×D12—38no—
177C2×D12—68no—
178C2×D12—124no—
179C3×Q16—28no—
180C3×SD16—28no—
181C3×M16C22×D318yes—
182C3×C4⋊C4—44no—
183C3×C42C22×D314yes—
184#216—38no—
185#216—68no—
186#215—38no—
187#215—68no—
188#215—68no—
189#215—68no—
190#215—68no—
191#215—68no—
192#215—68no—
193#214—38no—
194#213—38no—
195#213—68no—
196#208—38no—
197#208—68no—
198C2×C3⋊C8—38no—
199C2×C3⋊C8—68no—
200D24—68no—
201#204—68no—
202ΓL(1,𝔽25)—68no—
203D3×C8—68no—
204C22×C32—22no—
205C22×C32H(5,𝔽2)11yescharacteristic
206C2×C3⋊D3—22no—
207C2×C3⋊D3—42no—
208C2×C3⋊D3—82no—
209C2×C3⋊D3—162no—
210C32×C4—22no—
211C32×C4—22no—
212C32×C4—41no—
213C32×C4—41no—
214C32×C4C22×D412yes—
215C3⋊Dic3—22no—
2162−1+4—91no—
2172−1+4C2×C3⋊D311yescharacteristic
218H(5,𝔽2)—92no—
219#137—92no—
220#137—182no—
221#137—182no—
222#137C2×C3⋊D312yescomplemented
223AGL(1,ℤ/8)—92no—
224AGL(1,ℤ/8)—92no—
225AGL(1,ℤ/8)—182no—
226AGL(1,ℤ/8)—182no—
227#135—92no—
228#135—182no—
229#135—182no—
230C2×SD16—92no—
231C2×SD16—92no—
232C2×SD16—182no—
233C2×SD16—182no—
234#131—92no—
235#131—92no—
236C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
237#127—91no—
238#108—92no—
239#104—92no—
240#104C2×C3⋊D312yescomplemented
241#101—91no—
242#101C2×C3⋊D311yescharacteristic, complemented
243#100—92no—
244C4×C8—91no—
245C22×D3—68no—
246C22×D3—128no—
247C3×Q8—28no—
248C3×Q8—28no—
249C3×Q8—44no—
250C3×Q8D3×D418yes—
251C3×D4—28no—
252C3×D4—44no—
253C3×D4D3×D418yes—
254C2×C3×C4—24no—
255C2×C3×C4—28no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—48no—
259C2×C3×C4C23×D314yes—
260#67—68no—
261#67—128no—
262D12—38no—
263D12—68no—
264D12—68no—
265D12—128no—
266D12—124no—
267D12—248no—
268C4×D3—68no—
269C4×D3—128no—
270C4×D3—128no—
271Dic6—38no—
272Dic6—124no—
273C3×C8—28no—
274C3⋊C8—38no—
275C3⋊C8—38no—
276C3⋊C8—68no—
277C2×C32—21no—
278C2×C32—42no—
279C2×C32D4211yescharacteristic
280C3⋊D3—42no—
281C3⋊D3—82no—
282#41—22no—
283#41—41no—
284#41—92no—
285#41—182no—
286#41—182no—
287#41—182no—
288#41—361no—
289#41C22×C3⋊D312yes—
290C2×Q8—22no—
291C2×Q8—182no—
292C2×Q8C22×C3⋊D311yescharacteristic
293C2×Q8C22×C3⋊D311yescharacteristic
294C2×D4—92no—
295C2×D4—182no—
296C2×D4—182no—
297C2×D4—361no—
298C2×D4—362no—
299Q16—22no—
300Q16—92no—
301Q16—182no—
302SD16—22no—
303SD16—92no—
304SD16—92no—
305SD16—182no—
306SD16—182no—
307SD16—182no—
308SD16—182no—
309SD16—182no—
310SD16—182no—
311SD16—182no—
312D8—92no—
313D8—182no—
314D8—182no—
315M16—92no—
316M16—182no—
317M16—182no—
318M16C22×C3⋊D312yes—
319C2×C8—92no—
320C2×C8—182no—
321C2×C8—182no—
322C4⋊C4—41no—
323C42C22×C3⋊D311yescharacteristic
324C22×C3—28no—
325C22×C3#100414yes—
326C2×D3—68no—
327C2×D3—128no—
328C2×D3—248no—
329C2×D3—488no—
330C3×C4—28no—
331C3×C4—28no—
332C3×C4—44no—
333C3×C4—44no—
334C3×C4C2×D3×D418yes—
335Dic3—68no—
336C32#329111yescharacteristic, complemented, Sylow
337C23—182no—
338C23—362no—
339Q8—22no—
340Q8—22no—
341Q8—41no—
342Q8—92no—
343Q8—361no—
344Q8D4×C3⋊D312yes—
345D4—22no—
346D4—41no—
347D4—92no—
348D4—182no—
349D4—182no—
350D4—182no—
351D4—362no—
352D4—361no—
353D4—362no—
354D4—722no—
355D4D4×C3⋊D312yes—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—182no—
362C2×C4—362no—
363C2×C4—362no—
364C2×C4C23×C3⋊D311yescharacteristic
365C8—22no—
366C8—92no—
367C8—92no—
368C8—182no—
369C2×C3—24no—
370C2×C3—48no—
371C2×C3#559014yes—
372D3—128no—
373D3—248no—
374C22—22no—
375C22—182no—
376C22—362no—
377C22—722no—
378C22—1442no—
379C22#6436111yescharacteristic
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—182no—
385C4C2×D4×C3⋊D312yes—
386C3#8030214yescomplemented
387C2—21no—
388C2—42no—
389C2—362no—
390C2—722no—
391C2#1059606111yescharacteristic
subgroupG/H
centerC2#10596061
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#456C2
socleC2×C32D42
hypercenter#456C3⋊D3
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #10596308C2semidirect
2. #10596249C2semidirect
3. C32×#456C2semidirect
4. #10592902C2semidirect
5. #10592794C2semidirect
6. #10592784C2semidirect
7. #10592523C2semidirect
8. #10592521C2semidirect
9. #10592453C2semidirect
12. #64366C22semidirect
14. C32×#137C22semidirect
15. C32×C4⋊Q8C22semidirect
20. #64157C22semidirect
22. #64151C22semidirect
24. C2×#3755C22semidirect
25. C2×#3755C22semidirect
31. #64116C22semidirect
33. C32×#104C22semidirect
34. C32×#101C22semidirect
35. #63663C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
38. #63632C22semidirect
39. C4×C3⋊(C3⋊C8)C22semidirect
42. C3×#456D3semidirect
72. #3756D4semidirect
79. #3755D4semidirect
80. #3754D4semidirect
82. #3753D4semidirect
95. C3×#137C2×D3semidirect
96. C3×C4⋊Q8C2×D3semidirect
114. C3×#104C2×D3semidirect
115. C3×#101C2×D3semidirect
159. #456C3⋊D3semidirect
222. #137C2×C3⋊D3semidirect
236. C4⋊Q8C2×C3⋊D3semidirect
240. #104C2×C3⋊D3semidirect
242. #101C2×C3⋊D3semidirect
336. C32#3291semidirect
386. C3#80302semidirect

Maximal subgroups

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

subgroupindex
#105963082
#105962492
C32×#4562
#105929022
#105927942
#105927842
#105925232
#105925212
#105924532
#803023