Finite Group Databasebeta

← #11878644

Subgroups — #11878644

Order 1152.

1596 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 241 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#10596196C211yesmaximal, characteristic, complemented
2C3⋊D3×#127C211yesmaximal, characteristic, complemented
3C32×#486C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5#10592772C211yesmaximal, characteristic, complemented
6#10592485C214yesmaximal, complemented
7#10592472C214yesmaximal, complemented
8#10592394C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81566—34nomaximal
11C2×#3832—21no—
12C2×D4×C3⋊D3—21no—
13C2×D4×C3⋊D3—21no—
14C2×D4×C3⋊D3C2212yes—
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C32×#127C2211yescharacteristic
17#64156—21no—
18#64149—21no—
19#64149—21no—
20#64149C2212yes—
21C2×#3753C2214yescomplemented
22C2×#3745C2214yescomplemented
23#64104—21no—
24#64104C2212yes—
25#64102—21no—
26#64102C2212yescomplemented
27#64083C2211yescharacteristic
28#64083C2211yescharacteristic, complemented
29C42×C3⋊D3C2211yescharacteristic
30C32×#102C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63647C2212yes—
33#63641C2212yescomplemented
34#63636C2214yescomplemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36#5725—34no—
37D3×#127—34no—
38C3×#486D314yescomplemented
39#5088—34no—
40#5073—34no—
41#4786—316no—
42#4773—316no—
43#4695—34no—
44#4685—34no—
45C23×C3⋊D3—22no—
46C2×C32×Q8—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2312yes—
50C2×#638—22no—
51C2×#638—22no—
52C2×#638—22no—
53#3832—44no—
54D4×C3⋊D3—44no—
55D4×C3⋊D3—44no—
56D4×C3⋊D3—44no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C42C2311yescharacteristic
72#3753—44no—
73#3752—22no—
74#3752—22no—
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2312yes—
79#3745—44no—
80#3205—91noSylow
81C2×#239—64no—
82C2×D3×D4—38no—
83C2×D3×D4—64no—
84C2×D3×D4—64no—
85C3×C4⋊Q8C2×D314yescomplemented
86C3×#127C2×D314yes—
87#947—64no—
88#940—38no—
89#940—64no—
90#940—64no—
91C2×#213—316no—
92C2×D24—316no—
93#895—38no—
94#895—64no—
95#893—38no—
96#893—64no—
97#874—34no—
98#874—34no—
99C42×D3—34no—
100C3×#102C2×D3116yescomplemented
101C3×C4×C8C2×D314yescomplemented
102(C2×D3)⋊C8—38no—
103Dic3⋊C8—38no—
104#809—316no—
105C4×C3⋊C8—34no—
106C23×C32—22no—
107C22×C3⋊D3—22no—
108C22×C3⋊D3—22no—
109C22×C3⋊D3—44no—
110C22×C3⋊D3—44no—
111C22×C3⋊D3—44no—
112C22×C3⋊D3C2×D411yescharacteristic
113C32×Q8—42no—
114C32×D4—24no—
115C32×D4—42no—
116C32×D4—42no—
117C2×C32×C4—22no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2411yescharacteristic
121#638—44no—
122#638—44no—
123#638—44no—
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D411yescharacteristic
126C2×C3⋊Dic3C2×D411yescharacteristic
127C4⋊(C3⋊D3)—24no—
128C4⋊(C3⋊D3)—24no—
129C4⋊(C3⋊D3)—44no—
130C4⋊(C3⋊D3)—42no—
131C4⋊(C3⋊D3)—42no—
132C4⋊(C3⋊D3)—42no—
133C4⋊(C3⋊D3)—42no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—44no—
137C4×C3⋊D3D814yescomplemented
138C32×C8—22no—
139C3⋊(C3⋊C8)—22no—
140#532—91no—
141C2×#127—91no—
142#493—91no—
143#493—91no—
144#486—91no—
145#486C3⋊D311yescharacteristic, complemented
146#459—94no—
147#447—94no—
148#431—91no—
149C23×D3—68no—
150C2×C3×Q8—24no—
151C2×C3×D4—24no—
152C2×C3×D4—24no—
153C2×C3×D4C22×D318yes—
154C2×#67—68no—
155C2×#67—68no—
156C2×#67—68no—
157#239—1216no—
158D3×D4—1216no—
159D3×D4—1216no—
160D3×D4—1216no—
161C2×D12—38no—
162C2×D12—38no—
163C2×D12—68no—
164C2×D12—64no—
165C2×D12—64no—
166C2×D12—64no—
167C2×D12—64no—
168C2×C4×D3—34no—
169C2×C4×D3—34no—
170C2×C4×D3—34no—
171C2×C4×D3—68no—
172C2×C3×C8C22×D318yes—
173C3×C4⋊C4—24no—
174C3×C4⋊C4C22×D318yes—
175C3×C42C22×D314yes—
176#213—1216no—
177(C2×D3)⋊C4—68no—
178(C2×D3)⋊C4—68no—
179C4×Dic3—34no—
180C4×Dic3—34no—
181C4×Dic3—34no—
182C2×C3⋊C8—38no—
183D24—1216no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32—42no—
187C22×C32C22×D411yescharacteristic
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—88no—
197C2×C3⋊D3C2×D812yes—
198C32×C4—42no—
199C32×C4C2×D812yes—
200C32×C4AGL(1,ℤ/8)12yes—
201C32×C4H(5,𝔽2)12yes—
202C3⋊Dic3—21no—
203C3⋊Dic3—21no—
204C3⋊Dic3C2×D812yes—
205C2×#41—181no—
206C22×D4—92no—
207C22×D4—181no—
208C22×D4—181no—
209C2×D8—94no—
210C2×D8—94no—
211C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
212#127—92no—
213#127—91no—
214#127—91no—
215#127—181no—
216#127—181no—
217#127C2×C3⋊D311yescharacteristic
218#124—181no—
219#121—92no—
220#121—181no—
221C4×D4—92no—
222C4×D4—181no—
223C2×C42—91no—
224C4⋊C8—92no—
225#102—94no—
226#102C2×C3⋊D314yescomplemented
227C22⋊C8—92no—
228C4×C8—91no—
229C4×C8C2×C3⋊D311yescharacteristic, complemented
230C23×C3—28no—
231C22×D3—34no—
232C22×D3—68no—
233C22×D3—68no—
234C22×D3—1216no—
235C22×D3—1216no—
236C22×D3—1216no—
237C3×Q8—48no—
238C3×D4—216no—
239C3×D4—48no—
240C3×D4—48no—
241C2×C3×C4—28no—
242C2×C3×C4D3×D414yes—
243C2×C3×C4D3×D414yes—
244C2×C3×C4C23×D314yes—
245#67—1216no—
246#67—1216no—
247#67—1216no—
248C2×Dic3—34no—
249C2×Dic3—34no—
250C2×Dic3—34no—
251D12—616no—
252D12—616no—
253D12—1216no—
254D12—128no—
255D12—128no—
256D12—128no—
257D12—128no—
258C4×D3—316no—
259C4×D3—68no—
260C4×D3—68no—
261C4×D3—1216no—
262C3×C8—28no—
263C3⋊C8—68no—
264C2×C32—82no—
265C2×C32#53511yescharacteristic
266C2×C32C22×D811yescharacteristic
267C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
268C3⋊D3—22no—
269C3⋊D3—82no—
270C3⋊D3—82no—
271C24—182no—
272#41—364no—
273C2×Q8—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—92no—
277C2×D4—92no—
278C2×D4—182no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4—181no—
283C2×D4—181no—
284C2×D4—181no—
285C2×D4—181no—
286C2×D4—364no—
287C2×D4—364no—
288C2×D4—364no—
289C2×D4C22×C3⋊D312yes—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—182no—
294D8—364no—
295D8—364no—
296C2×C8—92no—
297C2×C8C22×C3⋊D312yes—
298C4⋊C4—21no—
299C4⋊C4C22×C3⋊D312yes—
300C22⋊C4—182no—
301C22⋊C4—182no—
302C42—91no—
303C42—91no—
304C42—91no—
305C42C22×C3⋊D311yescharacteristic
306C22×C3—48no—
307C22×C3—48no—
308C22×C3—48no—
309C22×C3C2×D3×D414yes—
310C2×D3—38no—
311C2×D3—64no—
312C2×D3—64no—
313C2×D3—128no—
314C2×D3—128no—
315C2×D3—128no—
316C2×D3—128no—
317C2×D3—128no—
318C2×D3—128no—
319C2×D3—2432no—
320C3×C4—48no—
321C3×C4D3×D818yes—
322C3×C4#91418yes—
323C3×C4#100918yes—
324Dic3—38no—
325Dic3—64no—
326Dic3—64no—
327C32#320511yescharacteristic, complemented, Sylow
328C23—22no—
329C23—91no—
330C23—182no—
331C23—182no—
332C23—364no—
333C23—364no—
334C23—364no—
335Q8—42no—
336D4—24no—
337D4—42no—
338D4—42no—
339D4—184no—
340D4—184no—
341D4—364no—
342D4—364no—
343D4—364no—
344D4—364no—
345D4—362no—
346D4—362no—
347D4—362no—
348D4—362no—
349C2×C4—22no—
350C2×C4—91no—
351C2×C4—94no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—364no—
357C2×C4D4×C3⋊D311yescharacteristic
358C2×C4D4×C3⋊D311yescharacteristic
359C2×C4C23×C3⋊D311yescharacteristic
360C8—22no—
361C8—182no—
362C2×C3—88no—
363C2×C3#567414yes—
364C2×C3C2×D3×D814yes—
365C2×C3C2×#91414yes—
366D3—68no—
367D3—248no—
368D3—248no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—92no—
373C22—181no—
374C22—181no—
375C22—362no—
376C22—362no—
377C22—362no—
378C22—362no—
379C22—362no—
380C22—362no—
381C22—728no—
382C22C2×D4×C3⋊D311yescharacteristic
383C4—42no—
384C4—92no—
385C4—181no—
386C4—181no—
387C4D8×C3⋊D312yes—
388C4#6412312yes—
389C4#6436612yes—
390C3#8156614yescomplemented
391C2—82no—
392C2—182no—
393C2—722no—
394C2—722no—
395C2#1059614511yescharacteristic
396C2C2×D8×C3⋊D311yescharacteristic
397C2C2×#6412311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#486C2
socleC22×C32C22×D4
hypercenter#486C3⋊D3
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. C3⋊D3×#127C2semidirect
3. C32×#486C2semidirect
4. #10592787C2semidirect
5. #10592772C2semidirect
6. #10592485C2semidirect
7. #10592472C2semidirect
8. #10592394C2semidirect
9. #10592384C2semidirect
15. C32×C4⋊Q8C22semidirect
21. C2×#3753C22semidirect
22. C2×#3745C22semidirect
26. #64102C22semidirect
28. #64083C22semidirect
30. C32×#102C22semidirect
31. C32×C4×C8C22semidirect
33. #63641C22semidirect
34. #63636C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
38. C3×#486D3semidirect
85. C3×C4⋊Q8C2×D3semidirect
100. C3×#102C2×D3semidirect
101. C3×C4×C8C2×D3semidirect
137. C4×C3⋊D3D8semidirect
145. #486C3⋊D3semidirect
211. C4⋊Q8C2×C3⋊D3semidirect
226. #102C2×C3⋊D3semidirect
229. C4×C8C2×C3⋊D3semidirect
327. C32#3205semidirect
390. C3#81566semidirect

Maximal subgroups

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

subgroupindex
#105961962
C3⋊D3×#1272
C32×#4862
#105927872
#105927722
#105924852
#105924722
#105923942
#105923842
#815663