Finite Group Databasebeta

← #11878760

Subgroups — #11878760

Order 1152.

1314 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 233 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
2#10596187C211yesmaximal, characteristic, complemented
3C32×#486C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5#10592772C211yesmaximal, characteristic, complemented
6#10592486C214yesmaximal, complemented
7#10592480C214yesmaximal, complemented
8#10592392C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81567—34nomaximal
11C2×#3832—21no—
12C2×#3830C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×#127C2211yescharacteristic
15#64156—21no—
16#64147—21no—
17#64147—21no—
18#64145C2212yes—
19D4×C3⋊Dic3—21no—
20D4×C3⋊Dic3—21no—
21C2×#3753C2214yes—
22C2×#3744C2214yes—
23#64104—21no—
24#64104C2212yes—
25#64102—21no—
26#64102C2212yes—
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×#102C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63647C2212yes—
33#63641C2212yes—
34#63637C2214yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5725—34no—
37#5716—34no—
38C3×#486D314yescomplemented
39#5093—34no—
40#5073—34no—
41#4787—316no—
42#4781—316no—
43#4693—34no—
44#4685—34no—
45C2×C32×Q8—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2312yes—
49C2×#638—22no—
50C22×C3⋊Dic3—22no—
51#3832—44no—
52#3830—44no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×#634C2312yes—
62C2×C32×C8C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C42C2311yescharacteristic
66#3757—22no—
67#3757—22no—
68#3753—44no—
69#3752—22no—
70#3752—22no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2312yes—
77#3744—44no—
78#3207—91noSylow
79C2×#239—64no—
80C2×#237—38no—
81C3×C4⋊Q8C2×D314yes—
82C3×#127C2×D314yes—
83#947—64no—
84#938—64no—
85#938—64no—
86#936—38no—
87D4×Dic3—64no—
88D4×Dic3—64no—
89C2×#213—316no—
90C2×#204—316no—
91#895—38no—
92#895—64no—
93#893—38no—
94#893—64no—
95#874—34no—
96C42×D3—34no—
97#869—34no—
98C3×#102C2×D3116yes—
99C3×C4×C8C2×D314yes—
100(C2×D3)⋊C8—38no—
101Dic3⋊C8—38no—
102#810—316no—
103C4×C3⋊C8—34no—
104C23×C32—22no—
105C22×C3⋊D3—22no—
106C22×C3⋊D3C2×D411yescharacteristic
107C32×Q8—42no—
108C32×D4—24no—
109C32×D4—42no—
110C32×D4—42no—
111C2×C32×C4—22no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2411yescharacteristic
115#638—44no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—44no—
118C2×C3⋊Dic3C2×D411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C4⋊(C3⋊D3)—24no—
122C4⋊(C3⋊D3)—44no—
123C4⋊(C3⋊D3)—42no—
124C4⋊(C3⋊D3)—42no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—44no—
129#634—24no—
130C32×C8—22no—
131C3⋊(C3⋊C8)—22no—
132#532—91no—
133#532—91no—
134#493—91no—
135#492—91no—
136#487—91no—
137#486C3⋊D311yescharacteristic, complemented
138#463—94no—
139#449—94no—
140#431—91no—
141C2×C3×Q8—24no—
142C2×C3×D4—24no—
143C2×C3×D4—24no—
144C2×C3×D4C22×D318yes—
145C2×#67—68no—
146C22×Dic3—68no—
147#239—1216no—
148#237—1216no—
149C2×D12—38no—
150C2×D12—68no—
151C2×D12—64no—
152C2×D12—64no—
153C2×C4×D3—34no—
154C2×C4×D3—34no—
155C2×C4×D3—34no—
156C2×C4×D3—68no—
157C2×Dic6—38no—
158C2×C3×C8C22×D318yes—
159C3×C4⋊C4—24no—
160C3×C4⋊C4C22×D318yes—
161C3×C42C22×D314yes—
162#217—68no—
163#217—68no—
164#213—1216no—
165(C2×D3)⋊C4—68no—
166(C2×D3)⋊C4—68no—
167C4⋊Dic3—64no—
168C4⋊Dic3—64no—
169C4×Dic3—34no—
170C4×Dic3—34no—
171C4×Dic3—34no—
172C2×C3⋊C8—38no—
173#204—1216no—
174C22×C32—42no—
175C22×C32—42no—
176C22×C32—42no—
177C22×C32C22×D411yescharacteristic
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C32×C4—42no—
185C32×C4#13512yes—
186C32×C4AGL(1,ℤ/8)12yes—
187C32×C4H(5,𝔽2)12yes—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—21no—
191C3⋊Dic3—42no—
192C2×#41—92no—
193C2×#41—181no—
194C2×SD16—94no—
195C2×D8—94no—
196C4⋊Q8—91no—
197C4⋊Q8C2×C3⋊D311yescharacteristic
198#127—91no—
199#127C2×C3⋊D311yescharacteristic
200#124—92no—
201#124—181no—
202#121—92no—
203#121—181no—
204#121—181no—
205#121—181no—
206C4×D4—92no—
207C4×D4—181no—
208C4×D4—181no—
209C4×D4—181no—
210C2×C42—91no—
211C4⋊C8—92no—
212#103—94no—
213#102C2×C3⋊D314yes—
214C22⋊C8—92no—
215C4×C8—91no—
216C4×C8C2×C3⋊D311yescharacteristic
217C23×C3—28no—
218C22×D3—34no—
219C22×D3—68no—
220C3×Q8—48no—
221C3×D4—216no—
222C3×D4—48no—
223C3×D4—48no—
224C2×C3×C4—28no—
225C2×C3×C4D3×D414yes—
226C2×C3×C4D3×D414yes—
227C2×C3×C4C23×D314yes—
228#67—1216no—
229C2×Dic3—34no—
230C2×Dic3—34no—
231C2×Dic3—34no—
232C2×Dic3—68no—
233C2×Dic3—1216no—
234D12—616no—
235D12—1216no—
236D12—128no—
237D12—128no—
238C4×D3—68no—
239C4×D3—68no—
240C4×D3—68no—
241C4×D3—1216no—
242Dic6—616no—
243C3×C8—28no—
244C3⋊C8—68no—
245C2×C32—82no—
246C2×C32#53511yescharacteristic
247C2×C32C2×#13511yescharacteristic
248C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
249C3⋊D3—41no—
250C3⋊D3—82no—
251#41—364no—
252#41—364no—
253C2×Q8—21no—
254C2×Q8—92no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—92no—
258C2×D4—182no—
259C2×D4—182no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4C22×C3⋊D312yes—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—182no—
267C22×C4—182no—
268SD16—364no—
269D8—364no—
270C2×C8—92no—
271C2×C8C22×C3⋊D312yes—
272C4⋊C4—21no—
273C4⋊C4—181no—
274C4⋊C4—181no—
275C4⋊C4C22×C3⋊D312yes—
276C22⋊C4—182no—
277C22⋊C4—182no—
278C22⋊C4—182no—
279C22⋊C4—182no—
280C42—91no—
281C42—91no—
282C42—91no—
283C42C22×C3⋊D311yescharacteristic
284C22×C3—48no—
285C22×C3—48no—
286C22×C3—48no—
287C22×C3C2×D3×D414yes—
288C2×D3—64no—
289C2×D3—64no—
290C2×D3—64no—
291C2×D3—128no—
292C2×D3—128no—
293C2×D3—128no—
294C3×C4—48no—
295C3×C4#91118yes—
296C3×C4#91618yes—
297C3×C4#100918yes—
298Dic3—64no—
299Dic3—64no—
300Dic3—64no—
301Dic3—128no—
302C32#320711yescharacteristic, complemented, Sylow
303C23—22no—
304C23—91no—
305C23—182no—
306Q8—42no—
307Q8—184no—
308D4—24no—
309D4—42no—
310D4—42no—
311D4—184no—
312D4—364no—
313D4—364no—
314D4—362no—
315D4—362no—
316C2×C4—22no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—182no—
321C2×C4—182no—
322C2×C4—182no—
323C2×C4—182no—
324C2×C4—364no—
325C2×C4—364no—
326C2×C4D4×C3⋊D311yescharacteristic
327C2×C4D4×C3⋊D311yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—22no—
330C8—182no—
331C2×C3—88no—
332C2×C3#567414yes—
333C2×C3C2×#91114yes—
334C2×C3C2×#91614yes—
335D3—124no—
336D3—248no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22—362no—
344C22—362no—
345C22—362no—
346C22C2×D4×C3⋊D311yescharacteristic
347C4—42no—
348C4—181no—
349C4—181no—
350C4—181no—
351C4—362no—
352C4#6412012yes—
353C4#6412512yes—
354C4#6436612yes—
355C3#8156714yescomplemented
356C2—82no—
357C2—361no—
358C2—722no—
359C2#1059614511yescharacteristic
360C2C2×#6412011yescharacteristic
361C2C2×#6412511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#486C2
socleC22×C32C22×D4
hypercenter#486C3⋊D3
hypocenterC32#3207
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. #10596187C2semidirect
3. C32×#486C2semidirect
4. #10592792C2semidirect
5. #10592772C2semidirect
6. #10592486C2semidirect
7. #10592480C2semidirect
8. #10592392C2semidirect
9. #10592384C2semidirect
38. C3×#486D3semidirect
137. #486C3⋊D3semidirect
302. C32#3207semidirect
355. C3#81567semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105961872
C32×#4862
#105927922
#105927722
#105924862
#105924802
#105923922
#105923842
#815673