Finite Group Databasebeta

← #11895728

Subgroups — #11895728

Order 1152.

1188 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#10596050C211yesmaximal, characteristic, complemented
2#10596048C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4#10592546C212yesmaximal, complemented
5#10592542C211yesmaximal, characteristic, complemented
6#10592542C212yesmaximal, complemented
7#10592541C211yesmaximal, characteristic, complemented
8#10592412C212yesmaximal, complemented
9#10592410C212yesmaximal, complemented
10#10592393C211yesmaximal, characteristic, complemented
11C4×#3745C211yesmaximal, characteristic, complemented
12#79969—34nomaximal
13C2×#3832—21no—
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16C2×#3745C2211yescharacteristic
17C2×#3745C2212yes—
18#64105—22no—
19#64104—21no—
20#64104—22no—
21C4⋊C4×C3⋊D3—21no—
22#64083C2211yescharacteristic
23#64083C2212yes—
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2212yes—
27C4×C4⋊(C3⋊D3)C2212yes—
28#64079C2212yes—
29#64078C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31C32×C4⋊C8C2212yes—
32C32×#97C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63648C2212yes—
35#63648C2212yes—
36#63648C2212yes—
37#63648C2211yescharacteristic
38#63648C2211yescharacteristic
39#63648C2212yes—
40#63645C2211yescharacteristic
41#63644C2212yes—
42#5579—34no—
43#5577—34no—
44C3×#446D314yescomplemented
45#4847—38no—
46#4843—38no—
47#4843—34no—
48#4842—34no—
49#4713—38no—
50#4711—38no—
51#4694—34no—
52C4×D24—34no—
53C2×C32×Q8D411yescharacteristic
54#3832—44no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2311yescharacteristic
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4⋊(C3⋊D3)C2311yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—22no—
66C2×#634—21no—
67C2×C32×C8C2312yes—
68C2×C32×C8C2311yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C32×C4⋊C4D411yescharacteristic
71C32×C4⋊C4D412yes—
72C32×C42C2311yescharacteristic
73C32×C42C2312yes—
74#3752—22no—
75#3752—21no—
76#3752—21no—
77#3752—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—22no—
83#3750—22no—
84#3745—22no—
85#3745—24no—
86#3366—91noSylow
87C2×#239—64no—
88C3×C4×Q8C2×D314yes—
89#946—64no—
90C2×D24—34no—
91C2×D24—38no—
92#896—68no—
93#895—64no—
94#895—68no—
95D3×C4⋊C4—64no—
96#874—34no—
97#874—38no—
98C4×D12—34no—
99C4×D12—34no—
100C4×D12—38no—
101C4×D12—38no—
102#870—38no—
103#869—34no—
104C3×C4⋊C8C2×D314yes—
105C3×C4⋊C8C2×D318yes—
106C3×#97C2×D318yes—
107C3×C4×C8C2×D314yes—
108#821—34no—
109#821—34no—
110#821—38no—
111#821—38no—
112#821—38no—
113#821—38no—
114#818—34no—
115#817—38no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—21no—
119C32×Q8—22no—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—44no—
134C4⋊(C3⋊D3)—42no—
135C4⋊(C3⋊D3)—81no—
136C4⋊(C3⋊D3)—82no—
137C4⋊(C3⋊D3)#4112yescomplemented
138C4×C3⋊D3—44no—
139C4×C3⋊D3—42no—
140C4×C3⋊D3—42no—
141C4×C3⋊D3—82no—
142#634—81no—
143C32×C8—22no—
144C32×C8—21no—
145C32×C8—21no—
146#554—91no—
147#550—91no—
148#490—92no—
149#486—91no—
150#478—92no—
151#476—91no—
152#459—92no—
153#459—91no—
154#446C3⋊D311yescharacteristic, complemented
155#442—92no—
156C4×D8—91no—
157C2×C3×Q8D1214yes—
158#239—1216no—
159C2×D12—34no—
160C2×D12—34no—
161C2×D12—38no—
162C2×D12—68no—
163C2×D12—64no—
164C2×D12—68no—
165C2×D12—64no—
166C2×C4×D3—64no—
167C2×C4×D3—68no—
168C2×C4×D3—64no—
169C2×C4×D3—68no—
170C2×Dic6—64no—
171C2×C3×C8C22×D318yes—
172C2×C3×C8C22×D314yes—
173C2×C3×C8C22×D314yes—
174C3×C4⋊C4D1214yes—
175C3×C4⋊C4D1218yes—
176C3×C42C22×D314yes—
177C3×C42C22×D318yes—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—64no—
180(C2×D3)⋊C4—64no—
181(C2×D3)⋊C4—68no—
182C4⋊Dic3—34no—
183C4⋊Dic3—38no—
184C4⋊Dic3—34no—
185C4⋊Dic3—64no—
186Dic3⋊C4—68no—
187Dic3⋊C4—68no—
188D24—68no—
189D24—616no—
190C22×C32C22×D411yescharacteristic
191C2×C3⋊D3—22no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—41no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—41no—
200C32×C4—22no—
201C32×C4—21no—
202C32×C4—22no—
203C32×C4AGL(1,ℤ/8)12yes—
204C32×C4C2×#4111yescharacteristic
205C32×C42−1+411yescharacteristic
206C3⋊Dic3—41no—
207C3⋊Dic3—41no—
208C3⋊Dic3—42no—
209C2×#41—181no—
210C2×D8—91no—
211C2×D8—92no—
212C4⋊Q8—91no—
213#127—91no—
214#127—92no—
215#125—92no—
216C22⋊Q8—181no—
217C22⋊Q8—182no—
218#121—181no—
219#121—182no—
220C4×Q8C2×C3⋊D311yescharacteristic
221C4×D4—91no—
222C4×D4—92no—
223C4×D4—91no—
224C4×D4—92no—
225C2×C4⋊C4—181no—
226#107—91no—
227#106—92no—
228C4⋊C8C2×C3⋊D311yescharacteristic
229C4⋊C8C2×C3⋊D312yes—
230#102—91no—
231#102—91no—
232#102—92no—
233#102—92no—
234#102—92no—
235#102—92no—
236#97C2×C3⋊D312yes—
237C4×C8C2×C3⋊D311yescharacteristic
238C22×D3—64no—
239C22×D3—68no—
240C22×D3—64no—
241C3×Q8—28no—
242C2×C3×C4C2×D1218yes—
243C2×C3×C4C2×D1218yes—
244C2×C3×C4C2×D1214yes—
245C2×C3×C4C2×D1214yes—
246C2×C3×C4C23×D314yes—
247C2×Dic3—64no—
248C2×Dic3—68no—
249C2×Dic3—64no—
250D12—38no—
251D12—64no—
252D12—64no—
253D12—68no—
254D12—64no—
255D12—68no—
256D12—1216no—
257D12—128no—
258D12—244no—
259D12—248no—
260C4×D3—1216no—
261C4×D3—128no—
262C4×D3—128no—
263C4×D3—248no—
264Dic6—244no—
265C3×C8—24no—
266C3×C8—28no—
267C3×C8—24no—
268C2×C32#54811yescharacteristic
269C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
270C2×C32#57611yescharacteristic
271C3⋊D3—42no—
272C3⋊D3—82no—
273C3⋊D3—81no—
274#41—364no—
275C2×Q8—181no—
276C2×Q8C4⋊(C3⋊D3)11yescharacteristic
277C2×D4—91no—
278C2×D4—91no—
279C2×D4—92no—
280C2×D4—182no—
281C2×D4—181no—
282C2×D4—181no—
283C2×D4—182no—
284C22×C4—181no—
285C22×C4—182no—
286C22×C4—181no—
287C22×C4—182no—
288D8—182no—
289D8—184no—
290C2×C8C22×C3⋊D311yescharacteristic
291C2×C8C22×C3⋊D311yescharacteristic
292C2×C8C22×C3⋊D312yes—
293C4⋊C4—92no—
294C4⋊C4—91no—
295C4⋊C4—91no—
296C4⋊C4—182no—
297C4⋊C4—181no—
298C4⋊C4—182no—
299C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
300C4⋊C4C4⋊(C3⋊D3)12yes—
301C22⋊C4—181no—
302C22⋊C4—182no—
303C22⋊C4—181no—
304C22⋊C4—182no—
305C42C22×C3⋊D311yescharacteristic
306C42C22×C3⋊D312yes—
307C22×C3C22×D1214yes—
308C2×D3—68no—
309C2×D3—124no—
310C2×D3—124no—
311C2×D3—128no—
312C2×D3—124no—
313C2×D3—128no—
314C2×D3—124no—
315C2×D3—128no—
316C2×D3—124no—
317C3×C4—28no—
318C3×C4—24no—
319C3×C4—28no—
320C3×C4#90818yes—
321C3×C4#100714yes—
322C3×C4D3×#4114yes—
323Dic3—124no—
324Dic3—124no—
325Dic3—128no—
326C32#336611yescharacteristic, complemented, Sylow
327C23—181no—
328C23—182no—
329C23—181no—
330Q8—22no—
331Q8—721no—
332D4—92no—
333D4—181no—
334D4—181no—
335D4—182no—
336D4—181no—
337D4—182no—
338D4—364no—
339D4—362no—
340D4—722no—
341D4—721no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—182no—
345C2×C4—364no—
346C2×C4—362no—
347C2×C4—362no—
348C2×C4—722no—
349C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
350C2×C4C2×C4⋊(C3⋊D3)12yes—
351C2×C4C2×C4⋊(C3⋊D3)12yes—
352C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
353C2×C4C23×C3⋊D311yescharacteristic
354C8—21no—
355C8—21no—
356C8—22no—
357C2×C3#557614yes—
358C2×C3C2×#90814yes—
359C2×C3#575214yes—
360D3—128no—
361D3—248no—
362D3—244no—
363C22—182no—
364C22—361no—
365C22—361no—
366C22—362no—
367C22—361no—
368C22—361no—
369C22—362no—
370C22—362no—
371C22—361no—
372C22C22×C4⋊(C3⋊D3)11yescharacteristic
373C4—22no—
374C4—22no—
375C4—21no—
376C4—361no—
377C4—361no—
378C4—362no—
379C4#6411712yes—
380C4#6436411yescharacteristic
381C4#41×C3⋊D311yescharacteristic
382C3#7996914yescomplemented
383C2—362no—
384C2—722no—
385C2—721no—
386C2#1059604711yescharacteristic
387C2C2×#6411711yescharacteristic
388C2#1059622311yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#446C2
socleC22×C32C22×D4
hypercenter#446C3⋊D3
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #10596050C2semidirect
2. #10596048C2semidirect
3. C32×#446C2semidirect
4. #10592546C2semidirect
5. #10592542C2semidirect
6. #10592542C2semidirect
7. #10592541C2semidirect
8. #10592412C2semidirect
9. #10592410C2semidirect
10. #10592393C2semidirect
11. C4×#3745C2semidirect
44. C3×#446D3semidirect
137. C4⋊(C3⋊D3)#41semidirect
154. #446C3⋊D3semidirect
326. C32#3366semidirect
382. C3#79969semidirect

Maximal subgroups

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

subgroupindex
#105960502
#105960482
C32×#4462
#105925462
#105925422
#105925412
#105924122
#105924102
#105923932
C4×#37452
#799693