Finite Group Databasebeta

← #11899621

Subgroups — #11899621

Order 1152.

1092 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#135C211yesmaximal, characteristic, complemented
2C2×#64121C211yesmaximal, characteristic, complemented
3C32×#509C211yesmaximal, characteristic, complemented
4#10592894C211yesmaximal, characteristic, complemented
5#10592846C211yesmaximal, characteristic, complemented
6#10592615C212yesmaximal, complemented
7#10592614C212yesmaximal, complemented
8#10592611C212yesmaximal, complemented
9#10592610C212yesmaximal, complemented
10#10592608C211yesmaximal, characteristic, complemented
11C3⋊D3×M32C211yesmaximal, characteristic, complemented
12#82035—34nomaximal
13#41×C3⋊D3—21no—
14C2×#3830—21no—
15C32×#135C2211yescharacteristic
16C2×C32×D8C2211yescharacteristic, complemented
17#64159—21no—
18C2×#3754—21no—
19#64128C2211yescharacteristic, complemented
20Q16×C3⋊D3C2211yescharacteristic, complemented
21#64125—21no—
22SD16×C3⋊D3—21no—
23#64121—21no—
24#64121—21no—
25#64121C2212yes—
26#64121C2211yescharacteristic, complemented
27#64121C2212yescomplemented
28D8×C3⋊D3C2211yescharacteristic, complemented
29C2×#3746C2211yescharacteristic, complemented
30#64113C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic
32C32×SD32C2212yescomplemented
33C32×D16C2212yescomplemented
34C32×M32C2211yescharacteristic, complemented
35#63656C2212yescomplemented
36#63654C2212yescomplemented
37#63654C2212yescomplemented
38#63653C2212yescomplemented
39#63639C2211yescharacteristic, complemented
40#63628C2212yescomplemented
41#63627C2212yescomplemented
42#63625C2212yescomplemented
43C16×C3⋊D3C2212yescomplemented
44D3×#135—34no—
45C2×#912—34no—
46C3×#509D314yescomplemented
47#5195—34no—
48#5147—34no—
49#4916—38no—
50#4915—38no—
51#4912—38no—
52#4911—38no—
53#4909—34no—
54D3×M32—34no—
55C32×#41—21no—
56C2×C32×D4—21no—
57C2×#638—41no—
58C22×C3⋊Dic3—41no—
59#3832—21no—
60Q8×C3⋊D3—21no—
61#3830—22no—
62#3830—22no—
63#3830—21no—
64#3830—41no—
65#3830—41no—
66#3830—41no—
67D4×C3⋊D3—21no—
68D4×C3⋊D3—41no—
69#3828—21no—
70#3828—41no—
71C2×C4×C3⋊D3—41no—
72C2×C4×C3⋊D3D411yescharacteristic
73C2×#634—21no—
74C32×Q16C2311yescharacteristic
75C32×SD16—21no—
76C32×D8—21no—
77C32×D8C2311yescharacteristic
78C32×D8C2312yes—
79C2×C32×C8C2311yescharacteristic
80#3756—21no—
81#3755—21no—
82#3754—22no—
83#3754—22no—
84#3754—21no—
85#3753—21no—
86C2×C3⋊(C3⋊C8)D411yescharacteristic
87#3746—21no—
88#3746C2311yescharacteristic
89#3746C2312yes—
90#3745C2311yescharacteristic
91#3744—21no—
92C8×C3⋊D3D411yescharacteristic
93C8×C3⋊D3D411yescharacteristic
94C8×C3⋊D3C2311yescharacteristic
95C8×C3⋊D3C2311yescharacteristic
96C32×C16C2312yes—
97C3⋊(C3⋊C16)C2312yes—
98#3414—91noSylow
99D3×#41—64no—
100C2×#237—64no—
101C3×#135C2×D314yes—
102C2×C3×D8C2×D314yescomplemented
103#950—64no—
104C2×#214—64no—
105#919—34no—
106D3×Q16—34no—
107#916—64no—
108D3×SD16—64no—
109#912—38no—
110#912—34no—
111#912—38no—
112#912—64no—
113#912—64no—
114D3×D8—34no—
115C2×Dic12—34no—
116#904—34no—
117C2×D3×C8—34no—
118C3×SD32C2×D318yescomplemented
119C3×D16C2×D318yescomplemented
120C3×M32C2×D314yescomplemented
121#829—38no—
122#827—38no—
123#827—38no—
124#826—38no—
125#812—34no—
126Dic24—38no—
127#800—38no—
128#798—38no—
129D3×C16—38no—
130C23×C32—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3D811yescharacteristic
133C32×Q8—21no—
134C32×D4—21no—
135C32×D4—22no—
136C32×D4—41no—
137C32×D4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140#638—41no—
141#638—41no—
142#638—42no—
143#638—42no—
144#638—41no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—42no—
148C2×C3⋊Dic3—42no—
149C2×C3⋊Dic3D811yescharacteristic
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)—41no—
152C4×C3⋊D3—41no—
153C4×C3⋊D3—41no—
154C4×C3⋊D3—41no—
155C4×C3⋊D3D811yescharacteristic
156C4×C3⋊D3D811yescharacteristic
157C4×C3⋊D3C2×D411yescharacteristic
158C4×C3⋊D3C2×D411yescharacteristic
159#634—21no—
160#634—22no—
161#634—41no—
162#634—41no—
163C32×C8C2×D411yescharacteristic
164C32×C8C2411yescharacteristic
165C3⋊(C3⋊C8)C2×D411yescharacteristic
166C3⋊(C3⋊C8)C2×D411yescharacteristic
167C2×#135—91no—
168C2×#135—91no—
169#510—91no—
170#510—92no—
171#510—91no—
172#509—91no—
173#509—92no—
174#509C3⋊D311yescharacteristic, complemented
175#508—92no—
176#508—92no—
177C2×M32—91no—
178C3×#41—24no—
179C2×C3×D4—24no—
180C2×#67—124no—
181C22×Dic3—124no—
182#239—64no—
183D3×Q8—64no—
184#237—68no—
185#237—68no—
186#237—64no—
187#237—124no—
188#237—124no—
189#237—124no—
190D3×D4—64no—
191D3×D4—124no—
192#235—64no—
193#235—124no—
194C2×C4×D3—34no—
195C2×C4×D3—124no—
196C2×Dic6—64no—
197C3×Q16C22×D314yes—
198C3×SD16—24no—
199C3×D8—24no—
200C3×D8C22×D318yes—
201C3×D8C22×D314yes—
202C2×C3×C8C22×D314yes—
203#216—64no—
204#215—64no—
205#214—68no—
206#214—68no—
207#214—64no—
208#213—64no—
209C2×C3⋊C8—34no—
210Dic12—38no—
211Dic12—34no—
212Dic12—64no—
213D24—34no—
214#204—64no—
215D3×C8—34no—
216D3×C8—34no—
217D3×C8—34no—
218D3×C8—34no—
219C3×C16C22×D318yes—
220C3⋊C16—38no—
221C22×C32—42no—
222C22×C32—41no—
223C22×C32—82no—
224C22×C32C2×D811yescharacteristic
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—82no—
228C2×C3⋊D3C2×D811yescharacteristic
229C2×C3⋊D3C2×D811yescharacteristic
230C32×C4—41no—
231C32×C4C2×D811yescharacteristic
232C32×C4C22×D411yescharacteristic
233C3⋊Dic3—41no—
234C3⋊Dic3—42no—
235C3⋊Dic3C2×D811yescharacteristic
236C3⋊Dic3C2×D811yescharacteristic
237C2×#41—181no—
238C2×#41—181no—
239#135—91no—
240#135—92no—
241#135—91no—
242#135—92no—
243#135—91no—
244#135—181no—
245#135—181no—
246#135—181no—
247#135—181no—
248#135C2×C3⋊D311yescharacteristic
249C2×Q16—91no—
250C2×Q16—91no—
251C2×SD16—181no—
252C2×SD16—181no—
253C2×D8—91no—
254C2×D8C2×C3⋊D311yescharacteristic, complemented
255C22×C8—91no—
256Q32—92no—
257Q32—92no—
258SD32—92no—
259SD32—92no—
260SD32—92no—
261SD32C2×C3⋊D312yescomplemented
262D16—92no—
263D16C2×C3⋊D312yescomplemented
264M32—91no—
265M32—92no—
266M32C2×C3⋊D311yescharacteristic, complemented
267C2×C16—92no—
268C23×C3—44no—
269C22×D3—34no—
270C22×D3—124no—
271C3×Q8—24no—
272C3×D4—24no—
273C3×D4—28no—
274C3×D4—44no—
275C3×D4—44no—
276C2×C3×C4—44no—
277C2×C3×C4D3×D414yes—
278#67—124no—
279#67—124no—
280#67—128no—
281#67—128no—
282#67—124no—
283C2×Dic3—34no—
284C2×Dic3—124no—
285C2×Dic3—128no—
286C2×Dic3—128no—
287C2×Dic3—124no—
288D12—64no—
289D12—124no—
290C4×D3—34no—
291C4×D3—34no—
292C4×D3—34no—
293C4×D3—34no—
294C4×D3—124no—
295C4×D3—124no—
296C4×D3—124no—
297Dic6—64no—
298Dic6—68no—
299Dic6—124no—
300Dic6—124no—
301C3×C8D3×D414yes—
302C3×C8C23×D314yes—
303C3⋊C8—34no—
304C3⋊C8—34no—
305C2×C32—21no—
306C2×C32—81no—
307C2×C32—82no—
308C2×C32C22×D811yescharacteristic
309C3⋊D3—21no—
310C3⋊D3—21no—
311C3⋊D3—81no—
312#41—21no—
313#41—182no—
314#41—182no—
315#41—181no—
316#41—181no—
317#41—181no—
318#41—361no—
319#41—361no—
320#41—361no—
321#41—361no—
322C2×Q8—181no—
323C2×Q8—181no—
324C2×D4—21no—
325C2×D4—181no—
326C2×D4—361no—
327C2×D4—361no—
328C22×C4—91no—
329C22×C4—361no—
330C22×C4—361no—
331Q16—91no—
332Q16—92no—
333Q16—181no—
334Q16—181no—
335Q16C22×C3⋊D311yescharacteristic
336SD16—21no—
337SD16—182no—
338SD16—182no—
339SD16—181no—
340SD16—181no—
341SD16—181no—
342D8—21no—
343D8—91no—
344D8—181no—
345D8C22×C3⋊D312yes—
346D8C22×C3⋊D311yescharacteristic
347C2×C8—91no—
348C2×C8—91no—
349C2×C8—91no—
350C2×C8—91no—
351C2×C8—91no—
352C2×C8C22×C3⋊D311yescharacteristic
353C16—92no—
354C16C22×C3⋊D312yes—
355C22×C3—48no—
356C22×C3—44no—
357C22×C3—88no—
358C22×C3D3×D814yes—
359C2×D3—34no—
360C2×D3—34no—
361C2×D3—124no—
362C2×D3—124no—
363C2×D3—248no—
364C3×C4—44no—
365C3×C4D3×D814yes—
366C3×C4C2×D3×D414yes—
367Dic3—34no—
368Dic3—34no—
369Dic3—124no—
370Dic3—128no—
371C32#341411yescharacteristic, complemented, Sylow
372C23—41no—
373C23—91no—
374C23—361no—
375Q8—21no—
376Q8—182no—
377Q8—181no—
378Q8—361no—
379Q8—361no—
380D4—22no—
381D4—21no—
382D4—41no—
383D4—41no—
384D4—181no—
385D4—361no—
386D4—361no—
387D4—361no—
388D4—362no—
389D4—362no—
390D4—361no—
391C2×C4—41no—
392C2×C4—91no—
393C2×C4—91no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4—362no—
401C2×C4—362no—
402C2×C4—361no—
403C2×C4—361no—
404C2×C4D4×C3⋊D311yescharacteristic
405C8—91no—
406C8—91no—
407C8D4×C3⋊D311yescharacteristic
408C8C23×C3⋊D311yescharacteristic
409C2×C3—24no—
410C2×C3—84no—
411C2×C3—88no—
412C2×C3C2×D3×D814yes—
413D3—64no—
414D3—64no—
415D3—244no—
416C22—41no—
417C22—42no—
418C22—82no—
419C22—91no—
420C22—91no—
421C22—361no—
422C22—361no—
423C22—722no—
424C22D8×C3⋊D311yescharacteristic
425C4—41no—
426C4—91no—
427C4—91no—
428C4—361no—
429C4—362no—
430C4D8×C3⋊D311yescharacteristic
431C4C2×D4×C3⋊D311yescharacteristic
432C3#8203514yescomplemented
433C2—21no—
434C2—82no—
435C2—81no—
436C2—181no—
437C2—181no—
438C2—721no—
439C2C2×D8×C3⋊D311yescharacteristic
subgroupG/H
centerC2C2×D8×C3⋊D3
commutator, cosocleC32×C8C24
FrattiniC8C23×C3⋊D3
FittingC32×#509C2
socleC2×C32C22×D8
hypercenter#509C3⋊D3
hypocenterC32#3414
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#135C2semidirect
2. C2×#64121C2semidirect
3. C32×#509C2semidirect
4. #10592894C2semidirect
5. #10592846C2semidirect
6. #10592615C2semidirect
7. #10592614C2semidirect
8. #10592611C2semidirect
9. #10592610C2semidirect
10. #10592608C2semidirect
11. C3⋊D3×M32C2semidirect
16. C2×C32×D8C22semidirect
19. #64128C22semidirect
20. Q16×C3⋊D3C22semidirect
26. #64121C22semidirect
27. #64121C22semidirect
28. D8×C3⋊D3C22semidirect
29. C2×#3746C22semidirect
32. C32×SD32C22semidirect
33. C32×D16C22semidirect
34. C32×M32C22semidirect
35. #63656C22semidirect
36. #63654C22semidirect
37. #63654C22semidirect
38. #63653C22semidirect
39. #63639C22semidirect
40. #63628C22semidirect
41. #63627C22semidirect
42. #63625C22semidirect
43. C16×C3⋊D3C22semidirect
46. C3×#509D3semidirect
102. C2×C3×D8C2×D3semidirect
118. C3×SD32C2×D3semidirect
119. C3×D16C2×D3semidirect
120. C3×M32C2×D3semidirect
174. #509C3⋊D3semidirect
254. C2×D8C2×C3⋊D3semidirect
261. SD32C2×C3⋊D3semidirect
263. D16C2×C3⋊D3semidirect
266. M32C2×C3⋊D3semidirect
371. C32#3414semidirect
432. C3#82035semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1352
C2×#641212
C32×#5092
#105928942
#105928462
#105926152
#105926142
#105926112
#105926102
#105926082
C3⋊D3×M322
#820353