Finite Group Databasebeta

← #11870852

Subgroups — #11870852

Order 1152.

1362 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10596095C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic
5#10592864C212yesmaximal, complemented
6SD16×C3⋊Dic3C212yesmaximal, complemented
7#10592743C211yesmaximal, characteristic, complemented
8#10592462C212yesmaximal, complemented
9#10592455C212yesmaximal, complemented
10#10592434C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#80133—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3—21no—
15C2×C32×SD16C2212yes—
16C32×C22⋊Q8C2211yescharacteristic
17C2×#3757—21no—
18#64156C2211yescharacteristic, complemented
19Q8×C3⋊Dic3C2211yescharacteristic, complemented
20D4×C3⋊Dic3—21no—
21D4×C3⋊Dic3—21no—
22D4×C3⋊Dic3C2212yes—
23D4×C3⋊Dic3C2212yes—
24C2×#3753C2212yes—
25#64139C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28#64107—21no—
29#64102C2211yescharacteristic, complemented
30#64101—21no—
31#64099C2211yescharacteristic, complemented
32#64095—21no—
33#64090—21no—
34C32×#102C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63662C2212yescomplemented
37#63659C2212yes—
38#63657C2211yescharacteristic
39#63648C2212yescomplemented
40#63644C2212yescomplemented
41#63641C2212yescomplemented
42C8×C3⋊Dic3C2212yescomplemented
43#63634C2212yescomplemented
44C2×D4×Dic3—34no—
45#5624—34no—
46C3×#450D314yescomplemented
47#5217—34no—
48#5165—38no—
49Dic3×SD16—38no—
50#5044—34no—
51#4763—38no—
52#4756—38no—
53#4735—34no—
54#4718—34no—
55C24×C32—21no—
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—24no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3—44no—
66C22×C3⋊Dic3D411yescharacteristic
67C22×C3⋊Dic3D411yescharacteristic
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C32×SD16—24no—
71C2×C32×C8C2312yes—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75#3757—22no—
76#3757—22no—
77#3753—24no—
78#3752—21no—
79#3752—21no—
80#3752—21no—
81#3752—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2312yes—
94#3105—91noSylow
95C22×C3×D4C2×D314yes—
96C23×Dic3—64no—
97C2×C3×SD16C2×D318yes—
98C3×C22⋊Q8C2×D314yes—
99C2×#217—64no—
100#947—34no—
101Q8×Dic3—34no—
102D4×Dic3—38no—
103D4×Dic3—38no—
104D4×Dic3—64no—
105D4×Dic3—64no—
106C2×#213—38no—
107#930—34no—
108C2×C4⋊Dic3—34no—
109C2×C4×Dic3—34no—
110#898—64no—
111#893—34no—
112#892—64no—
113#890—34no—
114#886—64no—
115#67⋊C4—64no—
116C3×#102C2×D318yes—
117C3×C22⋊C8C2×D314yes—
118#835—38no—
119#832—38no—
120#830—34no—
121#821—38no—
122#817—38no—
123Dic3⋊C8—38no—
124C8×Dic3—38no—
125#807—38no—
126C23×C32—24no—
127C23×C32—22no—
128C23×C32—42no—
129C23×C32—42no—
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—21no—
132C32×Q8—22no—
133C32×D4—24no—
134C32×D4—22no—
135C32×D4#4114yes—
136C2×C32×C4—22no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2411yescharacteristic
141#638—42no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—44no—
147C2×C3⋊Dic3—42no—
148C2×C3⋊Dic3—44no—
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C4⋊(C3⋊D3)—22no—
154C4×C3⋊D3—42no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157#529—91no—
158C2×C4×D4—91no—
159#484—91no—
160#481—91no—
161#478—92no—
162#463—92no—
163#450C3⋊D311yescharacteristic, complemented
164#447—91no—
165C4×SD16—92no—
166C4×D8—92no—
167#431—91no—
168C24×C3—24no—
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—216no—
171C2×C3×D4—24no—
172C2×C3×D4C22×D318yes—
173C22×C3×C4C22×D314yes—
174C2×#67—64no—
175C22×Dic3—34no—
176C22×Dic3—34no—
177C22×Dic3—68no—
178C22×Dic3—68no—
179C22×Dic3—64no—
180C22×Dic3—1216no—
181C2×D12—34no—
182C2×C4×D3—64no—
183C3×SD16—216no—
184C2×C3×C8C22×D318yes—
185C3×C4⋊C4—24no—
186C3×C4⋊C4C22×D314yes—
187C3×C22⋊C4—24no—
188#217—68no—
189#217—68no—
190#213—616no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3—38no—
196C4⋊Dic3—34no—
197C4⋊Dic3—64no—
198C4⋊Dic3—64no—
199C4⋊Dic3—64no—
200Dic3⋊C4—64no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—64no—
206C2×C3⋊C8—38no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—24no—
210C22×C32—48no—
211C22×C32—42no—
212C22×C32—42no—
213C22×C32#13512yes—
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C32×C4C2×#4112yes—
222C3⋊Dic3—21no—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—41no—
226C3⋊Dic3—42no—
227C3⋊Dic3AGL(1,ℤ/8)12yes—
228C22×D4C2×C3⋊D311yescharacteristic
229C23×C4—181no—
230C2×SD16C2×C3⋊D312yes—
231C2×D8—92no—
232#126—181no—
233#125—91no—
234#124—91no—
235#123—181no—
236C22⋊Q8C2×C3⋊D311yescharacteristic
237#121—91no—
238C4×Q8—91no—
239C4×D4—92no—
240C4×D4—92no—
241C4×D4—91no—
242C4×D4—181no—
243C4×D4—181no—
244C4×D4—181no—
245#117—181no—
246C2×C4⋊C4—91no—
247C2×C22⋊C4—181no—
248C2×C42—91no—
249#107—92no—
250#106—92no—
251C4⋊C8—92no—
252#103—92no—
253#102—92no—
254#102—92no—
255#102C2×C3⋊D312yes—
256C22⋊C8—91no—
257C22⋊C8C2×C3⋊D311yescharacteristic
258C4×C8—92no—
259C23×C3—216no—
260C23×C3—28no—
261C23×C3—48no—
262C23×C3—48no—
263C23×C3D3×D414yes—
264C22×D3—64no—
265C3×Q8—28no—
266C3×D4—216no—
267C3×D4—28no—
268C3×D4#237116yes—
269C2×C3×C4—28no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4D3×D414yes—
273C2×C3×C4C23×D314yes—
274#67—128no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—68no—
280C2×Dic3—68no—
281C2×Dic3—64no—
282C2×Dic3—68no—
283C2×Dic3—1216no—
284C2×Dic3—1216no—
285C2×Dic3—128no—
286D12—68no—
287C4×D3—128no—
288C3×C8—28no—
289C3⋊C8—68no—
290C2×C32—22no—
291C2×C32—44no—
292C2×C32#52511yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
295C3⋊D3—81no—
296C24—21no—
297C2×Q8C22×C3⋊D311yescharacteristic
298C2×D4—24no—
299C2×D4—21no—
300C2×D4—91no—
301C2×D4—181no—
302C2×D4C22×C3⋊D312yes—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—181no—
306C22×C4—182no—
307C22×C4—182no—
308C22×C4—181no—
309C22×C4—364no—
310C22×C4C22×C3⋊D311yescharacteristic
311SD16—24no—
312D8—184no—
313C2×C8—92no—
314C2×C8C22×C3⋊D312yes—
315C4⋊C4—21no—
316C4⋊C4—91no—
317C4⋊C4—92no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4C22×C3⋊D311yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—182no—
328C22⋊C4—182no—
329C22⋊C4—181no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—91no—
334C42—181no—
335C22×C3—24no—
336C22×C3—24no—
337C22×C3—216no—
338C22×C3—432no—
339C22×C3—48no—
340C22×C3—48no—
341C22×C3#91618yes—
342C22×C3C2×D3×D414yes—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C3×C4—24no—
347C3×C4—44no—
348C3×C4—44no—
349C3×C4C2×#23718yes—
350Dic3—38no—
351Dic3—64no—
352Dic3—64no—
353Dic3—64no—
354Dic3—124no—
355Dic3—128no—
356C32#310511yescharacteristic, complemented, Sylow
357C23—24no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23—181no—
362C23D4×C3⋊D311yescharacteristic
363Q8—22no—
364D4—24no—
365D4—22no—
366D4—182no—
367D4—362no—
368D4#383014yes—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—91no—
373C2×C4—91no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—181no—
379C2×C4—182no—
380C2×C4—362no—
381C2×C4—364no—
382C2×C4—364no—
383C2×C4—362no—
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4C23×C3⋊D311yescharacteristic
386C8—22no—
387C8—182no—
388C2×C3—28no—
389C2×C3—416no—
390C2×C3#558614yes—
391C2×C3C2×#91614yes—
392C2×C3D3×AGL(1,ℤ/8)14yes—
393D3—244no—
394C22—21no—
395C22—21no—
396C22—24no—
397C22—48no—
398C22—42no—
399C22—42no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6412512yes—
404C22C2×D4×C3⋊D311yescharacteristic
405C4—21no—
406C4—41no—
407C4—41no—
408C4—92no—
409C4—181no—
410C4—181no—
411C4—181no—
412C4—361no—
413C4—362no—
414C4C2×#383012yes—
415C3#8013314yescomplemented
416C2—22no—
417C2—44no—
418C2—721no—
419C2#1059605711yescharacteristic
420C2C2×#6412511yescharacteristic
421C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radical#10592916C2
hypercenter#450C3⋊D3
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. #10596095C2semidirect
3. C32×#450C2semidirect
5. #10592864C2semidirect
6. SD16×C3⋊Dic3C2semidirect
7. #10592743C2semidirect
8. #10592462C2semidirect
9. #10592455C2semidirect
10. #10592434C2semidirect
11. #10592417C2semidirect
18. #64156C22semidirect
19. Q8×C3⋊Dic3C22semidirect
29. #64102C22semidirect
31. #64099C22semidirect
36. #63662C22semidirect
39. #63648C22semidirect
40. #63644C22semidirect
41. #63641C22semidirect
42. C8×C3⋊Dic3C22semidirect
43. #63634C22semidirect
46. C3×#450D3semidirect
163. #450C3⋊D3semidirect
356. C32#3105semidirect
415. C3#80133semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
#105960952
C32×#4502
#105929162
#105928642
SD16×C3⋊Dic32
#105927432
#105924622
#105924552
#105924342
#105924172
#801333