Finite Group Databasebeta

← #11870402

Subgroups — #11870402

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10596067C211yesmaximal, characteristic, complemented
3C32×#447C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic, complemented
5#10592849C212yesmaximal, complemented
6D8×C3⋊Dic3C212yesmaximal, complemented
7#10592732C211yesmaximal, characteristic, complemented
8#10592458C212yesmaximal, complemented
9#10592455C212yesmaximal, complemented
10#10592435C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#79988—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3—21no—
15C2×#3830—21no—
16C2×C32×D8C2212yes—
17C32×#121C2211yescharacteristic
18C2×#3757—21no—
19#64149C2211yescharacteristic, complemented
20#64148—21no—
21D4×C3⋊Dic3—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2212yes—
24D4×C3⋊Dic3C2212yes—
25D4×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3753C2212yes—
27#64139C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64102C2211yescharacteristic, complemented
31#64097C2211yescharacteristic, complemented
32#64094—21no—
33#64090—21no—
34C32×#102C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63659C2212yes—
37#63659C2212yescomplemented
38#63657C2211yescharacteristic
39#63648C2212yescomplemented
40#63645C2212yescomplemented
41#63641C2212yescomplemented
42C8×C3⋊Dic3C2212yescomplemented
43#63634C2212yescomplemented
44C2×D4×Dic3—34no—
45#5596—34no—
46C3×#447D314yescomplemented
47#5217—34no—
48#5150—38no—
49Dic3×D8—38no—
50#5033—34no—
51#4759—38no—
52#4756—38no—
53#4736—34no—
54#4718—34no—
55C24×C32—21no—
56C2×C32×D4—24no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C2×C32×D4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C2×#638—21no—
64C2×#638—21no—
65C22×C3⋊Dic3—21no—
66C22×C3⋊Dic3—21no—
67C22×C3⋊Dic3—22no—
68C22×C3⋊Dic3—22no—
69C22×C3⋊Dic3—44no—
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72#3830—44no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634—21no—
76C32×D8—24no—
77C2×C32×C8C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80#3757—21no—
81#3757—22no—
82#3757—22no—
83#3753—24no—
84#3752—21no—
85#3752—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2312yes—
89#3750—21no—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95#3100—91noSylow
96C22×C3×D4C2×D314yes—
97C23×Dic3—64no—
98C2×#237—64no—
99C2×C3×D8C2×D318yes—
100C3×#121C2×D314yes—
101C2×#217—64no—
102#940—34no—
103#939—64no—
104D4×Dic3—34no—
105D4×Dic3—38no—
106D4×Dic3—38no—
107D4×Dic3—64no—
108D4×Dic3—64no—
109C2×#213—38no—
110#930—34no—
111C2×C4⋊Dic3—34no—
112C2×C4×Dic3—34no—
113#893—34no—
114#888—34no—
115#885—64no—
116#67⋊C4—64no—
117C3×#102C2×D318yes—
118C3×C22⋊C8C2×D314yes—
119#832—38no—
120#832—38no—
121#830—34no—
122#821—38no—
123#818—38no—
124Dic3⋊C8—38no—
125C8×Dic3—38no—
126#807—38no—
127C23×C32—24no—
128C23×C32—22no—
129C23×C32—21no—
130C23×C32—42no—
131C23×C32—42no—
132C23×C32C2×D411yescharacteristic
133C22×C3⋊D3—21no—
134C32×D4—24no—
135C32×D4—22no—
136C32×D4—22no—
137C32×D4—42no—
138C32×D4#4114yescomplemented
139C2×C32×C4—22no—
140C2×C32×C4—21no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2411yescharacteristic
143#638—42no—
144#638—42no—
145#638—42no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—42no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3—44no—
152C2×C3⋊Dic3—44no—
153C2×C3⋊Dic3D814yescomplemented
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4⋊(C3⋊D3)—22no—
159C4×C3⋊D3—42no—
160#634—42no—
161C32×C8—22no—
162C3⋊(C3⋊C8)—22no—
163#532—91no—
164C2×C4×D4—91no—
165#480—91no—
166#480—91no—
167#474—92no—
168#459—92no—
169#447—91no—
170#447C3⋊D311yescharacteristic, complemented
171C4×D8—92no—
172C4×D8—92no—
173#431—91no—
174C24×C3—24no—
175C2×C3×D4—216no—
176C2×C3×D4—24no—
177C2×C3×D4—24no—
178C2×C3×D4C22×D314yes—
179C2×C3×D4C22×D318yes—
180C22×C3×C4C22×D314yes—
181C2×#67—64no—
182C2×#67—64no—
183C2×#67—64no—
184C22×Dic3—34no—
185C22×Dic3—34no—
186C22×Dic3—64no—
187C22×Dic3—68no—
188C22×Dic3—68no—
189C22×Dic3—64no—
190C22×Dic3—1216no—
191#237—1216no—
192C2×D12—34no—
193C2×C4×D3—64no—
194C2×Dic6—64no—
195C3×D8—216no—
196C2×C3×C8C22×D318yes—
197C3×C4⋊C4C22×D314yes—
198C3×C22⋊C4—24no—
199#217—64no—
200#217—68no—
201#217—68no—
202#213—616no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—38no—
206C4⋊Dic3—34no—
207C4⋊Dic3—64no—
208Dic3⋊C4—64no—
209C4×Dic3—34no—
210C4×Dic3—34no—
211C4×Dic3—34no—
212C4×Dic3—34no—
213C2×C3⋊C8—38no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—24no—
217C22×C32—48no—
218C22×C32—42no—
219C22×C32—42no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32C2×D812yes—
224C22×C32C22×D411yescharacteristic
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C32×C4—21no—
229C32×C4—41no—
230C32×C4C2×#4112yes—
231C3⋊Dic3—21no—
232C3⋊Dic3—21no—
233C3⋊Dic3—41no—
234C3⋊Dic3—42no—
235C3⋊Dic3C2×D812yes—
236C3⋊Dic3C2×D812yes—
237C2×#41—181no—
238C22×D4C2×C3⋊D311yescharacteristic
239C23×C4—181no—
240C2×D8—92no—
241C2×D8C2×C3⋊D312yes—
242C4⋊Q8—91no—
243#127—91no—
244#124—181no—
245#121—91no—
246#121—181no—
247#121C2×C3⋊D311yescharacteristic
248C4×D4—92no—
249C4×D4—92no—
250C4×D4—91no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254C4×D4—181no—
255C2×C4⋊C4—91no—
256C2×C22⋊C4—181no—
257C2×C42—91no—
258#107—92no—
259#107—92no—
260C4⋊C8—92no—
261#102—92no—
262#102—92no—
263#102—92no—
264#102C2×C3⋊D312yes—
265C22⋊C8—91no—
266C22⋊C8C2×C3⋊D311yescharacteristic
267C4×C8—92no—
268C23×C3—216no—
269C23×C3—28no—
270C23×C3—24no—
271C23×C3—48no—
272C23×C3—48no—
273C23×C3D3×D414yes—
274C22×D3—64no—
275C3×D4—216no—
276C3×D4—28no—
277C3×D4—28no—
278C3×D4—48no—
279C3×D4#237116yescomplemented
280C2×C3×C4—28no—
281C2×C3×C4—24no—
282C2×C3×C4D3×D414yes—
283C2×C3×C4C23×D314yes—
284#67—128no—
285#67—128no—
286#67—128no—
287C2×Dic3—316no—
288C2×Dic3—34no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—34no—
292C2×Dic3—64no—
293C2×Dic3—68no—
294C2×Dic3—128no—
295C2×Dic3—1216no—
296C2×Dic3—1216no—
297C2×Dic3—124no—
298C2×Dic3—128no—
299D12—68no—
300C4×D3—128no—
301Dic6—128no—
302C3×C8—28no—
303C3⋊C8—68no—
304C2×C32—22no—
305C2×C32—44no—
306C2×C32—81no—
307C2×C32#52511yescharacteristic
308C2×C32C22×D811yescharacteristic
309C2×C32#57511yescharacteristic
310C3⋊D3—81no—
311C24—21no—
312#41—364no—
313C2×Q8—181no—
314C2×D4—24no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—91no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4C22×C3⋊D311yescharacteristic
322C2×D4C22×C3⋊D312yes—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—181no—
326C22×C4—182no—
327C22×C4—182no—
328C22×C4—181no—
329C22×C4—181no—
330C22×C4—364no—
331C22×C4C22×C3⋊D311yescharacteristic
332D8—24no—
333D8—184no—
334C2×C8—92no—
335C2×C8C22×C3⋊D312yes—
336C4⋊C4—92no—
337C4⋊C4—91no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4C22×C3⋊D311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—181no—
343C22⋊C4—182no—
344C22⋊C4—182no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C42—91no—
348C42—91no—
349C42—91no—
350C42—91no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—216no—
354C22×C3—432no—
355C22×C3—48no—
356C22×C3—48no—
357C22×C3—44no—
358C22×C3—44no—
359C22×C3—44no—
360C22×C3D3×D818yes—
361C22×C3C2×D3×D414yes—
362C2×D3—124no—
363C2×D3—124no—
364C2×D3—124no—
365C3×C4—24no—
366C3×C4—44no—
367C3×C4C2×#23718yes—
368Dic3—38no—
369Dic3—38no—
370Dic3—64no—
371Dic3—64no—
372Dic3—124no—
373Dic3—128no—
374C32#310011yescharacteristic, complemented, Sylow
375C23—24no—
376C23—22no—
377C23—21no—
378C23—42no—
379C23—42no—
380C23—181no—
381C23D4×C3⋊D311yescharacteristic
382Q8—362no—
383D4—24no—
384D4—22no—
385D4—22no—
386D4—42no—
387D4—182no—
388D4—362no—
389D4—362no—
390D4—362no—
391D4#383014yescomplemented
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—94no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—182no—
400C2×C4—181no—
401C2×C4—362no—
402C2×C4—364no—
403C2×C4—364no—
404C2×C4—362no—
405C2×C4—361no—
406C2×C4—362no—
407C2×C4D4×C3⋊D311yescharacteristic
408C2×C4C23×C3⋊D311yescharacteristic
409C8—22no—
410C8—182no—
411C2×C3—28no—
412C2×C3—416no—
413C2×C3—84no—
414C2×C3#558614yes—
415C2×C3C2×D3×D814yes—
416C2×C3#577314yes—
417D3—244no—
418C22—21no—
419C22—21no—
420C22—24no—
421C22—48no—
422C22—42no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—361no—
428C22—361no—
429C22—361no—
430C22D8×C3⋊D312yes—
431C22C2×D4×C3⋊D311yescharacteristic
432C4—21no—
433C4—41no—
434C4—92no—
435C4—92no—
436C4—181no—
437C4—181no—
438C4—362no—
439C4—361no—
440C4C2×#383012yes—
441C3#7998814yescomplemented
442C2—22no—
443C2—44no—
444C2—81no—
445C2—721no—
446C2#1059605711yescharacteristic
447C2C2×D8×C3⋊D311yescharacteristic
448C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#447C2
socleC22×C32C22×D4
hypercenter#447C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. #10596067C2semidirect
3. C32×#447C2semidirect
4. #10592916C2semidirect
5. #10592849C2semidirect
6. D8×C3⋊Dic3C2semidirect
7. #10592732C2semidirect
8. #10592458C2semidirect
9. #10592455C2semidirect
10. #10592435C2semidirect
11. #10592417C2semidirect
19. #64149C22semidirect
25. D4×C3⋊Dic3C22semidirect
30. #64102C22semidirect
31. #64097C22semidirect
37. #63659C22semidirect
39. #63648C22semidirect
40. #63645C22semidirect
41. #63641C22semidirect
42. C8×C3⋊Dic3C22semidirect
43. #63634C22semidirect
46. C3×#447D3semidirect
138. C32×D4#41semidirect
153. C2×C3⋊Dic3D8semidirect
170. #447C3⋊D3semidirect
279. C3×D4#237semidirect
374. C32#3100semidirect
391. D4#3830semidirect
441. C3#79988semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
#105960672
C32×#4472
#105929162
#105928492
D8×C3⋊Dic32
#105927322
#105924582
#105924552
#105924352
#105924172
#799883