Finite Group Databasebeta

← #11872708

Subgroups — #11872708

Order 1152.

1254 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596190C211yesmaximal, characteristic, complemented
2#10596016C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4#10592855C211yesmaximal, characteristic, complemented
5#10592855C211yesmaximal, characteristic, complemented
6#10592851C211yesmaximal, characteristic, complemented
7D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592771C211yesmaximal, characteristic, complemented
9#10592708C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592539C211yesmaximal, characteristic, complemented
12#10592484C211yesmaximal, characteristic, complemented
13#10592483C211yesmaximal, characteristic, complemented
14#10592478C211yesmaximal, characteristic, complemented
15#10592455C211yesmaximal, characteristic, complemented
16#80317—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×C32×D8C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×#127C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22#64148—21no—
23#64148—21no—
24#64147C2211yescharacteristic
25#64147C2211yescharacteristic
26#64144—21no—
27#64144—21no—
28D4×C3⋊Dic3C2211yescharacteristic
29D4×C3⋊Dic3C2211yescharacteristic, complemented
30D4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×#3753C2211yescharacteristic
32C2×#3753C2211yescharacteristic
33C4×#638—21no—
34C2×#3752—21no—
35#64102C2211yescharacteristic
36#64101C2211yescharacteristic
37#64090—21no—
38C22⋊C4×C3⋊D3—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40#64081C2211yescharacteristic
41#64079C2211yescharacteristic, complemented
42C32×C4⋊C8C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic, complemented
48#63659C2211yescharacteristic, complemented
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63647C2211yescharacteristic
53#63645C2211yescharacteristic, complemented
54#63644C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56C8×C3⋊Dic3C2211yescharacteristic, complemented
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
60#5719—34no—
61#5545—34no—
62C3×#459D314yescomplemented
63#5156—34no—
64#5156—34no—
65#5152—34no—
66Dic3×D8—34no—
67#5072—34no—
68#5009—34no—
69#4847—34no—
70#4840—34no—
71#4785—34no—
72#4784—34no—
73#4779—34no—
74#4756—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4—21no—
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C2×C32×D4C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C2×#638—21no—
83C2×#638—21no—
84C2×#638—21no—
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3—21no—
87C22×C3⋊Dic3—21no—
88D4×C3⋊D3—22no—
89D4×C3⋊D3—22no—
90C2×C4⋊(C3⋊D3)C2311yescharacteristic
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C32×D8—22no—
95C32×D8—22no—
96C2×C32×C8C2311yescharacteristic
97C2×C32×C8C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C42C2311yescharacteristic
101#3757—21no—
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3753—22no—
107#3753—22no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752D411yescharacteristic
112#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750D411yescharacteristic
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3122—91noSylow
125C2×D3×D4—34no—
126C2×C3×D8C2×D314yes—
127C2×C3×D8C2×D314yes—
128C3×#127C2×D314yescomplemented
129C3×C4×D4C2×D314yes—
130#939—64no—
131#939—64no—
132#938—34no—
133#938—34no—
134#935—64no—
135#935—64no—
136D4×Dic3—34no—
137D4×Dic3—34no—
138D4×Dic3—34no—
139C2×#213—34no—
140C2×#213—34no—
141C4×#67—64no—
142C2×(C2×D3)⋊C4—64no—
143#893—34no—
144#892—34no—
145#67⋊C4—64no—
146D3×C22⋊C4—64no—
147C4×D12—34no—
148#872—34no—
149#870—34no—
150C3×C4⋊C8C2×D314yescomplemented
151C3×#102C2×D314yescomplemented
152C3×#102C2×D314yescomplemented
153#832—34no—
154#832—34no—
155#832—34no—
156#832—34no—
157#821—34no—
158#821—34no—
159(C2×D3)⋊C8—34no—
160(C2×D3)⋊C8—34no—
161#818—34no—
162#817—34no—
163#815—34no—
164C8×Dic3—34no—
165#808—34no—
166#807—34no—
167C4⋊(C3⋊C8)—34no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—24no—
173C22×C3⋊D3—81no—
174C22×C3⋊D3—81no—
175C22×C3⋊D3C2×D411yescharacteristic
176C32×D4—21no—
177C32×D4—21no—
178C32×D4—21no—
179C32×D4—21no—
180C32×D4—21no—
181C32×D4—81no—
182C32×D4—81no—
183C32×D4#4112yes—
184C2×C32×C4—21no—
185C2×C32×C4—81no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—24no—
190#638—81no—
191#638—81no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—81no—
196C2×C3⋊Dic3—81no—
197C2×C3⋊Dic3—81no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4⋊(C3⋊D3)—21no—
202C4⋊(C3⋊D3)#4112yes—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205C4×C3⋊D3—81no—
206C4×C3⋊D3—81no—
207C32×C8—21no—
208C32×C8—21no—
209C3⋊(C3⋊C8)—21no—
210C3⋊(C3⋊C8)—21no—
211#540—91no—
212#518—91no—
213#482—91no—
214#482—91no—
215#478—91no—
216#478—91no—
217#459—91no—
218#459C3⋊D311yescharacteristic, complemented
219#447—91no—
220#447—91no—
221#442—91no—
222#442—91no—
223C4×D8—91no—
224C4×D8—91no—
225#433—91no—
226C23×D3—64no—
227C2×C3×D4—24no—
228C2×C3×D4—24no—
229C2×C3×D4C22×D314yes—
230C2×C3×D4C22×D314yes—
231C2×C3×D4C22×D314yes—
232C22×C3×C4—24no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C22×Dic3—64no—
237C22×Dic3—64no—
238C22×Dic3—64no—
239D3×D4—68no—
240D3×D4—68no—
241C2×D12—34no—
242C2×C4×D3—34no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C3×D8—28no—
246C3×D8—28no—
247C2×C3×C8C22×D314yes—
248C2×C3×C8C22×D314yes—
249C3×C4⋊C4C22×D314yes—
250C3×C22⋊C4—24no—
251C3×C42C22×D314yes—
252#217—64no—
253#217—64no—
254#217—64no—
255#217—64no—
256#217—64no—
257#213—68no—
258#213—68no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—34no—
267Dic3⋊C4—34no—
268Dic3⋊C4—34no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C4×Dic3—34no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275C22×C32—22no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—21no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—84no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4C2×#4111yescharacteristic
296C32×C4C2×#4111yescharacteristic
297C3⋊Dic3—21no—
298C3⋊Dic3—21no—
299C3⋊Dic3—21no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C22×D4—91no—
304C2×D8—91no—
305C2×D8—91no—
306C2×D8C2×C3⋊D311yescharacteristic
307C2×D8C2×C3⋊D311yescharacteristic
308#127C2×C3⋊D311yescharacteristic, complemented
309#125—91no—
310#123—181no—
311#123—181no—
312#121—91no—
313#121—91no—
314#121—181no—
315#121—181no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—91no—
321C4×D4—181no—
322C4×D4—181no—
323C4×D4C2×C3⋊D311yescharacteristic
324#117—91no—
325#117—91no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328#107—91no—
329#107—91no—
330#106—91no—
331#106—91no—
332C4⋊C8—91no—
333C4⋊C8C2×C3⋊D311yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340#102C2×C3⋊D311yescharacteristic, complemented
341#102C2×C3⋊D311yescharacteristic, complemented
342C22⋊C8—91no—
343C22⋊C8—91no—
344#97—91no—
345C4×C8—91no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C22×D3—34no—
350C22×D3—64no—
351C22×D3—616no—
352C22×D3—244no—
353C22×D3—244no—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—24no—
357C3×D4—24no—
358C3×D4—24no—
359C3×D4—84no—
360C3×D4—84no—
361C3×D4#23718yes—
362C2×C3×C4—24no—
363C2×C3×C4—84no—
364C2×C3×C4D3×D414yes—
365C2×C3×C4D3×D414yes—
366C2×C3×C4C23×D314yes—
367#67—616no—
368#67—244no—
369#67—244no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—244no—
377C2×Dic3—244no—
378C2×Dic3—244no—
379D12—38no—
380D12—64no—
381C4×D3—64no—
382C4×D3—64no—
383C4×D3—244no—
384C4×D3—244no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—42no—
390C2×C32—81no—
391C2×C32—81no—
392C2×C32#52511yescharacteristic
393C2×C32#57611yescharacteristic
394C2×C32#57611yescharacteristic
395C3⋊D3—41no—
396C3⋊D3—42no—
397C24—181no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—91no—
401C2×D4—181no—
402C2×D4—182no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4C22×C3⋊D311yescharacteristic
407C2×D4C22×C3⋊D311yescharacteristic
408C2×D4C22×C3⋊D311yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4—181no—
416D8—22no—
417D8—22no—
418D8—182no—
419D8—182no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8C22×C3⋊D311yescharacteristic
423C2×C8C22×C3⋊D311yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—91no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4C22×C3⋊D311yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—91no—
434C22⋊C4—91no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C42—91no—
444C42—181no—
445C42C22×C3⋊D311yescharacteristic
446C22×C3—28no—
447C22×C3—44no—
448C22×C3—44no—
449C22×C3—44no—
450C22×C3—44no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—44no—
455C22×C3C2×D3×D414yes—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—64no—
459C2×D3—68no—
460C2×D3—124no—
461C2×D3—124no—
462C2×D3—2416no—
463C3×C4—24no—
464C3×C4—24no—
465C3×C4—44no—
466C3×C4C2×#23714yes—
467C3×C4D3×#4114yes—
468Dic3—64no—
469Dic3—64no—
470Dic3—64no—
471Dic3—124no—
472Dic3—124no—
473Dic3—124no—
474C32#312211yescharacteristic, complemented, Sylow
475C23—21no—
476C23—21no—
477C23—21no—
478C23—91no—
479C23—184no—
480C23—181no—
481C23—721no—
482C23—721no—
483D4—21no—
484D4—21no—
485D4—21no—
486D4—21no—
487D4—21no—
488D4—81no—
489D4—81no—
490D4—92no—
491D4—184no—
492D4—181no—
493D4—721no—
494D4—721no—
495D4#383012yes—
496C2×C4—21no—
497C2×C4—81no—
498C2×C4—91no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—721no—
507C2×C4—721no—
508C2×C4—721no—
509C2×C4—721no—
510C2×C4—721no—
511C2×C4D4×C3⋊D311yescharacteristic
512C2×C4D4×C3⋊D311yescharacteristic
513C2×C4C23×C3⋊D311yescharacteristic
514C8—21no—
515C8—21no—
516C8—181no—
517C8—181no—
518C2×C3—48no—
519C2×C3—84no—
520C2×C3—84no—
521C2×C3#560614yes—
522C2×C3#575714yes—
523C2×C3#577414yes—
524D3—124no—
525D3—128no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—181no—
536C22—181no—
537C22—181no—
538C22—182no—
539C22—361no—
540C22—361no—
541C22—724no—
542C22C2×D4×C3⋊D311yescharacteristic
543C4—21no—
544C4—21no—
545C4—41no—
546C4—181no—
547C4—181no—
548C4—181no—
549C4—361no—
550C4—361no—
551C4—361no—
552C4C2×#383011yescharacteristic
553C4#41×C3⋊D311yescharacteristic
554C3#8031714yescomplemented
555C2—42no—
556C2—81no—
557C2—81no—
558C2—361no—
559C2—362no—
560C2#1059607711yescharacteristic
561C2#1059622811yescharacteristic
562C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10596190C2semidirect
2. #10596016C2semidirect
3. C32×#459C2semidirect
4. #10592855C2semidirect
5. #10592855C2semidirect
6. #10592851C2semidirect
7. D8×C3⋊Dic3C2semidirect
8. #10592771C2semidirect
9. #10592708C2semidirect
10. #10592546C2semidirect
11. #10592539C2semidirect
12. #10592484C2semidirect
13. #10592483C2semidirect
14. #10592478C2semidirect
15. #10592455C2semidirect
20. C32×#127C22semidirect
29. D4×C3⋊Dic3C22semidirect
30. D4×C3⋊Dic3C22semidirect
41. #64079C22semidirect
42. C32×C4⋊C8C22semidirect
43. C32×#102C22semidirect
44. C32×#102C22semidirect
47. #63659C22semidirect
48. #63659C22semidirect
53. #63645C22semidirect
54. #63644C22semidirect
55. #63642C22semidirect
56. C8×C3⋊Dic3C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4⋊(C3⋊(C3⋊C8))C22semidirect
62. C3×#459D3semidirect
128. C3×#127C2×D3semidirect
150. C3×C4⋊C8C2×D3semidirect
151. C3×#102C2×D3semidirect
152. C3×#102C2×D3semidirect
218. #459C3⋊D3semidirect
308. #127C2×C3⋊D3semidirect
333. C4⋊C8C2×C3⋊D3semidirect
340. #102C2×C3⋊D3semidirect
341. #102C2×C3⋊D3semidirect
474. C32#3122semidirect
554. C3#80317semidirect

Maximal subgroups

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

subgroupindex
#105961902
#105960162
C32×#4592
#105928552
#105928512
D8×C3⋊Dic32
#105927712
#105927082
#105925462
#105925392
#105924842
#105924832
#105924782
#105924552
#803173