Finite Group Databasebeta

← #10595296

Subgroups — #10595296

Order 576.

733 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3811C211yesmaximal, characteristic, complemented
2C2×#3804C211yesmaximal, characteristic, complemented
3#64146C211yesmaximal, characteristic, complemented
4C3×#939C211yesmaximal, characteristic, complemented
5C3×#938C211yesmaximal, characteristic, complemented
6#63983C211yesmaximal, characteristic, complemented
7#63974C211yesmaximal, characteristic, complemented
8#63969C211yesmaximal, characteristic, complemented
9#63959C211yesmaximal, characteristic, complemented
10#63958C211yesmaximal, characteristic, complemented
11#63952C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#63904C211yesmaximal, characteristic, complemented
14#63895C211yesmaximal, characteristic, complemented
15#63854C211yesmaximal, characteristic, complemented
16#5612—31nomaximal
17#5610—31nomaximal
18C23×C3⋊D3C2211yescharacteristic
19C22×D32C2211yescharacteristic
20C2×C32×D4C2211yescharacteristic, complemented
21C2×#638C2211yescharacteristic
22C2×#638C2211yescharacteristic, complemented
23C2×C3×#67C2211yescharacteristic
24C2×C3×#67C2211yescharacteristic
25C2×C3×#67C2211yescharacteristic, complemented
26C2×C3×#67C2211yescharacteristic, complemented
27C22×C3×Dic3C2211yescharacteristic, complemented
28C2×C3×C4×D3C2211yescharacteristic, complemented
29#3811—24no—
30C2×#627C2211yescharacteristic, complemented
31C2×#626C2211yescharacteristic
32C2×#626C2211yescharacteristic
33C2×#624C2211yescharacteristic
34C2×#624C2211yescharacteristic, complemented
35C2×#624C2211yescharacteristic, complemented
36#3804—24no—
37C2×D3×Dic3C2211yescharacteristic, complemented
38#3757C2211yescharacteristic, complemented
39#3752C2211yescharacteristic
40#3752C2211yescharacteristic, complemented
41C3×#217C2211yescharacteristic, complemented
42C3×#217C2211yescharacteristic, complemented
43C3×#217C2211yescharacteristic, complemented
44C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊C4C2211yescharacteristic, complemented
47#3724C2211yescharacteristic, complemented
48Dic3⋊Dic3C2211yescharacteristic, complemented
49#3722C2211yescharacteristic
50#3722C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54Dic32C2211yescharacteristic, complemented
55C2×#237—31no—
56C2×D3×D4—31no—
57C2×D3×D4—31no—
58C2×#235—31no—
59C3×#121—31no—
60C3×#121—31no—
61#939D311yescharacteristic, complemented
62#938—31no—
63#938D311yescharacteristic, complemented
64#937—31no—
65#937—31no—
66#937—31no—
67#937—31no—
68#937—61no—
69#936—31no—
70#935—31no—
71C4×#67—31no—
72C4×#67—31no—
73C2×(C2×D3)⋊C4—31no—
74#897—31no—
75#896—31no—
76#894—31no—
77#893—31no—
78#885—31no—
79#884—31no—
80#883—31no—
81#883—31no—
82#67⋊C4—31no—
83D3×C22⋊C4—31no—
84D3×C22⋊C4—31no—
85D3×C22⋊C4—31no—
86C23×C32C2311yescharacteristic
87C23×C32C2311yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3C2311yescharacteristic
92C22×C3⋊D3C2311yescharacteristic
93C22×C3×D3C2311yescharacteristic
94C22×C3×D3C2311yescharacteristic
95C2×D32—22no—
96C2×D32—22no—
97C2×D32—41no—
98C32×D4—41no—
99C2×C32×C4C2311yescharacteristic
100#638—22no—
101#638—22no—
102C2×C3⋊Dic3C2311yescharacteristic
103C2×C3⋊Dic3C2311yescharacteristic
104C3×#67—22no—
105C3×#67—22no—
106C3×#67—22no—
107C3×#67—41no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3C2311yescharacteristic
110C2×C3×Dic3C2311yescharacteristic
111C2×C3×Dic3C2311yescharacteristic
112C2×C3×Dic3C2311yescharacteristic
113C2×C3×Dic3C2311yescharacteristic
114C2×C3×Dic3C2311yescharacteristic
115C3×C4×D3—41no—
116#627—22no—
117#626—22no—
118#626D414yescomplemented
119#624—22no—
120#624—22no—
121#624—41no—
122D3×Dic3—22no—
123#546—91noSylow
124C23×D3—31no—
125C23×D3—31no—
126C23×D3—31no—
127C23×D3—31no—
128C23×D3—61no—
129C2×C3×D4—21no—
130C2×C3×D4—31no—
131C2×C3×D4—31no—
132C2×C3×D4—31no—
133C2×C3×D4—31no—
134C2×C3×D4C2×D311yescharacteristic, complemented
135C2×C3×D4C2×D311yescharacteristic, complemented
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C2×#67—31no—
139C2×#67—31no—
140C2×#67—31no—
141C2×#67—31no—
142C2×#67—31no—
143C2×#67—31no—
144C2×#67—61no—
145C2×#67—61no—
146C2×#67C2×D311yescharacteristic
147C2×#67C2×D311yescharacteristic
148C2×#67C2×D311yescharacteristic, complemented
149C2×#67C2×D311yescharacteristic, complemented
150C22×Dic3—31no—
151C22×Dic3C2×D311yescharacteristic, complemented
152#237—64no—
153D3×D4—64no—
154D3×D4—64no—
155#235—64no—
156C2×D12—31no—
157C2×D12—31no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—31no—
161C2×C4×D3—31no—
162C2×C4×D3—31no—
163C2×C4×D3—31no—
164C2×C4×D3—31no—
165C2×C4×D3C2×D311yescharacteristic, complemented
166C2×Dic6—31no—
167C2×Dic6—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C22⋊C4—31no—
171C3×C22⋊C4—31no—
172C3×C22⋊C4—31no—
173C3×C22⋊C4—31no—
174#217—31no—
175#217—31no—
176#217—31no—
177#217—31no—
178#217—31no—
179#217—61no—
180#217C2×D311yescharacteristic, complemented
181#217C2×D311yescharacteristic, complemented
182#217C2×D311yescharacteristic, complemented
183(C2×D3)⋊C4—31no—
184(C2×D3)⋊C4—31no—
185(C2×D3)⋊C4—31no—
186(C2×D3)⋊C4—31no—
187(C2×D3)⋊C4—31no—
188(C2×D3)⋊C4—31no—
189(C2×D3)⋊C4—31no—
190(C2×D3)⋊C4—31no—
191(C2×D3)⋊C4—31no—
192(C2×D3)⋊C4—31no—
193(C2×D3)⋊C4—31no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4C2×D311yescharacteristic, complemented
197C4⋊Dic3—31no—
198C4⋊Dic3C2×D311yescharacteristic, complemented
199Dic3⋊C4—31no—
200Dic3⋊C4—31no—
201Dic3⋊C4—31no—
202Dic3⋊C4C2×D311yescharacteristic, complemented
203C4×Dic3—31no—
204C4×Dic3—31no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C2411yescharacteristic
212C2×C3⋊D3—21no—
213C2×C3⋊D3—21no—
214C2×C3⋊D3—21no—
215C2×C3⋊D3—21no—
216C2×C3⋊D3—44no—
217C2×C3⋊D3C2×D412yes—
218C2×C3⋊D3#4112yescomplemented
219C2×C3×D3—21no—
220C2×C3×D3—21no—
221C2×C3×D3—21no—
222C2×C3×D3—21no—
223C2×C3×D3—21no—
224C2×C3×D3C2×D412yes—
225D32—44no—
226C32×C4—21no—
227C3⋊Dic3—21no—
228C3⋊Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—21no—
233C3×Dic3—21no—
234C3×Dic3C2×D412yes—
235C2×#41—91no—
236C22×D4—91no—
237#124—91no—
238#123—91no—
239#123—91no—
240C22⋊Q8—91no—
241#121—31no—
242#121—31no—
243#121—91no—
244#120—91no—
245#120—91no—
246C4×D4—91no—
247C4×D4—91no—
248C2×C22⋊C4—91no—
249C2×C22⋊C4—91no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—31no—
253C23×C3—31no—
254C23×C3C22×D311yescharacteristic
255C23×C3C22×D311yescharacteristic
256C23×C3C22×D311yescharacteristic
257C23×C3C22×D311yescharacteristic
258C22×D3—31no—
259C22×D3—31no—
260C22×D3—31no—
261C22×D3—31no—
262C22×D3—61no—
263C22×D3—61no—
264C22×D3—62no—
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—62no—
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—122no—
273C22×D3—122no—
274C22×D3—121no—
275C22×D3—121no—
276C22×D3—121no—
277C22×D3—121no—
278C22×D3—122no—
279C22×D3C22×D311yescharacteristic
280C22×D3C22×D311yescharacteristic
281C3×D4—41no—
282C3×D4—41no—
283C3×D4—42no—
284C3×D4—62no—
285C3×D4—62no—
286C3×D4—62no—
287C3×D4—121no—
288C2×C3×C4—21no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—31no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—62no—
296C2×C3×C4—121no—
297C2×C3×C4C22×D311yescharacteristic
298C2×C3×C4C22×D311yescharacteristic
299#67—22no—
300#67—22no—
301#67—22no—
302#67—34no—
303#67—41no—
304#67—62no—
305#67—62no—
306#67—62no—
307#67—62no—
308#67—62no—
309#67—122no—
310#67—122no—
311C2×Dic3—22no—
312C2×Dic3—31no—
313C2×Dic3—31no—
314C2×Dic3—31no—
315C2×Dic3—31no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—62no—
319C2×Dic3C22×D311yescharacteristic
320C2×Dic3C22×D311yescharacteristic
321C2×Dic3C22×D311yescharacteristic
322C2×Dic3C22×D311yescharacteristic
323C2×Dic3C22×D311yescharacteristic
324C2×Dic3C22×D311yescharacteristic
325D12—34no—
326D12—62no—
327C4×D3—41no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—121no—
334C4×D3—121no—
335Dic6—62no—
336Dic6—62no—
337C2×C32—41no—
338C2×C32—41no—
339C2×C32C22×D411yescharacteristic
340C2×C32C2×#4111yescharacteristic
341C2×C32H(5,𝔽2)11yescharacteristic
342C3⋊D3—22no—
343C3⋊D3—22no—
344C3×D3—22no—
345C3×D3—41no—
346C24—91no—
347C24—91no—
348#41—184no—
349C2×Q8—91no—
350C2×D4—31no—
351C2×D4—31no—
352C2×D4—31no—
353C2×D4—31no—
354C2×D4—91no—
355C2×D4—91no—
356C2×D4—91no—
357C2×D4—91no—
358C2×D4—184no—
359C2×D4D3211yescharacteristic, complemented
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—91no—
366C4⋊C4—31no—
367C4⋊C4—31no—
368C4⋊C4—91no—
369C4⋊C4—91no—
370C22⋊C4—31no—
371C22⋊C4—31no—
372C22⋊C4—31no—
373C22⋊C4—31no—
374C22⋊C4—91no—
375C22⋊C4—91no—
376C22⋊C4—91no—
377C22⋊C4—91no—
378C22⋊C4—91no—
379C22⋊C4—91no—
380C22⋊C4—91no—
381C22⋊C4—91no—
382C42—91no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—32no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—61no—
406C22×C3—61no—
407C22×C3—61no—
408C22×C3C23×D311yescharacteristic
409C22×C3C23×D311yescharacteristic
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—32no—
416C2×D3—32no—
417C2×D3—32no—
418C2×D3—32no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—61no—
422C2×D3—61no—
423C2×D3—61no—
424C2×D3—61no—
425C2×D3—61no—
426C2×D3—61no—
427C2×D3—61no—
428C2×D3—61no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C2×D3—128no—
438C2×D3D3×D412yes—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—32no—
442C3×C4—41no—
443C3×C4—61no—
444C3×C4—61no—
445C3×C4—61no—
446C3×C4—61no—
447C3×C4—61no—
448Dic3—21no—
449Dic3—21no—
450Dic3—21no—
451Dic3—21no—
452Dic3—21no—
453Dic3—61no—
454Dic3—61no—
455Dic3—61no—
456Dic3—61no—
457Dic3—121no—
458Dic3—121no—
459Dic3D3×D412yes—
460C32#54611yescharacteristic, complemented, Sylow
461C23—31no—
462C23—31no—
463C23—91no—
464C23—91no—
465C23—182no—
466C23—182no—
467C23—182no—
468C23—182no—
469C23—361no—
470C23—361no—
471C23C2×D3211yescharacteristic
472C23C2×D3211yescharacteristic
473Q8—182no—
474D4—41no—
475D4—62no—
476D4—62no—
477D4—62no—
478D4—94no—
479D4—121no—
480D4—182no—
481D4—182no—
482D4—182no—
483C2×C4—31no—
484C2×C4—31no—
485C2×C4—31no—
486C2×C4—31no—
487C2×C4—31no—
488C2×C4—31no—
489C2×C4—62no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—121no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—361no—
497C2×C4C2×D3211yescharacteristic
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—42no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—62no—
507C2×C3—81no—
508C2×C3—121no—
509C2×C3C2×D3×D411yescharacteristic
510C2×C3C2×D3×D411yescharacteristic
511C2×C3#100411yescharacteristic
512C2×C3#100411yescharacteristic
513C2×C3D3×#4111yescharacteristic
514C2×C3D3×#4111yescharacteristic
515D3—22no—
516D3—41no—
517D3—62no—
518D3—62no—
519D3—62no—
520D3—62no—
521D3—122no—
522D3—122no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—32no—
530C22—61no—
531C22—61no—
532C22—61no—
533C22—61no—
534C22—61no—
535C22—92no—
536C22—92no—
537C22—181no—
538C22—181no—
539C22—181no—
540C22—181no—
541C22—364no—
542C22—364no—
543C22C22×D3211yescharacteristic
544C4—21no—
545C4—32no—
546C4—61no—
547C4—61no—
548C4—61no—
549C4—61no—
550C4—61no—
551C4—181no—
552C4—181no—
553C3—21no—
554C3#561011yescharacteristic, complemented
555C3#561211yescharacteristic, complemented
556C2—41no—
557C2—41no—
558C2—62no—
559C2—121no—
560C2—182no—
561C2—182no—
562C2D32×D411yescharacteristic
563C2#6431211yescharacteristic
564C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×D4C22
hypercenterC2×D4D32
hypocenterC32#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#3811C2semidirect
2. C2×#3804C2semidirect
3. #64146C2semidirect
4. C3×#939C2semidirect
5. C3×#938C2semidirect
6. #63983C2semidirect
7. #63974C2semidirect
8. #63969C2semidirect
9. #63959C2semidirect
10. #63958C2semidirect
11. #63952C2semidirect
12. D3×(C2×D3)⋊C4C2semidirect
13. #63904C2semidirect
14. #63895C2semidirect
15. #63854C2semidirect
20. C2×C32×D4C22semidirect
22. C2×#638C22semidirect
25. C2×C3×#67C22semidirect
26. C2×C3×#67C22semidirect
27. C22×C3×Dic3C22semidirect
28. C2×C3×C4×D3C22semidirect
30. C2×#627C22semidirect
34. C2×#624C22semidirect
35. C2×#624C22semidirect
37. C2×D3×Dic3C22semidirect
38. #3757C22semidirect
40. #3752C22semidirect
41. C3×#217C22semidirect
42. C3×#217C22semidirect
43. C3×#217C22semidirect
44. C3×(C2×D3)⋊C4C22semidirect
45. C3×C4⋊Dic3C22semidirect
46. C3×Dic3⋊C4C22semidirect
47. #3724C22semidirect
48. Dic3⋊Dic3C22semidirect
51. (C2×D3)⋊Dic3C22semidirect
52. (C2×D3)⋊Dic3C22semidirect
53. (C2×D3)⋊Dic3C22semidirect
54. Dic32C22semidirect
61. #939D3semidirect
63. #938D3semidirect
118. #626D4semidirect
134. C2×C3×D4C2×D3semidirect
135. C2×C3×D4C2×D3semidirect
148. C2×#67C2×D3semidirect
149. C2×#67C2×D3semidirect
151. C22×Dic3C2×D3semidirect
165. C2×C4×D3C2×D3semidirect
180. #217C2×D3semidirect
181. #217C2×D3semidirect
182. #217C2×D3semidirect
196. (C2×D3)⋊C4C2×D3semidirect
198. C4⋊Dic3C2×D3semidirect
202. Dic3⋊C4C2×D3semidirect
218. C2×C3⋊D3#41semidirect
359. C2×D4D32semidirect
460. C32#546semidirect
554. C3#5610semidirect
555. C3#5612semidirect

Maximal subgroups

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

subgroupindex
C2×#38112
C2×#38042
#641462
C3×#9392
C3×#9382
#639832
#639742
#639692
#639592
#639582
#639522
D3×(C2×D3)⋊C42
#639042
#638952
#638542
#56123
#56103