Finite Group Databasebeta

← #10594063

Subgroups — #10594063

Order 576.

734 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#626C211yesmaximal, characteristic, complemented
2C2×#3796C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#882C211yesmaximal, characteristic, complemented
5C3×#878C211yesmaximal, characteristic, complemented
6#63981C211yesmaximal, characteristic, complemented
7Dic3×#67C211yesmaximal, characteristic, complemented
8D3×#217C211yesmaximal, characteristic, complemented
9#63916C211yesmaximal, characteristic, complemented
10#63907C211yesmaximal, characteristic, complemented
11#63890C211yesmaximal, characteristic, complemented
12#63886C211yesmaximal, characteristic, complemented
13#63886C211yesmaximal, characteristic, complemented
14#63881C211yesmaximal, characteristic, complemented
15#63853C211yesmaximal, characteristic, complemented
16#5630—31nomaximal
17#5591—31nomaximal
18C23×C3⋊D3C2211yescharacteristic
19C23×C3×D3C2211yescharacteristic
20C2×C4×C3⋊D3C2211yescharacteristic, complemented
21C2×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×#67C2211yescharacteristic
23C22×C3×Dic3C2211yescharacteristic
24C2×C3×D12C2211yescharacteristic, complemented
25C2×C3×D12C2211yescharacteristic, complemented
26C2×C3×Dic6C2211yescharacteristic, complemented
27C2×#626—24no—
28C2×#626C2211yescharacteristic
29C2×#626C2211yescharacteristic
30C2×#626C2211yescharacteristic
31C2×#626C2211yescharacteristic
32C2×#626C2211yescharacteristic, complemented
33C2×#626C2211yescharacteristic, complemented
34C2×D3×Dic3C2211yescharacteristic, complemented
35C2×D3×Dic3C2211yescharacteristic, complemented
36C2×D3×Dic3C2211yescharacteristic, complemented
37#3796—24no—
38C32×C22⋊C4C2211yescharacteristic
39#3757C2211yescharacteristic
40#3752C2211yescharacteristic, complemented
41#3752C2211yescharacteristic, complemented
42C3×#217C2211yescharacteristic
43C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×Dic3⋊C4C2211yescharacteristic, complemented
48Dic3⋊Dic3C2211yescharacteristic, complemented
49#3722C2211yescharacteristic, complemented
50#3722C2211yescharacteristic, complemented
51(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54Dic32C2211yescharacteristic, complemented
55C22×#67—31no—
56C2×#239—31no—
57C2×#237—31no—
58C22×D12—31no—
59C3×C22⋊Q8—31no—
60C3×#120—31no—
61C2×#217—31no—
62#947—31no—
63#939—31no—
64#939—31no—
65#938—31no—
66#937—31no—
67D4×Dic3—31no—
68C4×#67—31no—
69#895—31no—
70#895—31no—
71#895—31no—
72#894—31no—
73#894—31no—
74#893—31no—
75#886—31no—
76#885—31no—
77#883—31no—
78#882—31no—
79#882D311yescharacteristic, complemented
80#67⋊C4—31no—
81D3×C22⋊C4—31no—
82D3×C22⋊C4—31no—
83D3×C22⋊C4—31no—
84D3×C22⋊C4—61no—
85#878D311yescharacteristic, complemented
86C23×C32C2311yescharacteristic
87C22×C3⋊D3—22no—
88C22×C3⋊D3—22no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3C2311yescharacteristic
91C22×C3⋊D3C2311yescharacteristic
92C22×C3×D3—22no—
93C22×C3×D3—22no—
94C22×C3×D3—41no—
95C22×C3×D3C2311yescharacteristic
96C22×C3×D3C2311yescharacteristic
97C22×C3×D3C2311yescharacteristic
98C2×C32×C4C2311yescharacteristic
99C2×C32×C4C2311yescharacteristic
100C2×C3⋊Dic3C2311yescharacteristic
101C2×C3⋊Dic3C2311yescharacteristic
102C4×C3⋊D3—22no—
103C4×C3⋊D3—41no—
104C3×#67—22no—
105C2×C3×Dic3—22no—
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C2×C3×Dic3C2311yescharacteristic
109C2×C3×Dic3C2311yescharacteristic
110C2×C3×Dic3C2311yescharacteristic
111C3×D12—22no—
112C3×D12—41no—
113C3×Dic6—22no—
114#626—22no—
115#626—22no—
116#626—22no—
117#626—22no—
118#626—41no—
119#626D414yescomplemented
120D3×Dic3—22no—
121D3×Dic3—22no—
122D3×Dic3—41no—
123#546—91noSylow
124C24×C3—31no—
125C23×D3—31no—
126C23×D3—31no—
127C23×D3—61no—
128C23×D3C2×D311yescharacteristic
129C2×C3×Q8—31no—
130C2×C3×D4—31no—
131C2×C3×D4—31no—
132C2×C3×D4—31no—
133C22×C3×C4—31no—
134C2×#67—31no—
135C2×#67—31no—
136C2×#67—31no—
137C2×#67—31no—
138C2×#67—31no—
139C2×#67—31no—
140C2×#67—64no—
141C2×#67C2×D311yescharacteristic
142C22×Dic3—31no—
143C22×Dic3—31no—
144C22×Dic3—31no—
145C22×Dic3C2×D311yescharacteristic
146#239—64no—
147#237—64no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—31no—
151C2×D12—31no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—64no—
155C2×D12C2×D311yescharacteristic, complemented
156C2×D12C2×D311yescharacteristic, complemented
157C2×C4×D3—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—61no—
165C2×C4×D3—61no—
166C2×Dic6C2×D311yescharacteristic, complemented
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C22⋊C4—21no—
171C3×C22⋊C4—31no—
172C3×C22⋊C4—31no—
173C3×C22⋊C4—31no—
174C3×C22⋊C4C2×D311yescharacteristic
175C3×C22⋊C4C2×D311yescharacteristic
176#217—31no—
177#217—31no—
178#217—31no—
179#217—31no—
180#217—31no—
181#217—61no—
182#217C2×D311yescharacteristic
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
197(C2×D3)⋊C4C2×D311yescharacteristic, complemented
198C4⋊Dic3—31no—
199C4⋊Dic3C2×D311yescharacteristic, complemented
200Dic3⋊C4—31no—
201Dic3⋊C4C2×D311yescharacteristic, complemented
202Dic3⋊C4C2×D311yescharacteristic, complemented
203C4×Dic3—31no—
204C4×Dic3—31no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32#4112yescomplemented
208C22×C32C2411yescharacteristic
209C2×C3⋊D3—21no—
210C2×C3⋊D3—21no—
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3—21no—
214C2×C3⋊D3—44no—
215C2×C3⋊D3C2×D412yes—
216C2×C3×D3—21no—
217C2×C3×D3—21no—
218C2×C3×D3—21no—
219C2×C3×D3—21no—
220C2×C3×D3—21no—
221C2×C3×D3—21no—
222C2×C3×D3—21no—
223C2×C3×D3—21no—
224C2×C3×D3—44no—
225C2×C3×D3C2×D412yes—
226C32×C4—21no—
227C32×C4—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—31no—
241#121—91no—
242#121—91no—
243#121—91no—
244#120—31no—
245#120—91no—
246C4×D4—91no—
247C4×D4—91no—
248C2×C22⋊C4—91no—
249C2×C22⋊C4—91no—
250C23×C3—21no—
251C23×C3—31no—
252C23×C3—31no—
253C23×C3—31no—
254C23×C3—62no—
255C23×C3—62no—
256C23×C3—121no—
257C23×C3C22×D311yescharacteristic
258C23×C3C22×D311yescharacteristic
259C22×D3—22no—
260C22×D3—22no—
261C22×D3—31no—
262C22×D3—31no—
263C22×D3—31no—
264C22×D3—31no—
265C22×D3—41no—
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—62no—
269C22×D3—62no—
270C22×D3—64no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—122no—
274C22×D3—121no—
275C22×D3—121no—
276C22×D3—122no—
277C22×D3C22×D311yescharacteristic
278C22×D3C22×D311yescharacteristic
279C22×D3C22×D311yescharacteristic
280C3×Q8—62no—
281C3×D4—62no—
282C3×D4—62no—
283C3×D4—121no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—31no—
287C2×C3×C4—31no—
288C2×C3×C4—31no—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—62no—
292C2×C3×C4C22×D311yescharacteristic
293C2×C3×C4C22×D311yescharacteristic
294C2×C3×C4C22×D311yescharacteristic
295C2×C3×C4C22×D311yescharacteristic
296#67—22no—
297#67—34no—
298#67—62no—
299#67—62no—
300#67—62no—
301#67—62no—
302#67—121no—
303C2×Dic3—22no—
304C2×Dic3—31no—
305C2×Dic3—31no—
306C2×Dic3—31no—
307C2×Dic3—31no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—121no—
313C2×Dic3C22×D311yescharacteristic
314C2×Dic3C22×D311yescharacteristic
315C2×Dic3C22×D311yescharacteristic
316C2×Dic3C22×D311yescharacteristic
317C2×Dic3C22×D311yescharacteristic
318D12—22no—
319D12—34no—
320D12—41no—
321D12—62no—
322D12—62no—
323D12—62no—
324D12—62no—
325D12—121no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—122no—
331C4×D3—121no—
332C4×D3—121no—
333C4×D3—121no—
334C4×D3—122no—
335Dic6—22no—
336C2×C32—22no—
337C2×C32C22×D411yescharacteristic
338C2×C32C2×#4111yescharacteristic
339C2×C32H(5,𝔽2)11yescharacteristic
340C3⋊D3—22no—
341C3⋊D3—41no—
342C3×D3—22no—
343C3×D3—41no—
344C3×D3—41no—
345C24—31no—
346C24—91no—
347#41—184no—
348C2×Q8—31no—
349C2×D4—31no—
350C2×D4—31no—
351C2×D4—31no—
352C2×D4—91no—
353C2×D4—91no—
354C2×D4—91no—
355C2×D4—91no—
356C2×D4—91no—
357C2×D4—91no—
358C2×D4—184no—
359C22×C4—31no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C4⋊C4—31no—
366C4⋊C4—31no—
367C4⋊C4—31no—
368C4⋊C4—91no—
369C22⋊C4—31no—
370C22⋊C4—31no—
371C22⋊C4—31no—
372C22⋊C4—91no—
373C22⋊C4—91no—
374C22⋊C4—91no—
375C22⋊C4—91no—
376C22⋊C4—91no—
377C22⋊C4—91no—
378C22⋊C4—91no—
379C22⋊C4—91no—
380C22⋊C4D3211yescharacteristic
381C42—91no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—32no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—61no—
392C22×C3—61no—
393C22×C3—61no—
394C22×C3—61no—
395C22×C3—61no—
396C22×C3—61no—
397C22×C3—61no—
398C22×C3—61no—
399C22×C3—124no—
400C22×C3#23712yescomplemented
401C22×C3#23912yescomplemented
402C22×C3C23×D311yescharacteristic
403C22×C3C23×D311yescharacteristic
404C2×D3—21no—
405C2×D3—21no—
406C2×D3—21no—
407C2×D3—21no—
408C2×D3—21no—
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—32no—
413C2×D3—32no—
414C2×D3—44no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—61no—
419C2×D3—61no—
420C2×D3—61no—
421C2×D3—61no—
422C2×D3—62no—
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—124no—
432C2×D3—124no—
433C2×D3—128no—
434C2×D3D3×D412yes—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—32no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—61no—
443C3×C4—61no—
444C3×C4—61no—
445C3×C4—61no—
446Dic3—21no—
447Dic3—21no—
448Dic3—21no—
449Dic3—21no—
450Dic3—61no—
451Dic3—61no—
452Dic3—61no—
453Dic3—61no—
454Dic3—121no—
455Dic3—121no—
456Dic3D3×D412yes—
457C32#54611yescharacteristic, complemented, Sylow
458C23—31no—
459C23—31no—
460C23—31no—
461C23—62no—
462C23—62no—
463C23—91no—
464C23—91no—
465C23—121no—
466C23—182no—
467C23—182no—
468C23—361no—
469C23C2×D3211yescharacteristic
470Q8—62no—
471D4—62no—
472D4—62no—
473D4—94no—
474D4—121no—
475D4—182no—
476D4—182no—
477D4—182no—
478D4—182no—
479D4—361no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—31no—
485C2×C4—62no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—182no—
491C2×C4—361no—
492C2×C4—361no—
493C2×C4C2×D3211yescharacteristic
494C2×C4C2×D3211yescharacteristic
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—42no—
501C2×C3—62no—
502C2×C3—121no—
503C2×C3—121no—
504C2×C3C2×D3×D411yescharacteristic
505C2×C3C2×D3×D411yescharacteristic
506C2×C3C2×#23711yescharacteristic
507C2×C3#100411yescharacteristic
508C2×C3C2×#23911yescharacteristic
509C2×C3#100911yescharacteristic
510D3—22no—
511D3—41no—
512D3—41no—
513D3—64no—
514D3—62no—
515D3—62no—
516D3—122no—
517D3—121no—
518D3—121no—
519C22—21no—
520C22—21no—
521C22—32no—
522C22—61no—
523C22—61no—
524C22—61no—
525C22—61no—
526C22—61no—
527C22—61no—
528C22—61no—
529C22—61no—
530C22—92no—
531C22—124no—
532C22—181no—
533C22—181no—
534C22—181no—
535C22—181no—
536C22—181no—
537C22—364no—
538C22#379612yescomplemented
539C22C22×D3211yescharacteristic
540C4—21no—
541C4—21no—
542C4—32no—
543C4—61no—
544C4—61no—
545C4—61no—
546C4—61no—
547C4—181no—
548C4—181no—
549C3—21no—
550C3#559111yescharacteristic, complemented
551C3#563011yescharacteristic, complemented
552C2—22no—
553C2—62no—
554C2—121no—
555C2—121no—
556C2—182no—
557C2—361no—
558C2C2×#379611yescharacteristic
559C2D32×D411yescharacteristic
560C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#626C2semidirect
2. C2×#3796C2semidirect
3. C22⋊C4×C3⋊D3C2semidirect
4. C3×#882C2semidirect
5. C3×#878C2semidirect
6. #63981C2semidirect
7. Dic3×#67C2semidirect
8. D3×#217C2semidirect
9. #63916C2semidirect
10. #63907C2semidirect
11. #63890C2semidirect
12. #63886C2semidirect
13. #63886C2semidirect
14. #63881C2semidirect
15. #63853C2semidirect
20. C2×C4×C3⋊D3C22semidirect
21. C2×C4×C3⋊D3C22semidirect
24. C2×C3×D12C22semidirect
25. C2×C3×D12C22semidirect
26. C2×C3×Dic6C22semidirect
32. C2×#626C22semidirect
33. C2×#626C22semidirect
34. C2×D3×Dic3C22semidirect
35. C2×D3×Dic3C22semidirect
36. C2×D3×Dic3C22semidirect
40. #3752C22semidirect
41. #3752C22semidirect
43. C3×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D3)⋊C4C22semidirect
45. C3×C4⋊Dic3C22semidirect
46. C3×Dic3⋊C4C22semidirect
47. C3×Dic3⋊C4C22semidirect
48. Dic3⋊Dic3C22semidirect
49. #3722C22semidirect
50. #3722C22semidirect
51. (C2×D3)⋊Dic3C22semidirect
52. (C2×D3)⋊Dic3C22semidirect
53. (C2×D3)⋊Dic3C22semidirect
54. Dic32C22semidirect
79. #882D3semidirect
85. #878D3semidirect
119. #626D4semidirect
155. C2×D12C2×D3semidirect
156. C2×D12C2×D3semidirect
166. C2×Dic6C2×D3semidirect
196. (C2×D3)⋊C4C2×D3semidirect
197. (C2×D3)⋊C4C2×D3semidirect
199. C4⋊Dic3C2×D3semidirect
201. Dic3⋊C4C2×D3semidirect
202. Dic3⋊C4C2×D3semidirect
207. C22×C32#41semidirect
400. C22×C3#237semidirect
401. C22×C3#239semidirect
457. C32#546semidirect
538. C22#3796semidirect
550. C3#5591semidirect
551. C3#5630semidirect

Maximal subgroups

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

subgroupindex
C22×#6262
C2×#37962
C22⋊C4×C3⋊D32
C3×#8822
C3×#8782
#639812
Dic3×#672
D3×#2172
#639162
#639072
#638902
#638862
#638812
#638532
#56303
#55913