Finite Group Databasebeta

← #10594238

Subgroups — #10594238

Order 576.

537 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64087C211yesmaximal, characteristic, complemented
2C3×#882C211yesmaximal, characteristic, complemented
3C3×#67⋊C4C211yesmaximal, characteristic, complemented
4#63980C211yesmaximal, characteristic, complemented
5#63976C211yesmaximal, characteristic, complemented
6Dic3×#67C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#63913C211yesmaximal, characteristic, complemented
9#63908C211yesmaximal, characteristic, complemented
10#63905C211yesmaximal, characteristic, complemented
11#63885C211yesmaximal, characteristic, complemented
12#63884C211yesmaximal, characteristic, complemented
13#63861C211yesmaximal, characteristic, complemented
14#63860C211yesmaximal, characteristic, complemented
15#63859C211yesmaximal, characteristic, complemented
16#5593—31nomaximal
17#5560—31nomaximal
18C23×C3×D3C2211yescharacteristic
19C22×C3⋊Dic3C2211yescharacteristic
20C2×#634C2211yescharacteristic, complemented
21C2×C3×#67C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C22×C3×Dic3C2211yescharacteristic
24C2×C3×D12C2211yescharacteristic
25C2×C3×D12C2211yescharacteristic
26C2×C3×C4×D3C2211yescharacteristic, complemented
27C2×#625C2211yescharacteristic
28C2×#625C2211yescharacteristic
29C2×#625C2211yescharacteristic, complemented
30C2×D3×Dic3C2211yescharacteristic, complemented
31C32×C22⋊C4C2211yescharacteristic
32#3757C2211yescharacteristic
33C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34#3750C2211yescharacteristic, complemented
35#3750C2211yescharacteristic, complemented
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C3×Dic3⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic3C2211yescharacteristic, complemented
41#3724C2211yescharacteristic, complemented
42Dic3⋊Dic3C2211yescharacteristic, complemented
43(C2×D3)⋊Dic3C2211yescharacteristic
44(C2×D3)⋊Dic3C2211yescharacteristic
45(C2×D3)⋊Dic3C2211yescharacteristic
46(C2×D3)⋊Dic3C2211yescharacteristic
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52Dic32C2211yescharacteristic, complemented
53C3×#120—31no—
54C3×C4×D4—31no—
55#953—31no—
56C2×#217—31no—
57#939—31no—
58#939—31no—
59#939—31no—
60#938—31no—
61#937—31no—
62#936—31no—
63#935—31no—
64D4×Dic3—31no—
65#930—31no—
66#929—31no—
67C4×#67—31no—
68C2×(C2×D3)⋊C4—31no—
69#898—31no—
70#894—31no—
71#885—31no—
72#885—31no—
73#884—31no—
74#883—31no—
75#882D311yescharacteristic, complemented
76#67⋊C4D311yescharacteristic, complemented
77#879—31no—
78#879—31no—
79#878—31no—
80#878—31no—
81#878—61no—
82#876—31no—
83#875—31no—
84C23×C32C2311yescharacteristic
85C22×C3×D3—22no—
86C22×C3×D3—41no—
87C22×C3×D3—41no—
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C22×C3×D3C2311yescharacteristic
91C22×C3×D3C2311yescharacteristic
92C2×C32×C4C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98C2×C3⋊Dic3C2311yescharacteristic
99#634—41no—
100C3×#67—22no—
101C3×#67—22no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C3×D12—41no—
108C3×D12—41no—
109C3×C4×D3—41no—
110#625—41no—
111#625—41no—
112#625—41no—
113D3×Dic3—41no—
114#538—91noSylow
115C24×C3—31no—
116C23×D3C2×D311yescharacteristic
117C2×C3×D4—31no—
118C2×C3×D4—31no—
119C2×C3×D4—31no—
120C2×C3×D4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—31no—
126C2×#67—31no—
127C2×#67—31no—
128C2×#67—31no—
129C2×#67C2×D311yescharacteristic
130C2×#67C2×D311yescharacteristic
131C22×Dic3—31no—
132C22×Dic3—31no—
133C22×Dic3—31no—
134C22×Dic3—61no—
135C22×Dic3C2×D311yescharacteristic
136C2×D12C2×D311yescharacteristic
137C2×D12C2×D311yescharacteristic
138C2×C4×D3—31no—
139C2×C4×D3C2×D311yescharacteristic, complemented
140C2×Dic6—31no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C3×C4⋊C4—31no—
144C3×C22⋊C4—21no—
145C3×C22⋊C4—31no—
146C3×C22⋊C4—31no—
147C3×C22⋊C4—31no—
148C3×C22⋊C4C2×D311yescharacteristic
149C3×C22⋊C4C2×D311yescharacteristic
150C3×C42—31no—
151#217—31no—
152#217—31no—
153#217—31no—
154#217—31no—
155#217—31no—
156#217—31no—
157#217—31no—
158#217—31no—
159#217—31no—
160#217—31no—
161#217—31no—
162#217—61no—
163(C2×D3)⋊C4—31no—
164(C2×D3)⋊C4—31no—
165(C2×D3)⋊C4—31no—
166(C2×D3)⋊C4—31no—
167(C2×D3)⋊C4—31no—
168(C2×D3)⋊C4—31no—
169(C2×D3)⋊C4—31no—
170(C2×D3)⋊C4—31no—
171(C2×D3)⋊C4—31no—
172(C2×D3)⋊C4C2×D311yescharacteristic
173(C2×D3)⋊C4C2×D311yescharacteristic
174(C2×D3)⋊C4C2×D311yescharacteristic, complemented
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—61no—
179Dic3⋊C4—31no—
180Dic3⋊C4—31no—
181Dic3⋊C4—31no—
182Dic3⋊C4—31no—
183Dic3⋊C4—31no—
184Dic3⋊C4—31no—
185Dic3⋊C4—31no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4C2×D311yescharacteristic, complemented
189C4×Dic3—31no—
190C4×Dic3—31no—
191C4×Dic3C2×D311yescharacteristic, complemented
192C22×C32—21no—
193C22×C32—21no—
194C22×C32#4112yes—
195C22×C32C2411yescharacteristic
196C2×C3×D3—21no—
197C2×C3×D3—21no—
198C2×C3×D3—21no—
199C2×C3×D3—21no—
200C2×C3×D3—21no—
201C2×C3×D3—21no—
202C2×C3×D3—21no—
203C2×C3×D3—21no—
204C2×C3×D3—21no—
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3—21no—
208C2×C3×D3—44no—
209C32×C4—21no—
210C32×C4—21no—
211C3⋊Dic3—21no—
212C3⋊Dic3—21no—
213C3⋊Dic3—21no—
214C3⋊Dic3—21no—
215C3×Dic3—21no—
216C3×Dic3—21no—
217C3×Dic3—21no—
218C3×Dic3—21no—
219#126—91no—
220#126—91no—
221#124—91no—
222#124—91no—
223#123—91no—
224#123—91no—
225C22⋊Q8—91no—
226#121—91no—
227#121—91no—
228#121—91no—
229#120—31no—
230#120—91no—
231C4×D4—31no—
232C4×D4—91no—
233C2×C22⋊C4—91no—
234C23×C3—21no—
235C23×C3—31no—
236C23×C3—31no—
237C23×C3—31no—
238C23×C3—31no—
239C23×C3—62no—
240C23×C3—121no—
241C23×C3—121no—
242C23×C3C22×D311yescharacteristic
243C23×C3C22×D311yescharacteristic
244C22×D3—22no—
245C22×D3—41no—
246C22×D3—41no—
247C22×D3C22×D311yescharacteristic
248C22×D3C22×D311yescharacteristic
249C22×D3C22×D311yescharacteristic
250C22×D3C22×D311yescharacteristic
251C3×D4—62no—
252C3×D4—62no—
253C3×D4—121no—
254C3×D4—121no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4C22×D311yescharacteristic
264C2×C3×C4C22×D311yescharacteristic
265C2×C3×C4C22×D311yescharacteristic
266C2×C3×C4C22×D311yescharacteristic
267#67—22no—
268#67—22no—
269#67—121no—
270#67—121no—
271#67—121no—
272#67—121no—
273#67—121no—
274#67—121no—
275C2×Dic3—31no—
276C2×Dic3—31no—
277C2×Dic3—31no—
278C2×Dic3—31no—
279C2×Dic3—31no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—41no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—122no—
292C2×Dic3C22×D311yescharacteristic
293C2×Dic3C22×D311yescharacteristic
294C2×Dic3C22×D311yescharacteristic
295C2×Dic3C22×D311yescharacteristic
296D12—41no—
297D12—41no—
298C4×D3—41no—
299C4×D3—121no—
300Dic6—121no—
301Dic6—121no—
302Dic6—122no—
303C2×C32—22no—
304C2×C32C2×#4111yescharacteristic
305C2×C32H(5,𝔽2)11yescharacteristic
306C2×C32H(5,𝔽2)11yescharacteristic
307C3×D3—41no—
308C3×D3—41no—
309C3×D3—41no—
310C3×D3—41no—
311C24—31no—
312C2×Q8—91no—
313C2×D4—31no—
314C2×D4—31no—
315C2×D4—31no—
316C2×D4—31no—
317C2×D4—91no—
318C2×D4—91no—
319C2×D4—91no—
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—91no—
323C22×C4—91no—
324C4⋊C4—31no—
325C4⋊C4—91no—
326C4⋊C4—91no—
327C4⋊C4—91no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C22⋊C4—31no—
331C22⋊C4—31no—
332C22⋊C4—31no—
333C22⋊C4—91no—
334C22⋊C4—91no—
335C22⋊C4—91no—
336C22⋊C4—91no—
337C22⋊C4—91no—
338C22⋊C4—91no—
339C22⋊C4—91no—
340C22⋊C4—91no—
341C22⋊C4—91no—
342C22⋊C4—91no—
343C22⋊C4D3211yescharacteristic
344C42—31no—
345C42—91no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—22no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—61no—
355C22×C3—61no—
356C22×C3—61no—
357C22×C3—61no—
358C22×C3—61no—
359C22×C3—61no—
360C22×C3—61no—
361C22×C3—61no—
362C22×C3—61no—
363C22×C3—61no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—124no—
367C22×C3#23512yes—
368C22×C3#23712yes—
369C22×C3C23×D311yescharacteristic
370C22×C3C23×D311yescharacteristic
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—21no—
377C2×D3—21no—
378C2×D3—21no—
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—44no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—61no—
391C3×C4—61no—
392C3×C4—61no—
393C3×C4—61no—
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—21no—
398Dic3—62no—
399Dic3—61no—
400Dic3—61no—
401Dic3—61no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—61no—
406Dic3—61no—
407Dic3—121no—
408Dic3—121no—
409Dic3—121no—
410C32#53811yescharacteristic, complemented, Sylow
411C23—31no—
412C23—31no—
413C23—31no—
414C23—31no—
415C23—62no—
416C23—121no—
417C23—121no—
418C23C2×D3211yescharacteristic
419Q8—361no—
420D4—62no—
421D4—62no—
422D4—121no—
423D4—121no—
424D4—361no—
425D4—361no—
426D4—361no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—91no—
432C2×C4—91no—
433C2×C4—91no—
434C2×C4—91no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4C2×D3211yescharacteristic
440C2×C4C2×D3211yescharacteristic
441C2×C3—22no—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—42no—
447C2×C3—121no—
448C2×C3—121no—
449C2×C3—121no—
450C2×C3—121no—
451C2×C3C2×#23511yescharacteristic
452C2×C3C2×#23711yescharacteristic
453C2×C3#100411yescharacteristic
454C2×C3#100411yescharacteristic
455C2×C3#100411yescharacteristic
456C2×C3#100911yescharacteristic
457D3—41no—
458D3—41no—
459D3—41no—
460D3—41no—
461C22—21no—
462C22—21no—
463C22—61no—
464C22—61no—
465C22—61no—
466C22—61no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—61no—
473C22—61no—
474C22—61no—
475C22—124no—
476C22#379512yes—
477C22C22×D3211yescharacteristic
478C4—21no—
479C4—21no—
480C4—61no—
481C4—61no—
482C4—61no—
483C4—61no—
484C4—181no—
485C4—181no—
486C4—181no—
487C4—181no—
488C3—21no—
489C3#556011yescharacteristic, complemented
490C3#559311yescharacteristic, complemented
491C2—22no—
492C2—121no—
493C2—121no—
494C2—121no—
495C2—121no—
496C2C2×#379511yescharacteristic
497C2#6431311yescharacteristic
498C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #64087C2semidirect
2. C3×#882C2semidirect
3. C3×#67⋊C4C2semidirect
4. #63980C2semidirect
5. #63976C2semidirect
6. Dic3×#67C2semidirect
7. C2×(C2×D3)⋊Dic3C2semidirect
8. #63913C2semidirect
9. #63908C2semidirect
10. #63905C2semidirect
11. #63885C2semidirect
12. #63884C2semidirect
13. #63861C2semidirect
14. #63860C2semidirect
15. #63859C2semidirect
20. C2×#634C22semidirect
26. C2×C3×C4×D3C22semidirect
29. C2×#625C22semidirect
30. C2×D3×Dic3C22semidirect
33. C4⋊(C3⋊Dic3)C22semidirect
34. #3750C22semidirect
35. #3750C22semidirect
38. C3×(C2×D3)⋊C4C22semidirect
39. C3×Dic3⋊C4C22semidirect
40. C3×C4×Dic3C22semidirect
41. #3724C22semidirect
42. Dic3⋊Dic3C22semidirect
49. (C2×D3)⋊Dic3C22semidirect
50. (C2×D3)⋊Dic3C22semidirect
51. (C2×D3)⋊Dic3C22semidirect
52. Dic32C22semidirect
75. #882D3semidirect
76. #67⋊C4D3semidirect
139. C2×C4×D3C2×D3semidirect
174. (C2×D3)⋊C4C2×D3semidirect
188. Dic3⋊C4C2×D3semidirect
191. C4×Dic3C2×D3semidirect
410. C32#538semidirect
489. C3#5560semidirect
490. C3#5593semidirect

Maximal subgroups

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

subgroupindex
#640872
C3×#8822
C3×#67⋊C42
#639802
#639762
Dic3×#672
C2×(C2×D3)⋊Dic32
#639132
#639082
#639052
#638852
#638842
#638612
#638602
#638592
#55933
#55603