Finite Group Databasebeta

← #10594126

Subgroups — #10594126

Order 576.

538 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64094C211yesmaximal, characteristic, complemented
2C3×#882C211yesmaximal, characteristic, complemented
3C3×#879C211yesmaximal, characteristic, complemented
4#63977C211yesmaximal, characteristic, complemented
5#63969C211yesmaximal, characteristic, complemented
6D3×#217C211yesmaximal, characteristic, complemented
7#63958C211yesmaximal, characteristic, complemented
8#63898C211yesmaximal, characteristic, complemented
9#63896C211yesmaximal, characteristic, complemented
10#63886C211yesmaximal, characteristic, complemented
11#63886C211yesmaximal, characteristic, complemented
12#63880C211yesmaximal, characteristic, complemented
13#63862C211yesmaximal, characteristic, complemented
14#63860C211yesmaximal, characteristic, complemented
15#63854C211yesmaximal, characteristic, complemented
16#5704—31nomaximal
17#5593—31nomaximal
18C23×C3×D3C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#634C2211yescharacteristic, complemented
21C2×C3×#67C2211yescharacteristic
22C2×C3×D12C2211yescharacteristic
23C2×C3×D12C2211yescharacteristic
24C2×#626C2211yescharacteristic
25C2×#626C2211yescharacteristic
26C2×#626C2211yescharacteristic, complemented
27C2×#624C2211yescharacteristic, complemented
28C2×D3×Dic3C2211yescharacteristic
29C2×D3×Dic3C2211yescharacteristic
30C2×D3×Dic3C2211yescharacteristic, complemented
31C32×C22⋊C4C2211yescharacteristic
32#3757C2211yescharacteristic
33#3752C2211yescharacteristic, complemented
34#3752C2211yescharacteristic, complemented
35C4×C3⋊Dic3C2211yescharacteristic, complemented
36C3×#217C2211yescharacteristic
37C3×#217C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×C4⋊Dic3C2211yescharacteristic, complemented
41C3×Dic3⋊C4C2211yescharacteristic, complemented
42C3×Dic3⋊C4C2211yescharacteristic, complemented
43C3×C4×Dic3C2211yescharacteristic, complemented
44#3724C2211yescharacteristic, complemented
45Dic3⋊Dic3C2211yescharacteristic, complemented
46Dic3⋊Dic3C2211yescharacteristic, complemented
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×#126—31no—
54C3×#120—31no—
55#953—31no—
56C2×#217—31no—
57#939—31no—
58#939—31no—
59#938—31no—
60#936—31no—
61#935—31no—
62D4×Dic3—31no—
63#898—31no—
64#896—31no—
65#895—31no—
66#895—31no—
67#894—31no—
68#893—31no—
69#885—31no—
70#885—31no—
71#885—61no—
72#884—31no—
73#883—31no—
74#883—31no—
75#882—31no—
76#882D311yescharacteristic, complemented
77#67⋊C4—31no—
78D3×C22⋊C4—31no—
79#879—31no—
80#879D311yescharacteristic, complemented
81#878—31no—
82#875—31no—
83C4×D12—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3×D3—22no—
87C22×C3×D3—41no—
88C22×C3×D3—41no—
89C22×C3×D3C2311yescharacteristic
90C22×C3×D3C2311yescharacteristic
91C22×C3×D3C2311yescharacteristic
92C2×C32×C4C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94#638—41no—
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98#634—41no—
99C3×#67—41no—
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C3×D12—22no—
106C3×D12—41no—
107#626—22no—
108#626—41no—
109#626—41no—
110#624—41no—
111D3×Dic3—41no—
112D3×Dic3—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×#67—31no—
121C2×#67—31no—
122C2×#67—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—61no—
126C2×#67C2×D311yescharacteristic
127C22×Dic3—31no—
128C22×Dic3—31no—
129C22×Dic3—31no—
130C2×D12—31no—
131C2×D12—31no—
132C2×D12—31no—
133C2×D12C2×D311yescharacteristic
134C2×D12C2×D311yescharacteristic
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×C4×D3—31no—
138C2×C4×D3—31no—
139C2×C4×D3—31no—
140C2×Dic6—31no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C22⋊C4—21no—
147C3×C22⋊C4—31no—
148C3×C22⋊C4—31no—
149C3×C22⋊C4—31no—
150C3×C22⋊C4—31no—
151C3×C22⋊C4C2×D311yescharacteristic
152C3×C22⋊C4C2×D311yescharacteristic
153C3×C42—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#217C2×D311yescharacteristic
164#217C2×D311yescharacteristic
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)⋊C4—31no—
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—31no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4C2×D311yescharacteristic
178(C2×D3)⋊C4C2×D311yescharacteristic
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3C2×D311yescharacteristic, complemented
182Dic3⋊C4—31no—
183Dic3⋊C4—31no—
184Dic3⋊C4—31no—
185Dic3⋊C4—31no—
186Dic3⋊C4C2×D311yescharacteristic, complemented
187Dic3⋊C4C2×D311yescharacteristic, complemented
188C4×Dic3—31no—
189C4×Dic3—31no—
190C4×Dic3—61no—
191C4×Dic3C2×D311yescharacteristic, complemented
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—21no—
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—44no—
208C2×C3×D3#4112yes—
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—31no—
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—91no—
232C4×D4—91no—
233C2×C22⋊C4—91no—
234C23×C3—21no—
235C23×C3—31no—
236C23×C3—31no—
237C23×C3—31no—
238C23×C3—62no—
239C23×C3—121no—
240C23×C3—121no—
241C23×C3C22×D311yescharacteristic
242C23×C3C22×D311yescharacteristic
243C22×D3—22no—
244C22×D3—31no—
245C22×D3—31no—
246C22×D3—41no—
247C22×D3—41no—
248C22×D3—61no—
249C22×D3C22×D311yescharacteristic
250C22×D3C22×D311yescharacteristic
251C22×D3C22×D311yescharacteristic
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—31no—
262C2×C3×C4C22×D311yescharacteristic
263C2×C3×C4C22×D311yescharacteristic
264C2×C3×C4C22×D311yescharacteristic
265C2×C3×C4C22×D311yescharacteristic
266#67—41no—
267#67—62no—
268#67—121no—
269#67—121no—
270#67—121no—
271#67—121no—
272#67—122no—
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—31no—
276C2×Dic3—31no—
277C2×Dic3—31no—
278C2×Dic3—31no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3C22×D311yescharacteristic
286C2×Dic3C22×D311yescharacteristic
287C2×Dic3C22×D311yescharacteristic
288C2×Dic3C22×D311yescharacteristic
289C2×Dic3C22×D311yescharacteristic
290D12—22no—
291D12—41no—
292D12—62no—
293D12—121no—
294D12—121no—
295C4×D3—121no—
296C4×D3—121no—
297C4×D3—121no—
298C4×D3—121no—
299C4×D3—121no—
300Dic6—121no—
301Dic6—121no—
302Dic6—122no—
303C2×C32—41no—
304C2×C32C2×#4111yescharacteristic
305C2×C32H(5,𝔽2)11yescharacteristic
306C2×C32H(5,𝔽2)11yescharacteristic
307C3⋊D3—41no—
308C3×D3—22no—
309C3×D3—41no—
310C3×D3—41no—
311C24—31no—
312C2×Q8—91no—
313C2×D4—31no—
314C2×D4—31no—
315C2×D4—31no—
316C2×D4—91no—
317C2×D4—91no—
318C2×D4—91no—
319C2×D4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—91no—
324C4⋊C4—31no—
325C4⋊C4—31no—
326C4⋊C4—31no—
327C4⋊C4—91no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C22⋊C4—31no—
331C22⋊C4—31no—
332C22⋊C4—31no—
333C22⋊C4—31no—
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—21no—
352C22×C3—21no—
353C22×C3—32no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
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—124no—
366C22×C3C23×D311yescharacteristic
367C22×C3C23×D311yescharacteristic
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—44no—
377C2×D3—61no—
378C2×D3—61no—
379C2×D3—61no—
380C2×D3—61no—
381C2×D3—61no—
382C2×D3—61no—
383C2×D3—121no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3#23712yes—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—61no—
394C3×C4—61no—
395C3×C4—61no—
396C3×C4—61no—
397C3×C4—61no—
398Dic3—21no—
399Dic3—21no—
400Dic3—21no—
401Dic3—21no—
402Dic3—21no—
403Dic3—62no—
404Dic3—61no—
405Dic3—61no—
406Dic3—61no—
407Dic3—61no—
408Dic3—61no—
409Dic3—61no—
410Dic3—121no—
411Dic3—121no—
412C32#53811yescharacteristic, complemented, Sylow
413C23—31no—
414C23—31no—
415C23—31no—
416C23—62no—
417C23—91no—
418C23—121no—
419C23—121no—
420C23C2×D3211yescharacteristic
421Q8—361no—
422D4—62no—
423D4—121no—
424D4—121no—
425D4—182no—
426D4—361no—
427D4—361no—
428D4—361no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—91no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4—361no—
440C2×C4—361no—
441C2×C4C2×D3211yescharacteristic
442C2×C4C2×D3211yescharacteristic
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—62no—
449C2×C3—81no—
450C2×C3—121no—
451C2×C3—121no—
452C2×C3C2×#23711yescharacteristic
453C2×C3#100411yescharacteristic
454C2×C3#100411yescharacteristic
455C2×C3D3×#4111yescharacteristic
456C2×C3#100911yescharacteristic
457C2×C3#100911yescharacteristic
458D3—22no—
459D3—41no—
460D3—41no—
461D3—121no—
462D3—121no—
463D3—241no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—32no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—61no—
473C22—61no—
474C22—61no—
475C22—61no—
476C22—124no—
477C22—181no—
478C22—181no—
479C22—181no—
480C22C22×D3211yescharacteristic
481C4—21no—
482C4—21no—
483C4—61no—
484C4—61no—
485C4—61no—
486C4—61no—
487C4—61no—
488C4—181no—
489C4—181no—
490C4—181no—
491C3—21no—
492C3#559311yescharacteristic, complemented
493C3#570411yescharacteristic, complemented
494C2—41no—
495C2—62no—
496C2—121no—
497C2—121no—
498C2—361no—
499C2#6430711yescharacteristic
500C2D3×#23711yescharacteristic
501C2#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. #64094C2semidirect
2. C3×#882C2semidirect
3. C3×#879C2semidirect
4. #63977C2semidirect
5. #63969C2semidirect
6. D3×#217C2semidirect
7. #63958C2semidirect
8. #63898C2semidirect
9. #63896C2semidirect
10. #63886C2semidirect
11. #63886C2semidirect
12. #63880C2semidirect
13. #63862C2semidirect
14. #63860C2semidirect
15. #63854C2semidirect
20. C2×#634C22semidirect
26. C2×#626C22semidirect
27. C2×#624C22semidirect
30. C2×D3×Dic3C22semidirect
33. #3752C22semidirect
34. #3752C22semidirect
35. C4×C3⋊Dic3C22semidirect
40. C3×C4⋊Dic3C22semidirect
41. C3×Dic3⋊C4C22semidirect
42. C3×Dic3⋊C4C22semidirect
43. C3×C4×Dic3C22semidirect
44. #3724C22semidirect
45. Dic3⋊Dic3C22semidirect
46. Dic3⋊Dic3C22semidirect
51. (C2×D3)⋊Dic3C22semidirect
52. (C2×D3)⋊Dic3C22semidirect
76. #882D3semidirect
80. #879D3semidirect
181. C4⋊Dic3C2×D3semidirect
186. Dic3⋊C4C2×D3semidirect
187. Dic3⋊C4C2×D3semidirect
191. C4×Dic3C2×D3semidirect
412. C32#538semidirect
492. C3#5593semidirect
493. C3#5704semidirect

Maximal subgroups

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

subgroupindex
#640942
C3×#8822
C3×#8792
#639772
#639692
D3×#2172
#639582
#638982
#638962
#638862
#638802
#638622
#638602
#638542
#57043
#55933