Finite Group Databasebeta

← #10595129

Subgroups — #10595129

Order 576.

707 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3804C211yesmaximal, characteristic, complemented
2C22×D3×Dic3C211yesmaximal, characteristic, complemented
3#64148C211yesmaximal, characteristic, complemented
4C3×#937C211yesmaximal, characteristic, complemented
5C3×D4×Dic3C211yesmaximal, characteristic, complemented
6#63982C211yesmaximal, characteristic, complemented
7#63977C211yesmaximal, characteristic, complemented
8Dic3×#67C211yesmaximal, characteristic, complemented
9#63971C211yesmaximal, characteristic, complemented
10#63969C211yesmaximal, characteristic, complemented
11#63952C211yesmaximal, characteristic, complemented
12#63899C211yesmaximal, characteristic, complemented
13#63890C211yesmaximal, characteristic, complemented
14#63880C211yesmaximal, characteristic, complemented
15#63877C211yesmaximal, characteristic, complemented
16#5586—31nomaximal
17#5547—31nomaximal
18C23×C3×D3C2211yescharacteristic
19C2×C32×D4C2211yescharacteristic
20C2×#638C2211yescharacteristic
21C2×#638C2211yescharacteristic, complemented
22C22×C3⋊Dic3C2211yescharacteristic
23C2×C3×#67C2211yescharacteristic
24C2×C3×#67C2211yescharacteristic
25C22×C3×Dic3C2211yescharacteristic
26C22×C3×Dic3C2211yescharacteristic, complemented
27C2×#627C2211yescharacteristic, complemented
28C2×#626C2211yescharacteristic
29C2×#626C2211yescharacteristic
30C2×#624C2211yescharacteristic, complemented
31#3804—24no—
32C2×D3×Dic3—24no—
33C2×D3×Dic3C2211yescharacteristic
34C2×D3×Dic3C2211yescharacteristic
35C2×D3×Dic3C2211yescharacteristic
36C2×D3×Dic3C2211yescharacteristic
37#3757C2211yescharacteristic, complemented
38#3752C2211yescharacteristic, complemented
39#3750C2211yescharacteristic, complemented
40C3×#217C2211yescharacteristic
41C3×#217C2211yescharacteristic
42C3×#217C2211yescharacteristic, complemented
43C3×(C2×D3)⋊C4C2211yescharacteristic
44C3×(C2×D3)⋊C4C2211yescharacteristic
45C3×C4⋊Dic3C2211yescharacteristic, complemented
46C3×C4×Dic3C2211yescharacteristic, complemented
47#3724C2211yescharacteristic, complemented
48#3724C2211yescharacteristic, complemented
49Dic3⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic3C2211yescharacteristic, complemented
51#3722C2211yescharacteristic, complemented
52(C2×D3)⋊Dic3C2211yescharacteristic
53(C2×D3)⋊Dic3C2211yescharacteristic
54Dic32C2211yescharacteristic, complemented
55C23×Dic3—31no—
56C2×#237—31no—
57C2×#235—31no—
58C22×C4×D3—31no—
59C3×#120—31no—
60C3×C4×D4—31no—
61#953—31no—
62#939—31no—
63#939—31no—
64#939—31no—
65#939—61no—
66#937D311yescharacteristic, complemented
67#935—31no—
68D4×Dic3—31no—
69D4×Dic3D311yescharacteristic, complemented
70C4×#67—31no—
71C4×#67—31no—
72#896—31no—
73#894—31no—
74#886—31no—
75#884—31no—
76#883—31no—
77#882—31no—
78#67⋊C4—31no—
79#67⋊C4—31no—
80#878—31no—
81#878—31no—
82#878—31no—
83#877—31no—
84C4×D12—31no—
85#872—31no—
86C23×C32C2311yescharacteristic
87C23×C32C2311yescharacteristic
88C22×C3⋊D3C2311yescharacteristic
89C22×C3×D3—22no—
90C22×C3×D3—22no—
91C22×C3×D3—22no—
92C22×C3×D3C2311yescharacteristic
93C22×C3×D3C2311yescharacteristic
94C32×D4—22no—
95C2×C32×C4C2311yescharacteristic
96#638—22no—
97#638—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C2311yescharacteristic
100C2×C3⋊Dic3C2311yescharacteristic
101C2×C3⋊Dic3C2311yescharacteristic
102C3×#67—22no—
103C3×#67—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—22no—
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C2×C3×Dic3C2311yescharacteristic
109C2×C3×Dic3C2311yescharacteristic
110C2×C3×Dic3C2311yescharacteristic
111C2×C3×Dic3C2311yescharacteristic
112#627—22no—
113#626—22no—
114#626—22no—
115#624—22no—
116D3×Dic3—22no—
117D3×Dic3—22no—
118D3×Dic3—22no—
119D3×Dic3D414yescomplemented
120#525—91noSylow
121C24×C3—31no—
122C23×D3C2×D311yescharacteristic
123C2×C3×D4—21no—
124C2×C3×D4—31no—
125C2×C3×D4—31no—
126C2×C3×D4C2×D311yescharacteristic
127C2×C3×D4C2×D311yescharacteristic
128C22×C3×C4—31no—
129C22×C3×C4—31no—
130C2×#67—31no—
131C2×#67—31no—
132C2×#67—31no—
133C2×#67—31no—
134C2×#67—31no—
135C2×#67—31no—
136C2×#67—61no—
137C2×#67—61no—
138C2×#67C2×D311yescharacteristic
139C2×#67C2×D311yescharacteristic
140C22×Dic3—31no—
141C22×Dic3—31no—
142C22×Dic3—31no—
143C22×Dic3—31no—
144C22×Dic3—31no—
145C22×Dic3—31no—
146C22×Dic3—61no—
147C22×Dic3—64no—
148C22×Dic3C2×D311yescharacteristic
149C22×Dic3C2×D311yescharacteristic, complemented
150#237—64no—
151#235—64no—
152C2×D12—31no—
153C2×D12—31no—
154C2×C4×D3—31no—
155C2×C4×D3—31no—
156C2×C4×D3—31no—
157C2×C4×D3—31no—
158C2×C4×D3—31no—
159C2×C4×D3—31no—
160C2×C4×D3—64no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C3×C4⋊C4—31no—
164C3×C22⋊C4—31no—
165C3×C22⋊C4—31no—
166C3×C22⋊C4—31no—
167C3×C22⋊C4—31no—
168C3×C22⋊C4—31no—
169C3×C42—31no—
170#217—31no—
171#217—31no—
172#217—31no—
173#217—31no—
174#217—61no—
175#217C2×D311yescharacteristic
176#217C2×D311yescharacteristic
177#217C2×D311yescharacteristic, complemented
178(C2×D3)⋊C4—31no—
179(C2×D3)⋊C4—31no—
180(C2×D3)⋊C4—31no—
181(C2×D3)⋊C4—31no—
182(C2×D3)⋊C4—31no—
183(C2×D3)⋊C4—31no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4C2×D311yescharacteristic
186(C2×D3)⋊C4C2×D311yescharacteristic
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3C2×D311yescharacteristic, complemented
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4—31no—
193Dic3⋊C4—31no—
194Dic3⋊C4—31no—
195Dic3⋊C4—31no—
196Dic3⋊C4—31no—
197Dic3⋊C4—31no—
198Dic3⋊C4—61no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3C2×D311yescharacteristic, complemented
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—21no—
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—28no—
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C2×C3×D3—21no—
216C2×C3×D3—21no—
217C2×C3×D3C2×D412yes—
218C2×C3×D3#4112yescomplemented
219C32×C4—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3C2×D412yes—
223C3×Dic3—21no—
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3C2×D412yes—
229C2×#41—91no—
230C23×C4—91no—
231#123—91no—
232#123—91no—
233C22⋊Q8—91no—
234C22⋊Q8—91no—
235#121—91no—
236#121—91no—
237#120—31no—
238#120—91no—
239C4×D4—31no—
240C4×D4—91no—
241C4×D4—91no—
242C4×D4—91no—
243#117—91no—
244C23×C3—21no—
245C23×C3—21no—
246C23×C3—31no—
247C23×C3—31no—
248C23×C3—62no—
249C23×C3—62no—
250C23×C3—62no—
251C23×C3C22×D311yescharacteristic
252C23×C3C22×D311yescharacteristic
253C23×C3C22×D311yescharacteristic
254C23×C3C22×D311yescharacteristic
255C22×D3—22no—
256C22×D3—22no—
257C22×D3—22no—
258C22×D3—31no—
259C22×D3—31no—
260C22×D3—61no—
261C22×D3C22×D311yescharacteristic
262C22×D3C22×D311yescharacteristic
263C3×D4—22no—
264C3×D4—22no—
265C3×D4—42no—
266C3×D4—62no—
267C3×D4—62no—
268C2×C3×C4—21no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4C22×D311yescharacteristic
278C2×C3×C4C22×D311yescharacteristic
279#67—22no—
280#67—22no—
281#67—62no—
282#67—62no—
283#67—62no—
284#67—62no—
285#67—62no—
286#67—62no—
287#67—122no—
288#67—122no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—34no—
294C2×Dic3—31no—
295C2×Dic3—31no—
296C2×Dic3—31no—
297C2×Dic3—31no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3C22×D311yescharacteristic
308C2×Dic3C22×D311yescharacteristic
309C2×Dic3C22×D311yescharacteristic
310C2×Dic3C22×D311yescharacteristic
311C2×Dic3C22×D311yescharacteristic
312C2×Dic3C22×D311yescharacteristic
313D12—62no—
314D12—62no—
315C4×D3—34no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—62no—
321Dic6—62no—
322Dic6—62no—
323C2×C32—22no—
324C2×C32—41no—
325C2×C32C22×D411yescharacteristic
326C2×C32C2×#4111yescharacteristic
327C2×C32C2×#4111yescharacteristic
328C3⋊D3—41no—
329C3×D3—22no—
330C3×D3—22no—
331C24—31no—
332#41—184no—
333C2×Q8—91no—
334C2×D4—31no—
335C2×D4—31no—
336C2×D4—91no—
337C2×D4—91no—
338C2×D4—91no—
339C2×D4—91no—
340C2×D4D3211yescharacteristic
341C22×C4—31no—
342C22×C4—31no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—184no—
350C4⋊C4—31no—
351C4⋊C4—91no—
352C4⋊C4—91no—
353C4⋊C4—91no—
354C4⋊C4—91no—
355C4⋊C4—91no—
356C22⋊C4—31no—
357C22⋊C4—31no—
358C22⋊C4—31no—
359C22⋊C4—31no—
360C22⋊C4—31no—
361C22⋊C4—91no—
362C22⋊C4—91no—
363C22⋊C4—91no—
364C22⋊C4—91no—
365C22⋊C4—91no—
366C42—31no—
367C42—91no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—32no—
381C22×C3—32no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—68no—
388C22×C3—61no—
389C22×C3—61no—
390C22×C3—61no—
391C22×C3—61no—
392C22×C3#23512yescomplemented
393C22×C3#23712yescomplemented
394C22×C3C23×D311yescharacteristic
395C22×C3C23×D311yescharacteristic
396C2×D3—28no—
397C2×D3—21no—
398C2×D3—21no—
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—61no—
402C2×D3—61no—
403C2×D3—61no—
404C2×D3—61no—
405C2×D3—61no—
406C2×D3—61no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3D3×D412yes—
411C2×D3#23712yescomplemented
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—32no—
415C3×C4—41no—
416C3×C4—61no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—61no—
421Dic3—21no—
422Dic3—21no—
423Dic3—21no—
424Dic3—21no—
425Dic3—21no—
426Dic3—32no—
427Dic3—32no—
428Dic3—62no—
429Dic3—61no—
430Dic3—61no—
431Dic3—61no—
432Dic3—61no—
433Dic3—121no—
434Dic3—121no—
435Dic3D3×D412yes—
436C32#52511yescharacteristic, complemented, Sylow
437C23—31no—
438C23—31no—
439C23—62no—
440C23—62no—
441C23—62no—
442C23—91no—
443C23C2×D3211yescharacteristic
444C23C2×D3211yescharacteristic
445Q8—182no—
446D4—22no—
447D4—62no—
448D4—62no—
449D4—182no—
450D4—182no—
451D4—182no—
452D4—182no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—94no—
462C2×C4—91no—
463C2×C4—91no—
464C2×C4—91no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4—182no—
470C2×C4C2×D3211yescharacteristic
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—42no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3—62no—
480C2×C3—62no—
481C2×C3—81no—
482C2×C3C2×#23511yescharacteristic
483C2×C3C2×D3×D411yescharacteristic
484C2×C3C2×D3×D411yescharacteristic
485C2×C3C2×#23711yescharacteristic
486C2×C3C2×#23711yescharacteristic
487C2×C3D3×#4111yescharacteristic
488D3—22no—
489D3—22no—
490D3—121no—
491D3—121no—
492D3—241no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—32no—
499C22—32no—
500C22—68no—
501C22—61no—
502C22—61no—
503C22—61no—
504C22—61no—
505C22—181no—
506C22—181no—
507C22—181no—
508C22#380412yescomplemented
509C22C22×D3211yescharacteristic
510C4—21no—
511C4—32no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—92no—
518C4—181no—
519C4—181no—
520C3—21no—
521C3#554711yescharacteristic, complemented
522C3#558611yescharacteristic, complemented
523C2—22no—
524C2—41no—
525C2—62no—
526C2—62no—
527C2—361no—
528C2D32×D411yescharacteristic
529C2D3×#23711yescharacteristic
530C2C2×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×D4C22
hypercenterC2×D4D32
hypocenterC32#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#3804C2semidirect
2. C22×D3×Dic3C2semidirect
3. #64148C2semidirect
4. C3×#937C2semidirect
5. C3×D4×Dic3C2semidirect
6. #63982C2semidirect
7. #63977C2semidirect
8. Dic3×#67C2semidirect
9. #63971C2semidirect
10. #63969C2semidirect
11. #63952C2semidirect
12. #63899C2semidirect
13. #63890C2semidirect
14. #63880C2semidirect
15. #63877C2semidirect
21. C2×#638C22semidirect
26. C22×C3×Dic3C22semidirect
27. C2×#627C22semidirect
30. C2×#624C22semidirect
37. #3757C22semidirect
38. #3752C22semidirect
39. #3750C22semidirect
42. C3×#217C22semidirect
45. C3×C4⋊Dic3C22semidirect
46. C3×C4×Dic3C22semidirect
47. #3724C22semidirect
48. #3724C22semidirect
49. Dic3⋊Dic3C22semidirect
50. Dic3⋊Dic3C22semidirect
51. #3722C22semidirect
54. Dic32C22semidirect
66. #937D3semidirect
69. D4×Dic3D3semidirect
119. D3×Dic3D4semidirect
149. C22×Dic3C2×D3semidirect
177. #217C2×D3semidirect
189. C4⋊Dic3C2×D3semidirect
201. C4×Dic3C2×D3semidirect
207. C22×C32#41semidirect
218. C2×C3×D3#41semidirect
392. C22×C3#235semidirect
393. C22×C3#237semidirect
411. C2×D3#237semidirect
436. C32#525semidirect
508. C22#3804semidirect
521. C3#5547semidirect
522. C3#5586semidirect

Maximal subgroups

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

subgroupindex
C2×#38042
C22×D3×Dic32
#641482
C3×#9372
C3×D4×Dic32
#639822
#639772
Dic3×#672
#639712
#639692
#639522
#638992
#638902
#638802
#638772
#55863
#55473