Finite Group Databasebeta

← #10594663

Subgroups — #10594663

Order 576.

551 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
1#64104C211yesmaximal, characteristic, complemented
2C3×#898C211yesmaximal, characteristic, complemented
3C3×#894C211yesmaximal, characteristic, complemented
4#63923C211yesmaximal, characteristic, complemented
5#63923C211yesmaximal, characteristic, complemented
6#63922C211yesmaximal, characteristic, complemented
7#63912C211yesmaximal, characteristic, complemented
8#63911C211yesmaximal, characteristic, complemented
9#63910C211yesmaximal, characteristic, complemented
10#63910C211yesmaximal, characteristic, complemented
11#63909C211yesmaximal, characteristic, complemented
12#63906C211yesmaximal, characteristic, complemented
13#63868C211yesmaximal, characteristic, complemented
14#63854C211yesmaximal, characteristic, complemented
15#63853C211yesmaximal, characteristic, complemented
16#5711—31nomaximal
17#5666—31nomaximal
18C22×D32C2211yescharacteristic
19C2×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×D12C2211yescharacteristic
24C2×C3×C4×D3C2211yescharacteristic, complemented
25C2×#626C2211yescharacteristic
26C2×#626C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#626C2211yescharacteristic
29C2×#626C2211yescharacteristic
30C2×#626C2211yescharacteristic, complemented
31C2×#626C2211yescharacteristic, complemented
32C2×#625C2211yescharacteristic
33C2×#624C2211yescharacteristic, complemented
34C32×C4⋊C4C2211yescharacteristic, complemented
35#3752C2211yescharacteristic
36#3752C2211yescharacteristic, complemented
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×C4⋊Dic3C2211yescharacteristic, complemented
44C3×Dic3⋊C4C2211yescharacteristic, complemented
45C3×Dic3⋊C4C2211yescharacteristic, complemented
46C3×C4×Dic3C2211yescharacteristic, complemented
47#3724C2211yescharacteristic, complemented
48Dic3⋊Dic3C2211yescharacteristic, complemented
49#3722C2211yescharacteristic
50#3722C2211yescharacteristic
51#3722C2211yescharacteristic, complemented
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×#126—31no—
54C3×#123—31no—
55#940—31no—
56#937—31no—
57#930—31no—
58#930—31no—
59#898—31no—
60#898D311yescharacteristic, complemented
61#895—31no—
62#895—31no—
63#895—31no—
64#895—31no—
65#895—31no—
66#895—61no—
67#894—31no—
68#894—31no—
69#894D311yescharacteristic, complemented
70#884—31no—
71#884—31no—
72#884—31no—
73#884—31no—
74#884—31no—
75#883—31no—
76#883—31no—
77#882—31no—
78#882—31no—
79#882—31no—
80#882—31no—
81#882—31no—
82#876—31no—
83#874—31no—
84C22×C3⋊D3C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3⋊D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C2×D32—41no—
91C2×D32—41no—
92C2×D32—41no—
93C2×C32×C4C2311yescharacteristic
94C2×C32×C4C2311yescharacteristic
95C2×C32×C4C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C4⋊(C3⋊D3)—41no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4×C3⋊D3—41no—
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C3×D12—41no—
107C3×C4×D3—41no—
108#626—41no—
109#626—41no—
110#626—41no—
111#626—41no—
112#626—41no—
113#626—41no—
114#626—41no—
115#625—41no—
116#624—41no—
117#560—91noSylow
118C23×D3—31no—
119C23×D3—31no—
120C2×C3×D4—31no—
121C22×C3×C4—31no—
122C2×#67—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—31no—
126C2×#67—31no—
127C2×#67—31no—
128C2×#67—31no—
129C2×#67—31no—
130C2×#67—31no—
131C2×D12—31no—
132C2×D12—31no—
133C2×D12—31no—
134C2×D12—31no—
135C2×D12—31no—
136C2×D12—31no—
137C2×D12—31no—
138C2×D12—31no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—31no—
142C2×D12—31no—
143C2×D12—31no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12C2×D311yescharacteristic
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—31no—
151C2×C4×D3—31no—
152C2×C4×D3—61no—
153C2×C4×D3C2×D311yescharacteristic, complemented
154C3×C4⋊C4—21no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4C2×D311yescharacteristic, complemented
159C3×C4⋊C4C2×D311yescharacteristic, complemented
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4—31no—
163C3×C22⋊C4—31no—
164C3×C22⋊C4—31no—
165C3×C22⋊C4—31no—
166C3×C42—31no—
167#217—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—31no—
176(C2×D3)⋊C4—31no—
177(C2×D3)⋊C4—31no—
178(C2×D3)⋊C4—31no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4C2×D311yescharacteristic
182(C2×D3)⋊C4C2×D311yescharacteristic
183(C2×D3)⋊C4C2×D311yescharacteristic
184(C2×D3)⋊C4C2×D311yescharacteristic
185(C2×D3)⋊C4C2×D311yescharacteristic
186(C2×D3)⋊C4C2×D311yescharacteristic, complemented
187C4⋊Dic3—31no—
188C4⋊Dic3C2×D311yescharacteristic, complemented
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4C2×D311yescharacteristic, complemented
193Dic3⋊C4C2×D311yescharacteristic, complemented
194C4×Dic3C2×D311yescharacteristic, complemented
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—21no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—21no—
213C2×C3×D3—21no—
214D32—44no—
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—21no—
218C3⋊Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—21no—
224#127—91no—
225#126—31no—
226#126—91no—
227#123—31no—
228#123—91no—
229#123—91no—
230#121—91no—
231#121—91no—
232#121—91no—
233#121—91no—
234#121—91no—
235#121—91no—
236#120—91no—
237#120—91no—
238#120—91no—
239C23×C3—31no—
240C23×C3—31no—
241C23×C3—31no—
242C22×D3—31no—
243C22×D3—31no—
244C22×D3—31no—
245C22×D3—31no—
246C22×D3—31no—
247C22×D3—31no—
248C22×D3—61no—
249C22×D3—61no—
250C22×D3—61no—
251C22×D3—121no—
252C22×D3—121no—
253C22×D3—121no—
254C22×D3—121no—
255C22×D3—121no—
256C22×D3—121no—
257C22×D3C22×D311yescharacteristic
258C22×D3C22×D311yescharacteristic
259C22×D3C22×D311yescharacteristic
260C3×D4—121no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—31no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—121no—
270C2×C3×C4C22×D311yescharacteristic
271C2×C3×C4C22×D311yescharacteristic
272C2×C3×C4C22×D311yescharacteristic
273C2×C3×C4C22×D311yescharacteristic
274C2×C3×C4C22×D311yescharacteristic
275C2×C3×C4C22×D311yescharacteristic
276#67—121no—
277#67—121no—
278#67—121no—
279#67—121no—
280#67—121no—
281#67—121no—
282#67—121no—
283#67—121no—
284#67—121no—
285C2×Dic3—31no—
286C2×Dic3—31no—
287C2×Dic3—61no—
288C2×Dic3C22×D311yescharacteristic
289C2×Dic3C22×D311yescharacteristic
290C2×Dic3C22×D311yescharacteristic
291C2×Dic3C22×D311yescharacteristic
292C2×Dic3C22×D311yescharacteristic
293D12—41no—
294D12—121no—
295D12—121no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—121no—
300D12—122no—
301D12—122no—
302D12—122no—
303D12—121no—
304D12—121no—
305D12—121no—
306D12—121no—
307D12—121no—
308D12—121no—
309D12—121no—
310C4×D3—41no—
311C4×D3—121no—
312C4×D3—121no—
313C4×D3—121no—
314C4×D3—121no—
315C4×D3—122no—
316C2×C32H(5,𝔽2)11yescharacteristic
317C2×C32H(5,𝔽2)11yescharacteristic
318C2×C32H(5,𝔽2)11yescharacteristic
319C3⋊D3—41no—
320C3⋊D3—41no—
321C3⋊D3—41no—
322C3×D3—41no—
323C3×D3—41no—
324C3×D3—41no—
325C24—91no—
326C2×D4—31no—
327C2×D4—91no—
328C2×D4—91no—
329C2×D4—91no—
330C2×D4—91no—
331C2×D4—91no—
332C2×D4—91no—
333C2×D4—91no—
334C2×D4—91no—
335C2×D4—91no—
336C2×D4—91no—
337C2×D4—91no—
338C22×C4—31no—
339C22×C4—91no—
340C22×C4—91no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—91no—
345C4⋊C4—91no—
346C4⋊C4D3211yescharacteristic, complemented
347C22⋊C4—31no—
348C22⋊C4—31no—
349C22⋊C4—31no—
350C22⋊C4—31no—
351C22⋊C4—31no—
352C22⋊C4—31no—
353C22⋊C4—91no—
354C22⋊C4—91no—
355C22⋊C4—91no—
356C22⋊C4—91no—
357C22⋊C4—91no—
358C22⋊C4—91no—
359C42—31no—
360C22×C3—21no—
361C22×C3—61no—
362C22×C3—61no—
363C22×C3—61no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—61no—
368C22×C3—61no—
369C22×C3—61no—
370C22×C3C23×D311yescharacteristic
371C22×C3C23×D311yescharacteristic
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—62no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—61no—
388C2×D3—61no—
389C2×D3—61no—
390C2×D3—61no—
391C2×D3—61no—
392C2×D3—61no—
393C2×D3—61no—
394C2×D3—61no—
395C2×D3—61no—
396C2×D3—61no—
397C2×D3—61no—
398C2×D3—61no—
399C2×D3—61no—
400C2×D3—121no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—124no—
409C2×D3—124no—
410C3×C4—22no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—41no—
418C3×C4—41no—
419C3×C4—61no—
420C3×C4—61no—
421C3×C4—61no—
422C3×C4—61no—
423C3×C4—61no—
424Dic3—21no—
425Dic3—21no—
426Dic3—21no—
427Dic3—21no—
428Dic3—21no—
429Dic3—61no—
430Dic3—61no—
431Dic3—121no—
432C32#56011yescharacteristic, complemented, Sylow
433C23—31no—
434C23—31no—
435C23—31no—
436C23—91no—
437C23—91no—
438C23—91no—
439C23—361no—
440C23—361no—
441C23—361no—
442D4—121no—
443D4—361no—
444D4—361no—
445D4—361no—
446D4—361no—
447D4—361no—
448D4—361no—
449D4—361no—
450D4—361no—
451D4—361no—
452D4—361no—
453D4—361no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—91no—
460C2×C4—121no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4C2×D3211yescharacteristic
464C2×C4C2×D3211yescharacteristic
465C2×C4C2×D3211yescharacteristic
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—121no—
470C2×C3—121no—
471C2×C3—121no—
472C2×C3#100411yescharacteristic
473C2×C3#100911yescharacteristic
474C2×C3#100911yescharacteristic
475C2×C3#100911yescharacteristic
476C2×C3#100911yescharacteristic
477C2×C3#100911yescharacteristic
478D3—41no—
479D3—41no—
480D3—41no—
481D3—122no—
482D3—121no—
483D3—121no—
484D3—121no—
485D3—121no—
486D3—121no—
487D3—121no—
488D3—241no—
489D3—241no—
490C22—61no—
491C22—61no—
492C22—61no—
493C22—61no—
494C22—61no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—181no—
500C22—181no—
501C22—181no—
502C22—181no—
503C22—181no—
504C22—181no—
505C22—181no—
506C22—181no—
507C22—181no—
508C22—364no—
509C22C22×D3211yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—61no—
518C4—181no—
519C3—21no—
520C3#566611yescharacteristic, complemented
521C3#571111yescharacteristic, complemented
522C2—121no—
523C2—121no—
524C2—121no—
525C2—361no—
526C2—361no—
527C2—361no—
528C2#6430811yescharacteristic
529C2#6431411yescharacteristic
530C2#6432011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
hypercenterC4⋊C4D32
hypocenterC32#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64104C2semidirect
2. C3×#898C2semidirect
3. C3×#894C2semidirect
4. #63923C2semidirect
5. #63923C2semidirect
6. #63922C2semidirect
7. #63912C2semidirect
8. #63911C2semidirect
9. #63910C2semidirect
10. #63910C2semidirect
11. #63909C2semidirect
12. #63906C2semidirect
13. #63868C2semidirect
14. #63854C2semidirect
15. #63853C2semidirect
21. C2×C4⋊(C3⋊D3)C22semidirect
22. C2×C4×C3⋊D3C22semidirect
24. C2×C3×C4×D3C22semidirect
30. C2×#626C22semidirect
31. C2×#626C22semidirect
33. C2×#624C22semidirect
34. C32×C4⋊C4C22semidirect
36. #3752C22semidirect
42. C3×(C2×D3)⋊C4C22semidirect
43. C3×C4⋊Dic3C22semidirect
44. C3×Dic3⋊C4C22semidirect
45. C3×Dic3⋊C4C22semidirect
46. C3×C4×Dic3C22semidirect
47. #3724C22semidirect
48. Dic3⋊Dic3C22semidirect
51. #3722C22semidirect
60. #898D3semidirect
69. #894D3semidirect
153. C2×C4×D3C2×D3semidirect
158. C3×C4⋊C4C2×D3semidirect
159. C3×C4⋊C4C2×D3semidirect
186. (C2×D3)⋊C4C2×D3semidirect
188. C4⋊Dic3C2×D3semidirect
192. Dic3⋊C4C2×D3semidirect
193. Dic3⋊C4C2×D3semidirect
194. C4×Dic3C2×D3semidirect
346. C4⋊C4D32semidirect
432. C32#560semidirect
520. C3#5666semidirect
521. C3#5711semidirect

Maximal subgroups

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

subgroupindex
#641042
C3×#8982
C3×#8942
#639232
#639222
#639122
#639112
#639102
#639092
#639062
#638682
#638542
#638532
#57113
#56663