Finite Group Databasebeta

← #10594297

Subgroups — #10594297

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×#884C211yesmaximal, characteristic, complemented
3C3×#67⋊C4C211yesmaximal, characteristic, complemented
4#63983C211yesmaximal, characteristic, complemented
5#63978C211yesmaximal, characteristic, complemented
6#63970C211yesmaximal, characteristic, complemented
7#63961C211yesmaximal, characteristic, complemented
8#63922C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C4×#625C211yesmaximal, characteristic, complemented
11#63896C211yesmaximal, characteristic, complemented
12#63868C211yesmaximal, characteristic, complemented
13#63862C211yesmaximal, characteristic, complemented
14#63860C211yesmaximal, characteristic, complemented
15#63850C211yesmaximal, characteristic, complemented
16#5613—31nomaximal
17#5560—31nomaximal
18C22×D32C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#634C2211yescharacteristic, complemented
21C2×C3×#67C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×#67C2211yescharacteristic, complemented
24C22×C3×Dic3C2211yescharacteristic, complemented
25C2×C3×D12C2211yescharacteristic
26C2×C3×C4×D3C2211yescharacteristic
27C2×C3×C4×D3C2211yescharacteristic, complemented
28C2×#626C2211yescharacteristic
29C2×#625C2211yescharacteristic
30C2×D3×Dic3C2211yescharacteristic
31C32×C22⋊C4C2211yescharacteristic, complemented
32#3757C2211yescharacteristic, complemented
33#3752C2211yescharacteristic
34#3752C2211yescharacteristic
35C4×C3⋊Dic3C2211yescharacteristic, complemented
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic, complemented
39C3×Dic3⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic3C2211yescharacteristic, complemented
41#3724C2211yescharacteristic, complemented
42#3724C2211yescharacteristic, complemented
43Dic3⋊Dic3C2211yescharacteristic, complemented
44Dic3⋊Dic3C2211yescharacteristic, complemented
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
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×#121—31no—
54C3×C4×D4—31no—
55#939—31no—
56#939—31no—
57#938—31no—
58#937—31no—
59#937—31no—
60#937—31no—
61#936—31no—
62#935—31no—
63#930—31no—
64#929—31no—
65#929—31no—
66C4×#67—31no—
67C4×#67—31no—
68C2×(C2×D3)⋊C4—31no—
69#898—31no—
70#898—31no—
71#896—31no—
72#894—31no—
73#885—31no—
74#885—31no—
75#885—61no—
76#884D311yescharacteristic, complemented
77#882—31no—
78#67⋊C4D311yescharacteristic, complemented
79D3×C22⋊C4—31no—
80#879—31no—
81#878—31no—
82#876—31no—
83#875—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C2×D32—22no—
90C2×D32—41no—
91C2×D32—41no—
92C2×C32×C4C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94#638—41no—
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98#634—41no—
99C3×#67—22no—
100C3×#67—41no—
101C3×#67—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C3×D12—41no—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111#626—41no—
112#625—22no—
113D3×Dic3—41no—
114#538—91noSylow
115C23×D3—31no—
116C23×D3—31no—
117C2×C3×D4—31no—
118C2×C3×D4—31no—
119C2×C3×D4—31no—
120C2×C3×D4—31no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C2×#67—31no—
125C2×#67—31no—
126C2×#67—31no—
127C2×#67—31no—
128C2×#67—31no—
129C2×#67—61no—
130C2×#67C2×D311yescharacteristic
131C2×#67C2×D311yescharacteristic
132C2×#67C2×D311yescharacteristic, complemented
133C22×Dic3—31no—
134C22×Dic3C2×D311yescharacteristic, complemented
135C2×D12—31no—
136C2×D12C2×D311yescharacteristic
137C2×C4×D3—31no—
138C2×C4×D3C2×D311yescharacteristic
139C2×C4×D3C2×D311yescharacteristic, complemented
140C2×Dic6—31no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—31no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—31no—
147C3×C22⋊C4—31no—
148C3×C22⋊C4C2×D311yescharacteristic, complemented
149C3×C22⋊C4C2×D311yescharacteristic, complemented
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—61no—
160(C2×D3)⋊C4—31no—
161(C2×D3)⋊C4—31no—
162(C2×D3)⋊C4—31no—
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)⋊C4—31no—
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4C2×D311yescharacteristic
177(C2×D3)⋊C4C2×D311yescharacteristic
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180Dic3⋊C4—31no—
181Dic3⋊C4—31no—
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#4112yes—
208D32—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—31no—
227#121—91no—
228#121—91no—
229#120—91no—
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×C3C22×D311yescharacteristic
239C23×C3C22×D311yescharacteristic
240C22×D3—31no—
241C22×D3—31no—
242C22×D3—61no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—121no—
246C22×D3—121no—
247C22×D3—121no—
248C22×D3—121no—
249C22×D3C22×D311yescharacteristic
250C22×D3C22×D311yescharacteristic
251C22×D3C22×D311yescharacteristic
252C3×D4—62no—
253C3×D4—121no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4C22×D311yescharacteristic
267C2×C3×C4C22×D311yescharacteristic
268C2×C3×C4C22×D311yescharacteristic
269C2×C3×C4C22×D311yescharacteristic
270#67—22no—
271#67—41no—
272#67—41no—
273#67—62no—
274#67—62no—
275#67—121no—
276#67—121no—
277#67—121no—
278#67—122no—
279C2×Dic3—31no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—31no—
285C2×Dic3—41no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—121no—
290C2×Dic3C22×D311yescharacteristic
291C2×Dic3C22×D311yescharacteristic
292C2×Dic3C22×D311yescharacteristic
293C2×Dic3C22×D311yescharacteristic
294C2×Dic3C22×D311yescharacteristic
295D12—41no—
296D12—121no—
297C4×D3—41no—
298C4×D3—41no—
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—91no—
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—31no—
323C22×C4—91no—
324C4⋊C4—31no—
325C4⋊C4—31no—
326C4⋊C4—91no—
327C4⋊C4—91no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C22⋊C4—31no—
331C22⋊C4—31no—
332C22⋊C4—91no—
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, complemented
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×C3C23×D311yescharacteristic
366C22×C3C23×D311yescharacteristic
367C2×D3—21no—
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—61no—
376C2×D3—61no—
377C2×D3—61no—
378C2×D3—61no—
379C2×D3—61no—
380C2×D3—61no—
381C2×D3—121no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—124no—
385C2×D3—124no—
386C2×D3#23512yes—
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—91no—
417C23—182no—
418C23—361no—
419C23—361no—
420C23C2×D3211yescharacteristic
421Q8—361no—
422D4—62no—
423D4—121no—
424D4—121no—
425D4—121no—
426D4—182no—
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—121no—
438C2×C4—121no—
439C2×C4—121no—
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×#23511yescharacteristic
453C2×C3#100411yescharacteristic
454C2×C3#100411yescharacteristic
455C2×C3#100411yescharacteristic
456C2×C3D3×#4111yescharacteristic
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—181no—
477C22—181no—
478C22—181no—
479C22—364no—
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#556011yescharacteristic, complemented
493C3#561311yescharacteristic, complemented
494C2—41no—
495C2—62no—
496C2—121no—
497C2—121no—
498C2—361no—
499C2D3×#23511yescharacteristic
500C2#6431311yescharacteristic
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×#884C2semidirect
3. C3×#67⋊C4C2semidirect
4. #63983C2semidirect
5. #63978C2semidirect
6. #63970C2semidirect
7. #63961C2semidirect
8. #63922C2semidirect
9. D3×(C2×D3)⋊C4C2semidirect
10. C4×#625C2semidirect
11. #63896C2semidirect
12. #63868C2semidirect
13. #63862C2semidirect
14. #63860C2semidirect
15. #63850C2semidirect
20. C2×#634C22semidirect
23. C2×C3×#67C22semidirect
24. C22×C3×Dic3C22semidirect
27. C2×C3×C4×D3C22semidirect
31. C32×C22⋊C4C22semidirect
32. #3757C22semidirect
35. C4×C3⋊Dic3C22semidirect
38. C3×Dic3⋊C4C22semidirect
39. C3×Dic3⋊C4C22semidirect
40. C3×C4×Dic3C22semidirect
41. #3724C22semidirect
42. #3724C22semidirect
43. Dic3⋊Dic3C22semidirect
44. Dic3⋊Dic3C22semidirect
51. (C2×D3)⋊Dic3C22semidirect
52. (C2×D3)⋊Dic3C22semidirect
76. #884D3semidirect
78. #67⋊C4D3semidirect
132. C2×#67C2×D3semidirect
134. C22×Dic3C2×D3semidirect
139. C2×C4×D3C2×D3semidirect
148. C3×C22⋊C4C2×D3semidirect
149. C3×C22⋊C4C2×D3semidirect
186. Dic3⋊C4C2×D3semidirect
187. Dic3⋊C4C2×D3semidirect
191. C4×Dic3C2×D3semidirect
343. C22⋊C4D32semidirect
412. C32#538semidirect
492. C3#5560semidirect
493. C3#5613semidirect

Maximal subgroups

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

subgroupindex
#640942
C3×#8842
C3×#67⋊C42
#639832
#639782
#639702
#639612
#639222
D3×(C2×D3)⋊C42
C4×#6252
#638962
#638682
#638622
#638602
#638502
#56133
#55603