Finite Group Databasebeta

← #10594298

Subgroups — #10594298

Order 576.

547 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64093C211yesmaximal, characteristic, complemented
2C3×#885C211yesmaximal, characteristic, complemented
3C3×#67⋊C4C211yesmaximal, characteristic, complemented
4#63983C211yesmaximal, characteristic, complemented
5#63978C211yesmaximal, characteristic, complemented
6#63971C211yesmaximal, characteristic, complemented
7#63966C211yesmaximal, characteristic, complemented
8#63923C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C4×#626C211yesmaximal, characteristic, complemented
11#63887C211yesmaximal, characteristic, complemented
12#63868C211yesmaximal, characteristic, complemented
13#63864C211yesmaximal, characteristic, complemented
14#63859C211yesmaximal, characteristic, complemented
15#63853C211yesmaximal, characteristic, complemented
16#5678—31nomaximal
17#5560—31nomaximal
18C22×D32C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#638C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#67C2211yescharacteristic
24C2×C3×#67C2211yescharacteristic
25C22×C3×Dic3C2211yescharacteristic, complemented
26C2×C3×C4×D3C2211yescharacteristic
27C2×C3×Dic6C2211yescharacteristic, complemented
28C2×#626C2211yescharacteristic
29C2×#626C2211yescharacteristic
30C2×D3×Dic3C2211yescharacteristic
31C32×C22⋊C4C2211yescharacteristic, complemented
32#3752C2211yescharacteristic
33#3750C2211yescharacteristic, complemented
34C3×#217C2211yescharacteristic, complemented
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic, complemented
39C3×C4×Dic3C2211yescharacteristic, complemented
40C3×C4×Dic3C2211yescharacteristic, complemented
41#3724C2211yescharacteristic, complemented
42Dic3⋊Dic3C2211yescharacteristic, complemented
43Dic3⋊Dic3C2211yescharacteristic, complemented
44Dic3⋊Dic3C2211yescharacteristic, complemented
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic, complemented
49#3722C2211yescharacteristic, complemented
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×#124—31no—
54C3×C4×D4—31no—
55#947—31no—
56#946—31no—
57#939—31no—
58#939—31no—
59#937—31no—
60#937—31no—
61#930—31no—
62#929—31no—
63C4×#67—31no—
64C2×(C2×D3)⋊C4—31no—
65#898—31no—
66#894—31no—
67#886—31no—
68#885D311yescharacteristic, complemented
69#884—31no—
70#884—31no—
71#884—31no—
72#884—61no—
73#883—31no—
74#882—31no—
75#882—31no—
76#67⋊C4D311yescharacteristic, complemented
77D3×C22⋊C4—31no—
78#879—31no—
79#878—31no—
80#876—31no—
81#876—31no—
82#875—31no—
83C4×D12—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—
95#638—41no—
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98C4⋊(C3⋊D3)—41no—
99C4×C3⋊D3—41no—
100C3×#67—22no—
101C3×#67—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C2×C3×Dic3C2311yescharacteristic
109C3×C4×D3—41no—
110C3×Dic6—41no—
111#626—22no—
112#626—41no—
113D3×Dic3—41no—
114#538—91noSylow
115C23×D3—31no—
116C23×D3—31no—
117C2×C3×Q8—31no—
118C2×C3×D4—31no—
119C2×C3×D4—31no—
120C22×C3×C4—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—61no—
129C2×#67—61no—
130C2×#67C2×D311yescharacteristic
131C2×#67C2×D311yescharacteristic
132C22×Dic3—31no—
133C22×Dic3C2×D311yescharacteristic, complemented
134C2×D12—31no—
135C2×D12—31no—
136C2×D12—31no—
137C2×D12—31no—
138C2×D12—61no—
139C2×C4×D3—31no—
140C2×C4×D3—31no—
141C2×C4×D3—31no—
142C2×C4×D3—61no—
143C2×C4×D3C2×D311yescharacteristic
144C2×Dic6C2×D311yescharacteristic, complemented
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, complemented
152C3×C22⋊C4C2×D311yescharacteristic, complemented
153C3×C42—31no—
154C3×C42—31no—
155#217—31no—
156#217—31no—
157#217—31no—
158#217C2×D311yescharacteristic, complemented
159(C2×D3)⋊C4—31no—
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)⋊C4C2×D311yescharacteristic
176(C2×D3)⋊C4C2×D311yescharacteristic
177(C2×D3)⋊C4C2×D311yescharacteristic
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181Dic3⋊C4—31no—
182Dic3⋊C4—31no—
183Dic3⋊C4—31no—
184Dic3⋊C4—31no—
185Dic3⋊C4—31no—
186Dic3⋊C4—31no—
187Dic3⋊C4—31no—
188Dic3⋊C4—61no—
189Dic3⋊C4C2×D311yescharacteristic, complemented
190C4×Dic3C2×D311yescharacteristic, complemented
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—31no—
222#124—91no—
223#123—91no—
224#123—91no—
225C22⋊Q8—91no—
226#121—91no—
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×C3C22×D311yescharacteristic
238C23×C3C22×D311yescharacteristic
239C22×D3—31no—
240C22×D3—31no—
241C22×D3—31no—
242C22×D3—31no—
243C22×D3—61no—
244C22×D3—61no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—121no—
248C22×D3—121no—
249C22×D3—121no—
250C22×D3—121no—
251C22×D3C22×D311yescharacteristic
252C22×D3C22×D311yescharacteristic
253C3×Q8—121no—
254C3×D4—62no—
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—31no—
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—62no—
273#67—121no—
274#67—121no—
275#67—121no—
276#67—121no—
277#67—121no—
278#67—122no—
279#67—122no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—41no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—121no—
288C2×Dic3C22×D311yescharacteristic
289C2×Dic3C22×D311yescharacteristic
290C2×Dic3C22×D311yescharacteristic
291C2×Dic3C22×D311yescharacteristic
292C2×Dic3C22×D311yescharacteristic
293C2×Dic3C22×D311yescharacteristic
294D12—62no—
295D12—121no—
296D12—121no—
297D12—122no—
298D12—121no—
299C4×D3—41no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—122no—
303C4×D3—121no—
304Dic6—41no—
305C2×C32—41no—
306C2×C32C2×#4111yescharacteristic
307C2×C32H(5,𝔽2)11yescharacteristic
308C2×C32H(5,𝔽2)11yescharacteristic
309C3⋊D3—41no—
310C3⋊D3—41no—
311C3×D3—22no—
312C3×D3—41no—
313C24—91no—
314C2×Q8—31no—
315C2×D4—31no—
316C2×D4—31no—
317C2×D4—91no—
318C2×D4—91no—
319C2×D4—91no—
320C2×D4—91no—
321C2×D4—91no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—91no—
325C22×C4—91no—
326C4⋊C4—31no—
327C4⋊C4—91no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C4⋊C4—91no—
331C4⋊C4—91no—
332C22⋊C4—31no—
333C22⋊C4—31no—
334C22⋊C4—31no—
335C22⋊C4—31no—
336C22⋊C4—91no—
337C22⋊C4—91no—
338C22⋊C4—91no—
339C22⋊C4—91no—
340C22⋊C4—91no—
341C22⋊C4—91no—
342C22⋊C4—91no—
343C22⋊C4—91no—
344C22⋊C4—91no—
345C22⋊C4D3211yescharacteristic, complemented
346C42—31no—
347C42—31no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—32no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—61no—
360C22×C3—61no—
361C22×C3—61no—
362C22×C3—61no—
363C22×C3—61no—
364C22×C3C23×D311yescharacteristic
365C22×C3C23×D311yescharacteristic
366C2×D3—21no—
367C2×D3—21no—
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—62no—
372C2×D3—61no—
373C2×D3—61no—
374C2×D3—61no—
375C2×D3—61no—
376C2×D3—61no—
377C2×D3—61no—
378C2×D3—61no—
379C2×D3—61no—
380C2×D3—61no—
381C2×D3—61no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—124no—
390C2×D3—124no—
391C2×D3#23512yes—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—61no—
399C3×C4—61no—
400C3×C4—61no—
401C3×C4—61no—
402C3×C4—61no—
403C3×C4—61no—
404Dic3—21no—
405Dic3—21no—
406Dic3—21no—
407Dic3—21no—
408Dic3—21no—
409Dic3—21no—
410Dic3—62no—
411Dic3—61no—
412Dic3—61no—
413Dic3—61no—
414Dic3—61no—
415Dic3—121no—
416C32#53811yescharacteristic, complemented, Sylow
417C23—31no—
418C23—31no—
419C23—91no—
420C23—91no—
421C23—182no—
422C23—361no—
423C23—361no—
424C23C2×D3211yescharacteristic
425Q8—121no—
426D4—62no—
427D4—121no—
428D4—182no—
429D4—361no—
430D4—361no—
431D4—361no—
432D4—361no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—31no—
438C2×C4—31no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—361no—
444C2×C4—361no—
445C2×C4C2×D3211yescharacteristic
446C2×C4C2×D3211yescharacteristic
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—62no—
453C2×C3—81no—
454C2×C3—121no—
455C2×C3C2×#23511yescharacteristic
456C2×C3#100411yescharacteristic
457C2×C3#100411yescharacteristic
458C2×C3D3×#4111yescharacteristic
459C2×C3#100911yescharacteristic
460C2×C3#100911yescharacteristic
461D3—22no—
462D3—41no—
463D3—122no—
464D3—121no—
465D3—121no—
466D3—121no—
467D3—121no—
468D3—241no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—32no—
473C22—61no—
474C22—61no—
475C22—61no—
476C22—61no—
477C22—61no—
478C22—181no—
479C22—181no—
480C22—181no—
481C22—181no—
482C22—181no—
483C22—181no—
484C22—364no—
485C22C22×D3211yescharacteristic
486C4—21no—
487C4—21no—
488C4—61no—
489C4—61no—
490C4—61no—
491C4—61no—
492C4—61no—
493C4—61no—
494C4—181no—
495C4—181no—
496C3—21no—
497C3#556011yescharacteristic, complemented
498C3#567811yescharacteristic, complemented
499C2—41no—
500C2—62no—
501C2—121no—
502C2—361no—
503C2—361no—
504C2D3×#23511yescharacteristic
505C2#6431411yescharacteristic
506C2#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. #64093C2semidirect
2. C3×#885C2semidirect
3. C3×#67⋊C4C2semidirect
4. #63983C2semidirect
5. #63978C2semidirect
6. #63971C2semidirect
7. #63966C2semidirect
8. #63923C2semidirect
9. D3×(C2×D3)⋊C4C2semidirect
10. C4×#626C2semidirect
11. #63887C2semidirect
12. #63868C2semidirect
13. #63864C2semidirect
14. #63859C2semidirect
15. #63853C2semidirect
20. C2×#638C22semidirect
22. C2×C4×C3⋊D3C22semidirect
25. C22×C3×Dic3C22semidirect
27. C2×C3×Dic6C22semidirect
31. C32×C22⋊C4C22semidirect
33. #3750C22semidirect
34. C3×#217C22semidirect
38. C3×Dic3⋊C4C22semidirect
39. C3×C4×Dic3C22semidirect
40. C3×C4×Dic3C22semidirect
41. #3724C22semidirect
42. Dic3⋊Dic3C22semidirect
43. Dic3⋊Dic3C22semidirect
44. Dic3⋊Dic3C22semidirect
48. #3722C22semidirect
49. #3722C22semidirect
68. #885D3semidirect
76. #67⋊C4D3semidirect
133. C22×Dic3C2×D3semidirect
144. C2×Dic6C2×D3semidirect
151. C3×C22⋊C4C2×D3semidirect
152. C3×C22⋊C4C2×D3semidirect
158. #217C2×D3semidirect
189. Dic3⋊C4C2×D3semidirect
190. C4×Dic3C2×D3semidirect
191. C4×Dic3C2×D3semidirect
345. C22⋊C4D32semidirect
416. C32#538semidirect
497. C3#5560semidirect
498. C3#5678semidirect

Maximal subgroups

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

subgroupindex
#640932
C3×#8852
C3×#67⋊C42
#639832
#639782
#639712
#639662
#639232
D3×(C2×D3)⋊C42
C4×#6262
#638872
#638682
#638642
#638592
#638532
#56783
#55603