Finite Group Databasebeta

← #10595003

Subgroups — #10595003

Order 576.

667 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#235C211yesmaximal, characteristic, complemented
2C2×#3798C211yesmaximal, characteristic, complemented
3C4×#638C211yesmaximal, characteristic, complemented
4C3×C4×#67C211yesmaximal, characteristic, complemented
5#63979C211yesmaximal, characteristic, complemented
6#63971C211yesmaximal, characteristic, complemented
7#63970C211yesmaximal, characteristic, complemented
8#63959C211yesmaximal, characteristic, complemented
9#63907C211yesmaximal, characteristic, complemented
10C4×#626C211yesmaximal, characteristic, complemented
11C4×#625C211yesmaximal, characteristic, complemented
12#63886C211yesmaximal, characteristic, complemented
13#63885C211yesmaximal, characteristic, complemented
14C4×D3×Dic3C211yesmaximal, characteristic, complemented
15#63839C211yesmaximal, characteristic, complemented
16#5832—31nomaximal
17#5548—31nomaximal
18C22×C32×C4C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×#67C2211yescharacteristic
24C3×#235—24no—
25C2×C3×D12C2211yescharacteristic
26C2×C3×C4×D3C2211yescharacteristic
27C2×C3×C4×D3C2211yescharacteristic
28C2×C3×C4×D3C2211yescharacteristic
29C2×C3×Dic6C2211yescharacteristic
30C2×#627C2211yescharacteristic
31C2×#626C2211yescharacteristic
32C2×#626C2211yescharacteristic
33C2×#626C2211yescharacteristic
34C2×#625C2211yescharacteristic
35C2×#625C2211yescharacteristic
36C2×D3×Dic3C2211yescharacteristic
37C2×D3×Dic3C2211yescharacteristic
38#3798—24no—
39#3757C2211yescharacteristic
40#3752C2211yescharacteristic
41#3750C2211yescharacteristic
42C4×C3⋊Dic3C2211yescharacteristic
43C3×#217C2211yescharacteristic
44C3×(C2×D3)⋊C4C2211yescharacteristic
45C3×Dic3⋊C4C2211yescharacteristic
46C3×C4×Dic3C2211yescharacteristic
47#3724C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49#3722C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53Dic32C2211yescharacteristic
54Dic32C2211yescharacteristic
55C2×C3×#41—31no—
56C2×#235—31no—
57C2×#235—31no—
58C2×#235D311yescharacteristic, complemented
59C3×C4×D4—31no—
60#947—31no—
61#944—31no—
62#940—31no—
63#940—31no—
64#939—31no—
65#939—31no—
66#939—31no—
67#939—31no—
68#938—31no—
69#936—31no—
70C4×#67—31no—
71C4×#67—31no—
72C4×#67—31no—
73C4×#67—31no—
74C4×#67—31no—
75C4×#67—61no—
76C4×#67D311yescharacteristic, complemented
77C2×C4×Dic3—31no—
78#895—31no—
79#888—31no—
80#885—31no—
81#885—31no—
82#884—31no—
83#884—31no—
84C4×D12—31no—
85C42×D3—31no—
86C23×C32C2311yescharacteristic
87C22×C3⋊D3C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C22×C3×D3C2311yescharacteristic
91C2×C32×C4—22no—
92C2×C32×C4C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94#638—22no—
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98C4×C3⋊D3—22no—
99C3×#67—22no—
100C3×#67—22no—
101C3×#67—22no—
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C3×D12—22no—
108C3×C4×D3—22no—
109C3×C4×D3—22no—
110C3×C4×D3D414yescomplemented
111C3×Dic6—22no—
112#627—22no—
113#626—22no—
114#626—22no—
115#626—22no—
116#625—22no—
117#625—22no—
118D3×Dic3—22no—
119D3×Dic3—22no—
120#532—91noSylow
121C3×#41—64no—
122C2×C3×Q8—31no—
123C2×C3×D4—31no—
124C2×C3×D4—31no—
125C2×C3×D4—31no—
126C2×C3×D4—31no—
127C22×C3×C4—21no—
128C22×C3×C4—31no—
129C22×C3×C4—31no—
130C22×C3×C4—31no—
131C22×C3×C4C2×D311yescharacteristic
132C22×C3×C4C2×D311yescharacteristic
133C2×#67—31no—
134C2×#67—31no—
135C2×#67—31no—
136C2×#67—31no—
137C2×#67—31no—
138C2×#67—31no—
139C2×#67—31no—
140C2×#67—31no—
141C2×#67—31no—
142C2×#67—61no—
143C2×#67C2×D311yescharacteristic
144C2×#67C2×D311yescharacteristic
145C2×#67C2×D311yescharacteristic
146C22×Dic3—31no—
147C22×Dic3—31no—
148#235—24no—
149#235—64no—
150#235—64no—
151C2×D12—31no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12C2×D311yescharacteristic
155C2×C4×D3—31no—
156C2×C4×D3—31no—
157C2×C4×D3—31no—
158C2×C4×D3—31no—
159C2×C4×D3—61no—
160C2×C4×D3C2×D311yescharacteristic
161C2×C4×D3C2×D311yescharacteristic
162C2×C4×D3C2×D311yescharacteristic
163C2×Dic6—31no—
164C2×Dic6—31no—
165C2×Dic6C2×D311yescharacteristic
166C3×C4⋊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—31no—
175#217—61no—
176#217C2×D311yescharacteristic
177(C2×D3)⋊C4—31no—
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
186C4⋊Dic3—31no—
187Dic3⋊C4—31no—
188Dic3⋊C4—31no—
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4—61no—
193Dic3⋊C4C2×D311yescharacteristic
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—31no—
197C4×Dic3—31no—
198C4×Dic3—31no—
199C4×Dic3—31no—
200C4×Dic3—61no—
201C4×Dic3C2×D311yescharacteristic
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32C2411yescharacteristic
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—
214C2×C3×D3—21no—
215C2×C3×D3—21no—
216C2×C3×D3—21no—
217C2×C3×D3C2×D412yes—
218C32×C4—21no—
219C32×C4C2×D412yes—
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3#4112yescomplemented
223C3×Dic3—21no—
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3C2×D412yes—
227C3×Dic3#4112yescomplemented
228C2×#41—31no—
229C2×#41—91no—
230C4⋊Q8—91no—
231#127—91no—
232#124—91no—
233#124—91no—
234#121—91no—
235#121—91no—
236#121—91no—
237#121—91no—
238C4×D4—31no—
239C4×D4—91no—
240C4×D4—91no—
241C4×D4—91no—
242C2×C42—91no—
243C23×C3—21no—
244C23×C3—31no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3C22×D311yescharacteristic
248C23×C3C22×D311yescharacteristic
249C22×D3—31no—
250C22×D3—31no—
251C22×D3—61no—
252C22×D3C22×D311yescharacteristic
253C22×D3C22×D311yescharacteristic
254C22×D3C22×D311yescharacteristic
255C3×Q8—62no—
256C3×D4—62no—
257C3×D4—62no—
258C3×D4—62no—
259C3×D4—62no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—31no—
265C2×C3×C4—31no—
266C2×C3×C4—34no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—42no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4C22×D311yescharacteristic
274C2×C3×C4C22×D311yescharacteristic
275C2×C3×C4C22×D311yescharacteristic
276C2×C3×C4C22×D311yescharacteristic
277#67—22no—
278#67—22no—
279#67—22no—
280#67—62no—
281#67—62no—
282#67—62no—
283#67—62no—
284#67—62no—
285#67—62no—
286#67—64no—
287#67—62no—
288#67—62no—
289#67—62no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—31no—
295C2×Dic3—31no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3C22×D311yescharacteristic
302C2×Dic3C22×D311yescharacteristic
303C2×Dic3C22×D311yescharacteristic
304C2×Dic3C22×D311yescharacteristic
305C2×Dic3C22×D311yescharacteristic
306D12—22no—
307D12—62no—
308D12—62no—
309D12—62no—
310C4×D3—22no—
311C4×D3—22no—
312C4×D3—62no—
313C4×D3—62no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—122no—
317C4×D3#6714yescomplemented
318Dic6—22no—
319Dic6—62no—
320Dic6—62no—
321C2×C32—41no—
322C2×C32C22×D411yescharacteristic
323C2×C32C2×#4111yescharacteristic
324C2×C32C2×#4111yescharacteristic
325C3⋊D3—41no—
326C3×D3—22no—
327C3×D3—41no—
328C3×D3—41no—
329#41—64no—
330#41—184no—
331C2×Q8—31no—
332C2×Q8—91no—
333C2×D4—31no—
334C2×D4—31no—
335C2×D4—31no—
336C2×D4—31no—
337C2×D4—91no—
338C2×D4—91no—
339C2×D4—91no—
340C2×D4—91no—
341C2×D4—91no—
342C2×D4—91no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4D3211yescharacteristic
350C4⋊C4—31no—
351C4⋊C4—91no—
352C4⋊C4—91no—
353C4⋊C4—91no—
354C22⋊C4—31no—
355C22⋊C4—31no—
356C22⋊C4—91no—
357C22⋊C4—91no—
358C22⋊C4—91no—
359C22⋊C4—91no—
360C22⋊C4—91no—
361C22⋊C4—91no—
362C42—31no—
363C42—91no—
364C42—91no—
365C42—91no—
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—32no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—61no—
378C22×C3—61no—
379C22×C3—61no—
380C22×C3—61no—
381C22×C3—61no—
382C22×C3—61no—
383C22×C3—61no—
384C22×C3—61no—
385C22×C3C23×D311yescharacteristic
386C22×C3C23×D311yescharacteristic
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—21no—
390C2×D3—21no—
391C2×D3—21no—
392C2×D3—21no—
393C2×D3—21no—
394C2×D3—21no—
395C2×D3—62no—
396C2×D3—61no—
397C2×D3—61no—
398C2×D3—61no—
399C2×D3—61no—
400C2×D3—61no—
401C2×D3—61no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3C2×#6712yes—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—22no—
408C3×C4—32no—
409C3×C4—32no—
410C3×C4—41no—
411C3×C4—61no—
412C3×C4—61no—
413C3×C4—61no—
414C3×C4D3×D412yes—
415C3×C4C2×#6712yes—
416Dic3—21no—
417Dic3—21no—
418Dic3—21no—
419Dic3—32no—
420Dic3—32no—
421Dic3—62no—
422Dic3—61no—
423Dic3—61no—
424Dic3—61no—
425Dic3—61no—
426Dic3—121no—
427Dic3—121no—
428Dic3#23512yescomplemented
429Dic3C2×#6712yes—
430C32#53211yescharacteristic, complemented, Sylow
431C23—31no—
432C23—31no—
433C23—31no—
434C23—91no—
435C23C2×D3211yescharacteristic
436Q8—62no—
437Q8—182no—
438D4—62no—
439D4—62no—
440D4—62no—
441D4—62no—
442D4—182no—
443D4—182no—
444D4—182no—
445D4—182no—
446D4—182no—
447D4—182no—
448C2×C4—22no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—34no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4—182no—
463C2×C4C2×D3211yescharacteristic
464C2×C4C2×D3211yescharacteristic
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—42no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—62no—
472C2×C3—121no—
473C2×C3—121no—
474C2×C3C2×#23511yescharacteristic
475C2×C3C2×D3×D411yescharacteristic
476C2×C3D3×#4111yescharacteristic
477C2×C3D3×#4111yescharacteristic
478C2×C3D3×#4111yescharacteristic
479C2×C3C22×#6711yescharacteristic
480D3—22no—
481D3—41no—
482D3—41no—
483D3—122no—
484D3—121no—
485D3—121no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—32no—
490C22—61no—
491C22—61no—
492C22—61no—
493C22—61no—
494C22—61no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—181no—
499C22—181no—
500C22—181no—
501C22C22×D3211yescharacteristic
502C4—21no—
503C4—32no—
504C4—32no—
505C4—61no—
506C4—61no—
507C4—61no—
508C4—92no—
509C4—181no—
510C4—181no—
511C4D3×#6712yes—
512C3—21no—
513C3#554811yescharacteristic, complemented
514C3#583211yescharacteristic, complemented
515C2—41no—
516C2—62no—
517C2—121no—
518C2—121no—
519C2—361no—
520C2D3×#23511yescharacteristic
521C2#6430611yescharacteristic
522C2C2×D3×#6711yescharacteristic
subgroupG/H
centerC2×C4C2×D32
commutator, socle, cosocleC22×C32C24
FrattiniC22C22×D32
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#235C2semidirect
2. C2×#3798C2semidirect
3. C4×#638C2semidirect
4. C3×C4×#67C2semidirect
5. #63979C2semidirect
6. #63971C2semidirect
7. #63970C2semidirect
8. #63959C2semidirect
9. #63907C2semidirect
10. C4×#626C2semidirect
11. C4×#625C2semidirect
12. #63886C2semidirect
13. #63885C2semidirect
14. C4×D3×Dic3C2semidirect
15. #63839C2semidirect
58. C2×#235D3semidirect
76. C4×#67D3semidirect
110. C3×C4×D3D4semidirect
222. C3⋊Dic3#41semidirect
227. C3×Dic3#41semidirect
317. C4×D3#67semidirect
428. Dic3#235semidirect
430. C32#532semidirect
513. C3#5548semidirect
514. C3#5832semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#2352
C2×#37982
C4×#6382
C3×C4×#672
#639792
#639712
#639702
#639592
#639072
C4×#6262
C4×#6252
#638862
#638852
C4×D3×Dic32
#638392
#58323
#55483