Finite Group Databasebeta

← #10595149

Subgroups — #10595149

Order 576.

631 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#237C211yesmaximal, characteristic, complemented
2C2×#3804C211yesmaximal, characteristic, complemented
3#64148C211yesmaximal, characteristic, complemented
4C3×#935C211yesmaximal, characteristic, complemented
5#67⋊Dic3C211yesmaximal, characteristic, complemented
6#63971C211yesmaximal, characteristic, complemented
7#63969C211yesmaximal, characteristic, complemented
8C2×#3724C211yesmaximal, characteristic, complemented
9#63966C211yesmaximal, characteristic, complemented
10#63964C211yesmaximal, characteristic, complemented
11#63952C211yesmaximal, characteristic, complemented
12#63888C211yesmaximal, characteristic, complemented
13D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#63850C211yesmaximal, characteristic, complemented
15#63839C211yesmaximal, characteristic, complemented
16#5824—31nomaximal
17#5655—31nomaximal
18C2×C32×D4C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#638C2211yescharacteristic
21C22×C3⋊Dic3C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×#67C2211yescharacteristic
24C22×C3×Dic3C2211yescharacteristic
25C22×C3×Dic3C2211yescharacteristic
26C22×C3×Dic3C2211yescharacteristic
27C3×#237—24no—
28C2×C3×C4×D3C2211yescharacteristic
29C2×C3×Dic6C2211yescharacteristic
30C2×#627C2211yescharacteristic
31C2×#626C2211yescharacteristic
32C2×#624C2211yescharacteristic
33#3804—24no—
34C2×D3×Dic3C2211yescharacteristic
35C2×D3×Dic3C2211yescharacteristic
36#3757C2211yescharacteristic
37#3752C2211yescharacteristic
38#3750C2211yescharacteristic
39C3×#217C2211yescharacteristic
40C3×#217C2211yescharacteristic
41C3×#217C2211yescharacteristic
42C3×Dic3⋊C4C2211yescharacteristic
43C3×Dic3⋊C4C2211yescharacteristic
44#3724C2211yescharacteristic
45#3724C2211yescharacteristic
46#3724C2211yescharacteristic
47#3724C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49Dic3⋊Dic3C2211yescharacteristic
50Dic3⋊Dic3C2211yescharacteristic
51#3722C2211yescharacteristic
52#3722C2211yescharacteristic
53(C2×D3)⋊Dic3C2211yescharacteristic
54Dic32C2211yescharacteristic
55C2×C3×#41—31no—
56C2×#237—31no—
57C2×#237D311yescharacteristic, complemented
58C2×#235—31no—
59C3×#123—31no—
60#946—31no—
61#944—31no—
62#939—31no—
63#939—31no—
64#939—31no—
65#939—61no—
66#935—31no—
67#935D311yescharacteristic, complemented
68D4×Dic3—31no—
69#929—31no—
70#929—31no—
71C4×#67—31no—
72#924—31no—
73C2×Dic3⋊C4—31no—
74C2×Dic3⋊C4—31no—
75C2×Dic3⋊C4—31no—
76#896—31no—
77#894—31no—
78D3×C4⋊C4—31no—
79#888—31no—
80#886—31no—
81#884—31no—
82#883—31no—
83#67⋊C4—31no—
84#67⋊C4—31no—
85#878—31no—
86C23×C32C2311yescharacteristic
87C23×C32C2311yescharacteristic
88C22×C3⋊D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C32×D4—22no—
91C2×C32×C4C2311yescharacteristic
92#638—22no—
93#638—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98C3×#67—22no—
99C3×#67D414yescomplemented
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C2×C3×Dic3C2311yescharacteristic
109C2×C3×Dic3C2311yescharacteristic
110C3×C4×D3—22no—
111C3×Dic6—22no—
112#627—22no—
113#626—22no—
114#624—22no—
115D3×Dic3—22no—
116D3×Dic3—22no—
117#547—91noSylow
118C3×#41—64no—
119C2×C3×Q8—31no—
120C2×C3×D4—21no—
121C2×C3×D4—31no—
122C2×C3×D4—31no—
123C2×C3×D4C2×D311yescharacteristic
124C2×C3×D4C2×D311yescharacteristic
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C2×#67—31no—
130C2×#67—31no—
131C2×#67—31no—
132C2×#67—31no—
133C2×#67—31no—
134C2×#67—61no—
135C2×#67—61no—
136C2×#67C2×D311yescharacteristic
137C2×#67C2×D311yescharacteristic
138C22×Dic3—31no—
139C22×Dic3—31no—
140C22×Dic3—31no—
141C22×Dic3—31no—
142C22×Dic3—61no—
143C22×Dic3C2×D311yescharacteristic
144C22×Dic3C2×D311yescharacteristic
145C22×Dic3C2×D311yescharacteristic
146#237—24no—
147#237—64no—
148#235—64no—
149C2×D12—31no—
150C2×C4×D3—31no—
151C2×C4×D3—31no—
152C2×C4×D3—31no—
153C2×C4×D3—31no—
154C2×C4×D3C2×D311yescharacteristic
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6C2×D311yescharacteristic
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4—31no—
163#217—31no—
164#217—31no—
165#217—31no—
166#217—61no—
167#217C2×D311yescharacteristic
168#217C2×D311yescharacteristic
169#217C2×D311yescharacteristic
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—61no—
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—31no—
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4—31no—
193Dic3⋊C4—31no—
194Dic3⋊C4—61no—
195Dic3⋊C4C2×D311yescharacteristic
196Dic3⋊C4C2×D311yescharacteristic
197C4×Dic3—31no—
198C4×Dic3—31no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32C2×D412yes—
205C22×C32C2411yescharacteristic
206C2×C3⋊D3—21no—
207C2×C3⋊D3—21no—
208C2×C3⋊D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3C2×D412yes—
212C32×C4—21no—
213C3⋊Dic3—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3#4112yescomplemented
216C3×Dic3—21no—
217C3×Dic3—21no—
218C3×Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3C2×D412yes—
223C2×#41—31no—
224C2×#41—91no—
225C4⋊Q8—91no—
226#123—31no—
227#123—91no—
228#123—91no—
229#123—91no—
230C22⋊Q8—91no—
231C22⋊Q8—91no—
232#121—91no—
233#121—91no—
234C4×D4—91no—
235C4×D4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—91no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—31no—
241C23×C3C22×D311yescharacteristic
242C23×C3C22×D311yescharacteristic
243C23×C3C22×D311yescharacteristic
244C23×C3C22×D311yescharacteristic
245C22×D3—31no—
246C22×D3—31no—
247C22×D3—61no—
248C22×D3C22×D311yescharacteristic
249C3×Q8—62no—
250C3×D4—22no—
251C3×D4—22no—
252C3×D4—34no—
253C3×D4—42no—
254C3×D4—62no—
255C2×C3×C4—21no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4C22×D311yescharacteristic
268C2×C3×C4C22×D311yescharacteristic
269#67—22no—
270#67—62no—
271#67—62no—
272#67—62no—
273#67—62no—
274#67—62no—
275#67—122no—
276#67—122no—
277#67#6714yescomplemented
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—31no—
285C2×Dic3—31no—
286C2×Dic3—31no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—122no—
295C2×Dic3C22×D311yescharacteristic
296C2×Dic3C22×D311yescharacteristic
297C2×Dic3C22×D311yescharacteristic
298C2×Dic3C22×D311yescharacteristic
299C2×Dic3C22×D311yescharacteristic
300C2×Dic3C22×D311yescharacteristic
301C2×Dic3C22×D311yescharacteristic
302D12—62no—
303C4×D3—22no—
304C4×D3—62no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—62no—
308Dic6—22no—
309Dic6—62no—
310Dic6—62no—
311C2×C32—22no—
312C2×C32—41no—
313C2×C32C22×D411yescharacteristic
314C2×C32C2×#4111yescharacteristic
315C2×C322−1+411yescharacteristic
316C3⋊D3—41no—
317C3×D3—22no—
318#41—64no—
319#41—184no—
320C2×Q8—31no—
321C2×Q8—91no—
322C2×D4—31no—
323C2×D4—31no—
324C2×D4—91no—
325C2×D4—91no—
326C2×D4—91no—
327C2×D4D3211yescharacteristic
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C4⋊C4—31no—
337C4⋊C4—31no—
338C4⋊C4—91no—
339C4⋊C4—91no—
340C4⋊C4—91no—
341C4⋊C4—91no—
342C4⋊C4—91no—
343C4⋊C4—91no—
344C4⋊C4—91no—
345C4⋊C4—91no—
346C22⋊C4—31no—
347C22⋊C4—31no—
348C22⋊C4—31no—
349C22⋊C4—91no—
350C22⋊C4—91no—
351C22⋊C4—91no—
352C22⋊C4—91no—
353C22⋊C4—91no—
354C42—91no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—32no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—61no—
374C22×C3—61no—
375C22×C3D3×D412yes—
376C22×C3C2×#6712yes—
377C22×C3C23×D311yescharacteristic
378C22×C3C23×D311yescharacteristic
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—61no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3C2×#6712yes—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—32no—
394C3×C4—41no—
395C3×C4—61no—
396C3×C4—61no—
397C3×C4—61no—
398C3×C4—61no—
399C3×C4—61no—
400C3×C4—61no—
401Dic3—21no—
402Dic3—21no—
403Dic3—21no—
404Dic3—21no—
405Dic3—21no—
406Dic3—21no—
407Dic3—32no—
408Dic3—32no—
409Dic3—62no—
410Dic3—61no—
411Dic3—61no—
412Dic3—61no—
413Dic3—61no—
414Dic3—121no—
415Dic3—121no—
416Dic3C2×#6712yes—
417C32#54711yescharacteristic, complemented, Sylow
418C23—31no—
419C23—91no—
420C23C2×D3211yescharacteristic
421C23C2×D3211yescharacteristic
422Q8—62no—
423Q8—182no—
424D4—22no—
425D4—34no—
426D4—62no—
427D4—182no—
428D4—182no—
429D4—182no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—31no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—91no—
442C2×C4—91no—
443C2×C4—91no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4C2×D3211yescharacteristic
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—42no—
455C2×C3—41no—
456C2×C3—41no—
457C2×C3—62no—
458C2×C3—81no—
459C2×C3C2×D3×D411yescharacteristic
460C2×C3D3×#4111yescharacteristic
461C2×C3D3×#4111yescharacteristic
462C2×C3#101011yescharacteristic
463C2×C3#101011yescharacteristic
464C2×C3C22×#6711yescharacteristic
465D3—22no—
466D3—121no—
467D3—121no—
468D3—241no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—32no—
475C22—61no—
476C22—61no—
477C22—181no—
478C22—181no—
479C22—181no—
480C22D3×#6712yes—
481C22C22×D3211yescharacteristic
482C4—21no—
483C4—32no—
484C4—61no—
485C4—61no—
486C4—61no—
487C4—61no—
488C4—61no—
489C4—61no—
490C4—92no—
491C4—181no—
492C4—181no—
493C3—21no—
494C3#565511yescharacteristic, complemented
495C3#582411yescharacteristic, complemented
496C2—22no—
497C2—41no—
498C2—62no—
499C2—361no—
500C2#6430911yescharacteristic
501C2#6431211yescharacteristic
502C2C2×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×D4C22
hypercenterC2×D4D32
hypocenterC32#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#237C2semidirect
2. C2×#3804C2semidirect
3. #64148C2semidirect
4. C3×#935C2semidirect
5. #67⋊Dic3C2semidirect
6. #63971C2semidirect
7. #63969C2semidirect
8. C2×#3724C2semidirect
9. #63966C2semidirect
10. #63964C2semidirect
11. #63952C2semidirect
12. #63888C2semidirect
13. D3×Dic3⋊C4C2semidirect
14. #63850C2semidirect
15. #63839C2semidirect
57. C2×#237D3semidirect
67. #935D3semidirect
99. C3×#67D4semidirect
215. C3⋊Dic3#41semidirect
277. #67#67semidirect
417. C32#547semidirect
494. C3#5655semidirect
495. C3#5824semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#2372
C2×#38042
#641482
C3×#9352
#67⋊Dic32
#639712
#639692
C2×#37242
#639662
#639642
#639522
#638882
D3×Dic3⋊C42
#638502
#638392
#58243
#56553