Finite Group Databasebeta

← #10595089

Subgroups — #10595089

Order 576.

547 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
1C4×#638C211yesmaximal, characteristic, complemented
2C3×#930C211yesmaximal, characteristic, complemented
3C3×#929C211yesmaximal, characteristic, complemented
4#63983C211yesmaximal, characteristic, complemented
5#63970C211yesmaximal, characteristic, complemented
6#63959C211yesmaximal, characteristic, complemented
7#63958C211yesmaximal, characteristic, complemented
8#63922C211yesmaximal, characteristic, complemented
9#63921C211yesmaximal, characteristic, complemented
10#63915C211yesmaximal, characteristic, complemented
11#63895C211yesmaximal, characteristic, complemented
12#63884C211yesmaximal, characteristic, complemented
13#63881C211yesmaximal, characteristic, complemented
14#63862C211yesmaximal, characteristic, complemented
15#63858C211yesmaximal, characteristic, complemented
16#5657—31nomaximal
17#5613—31nomaximal
18C22×D32C2211yescharacteristic
19C22×C32×C4C2211yescharacteristic, complemented
20C2×#638C2211yescharacteristic
21C2×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×#67C2211yescharacteristic
24C2×C3×#67C2211yescharacteristic, complemented
25C2×C3×D12C2211yescharacteristic
26C2×#627C2211yescharacteristic, complemented
27C2×#626C2211yescharacteristic
28C2×#625C2211yescharacteristic
29C2×#624C2211yescharacteristic
30C2×D3×Dic3C2211yescharacteristic, complemented
31#3757C2211yescharacteristic, complemented
32#3752C2211yescharacteristic
33#3750C2211yescharacteristic, complemented
34C4×C3⋊Dic3C2211yescharacteristic, complemented
35C3×#217C2211yescharacteristic, complemented
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C3×C4⋊Dic3C2211yescharacteristic, complemented
41C3×Dic3⋊C4C2211yescharacteristic, complemented
42C3×Dic3⋊C4C2211yescharacteristic, complemented
43Dic3⋊Dic3C2211yescharacteristic, complemented
44Dic3⋊Dic3C2211yescharacteristic, complemented
45#3722C2211yescharacteristic
46(C2×D3)⋊Dic3C2211yescharacteristic
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52Dic32C2211yescharacteristic, complemented
53C3×#123—31no—
54C3×#121—31no—
55#939—31no—
56#938—31no—
57#938—31no—
58#937—31no—
59#937—31no—
60#937—31no—
61#936—31no—
62#935—31no—
63#930D311yescharacteristic, complemented
64#929D311yescharacteristic, complemented
65C4×#67—31no—
66C4×#67—31no—
67C4×#67—61no—
68#898—31no—
69#898—31no—
70#897—31no—
71#896—31no—
72#894—31no—
73#893—31no—
74#885—31no—
75#885—31no—
76#885—31no—
77#884—31no—
78#882—31no—
79#67⋊C4—31no—
80D3×C22⋊C4—31no—
81D3×C22⋊C4—31no—
82#879—31no—
83#879—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×C4—41no—
93C2×C32×C4C2311yescharacteristic
94C2×C32×C4C2311yescharacteristic
95#638—22no—
96C2×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊Dic3C2311yescharacteristic
98C2×C3⋊Dic3C2311yescharacteristic
99C4×C3⋊D3—41no—
100C3×#67—41no—
101C3×#67—41no—
102C3×#67—41no—
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C3×D12—41no—
109#627—41no—
110#626—22no—
111#625—41no—
112#624—41no—
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—21no—
122C22×C3×C4C2×D311yescharacteristic, complemented
123C22×C3×C4C2×D311yescharacteristic, complemented
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—
134C2×D12—31no—
135C2×D12C2×D311yescharacteristic
136C2×C4×D3—31no—
137C2×C4×D3—31no—
138C2×C4×D3—31no—
139C2×C4×D3—31no—
140C2×C4×D3—31no—
141C2×C4×D3—61no—
142C2×Dic6—31no—
143C2×Dic6—31no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—31no—
147C3×C22⋊C4—31no—
148C3×C22⋊C4—31no—
149C3×C22⋊C4—31no—
150C3×C22⋊C4—31no—
151C3×C22⋊C4—31no—
152#217—31no—
153#217—31no—
154#217—31no—
155#217—31no—
156#217—31no—
157#217—31no—
158#217—31no—
159#217—31no—
160#217—61no—
161#217C2×D311yescharacteristic, complemented
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—61no—
173(C2×D3)⋊C4C2×D311yescharacteristic
174(C2×D3)⋊C4C2×D311yescharacteristic
175(C2×D3)⋊C4C2×D311yescharacteristic
176(C2×D3)⋊C4C2×D311yescharacteristic, complemented
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3C2×D311yescharacteristic, complemented
180Dic3⋊C4—31no—
181Dic3⋊C4—31no—
182Dic3⋊C4—31no—
183Dic3⋊C4—31no—
184Dic3⋊C4—61no—
185Dic3⋊C4C2×D311yescharacteristic, complemented
186Dic3⋊C4C2×D311yescharacteristic, complemented
187C4×Dic3—31no—
188C4×Dic3—31no—
189C4×Dic3—31no—
190C4×Dic3—31no—
191C4×Dic3—61no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32C2411yescharacteristic
196C2×C3⋊D3—21no—
197C2×C3⋊D3—21no—
198C2×C3⋊D3#4112yes—
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—
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—31no—
224#123—91no—
225C22⋊Q8—91no—
226#121—31no—
227#121—91no—
228#121—91no—
229#120—91no—
230#120—91no—
231C4×D4—91no—
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—121no—
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—41no—
264C2×C3×C4—41no—
265C2×C3×C4—42no—
266C2×C3×C4C22×D311yescharacteristic
267C2×C3×C4C22×D311yescharacteristic
268C2×C3×C4C22×D311yescharacteristic
269C2×C3×C4C22×D311yescharacteristic
270#67—41no—
271#67—41no—
272#67—41no—
273#67—62no—
274#67—62no—
275#67—62no—
276#67—64no—
277#67—121no—
278#67—121no—
279C2×Dic3—31no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—31no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—121no—
289C2×Dic3C22×D311yescharacteristic
290C2×Dic3C22×D311yescharacteristic
291C2×Dic3C22×D311yescharacteristic
292C2×Dic3C22×D311yescharacteristic
293C2×Dic3C22×D311yescharacteristic
294D12—41no—
295D12—62no—
296C4×D3—121no—
297C4×D3—121no—
298C4×D3—121no—
299C4×D3—121no—
300C4×D3—121no—
301C4×D3—122no—
302Dic6—121no—
303Dic6—121no—
304C2×C32—41no—
305C2×C32C2×#4111yescharacteristic
306C2×C32H(5,𝔽2)11yescharacteristic
307C2×C32H(5,𝔽2)11yescharacteristic
308C3⋊D3—22no—
309C3×D3—41no—
310C3×D3—41no—
311C3×D3—41no—
312C24—91no—
313C2×Q8—91no—
314C2×D4—31no—
315C2×D4—31no—
316C2×D4—31no—
317C2×D4—31no—
318C2×D4—91no—
319C2×D4—91no—
320C2×D4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4D3211yescharacteristic, complemented
325C4⋊C4—31no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C4⋊C4—91no—
331C22⋊C4—31no—
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—
345C42—91no—
346C42—91no—
347C22×C3—22no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
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×C3—61no—
366C22×C3C23×D311yescharacteristic
367C22×C3C23×D311yescharacteristic
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—21no—
377C2×D3—32no—
378C2×D3—32no—
379C2×D3—62no—
380C2×D3—61no—
381C2×D3—61no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—124no—
387C2×D3—124no—
388C3×C4—22no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—41no—
394C3×C4—61no—
395C3×C4—61no—
396C3×C4—61no—
397C3×C4—61no—
398C3×C4—61no—
399Dic3—21no—
400Dic3—21no—
401Dic3—21no—
402Dic3—21no—
403Dic3—21no—
404Dic3—62no—
405Dic3—61no—
406Dic3—61no—
407Dic3—61no—
408Dic3—61no—
409Dic3—61no—
410Dic3—61no—
411Dic3—121no—
412Dic3—121no—
413C32#53811yescharacteristic, complemented, Sylow
414C23—31no—
415C23—31no—
416C23—31no—
417C23—91no—
418C23—182no—
419C23—361no—
420C23—361no—
421C23C2×D3211yescharacteristic
422Q8—361no—
423D4—121no—
424D4—121no—
425D4—121no—
426D4—121no—
427D4—182no—
428D4—182no—
429D4—361no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—41no—
436C2×C4—91no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—361no—
440C2×C4—361no—
441C2×C4—361no—
442C2×C4C2×D3211yescharacteristic
443C2×C4C2×D3211yescharacteristic
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—42no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—121no—
451C2×C3—121no—
452C2×C3—121no—
453C2×C3#100411yescharacteristic
454C2×C3#100411yescharacteristic
455C2×C3#100411yescharacteristic
456C2×C3D3×#4111yescharacteristic
457C2×C3D3×#4111yescharacteristic
458C2×C3#100911yescharacteristic
459D3—41no—
460D3—41no—
461D3—41no—
462D3—62no—
463D3—62no—
464D3—122no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—61no—
473C22—61no—
474C22—61no—
475C22—61no—
476C22—61no—
477C22—92no—
478C22—181no—
479C22—181no—
480C22—364no—
481C22C22×D3211yescharacteristic
482C4—21no—
483C4—21no—
484C4—61no—
485C4—61no—
486C4—61no—
487C4—61no—
488C4—61no—
489C4—181no—
490C4—181no—
491C4—181no—
492C3—21no—
493C3#561311yescharacteristic, complemented
494C3#565711yescharacteristic, complemented
495C2—41no—
496C2—121no—
497C2—121no—
498C2—121no—
499C2—182no—
500C2#6430611yescharacteristic
501C2#6430711yescharacteristic
502C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×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. C4×#638C2semidirect
2. C3×#930C2semidirect
3. C3×#929C2semidirect
4. #63983C2semidirect
5. #63970C2semidirect
6. #63959C2semidirect
7. #63958C2semidirect
8. #63922C2semidirect
9. #63921C2semidirect
10. #63915C2semidirect
11. #63895C2semidirect
12. #63884C2semidirect
13. #63881C2semidirect
14. #63862C2semidirect
15. #63858C2semidirect
19. C22×C32×C4C22semidirect
24. C2×C3×#67C22semidirect
26. C2×#627C22semidirect
30. C2×D3×Dic3C22semidirect
31. #3757C22semidirect
33. #3750C22semidirect
34. C4×C3⋊Dic3C22semidirect
35. C3×#217C22semidirect
39. C3×(C2×D3)⋊C4C22semidirect
40. C3×C4⋊Dic3C22semidirect
41. C3×Dic3⋊C4C22semidirect
42. C3×Dic3⋊C4C22semidirect
43. Dic3⋊Dic3C22semidirect
44. Dic3⋊Dic3C22semidirect
51. (C2×D3)⋊Dic3C22semidirect
52. Dic32C22semidirect
63. #930D3semidirect
64. #929D3semidirect
122. C22×C3×C4C2×D3semidirect
123. C22×C3×C4C2×D3semidirect
132. C2×#67C2×D3semidirect
161. #217C2×D3semidirect
176. (C2×D3)⋊C4C2×D3semidirect
179. C4⋊Dic3C2×D3semidirect
185. Dic3⋊C4C2×D3semidirect
186. Dic3⋊C4C2×D3semidirect
324. C22×C4D32semidirect
413. C32#538semidirect
493. C3#5613semidirect
494. C3#5657semidirect

Maximal subgroups

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

subgroupindex
C4×#6382
C3×#9302
C3×#9292
#639832
#639702
#639592
#639582
#639222
#639212
#639152
#638952
#638842
#638812
#638622
#638582
#56573
#56133