Finite Group Databasebeta

← #10594467

Subgroups — #10594467

Order 576.

527 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
1#64104C211yesmaximal, characteristic, complemented
2C3×#894C211yesmaximal, characteristic, complemented
3C3×#889C211yesmaximal, characteristic, complemented
4#63911C211yesmaximal, characteristic, complemented
5#63910C211yesmaximal, characteristic, complemented
6#63910C211yesmaximal, characteristic, complemented
7#63910C211yesmaximal, characteristic, complemented
8#63909C211yesmaximal, characteristic, complemented
9#63904C211yesmaximal, characteristic, complemented
10#63897C211yesmaximal, characteristic, complemented
11#63890C211yesmaximal, characteristic, complemented
12#63886C211yesmaximal, characteristic, complemented
13#63881C211yesmaximal, characteristic, complemented
14#63853C211yesmaximal, characteristic, complemented
15#63836C211yesmaximal, characteristic, complemented
16#5697—31nomaximal
17#5663—31nomaximal
18C2×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊D3C2211yescharacteristic
22C2×C3×D12C2211yescharacteristic
23C2×C3×C4×D3C2211yescharacteristic
24C2×#626C2211yescharacteristic
25C2×#626C2211yescharacteristic
26C2×#626C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#626C2211yescharacteristic
29C2×#626C2211yescharacteristic
30C2×#624C2211yescharacteristic
31C2×#624C2211yescharacteristic
32C2×D3×Dic3C2211yescharacteristic
33C32×C4⋊C4C2211yescharacteristic
34#3752C2211yescharacteristic
35#3752C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×C4⋊Dic3C2211yescharacteristic
40C3×Dic3⋊C4C2211yescharacteristic
41C3×Dic3⋊C4C2211yescharacteristic
42C3×Dic3⋊C4C2211yescharacteristic
43C3×Dic3⋊C4C2211yescharacteristic
44C3×Dic3⋊C4C2211yescharacteristic
45C3×C4×Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49#3722C2211yescharacteristic
50#3722C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#125—31no—
54C3×#123—31no—
55#940—31no—
56#939—31no—
57#930—31no—
58C4×#67—31no—
59#895—31no—
60#895—31no—
61#895—31no—
62#895—31no—
63#895—31no—
64#895—31no—
65#895—31no—
66#895—61no—
67#894—31no—
68#894—31no—
69#894—31no—
70#894—31no—
71#894D311yescharacteristic, complemented
72#893—31no—
73#893—31no—
74#892—31no—
75#889D311yescharacteristic, complemented
76#886—31no—
77#884—31no—
78#884—31no—
79#884—31no—
80#883—31no—
81#67⋊C4—31no—
82#874—31no—
83#872—31no—
84C22×C3⋊D3C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3⋊D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C4⋊(C3⋊D3)—41no—
94C4⋊(C3⋊D3)—41no—
95C4⋊(C3⋊D3)—41no—
96C4×C3⋊D3—41no—
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C3×D12—41no—
104C3×C4×D3—41no—
105#626—22no—
106#626—22no—
107#626—41no—
108#626—41no—
109#626—41no—
110#626—41no—
111#624—22no—
112#624—41no—
113D3×Dic3—41no—
114#540—91noSylow
115C2×C3×D4—31no—
116C22×C3×C4—31no—
117C2×#67—31no—
118C2×#67—31no—
119C2×#67—31no—
120C2×#67—31no—
121C2×#67—31no—
122C2×#67—31no—
123C22×Dic3—31no—
124C2×D12—31no—
125C2×D12—31no—
126C2×D12—31no—
127C2×D12—31no—
128C2×D12—31no—
129C2×D12—31no—
130C2×D12—31no—
131C2×D12—31no—
132C2×D12—31no—
133C2×D12—31no—
134C2×D12—31no—
135C2×D12—31no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12C2×D311yescharacteristic
140C2×C4×D3—31no—
141C2×C4×D3—31no—
142C2×C4×D3—31no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—31no—
146C2×C4×D3—31no—
147C2×C4×D3—61no—
148C2×C4×D3C2×D311yescharacteristic
149C3×C4⋊C4—21no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4C2×D311yescharacteristic
157C3×C4⋊C4C2×D311yescharacteristic
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C42—31no—
162#217—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—31no—
175(C2×D3)⋊C4—31no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4C2×D311yescharacteristic
179(C2×D3)⋊C4C2×D311yescharacteristic
180(C2×D3)⋊C4C2×D311yescharacteristic
181C4⋊Dic3—31no—
182C4⋊Dic3C2×D311yescharacteristic
183Dic3⋊C4—31no—
184Dic3⋊C4C2×D311yescharacteristic
185Dic3⋊C4C2×D311yescharacteristic
186Dic3⋊C4C2×D311yescharacteristic
187Dic3⋊C4C2×D311yescharacteristic
188Dic3⋊C4C2×D311yescharacteristic
189C4×Dic3—31no—
190C4×Dic3—31no—
191C4×Dic3C2×D311yescharacteristic
192C22×C32C2411yescharacteristic
193C2×C3⋊D3—21no—
194C2×C3⋊D3—21no—
195C2×C3⋊D3—21no—
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—21no—
208C32×C4—21no—
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#4112yes—
218#127—91no—
219#125—31no—
220#123—31no—
221#123—91no—
222#123—91no—
223#123—91no—
224#121—91no—
225#121—91no—
226#121—91no—
227#121—91no—
228#121—91no—
229#121—91no—
230C4×D4—91no—
231C4×D4—91no—
232#117—91no—
233C23×C3—31no—
234C23×C3—31no—
235C22×D3—31no—
236C22×D3—31no—
237C22×D3—31no—
238C22×D3—31no—
239C22×D3—31no—
240C22×D3—31no—
241C22×D3—61no—
242C22×D3—61no—
243C22×D3—61no—
244C22×D3C22×D311yescharacteristic
245C22×D3C22×D311yescharacteristic
246C3×D4—121no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—31no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—121no—
257C2×C3×C4C22×D311yescharacteristic
258C2×C3×C4C22×D311yescharacteristic
259C2×C3×C4C22×D311yescharacteristic
260C2×C3×C4C22×D311yescharacteristic
261C2×C3×C4C22×D311yescharacteristic
262C2×C3×C4C22×D311yescharacteristic
263#67—62no—
264#67—62no—
265#67—121no—
266#67—121no—
267#67—121no—
268#67—121no—
269C2×Dic3—31no—
270C2×Dic3—31no—
271C2×Dic3—61no—
272C2×Dic3—121no—
273C2×Dic3C22×D311yescharacteristic
274C2×Dic3C22×D311yescharacteristic
275C2×Dic3C22×D311yescharacteristic
276C2×Dic3C22×D311yescharacteristic
277C2×Dic3C22×D311yescharacteristic
278C2×Dic3C22×D311yescharacteristic
279D12—41no—
280D12—62no—
281D12—62no—
282D12—121no—
283D12—121no—
284D12—121no—
285D12—121no—
286D12—121no—
287D12—121no—
288D12—122no—
289D12—122no—
290D12—122no—
291D12—121no—
292D12—121no—
293D12—121no—
294D12—121no—
295C4×D3—41no—
296C4×D3—62no—
297C4×D3—62no—
298C4×D3—121no—
299C4×D3—121no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—122no—
304C2×C32C2×#4111yescharacteristic
305C2×C32H(5,𝔽2)11yescharacteristic
306C2×C32H(5,𝔽2)11yescharacteristic
307C3⋊D3—41no—
308C3⋊D3—41no—
309C3⋊D3—41no—
310C3×D3—41no—
311C3×D3—41no—
312C2×D4—31no—
313C2×D4—91no—
314C2×D4—91no—
315C2×D4—91no—
316C2×D4—91no—
317C2×D4—91no—
318C2×D4—91no—
319C2×D4—91no—
320C2×D4—91no—
321C2×D4—91no—
322C22×C4—31no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C4⋊C4—31no—
328C4⋊C4—31no—
329C4⋊C4—31no—
330C4⋊C4—31no—
331C4⋊C4—31no—
332C4⋊C4—31no—
333C4⋊C4—91no—
334C4⋊C4D3211yescharacteristic
335C22⋊C4—31no—
336C22⋊C4—31no—
337C22⋊C4—31no—
338C22⋊C4—91no—
339C22⋊C4—91no—
340C22⋊C4—91no—
341C22⋊C4—91no—
342C22⋊C4—91no—
343C22⋊C4—91no—
344C22⋊C4—91no—
345C42—31no—
346C42—91no—
347C22×C3—21no—
348C22×C3—61no—
349C22×C3—61no—
350C22×C3—61no—
351C22×C3—61no—
352C22×C3—61no—
353C22×C3—61no—
354C22×C3C23×D311yescharacteristic
355C22×C3C23×D311yescharacteristic
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—21no—
360C2×D3—21no—
361C2×D3—21no—
362C2×D3—62no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—61no—
366C2×D3—61no—
367C2×D3—61no—
368C2×D3—61no—
369C2×D3—61no—
370C2×D3—61no—
371C2×D3—61no—
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—121no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—121no—
389C3×C4—22no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—32no—
397C3×C4—41no—
398C3×C4—41no—
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—61no—
410Dic3—61no—
411Dic3—121no—
412Dic3#23912yes—
413C32#54011yescharacteristic, complemented, Sylow
414C23—31no—
415C23—31no—
416C23—91no—
417C23—91no—
418C23—91no—
419D4—121no—
420D4—182no—
421D4—182no—
422D4—361no—
423D4—361no—
424D4—361no—
425D4—361no—
426D4—361no—
427D4—361no—
428D4—361no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—91no—
436C2×C4—121no—
437C2×C4—182no—
438C2×C4—361no—
439C2×C4—361no—
440C2×C4—361no—
441C2×C4C2×D3211yescharacteristic
442C2×C4C2×D3211yescharacteristic
443C2×C4C2×D3211yescharacteristic
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—121no—
448C2×C3—121no—
449C2×C3#100411yescharacteristic
450C2×C3C2×#23911yescharacteristic
451C2×C3D3×#4111yescharacteristic
452C2×C3#100911yescharacteristic
453C2×C3#100911yescharacteristic
454C2×C3#100911yescharacteristic
455D3—41no—
456D3—41no—
457D3—122no—
458D3—121no—
459D3—121no—
460D3—121no—
461D3—121no—
462D3—121no—
463D3—121no—
464D3—241no—
465D3—241no—
466C22—61no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—181no—
473C22—181no—
474C22—181no—
475C22—181no—
476C22—181no—
477C22—181no—
478C22—181no—
479C22—181no—
480C22—181no—
481C22C22×D3211yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—32no—
486C4—61no—
487C4—61no—
488C4—61no—
489C4—61no—
490C4—61no—
491C4—181no—
492C3—21no—
493C3#566311yescharacteristic, complemented
494C3#569711yescharacteristic, complemented
495C2—121no—
496C2—121no—
497C2—361no—
498C2—361no—
499C2—361no—
500C2#6430811yescharacteristic
501C2#6431411yescharacteristic
502C2D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
hypercenterC4⋊C4D32
hypocenterC32#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64104C2semidirect
2. C3×#894C2semidirect
3. C3×#889C2semidirect
4. #63911C2semidirect
5. #63910C2semidirect
6. #63910C2semidirect
7. #63910C2semidirect
8. #63909C2semidirect
9. #63904C2semidirect
10. #63897C2semidirect
11. #63890C2semidirect
12. #63886C2semidirect
13. #63881C2semidirect
14. #63853C2semidirect
15. #63836C2semidirect
71. #894D3semidirect
75. #889D3semidirect
413. C32#540semidirect
493. C3#5663semidirect
494. C3#5697semidirect

Maximal subgroups

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

subgroupindex
#641042
C3×#8942
C3×#8892
#639112
#639102
#639092
#639042
#638972
#638902
#638862
#638812
#638532
#638362
#56973
#56633