Finite Group Databasebeta

← #10594978

Subgroups — #10594978

Order 576.

487 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64139C211yesmaximal, characteristic, complemented
2C3×#929C211yesmaximal, characteristic, complemented
3C3×#924C211yesmaximal, characteristic, complemented
4#63975C211yesmaximal, characteristic, complemented
5#63971C211yesmaximal, characteristic, complemented
6#63958C211yesmaximal, characteristic, complemented
7#63953C211yesmaximal, characteristic, complemented
8#63910C211yesmaximal, characteristic, complemented
9#63907C211yesmaximal, characteristic, complemented
10#63897C211yesmaximal, characteristic, complemented
11#63895C211yesmaximal, characteristic, complemented
12#63893C211yesmaximal, characteristic, complemented
13#63890C211yesmaximal, characteristic, complemented
14#63888C211yesmaximal, characteristic, complemented
15#63845C211yesmaximal, characteristic, complemented
16#5667—31nomaximal
17#5647—31nomaximal
18C22×C32×C4C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#638C2211yescharacteristic
21C2×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×Dic6C2211yescharacteristic
24C2×#627C2211yescharacteristic
25C2×#626C2211yescharacteristic
26C2×#626C2211yescharacteristic
27C2×#624C2211yescharacteristic
28C2×#624C2211yescharacteristic
29C2×D3×Dic3C2211yescharacteristic
30#3752C2211yescharacteristic
31#3752C2211yescharacteristic
32C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#217C2211yescharacteristic
34C3×#217C2211yescharacteristic
35C3×#217C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×C4⋊Dic3C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×Dic3⋊C4C2211yescharacteristic
41C3×Dic3⋊C4C2211yescharacteristic
42C3×Dic3⋊C4C2211yescharacteristic
43#3724C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49#3722C2211yescharacteristic
50#3722C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#123—31no—
54C3×C22⋊Q8—31no—
55#947—31no—
56#946—31no—
57#939—31no—
58#938—31no—
59#930—31no—
60#930—31no—
61#930—61no—
62#929D311yescharacteristic, complemented
63#924D311yescharacteristic, complemented
64#897—31no—
65#897—31no—
66#896—31no—
67#896—31no—
68#895—31no—
69#894—31no—
70#894—31no—
71#894—31no—
72#890—31no—
73#889—31no—
74#886—31no—
75#885—31no—
76#885—31no—
77#885—31no—
78#884—31no—
79#884—31no—
80#884—31no—
81#883—31no—
82#883—31no—
83#878—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3⋊D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C2×C32×C4—41no—
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91#638—41no—
92#638—41no—
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C4⋊(C3⋊D3)—41no—
96C3×#67—41no—
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C3×Dic6—41no—
105#627—41no—
106#626—41no—
107#626—41no—
108#624—41no—
109#624—41no—
110D3×Dic3—41no—
111#562—91noSylow
112C2×C3×Q8—31no—
113C2×C3×D4—31no—
114C22×C3×C4—21no—
115C22×C3×C4C2×D311yescharacteristic
116C22×C3×C4C2×D311yescharacteristic
117C2×#67—31no—
118C2×#67—31no—
119C2×#67—31no—
120C2×#67—31no—
121C2×#67—31no—
122C2×#67—31no—
123C2×#67—61no—
124C2×#67—61no—
125C2×#67C2×D311yescharacteristic
126C22×Dic3—31no—
127C2×D12—31no—
128C2×D12—31no—
129C2×D12—31no—
130C2×D12—31no—
131C2×D12—61no—
132C2×C4×D3—31no—
133C2×C4×D3—31no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×Dic6—31no—
138C2×Dic6—31no—
139C2×Dic6C2×D311yescharacteristic
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—31no—
145C3×C22⋊C4—31no—
146C3×C22⋊C4—31no—
147C3×C22⋊C4—31no—
148C3×C22⋊C4—31no—
149C3×C22⋊C4—31no—
150#217—31no—
151#217C2×D311yescharacteristic
152#217C2×D311yescharacteristic
153#217C2×D311yescharacteristic
154(C2×D3)⋊C4—31no—
155(C2×D3)⋊C4—31no—
156(C2×D3)⋊C4—31no—
157(C2×D3)⋊C4—31no—
158(C2×D3)⋊C4—31no—
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—61no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4C2×D311yescharacteristic
170(C2×D3)⋊C4C2×D311yescharacteristic
171C4⋊Dic3—31no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3C2×D311yescharacteristic
178Dic3⋊C4—31no—
179Dic3⋊C4—31no—
180Dic3⋊C4—31no—
181Dic3⋊C4—31no—
182Dic3⋊C4—31no—
183Dic3⋊C4C2×D311yescharacteristic
184Dic3⋊C4C2×D311yescharacteristic
185Dic3⋊C4C2×D311yescharacteristic
186Dic3⋊C4C2×D311yescharacteristic
187C4×Dic3—31no—
188C4×Dic3—31no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
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—
202C32×C4—21no—
203C32×C4—21no—
204C3⋊Dic3—21no—
205C3⋊Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3—21no—
208C3×Dic3—21no—
209C3×Dic3—21no—
210C3×Dic3—21no—
211C3×Dic3—21no—
212C3×Dic3—21no—
213#125—91no—
214#124—91no—
215#124—91no—
216#123—31no—
217#123—91no—
218#123—91no—
219#123—91no—
220C22⋊Q8—31no—
221C22⋊Q8—91no—
222C22⋊Q8—91no—
223C22⋊Q8—91no—
224#121—91no—
225#121—91no—
226#121—91no—
227#121—91no—
228C23×C3—21no—
229C23×C3—31no—
230C23×C3C22×D311yescharacteristic
231C23×C3C22×D311yescharacteristic
232C22×D3—31no—
233C22×D3—31no—
234C22×D3—31no—
235C22×D3—31no—
236C22×D3—61no—
237C22×D3—61no—
238C22×D3C22×D311yescharacteristic
239C3×Q8—121no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—31no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—42no—
253C2×C3×C4C22×D311yescharacteristic
254C2×C3×C4C22×D311yescharacteristic
255C2×C3×C4C22×D311yescharacteristic
256C2×C3×C4C22×D311yescharacteristic
257#67—41no—
258#67—121no—
259#67—121no—
260#67—121no—
261#67—121no—
262#67—121no—
263#67—121no—
264#67—122no—
265#67—122no—
266C2×Dic3—31no—
267C2×Dic3—31no—
268C2×Dic3—31no—
269C2×Dic3—31no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—121no—
273C2×Dic3C22×D311yescharacteristic
274C2×Dic3C22×D311yescharacteristic
275C2×Dic3C22×D311yescharacteristic
276C2×Dic3C22×D311yescharacteristic
277C2×Dic3C22×D311yescharacteristic
278C2×Dic3C22×D311yescharacteristic
279C2×Dic3C22×D311yescharacteristic
280D12—121no—
281D12—121no—
282D12—122no—
283D12—121no—
284D12—121no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—121no—
288C4×D3—121no—
289C4×D3—121no—
290Dic6—41no—
291Dic6—121no—
292Dic6—121no—
293C2×C32—41no—
294C2×C32H(5,𝔽2)11yescharacteristic
295C2×C32H(5,𝔽2)11yescharacteristic
296C2×C322−1+411yescharacteristic
297C3⋊D3—41no—
298C3⋊D3—41no—
299C3×D3—41no—
300C2×Q8—31no—
301C2×Q8—91no—
302C2×D4—31no—
303C2×D4—91no—
304C2×D4—91no—
305C2×D4—91no—
306C2×D4—91no—
307C2×D4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4D3211yescharacteristic
312C4⋊C4—31no—
313C4⋊C4—31no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—91no—
321C4⋊C4—91no—
322C22⋊C4—31no—
323C22⋊C4—31no—
324C22⋊C4—31no—
325C22⋊C4—31no—
326C22⋊C4—31no—
327C22⋊C4—91no—
328C22⋊C4—91no—
329C22⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C22⋊C4—91no—
333C22⋊C4—91no—
334C42—91no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—61no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3C23×D311yescharacteristic
349C22×C3C23×D311yescharacteristic
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—61no—
356C2×D3—61no—
357C2×D3—61no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C3×C4—22no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—41no—
377C3×C4—61no—
378C3×C4—61no—
379C3×C4—61no—
380C3×C4—61no—
381C3×C4—61no—
382C3×C4—61no—
383C3×C4—61no—
384Dic3—21no—
385Dic3—21no—
386Dic3—21no—
387Dic3—21no—
388Dic3—21no—
389Dic3—21no—
390Dic3—21no—
391Dic3—61no—
392Dic3—61no—
393Dic3—61no—
394Dic3—61no—
395Dic3—121no—
396Dic3—121no—
397C32#56211yescharacteristic, complemented, Sylow
398C23—31no—
399C23—91no—
400C23—91no—
401C23C2×D3211yescharacteristic
402Q8—121no—
403Q8—361no—
404D4—121no—
405D4—361no—
406D4—361no—
407D4—361no—
408D4—361no—
409D4—361no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—41no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—361no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4C2×D3211yescharacteristic
424C2×C4C2×D3211yescharacteristic
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—42no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—121no—
432C2×C3#100411yescharacteristic
433C2×C3#100411yescharacteristic
434C2×C3#100711yescharacteristic
435C2×C3#100911yescharacteristic
436C2×C3#100911yescharacteristic
437C2×C3#101011yescharacteristic
438D3—41no—
439D3—121no—
440D3—121no—
441D3—121no—
442D3—121no—
443D3—241no—
444D3—241no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—61no—
449C22—61no—
450C22—61no—
451C22—181no—
452C22—181no—
453C22—181no—
454C22—181no—
455C22—181no—
456C22—181no—
457C22C22×D3211yescharacteristic
458C4—21no—
459C4—21no—
460C4—61no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—61no—
465C4—61no—
466C4—61no—
467C4—181no—
468C4—181no—
469C3—21no—
470C3#564711yescharacteristic, complemented
471C3#566711yescharacteristic, complemented
472C2—41no—
473C2—121no—
474C2—361no—
475C2—361no—
476C2#6429711yescharacteristic
477C2#6430811yescharacteristic
478C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #64139C2semidirect
2. C3×#929C2semidirect
3. C3×#924C2semidirect
4. #63975C2semidirect
5. #63971C2semidirect
6. #63958C2semidirect
7. #63953C2semidirect
8. #63910C2semidirect
9. #63907C2semidirect
10. #63897C2semidirect
11. #63895C2semidirect
12. #63893C2semidirect
13. #63890C2semidirect
14. #63888C2semidirect
15. #63845C2semidirect
62. #929D3semidirect
63. #924D3semidirect
397. C32#562semidirect
470. C3#5647semidirect
471. C3#5667semidirect

Maximal subgroups

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

subgroupindex
#641392
C3×#9292
C3×#9242
#639752
#639712
#639582
#639532
#639102
#639072
#638972
#638952
#638932
#638902
#638882
#638452
#56673
#56473