Finite Group Databasebeta

← #10595417

Subgroups — #10595417

Order 576.

477 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64155C211yesmaximal, characteristic, complemented
2C3×#947C211yesmaximal, characteristic, complemented
3C3×#946C211yesmaximal, characteristic, complemented
4#63912C211yesmaximal, characteristic, complemented
5#63906C211yesmaximal, characteristic, complemented
6#63905C211yesmaximal, characteristic, complemented
7#63899C211yesmaximal, characteristic, complemented
8#63893C211yesmaximal, characteristic, complemented
9#63891C211yesmaximal, characteristic, complemented
10#63890C211yesmaximal, characteristic, complemented
11#63886C211yesmaximal, characteristic, complemented
12#63885C211yesmaximal, characteristic, complemented
13#63867C211yesmaximal, characteristic, complemented
14#63853C211yesmaximal, characteristic, complemented
15#63852C211yesmaximal, characteristic, complemented
16#5684—31nomaximal
17#5647—31nomaximal
18C2×C32×Q8C2211yescharacteristic
19C2×C4×C3⋊D3C2211yescharacteristic
20C2×C3×D12C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×#627C2211yescharacteristic
23C2×#626C2211yescharacteristic
24C2×#626C2211yescharacteristic
25C2×#626C2211yescharacteristic
26C2×#625C2211yescharacteristic
27C2×#625C2211yescharacteristic
28C2×D3×Dic3C2211yescharacteristic
29C2×D3×Dic3C2211yescharacteristic
30#3752C2211yescharacteristic
31#3752C2211yescharacteristic
32C4⋊(C3⋊Dic3)C2211yescharacteristic
33#3750C2211yescharacteristic
34#3750C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×C4⋊Dic3C2211yescharacteristic
42C3×Dic3⋊C4C2211yescharacteristic
43C3×Dic3⋊C4C2211yescharacteristic
44C3×C4×Dic3C2211yescharacteristic
45#3724C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49#3722C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×#124—31no—
54C3×C22⋊Q8—31no—
55#947D311yescharacteristic, complemented
56#946—31no—
57#946—31no—
58#946—61no—
59#946D311yescharacteristic, complemented
60#939—31no—
61#939—31no—
62#930—31no—
63#929—31no—
64#897—31no—
65#896—31no—
66#895—31no—
67#894—31no—
68#894—31no—
69#889—31no—
70#886—31no—
71#886—31no—
72#885—31no—
73#884—31no—
74#884—31no—
75#884—31no—
76#884—31no—
77#883—31no—
78#883—31no—
79#883—31no—
80#878—31no—
81#878—31no—
82#875—31no—
83#870—31no—
84C22×C3⋊D3C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C32×Q8—41no—
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊D3—41no—
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C3×D12—41no—
102C3×C4×D3—41no—
103#627—41no—
104#626—41no—
105#626—41no—
106#626—41no—
107#625—41no—
108#625—41no—
109D3×Dic3—41no—
110D3×Dic3—41no—
111#562—91noSylow
112C2×C3×Q8—21no—
113C2×C3×Q8C2×D311yescharacteristic
114C2×C3×Q8C2×D311yescharacteristic
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—
123C2×#67—31no—
124C22×Dic3—31no—
125C22×Dic3—31no—
126C2×D12—31no—
127C2×D12—31no—
128C2×D12—31no—
129C2×D12C2×D311yescharacteristic
130C2×C4×D3—31no—
131C2×C4×D3—31no—
132C2×C4×D3—31no—
133C2×C4×D3—31no—
134C2×C4×D3—61no—
135C2×C4×D3C2×D311yescharacteristic
136C2×Dic6—31no—
137C2×Dic6—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C22⋊C4—31no—
142C3×C22⋊C4—31no—
143C3×C22⋊C4—31no—
144C3×C22⋊C4—31no—
145C3×C22⋊C4—31no—
146C3×C22⋊C4—31no—
147C3×C42—31no—
148#217—31no—
149#217—31no—
150#217—31no—
151(C2×D3)⋊C4—31no—
152(C2×D3)⋊C4—31no—
153(C2×D3)⋊C4—31no—
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—61no—
161(C2×D3)⋊C4—61no—
162(C2×D3)⋊C4C2×D311yescharacteristic
163(C2×D3)⋊C4C2×D311yescharacteristic
164(C2×D3)⋊C4C2×D311yescharacteristic
165(C2×D3)⋊C4C2×D311yescharacteristic
166(C2×D3)⋊C4C2×D311yescharacteristic
167(C2×D3)⋊C4C2×D311yescharacteristic
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—31no—
173C4⋊Dic3—61no—
174C4⋊Dic3C2×D311yescharacteristic
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—31no—
178Dic3⋊C4—31no—
179Dic3⋊C4—31no—
180Dic3⋊C4—31no—
181Dic3⋊C4—31no—
182Dic3⋊C4—31no—
183Dic3⋊C4—31no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4C2×D311yescharacteristic
187Dic3⋊C4C2×D311yescharacteristic
188C4×Dic3C2×D311yescharacteristic
189C22×C32C2411yescharacteristic
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3—21no—
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—
204C32×C4—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—31no—
215#124—91no—
216#123—91no—
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—31no—
229C23×C3—31no—
230C23×C3—31no—
231C22×D3—31no—
232C22×D3—31no—
233C22×D3—61no—
234C22×D3C22×D311yescharacteristic
235C22×D3C22×D311yescharacteristic
236C22×D3C22×D311yescharacteristic
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—42no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—121no—
250C2×C3×C4C22×D311yescharacteristic
251C2×C3×C4C22×D311yescharacteristic
252C2×C3×C4C22×D311yescharacteristic
253C2×C3×C4C22×D311yescharacteristic
254C2×C3×C4C22×D311yescharacteristic
255C2×C3×C4C22×D311yescharacteristic
256#67—121no—
257#67—121no—
258#67—121no—
259#67—121no—
260#67—121no—
261#67—121no—
262#67—121no—
263C2×Dic3—31no—
264C2×Dic3—31no—
265C2×Dic3—31no—
266C2×Dic3—31no—
267C2×Dic3—31no—
268C2×Dic3—31no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—121no—
273C2×Dic3—121no—
274C2×Dic3C22×D311yescharacteristic
275C2×Dic3C22×D311yescharacteristic
276C2×Dic3C22×D311yescharacteristic
277C2×Dic3C22×D311yescharacteristic
278C2×Dic3C22×D311yescharacteristic
279D12—41no—
280D12—121no—
281D12—121no—
282D12—121no—
283C4×D3—41no—
284C4×D3—121no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—121no—
288C4×D3—122no—
289Dic6—121no—
290Dic6—121no—
291C2×C32H(5,𝔽2)11yescharacteristic
292C2×C32H(5,𝔽2)11yescharacteristic
293C2×C322−1+411yescharacteristic
294C3⋊D3—41no—
295C3×D3—41no—
296C3×D3—41no—
297C3×D3—41no—
298C2×Q8—91no—
299C2×Q8D3211yescharacteristic
300C2×D4—31no—
301C2×D4—91no—
302C2×D4—91no—
303C2×D4—91no—
304C2×D4—91no—
305C2×D4—91no—
306C22×C4—31no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C4⋊C4—31no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—91no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C22⋊C4—31no—
321C22⋊C4—31no—
322C22⋊C4—31no—
323C22⋊C4—31no—
324C22⋊C4—31no—
325C22⋊C4—31no—
326C22⋊C4—91no—
327C22⋊C4—91no—
328C22⋊C4—91no—
329C22⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C42—31no—
333C22×C3—21no—
334C22×C3—61no—
335C22×C3—61no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3—61no—
340C22×C3—61no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3C23×D311yescharacteristic
344C22×C3C23×D311yescharacteristic
345C2×D3—21no—
346C2×D3—21no—
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—21no—
354C2×D3—62no—
355C2×D3—61no—
356C2×D3—61no—
357C2×D3—61no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—121no—
362C2×D3—121no—
363C3×C4—22no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—61no—
373C3×C4—61no—
374C3×C4—61no—
375C3×C4—61no—
376C3×C4—61no—
377Dic3—21no—
378Dic3—21no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—61no—
383Dic3—61no—
384Dic3—61no—
385Dic3—61no—
386Dic3—61no—
387Dic3—61no—
388Dic3—121no—
389Dic3—121no—
390Dic3—121no—
391C32#56211yescharacteristic, complemented, Sylow
392C23—31no—
393C23—31no—
394C23—31no—
395C23—91no—
396Q8—41no—
397Q8—361no—
398D4—121no—
399D4—361no—
400D4—361no—
401D4—361no—
402D4—361no—
403D4—361no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—91no—
412C2×C4—121no—
413C2×C4—361no—
414C2×C4—361no—
415C2×C4—361no—
416C2×C4C2×D3211yescharacteristic
417C2×C4C2×D3211yescharacteristic
418C2×C4C2×D3211yescharacteristic
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—121no—
423C2×C3—121no—
424C2×C3—121no—
425C2×C3#100411yescharacteristic
426C2×C3#100411yescharacteristic
427C2×C3#100711yescharacteristic
428C2×C3#100911yescharacteristic
429C2×C3#100911yescharacteristic
430C2×C3#101011yescharacteristic
431D3—41no—
432D3—41no—
433D3—41no—
434D3—122no—
435D3—121no—
436D3—121no—
437C22—61no—
438C22—61no—
439C22—61no—
440C22—61no—
441C22—61no—
442C22—61no—
443C22—61no—
444C22—61no—
445C22—61no—
446C22—181no—
447C22—181no—
448C22—181no—
449C22C22×D3211yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—61no—
454C4—61no—
455C4—61no—
456C4—61no—
457C4—61no—
458C4—181no—
459C4—181no—
460C4—181no—
461C3—21no—
462C3#564711yescharacteristic, complemented
463C3#568411yescharacteristic, complemented
464C2—121no—
465C2—121no—
466C2—121no—
467C2—361no—
468C2#6431511yescharacteristic
469C2#6432011yescharacteristic
470C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×Q8C22
hypercenterC2×Q8D32
hypocenterC32#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #64155C2semidirect
2. C3×#947C2semidirect
3. C3×#946C2semidirect
4. #63912C2semidirect
5. #63906C2semidirect
6. #63905C2semidirect
7. #63899C2semidirect
8. #63893C2semidirect
9. #63891C2semidirect
10. #63890C2semidirect
11. #63886C2semidirect
12. #63885C2semidirect
13. #63867C2semidirect
14. #63853C2semidirect
15. #63852C2semidirect
55. #947D3semidirect
59. #946D3semidirect
391. C32#562semidirect
462. C3#5647semidirect
463. C3#5684semidirect

Maximal subgroups

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

subgroupindex
#641552
C3×#9472
C3×#9462
#639122
#639062
#639052
#638992
#638932
#638912
#638902
#638862
#638852
#638672
#638532
#638522
#56843
#56473