Finite Group Databasebeta

← #10594549

Subgroups — #10594549

Order 576.

511 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64103C211yesmaximal, characteristic, complemented
2C3×#894C211yesmaximal, characteristic, complemented
3C3×#887C211yesmaximal, characteristic, complemented
4#63911C211yesmaximal, characteristic
5#63907C211yesmaximal, characteristic, complemented
6#63907C211yesmaximal, characteristic, complemented
7#63904C211yesmaximal, characteristic, complemented
8C4×#626C211yesmaximal, characteristic, complemented
9#63897C211yesmaximal, characteristic, complemented
10#63884C211yesmaximal, characteristic, complemented
11#63881C211yesmaximal, characteristic, complemented
12#63880C211yesmaximal, characteristic, complemented
13#63852C211yesmaximal, characteristic, complemented
14#63852C211yesmaximal, characteristic, complemented
15#63837C211yesmaximal, characteristic, complemented
16#5664—31nomaximal
17#5585—31nomaximal
18C2×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C4×C3⋊D3C2211yescharacteristic
20C2×C3×D12C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×Dic6C2211yescharacteristic
23C2×#627C2211yescharacteristic
24C2×#626C2211yescharacteristic
25C2×#626C2211yescharacteristic
26C2×#626C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#624C2211yescharacteristic
29C2×D3×Dic3C2211yescharacteristic
30C32×C4⋊C4C2211yescharacteristic
31#3752C2211yescharacteristic
32#3752C2211yescharacteristic
33#3752C2211yescharacteristic
34#3750C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×Dic3⋊C4C2211yescharacteristic
41C3×C4×Dic3C2211yescharacteristic
42C3×C4×Dic3C2211yescharacteristic
43C3×C4×Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
47#3722C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#123—31no—
54C3×C4×Q8—31no—
55#947—31no—
56#947—31no—
57#940—31no—
58#935—31no—
59C4×#67—31no—
60C4×#67—31no—
61#894—31no—
62#894—31no—
63#894—31no—
64#894—31no—
65#894—31no—
66#894—61no—
67#894D311yescharacteristic, complemented
68#893—31no—
69#893—31no—
70#887—31no—
71#887D311yescharacteristic, complemented
72#885—31no—
73#885—31no—
74#885—31no—
75#885—31no—
76#67⋊C4—31no—
77#67⋊C4—31no—
78#875—31no—
79#875—31no—
80#874—31no—
81C4×D12—31no—
82C4×D12—31no—
83C4×Dic6—31no—
84C22×C3⋊D3C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C4⋊(C3⋊D3)—41no—
94C4×C3⋊D3—41no—
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C3×D12—41no—
102C3×C4×D3—41no—
103C3×Dic6—22no—
104#627—22no—
105#626—22no—
106#626—22no—
107#626—22no—
108#626—22no—
109#624—41no—
110D3×Dic3—41no—
111#559—91noSylow
112C2×C3×Q8—31no—
113C2×C3×D4—31no—
114C22×C3×C4—31no—
115C2×#67—31no—
116C2×#67—31no—
117C2×#67—31no—
118C2×#67—31no—
119C22×Dic3—31no—
120C2×D12—31no—
121C2×D12—31no—
122C2×D12—31no—
123C2×D12—31no—
124C2×D12—31no—
125C2×D12—31no—
126C2×D12—61no—
127C2×D12C2×D311yescharacteristic
128C2×C4×D3—31no—
129C2×C4×D3—31no—
130C2×C4×D3—31no—
131C2×C4×D3—31no—
132C2×C4×D3—31no—
133C2×C4×D3—61no—
134C2×C4×D3C2×D311yescharacteristic
135C2×Dic6—31no—
136C2×Dic6—31no—
137C2×Dic6C2×D311yescharacteristic
138C3×C4⋊C4—21no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4C2×D311yescharacteristic
143C3×C4⋊C4C2×D311yescharacteristic
144C3×C22⋊C4—31no—
145C3×C22⋊C4—31no—
146C3×C22⋊C4—31no—
147C3×C42—31no—
148C3×C42—31no—
149C3×C42—31no—
150#217—31no—
151#217—31no—
152#217—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—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—31no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4—61no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4C2×D311yescharacteristic
172(C2×D3)⋊C4C2×D311yescharacteristic
173(C2×D3)⋊C4C2×D311yescharacteristic
174C4⋊Dic3—31no—
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—31no—
178Dic3⋊C4—61no—
179Dic3⋊C4C2×D311yescharacteristic
180Dic3⋊C4C2×D311yescharacteristic
181Dic3⋊C4C2×D311yescharacteristic
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3—31no—
186C4×Dic3C2×D311yescharacteristic
187C4×Dic3C2×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#4112yes—
212C3×Dic3#4112yes—
213#127—91no—
214#124—91no—
215#124—91no—
216#124—91no—
217#124—91no—
218#123—31no—
219#123—91no—
220#123—91no—
221#123—91no—
222C4×Q8—31no—
223C4×Q8—91no—
224C4×D4—91no—
225C4×D4—91no—
226C4×D4—91no—
227C4×D4—91no—
228C23×C3—31no—
229C23×C3—31no—
230C22×D3—31no—
231C22×D3—31no—
232C22×D3—31no—
233C22×D3—31no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3C22×D311yescharacteristic
237C22×D3C22×D311yescharacteristic
238C3×Q8—62no—
239C3×D4—121no—
240C2×C3×C4—21no—
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—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—62no—
257#67—62no—
258#67—62no—
259#67—62no—
260C2×Dic3—31no—
261C2×Dic3—31no—
262C2×Dic3—31no—
263C2×Dic3—31no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—121no—
267C2×Dic3C22×D311yescharacteristic
268C2×Dic3C22×D311yescharacteristic
269C2×Dic3C22×D311yescharacteristic
270C2×Dic3C22×D311yescharacteristic
271C2×Dic3C22×D311yescharacteristic
272C2×Dic3C22×D311yescharacteristic
273D12—41no—
274D12—62no—
275D12—62no—
276D12—62no—
277D12—62no—
278D12—121no—
279D12—121no—
280D12—122no—
281C4×D3—41no—
282C4×D3—121no—
283C4×D3—121no—
284C4×D3—121no—
285C4×D3—121no—
286C4×D3—121no—
287C4×D3—122no—
288Dic6—22no—
289Dic6—62no—
290Dic6—62no—
291C2×C32C2×#4111yescharacteristic
292C2×C32C2×#4111yescharacteristic
293C2×C32H(5,𝔽2)11yescharacteristic
294C3⋊D3—41no—
295C3⋊D3—41no—
296C3×D3—41no—
297C3×D3—41no—
298C2×Q8—31no—
299C2×Q8—91no—
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⋊C4D3211yescharacteristic
316C22⋊C4—31no—
317C22⋊C4—31no—
318C22⋊C4—31no—
319C22⋊C4—91no—
320C22⋊C4—91no—
321C22⋊C4—91no—
322C22⋊C4—91no—
323C22⋊C4—91no—
324C22⋊C4—91no—
325C22⋊C4—91no—
326C22⋊C4—91no—
327C22⋊C4—91no—
328C42—31no—
329C42—31no—
330C42—31no—
331C42—91no—
332C42—91no—
333C22×C3—21no—
334C22×C3—61no—
335C22×C3—61no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3—61no—
340C22×C3C23×D311yescharacteristic
341C22×C3C23×D311yescharacteristic
342C2×D3—21no—
343C2×D3—21no—
344C2×D3—21no—
345C2×D3—21no—
346C2×D3—21no—
347C2×D3—21no—
348C2×D3—62no—
349C2×D3—61no—
350C2×D3—61no—
351C2×D3—61no—
352C2×D3—61no—
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—121no—
362C2×D3—121no—
363C2×D3—121no—
364C2×D3—121no—
365C2×D3—121no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—32no—
373C3×C4—32no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—61no—
378C3×C4—61no—
379C3×C4—61no—
380C3×C4—61no—
381Dic3—21no—
382Dic3—21no—
383Dic3—21no—
384Dic3—21no—
385Dic3—61no—
386Dic3—61no—
387Dic3—61no—
388Dic3—61no—
389Dic3—121no—
390Dic3—121no—
391Dic3#23512yes—
392Dic3#23912yes—
393C32#55911yescharacteristic, complemented, Sylow
394C23—31no—
395C23—31no—
396C23—91no—
397C23—91no—
398Q8—62no—
399Q8—182no—
400D4—121no—
401D4—182no—
402D4—182no—
403D4—182no—
404D4—182no—
405D4—361no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—91no—
413C2×C4—91no—
414C2×C4—121no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4—361no—
418C2×C4C2×D3211yescharacteristic
419C2×C4C2×D3211yescharacteristic
420C2×C4C2×D3211yescharacteristic
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—121no—
425C2×C3—121no—
426C2×C3C2×#23511yescharacteristic
427C2×C3#100411yescharacteristic
428C2×C3C2×#23911yescharacteristic
429C2×C3D3×#4111yescharacteristic
430C2×C3D3×#4111yescharacteristic
431C2×C3#100911yescharacteristic
432D3—41no—
433D3—41no—
434D3—122no—
435D3—121no—
436D3—121no—
437D3—121no—
438D3—121no—
439D3—241no—
440C22—61no—
441C22—61no—
442C22—61no—
443C22—61no—
444C22—61no—
445C22—61no—
446C22—181no—
447C22—181no—
448C22—181no—
449C22—181no—
450C22—181no—
451C22—181no—
452C22C22×D3211yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—32no—
457C4—32no—
458C4—61no—
459C4—61no—
460C4—61no—
461C4—61no—
462C4—181no—
463C4—181no—
464C3—21no—
465C3#558511yescharacteristic, complemented
466C3#566411yescharacteristic, complemented
467C2—121no—
468C2—121no—
469C2—361no—
470C2—361no—
471C2D3×#23511yescharacteristic
472C2#6431411yescharacteristic
473C2D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radical#63911C2
hypercenterC4⋊C4D32
hypocenterC32#559
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64103C2semidirect
2. C3×#894C2semidirect
3. C3×#887C2semidirect
5. #63907C2semidirect
6. #63907C2semidirect
7. #63904C2semidirect
8. C4×#626C2semidirect
9. #63897C2semidirect
10. #63884C2semidirect
11. #63881C2semidirect
12. #63880C2semidirect
13. #63852C2semidirect
14. #63852C2semidirect
15. #63837C2semidirect
67. #894D3semidirect
71. #887D3semidirect
393. C32#559semidirect
465. C3#5585semidirect
466. C3#5664semidirect

Maximal subgroups

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

subgroupindex
#641032
C3×#8942
C3×#8872
#639112
#639072
#639042
C4×#6262
#638972
#638842
#638812
#638802
#638522
#638372
#56643
#55853