Finite Group Databasebeta

← #10594490

Subgroups — #10594490

Order 576.

473 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64105C211yesmaximal, characteristic, complemented
2C3×#894C211yesmaximal, characteristic, complemented
3C3×#890C211yesmaximal, characteristic, complemented
4#63916C211yesmaximal, characteristic
5#63904C211yesmaximal, characteristic, complemented
6#63896C211yesmaximal, characteristic, complemented
7#63884C211yesmaximal, characteristic, complemented
8#63883C211yesmaximal, characteristic, complemented
9#63880C211yesmaximal, characteristic, complemented
10#63859C211yesmaximal, characteristic, complemented
11#63858C211yesmaximal, characteristic, complemented
12#63857C211yesmaximal, characteristic, complemented
13#63854C211yesmaximal, characteristic, complemented
14#63854C211yesmaximal, characteristic, complemented
15#63847C211yesmaximal, characteristic, complemented
16#5692—31nomaximal
17#5660—31nomaximal
18C2×C4×C3⋊D3C2211yescharacteristic
19C2×#634C2211yescharacteristic
20C2×C3×D12C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×#626C2211yescharacteristic
23C2×#626C2211yescharacteristic
24C2×#624C2211yescharacteristic
25C2×#624C2211yescharacteristic
26C2×D3×Dic3C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28#3752C2211yescharacteristic
29#3752C2211yescharacteristic
30#3750C2211yescharacteristic
31#3750C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×(C2×D3)⋊C4C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×C4⋊Dic3C2211yescharacteristic
36C3×C4⋊Dic3C2211yescharacteristic
37C3×C4⋊Dic3C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×Dic3⋊C4C2211yescharacteristic
41C3×C4×Dic3C2211yescharacteristic
42#3724C2211yescharacteristic
43#3724C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#125—31no—
54C3×#123—31no—
55#938—31no—
56#935—31no—
57C4×#67—31no—
58#924—31no—
59#898—31no—
60#897—31no—
61#896—31no—
62#896—31no—
63#896—31no—
64#896—61no—
65#895—31no—
66#894—31no—
67#894—31no—
68#894—31no—
69#894D311yescharacteristic, complemented
70#893—31no—
71D3×C4⋊C4—31no—
72D3×C4⋊C4—31no—
73#890D311yescharacteristic, complemented
74#889—31no—
75#889—31no—
76#883—31no—
77#883—31no—
78#67⋊C4—31no—
79#879—31no—
80#879—31no—
81#878—31no—
82#876—31no—
83C4×D12—31no—
84C22×C3⋊D3C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊D3—41no—
94#634—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—
103#626—22no—
104#626—22no—
105#624—22no—
106#624—41no—
107D3×Dic3—41no—
108#539—91noSylow
109C2×C3×D4—31no—
110C22×C3×C4—31no—
111C2×#67—31no—
112C2×#67—31no—
113C22×Dic3—31no—
114C2×D12—31no—
115C2×D12—31no—
116C2×D12C2×D311yescharacteristic
117C2×C4×D3—31no—
118C2×C4×D3—31no—
119C2×C4×D3—31no—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—31no—
124C2×C4×D3—61no—
125C2×C4×D3C2×D311yescharacteristic
126C2×Dic6—31no—
127C2×Dic6—31no—
128C2×Dic6—61no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—31no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4C2×D311yescharacteristic
137C3×C4⋊C4C2×D311yescharacteristic
138C3×C22⋊C4—31no—
139C3×C22⋊C4—31no—
140C3×C22⋊C4—31no—
141C3×C42—31no—
142#217—31no—
143#217—31no—
144#217—31no—
145#217—31no—
146#217—31no—
147(C2×D3)⋊C4—31no—
148(C2×D3)⋊C4—31no—
149(C2×D3)⋊C4—31no—
150(C2×D3)⋊C4—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—61no—
157(C2×D3)⋊C4—61no—
158(C2×D3)⋊C4C2×D311yescharacteristic
159(C2×D3)⋊C4C2×D311yescharacteristic
160(C2×D3)⋊C4C2×D311yescharacteristic
161C4⋊Dic3—31no—
162C4⋊Dic3—31no—
163C4⋊Dic3—31no—
164C4⋊Dic3C2×D311yescharacteristic
165C4⋊Dic3C2×D311yescharacteristic
166C4⋊Dic3C2×D311yescharacteristic
167Dic3⋊C4—31no—
168Dic3⋊C4—31no—
169Dic3⋊C4—31no—
170Dic3⋊C4—31no—
171Dic3⋊C4—31no—
172Dic3⋊C4—31no—
173Dic3⋊C4—31no—
174Dic3⋊C4—31no—
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—31no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180Dic3⋊C4C2×D311yescharacteristic
181Dic3⋊C4C2×D311yescharacteristic
182Dic3⋊C4C2×D311yescharacteristic
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3C2×D311yescharacteristic
186C22×C32C2411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3#4112yes—
190C2×C3×D3—21no—
191C2×C3×D3—21no—
192C2×C3×D3—21no—
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C3⋊Dic3—21no—
200C3⋊Dic3—21no—
201C3⋊Dic3—21no—
202C3×Dic3—21no—
203C3×Dic3—21no—
204C3×Dic3—21no—
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3—21no—
208#126—91no—
209#126—91no—
210#125—31no—
211#125—91no—
212#123—31no—
213#123—91no—
214#123—91no—
215#123—91no—
216C22⋊Q8—91no—
217C22⋊Q8—91no—
218C22⋊Q8—91no—
219#121—91no—
220C4×D4—91no—
221C4×D4—91no—
222C2×C4⋊C4—91no—
223C23×C3—31no—
224C23×C3—31no—
225C22×D3—31no—
226C22×D3—31no—
227C22×D3—61no—
228C22×D3C22×D311yescharacteristic
229C22×D3C22×D311yescharacteristic
230C3×D4—121no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—121no—
241C2×C3×C4C22×D311yescharacteristic
242C2×C3×C4C22×D311yescharacteristic
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247#67—62no—
248#67—62no—
249C2×Dic3—31no—
250C2×Dic3—31no—
251C2×Dic3—31no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—121no—
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C2×Dic3C22×D311yescharacteristic
262C2×Dic3C22×D311yescharacteristic
263C2×Dic3C22×D311yescharacteristic
264C2×Dic3C22×D311yescharacteristic
265D12—41no—
266D12—62no—
267D12—62no—
268C4×D3—41no—
269C4×D3—62no—
270C4×D3—62no—
271C4×D3—121no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275C4×D3—122no—
276C4×D3—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—122no—
280C2×C32C2×#4111yescharacteristic
281C2×C32H(5,𝔽2)11yescharacteristic
282C2×C322−1+411yescharacteristic
283C3⋊D3—22no—
284C3×D3—41no—
285C3×D3—41no—
286C2×Q8—91no—
287C2×D4—31no—
288C2×D4—91no—
289C2×D4—91no—
290C22×C4—31no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—91no—
295C4⋊C4—31no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—91no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C4⋊C4—91no—
307C4⋊C4—91no—
308C4⋊C4D3211yescharacteristic
309C22⋊C4—31no—
310C22⋊C4—31no—
311C22⋊C4—31no—
312C22⋊C4—91no—
313C22⋊C4—91no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C22⋊C4—91no—
317C22⋊C4—91no—
318C22⋊C4—91no—
319C42—31no—
320C42—91no—
321C22×C3—21no—
322C22×C3—61no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3—61no—
327C22×C3—61no—
328C22×C3C23×D311yescharacteristic
329C22×C3C23×D311yescharacteristic
330C2×D3—21no—
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—21no—
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—32no—
337C2×D3—32no—
338C2×D3—62no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—121no—
344C2×D3—121no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—61no—
355C3×C4—61no—
356C3×C4—61no—
357C3×C4—61no—
358C3×C4—61no—
359C3×C4—61no—
360Dic3—21no—
361Dic3—21no—
362Dic3—21no—
363Dic3—21no—
364Dic3—21no—
365Dic3—21no—
366Dic3—62no—
367Dic3—61no—
368Dic3—61no—
369Dic3—61no—
370Dic3—61no—
371Dic3—61no—
372Dic3—61no—
373Dic3—121no—
374Dic3—121no—
375C32#53911yescharacteristic, complemented, Sylow
376C23—31no—
377C23—31no—
378C23—91no—
379Q8—361no—
380D4—121no—
381D4—182no—
382D4—182no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—91no—
392C2×C4—121no—
393C2×C4—182no—
394C2×C4—361no—
395C2×C4—361no—
396C2×C4—361no—
397C2×C4C2×D3211yescharacteristic
398C2×C4C2×D3211yescharacteristic
399C2×C4C2×D3211yescharacteristic
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—121no—
404C2×C3—121no—
405C2×C3#100411yescharacteristic
406C2×C3#100711yescharacteristic
407C2×C3D3×#4111yescharacteristic
408C2×C3D3×#4111yescharacteristic
409C2×C3#100911yescharacteristic
410C2×C3#101011yescharacteristic
411D3—41no—
412D3—41no—
413D3—62no—
414D3—62no—
415D3—122no—
416C22—61no—
417C22—61no—
418C22—61no—
419C22—61no—
420C22—61no—
421C22—61no—
422C22—92no—
423C22—181no—
424C22—181no—
425C22C22×D3211yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—61no—
430C4—61no—
431C4—61no—
432C4—61no—
433C4—61no—
434C4—61no—
435C4—181no—
436C4—181no—
437C4—181no—
438C3—21no—
439C3#566011yescharacteristic, complemented
440C3#569211yescharacteristic, complemented
441C2—121no—
442C2—121no—
443C2—182no—
444C2#6429711yescharacteristic
445C2#6431411yescharacteristic
446C2#6431911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radical#63916C2
hypercenterC4⋊C4D32
hypocenterC32#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64105C2semidirect
2. C3×#894C2semidirect
3. C3×#890C2semidirect
5. #63904C2semidirect
6. #63896C2semidirect
7. #63884C2semidirect
8. #63883C2semidirect
9. #63880C2semidirect
10. #63859C2semidirect
11. #63858C2semidirect
12. #63857C2semidirect
13. #63854C2semidirect
14. #63854C2semidirect
15. #63847C2semidirect
69. #894D3semidirect
73. #890D3semidirect
375. C32#539semidirect
439. C3#5660semidirect
440. C3#5692semidirect

Maximal subgroups

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

subgroupindex
#641052
C3×#8942
C3×#8902
#639162
#639042
#638962
#638842
#638832
#638802
#638592
#638582
#638572
#638542
#638472
#56923
#56603