Finite Group Databasebeta

← #10594574

Subgroups — #10594574

Order 576.

483 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64102C211yesmaximal, characteristic, complemented
2C3×#896C211yesmaximal, characteristic, complemented
3C3×#889C211yesmaximal, characteristic, complemented
4#63910C211yesmaximal, characteristic
5C4×#626C211yesmaximal, characteristic, complemented
6#63897C211yesmaximal, characteristic, complemented
7#63888C211yesmaximal, characteristic, complemented
8#63883C211yesmaximal, characteristic, complemented
9#63871C211yesmaximal, characteristic, complemented
10#63870C211yesmaximal, characteristic, complemented
11#63868C211yesmaximal, characteristic, complemented
12#63862C211yesmaximal, characteristic, complemented
13#63854C211yesmaximal, characteristic, complemented
14#63853C211yesmaximal, characteristic, complemented
15#63850C211yesmaximal, characteristic, complemented
16#5692—31nomaximal
17#5638—31nomaximal
18C2×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C4×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×Dic6C2211yescharacteristic
23C2×#626C2211yescharacteristic
24C2×#626C2211yescharacteristic
25C2×#624C2211yescharacteristic
26C2×#624C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28#3752C2211yescharacteristic
29#3752C2211yescharacteristic
30C4×C3⋊Dic3C2211yescharacteristic
31C3×(C2×D3)⋊C4C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×C4⋊Dic3C2211yescharacteristic
34C3×Dic3⋊C4C2211yescharacteristic
35C3×Dic3⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×C4×Dic3C2211yescharacteristic
41#3724C2211yescharacteristic
42#3724C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49#3722C2211yescharacteristic
50#3722C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×#125—31no—
54C3×C22⋊Q8—31no—
55#946—31no—
56#946—31no—
57#929—31no—
58C4×#67—31no—
59#898—31no—
60#898—31no—
61#897—31no—
62#896—31no—
63#896D311yescharacteristic, complemented
64#895—31no—
65#894—31no—
66#894—31no—
67#894—31no—
68#894—31no—
69#894—31no—
70#893—31no—
71#893—31no—
72#893—61no—
73D3×C4⋊C4—31no—
74D3×C4⋊C4—31no—
75#889—31no—
76#889—31no—
77#889D311yescharacteristic, complemented
78#884—31no—
79#883—31no—
80#883—31no—
81#879—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
92C4⋊(C3⋊D3)—22no—
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
101C2×C3×Dic3C2311yescharacteristic
102C3×C4×D3—41no—
103C3×Dic6—41no—
104#626—22no—
105#626—41no—
106#624—22no—
107#624—41no—
108#539—91noSylow
109C2×C3×Q8—31no—
110C22×C3×C4—31no—
111C2×#67—31no—
112C2×#67—31no—
113C2×D12—31no—
114C2×D12—31no—
115C2×D12—31no—
116C2×D12—31no—
117C2×D12—61no—
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—31no—
125C2×C4×D3—31no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3C2×D311yescharacteristic
129C2×Dic6C2×D311yescharacteristic
130C3×C4⋊C4—21no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4C2×D311yescharacteristic
139C3×C4⋊C4C2×D311yescharacteristic
140C3×C22⋊C4—31no—
141C3×C22⋊C4—31no—
142C3×C42—31no—
143#217—31no—
144#217—31no—
145(C2×D3)⋊C4—31no—
146(C2×D3)⋊C4—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—31no—
157(C2×D3)⋊C4—31no—
158(C2×D3)⋊C4—31no—
159(C2×D3)⋊C4—61no—
160(C2×D3)⋊C4—61no—
161(C2×D3)⋊C4C2×D311yescharacteristic
162(C2×D3)⋊C4C2×D311yescharacteristic
163C4⋊Dic3—31no—
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
177Dic3⋊C4C2×D311yescharacteristic
178Dic3⋊C4C2×D311yescharacteristic
179Dic3⋊C4C2×D311yescharacteristic
180Dic3⋊C4C2×D311yescharacteristic
181Dic3⋊C4C2×D311yescharacteristic
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—61no—
185C4×Dic3C2×D311yescharacteristic
186C22×C32C2411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3#4112yes—
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—91no—
213#123—91no—
214#123—91no—
215#123—91no—
216C22⋊Q8—31no—
217C22⋊Q8—91no—
218C22⋊Q8—91no—
219#121—91no—
220C4×D4—91no—
221C4×D4—91no—
222C2×C4⋊C4—91no—
223C23×C3—31no—
224C22×D3—31no—
225C22×D3—31no—
226C22×D3—31no—
227C22×D3—31no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3C22×D311yescharacteristic
231C3×Q8—121no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—121no—
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247C2×C3×C4C22×D311yescharacteristic
248C2×C3×C4C22×D311yescharacteristic
249#67—62no—
250#67—121no—
251C2×Dic3—31no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C2×Dic3C22×D311yescharacteristic
262C2×Dic3C22×D311yescharacteristic
263C2×Dic3C22×D311yescharacteristic
264D12—62no—
265D12—62no—
266D12—64no—
267D12—62no—
268D12—121no—
269C4×D3—41no—
270C4×D3—62no—
271C4×D3—62no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275C4×D3—121no—
276C4×D3—121no—
277C4×D3—121no—
278C4×D3—122no—
279C4×D3—122no—
280Dic6—41no—
281C2×C32C2×#4111yescharacteristic
282C2×C32H(5,𝔽2)11yescharacteristic
283C2×C322−1+411yescharacteristic
284C3⋊D3—22no—
285C3⋊D3—41no—
286C3×D3—41no—
287C2×Q8—31no—
288C2×D4—91no—
289C2×D4—91no—
290C2×D4—91no—
291C22×C4—31no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C4⋊C4—91no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4D3211yescharacteristic
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—
319C22⋊C4—91no—
320C42—31no—
321C42—91no—
322C22×C3—21no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3C23×D311yescharacteristic
327C22×C3C23×D311yescharacteristic
328C2×D3—21no—
329C2×D3—21no—
330C2×D3—21no—
331C2×D3—32no—
332C2×D3—32no—
333C2×D3—62no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—61no—
337C2×D3—61no—
338C2×D3—62no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—61no—
344C2×D3—61no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C3×C4—22no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—61no—
359C3×C4—61no—
360C3×C4—61no—
361C3×C4—61no—
362C3×C4—61no—
363C3×C4—61no—
364C3×C4—61no—
365Dic3—21no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—21no—
370Dic3—21no—
371Dic3—21no—
372Dic3—62no—
373Dic3—61no—
374Dic3—61no—
375Dic3—61no—
376Dic3—61no—
377Dic3—121no—
378C32#53911yescharacteristic, complemented, Sylow
379C23—31no—
380C23—91no—
381C23—91no—
382Q8—121no—
383D4—182no—
384D4—182no—
385D4—361no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—91no—
394C2×C4—91no—
395C2×C4—121no—
396C2×C4—182no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4C2×D3211yescharacteristic
401C2×C4C2×D3211yescharacteristic
402C2×C4C2×D3211yescharacteristic
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—121no—
407C2×C3#100411yescharacteristic
408C2×C3#100711yescharacteristic
409C2×C3#100711yescharacteristic
410C2×C3D3×#4111yescharacteristic
411C2×C3D3×#4111yescharacteristic
412C2×C3#100911yescharacteristic
413D3—41no—
414D3—62no—
415D3—62no—
416D3—122no—
417D3—122no—
418D3—121no—
419D3—121no—
420C22—61no—
421C22—61no—
422C22—61no—
423C22—92no—
424C22—181no—
425C22—181no—
426C22—181no—
427C22—181no—
428C22—181no—
429C22C22×D3211yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—61no—
434C4—61no—
435C4—61no—
436C4—61no—
437C4—61no—
438C4—61no—
439C4—61no—
440C4—181no—
441C4—181no—
442C3—21no—
443C3#563811yescharacteristic, complemented
444C3#569211yescharacteristic, complemented
445C2—121no—
446C2—182no—
447C2—361no—
448C2#6430611yescharacteristic
449C2#6431411yescharacteristic
450C2#6431611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radical#63910C2
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. #64102C2semidirect
2. C3×#896C2semidirect
3. C3×#889C2semidirect
5. C4×#626C2semidirect
6. #63897C2semidirect
7. #63888C2semidirect
8. #63883C2semidirect
9. #63871C2semidirect
10. #63870C2semidirect
11. #63868C2semidirect
12. #63862C2semidirect
13. #63854C2semidirect
14. #63853C2semidirect
15. #63850C2semidirect
63. #896D3semidirect
77. #889D3semidirect
378. C32#539semidirect
443. C3#5638semidirect
444. C3#5692semidirect

Maximal subgroups

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

subgroupindex
#641022
C3×#8962
C3×#8892
#639102
C4×#6262
#638972
#638882
#638832
#638712
#638702
#638682
#638622
#638542
#638532
#638502
#56923
#56383