Finite Group Databasebeta

← #10594422

Subgroups — #10594422

Order 576.

507 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64103C211yesmaximal, characteristic, complemented
2C3×#892C211yesmaximal, characteristic, complemented
3C3×#889C211yesmaximal, characteristic, complemented
4#63910C211yesmaximal, characteristic
5#63904C211yesmaximal, characteristic, complemented
6#63904C211yesmaximal, characteristic, complemented
7#63895C211yesmaximal, characteristic, complemented
8#63894C211yesmaximal, characteristic, complemented
9C4×#624C211yesmaximal, characteristic, complemented
10#63858C211yesmaximal, characteristic, complemented
11#63853C211yesmaximal, characteristic, complemented
12#63852C211yesmaximal, characteristic, complemented
13#63848C211yesmaximal, characteristic, complemented
14#63837C211yesmaximal, characteristic, complemented
15#63836C211yesmaximal, characteristic, complemented
16#5691—31nomaximal
17#5528—31nomaximal
18C2×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C4×C3⋊D3C2211yescharacteristic
20C2×C3×C4×D3C2211yescharacteristic
21C2×#627C2211yescharacteristic
22C2×#626C2211yescharacteristic
23C2×#626C2211yescharacteristic
24C2×#624C2211yescharacteristic
25C2×#624C2211yescharacteristic
26C2×#624C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28#3752C2211yescharacteristic
29#3752C2211yescharacteristic
30#3752C2211yescharacteristic
31#3750C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×(C2×D3)⋊C4C2211yescharacteristic
34C3×C4⋊Dic3C2211yescharacteristic
35C3×C4⋊Dic3C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×C4×Dic3C2211yescharacteristic
41C3×C4×Dic3C2211yescharacteristic
42C3×C4×Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
47#3722C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50Dic32C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#125—31no—
54C3×#117—31no—
55C4×#67—31no—
56C4×#67—31no—
57#898—31no—
58#898—31no—
59#898—31no—
60#897—31no—
61#896—31no—
62#895—31no—
63#894—31no—
64#894—31no—
65#894—31no—
66#894—61no—
67#893—31no—
68#893—31no—
69#893—31no—
70#892—31no—
71#892D311yescharacteristic, complemented
72#889D311yescharacteristic, complemented
73#887—31no—
74#885—31no—
75#884—31no—
76#883—31no—
77#879—31no—
78#875—31no—
79C4×D12—31no—
80#872—31no—
81C42×D3—31no—
82C42×D3—31no—
83C4×Dic6—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—22no—
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C3×C4×D3—22no—
102#627—22no—
103#626—22no—
104#626—22no—
105#624—22no—
106#624—22no—
107#624—22no—
108#529—91noSylow
109C22×C3×C4—31no—
110C2×#67—31no—
111C2×#67—31no—
112C2×D12—31no—
113C2×D12—31no—
114C2×D12—31no—
115C2×D12—31no—
116C2×D12—61no—
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—31no—
125C2×C4×D3—61no—
126C2×C4×D3C2×D311yescharacteristic
127C2×Dic6—31no—
128C2×Dic6—31no—
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×C42—31no—
141C3×C42—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)⋊C4—61no—
162(C2×D3)⋊C4C2×D311yescharacteristic
163(C2×D3)⋊C4C2×D311yescharacteristic
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3C2×D311yescharacteristic
167C4⋊Dic3C2×D311yescharacteristic
168Dic3⋊C4—31no—
169Dic3⋊C4—31no—
170Dic3⋊C4—31no—
171Dic3⋊C4—31no—
172Dic3⋊C4—61no—
173Dic3⋊C4C2×D311yescharacteristic
174Dic3⋊C4C2×D311yescharacteristic
175Dic3⋊C4C2×D311yescharacteristic
176Dic3⋊C4C2×D311yescharacteristic
177C4×Dic3—31no—
178C4×Dic3—31no—
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3C2×D311yescharacteristic
184C4×Dic3C2×D311yescharacteristic
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#4112yes—
207C3×Dic3#4112yes—
208#126—91no—
209#126—91no—
210#125—31no—
211#124—91no—
212#123—91no—
213#123—91no—
214C22⋊Q8—91no—
215#121—91no—
216C4×Q8—91no—
217C4×D4—91no—
218C4×D4—91no—
219C4×D4—91no—
220#117—31no—
221#117—91no—
222C2×C42—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
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—31no—
241C2×C3×C4—62no—
242C2×C3×C4C22×D311yescharacteristic
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247C2×C3×C4C22×D311yescharacteristic
248#67—62no—
249#67—62no—
250C2×Dic3—31no—
251C2×Dic3—31no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3C22×D311yescharacteristic
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C2×Dic3C22×D311yescharacteristic
262C2×Dic3C22×D311yescharacteristic
263D12—62no—
264D12—62no—
265D12—62no—
266D12—62no—
267D12—122no—
268C4×D3—22no—
269C4×D3—62no—
270C4×D3—62no—
271C4×D3—62no—
272C4×D3—62no—
273C4×D3—62no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—122no—
278Dic6—62no—
279Dic6—62no—
280C2×C32C2×#4111yescharacteristic
281C2×C32C2×#4111yescharacteristic
282C2×C32C2×#4111yescharacteristic
283C3⋊D3—22no—
284C3⋊D3—41no—
285C3×D3—41no—
286C2×Q8—91no—
287C2×D4—91no—
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⋊C4D3211yescharacteristic
305C22⋊C4—31no—
306C22⋊C4—31no—
307C22⋊C4—91no—
308C22⋊C4—91no—
309C22⋊C4—91no—
310C22⋊C4—91no—
311C22⋊C4—91no—
312C22⋊C4—91no—
313C22⋊C4—91no—
314C22⋊C4—91no—
315C42—31no—
316C42—31no—
317C42—31no—
318C42—91no—
319C42—91no—
320C42—91no—
321C22×C3—21no—
322C22×C3—61no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3C23×D311yescharacteristic
326C22×C3C23×D311yescharacteristic
327C2×D3—21no—
328C2×D3—21no—
329C2×D3—21no—
330C2×D3—32no—
331C2×D3—32no—
332C2×D3—62no—
333C2×D3—61no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—61no—
337C2×D3—61no—
338C2×D3—61no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—32no—
355C3×C4—32no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—61no—
360C3×C4—61no—
361C3×C4—61no—
362C3×C4—61no—
363C3×C4—61no—
364Dic3—21no—
365Dic3—21no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—61no—
370Dic3—61no—
371Dic3—61no—
372Dic3—61no—
373Dic3—121no—
374Dic3—121no—
375Dic3#23512yes—
376Dic3#23912yes—
377C32#52911yescharacteristic, complemented, Sylow
378C23—31no—
379C23—91no—
380C23—91no—
381Q8—182no—
382D4—182no—
383D4—182no—
384D4—182no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—62no—
393C2×C4—91no—
394C2×C4—91no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4C2×D3211yescharacteristic
400C2×C4C2×D3211yescharacteristic
401C2×C4C2×D3211yescharacteristic
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—121no—
406C2×C3C2×#23511yescharacteristic
407C2×C3C2×#23911yescharacteristic
408C2×C3D3×#4111yescharacteristic
409C2×C3D3×#4111yescharacteristic
410C2×C3D3×#4111yescharacteristic
411C2×C3D3×#4111yescharacteristic
412D3—41no—
413D3—62no—
414D3—62no—
415D3—122no—
416D3—121no—
417D3—121no—
418D3—241no—
419C22—61no—
420C22—61no—
421C22—61no—
422C22—92no—
423C22—181no—
424C22—181no—
425C22—181no—
426C22—181no—
427C22—181no—
428C22C22×D3211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—32no—
433C4—32no—
434C4—61no—
435C4—61no—
436C4—61no—
437C4—61no—
438C4—61no—
439C4—181no—
440C4—181no—
441C3—21no—
442C3#552811yescharacteristic, complemented
443C3#569111yescharacteristic, complemented
444C2—121no—
445C2—182no—
446C2—361no—
447C2D3×#23511yescharacteristic
448C2#6431211yescharacteristic
449C2D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radical#63910C2
hypercenterC4⋊C4D32
hypocenterC32#529
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×#892C2semidirect
3. C3×#889C2semidirect
5. #63904C2semidirect
6. #63904C2semidirect
7. #63895C2semidirect
8. #63894C2semidirect
9. C4×#624C2semidirect
10. #63858C2semidirect
11. #63853C2semidirect
12. #63852C2semidirect
13. #63848C2semidirect
14. #63837C2semidirect
15. #63836C2semidirect
71. #892D3semidirect
72. #889D3semidirect
377. C32#529semidirect
442. C3#5528semidirect
443. C3#5691semidirect

Maximal subgroups

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

subgroupindex
#641032
C3×#8922
C3×#8892
#639102
#639042
#638952
#638942
C4×#6242
#638582
#638532
#638522
#638482
#638372
#638362
#56913
#55283