Finite Group Databasebeta

← #10594406

Subgroups — #10594406

Order 576.

464 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64098C211yesmaximal, characteristic, complemented
2C3×#896C211yesmaximal, characteristic, complemented
3C3×#893C211yesmaximal, characteristic, complemented
4#63905C211yesmaximal, characteristic, complemented
5#63905C211yesmaximal, characteristic, complemented
6C4×#625C211yesmaximal, characteristic, complemented
7#63891C211yesmaximal, characteristic, complemented
8#63887C211yesmaximal, characteristic, complemented
9#63885C211yesmaximal, characteristic
10#63884C211yesmaximal, characteristic, complemented
11D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#63867C211yesmaximal, characteristic, complemented
13#63862C211yesmaximal, characteristic, complemented
14#63859C211yesmaximal, characteristic, complemented
15#63856C211yesmaximal, characteristic, complemented
16#5638—31nomaximal
17#5564—31nomaximal
18C2×C3×D12C2211yescharacteristic
19C2×C3×C4×D3C2211yescharacteristic
20C2×C3×C4×D3C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×Dic6C2211yescharacteristic
23C2×#625C2211yescharacteristic
24C2×#625C2211yescharacteristic
25C2×D3×Dic3C2211yescharacteristic
26C2×D3×Dic3C2211yescharacteristic
27C32×C4⋊C4C2211yescharacteristic
28C4⋊(C3⋊Dic3)C2211yescharacteristic
29#3750C2211yescharacteristic
30#3750C2211yescharacteristic
31#3750C2211yescharacteristic
32#3750C2211yescharacteristic
33C4×C3⋊Dic3C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×C4×Dic3C2211yescharacteristic
41#3724C2211yescharacteristic
42#3724C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
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
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×C22⋊Q8—31no—
54C3×C4×D4—31no—
55#946—31no—
56#946—31no—
57#939—31no—
58#935—31no—
59#929—31no—
60#929—31no—
61C4×#67—31no—
62C4×#67—31no—
63#924—31no—
64C2×Dic3⋊C4—31no—
65#898—31no—
66#896D311yescharacteristic, complemented
67#894—31no—
68#893D311yescharacteristic, complemented
69D3×C4⋊C4—31no—
70#889—31no—
71#889—31no—
72#889—31no—
73#889—61no—
74#886—31no—
75#884—31no—
76#883—31no—
77#883—31no—
78#883—31no—
79#879—31no—
80#879—31no—
81#878—31no—
82#876—31no—
83#870—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
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C3×D12—22no—
100C3×C4×D3—41no—
101C3×C4×D3—41no—
102C3×C4×D3—41no—
103C3×Dic6—41no—
104#625—22no—
105#625—41no—
106D3×Dic3—22no—
107D3×Dic3—41no—
108#539—91noSylow
109C2×C3×Q8—31no—
110C2×C3×D4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C2×#67—31no—
115C2×#67—31no—
116C2×#67—31no—
117C2×#67—31no—
118C22×Dic3—31no—
119C22×Dic3—31no—
120C2×D12C2×D311yescharacteristic
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3C2×D311yescharacteristic
124C2×C4×D3C2×D311yescharacteristic
125C2×C4×D3C2×D311yescharacteristic
126C2×Dic6C2×D311yescharacteristic
127C3×C4⋊C4—21no—
128C3×C4⋊C4—31no—
129C3×C4⋊C4—31no—
130C3×C4⋊C4C2×D311yescharacteristic
131C3×C4⋊C4C2×D311yescharacteristic
132C3×C22⋊C4—31no—
133C3×C22⋊C4—31no—
134C3×C22⋊C4—31no—
135C3×C22⋊C4—31no—
136C3×C42—31no—
137#217—31no—
138#217—31no—
139#217—31no—
140#217—31no—
141#217—31no—
142#217—31no—
143(C2×D3)⋊C4—31no—
144(C2×D3)⋊C4—31no—
145(C2×D3)⋊C4—31no—
146(C2×D3)⋊C4—31no—
147(C2×D3)⋊C4—31no—
148(C2×D3)⋊C4—31no—
149(C2×D3)⋊C4C2×D311yescharacteristic
150(C2×D3)⋊C4C2×D311yescharacteristic
151(C2×D3)⋊C4C2×D311yescharacteristic
152(C2×D3)⋊C4C2×D311yescharacteristic
153C4⋊Dic3—31no—
154C4⋊Dic3—31no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—61no—
160Dic3⋊C4—31no—
161Dic3⋊C4—31no—
162Dic3⋊C4—31no—
163Dic3⋊C4—31no—
164Dic3⋊C4—31no—
165Dic3⋊C4—31no—
166Dic3⋊C4—31no—
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—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
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—21no—
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3#4112yes—
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—91no—
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—31no—
221C4×D4—91no—
222C2×C4⋊C4—91no—
223C23×C3—31no—
224C23×C3—31no—
225C23×C3—31no—
226C22×D3C22×D311yescharacteristic
227C22×D3C22×D311yescharacteristic
228C22×D3C22×D311yescharacteristic
229C3×Q8—121no—
230C3×D4—62no—
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—121no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
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—
250#67—121no—
251#67—121no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C2×Dic3—31no—
256C2×Dic3—31no—
257C2×Dic3—31no—
258C2×Dic3—31no—
259C2×Dic3—31no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—62no—
265C2×Dic3—121no—
266C2×Dic3C22×D311yescharacteristic
267C2×Dic3C22×D311yescharacteristic
268C2×Dic3C22×D311yescharacteristic
269C2×Dic3C22×D311yescharacteristic
270C2×Dic3C22×D311yescharacteristic
271D12—22no—
272C4×D3—41no—
273C4×D3—41no—
274C4×D3—41no—
275C4×D3—62no—
276C4×D3—121no—
277Dic6—41no—
278C2×C32C2×#4111yescharacteristic
279C2×C32H(5,𝔽2)11yescharacteristic
280C2×C322−1+411yescharacteristic
281C3×D3—22no—
282C3×D3—41no—
283C3×D3—41no—
284C2×Q8—31no—
285C2×D4—31no—
286C2×D4—91no—
287C2×D4—91no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—31no—
291C22×C4—91no—
292C22×C4—91no—
293C4⋊C4—31no—
294C4⋊C4—31no—
295C4⋊C4—91no—
296C4⋊C4—91no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—91no—
300C4⋊C4—91no—
301C4⋊C4—91no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C4⋊C4D3211yescharacteristic
307C22⋊C4—31no—
308C22⋊C4—31no—
309C22⋊C4—31no—
310C22⋊C4—31no—
311C22⋊C4—91no—
312C22⋊C4—91no—
313C22⋊C4—91no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C22⋊C4—91no—
317C42—31no—
318C42—91no—
319C22×C3—21no—
320C22×C3—32no—
321C22×C3—61no—
322C22×C3—61no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3—61no—
327C22×C3—61no—
328C22×C3—61no—
329C22×C3C23×D311yescharacteristic
330C22×C3C23×D311yescharacteristic
331C2×D3—21no—
332C2×D3—21no—
333C2×D3—21no—
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C2×D3—21no—
338C2×D3—21no—
339C2×D3#23512yes—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—61no—
350C3×C4—61no—
351C3×C4—61no—
352C3×C4—61no—
353C3×C4—61no—
354Dic3—21no—
355Dic3—21no—
356Dic3—21no—
357Dic3—21no—
358Dic3—21no—
359Dic3—62no—
360Dic3—61no—
361Dic3—61no—
362Dic3—61no—
363Dic3—61no—
364Dic3—61no—
365Dic3—61no—
366Dic3—61no—
367Dic3—61no—
368Dic3—121no—
369Dic3—121no—
370Dic3—121no—
371C32#53911yescharacteristic, complemented, Sylow
372C23—31no—
373C23—31no—
374C23—31no—
375Q8—121no—
376D4—62no—
377D4—182no—
378D4—361no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—182no—
392C2×C4—361no—
393C2×C4C2×D3211yescharacteristic
394C2×C4C2×D3211yescharacteristic
395C2×C4C2×D3211yescharacteristic
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—62no—
400C2×C3—121no—
401C2×C3—121no—
402C2×C3C2×#23511yescharacteristic
403C2×C3#100411yescharacteristic
404C2×C3#100411yescharacteristic
405C2×C3#100711yescharacteristic
406C2×C3D3×#4111yescharacteristic
407C2×C3#101011yescharacteristic
408D3—22no—
409D3—41no—
410D3—41no—
411C22—32no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—61no—
417C22—61no—
418C22—61no—
419C22—61no—
420C22C22×D3211yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—61no—
425C4—61no—
426C4—61no—
427C4—61no—
428C4—61no—
429C4—181no—
430C4—181no—
431C4—181no—
432C4—181no—
433C3—21no—
434C3#556411yescharacteristic, complemented
435C3#563811yescharacteristic, complemented
436C2—62no—
437C2—121no—
438C2—121no—
439C2D3×#23511yescharacteristic
440C2#6431311yescharacteristic
441C2#6431511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radical#63885C2
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. #64098C2semidirect
2. C3×#896C2semidirect
3. C3×#893C2semidirect
4. #63905C2semidirect
5. #63905C2semidirect
6. C4×#625C2semidirect
7. #63891C2semidirect
8. #63887C2semidirect
10. #63884C2semidirect
11. D3×Dic3⋊C4C2semidirect
12. #63867C2semidirect
13. #63862C2semidirect
14. #63859C2semidirect
15. #63856C2semidirect
66. #896D3semidirect
68. #893D3semidirect
371. C32#539semidirect
434. C3#5564semidirect
435. C3#5638semidirect

Maximal subgroups

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

subgroupindex
#640982
C3×#8962
C3×#8932
#639052
C4×#6252
#638912
#638872
#638852
#638842
D3×Dic3⋊C42
#638672
#638622
#638592
#638562
#56383
#55643