Finite Group Databasebeta

← #10595201

Subgroups — #10595201

Order 576.

471 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#64144C211yesmaximal, characteristic, complemented
2C3×#939C211yesmaximal, characteristic
3C3×#936C211yesmaximal, characteristic, complemented
4#63982C211yesmaximal, characteristic, complemented
5#67⋊Dic3C211yesmaximal, characteristic, complemented
6#63969C211yesmaximal, characteristic, complemented
7#63964C211yesmaximal, characteristic, complemented
8#63959C211yesmaximal, characteristic, complemented
9#63959C211yesmaximal, characteristic, complemented
10#63956C211yesmaximal, characteristic, complemented
11#63955C211yesmaximal, characteristic, complemented
12#63887C211yesmaximal, characteristic, complemented
13#63859C211yesmaximal, characteristic, complemented
14#63839C211yesmaximal, characteristic, complemented
15#63837C211yesmaximal, characteristic, complemented
16#5669—31nomaximal
17#5603—31nomaximal
18C2×C32×D4C2211yescharacteristic
19C22×C3⋊Dic3C2211yescharacteristic
20C2×C3×#67C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C22×C3×Dic3C2211yescharacteristic
23C2×C3×Dic6C2211yescharacteristic
24C2×#627C2211yescharacteristic
25C2×#627C2211yescharacteristic
26C2×D3×Dic3C2211yescharacteristic
27#3757C2211yescharacteristic
28#3757C2211yescharacteristic
29#3757C2211yescharacteristic
30#3750C2211yescharacteristic
31#3750C2211yescharacteristic
32C3×#217C2211yescharacteristic
33C3×#217C2211yescharacteristic
34C3×#217C2211yescharacteristic
35C3×#217C2211yescharacteristic
36C3×#217C2211yescharacteristic
37C3×(C2×D3)⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×C4×Dic3C2211yescharacteristic
40#3724C2211yescharacteristic
41#3724C2211yescharacteristic
42Dic3⋊Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50Dic32C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#124—31no—
54C3×#121—31no—
55#946—31no—
56#944—31no—
57#939D311yescharacteristic
58#936—31no—
59#936—31no—
60#936D311yescharacteristic, complemented
61#935—31no—
62#935—31no—
63#935—31no—
64#935—61no—
65D4×Dic3—31no—
66#926—31no—
67#924—31no—
68#888—31no—
69#887—31no—
70#885—31no—
71#885—31no—
72#883—31no—
73#67⋊C4—31no—
74#879—31no—
75#879—31no—
76#879—31no—
77#878—31no—
78#878—31no—
79#878—31no—
80#878—31no—
81#877—31no—
82#876—31no—
83C4×Dic6—31no—
84C23×C32C2311yescharacteristic
85C23×C32C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C32×D4—41no—
88C2×C32×C4C2311yescharacteristic
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊Dic3C2311yescharacteristic
94C3×#67—22no—
95C3×#67—41no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C3×Dic6—41no—
105#627—22no—
106#627—41no—
107D3×Dic3—41no—
108#542—91noSylow
109C2×C3×Q8—31no—
110C2×C3×D4—21no—
111C2×C3×D4—31no—
112C2×C3×D4—31no—
113C2×C3×D4C2×D311yescharacteristic
114C2×C3×D4C2×D311yescharacteristic
115C22×C3×C4—31no—
116C2×#67C2×D311yescharacteristic
117C2×#67C2×D311yescharacteristic
118C22×Dic3—31no—
119C22×Dic3—31no—
120C22×Dic3—31no—
121C22×Dic3—61no—
122C22×Dic3C2×D311yescharacteristic
123C2×C4×D3—31no—
124C2×Dic6—31no—
125C2×Dic6—31no—
126C2×Dic6—31no—
127C2×Dic6—31no—
128C2×Dic6C2×D311yescharacteristic
129C3×C4⋊C4—31no—
130C3×C22⋊C4—31no—
131C3×C22⋊C4—31no—
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#217—31no—
144#217—31no—
145#217—31no—
146#217—61no—
147#217—61no—
148#217—61no—
149#217C2×D311yescharacteristic
150#217C2×D311yescharacteristic
151#217C2×D311yescharacteristic
152#217C2×D311yescharacteristic
153#217C2×D311yescharacteristic
154(C2×D3)⋊C4—31no—
155(C2×D3)⋊C4—31no—
156(C2×D3)⋊C4—31no—
157(C2×D3)⋊C4C2×D311yescharacteristic
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—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⋊C4C2×D311yescharacteristic
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3C2×D311yescharacteristic
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32C2411yescharacteristic
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—21no—
196C32×C4—21no—
197C3⋊Dic3—21no—
198C3⋊Dic3—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#4112yes—
208C4⋊Q8—91no—
209#126—91no—
210#126—91no—
211#124—31no—
212#124—91no—
213#124—91no—
214#123—91no—
215#123—91no—
216C22⋊Q8—91no—
217C22⋊Q8—91no—
218C22⋊Q8—91no—
219#121—31no—
220C4×Q8—91no—
221C4×D4—91no—
222#117—91no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—31no—
226C23×C3C22×D311yescharacteristic
227C23×C3C22×D311yescharacteristic
228C23×C3C22×D311yescharacteristic
229C23×C3C22×D311yescharacteristic
230C22×D3C22×D311yescharacteristic
231C3×Q8—121no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—42no—
235C3×D4—62no—
236C3×D4—121no—
237C2×C3×C4—21no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—62no—
246C2×C3×C4C22×D311yescharacteristic
247C2×C3×C4C22×D311yescharacteristic
248#67—22no—
249#67—41no—
250C2×Dic3—22no—
251C2×Dic3—31no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C2×Dic3—31no—
256C2×Dic3—31no—
257C2×Dic3—31no—
258C2×Dic3—31no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265C2×Dic3—121no—
266C2×Dic3—122no—
267C2×Dic3C22×D311yescharacteristic
268C2×Dic3C22×D311yescharacteristic
269C2×Dic3C22×D311yescharacteristic
270C2×Dic3C22×D311yescharacteristic
271C2×Dic3C22×D311yescharacteristic
272C2×Dic3C22×D311yescharacteristic
273C2×Dic3C22×D311yescharacteristic
274C4×D3—121no—
275Dic6—41no—
276Dic6—62no—
277Dic6—62no—
278Dic6—121no—
279Dic6—121no—
280C2×C32—41no—
281C2×C32—41no—
282C2×C32C2×#4111yescharacteristic
283C2×C32H(5,𝔽2)11yescharacteristic
284C2×C322−1+411yescharacteristic
285C3×D3—41no—
286C2×Q8—31no—
287C2×Q8—91no—
288C2×Q8—91no—
289C2×D4—31no—
290C2×D4—31no—
291C2×D4D3211yescharacteristic
292C22×C4—31no—
293C22×C4—91no—
294C22×C4—91no—
295C4⋊C4—31no—
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—
305C22⋊C4—31no—
306C22⋊C4—31no—
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—
319C42—91no—
320C42—91no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—61no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3C23×D311yescharacteristic
344C22×C3C23×D311yescharacteristic
345C2×D3—21no—
346C2×D3—21no—
347C2×D3—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—32no—
351C3×C4—41no—
352C3×C4—61no—
353C3×C4—61no—
354C3×C4—61no—
355C3×C4—61no—
356C3×C4—61no—
357C3×C4—61no—
358Dic3—21no—
359Dic3—21no—
360Dic3—21no—
361Dic3—21no—
362Dic3—21no—
363Dic3—21no—
364Dic3—61no—
365Dic3—61no—
366Dic3—61no—
367Dic3—61no—
368Dic3—61no—
369Dic3—61no—
370Dic3—61no—
371Dic3—61no—
372Dic3—121no—
373Dic3—121no—
374Dic3—121no—
375Dic3—121no—
376Dic3#23712yes—
377C32#54211yescharacteristic, complemented, Sylow
378C23—31no—
379C23C2×D3211yescharacteristic
380C23C2×D3211yescharacteristic
381Q8—121no—
382Q8—182no—
383Q8—361no—
384D4—41no—
385D4—62no—
386D4—121no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—62no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—361no—
400C2×C4—361no—
401C2×C4C2×D3211yescharacteristic
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—42no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—81no—
411C2×C3—121no—
412C2×C3C2×#23711yescharacteristic
413C2×C3#100411yescharacteristic
414C2×C3#100411yescharacteristic
415C2×C3D3×#4111yescharacteristic
416C2×C3#101011yescharacteristic
417C2×C3#101011yescharacteristic
418D3—41no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—61no—
426C22—61no—
427C22—61no—
428C22C22×D3211yescharacteristic
429C4—21no—
430C4—32no—
431C4—61no—
432C4—61no—
433C4—61no—
434C4—61no—
435C4—61no—
436C4—61no—
437C4—181no—
438C4—181no—
439C4—181no—
440C4—181no—
441C3—21no—
442C3#560311yescharacteristic, complemented
443C3#566911yescharacteristic, complemented
444C2—41no—
445C2—41no—
446C2—121no—
447C2#6430911yescharacteristic
448C2D3×#23711yescharacteristic
449C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×D4C22
prime radicalC3×#939C2
hypercenterC2×D4D32
hypocenterC32#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #64144C2semidirect
3. C3×#936C2semidirect
4. #63982C2semidirect
5. #67⋊Dic3C2semidirect
6. #63969C2semidirect
7. #63964C2semidirect
8. #63959C2semidirect
9. #63959C2semidirect
10. #63956C2semidirect
11. #63955C2semidirect
12. #63887C2semidirect
13. #63859C2semidirect
14. #63839C2semidirect
15. #63837C2semidirect
60. #936D3semidirect
377. C32#542semidirect
442. C3#5603semidirect
443. C3#5669semidirect

Maximal subgroups

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

subgroupindex
#641442
C3×#9392
C3×#9362
#639822
#67⋊Dic32
#639692
#639642
#639592
#639562
#639552
#638872
#638592
#638392
#638372
#56693
#56033