Finite Group Databasebeta

← #10594091

Subgroups — #10594091

Order 576.

466 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64088C211yesmaximal, characteristic, complemented
2C3×#883C211yesmaximal, characteristic, complemented
3C3×#67⋊C4C211yesmaximal, characteristic, complemented
4#63970C211yesmaximal, characteristic
5#63969C211yesmaximal, characteristic, complemented
6#63964C211yesmaximal, characteristic, complemented
7#63961C211yesmaximal, characteristic, complemented
8C4×#625C211yesmaximal, characteristic, complemented
9#63899C211yesmaximal, characteristic, complemented
10#63891C211yesmaximal, characteristic, complemented
11D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#63870C211yesmaximal, characteristic, complemented
13#63869C211yesmaximal, characteristic, complemented
14#63859C211yesmaximal, characteristic, complemented
15#63851C211yesmaximal, characteristic, complemented
16#5660—31nomaximal
17#5564—31nomaximal
18C2×C3×#67C2211yescharacteristic
19C2×C3×#67C2211yescharacteristic
20C22×C3×Dic3C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×C4×D3C2211yescharacteristic
23C2×#627C2211yescharacteristic
24C2×#625C2211yescharacteristic
25C2×D3×Dic3C2211yescharacteristic
26C2×D3×Dic3C2211yescharacteristic
27C32×C22⋊C4C2211yescharacteristic
28#3757C2211yescharacteristic
29#3757C2211yescharacteristic
30C4⋊(C3⋊Dic3)C2211yescharacteristic
31#3750C2211yescharacteristic
32#3750C2211yescharacteristic
33C4×C3⋊Dic3C2211yescharacteristic
34C3×#217C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D3)⋊C4C2211yescharacteristic
37C3×C4⋊Dic3C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×C4×Dic3C2211yescharacteristic
41#3724C2211yescharacteristic
42#3724C2211yescharacteristic
43#3724C2211yescharacteristic
44#3724C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×#123—31no—
54C3×C4×D4—31no—
55#939—31no—
56#938—31no—
57#935—31no—
58#935—31no—
59#929—31no—
60C4×#67—31no—
61C4×#67—31no—
62#924—31no—
63#924—31no—
64C2×Dic3⋊C4—31no—
65#896—31no—
66#896—31no—
67D3×C4⋊C4—31no—
68#890—31no—
69#889—31no—
70#889—31no—
71#886—31no—
72#883—31no—
73#883—31no—
74#883D311yescharacteristic, complemented
75#67⋊C4D311yescharacteristic, complemented
76#879—31no—
77#879—31no—
78#879—31no—
79#879—61no—
80#878—31no—
81#878—31no—
82#876—31no—
83#870—31no—
84C23×C32C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C3×#67—22no—
94C3×#67—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C3×C4×D3—41no—
103C3×C4×D3—41no—
104#627—41no—
105#625—22no—
106D3×Dic3—22no—
107D3×Dic3—41no—
108#539—91noSylow
109C2×C3×D4—31no—
110C2×C3×D4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C2×#67—31no—
115C2×#67—31no—
116C2×#67C2×D311yescharacteristic
117C2×#67C2×D311yescharacteristic
118C22×Dic3—31no—
119C22×Dic3—31no—
120C22×Dic3C2×D311yescharacteristic
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3C2×D311yescharacteristic
124C2×C4×D3C2×D311yescharacteristic
125C2×Dic6—31no—
126C2×Dic6—31no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—31no—
129C3×C4⋊C4—31no—
130C3×C22⋊C4—21no—
131C3×C22⋊C4—31no—
132C3×C22⋊C4—31no—
133C3×C22⋊C4—31no—
134C3×C22⋊C4C2×D311yescharacteristic
135C3×C22⋊C4C2×D311yescharacteristic
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—61no—
146#217—61no—
147#217C2×D311yescharacteristic
148(C2×D3)⋊C4—31no—
149(C2×D3)⋊C4—31no—
150(C2×D3)⋊C4—31no—
151(C2×D3)⋊C4—31no—
152(C2×D3)⋊C4C2×D311yescharacteristic
153(C2×D3)⋊C4C2×D311yescharacteristic
154C4⋊Dic3—31no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—61no—
161C4⋊Dic3C2×D311yescharacteristic
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—31no—
177Dic3⋊C4—31no—
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×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32C2411yescharacteristic
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—
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—21no—
208#126—91no—
209#126—91no—
210#125—91no—
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—31no—
221C4×D4—91no—
222C2×C4⋊C4—91no—
223C23×C3—21no—
224C23×C3—31no—
225C23×C3—31no—
226C23×C3C22×D311yescharacteristic
227C23×C3C22×D311yescharacteristic
228C22×D3C22×D311yescharacteristic
229C22×D3C22×D311yescharacteristic
230C3×D4—62no—
231C3×D4—121no—
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×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247#67—22no—
248#67—41no—
249#67—62no—
250#67—62no—
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—41no—
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
271C2×Dic3C22×D311yescharacteristic
272C4×D3—41no—
273C4×D3—41no—
274C4×D3—62no—
275C4×D3—121no—
276Dic6—121no—
277Dic6—121no—
278C2×C32—41no—
279C2×C32C2×#4111yescharacteristic
280C2×C32H(5,𝔽2)11yescharacteristic
281C2×C322−1+411yescharacteristic
282C3×D3—22no—
283C3×D3—41no—
284C2×Q8—91no—
285C2×D4—31no—
286C2×D4—31no—
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—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—
305C4⋊C4—91no—
306C4⋊C4—91no—
307C22⋊C4—31no—
308C22⋊C4—31no—
309C22⋊C4—31no—
310C22⋊C4—91no—
311C22⋊C4—91no—
312C22⋊C4—91no—
313C22⋊C4—91no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C22⋊C4D3211yescharacteristic
317C42—31no—
318C42—91no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—32no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—61no—
331C22×C3—61no—
332C22×C3—61no—
333C22×C3—61no—
334C22×C3—61no—
335C22×C3C23×D311yescharacteristic
336C22×C3C23×D311yescharacteristic
337C2×D3—21no—
338C2×D3—21no—
339C2×D3—21no—
340C2×D3—21no—
341C2×D3—21no—
342C2×D3#23512yes—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—61no—
350C3×C4—61no—
351C3×C4—61no—
352C3×C4—61no—
353C3×C4—61no—
354C3×C4—61no—
355Dic3—21no—
356Dic3—21no—
357Dic3—21no—
358Dic3—21no—
359Dic3—21no—
360Dic3—21no—
361Dic3—61no—
362Dic3—61no—
363Dic3—61no—
364Dic3—61no—
365Dic3—61no—
366Dic3—61no—
367Dic3—61no—
368Dic3—61no—
369Dic3—121no—
370Dic3—121no—
371Dic3—121no—
372Dic3—121no—
373C32#53911yescharacteristic, complemented, Sylow
374C23—31no—
375C23—31no—
376C23C2×D3211yescharacteristic
377Q8—361no—
378D4—62no—
379D4—121no—
380D4—182no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—91no—
388C2×C4—91no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—182no—
395C2×C4—361no—
396C2×C4C2×D3211yescharacteristic
397C2×C4C2×D3211yescharacteristic
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3—62no—
404C2×C3—81no—
405C2×C3—121no—
406C2×C3C2×#23511yescharacteristic
407C2×C3#100411yescharacteristic
408C2×C3#100411yescharacteristic
409C2×C3D3×#4111yescharacteristic
410C2×C3#101011yescharacteristic
411C2×C3#101011yescharacteristic
412D3—22no—
413D3—41no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—32no—
418C22—61no—
419C22—61no—
420C22—61no—
421C22—61no—
422C22—61no—
423C22C22×D3211yescharacteristic
424C4—21no—
425C4—21no—
426C4—61no—
427C4—61no—
428C4—61no—
429C4—61no—
430C4—61no—
431C4—61no—
432C4—181no—
433C4—181no—
434C4—181no—
435C4—181no—
436C3—21no—
437C3#556411yescharacteristic, complemented
438C3#566011yescharacteristic, complemented
439C2—41no—
440C2—62no—
441C2—121no—
442C2D3×#23511yescharacteristic
443C2#6430911yescharacteristic
444C2#6431311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
prime radical#63970C2
hypercenterC22⋊C4D32
hypocenterC32#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #64088C2semidirect
2. C3×#883C2semidirect
3. C3×#67⋊C4C2semidirect
5. #63969C2semidirect
6. #63964C2semidirect
7. #63961C2semidirect
8. C4×#625C2semidirect
9. #63899C2semidirect
10. #63891C2semidirect
11. D3×Dic3⋊C4C2semidirect
12. #63870C2semidirect
13. #63869C2semidirect
14. #63859C2semidirect
15. #63851C2semidirect
74. #883D3semidirect
75. #67⋊C4D3semidirect
373. C32#539semidirect
437. C3#5564semidirect
438. C3#5660semidirect

Maximal subgroups

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

subgroupindex
#640882
C3×#8832
C3×#67⋊C42
#639702
#639692
#639642
#639612
C4×#6252
#638992
#638912
D3×Dic3⋊C42
#638702
#638692
#638592
#638512
#56603
#55643