Finite Group Databasebeta

← #10595028

Subgroups — #10595028

Order 576.

523 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64139C211yesmaximal, characteristic, complemented
2C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#63978C211yesmaximal, characteristic, complemented
5#63978C211yesmaximal, characteristic, complemented
6#63952C211yesmaximal, characteristic, complemented
7#63952C211yesmaximal, characteristic, complemented
8#63910C211yesmaximal, characteristic, complemented
9#63904C211yesmaximal, characteristic, complemented
10#63897C211yesmaximal, characteristic, complemented
11#63868C211yesmaximal, characteristic, complemented
12#63861C211yesmaximal, characteristic, complemented
13#63850C211yesmaximal, characteristic, complemented
14#63845C211yesmaximal, characteristic, complemented
15#63836C211yesmaximal, characteristic, complemented
16#5540—31nomaximal
17#5514—31nomaximal
18C22×C32×C4C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#638C2211yescharacteristic
21C2×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C22×C3×Dic3C2211yescharacteristic
24C22×C3×Dic3C2211yescharacteristic
25C2×C3×C4×D3C2211yescharacteristic
26C2×#626C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#624C2211yescharacteristic
29C2×#624C2211yescharacteristic
30#3752C2211yescharacteristic
31#3752C2211yescharacteristic
32C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#217C2211yescharacteristic
34C3×(C2×D3)⋊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
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×C4×D4—31no—
54C2×C3×C4⋊C4—31no—
55#939—31no—
56#939—31no—
57#930—31no—
58#930—31no—
59#930—31no—
60#930—31no—
61#930—61no—
62#929—31no—
63C4×#67—31no—
64C4×#67—31no—
65C4×#67—31no—
66C4×#67D311yescharacteristic, complemented
67C2×Dic3⋊C4D311yescharacteristic, complemented
68#898—31no—
69#898—31no—
70#895—31no—
71#894—31no—
72#894—31no—
73#894—31no—
74#893—31no—
75#892—31no—
76#890—31no—
77#889—31no—
78#884—31no—
79#67⋊C4—31no—
80#67⋊C4—31no—
81#879—31no—
82#876—31no—
83#872—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3⋊D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C2×C32×C4—41no—
89C2×C32×C4C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91#638—22no—
92#638—22no—
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C4⋊(C3⋊D3)—41no—
96C3×#67—22no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C3×C4×D3—41no—
107#626—22no—
108#626—41no—
109#624—22no—
110#624—41no—
111#553—91noSylow
112C2×C3×D4—31no—
113C22×C3×C4—21no—
114C22×C3×C4—31no—
115C22×C3×C4—31no—
116C22×C3×C4—31no—
117C22×C3×C4C2×D311yescharacteristic
118C22×C3×C4C2×D311yescharacteristic
119C2×#67—31no—
120C2×#67—31no—
121C2×#67—31no—
122C2×#67—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—61no—
126C2×#67—61no—
127C2×#67C2×D311yescharacteristic
128C22×Dic3C2×D311yescharacteristic
129C22×Dic3C2×D311yescharacteristic
130C2×D12—31no—
131C2×D12—31no—
132C2×D12—31no—
133C2×D12—31no—
134C2×D12—61no—
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×C4×D3—31no—
138C2×C4×D3—31no—
139C2×C4×D3C2×D311yescharacteristic
140C3×C4⋊C4—31no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—31no—
145C3×C22⋊C4—31no—
146C3×C22⋊C4—31no—
147C3×C42—31no—
148#217—31no—
149#217—31no—
150#217C2×D311yescharacteristic
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—31no—
160(C2×D3)⋊C4—31no—
161(C2×D3)⋊C4—31no—
162(C2×D3)⋊C4—31no—
163(C2×D3)⋊C4—31no—
164(C2×D3)⋊C4—31no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—61no—
167(C2×D3)⋊C4C2×D311yescharacteristic
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—61no—
173Dic3⋊C4—31no—
174Dic3⋊C4—31no—
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—31no—
178Dic3⋊C4—31no—
179Dic3⋊C4C2×D311yescharacteristic
180Dic3⋊C4C2×D311yescharacteristic
181Dic3⋊C4C2×D311yescharacteristic
182Dic3⋊C4C2×D311yescharacteristic
183Dic3⋊C4C2×D311yescharacteristic
184C4×Dic3—31no—
185C4×Dic3—31no—
186C4×Dic3—31no—
187C4×Dic3—31no—
188C4×Dic3C2×D311yescharacteristic
189C22×C32—21no—
190C22×C32—21no—
191C22×C32#4112yes—
192C22×C32C2411yescharacteristic
193C2×C3⋊D3—21no—
194C2×C3⋊D3—21no—
195C2×C3⋊D3—21no—
196C2×C3⋊D3—21no—
197C2×C3⋊D3—21no—
198C2×C3⋊D3—21no—
199C2×C3×D3—21no—
200C2×C3×D3—21no—
201C2×C3×D3—21no—
202C32×C4—21no—
203C32×C4—21no—
204C3⋊Dic3—21no—
205C3⋊Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3—21no—
208C3×Dic3—21no—
209C3×Dic3—21no—
210C3×Dic3—21no—
211C3×Dic3—21no—
212C3×Dic3#4112yes—
213#126—91no—
214#126—91no—
215#125—91no—
216#123—91no—
217#123—91no—
218#121—91no—
219#121—91no—
220#121—91no—
221#121—91no—
222C4×D4—31no—
223C4×D4—91no—
224C4×D4—91no—
225C4×D4—91no—
226#117—91no—
227C2×C4⋊C4—31no—
228C23×C3—21no—
229C23×C3—31no—
230C23×C3C22×D311yescharacteristic
231C23×C3C22×D311yescharacteristic
232C22×D3—31no—
233C22×D3—31no—
234C22×D3—31no—
235C22×D3—31no—
236C22×D3—61no—
237C22×D3—61no—
238C22×D3C22×D311yescharacteristic
239C3×D4—62no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—42no—
252C2×C3×C4—62no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4C22×D311yescharacteristic
256C2×C3×C4C22×D311yescharacteristic
257C2×C3×C4C22×D311yescharacteristic
258C2×C3×C4C22×D311yescharacteristic
259#67—22no—
260#67—62no—
261#67—62no—
262#67—62no—
263#67—62no—
264#67—62no—
265#67—122no—
266#67—122no—
267#67—121no—
268C2×Dic3—22no—
269C2×Dic3—31no—
270C2×Dic3—31no—
271C2×Dic3—31no—
272C2×Dic3—31no—
273C2×Dic3—41no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3C22×D311yescharacteristic
277C2×Dic3C22×D311yescharacteristic
278C2×Dic3C22×D311yescharacteristic
279C2×Dic3C22×D311yescharacteristic
280C2×Dic3C22×D311yescharacteristic
281C2×Dic3C22×D311yescharacteristic
282C2×Dic3C22×D311yescharacteristic
283D12—62no—
284D12—121no—
285D12—121no—
286D12—122no—
287D12—121no—
288C4×D3—41no—
289C4×D3—62no—
290C4×D3—62no—
291C4×D3—121no—
292C4×D3—121no—
293C2×C32—22no—
294C2×C32C2×#4111yescharacteristic
295C2×C32C2×#4111yescharacteristic
296C2×C32H(5,𝔽2)11yescharacteristic
297C3⋊D3—41no—
298C3⋊D3—41no—
299C3×D3—41no—
300C2×D4—31no—
301C2×D4—91no—
302C2×D4—91no—
303C2×D4—91no—
304C2×D4—91no—
305C2×D4—91no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4D3211yescharacteristic
312C4⋊C4—31no—
313C4⋊C4—31no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—91no—
321C4⋊C4—91no—
322C22⋊C4—31no—
323C22⋊C4—31no—
324C22⋊C4—91no—
325C22⋊C4—91no—
326C22⋊C4—91no—
327C22⋊C4—91no—
328C22⋊C4—91no—
329C22⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C42—31no—
333C42—91no—
334C42—91no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—22no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—61no—
344C22×C3—61no—
345C22×C3—61no—
346C22×C3#23512yes—
347C22×C3#23912yes—
348C22×C3C23×D311yescharacteristic
349C22×C3C23×D311yescharacteristic
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—61no—
356C2×D3—61no—
357C2×D3—61no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C3×C4—22no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—32no—
377C3×C4—41no—
378C3×C4—61no—
379C3×C4—61no—
380C3×C4—61no—
381C3×C4—61no—
382C3×C4—61no—
383C3×C4—61no—
384Dic3—21no—
385Dic3—21no—
386Dic3—21no—
387Dic3—21no—
388Dic3—21no—
389Dic3—21no—
390Dic3—61no—
391Dic3—61no—
392Dic3—61no—
393Dic3—61no—
394Dic3—121no—
395Dic3—121no—
396Dic3#23512yes—
397C32#55311yescharacteristic, complemented, Sylow
398C23—31no—
399C23—91no—
400C23—91no—
401C23C2×D3211yescharacteristic
402D4—62no—
403D4—182no—
404D4—182no—
405D4—182no—
406D4—361no—
407D4—361no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—41no—
416C2×C4—62no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—182no—
422C2×C4—361no—
423C2×C4C2×D3211yescharacteristic
424C2×C4C2×D3211yescharacteristic
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—42no—
431C2×C3—121no—
432C2×C3C2×#23511yescharacteristic
433C2×C3C2×#23511yescharacteristic
434C2×C3#100411yescharacteristic
435C2×C3#100411yescharacteristic
436C2×C3C2×#23911yescharacteristic
437C2×C3D3×#4111yescharacteristic
438D3—41no—
439D3—121no—
440D3—121no—
441D3—121no—
442D3—121no—
443D3—241no—
444D3—241no—
445C22—21no—
446C22—21no—
447C22—61no—
448C22—61no—
449C22—61no—
450C22—181no—
451C22—181no—
452C22—181no—
453C22—181no—
454C22—181no—
455C22—181no—
456C22#379912yes—
457C22C22×D3211yescharacteristic
458C4—21no—
459C4—21no—
460C4—32no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—61no—
465C4—61no—
466C4—61no—
467C4—181no—
468C4—181no—
469C3—21no—
470C3#551411yescharacteristic, complemented
471C3#554011yescharacteristic, complemented
472C2—22no—
473C2—121no—
474C2—361no—
475C2—361no—
476C2C2×#379911yescharacteristic
477C2D3×#23511yescharacteristic
478C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
hypercenterC22×C4D32
hypocenterC32#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #64139C2semidirect
2. C3×C4×#67C2semidirect
3. C2×C3×Dic3⋊C4C2semidirect
4. #63978C2semidirect
5. #63978C2semidirect
6. #63952C2semidirect
7. #63952C2semidirect
8. #63910C2semidirect
9. #63904C2semidirect
10. #63897C2semidirect
11. #63868C2semidirect
12. #63861C2semidirect
13. #63850C2semidirect
14. #63845C2semidirect
15. #63836C2semidirect
66. C4×#67D3semidirect
67. C2×Dic3⋊C4D3semidirect
397. C32#553semidirect
470. C3#5514semidirect
471. C3#5540semidirect

Maximal subgroups

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

subgroupindex
#641392
C3×C4×#672
C2×C3×Dic3⋊C42
#639782
#639522
#639102
#639042
#638972
#638682
#638612
#638502
#638452
#638362
#55403
#55143