Finite Group Databasebeta

← #10594166

Subgroups — #10594166

Order 576.

561 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64091C211yesmaximal, characteristic
2C3×#878C211yesmaximal, characteristic, complemented
3C3×#877C211yesmaximal, characteristic, complemented
4#63974C211yesmaximal, characteristic, complemented
5#63966C211yesmaximal, characteristic, complemented
6C2×#3722C211yesmaximal, characteristic, complemented
7#63952C211yesmaximal, characteristic, complemented
8#63897C211yesmaximal, characteristic, complemented
9#63897C211yesmaximal, characteristic, complemented
10#63894C211yesmaximal, characteristic, complemented
11#63888C211yesmaximal, characteristic, complemented
12#63868C211yesmaximal, characteristic, complemented
13#63864C211yesmaximal, characteristic, complemented
14#63848C211yesmaximal, characteristic, complemented
15#63836C211yesmaximal, characteristic, complemented
16#5637—31nomaximal
17#5527—31nomaximal
18C23×C3⋊D3C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C3×Dic3C2211yescharacteristic
23C22×C3×Dic3C2211yescharacteristic
24C2×C3×Dic6C2211yescharacteristic, complemented
25C2×#624C2211yescharacteristic
26C2×#624C2211yescharacteristic
27C2×#624C2211yescharacteristic, complemented
28C32×C22⋊C4C2211yescharacteristic
29#3752C2211yescharacteristic
30#3752C2211yescharacteristic
31C3×#217C2211yescharacteristic
32C3×#217C2211yescharacteristic
33C3×C4⋊Dic3C2211yescharacteristic, complemented
34C3×Dic3⋊C4C2211yescharacteristic, complemented
35C3×Dic3⋊C4C2211yescharacteristic, complemented
36C3×Dic3⋊C4C2211yescharacteristic, complemented
37C3×Dic3⋊C4C2211yescharacteristic, complemented
38C3×C4×Dic3C2211yescharacteristic, complemented
39C3×C4×Dic3C2211yescharacteristic, complemented
40#3724C2211yescharacteristic, complemented
41Dic3⋊Dic3C2211yescharacteristic, complemented
42Dic3⋊Dic3C2211yescharacteristic, complemented
43#3722C2211yescharacteristic
44#3722C2211yescharacteristic
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49#3722C2211yescharacteristic, complemented
50#3722C2211yescharacteristic, complemented
51#3722C2211yescharacteristic, complemented
52Dic32C2211yescharacteristic, complemented
53C3×C22⋊Q8—31no—
54C3×#117—31no—
55#947—31no—
56#946—31no—
57#929—31no—
58C4×#67—31no—
59C2×(C2×D3)⋊C4—31no—
60C2×(C2×D3)⋊C4—31no—
61#898—31no—
62#898—31no—
63#898—31no—
64#896—31no—
65#894—31no—
66#894—31no—
67#894—31no—
68#894—31no—
69#893—31no—
70#892—31no—
71#886—31no—
72#882—31no—
73#882—31no—
74#882—61no—
75#67⋊C4—31no—
76D3×C22⋊C4—31no—
77D3×C22⋊C4—31no—
78#878D311yescharacteristic, complemented
79#877D311yescharacteristic, complemented
80#876—31no—
81#875—31no—
82C4×D12—31no—
83#872—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—22no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3C2311yescharacteristic
89C22×C3⋊D3C2311yescharacteristic
90C22×C3⋊D3C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C32×C4C2311yescharacteristic
93#638—22no—
94C2×C3⋊Dic3C2311yescharacteristic
95C4⋊(C3⋊D3)—22no—
96C4⋊(C3⋊D3)—41no—
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
106C2×C3×Dic3C2311yescharacteristic
107C3×Dic6—41no—
108#624—22no—
109#624—41no—
110#624—41no—
111#551—91noSylow
112C23×D3—31no—
113C23×D3—31no—
114C23×D3—61no—
115C2×C3×Q8—31no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C2×#67—31no—
119C2×#67—31no—
120C2×#67—61no—
121C22×Dic3C2×D311yescharacteristic
122C22×Dic3C2×D311yescharacteristic
123C2×D12—31no—
124C2×D12—31no—
125C2×D12—31no—
126C2×D12—31no—
127C2×D12—61no—
128C2×D12—61no—
129C2×C4×D3—31no—
130C2×C4×D3—31no—
131C2×C4×D3—31no—
132C2×C4×D3—31no—
133C2×C4×D3—31no—
134C2×C4×D3—31no—
135C2×Dic6C2×D311yescharacteristic, complemented
136C3×C4⋊C4—31no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C22⋊C4—21no—
142C3×C22⋊C4—31no—
143C3×C22⋊C4—31no—
144C3×C22⋊C4C2×D311yescharacteristic
145C3×C22⋊C4C2×D311yescharacteristic
146C3×C42—31no—
147C3×C42—31no—
148#217C2×D311yescharacteristic
149#217C2×D311yescharacteristic
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—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—31no—
166(C2×D3)⋊C4—31no—
167(C2×D3)⋊C4—31no—
168(C2×D3)⋊C4—31no—
169(C2×D3)⋊C4—31no—
170(C2×D3)⋊C4—31no—
171(C2×D3)⋊C4—31no—
172(C2×D3)⋊C4—61no—
173(C2×D3)⋊C4—61no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3C2×D311yescharacteristic, complemented
177Dic3⋊C4—31no—
178Dic3⋊C4—31no—
179Dic3⋊C4—31no—
180Dic3⋊C4—31no—
181Dic3⋊C4C2×D311yescharacteristic, complemented
182Dic3⋊C4C2×D311yescharacteristic, complemented
183Dic3⋊C4C2×D311yescharacteristic, complemented
184Dic3⋊C4C2×D311yescharacteristic, complemented
185C4×Dic3—31no—
186C4×Dic3—31no—
187C4×Dic3C2×D311yescharacteristic, complemented
188C4×Dic3C2×D311yescharacteristic, complemented
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—44no—
202C2×C3⋊D3#4112yes—
203C32×C4—21no—
204C32×C4—21no—
205C3⋊Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3—21no—
208C3×Dic3—21no—
209C3×Dic3—21no—
210C3×Dic3—21no—
211C3×Dic3—21no—
212C3×Dic3—21no—
213C3×Dic3—21no—
214#126—91no—
215#126—91no—
216#124—91no—
217#123—91no—
218#123—91no—
219#123—91no—
220C22⋊Q8—31no—
221C22⋊Q8—91no—
222#120—91no—
223C4×D4—91no—
224C4×D4—91no—
225#117—31no—
226#117—91no—
227C2×C22⋊C4—91no—
228C2×C22⋊C4—91no—
229C23×C3—21no—
230C23×C3C22×D311yescharacteristic
231C23×C3C22×D311yescharacteristic
232C22×D3—31no—
233C22×D3—31no—
234C22×D3—31no—
235C22×D3—31no—
236C22×D3—31no—
237C22×D3—31no—
238C22×D3—61no—
239C22×D3—61no—
240C22×D3—61no—
241C22×D3—62no—
242C22×D3—62no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—122no—
246C22×D3—122no—
247C22×D3—121no—
248C22×D3—121no—
249C22×D3—122no—
250C3×Q8—121no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—62no—
262C2×C3×C4—121no—
263C2×C3×C4C22×D311yescharacteristic
264C2×C3×C4C22×D311yescharacteristic
265C2×C3×C4C22×D311yescharacteristic
266C2×C3×C4C22×D311yescharacteristic
267#67—62no—
268#67—62no—
269#67—122no—
270C2×Dic3—22no—
271C2×Dic3—31no—
272C2×Dic3—31no—
273C2×Dic3—41no—
274C2×Dic3—61no—
275C2×Dic3C22×D311yescharacteristic
276C2×Dic3C22×D311yescharacteristic
277C2×Dic3C22×D311yescharacteristic
278C2×Dic3C22×D311yescharacteristic
279C2×Dic3C22×D311yescharacteristic
280C2×Dic3C22×D311yescharacteristic
281C2×Dic3C22×D311yescharacteristic
282C2×Dic3C22×D311yescharacteristic
283D12—62no—
284D12—62no—
285D12—122no—
286D12—121no—
287D12—121no—
288D12—122no—
289C4×D3—62no—
290C4×D3—62no—
291C4×D3—121no—
292C4×D3—121no—
293C4×D3—121no—
294C4×D3—121no—
295Dic6—41no—
296C2×C32—22no—
297C2×C32C2×#4111yescharacteristic
298C2×C32C2×#4111yescharacteristic
299C2×C32H(5,𝔽2)11yescharacteristic
300C3⋊D3—22no—
301C3⋊D3—41no—
302C3⋊D3—41no—
303C24—91no—
304C2×Q8—31no—
305C2×D4—91no—
306C2×D4—91no—
307C2×D4—91no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—91no—
313C4⋊C4—31no—
314C4⋊C4—31no—
315C4⋊C4—31no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—91no—
321C22⋊C4—31no—
322C22⋊C4—31no—
323C22⋊C4—91no—
324C22⋊C4—91no—
325C22⋊C4—91no—
326C22⋊C4—91no—
327C22⋊C4—91no—
328C22⋊C4—91no—
329C22⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C22⋊C4—91no—
333C22⋊C4—91no—
334C22⋊C4D3211yescharacteristic
335C42—31no—
336C42—31no—
337C42—91no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—22no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3#23512yes—
347C22×C3#23912yes—
348C22×C3C23×D311yescharacteristic
349C22×C3C23×D311yescharacteristic
350C2×D3—32no—
351C2×D3—32no—
352C2×D3—62no—
353C2×D3—61no—
354C2×D3—61no—
355C2×D3—61no—
356C2×D3—61no—
357C2×D3—62no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—61no—
366C2×D3—61no—
367C2×D3—61no—
368C2×D3—61no—
369C2×D3—61no—
370C2×D3—121no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—121no—
374C2×D3—121no—
375C2×D3—121no—
376C2×D3—121no—
377C2×D3—124no—
378C2×D3—124no—
379C2×D3—128no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—61no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—61no—
390C3×C4—61no—
391C3×C4—61no—
392C3×C4—61no—
393C3×C4—61no—
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—21no—
398Dic3—21no—
399Dic3—21no—
400Dic3—21no—
401Dic3—21no—
402Dic3—61no—
403Dic3—61no—
404Dic3—121no—
405C32#55111yescharacteristic, complemented, Sylow
406C23—91no—
407C23—91no—
408C23—91no—
409C23—182no—
410C23—182no—
411C23—361no—
412C23C2×D3211yescharacteristic
413Q8—121no—
414D4—182no—
415D4—182no—
416D4—361no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—62no—
426C2×C4—91no—
427C2×C4—121no—
428C2×C4—182no—
429C2×C4—361no—
430C2×C4—361no—
431C2×C4C2×D3211yescharacteristic
432C2×C4C2×D3211yescharacteristic
433C2×C3—22no—
434C2×C3—22no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—42no—
439C2×C3C2×#23511yescharacteristic
440C2×C3#100411yescharacteristic
441C2×C3C2×#23911yescharacteristic
442C2×C3D3×#4111yescharacteristic
443C2×C3D3×#4111yescharacteristic
444C2×C3#100911yescharacteristic
445D3—62no—
446D3—62no—
447D3—122no—
448D3—122no—
449D3—121no—
450D3—121no—
451D3—121no—
452D3—121no—
453D3—241no—
454C22—21no—
455C22—21no—
456C22—92no—
457C22—181no—
458C22—181no—
459C22—181no—
460C22—181no—
461C22—181no—
462C22—181no—
463C22—181no—
464C22—181no—
465C22—364no—
466C22#379912yes—
467C22C22×D3211yescharacteristic
468C4—21no—
469C4—21no—
470C4—61no—
471C4—61no—
472C4—61no—
473C4—61no—
474C4—61no—
475C4—61no—
476C4—61no—
477C4—61no—
478C4—181no—
479C3—21no—
480C3#552711yescharacteristic, complemented
481C3#563711yescharacteristic, complemented
482C2—22no—
483C2—182no—
484C2—361no—
485C2—361no—
486C2C2×#379911yescharacteristic
487C2#6431211yescharacteristic
488C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
prime radical#64091C2
hypercenterC22⋊C4D32
hypocenterC32#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#878C2semidirect
3. C3×#877C2semidirect
4. #63974C2semidirect
5. #63966C2semidirect
6. C2×#3722C2semidirect
7. #63952C2semidirect
8. #63897C2semidirect
9. #63897C2semidirect
10. #63894C2semidirect
11. #63888C2semidirect
12. #63868C2semidirect
13. #63864C2semidirect
14. #63848C2semidirect
15. #63836C2semidirect
24. C2×C3×Dic6C22semidirect
27. C2×#624C22semidirect
33. C3×C4⋊Dic3C22semidirect
34. C3×Dic3⋊C4C22semidirect
35. C3×Dic3⋊C4C22semidirect
36. C3×Dic3⋊C4C22semidirect
37. C3×Dic3⋊C4C22semidirect
38. C3×C4×Dic3C22semidirect
39. C3×C4×Dic3C22semidirect
40. #3724C22semidirect
41. Dic3⋊Dic3C22semidirect
42. Dic3⋊Dic3C22semidirect
49. #3722C22semidirect
50. #3722C22semidirect
51. #3722C22semidirect
52. Dic32C22semidirect
78. #878D3semidirect
79. #877D3semidirect
135. C2×Dic6C2×D3semidirect
176. C4⋊Dic3C2×D3semidirect
181. Dic3⋊C4C2×D3semidirect
182. Dic3⋊C4C2×D3semidirect
183. Dic3⋊C4C2×D3semidirect
184. Dic3⋊C4C2×D3semidirect
187. C4×Dic3C2×D3semidirect
188. C4×Dic3C2×D3semidirect
405. C32#551semidirect
480. C3#5527semidirect
481. C3#5637semidirect

Maximal subgroups

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

subgroupindex
#640912
C3×#8782
C3×#8772
#639742
#639662
C2×#37222
#639522
#638972
#638942
#638882
#638682
#638642
#638482
#638362
#56373
#55273