Finite Group Databasebeta

← #10594236

Subgroups — #10594236

Order 576.

551 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64093C211yesmaximal, characteristic, complemented
2C3×#882C211yesmaximal, characteristic, complemented
3C3×#879C211yesmaximal, characteristic, complemented
4#63977C211yesmaximal, characteristic, complemented
5#63977C211yesmaximal, characteristic, complemented
6#63971C211yesmaximal, characteristic, complemented
7#63958C211yesmaximal, characteristic, complemented
8#63916C211yesmaximal, characteristic, complemented
9#63911C211yesmaximal, characteristic, complemented
10#63910C211yesmaximal, characteristic, complemented
11#63886C211yesmaximal, characteristic, complemented
12#63884C211yesmaximal, characteristic, complemented
13#63859C211yesmaximal, characteristic, complemented
14#63854C211yesmaximal, characteristic, complemented
15#63853C211yesmaximal, characteristic, complemented
16#5711—31nomaximal
17#5595—31nomaximal
18C23×C3×D3C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#638C2211yescharacteristic
21C2×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#67C2211yescharacteristic
24C2×C3×D12C2211yescharacteristic
25C2×C3×D12C2211yescharacteristic
26C2×#626C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#626C2211yescharacteristic
29C2×#626C2211yescharacteristic
30C2×#626C2211yescharacteristic, complemented
31C2×#626C2211yescharacteristic, complemented
32C2×#624C2211yescharacteristic, complemented
33C2×D3×Dic3C2211yescharacteristic, complemented
34C32×C22⋊C4C2211yescharacteristic
35#3752C2211yescharacteristic, complemented
36#3750C2211yescharacteristic, complemented
37C3×#217C2211yescharacteristic
38C3×#217C2211yescharacteristic
39C3×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D3)⋊C4C2211yescharacteristic
41C3×C4⋊Dic3C2211yescharacteristic, complemented
42C3×Dic3⋊C4C2211yescharacteristic, complemented
43C3×Dic3⋊C4C2211yescharacteristic, complemented
44C3×C4×Dic3C2211yescharacteristic, complemented
45#3724C2211yescharacteristic, complemented
46Dic3⋊Dic3C2211yescharacteristic, complemented
47#3722C2211yescharacteristic, complemented
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×#126—31no—
54C3×#120—31no—
55#953—31no—
56#953—31no—
57#940—31no—
58#939—31no—
59#939—31no—
60#938—31no—
61#938—31no—
62#935—31no—
63#895—31no—
64#895—31no—
65#895—31no—
66#894—31no—
67#894—31no—
68#894—31no—
69#884—31no—
70#884—31no—
71#884—31no—
72#884—31no—
73#884—31no—
74#884—61no—
75#883—31no—
76#883—31no—
77#882—31no—
78#882—31no—
79#882D311yescharacteristic, complemented
80#879—31no—
81#879D311yescharacteristic, complemented
82#876—31no—
83#874—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3⋊D3C2311yescharacteristic
87C22×C3×D3—41no—
88C22×C3×D3—41no—
89C22×C3×D3—41no—
90C22×C3×D3C2311yescharacteristic
91C22×C3×D3C2311yescharacteristic
92C22×C3×D3C2311yescharacteristic
93C2×C32×C4C2311yescharacteristic
94C2×C32×C4C2311yescharacteristic
95#638—41no—
96#638—41no—
97C2×C3⋊Dic3C2311yescharacteristic
98C2×C3⋊Dic3C2311yescharacteristic
99C4⋊(C3⋊D3)—41no—
100C4×C3⋊D3—41no—
101C3×#67—41no—
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C3×D12—41no—
108C3×D12—41no—
109#626—41no—
110#626—41no—
111#626—41no—
112#626—41no—
113#626—41no—
114#626—41no—
115#624—41no—
116D3×Dic3—41no—
117#560—91noSylow
118C24×C3—31no—
119C23×D3C2×D311yescharacteristic
120C2×C3×D4—31no—
121C2×C3×D4—31no—
122C2×C3×D4—31no—
123C2×#67—31no—
124C2×#67—31no—
125C2×#67—31no—
126C2×#67—31no—
127C2×#67—31no—
128C2×#67—31no—
129C2×#67—31no—
130C2×#67—31no—
131C2×#67—31no—
132C2×#67—31no—
133C2×#67—61no—
134C2×#67—61no—
135C2×#67C2×D311yescharacteristic
136C22×Dic3—31no—
137C2×D12—31no—
138C2×D12—31no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—31no—
142C2×D12—31no—
143C2×D12—31no—
144C2×D12—31no—
145C2×D12—61no—
146C2×D12C2×D311yescharacteristic
147C2×D12C2×D311yescharacteristic
148C2×C4×D3—31no—
149C2×C4×D3—31no—
150C2×C4×D3—31no—
151C2×C4×D3—31no—
152C2×C4×D3—31no—
153C2×C4×D3—61no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C22⋊C4—21no—
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4C2×D311yescharacteristic
163C3×C22⋊C4C2×D311yescharacteristic
164C3×C42—31no—
165#217—31no—
166#217—31no—
167#217—31no—
168#217—31no—
169#217—31no—
170#217C2×D311yescharacteristic
171#217C2×D311yescharacteristic
172(C2×D3)⋊C4—31no—
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—31no—
175(C2×D3)⋊C4—31no—
176(C2×D3)⋊C4—31no—
177(C2×D3)⋊C4—31no—
178(C2×D3)⋊C4—31no—
179(C2×D3)⋊C4—31no—
180(C2×D3)⋊C4—31no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4C2×D311yescharacteristic
183(C2×D3)⋊C4C2×D311yescharacteristic
184C4⋊Dic3—31no—
185C4⋊Dic3C2×D311yescharacteristic, complemented
186Dic3⋊C4—31no—
187Dic3⋊C4—31no—
188Dic3⋊C4—31no—
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—61no—
192Dic3⋊C4C2×D311yescharacteristic, complemented
193Dic3⋊C4C2×D311yescharacteristic, complemented
194C4×Dic3C2×D311yescharacteristic, complemented
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32C2411yescharacteristic
199C2×C3⋊D3—21no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3—21no—
208C2×C3×D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—21no—
213C2×C3×D3—21no—
214C2×C3×D3—44no—
215C32×C4—21no—
216C32×C4—21no—
217C3⋊Dic3—21no—
218C3⋊Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—21no—
224#127—91no—
225#126—31no—
226#126—91no—
227#123—91no—
228#123—91no—
229#123—91no—
230#121—91no—
231#121—91no—
232#121—91no—
233#121—91no—
234#121—91no—
235#121—91no—
236#120—31no—
237#120—91no—
238#120—91no—
239C23×C3—21no—
240C23×C3—31no—
241C23×C3—31no—
242C23×C3—31no—
243C23×C3—121no—
244C23×C3—121no—
245C23×C3—121no—
246C23×C3C22×D311yescharacteristic
247C23×C3C22×D311yescharacteristic
248C22×D3—31no—
249C22×D3—31no—
250C22×D3—31no—
251C22×D3—31no—
252C22×D3—41no—
253C22×D3—41no—
254C22×D3—41no—
255C22×D3—61no—
256C22×D3—61no—
257C22×D3C22×D311yescharacteristic
258C22×D3C22×D311yescharacteristic
259C22×D3C22×D311yescharacteristic
260C3×D4—121no—
261C3×D4—121no—
262C3×D4—121no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4C22×D311yescharacteristic
271C2×C3×C4C22×D311yescharacteristic
272C2×C3×C4C22×D311yescharacteristic
273C2×C3×C4C22×D311yescharacteristic
274#67—41no—
275#67—121no—
276#67—121no—
277#67—121no—
278#67—121no—
279#67—121no—
280#67—121no—
281#67—121no—
282#67—121no—
283#67—121no—
284#67—121no—
285#67—122no—
286#67—122no—
287C2×Dic3—31no—
288C2×Dic3—31no—
289C2×Dic3—31no—
290C2×Dic3—31no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—121no—
294C2×Dic3C22×D311yescharacteristic
295C2×Dic3C22×D311yescharacteristic
296C2×Dic3C22×D311yescharacteristic
297C2×Dic3C22×D311yescharacteristic
298C2×Dic3C22×D311yescharacteristic
299D12—41no—
300D12—41no—
301D12—121no—
302D12—121no—
303D12—122no—
304D12—121no—
305D12—121no—
306D12—121no—
307D12—121no—
308D12—121no—
309D12—121no—
310C4×D3—121no—
311C4×D3—121no—
312C4×D3—121no—
313C4×D3—121no—
314C4×D3—122no—
315C4×D3—121no—
316C2×C32—41no—
317C2×C32H(5,𝔽2)11yescharacteristic
318C2×C32H(5,𝔽2)11yescharacteristic
319C2×C32H(5,𝔽2)11yescharacteristic
320C3⋊D3—41no—
321C3⋊D3—41no—
322C3×D3—41no—
323C3×D3—41no—
324C3×D3—41no—
325C24—31no—
326C2×D4—31no—
327C2×D4—31no—
328C2×D4—31no—
329C2×D4—91no—
330C2×D4—91no—
331C2×D4—91no—
332C2×D4—91no—
333C2×D4—91no—
334C2×D4—91no—
335C2×D4—91no—
336C2×D4—91no—
337C2×D4—91no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—91no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—91no—
345C4⋊C4—91no—
346C4⋊C4—91no—
347C22⋊C4—31no—
348C22⋊C4—31no—
349C22⋊C4—31no—
350C22⋊C4—31no—
351C22⋊C4—91no—
352C22⋊C4—91no—
353C22⋊C4—91no—
354C22⋊C4—91no—
355C22⋊C4—91no—
356C22⋊C4—91no—
357C22⋊C4—91no—
358C22⋊C4D3211yescharacteristic
359C42—31no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—61no—
371C22×C3—61no—
372C22×C3—61no—
373C22×C3—61no—
374C22×C3—61no—
375C22×C3—61no—
376C22×C3—61no—
377C22×C3—61no—
378C22×C3—61no—
379C22×C3—124no—
380C22×C3C23×D311yescharacteristic
381C22×C3C23×D311yescharacteristic
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—21no—
385C2×D3—21no—
386C2×D3—21no—
387C2×D3—21no—
388C2×D3—21no—
389C2×D3—21no—
390C2×D3—21no—
391C2×D3—44no—
392C2×D3—62no—
393C2×D3—61no—
394C2×D3—61no—
395C2×D3—61no—
396C2×D3—61no—
397C2×D3—61no—
398C2×D3—61no—
399C2×D3—61no—
400C2×D3—61no—
401C2×D3—61no—
402C2×D3—61no—
403C2×D3—61no—
404C2×D3—61no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—61no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—61no—
421Dic3—21no—
422Dic3—21no—
423Dic3—21no—
424Dic3—21no—
425Dic3—21no—
426Dic3—62no—
427Dic3—61no—
428Dic3—61no—
429Dic3—61no—
430Dic3—61no—
431Dic3—121no—
432C32#56011yescharacteristic, complemented, Sylow
433C23—31no—
434C23—31no—
435C23—31no—
436C23—91no—
437C23—91no—
438C23—121no—
439C23—121no—
440C23—121no—
441C23C2×D3211yescharacteristic
442D4—121no—
443D4—121no—
444D4—121no—
445D4—361no—
446D4—361no—
447D4—361no—
448D4—361no—
449D4—361no—
450D4—361no—
451D4—361no—
452D4—361no—
453D4—361no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—91no—
460C2×C4—91no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4C2×D3211yescharacteristic
465C2×C4C2×D3211yescharacteristic
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—81no—
472C2×C3—121no—
473C2×C3—121no—
474C2×C3—121no—
475C2×C3#100411yescharacteristic
476C2×C3#100411yescharacteristic
477C2×C3#100411yescharacteristic
478C2×C3#100911yescharacteristic
479C2×C3#100911yescharacteristic
480C2×C3#100911yescharacteristic
481D3—41no—
482D3—41no—
483D3—41no—
484D3—122no—
485D3—121no—
486D3—121no—
487D3—121no—
488D3—121no—
489D3—241no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—61no—
494C22—61no—
495C22—61no—
496C22—61no—
497C22—61no—
498C22—61no—
499C22—61no—
500C22—61no—
501C22—61no—
502C22—124no—
503C22—181no—
504C22—181no—
505C22—181no—
506C22—181no—
507C22—181no—
508C22—181no—
509C22C22×D3211yescharacteristic
510C4—21no—
511C4—21no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—181no—
518C4—181no—
519C3—21no—
520C3#559511yescharacteristic, complemented
521C3#571111yescharacteristic, complemented
522C2—41no—
523C2—121no—
524C2—121no—
525C2—121no—
526C2—361no—
527C2—361no—
528C2#6430711yescharacteristic
529C2#6431411yescharacteristic
530C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #64093C2semidirect
2. C3×#882C2semidirect
3. C3×#879C2semidirect
4. #63977C2semidirect
5. #63977C2semidirect
6. #63971C2semidirect
7. #63958C2semidirect
8. #63916C2semidirect
9. #63911C2semidirect
10. #63910C2semidirect
11. #63886C2semidirect
12. #63884C2semidirect
13. #63859C2semidirect
14. #63854C2semidirect
15. #63853C2semidirect
21. C2×C4⋊(C3⋊D3)C22semidirect
22. C2×C4×C3⋊D3C22semidirect
30. C2×#626C22semidirect
31. C2×#626C22semidirect
32. C2×#624C22semidirect
33. C2×D3×Dic3C22semidirect
35. #3752C22semidirect
36. #3750C22semidirect
41. C3×C4⋊Dic3C22semidirect
42. C3×Dic3⋊C4C22semidirect
43. C3×Dic3⋊C4C22semidirect
44. C3×C4×Dic3C22semidirect
45. #3724C22semidirect
46. Dic3⋊Dic3C22semidirect
47. #3722C22semidirect
52. (C2×D3)⋊Dic3C22semidirect
79. #882D3semidirect
81. #879D3semidirect
185. C4⋊Dic3C2×D3semidirect
192. Dic3⋊C4C2×D3semidirect
193. Dic3⋊C4C2×D3semidirect
194. C4×Dic3C2×D3semidirect
432. C32#560semidirect
520. C3#5595semidirect
521. C3#5711semidirect

Maximal subgroups

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

subgroupindex
#640932
C3×#8822
C3×#8792
#639772
#639712
#639582
#639162
#639112
#639102
#638862
#638842
#638592
#638542
#638532
#57113
#55953