Finite Group Databasebeta

← #10589666⋊C3 #13152665

Subgroups — #10589666⋊C3 #13152665

Order 1728.

701 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×3−1+2C211yesmaximal, characteristic, complemented
2#63501⋊C3C211yesmaximal, characteristic
3#63497⋊C3C211yesmaximal, characteristic, complemented
4#63491⋊C3C211yesmaximal, characteristic, complemented
5C4×#611⋊C3C211yesmaximal, characteristic, complemented
6#63486⋊C3C211yesmaximal, characteristic, complemented
7C2×(3−1+2⋊C4)⋊C4C211yesmaximal, characteristic, complemented
8#63458⋊C3C211yesmaximal, characteristic, complemented
9#63451⋊C3C211yesmaximal, characteristic, complemented
10#63448⋊C3C211yesmaximal, characteristic, complemented
11#63445⋊C3C211yesmaximal, characteristic, complemented
12#63441⋊C3C211yesmaximal, characteristic, complemented
13#63440⋊C3C211yesmaximal, characteristic, complemented
14#11721396C211yesmaximal, characteristic, complemented
15#63432⋊C3C211yesmaximal, characteristic, complemented
16C3×#5564—31nomaximal
17#10589666C311yesmaximal, characteristic, complemented
18C2×D4×3−1+2C2211yescharacteristic
19C22×C4×3−1+2C2211yescharacteristic
20C22×C4×3−1+2C2211yescharacteristic
21C2×#611⋊C3C2211yescharacteristic
22C2×#611⋊C3C2211yescharacteristic
23C22×3−1+2⋊C4C2211yescharacteristic
24C22×3−1+2⋊C4C2211yescharacteristic
25C2×C4×AGL(1,ℤ/9)C2211yescharacteristic
26C2×3−1+2⋊Q8C2211yescharacteristic
27C4⋊C4×3−1+2C2211yescharacteristic
28C22⋊C4×3−1+2C2211yescharacteristic
29C22⋊C4×3−1+2C2211yescharacteristic
30C42×3−1+2C2211yescharacteristic
31#3676⋊C3C2211yescharacteristic
32#3676⋊C3C2211yescharacteristic
33#3676⋊C3C2211yescharacteristic
34#3676⋊C3C2211yescharacteristic
35(C2×AGL(1,ℤ/9))⋊C4C2211yescharacteristic
36(C2×AGL(1,ℤ/9))⋊C4C2211yescharacteristic
37(C2×AGL(1,ℤ/9))⋊C4C2211yescharacteristic
38(C2×AGL(1,ℤ/9))⋊C4C2211yescharacteristic
39C4⋊(3−1+2⋊C4)C2211yescharacteristic
40C4⋊(3−1+2⋊C4)C2211yescharacteristic
41C4⋊(3−1+2⋊C4)C2211yescharacteristic
42(3−1+2⋊C4)⋊C4C2211yescharacteristic
43(3−1+2⋊C4)⋊C4C2211yescharacteristic
44(3−1+2⋊C4)⋊C4C2211yescharacteristic
45(3−1+2⋊C4)⋊C4C2211yescharacteristic
46(3−1+2⋊C4)⋊C4C2211yescharacteristic
47(3−1+2⋊C4)⋊C4C2211yescharacteristic
48(3−1+2⋊C4)⋊C4C2211yescharacteristic
49(3−1+2⋊C4)⋊C4C2211yescharacteristic
50(3−1+2⋊C4)⋊C4C2211yescharacteristic
51(3−1+2⋊C4)⋊C4C2211yescharacteristic
52C4×3−1+2⋊C4C2211yescharacteristic
53C32×C4×D4D311yescharacteristic
54C3×#939—31no—
55C3×#935—31no—
56C3×#929—31no—
57C3×C4×#67—31no—
58C3×#924—31no—
59C2×C3×Dic3⋊C4—31no—
60C3×#896—31no—
61C3×#889—31no—
62C3×#886—31no—
63C3×#883—31no—
64C3×#879—31no—
65C3×#878—31no—
66C3×#876—31no—
67C3×#870—31no—
68C4×D4×C9—21no—
69C4×D4×C9C2×C311yescharacteristic, complemented
70#63501C2×C311yescharacteristic
71#63497C2×C311yescharacteristic, complemented
72#63491C2×C311yescharacteristic, complemented
73C4×#611C2×C311yescharacteristic, complemented
74#63486C2×C311yescharacteristic, complemented
75C2×Dic9⋊C4C2×C311yescharacteristic, complemented
76#63458C2×C311yescharacteristic, complemented
77#63451C2×C311yescharacteristic, complemented
78#63448C2×C311yescharacteristic, complemented
79#63445C2×C311yescharacteristic, complemented
80#63441C2×C311yescharacteristic, complemented
81#63440C2×C311yescharacteristic, complemented
82#63438C2×C311yescharacteristic, complemented
83#63432C2×C311yescharacteristic, complemented
84C23×3−1+2C2311yescharacteristic
85C23×3−1+2C2311yescharacteristic
86C22×AGL(1,ℤ/9)C2311yescharacteristic
87D4×3−1+2—22no—
88C2×C4×3−1+2—41no—
89C2×C4×3−1+2—41no—
90C2×C4×3−1+2C2311yescharacteristic
91C2×C4×3−1+2C2311yescharacteristic
92C2×C4×3−1+2C2311yescharacteristic
93C2×C4×3−1+2C2311yescharacteristic
94C2×C4×3−1+2C2311yescharacteristic
95#611⋊C3—22no—
96#611⋊C3—41no—
97C2×3−1+2⋊C4—22no—
98C2×3−1+2⋊C4—41no—
99C2×3−1+2⋊C4C2311yescharacteristic
100C2×3−1+2⋊C4C2311yescharacteristic
101C2×3−1+2⋊C4C2311yescharacteristic
102C2×3−1+2⋊C4C2311yescharacteristic
103C2×3−1+2⋊C4C2311yescharacteristic
104C2×3−1+2⋊C4C2311yescharacteristic
105C2×3−1+2⋊C4C2311yescharacteristic
106C4×AGL(1,ℤ/9)—41no—
1073−1+2⋊Q8—41no—
108C3×#539—91no—
109#5564—31no—
110C2×C32×D4C2×D311yescharacteristic
111C22×C32×C4C2×D311yescharacteristic
112C22×C32×C4C2×D311yescharacteristic
113C2×C3×#67—31no—
114C2×C3×#67—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×Dic6—31no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C22⋊C4C2×D311yescharacteristic
121C32×C22⋊C4C2×D311yescharacteristic
122C32×C42C2×D311yescharacteristic
123C3×#217—31no—
124C3×#217—31no—
125C3×#217—31no—
126C3×#217—31no—
127C3×(C2×D3)⋊C4—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×C4×Dic3—31no—
145C2×D4×C9—21no—
146C2×D4×C9C22×C311yescharacteristic
147C22×C4×C9—21no—
148C22×C4×C9—21no—
149C22×C4×C9C22×C311yescharacteristic
150C22×C4×C9C22×C311yescharacteristic
151C2×#611C22×C311yescharacteristic
152C2×#611C22×C311yescharacteristic
153C22×Dic9C22×C311yescharacteristic
154C22×Dic9C22×C311yescharacteristic
155C2×C4×D9C22×C311yescharacteristic
156C2×Dic18C22×C311yescharacteristic
157C9×C4⋊C4—21no—
158C9×C4⋊C4C22×C311yescharacteristic
159C9×C22⋊C4—21no—
160C9×C22⋊C4—21no—
161C9×C22⋊C4C22×C311yescharacteristic
162C9×C22⋊C4C22×C311yescharacteristic
163C42×C9—21no—
164C42×C9C22×C311yescharacteristic
165#3676C22×C311yescharacteristic
166#3676C22×C311yescharacteristic
167#3676C22×C311yescharacteristic
168#3676C22×C311yescharacteristic
169(C2×D9)⋊C4C22×C311yescharacteristic
170(C2×D9)⋊C4C22×C311yescharacteristic
171(C2×D9)⋊C4C22×C311yescharacteristic
172(C2×D9)⋊C4C22×C311yescharacteristic
173C4⋊Dic9C22×C311yescharacteristic
174C4⋊Dic9C22×C311yescharacteristic
175C4⋊Dic9C22×C311yescharacteristic
176Dic9⋊C4C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178Dic9⋊C4C22×C311yescharacteristic
179Dic9⋊C4C22×C311yescharacteristic
180Dic9⋊C4C22×C311yescharacteristic
181Dic9⋊C4C22×C311yescharacteristic
182Dic9⋊C4C22×C311yescharacteristic
183Dic9⋊C4C22×C311yescharacteristic
184Dic9⋊C4C22×C311yescharacteristic
185Dic9⋊C4C22×C311yescharacteristic
186C4×Dic9C22×C311yescharacteristic
187C22×3−1+2—21no—
188C22×3−1+2—21no—
189C22×3−1+2—21no—
190C22×3−1+2—21no—
191C22×3−1+2—21no—
192C22×3−1+2#4112yes—
193C22×3−1+2C2411yescharacteristic
194C2×AGL(1,ℤ/9)—21no—
195C2×AGL(1,ℤ/9)—21no—
196C2×AGL(1,ℤ/9)—21no—
197C4×3−1+2—21no—
198C4×3−1+2—21no—
199C4×3−1+2—21no—
200C4×3−1+2—21no—
201C4×3−1+2—21no—
2023−1+2⋊C4—21no—
2033−1+2⋊C4—21no—
2043−1+2⋊C4—21no—
2053−1+2⋊C4—21no—
2063−1+2⋊C4—21no—
2073−1+2⋊C4—21no—
2083−1+2⋊C4—21no—
209C3×#126—91no—
210C3×#126—91no—
211C3×#125—91no—
212C3×#125—91no—
213C3×#123—91no—
214C3×#123—91no—
215C3×#123—91no—
216C3×#123—91no—
217C3×C22⋊Q8—91no—
218C3×C22⋊Q8—91no—
219C3×C22⋊Q8—91no—
220C3×#121—91no—
221C3×C4×D4—31no—
222C3×C4×D4—91no—
223C3×C4×D4C3×D311yescharacteristic
224C2×C3×C4⋊C4—91no—
225#939—31no—
226#935—31no—
227#929—31no—
228C4×#67—31no—
229#924—31no—
230C2×Dic3⋊C4—31no—
231#896—31no—
232#889—31no—
233#886—31no—
234#883—31no—
235#879—31no—
236#878—31no—
237#876—31no—
238#870—31no—
239C23×C32C22×D311yescharacteristic
240C23×C32C22×D311yescharacteristic
241C22×C3×D3—31no—
242C32×D4—22no—
243C2×C32×C4—41no—
244C2×C32×C4—41no—
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C3×#67—62no—
251C3×#67—121no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—62no—
260C2×C3×Dic3—121no—
261C3×C4×D3—121no—
262C3×Dic6—121no—
263C23×C9—21no—
264C23×C9—21no—
265C23×C9C23×C311yescharacteristic
266C23×C9C23×C311yescharacteristic
267C22×D9C23×C311yescharacteristic
268D4×C9—24no—
269D4×C9—22no—
270C2×C4×C9—21no—
271C2×C4×C9—21no—
272C2×C4×C9—21no—
273C2×C4×C9—21no—
274C2×C4×C9—21no—
275C2×C4×C9—41no—
276C2×C4×C9—41no—
277C2×C4×C9—42no—
278C2×C4×C9—42no—
279C2×C4×C9C23×C311yescharacteristic
280C2×C4×C9C23×C311yescharacteristic
281C2×C4×C9C23×C311yescharacteristic
282C2×C4×C9C23×C311yescharacteristic
283C2×C4×C9C23×C311yescharacteristic
284#611—22no—
285#611—41no—
286C2×Dic9—22no—
287C2×Dic9—41no—
288C2×Dic9C23×C311yescharacteristic
289C2×Dic9C23×C311yescharacteristic
290C2×Dic9C23×C311yescharacteristic
291C2×Dic9C23×C311yescharacteristic
292C2×Dic9C23×C311yescharacteristic
293C2×Dic9C23×C311yescharacteristic
294C2×Dic9C23×C311yescharacteristic
295C4×D9—41no—
296Dic18—41no—
297#539—91noSylow
298C2×3−1+2—22no—
299C2×3−1+2—41no—
300C2×3−1+2C2×#4111yescharacteristic
301C2×3−1+2H(5,𝔽2)11yescharacteristic
302C2×3−1+22−1+411yescharacteristic
303AGL(1,ℤ/9)—41no—
304C2×C3×Q8—91no—
305C2×C3×D4—31no—
306C2×C3×D4—91no—
307C2×C3×D4—91no—
308C2×C3×D4C2×C3×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—91no—
312C22×C3×C4—91no—
313C22×C3×C4—91no—
314C22×C3×C4C2×C3×D311yescharacteristic
315C22×C3×C4C2×C3×D311yescharacteristic
316C2×#67—31no—
317C2×#67—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C2×C4×D3—31no—
321C2×Dic6—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—91no—
324C3×C4⋊C4—91no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4C2×C3×D311yescharacteristic
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—91no—
340C3×C22⋊C4—91no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4C2×C3×D311yescharacteristic
348C3×C22⋊C4C2×C3×D311yescharacteristic
349C3×C42—31no—
350C3×C42—91no—
351C3×C42C2×C3×D311yescharacteristic
352#217—31no—
353#217—31no—
354#217—31no—
355#217—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—31no—
373C4×Dic3—31no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32#23512yes—
380C22×C32C23×D311yescharacteristic
381C2×C3×D3—61no—
382C2×C3×D3—61no—
383C2×C3×D3—61no—
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—21no—
389C3×Dic3—61no—
390C3×Dic3—61no—
391C3×Dic3—61no—
392C3×Dic3—61no—
393C3×Dic3—61no—
394C3×Dic3—61no—
395C3×Dic3—61no—
396C22×C9—21no—
397C22×C9—21no—
398C22×C9—22no—
399C22×C9—21no—
400C22×C9—21no—
401C22×C9—21no—
402C22×C9—21no—
403C22×C9—22no—
404C22×C9—41no—
405C22×C9—41no—
406C22×C9—41no—
407C22×C9—41no—
408C22×C9C3×#4112yes—
409C22×C9C24×C311yescharacteristic
410C2×D9—21no—
411C2×D9—21no—
412C2×D9—21no—
413C4×C9—22no—
414C4×C9—22no—
415C4×C9—21no—
416C4×C9—21no—
417C4×C9—21no—
418C4×C9—21no—
419C4×C9—21no—
420C4×C9—41no—
421C4×C9—41no—
422C4×C9—41no—
423Dic9—21no—
424Dic9—21no—
425Dic9—21no—
426Dic9—21no—
427Dic9—21no—
428Dic9—21no—
429Dic9—21no—
430#126—91no—
431#126—91no—
432#125—91no—
433#125—91no—
434#123—91no—
435#123—91no—
436#123—91no—
437#123—91no—
438C22⋊Q8—91no—
439C22⋊Q8—91no—
440C22⋊Q8—91no—
441#121—91no—
442C4×D4—91no—
443C4×D4AGL(1,ℤ/9)11yescharacteristic, complemented
444C2×C4⋊C4—91no—
4453−1+2#53911yescharacteristic, complemented, Sylow
446C23×C3—31no—
447C23×C3—31no—
448C23×C3—91no—
449C23×C3C22×C3×D311yescharacteristic
450C23×C3C22×C3×D311yescharacteristic
451C22×D3—31no—
452C3×Q8—361no—
453C3×D4—22no—
454C3×D4—62no—
455C3×D4—182no—
456C3×D4—361no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—91no—
465C2×C3×C4—91no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—91no—
470C2×C3×C4—91no—
471C2×C3×C4—121no—
472C2×C3×C4—121no—
473C2×C3×C4—182no—
474C2×C3×C4—361no—
475C2×C3×C4—361no—
476C2×C3×C4C22×C3×D311yescharacteristic
477C2×C3×C4C22×C3×D311yescharacteristic
478C2×C3×C4C22×C3×D311yescharacteristic
479C2×C3×C4C22×C3×D311yescharacteristic
480C2×C3×C4C22×C3×D311yescharacteristic
481#67—62no—
482#67—121no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—62no—
491C2×Dic3—121no—
492C4×D3—121no—
493Dic6—121no—
494C2×C32—22no—
495C2×C32—41no—
496C2×C32C2×#23511yescharacteristic
497C2×C32#100411yescharacteristic
498C2×C32#101011yescharacteristic
499C3×D3—121no—
500C2×C9—22no—
501C2×C9—21no—
502C2×C9—21no—
503C2×C9—21no—
504C2×C9—42no—
505C2×C9—42no—
506C2×C9—41no—
507C2×C9C2×C3×#4111yescharacteristic
508C2×C9C3×H(5,𝔽2)11yescharacteristic
509C2×C9C3×2−1+411yescharacteristic
510D9—41no—
511C2×Q8—91no—
512C2×D4—91no—
513C2×D4—91no—
514C2×D4C2×AGL(1,ℤ/9)11yescharacteristic
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
519C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
520C4⋊C4—91no—
521C4⋊C4—91no—
522C4⋊C4—91no—
523C4⋊C4—91no—
524C4⋊C4—91no—
525C4⋊C4—91no—
526C4⋊C4—91no—
527C4⋊C4—91no—
528C4⋊C4—91no—
529C4⋊C4—91no—
530C4⋊C4—91no—
531C4⋊C4—91no—
532C4⋊C4—91no—
533C4⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
534C22⋊C4—91no—
535C22⋊C4—91no—
536C22⋊C4—91no—
537C22⋊C4—91no—
538C22⋊C4—91no—
539C22⋊C4—91no—
540C22⋊C4—91no—
541C22⋊C4—91no—
542C22⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
543C22⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
544C42—91no—
545C42C2×AGL(1,ℤ/9)11yescharacteristic
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—31no—
552C22×C3—32no—
553C22×C3—61no—
554C22×C3—61no—
555C22×C3—61no—
556C22×C3—61no—
557C22×C3—61no—
558C22×C3—181no—
559C22×C3—181no—
560C22×C3—181no—
561C22×C3C3×#23512yes—
562C22×C3C23×C3×D311yescharacteristic
563C2×D3—61no—
564C2×D3—61no—
565C2×D3—61no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—61no—
572C3×C4—61no—
573C3×C4—61no—
574C3×C4—61no—
575C3×C4—61no—
576C3×C4—181no—
577C3×C4—181no—
578C3×C4—181no—
579C3×C4—181no—
580C3×C4—181no—
581C3×C4—181no—
582C3×C4—181no—
583Dic3—61no—
584Dic3—61no—
585Dic3—61no—
586Dic3—61no—
587Dic3—61no—
588Dic3—61no—
589Dic3—61no—
590C32#556411yescharacteristic
591C9—21no—
592C9C3×#53911yescharacteristic, complemented
593C23—91no—
594C23C22×AGL(1,ℤ/9)11yescharacteristic
595C23C22×AGL(1,ℤ/9)11yescharacteristic
596Q8—361no—
597D4—22no—
598D4—182no—
599D4—361no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—91no—
603C2×C4—91no—
604C2×C4—91no—
605C2×C4—91no—
606C2×C4—91no—
607C2×C4—91no—
608C2×C4—91no—
609C2×C4—182no—
610C2×C4—361no—
611C2×C4—361no—
612C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
613C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
614C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
615C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
616C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
617C2×C3—22no—
618C2×C3—31no—
619C2×C3—31no—
620C2×C3—31no—
621C2×C3—41no—
622C2×C3—62no—
623C2×C3—121no—
624C2×C3—361no—
625C2×C3C2×C3×#23511yescharacteristic
626C2×C3C3×#100411yescharacteristic
627C2×C3C3×#101011yescharacteristic
628D3—121no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—181no—
635C22—181no—
636C22—181no—
637C22#3697⋊C312yes—
638C22C23×AGL(1,ℤ/9)11yescharacteristic
639C4—21no—
640C4—21no—
641C4—21no—
642C4—21no—
643C4—21no—
644C4—181no—
645C4—181no—
646C4—181no—
647C4—181no—
648C4—181no—
649C4—181no—
650C4—181no—
651C3—31no—
652C3C3×#556411yescharacteristic
653C2—22no—
654C2—41no—
655C2—361no—
656C2C2×#3697⋊C311yescharacteristic
657C2#63710⋊C311yescharacteristic
658C2#1172264211yescharacteristic
subgroupG/H
centerC22C23×AGL(1,ℤ/9)
commutator, cosocleC22×C9C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC4×D4×3−1+2C2
prime radical#63501⋊C3C2
hypercenterC4×D4AGL(1,ℤ/9)
hypocenterC9C3×#539
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×D4×3−1+2C2semidirect
3. #63497⋊C3C2semidirect
4. #63491⋊C3C2semidirect
5. C4×#611⋊C3C2semidirect
6. #63486⋊C3C2semidirect
7. C2×(3−1+2⋊C4)⋊C4C2semidirect
8. #63458⋊C3C2semidirect
9. #63451⋊C3C2semidirect
10. #63448⋊C3C2semidirect
11. #63445⋊C3C2semidirect
12. #63441⋊C3C2semidirect
13. #63440⋊C3C2semidirect
14. #11721396C2semidirect
15. #63432⋊C3C2semidirect
17. #10589666C3semidirect
69. C4×D4×C9C2×C3semidirect
71. #63497C2×C3semidirect
72. #63491C2×C3semidirect
73. C4×#611C2×C3semidirect
74. #63486C2×C3semidirect
75. C2×Dic9⋊C4C2×C3semidirect
76. #63458C2×C3semidirect
77. #63451C2×C3semidirect
78. #63448C2×C3semidirect
79. #63445C2×C3semidirect
80. #63441C2×C3semidirect
81. #63440C2×C3semidirect
82. #63438C2×C3semidirect
83. #63432C2×C3semidirect
443. C4×D4AGL(1,ℤ/9)semidirect
445. 3−1+2#539semidirect
592. C9C3×#539semidirect

Maximal subgroups

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

subgroupindex
C4×D4×3−1+22
#63501⋊C32
#63497⋊C32
#63491⋊C32
C4×#611⋊C32
#63486⋊C32
C2×(3−1+2⋊C4)⋊C42
#63458⋊C32
#63451⋊C32
#63448⋊C32
#63445⋊C32
#63441⋊C32
#63440⋊C32
#117213962
#63432⋊C32
C3×#55643
#105896663