Finite Group Databasebeta

← C3×#10589771 #13153076

Subgroups — C3×#10589771 #13153076

Order 1728.

724 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#124C211yesmaximal, characteristic, complemented
2C3×#63508C211yesmaximal, characteristic, complemented
3C3×#63506C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic
5C3×#63497C211yesmaximal, characteristic, complemented
6C3×#63447C211yesmaximal, characteristic, complemented
7C3×#63447C211yesmaximal, characteristic, complemented
8C3×#63445C211yesmaximal, characteristic, complemented
9C3×#611⋊C4C211yesmaximal, characteristic, complemented
10C3×#63441C211yesmaximal, characteristic, complemented
11C3×#63440C211yesmaximal, characteristic, complemented
12C3×#63440C211yesmaximal, characteristic, complemented
13C3×#63439C211yesmaximal, characteristic, complemented
14C3×#63438C211yesmaximal, characteristic, complemented
15C3×C4×Dic18C211yesmaximal, characteristic, complemented
16C3×#5669—31nomaximal
17#10589771C311yesmaximal, characteristic, direct product factor
18C2×C3×Q8×C9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×Dic18C2211yescharacteristic
26C2×C3×Dic18C2211yescharacteristic
27C3×C9×C22⋊C4C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic
29C3×C9×C22⋊C4C2211yescharacteristic
30C3×C9×C22⋊C4C2211yescharacteristic
31C3×C42×C9C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C3×#3676C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C3×#3676C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×C4⋊Dic9C2211yescharacteristic
41C3×C4⋊Dic9C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×C4×Dic9C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#124D311yescharacteristic
54C3×#946—31no—
55C3×#944—31no—
56C3×#939—31no—
57C3×#935—31no—
58C3×#885—31no—
59C3×#885—31no—
60C3×#883—31no—
61C3×#67⋊C4—31no—
62C3×#879—31no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#877—31no—
66C3×#876—31no—
67C3×C4×Dic6—31no—
68C9×#124—21no—
69C9×#124C2×C311yescharacteristic, complemented
70#63508C2×C311yescharacteristic, complemented
71#63506C2×C311yescharacteristic, complemented
72#63501C2×C311yescharacteristic
73#63497C2×C311yescharacteristic, complemented
74#63447C2×C311yescharacteristic, complemented
75#63447C2×C311yescharacteristic, complemented
76#63445C2×C311yescharacteristic, complemented
77#611⋊C4C2×C311yescharacteristic, complemented
78#63441C2×C311yescharacteristic, complemented
79#63440C2×C311yescharacteristic, complemented
80#63440C2×C311yescharacteristic, complemented
81#63439C2×C311yescharacteristic, complemented
82#63438C2×C311yescharacteristic, complemented
83C4×Dic18C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C3×Q8×C9—41no—
88C3×D4×C9—41no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C3×#611—22no—
95C3×#611—41no—
96C2×C3×Dic9—22no—
97C2×C3×Dic9—41no—
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×C4×D9—41no—
106C3×Dic18—22no—
107C3×Dic18—41no—
108C3×#542—91no—
109#5669—31no—
110C2×C32×Q8C2×D311yescharacteristic
111C2×C32×D4C2×D311yescharacteristic
112C2×C3×#67—31no—
113C2×C3×#67—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C32×C22⋊C4C2×D311yescharacteristic
120C32×C22⋊C4C2×D311yescharacteristic
121C32×C22⋊C4C2×D311yescharacteristic
122C32×C22⋊C4C2×D311yescharacteristic
123C32×C42C2×D311yescharacteristic
124C3×#217—31no—
125C3×#217—31no—
126C3×#217—31no—
127C3×#217—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—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×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C2×Q8×C9—21no—
146C2×Q8×C9C22×C311yescharacteristic
147C2×D4×C9—21no—
148C2×D4×C9C22×C311yescharacteristic
149C2×#611C22×C311yescharacteristic
150C2×#611C22×C311yescharacteristic
151C22×Dic9C22×C311yescharacteristic
152C22×Dic9C22×C311yescharacteristic
153C2×C4×D9C22×C311yescharacteristic
154C2×Dic18C22×C311yescharacteristic
155C2×Dic18C22×C311yescharacteristic
156C9×C22⋊C4—21no—
157C9×C22⋊C4—21no—
158C9×C22⋊C4—21no—
159C9×C22⋊C4—21no—
160C9×C22⋊C4C22×C311yescharacteristic
161C9×C22⋊C4C22×C311yescharacteristic
162C9×C22⋊C4C22×C311yescharacteristic
163C9×C22⋊C4C22×C311yescharacteristic
164C42×C9—21no—
165C42×C9C22×C311yescharacteristic
166#3676C22×C311yescharacteristic
167#3676C22×C311yescharacteristic
168#3676C22×C311yescharacteristic
169#3676C22×C311yescharacteristic
170(C2×D9)⋊C4C22×C311yescharacteristic
171(C2×D9)⋊C4C22×C311yescharacteristic
172(C2×D9)⋊C4C22×C311yescharacteristic
173(C2×D9)⋊C4C22×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
184C4×Dic9C22×C311yescharacteristic
185C4×Dic9C22×C311yescharacteristic
186C4×Dic9C22×C311yescharacteristic
187C22×C3×C9—21no—
188C22×C3×C9—21no—
189C22×C3×C9—21no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9C2411yescharacteristic
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9—21no—
197C3×C4×C9—21no—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3×C4×C9—21no—
201C3×C4×C9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×Dic9—21no—
205C3×Dic9—21no—
206C3×Dic9—21no—
207C3×Dic9—21no—
208C3×Dic9#4112yes—
209C3×C4⋊Q8—91no—
210C3×#126—91no—
211C3×#126—91no—
212C3×#124—21no—
213C3×#124—91no—
214C3×#124—91no—
215C3×#124D911yescharacteristic, complemented
216C3×#124C3×D311yescharacteristic
217C3×#123—91no—
218C3×#123—91no—
219C3×C22⋊Q8—91no—
220C3×C22⋊Q8—91no—
221C3×C22⋊Q8—91no—
222C3×#121—91no—
223C3×C4×Q8—91no—
224C3×C4×D4—91no—
225C3×#117—91no—
226#946—31no—
227#944—31no—
228#939—31no—
229#935—31no—
230#885—31no—
231#885—31no—
232#883—31no—
233#67⋊C4—31no—
234#879—31no—
235#878—31no—
236#878—31no—
237#877—31no—
238#876—31no—
239C4×Dic6—31no—
240C23×C32C22×D311yescharacteristic
241C23×C32C22×D311yescharacteristic
242C22×C3×D3—31no—
243C32×Q8—41no—
244C32×D4—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—62no—
263C3×Dic6—121no—
264C23×C9—21no—
265C23×C9—21no—
266C23×C9C23×C311yescharacteristic
267C23×C9C23×C311yescharacteristic
268C22×D9C23×C311yescharacteristic
269Q8×C9—41no—
270Q8×C9—42no—
271D4×C9—41no—
272D4×C9—42no—
273C2×C4×C9—21no—
274C2×C4×C9—21no—
275C2×C4×C9—21no—
276C2×C4×C9—21no—
277C2×C4×C9—21no—
278C2×C4×C9C23×C311yescharacteristic
279C2×C4×C9C23×C311yescharacteristic
280C2×C4×C9C23×C311yescharacteristic
281C2×C4×C9C23×C311yescharacteristic
282C2×C4×C9C23×C311yescharacteristic
283#611—22no—
284#611—41no—
285C2×Dic9—22no—
286C2×Dic9—41no—
287C2×Dic9C23×C311yescharacteristic
288C2×Dic9C23×C311yescharacteristic
289C2×Dic9C23×C311yescharacteristic
290C2×Dic9C23×C311yescharacteristic
291C2×Dic9C23×C311yescharacteristic
292C2×Dic9C23×C311yescharacteristic
293C2×Dic9C23×C311yescharacteristic
294C4×D9—41no—
295Dic18—22no—
296Dic18—41no—
297#542—91noSylow
298C2×C3×C9—41no—
299C2×C3×C9—41no—
300C2×C3×C9C2×#4111yescharacteristic
301C2×C3×C9H(5,𝔽2)11yescharacteristic
302C2×C3×C92−1+411yescharacteristic
303C3×D9—41no—
304C2×C3×Q8—21no—
305C2×C3×Q8—91no—
306C2×C3×Q8—91no—
307C2×C3×Q8C2×D911yescharacteristic
308C2×C3×Q8C2×C3×D311yescharacteristic
309C2×C3×D4—21no—
310C2×C3×D4—91no—
311C2×C3×D4—91no—
312C2×C3×D4C2×D911yescharacteristic
313C2×C3×D4C2×C3×D311yescharacteristic
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×C3×C4—91no—
317C2×#67—31no—
318C2×#67—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C2×C4×D3—31no—
322C2×Dic6—31no—
323C2×Dic6—31no—
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×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—91no—
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⋊C4C2×D911yescharacteristic
347C3×C22⋊C4C2×D911yescharacteristic
348C3×C22⋊C4C2×D911yescharacteristic
349C3×C22⋊C4C2×D911yescharacteristic
350C3×C22⋊C4C2×C3×D311yescharacteristic
351C3×C22⋊C4C2×C3×D311yescharacteristic
352C3×C22⋊C4C2×C3×D311yescharacteristic
353C3×C22⋊C4C2×C3×D311yescharacteristic
354C3×C42—21no—
355C3×C42—91no—
356C3×C42—91no—
357C3×C42—91no—
358C3×C42C2×D911yescharacteristic
359C3×C42C2×C3×D311yescharacteristic
360#217—31no—
361#217—31no—
362#217—31no—
363#217—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370Dic3⋊C4—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32C23×D311yescharacteristic
388C2×C3×D3—61no—
389C2×C3×D3—61no—
390C2×C3×D3—61no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C3×Dic3—32no—
397C3×Dic3—61no—
398C3×Dic3—61no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C3×Dic3—61no—
403C22×C9—21no—
404C22×C9—21no—
405C22×C9—21no—
406C22×C9—21no—
407C22×C9—21no—
408C22×C9—21no—
409C22×C9—21no—
410C22×C9—41no—
411C22×C9—41no—
412C22×C9—41no—
413C22×C9—41no—
414C22×C9—41no—
415C22×C9—41no—
416C22×C9C24×C311yescharacteristic
417C2×D9—21no—
418C2×D9—21no—
419C2×D9—21no—
420C4×C9—22no—
421C4×C9—21no—
422C4×C9—21no—
423C4×C9—21no—
424C4×C9—21no—
425C4×C9—21no—
426C4×C9—41no—
427C4×C9—41no—
428C4×C9—41no—
429C4×C9—41no—
430Dic9—21no—
431Dic9—21no—
432Dic9—21no—
433Dic9—21no—
434Dic9—21no—
435Dic9—21no—
436Dic9C3×#4112yes—
437C4⋊Q8—91no—
438#126—91no—
439#126—91no—
440#124—91no—
441#124—91no—
442#124C3×D911yescharacteristic, complemented
443#123—91no—
444#123—91no—
445C22⋊Q8—91no—
446C22⋊Q8—91no—
447C22⋊Q8—91no—
448#121—91no—
449C4×Q8—91no—
450C4×D4—91no—
451#117—91no—
452C3×C9#54211yescharacteristic, complemented, Sylow
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—91no—
456C23×C3C22×D911yescharacteristic
457C23×C3C22×D911yescharacteristic
458C23×C3C22×C3×D311yescharacteristic
459C23×C3C22×C3×D311yescharacteristic
460C22×D3—31no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—42no—
464C3×Q8—182no—
465C3×Q8—361no—
466C3×D4—41no—
467C3×D4—41no—
468C3×D4—42no—
469C3×D4—182no—
470C3×D4—361no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—91no—
477C2×C3×C4—91no—
478C2×C3×C4—91no—
479C2×C3×C4—91no—
480C2×C3×C4—91no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—182no—
484C2×C3×C4—361no—
485C2×C3×C4—361no—
486C2×C3×C4C22×D911yescharacteristic
487C2×C3×C4C22×D911yescharacteristic
488C2×C3×C4C22×D911yescharacteristic
489C2×C3×C4C22×D911yescharacteristic
490C2×C3×C4C22×D911yescharacteristic
491C2×C3×C4C22×C3×D311yescharacteristic
492C2×C3×C4C22×C3×D311yescharacteristic
493C2×C3×C4C22×C3×D311yescharacteristic
494C2×C3×C4C22×C3×D311yescharacteristic
495C2×C3×C4C22×C3×D311yescharacteristic
496#67—62no—
497#67—121no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—62no—
506C2×Dic3—121no—
507C4×D3—121no—
508Dic6—62no—
509Dic6—121no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32#100411yescharacteristic
513C2×C32D3×#4111yescharacteristic
514C2×C32#101011yescharacteristic
515C3×D3—121no—
516C2×C9—21no—
517C2×C9—21no—
518C2×C9—21no—
519C2×C9—41no—
520C2×C9—41no—
521C2×C9—81no—
522C2×C9—81no—
523C2×C9C2×C3×#4111yescharacteristic
524C2×C9C3×H(5,𝔽2)11yescharacteristic
525C2×C9C3×2−1+411yescharacteristic
526D9—41no—
527C2×Q8—91no—
528C2×Q8—91no—
529C2×Q8C2×C3×D911yescharacteristic
530C2×D4—91no—
531C2×D4—91no—
532C2×D4C2×C3×D911yescharacteristic
533C22×C4—91no—
534C22×C4—91no—
535C22×C4—91no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—91no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—91no—
544C4⋊C4—91no—
545C4⋊C4—91no—
546C22⋊C4—91no—
547C22⋊C4—91no—
548C22⋊C4—91no—
549C22⋊C4—91no—
550C22⋊C4—91no—
551C22⋊C4—91no—
552C22⋊C4—91no—
553C22⋊C4—91no—
554C22⋊C4C2×C3×D911yescharacteristic
555C22⋊C4C2×C3×D911yescharacteristic
556C22⋊C4C2×C3×D911yescharacteristic
557C22⋊C4C2×C3×D911yescharacteristic
558C42—91no—
559C42—91no—
560C42—91no—
561C42C2×C3×D911yescharacteristic
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—181no—
582C22×C3—181no—
583C22×C3—181no—
584C22×C3C23×D911yescharacteristic
585C22×C3C23×C3×D311yescharacteristic
586C2×D3—61no—
587C2×D3—61no—
588C2×D3—61no—
589C3×C4—22no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—92no—
605C3×C4—181no—
606C3×C4—181no—
607C3×C4—181no—
608C3×C4—181no—
609C3×C4—181no—
610C3×C4—181no—
611Dic3—32no—
612Dic3—61no—
613Dic3—61no—
614Dic3—61no—
615Dic3—61no—
616Dic3—61no—
617Dic3—61no—
618C32#566911yescharacteristic
619C9—21no—
620C9C3×#54211yescharacteristic, complemented
621C23—91no—
622C23C22×C3×D911yescharacteristic
623C23C22×C3×D911yescharacteristic
624Q8—41no—
625Q8—182no—
626Q8—361no—
627D4—41no—
628D4—182no—
629D4—361no—
630C2×C4—91no—
631C2×C4—91no—
632C2×C4—91no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—91no—
636C2×C4—91no—
637C2×C4—182no—
638C2×C4—361no—
639C2×C4—361no—
640C2×C4C22×C3×D911yescharacteristic
641C2×C4C22×C3×D911yescharacteristic
642C2×C4C22×C3×D911yescharacteristic
643C2×C4C22×C3×D911yescharacteristic
644C2×C4C22×C3×D911yescharacteristic
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—41no—
649C2×C3—41no—
650C2×C3—41no—
651C2×C3—41no—
652C2×C3—81no—
653C2×C3—81no—
654C2×C3—361no—
655C2×C3#6371011yescharacteristic
656C2×C3#41×D911yescharacteristic
657C2×C3#6371611yescharacteristic
658C2×C3C3×#100411yescharacteristic
659C2×C3C3×D3×#4111yescharacteristic
660C2×C3C3×#101011yescharacteristic
661D3—121no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—181no—
669C22—181no—
670C22—181no—
671C22C23×C3×D911yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—92no—
678C4—181no—
679C4—181no—
680C4—181no—
681C4—181no—
682C4—181no—
683C4—181no—
684C3—21no—
685C3#1058977111yescharacteristic, direct product factor
686C3C3×#566911yescharacteristic
687C2—41no—
688C2—41no—
689C2—361no—
690C2C3×#6371011yescharacteristic
691C2C3×#41×D911yescharacteristic
692C2C3×#6371611yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#124C2
socleC22×C32C23×D3
prime radicalC3×#63501C2
hypercenterC3×#124D9
hypocenterC9C3×#542
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#124

Complements

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

NH ≅ G/Ntype
1. C3×C9×#124C2semidirect
2. C3×#63508C2semidirect
3. C3×#63506C2semidirect
5. C3×#63497C2semidirect
6. C3×#63447C2semidirect
7. C3×#63447C2semidirect
8. C3×#63445C2semidirect
9. C3×#611⋊C4C2semidirect
10. C3×#63441C2semidirect
11. C3×#63440C2semidirect
12. C3×#63440C2semidirect
13. C3×#63439C2semidirect
14. C3×#63438C2semidirect
15. C3×C4×Dic18C2semidirect
17. #10589771C3direct (N × H)
69. C9×#124C2×C3semidirect
70. #63508C2×C3semidirect
71. #63506C2×C3semidirect
73. #63497C2×C3semidirect
74. #63447C2×C3semidirect
75. #63447C2×C3semidirect
76. #63445C2×C3semidirect
77. #611⋊C4C2×C3semidirect
78. #63441C2×C3semidirect
79. #63440C2×C3semidirect
80. #63440C2×C3semidirect
81. #63439C2×C3semidirect
82. #63438C2×C3semidirect
83. C4×Dic18C2×C3semidirect
215. C3×#124D9semidirect
442. #124C3×D9semidirect
452. C3×C9#542semidirect
620. C9C3×#542semidirect
685. C3#10589771direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1242
C3×#635082
C3×#635062
C3×#635012
C3×#634972
C3×#634472
C3×#634452
C3×#611⋊C42
C3×#634412
C3×#634402
C3×#634392
C3×#634382
C3×C4×Dic182
C3×#56693
#105897713