Finite Group Databasebeta

← C3×#10589630 #13152489

Subgroups — C3×#10589630 #13152489

Order 1728.

778 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#117C211yesmaximal, characteristic, complemented
2C3×C4×#611C211yesmaximal, characteristic, complemented
3C3×C4×#611C211yesmaximal, characteristic, complemented
4C3×#63460C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6C3×#63456C211yesmaximal, characteristic, complemented
7C3×#63451C211yesmaximal, characteristic, complemented
8C3×#63447C211yesmaximal, characteristic, complemented
9C3×#63446C211yesmaximal, characteristic
10C3×#63445C211yesmaximal, characteristic, complemented
11C3×#63441C211yesmaximal, characteristic, complemented
12C3×C4×D36C211yesmaximal, characteristic, complemented
13C3×#63434C211yesmaximal, characteristic, complemented
14C3×C42×D9C211yesmaximal, characteristic, complemented
15C3×C4×Dic18C211yesmaximal, characteristic, complemented
16C3×#5528—31nomaximal
17#10589630C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×C9C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×C3×Dic18C2211yescharacteristic
27C3×C9×C4⋊C4C2211yescharacteristic
28C3×C9×C4⋊C4C2211yescharacteristic
29C3×C9×C22⋊C4C2211yescharacteristic
30C3×C9×C22⋊C4C2211yescharacteristic
31C3×C42×C9C2211yescharacteristic
32C3×C42×C9C2211yescharacteristic
33C3×#3676C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×C4⋊Dic9C2211yescharacteristic
42C3×C4⋊Dic9C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×C4×Dic9C2211yescharacteristic
50C3×C4×Dic9C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#117D311yescharacteristic
54C3×C4×#67—31no—
55C3×C4×#67—31no—
56C3×#898—31no—
57C3×#896—31no—
58C3×#894—31no—
59C3×#889—31no—
60C3×#885—31no—
61C3×#884—31no—
62C3×#883—31no—
63C3×#879—31no—
64C3×C4×D12—31no—
65C3×#872—31no—
66C3×C42×D3—31no—
67C3×C4×Dic6—31no—
68C9×#117—21no—
69C9×#117C2×C311yescharacteristic, complemented
70C4×#611C2×C311yescharacteristic, complemented
71C4×#611C2×C311yescharacteristic, complemented
72#63460C2×C311yescharacteristic, complemented
73#63458C2×C311yescharacteristic, complemented
74#63456C2×C311yescharacteristic, complemented
75#63451C2×C311yescharacteristic, complemented
76#63447C2×C311yescharacteristic, complemented
77#63446C2×C311yescharacteristic
78#63445C2×C311yescharacteristic, complemented
79#63441C2×C311yescharacteristic, complemented
80C4×D36C2×C311yescharacteristic, complemented
81#63434C2×C311yescharacteristic, complemented
82C42×D9C2×C311yescharacteristic, complemented
83C4×Dic18C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×C3×C4×C9—22no—
88C2×C3×C4×C9C2311yescharacteristic
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—22no—
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C3×D36—22no—
103C3×C4×D9—22no—
104C3×C4×D9—22no—
105C3×C4×D9—22no—
106C3×C4×D9—22no—
107C3×Dic18—22no—
108C3×#529—91no—
109#5528—31no—
110C22×C32×C4C2×D311yescharacteristic
111C2×C3×#67—31no—
112C2×C3×#67—31no—
113C2×C3×D12—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×Dic6—31no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C22⋊C4C2×D311yescharacteristic
122C32×C22⋊C4C2×D311yescharacteristic
123C32×C42C2×D311yescharacteristic
124C32×C42C2×D311yescharacteristic
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×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—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×C4×Dic3—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C22×C4×C9—21no—
146C22×C4×C9C22×C311yescharacteristic
147C2×#611C22×C311yescharacteristic
148C2×#611C22×C311yescharacteristic
149C2×D36C22×C311yescharacteristic
150C2×C4×D9C22×C311yescharacteristic
151C2×C4×D9C22×C311yescharacteristic
152C2×C4×D9C22×C311yescharacteristic
153C2×C4×D9C22×C311yescharacteristic
154C2×Dic18C22×C311yescharacteristic
155C9×C4⋊C4—21no—
156C9×C4⋊C4—21no—
157C9×C4⋊C4C22×C311yescharacteristic
158C9×C4⋊C4C22×C311yescharacteristic
159C9×C22⋊C4—21no—
160C9×C22⋊C4—21no—
161C9×C22⋊C4C22×C311yescharacteristic
162C9×C22⋊C4C22×C311yescharacteristic
163C42×C9—21no—
164C42×C9—21no—
165C42×C9C22×C311yescharacteristic
166C42×C9C22×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
173(C2×D9)⋊C4C22×C311yescharacteristic
174(C2×D9)⋊C4C22×C311yescharacteristic
175C4⋊Dic9C22×C311yescharacteristic
176C4⋊Dic9C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178Dic9⋊C4C22×C311yescharacteristic
179Dic9⋊C4C22×C311yescharacteristic
180Dic9⋊C4C22×C311yescharacteristic
181Dic9⋊C4C22×C311yescharacteristic
182Dic9⋊C4C22×C311yescharacteristic
183C4×Dic9C22×C311yescharacteristic
184C4×Dic9C22×C311yescharacteristic
185C4×Dic9C22×C311yescharacteristic
186C4×Dic9C22×C311yescharacteristic
187C22×C3×C9—21no—
188C22×C3×C9—21no—
189C22×C3×C9—21no—
190C22×C3×C9C2411yescharacteristic
191C2×C3×D9—21no—
192C2×C3×D9—21no—
193C2×C3×D9—21no—
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9#4112yes—
197C3×C4×C9—21no—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3×C4×C9—21no—
201C3×C4×C9—21no—
202C3×C4×C9#4112yes—
203C3×Dic9—21no—
204C3×Dic9—21no—
205C3×Dic9—21no—
206C3×Dic9—21no—
207C3×Dic9—21no—
208C3×Dic9#4112yes—
209C3×#126—91no—
210C3×#126—91no—
211C3×#125—91no—
212C3×#124—91no—
213C3×#123—91no—
214C3×#123—91no—
215C3×C22⋊Q8—91no—
216C3×#121—91no—
217C3×C4×Q8—91no—
218C3×C4×D4—91no—
219C3×C4×D4—91no—
220C3×C4×D4—91no—
221C3×#117—21no—
222C3×#117—91no—
223C3×#117D911yescharacteristic, complemented
224C3×#117C3×D311yescharacteristic
225C2×C3×C42—91no—
226C4×#67—31no—
227C4×#67—31no—
228#898—31no—
229#896—31no—
230#894—31no—
231#889—31no—
232#885—31no—
233#884—31no—
234#883—31no—
235#879—31no—
236C4×D12—31no—
237#872—31no—
238C42×D3—31no—
239C4×Dic6—31no—
240C23×C32C22×D311yescharacteristic
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C2×C32×C4—22no—
244C2×C32×C4C22×D311yescharacteristic
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—62no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C3×D12—62no—
259C3×C4×D3—62no—
260C3×C4×D3—62no—
261C3×C4×D3—62no—
262C3×C4×D3—62no—
263C3×Dic6—62no—
264C23×C9—21no—
265C23×C9C23×C311yescharacteristic
266C22×D9C23×C311yescharacteristic
267C22×D9C23×C311yescharacteristic
268C2×C4×C9—24no—
269C2×C4×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—21no—
276C2×C4×C9C23×C311yescharacteristic
277C2×C4×C9C23×C311yescharacteristic
278C2×C4×C9C23×C311yescharacteristic
279C2×C4×C9C23×C311yescharacteristic
280C2×C4×C9C23×C311yescharacteristic
281C2×C4×C9C23×C311yescharacteristic
282#611—22no—
283#611—22no—
284C2×Dic9C23×C311yescharacteristic
285C2×Dic9C23×C311yescharacteristic
286C2×Dic9C23×C311yescharacteristic
287C2×Dic9C23×C311yescharacteristic
288C2×Dic9C23×C311yescharacteristic
289C2×Dic9C23×C311yescharacteristic
290D36—22no—
291C4×D9—22no—
292C4×D9—22no—
293C4×D9—22no—
294C4×D9—22no—
295Dic18—22no—
296#529—91noSylow
297C2×C3×C9—41no—
298C2×C3×C9C2×#4111yescharacteristic
299C2×C3×C9C2×#4111yescharacteristic
300C2×C3×C9C2×#4111yescharacteristic
301C3×D9—22no—
302C3×D9—41no—
303C2×C3×Q8—91no—
304C2×C3×D4—91no—
305C2×C3×D4—91no—
306C2×C3×D4—91no—
307C22×C3×C4—21no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C22×C3×C4C2×D911yescharacteristic
313C22×C3×C4C2×C3×D311yescharacteristic
314C2×#67—31no—
315C2×#67—31no—
316C2×D12—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×Dic6—31no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
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⋊C4C2×D911yescharacteristic
333C3×C4⋊C4C2×D911yescharacteristic
334C3×C4⋊C4C2×C3×D311yescharacteristic
335C3×C4⋊C4C2×C3×D311yescharacteristic
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×C3×D311yescharacteristic
349C3×C22⋊C4C2×C3×D311yescharacteristic
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—91no—
353C3×C42—91no—
354C3×C42—91no—
355C3×C42—91no—
356C3×C42C2×D911yescharacteristic
357C3×C42C2×D911yescharacteristic
358C3×C42C2×C3×D311yescharacteristic
359C3×C42C2×C3×D311yescharacteristic
360#217—31no—
361#217—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—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—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32C23×D311yescharacteristic
384C2×C3×D3—32no—
385C2×C3×D3—61no—
386C2×C3×D3—61no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C2×C3×D3—61no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4#23512yes—
396C3×Dic3—32no—
397C3×Dic3—61no—
398C3×Dic3—61no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C22×C9—22no—
403C22×C9—21no—
404C22×C9—21no—
405C22×C9—21no—
406C22×C9—21no—
407C22×C9—41no—
408C22×C9—41no—
409C22×C9C24×C311yescharacteristic
410C2×D9—21no—
411C2×D9—21no—
412C2×D9—21no—
413C2×D9—21no—
414C2×D9—21no—
415C2×D9C3×#4112yes—
416C4×C9—22no—
417C4×C9—21no—
418C4×C9—21no—
419C4×C9—21no—
420C4×C9—21no—
421C4×C9—21no—
422C4×C9—22no—
423C4×C9—41no—
424C4×C9—41no—
425C4×C9—41no—
426C4×C9—41no—
427C4×C9C3×#4112yes—
428Dic9—21no—
429Dic9—21no—
430Dic9—21no—
431Dic9—21no—
432Dic9—21no—
433Dic9C3×#4112yes—
434#126—91no—
435#126—91no—
436#125—91no—
437#124—91no—
438#123—91no—
439#123—91no—
440C22⋊Q8—91no—
441#121—91no—
442C4×Q8—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446#117—91no—
447#117C3×D911yescharacteristic, complemented
448C2×C42—91no—
449C3×C9#52911yescharacteristic, complemented, Sylow
450C23×C3—21no—
451C23×C3—91no—
452C23×C3—91no—
453C23×C3C22×D911yescharacteristic
454C23×C3C22×C3×D311yescharacteristic
455C22×D3—31no—
456C22×D3—31no—
457C3×Q8—182no—
458C3×D4—182no—
459C3×D4—182no—
460C3×D4—182no—
461C2×C3×C4—24no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—91no—
471C2×C3×C4—91no—
472C2×C3×C4—91no—
473C2×C3×C4—91no—
474C2×C3×C4—91no—
475C2×C3×C4—91no—
476C2×C3×C4—182no—
477C2×C3×C4—182no—
478C2×C3×C4—182no—
479C2×C3×C4—182no—
480C2×C3×C4C22×D911yescharacteristic
481C2×C3×C4C22×D911yescharacteristic
482C2×C3×C4C22×D911yescharacteristic
483C2×C3×C4C22×D911yescharacteristic
484C2×C3×C4C22×D911yescharacteristic
485C2×C3×C4C22×D911yescharacteristic
486C2×C3×C4C22×C3×D311yescharacteristic
487C2×C3×C4C22×C3×D311yescharacteristic
488C2×C3×C4C22×C3×D311yescharacteristic
489C2×C3×C4C22×C3×D311yescharacteristic
490C2×C3×C4C22×C3×D311yescharacteristic
491C2×C3×C4C22×C3×D311yescharacteristic
492#67—62no—
493#67—62no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500D12—62no—
501C4×D3—62no—
502C4×D3—62no—
503C4×D3—62no—
504C4×D3—62no—
505Dic6—62no—
506C2×C32—41no—
507C2×C32C2×#23511yescharacteristic
508C2×C32D3×#4111yescharacteristic
509C2×C32D3×#4111yescharacteristic
510C3×D3—62no—
511C3×D3—121no—
512C2×C9—21no—
513C2×C9—21no—
514C2×C9—21no—
515C2×C9—42no—
516C2×C9—41no—
517C2×C9C2×C3×#4111yescharacteristic
518C2×C9C2×C3×#4111yescharacteristic
519C2×C9C2×C3×#4111yescharacteristic
520D9—22no—
521D9—41no—
522C2×Q8—91no—
523C2×D4—91no—
524C2×D4—91no—
525C2×D4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4C2×C3×D911yescharacteristic
531C4⋊C4—91no—
532C4⋊C4—91no—
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—91no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4C2×C3×D911yescharacteristic
540C4⋊C4C2×C3×D911yescharacteristic
541C22⋊C4—91no—
542C22⋊C4—91no—
543C22⋊C4—91no—
544C22⋊C4—91no—
545C22⋊C4—91no—
546C22⋊C4—91no—
547C22⋊C4—91no—
548C22⋊C4—91no—
549C22⋊C4C2×C3×D911yescharacteristic
550C22⋊C4C2×C3×D911yescharacteristic
551C42—91no—
552C42—91no—
553C42—91no—
554C42—91no—
555C42C2×C3×D911yescharacteristic
556C42C2×C3×D911yescharacteristic
557C22×C3—22no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—92no—
568C22×C3—181no—
569C22×C3—181no—
570C22×C3—181no—
571C22×C3—181no—
572C22×C3—181no—
573C22×C3C23×D911yescharacteristic
574C22×C3C23×C3×D311yescharacteristic
575C2×D3—32no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—61no—
580C2×D3—61no—
581C3×C4—22no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—22no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—92no—
598C3×C4—181no—
599C3×C4—181no—
600C3×C4—181no—
601C3×C4—181no—
602C3×C4—181no—
603C3×C4#369712yes—
604C3×C4C3×#23512yes—
605Dic3—32no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—61no—
610Dic3—61no—
611C32#552811yescharacteristic
612C9—21no—
613C9C3×#52911yescharacteristic, complemented
614C23—91no—
615C23—91no—
616C23C22×C3×D911yescharacteristic
617Q8—182no—
618D4—182no—
619D4—182no—
620D4—182no—
621C2×C4—22no—
622C2×C4—91no—
623C2×C4—91no—
624C2×C4—91no—
625C2×C4—91no—
626C2×C4—91no—
627C2×C4—91no—
628C2×C4—182no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4C22×C3×D911yescharacteristic
633C2×C4C22×C3×D911yescharacteristic
634C2×C4C22×C3×D911yescharacteristic
635C2×C4C22×C3×D911yescharacteristic
636C2×C4C22×C3×D911yescharacteristic
637C2×C4C22×C3×D911yescharacteristic
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—42no—
642C2×C3—41no—
643C2×C3—41no—
644C2×C3—182no—
645C2×C3—361no—
646C2×C3C2×#369711yescharacteristic
647C2×C3#41×D911yescharacteristic
648C2×C3#41×D911yescharacteristic
649C2×C3C2×C3×#23511yescharacteristic
650C2×C3C3×D3×#4111yescharacteristic
651C2×C3C3×D3×#4111yescharacteristic
652D3—62no—
653D3—121no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—92no—
658C22—181no—
659C22—181no—
660C22—181no—
661C22—181no—
662C22—181no—
663C22C23×C3×D911yescharacteristic
664C4—21no—
665C4—21no—
666C4—21no—
667C4—21no—
668C4—21no—
669C4—92no—
670C4—181no—
671C4—181no—
672C4—181no—
673C4—181no—
674C4—181no—
675C4C3×#369712yes—
676C3—21no—
677C3#1058963011yescharacteristic, direct product factor
678C3C3×#552811yescharacteristic
679C2—41no—
680C2—182no—
681C2—361no—
682C2C2×C3×#369711yescharacteristic
683C2C3×#41×D911yescharacteristic
684C2C3×#41×D911yescharacteristic
subgroupG/H
centerC2×C3×C4C22×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#117C2
socleC22×C32C23×D3
prime radicalC3×#63446C2
hypercenterC3×#117D9
hypocenterC9C3×#529
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
1. C3×C9×#117C2semidirect
2. C3×C4×#611C2semidirect
3. C3×C4×#611C2semidirect
4. C3×#63460C2semidirect
5. C3×#63458C2semidirect
6. C3×#63456C2semidirect
7. C3×#63451C2semidirect
8. C3×#63447C2semidirect
10. C3×#63445C2semidirect
11. C3×#63441C2semidirect
12. C3×C4×D36C2semidirect
13. C3×#63434C2semidirect
14. C3×C42×D9C2semidirect
15. C3×C4×Dic18C2semidirect
17. #10589630C3direct (N × H)
69. C9×#117C2×C3semidirect
70. C4×#611C2×C3semidirect
71. C4×#611C2×C3semidirect
72. #63460C2×C3semidirect
73. #63458C2×C3semidirect
74. #63456C2×C3semidirect
75. #63451C2×C3semidirect
76. #63447C2×C3semidirect
78. #63445C2×C3semidirect
79. #63441C2×C3semidirect
80. C4×D36C2×C3semidirect
81. #63434C2×C3semidirect
82. C42×D9C2×C3semidirect
83. C4×Dic18C2×C3semidirect
223. C3×#117D9semidirect
447. #117C3×D9semidirect
449. C3×C9#529semidirect
613. C9C3×#529semidirect
677. C3#10589630direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1172
C3×C4×#6112
C3×#634602
C3×#634582
C3×#634562
C3×#634512
C3×#634472
C3×#634462
C3×#634452
C3×#634412
C3×C4×D362
C3×#634342
C3×C42×D92
C3×C4×Dic182
C3×#55283
#105896303