Finite Group Databasebeta

← C3×#10589804 #13153208

Subgroups — C3×#10589804 #13153208

Order 1728.

696 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#126C211yesmaximal, characteristic, complemented
2C3×#63460C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4C3×#63458C211yesmaximal, characteristic, complemented
5C3×#63450C211yesmaximal, characteristic, complemented
6C3×#63449C211yesmaximal, characteristic, complemented
7C3×#63449C211yesmaximal, characteristic, complemented
8C3×#63447C211yesmaximal, characteristic
9C3×#63447C211yesmaximal, characteristic
10C3×#611⋊C4C211yesmaximal, characteristic
11C3×#63441C211yesmaximal, characteristic, complemented
12C3×#63440C211yesmaximal, characteristic, complemented
13C3×#63439C211yesmaximal, characteristic, complemented
14C3×#63434C211yesmaximal, characteristic, complemented
15C3×C4×Dic18C211yesmaximal, characteristic, complemented
16C3×#5702—31nomaximal
17#10589804C311yesmaximal, characteristic, direct product factor
18C2×C3×#611C2211yescharacteristic
19C22×C3×Dic9C2211yescharacteristic
20C2×C3×C4×D9C2211yescharacteristic
21C2×C3×Dic18C2211yescharacteristic
22C2×C3×Dic18C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25C3×C9×C4⋊C4C2211yescharacteristic
26C3×C9×C4⋊C4C2211yescharacteristic
27C3×C9×C22⋊C4C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic
29C3×C9×C22⋊C4C2211yescharacteristic
30C3×C42×C9C2211yescharacteristic
31C3×#3676C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×C4⋊Dic9C2211yescharacteristic
39C3×C4⋊Dic9C2211yescharacteristic
40C3×Dic9⋊C4C2211yescharacteristic
41C3×Dic9⋊C4C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×C4×Dic9C2211yescharacteristic
48C3×C4×Dic9C2211yescharacteristic
49C3×C4×Dic9C2211yescharacteristic
50C3×C4×Dic9C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#126D311yescharacteristic
54C3×#898—31no—
55C3×#898—31no—
56C3×#896—31no—
57C3×#888—31no—
58C3×#887—31no—
59C3×#887—31no—
60C3×#885—31no—
61C3×#885—31no—
62C3×#67⋊C4—31no—
63C3×#879—31no—
64C3×#878—31no—
65C3×#877—31no—
66C3×#872—31no—
67C3×C4×Dic6—31no—
68C9×#126—21no—
69C9×#126C2×C311yescharacteristic, complemented
70#63460C2×C311yescharacteristic, complemented
71#63460C2×C311yescharacteristic, complemented
72#63458C2×C311yescharacteristic, complemented
73#63450C2×C311yescharacteristic, complemented
74#63449C2×C311yescharacteristic, complemented
75#63449C2×C311yescharacteristic, complemented
76#63447C2×C311yescharacteristic
77#63447C2×C311yescharacteristic
78#611⋊C4C2×C311yescharacteristic
79#63441C2×C311yescharacteristic, complemented
80#63440C2×C311yescharacteristic, complemented
81#63439C2×C311yescharacteristic, complemented
82#63434C2×C311yescharacteristic, complemented
83C4×Dic18C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C3×#611—22no—
93C2×C3×Dic9—22no—
94C2×C3×Dic9C2311yescharacteristic
95C2×C3×Dic9C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C3×C4×D9—22no—
102C3×Dic18—22no—
103C3×Dic18—22no—
104C3×Dic18—22no—
105C3×#556—91no—
106#5702—31no—
107C2×C3×#67—31no—
108C22×C3×Dic3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D311yescharacteristic
116C32×C22⋊C4C2×D311yescharacteristic
117C32×C22⋊C4C2×D311yescharacteristic
118C32×C22⋊C4C2×D311yescharacteristic
119C32×C42C2×D311yescharacteristic
120C3×#217—31no—
121C3×#217—31no—
122C3×(C2×D3)⋊C4—31no—
123C3×(C2×D3)⋊C4—31no—
124C3×(C2×D3)⋊C4—31no—
125C3×(C2×D3)⋊C4—31no—
126C3×(C2×D3)⋊C4—31no—
127C3×C4⋊Dic3—31no—
128C3×C4⋊Dic3—31no—
129C3×Dic3⋊C4—31no—
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4—31no—
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136C3×C4×Dic3—31no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—31no—
142C2×#611C22×C311yescharacteristic
143C22×Dic9C22×C311yescharacteristic
144C2×C4×D9C22×C311yescharacteristic
145C2×Dic18C22×C311yescharacteristic
146C2×Dic18C22×C311yescharacteristic
147C2×Dic18C22×C311yescharacteristic
148C9×C4⋊C4—21no—
149C9×C4⋊C4—21no—
150C9×C4⋊C4—21no—
151C9×C4⋊C4C22×C311yescharacteristic
152C9×C4⋊C4C22×C311yescharacteristic
153C9×C4⋊C4C22×C311yescharacteristic
154C9×C22⋊C4—21no—
155C9×C22⋊C4—21no—
156C9×C22⋊C4—21no—
157C9×C22⋊C4C22×C311yescharacteristic
158C9×C22⋊C4C22×C311yescharacteristic
159C9×C22⋊C4C22×C311yescharacteristic
160C42×C9—21no—
161C42×C9C22×C311yescharacteristic
162#3676C22×C311yescharacteristic
163#3676C22×C311yescharacteristic
164(C2×D9)⋊C4C22×C311yescharacteristic
165(C2×D9)⋊C4C22×C311yescharacteristic
166(C2×D9)⋊C4C22×C311yescharacteristic
167(C2×D9)⋊C4C22×C311yescharacteristic
168(C2×D9)⋊C4C22×C311yescharacteristic
169C4⋊Dic9C22×C311yescharacteristic
170C4⋊Dic9C22×C311yescharacteristic
171Dic9⋊C4C22×C311yescharacteristic
172Dic9⋊C4C22×C311yescharacteristic
173Dic9⋊C4C22×C311yescharacteristic
174Dic9⋊C4C22×C311yescharacteristic
175Dic9⋊C4C22×C311yescharacteristic
176Dic9⋊C4C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178C4×Dic9C22×C311yescharacteristic
179C4×Dic9C22×C311yescharacteristic
180C4×Dic9C22×C311yescharacteristic
181C4×Dic9C22×C311yescharacteristic
182C4×Dic9C22×C311yescharacteristic
183C4×Dic9C22×C311yescharacteristic
184C22×C3×C9—21no—
185C22×C3×C9—21no—
186C22×C3×C9—21no—
187C22×C3×C9C2411yescharacteristic
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9—21no—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3×C4×C9—21no—
194C3×C4×C9—21no—
195C3×C4×C9—21no—
196C3×C4×C9—21no—
197C3×Dic9—21no—
198C3×Dic9—21no—
199C3×Dic9—21no—
200C3×Dic9—21no—
201C3×Dic9—21no—
202C3×Dic9#4112yes—
203C3×Dic9#4112yes—
204C3×C4⋊Q8—91no—
205C3×#126—21no—
206C3×#126—91no—
207C3×#126—91no—
208C3×#126—91no—
209C3×#126D911yescharacteristic, complemented
210C3×#126C3×D311yescharacteristic
211C3×#124—91no—
212C3×#124—91no—
213C3×C22⋊Q8—91no—
214C3×C22⋊Q8—91no—
215C3×C4×Q8—91no—
216C3×C4×Q8—91no—
217C3×C4×Q8—91no—
218C3×C4×D4—91no—
219C3×#117—91no—
220C3×#117—91no—
221#898—31no—
222#898—31no—
223#896—31no—
224#888—31no—
225#887—31no—
226#887—31no—
227#885—31no—
228#885—31no—
229#67⋊C4—31no—
230#879—31no—
231#878—31no—
232#877—31no—
233#872—31no—
234C4×Dic6—31no—
235C23×C32C22×D311yescharacteristic
236C22×C3×D3—31no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C3×#67—62no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—31no—
249C2×C3×Dic3—31no—
250C2×C3×Dic3—31no—
251C2×C3×Dic3—62no—
252C3×C4×D3—62no—
253C3×Dic6—62no—
254C3×Dic6—62no—
255C3×Dic6—62no—
256C23×C9—21no—
257C23×C9C23×C311yescharacteristic
258C22×D9C23×C311yescharacteristic
259C2×C4×C9—21no—
260C2×C4×C9—21no—
261C2×C4×C9—21no—
262C2×C4×C9—21no—
263C2×C4×C9—21no—
264C2×C4×C9—21no—
265C2×C4×C9C23×C311yescharacteristic
266C2×C4×C9C23×C311yescharacteristic
267C2×C4×C9C23×C311yescharacteristic
268C2×C4×C9C23×C311yescharacteristic
269C2×C4×C9C23×C311yescharacteristic
270C2×C4×C9C23×C311yescharacteristic
271#611—22no—
272C2×Dic9—22no—
273C2×Dic9C23×C311yescharacteristic
274C2×Dic9C23×C311yescharacteristic
275C2×Dic9C23×C311yescharacteristic
276C2×Dic9C23×C311yescharacteristic
277C2×Dic9C23×C311yescharacteristic
278C2×Dic9C23×C311yescharacteristic
279C2×Dic9C23×C311yescharacteristic
280C4×D9—22no—
281Dic18—22no—
282Dic18—22no—
283Dic18—22no—
284#556—91noSylow
285C2×C3×C9—41no—
286C2×C3×C9C2×#4111yescharacteristic
287C2×C3×C9C2×#4111yescharacteristic
288C2×C3×C92−1+411yescharacteristic
289C3×D9—41no—
290C2×C3×Q8—91no—
291C2×C3×Q8—91no—
292C2×C3×Q8—91no—
293C2×C3×D4—91no—
294C22×C3×C4—91no—
295C22×C3×C4—91no—
296C2×#67—31no—
297C22×Dic3—31no—
298C2×C4×D3—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—31no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—91no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—91no—
309C3×C4⋊C4—91no—
310C3×C4⋊C4—91no—
311C3×C4⋊C4—91no—
312C3×C4⋊C4—91no—
313C3×C4⋊C4—91no—
314C3×C4⋊C4C2×D911yescharacteristic
315C3×C4⋊C4C2×D911yescharacteristic
316C3×C4⋊C4C2×D911yescharacteristic
317C3×C4⋊C4C2×C3×D311yescharacteristic
318C3×C4⋊C4C2×C3×D311yescharacteristic
319C3×C4⋊C4C2×C3×D311yescharacteristic
320C3×C22⋊C4—21no—
321C3×C22⋊C4—21no—
322C3×C22⋊C4—21no—
323C3×C22⋊C4—91no—
324C3×C22⋊C4—91no—
325C3×C22⋊C4—91no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4—91no—
328C3×C22⋊C4—91no—
329C3×C22⋊C4—91no—
330C3×C22⋊C4C2×D911yescharacteristic
331C3×C22⋊C4C2×D911yescharacteristic
332C3×C22⋊C4C2×D911yescharacteristic
333C3×C22⋊C4C2×C3×D311yescharacteristic
334C3×C22⋊C4C2×C3×D311yescharacteristic
335C3×C22⋊C4C2×C3×D311yescharacteristic
336C3×C42—21no—
337C3×C42—91no—
338C3×C42—91no—
339C3×C42—91no—
340C3×C42—91no—
341C3×C42—91no—
342C3×C42—91no—
343C3×C42C2×D911yescharacteristic
344C3×C42C2×C3×D311yescharacteristic
345#217—31no—
346#217—31no—
347(C2×D3)⋊C4—31no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32C23×D311yescharacteristic
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C32×C4—21no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—21no—
380C3×Dic3—32no—
381C3×Dic3—32no—
382C3×Dic3—61no—
383C3×Dic3—61no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C22×C9—21no—
388C22×C9—21no—
389C22×C9—21no—
390C22×C9—21no—
391C22×C9—41no—
392C22×C9—41no—
393C22×C9—41no—
394C22×C9C24×C311yescharacteristic
395C2×D9—21no—
396C2×D9—21no—
397C2×D9—21no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—21no—
401C4×C9—21no—
402C4×C9—21no—
403C4×C9—21no—
404C4×C9—41no—
405C4×C9—41no—
406C4×C9—41no—
407C4×C9—41no—
408C4×C9—41no—
409C4×C9—41no—
410Dic9—21no—
411Dic9—21no—
412Dic9—21no—
413Dic9—21no—
414Dic9—21no—
415Dic9C3×#4112yes—
416Dic9C3×#4112yes—
417C4⋊Q8—91no—
418#126—91no—
419#126—91no—
420#126—91no—
421#126C3×D911yescharacteristic, complemented
422#124—91no—
423#124—91no—
424C22⋊Q8—91no—
425C22⋊Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×D4—91no—
430#117—91no—
431#117—91no—
432C3×C9#55611yescharacteristic, complemented, Sylow
433C23×C3—21no—
434C23×C3—91no—
435C23×C3C22×D911yescharacteristic
436C23×C3C22×C3×D311yescharacteristic
437C22×D3—31no—
438C3×Q8—182no—
439C3×Q8—182no—
440C3×Q8—182no—
441C3×D4—182no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4—91no—
451C2×C3×C4—91no—
452C2×C3×C4—91no—
453C2×C3×C4—91no—
454C2×C3×C4—91no—
455C2×C3×C4—182no—
456C2×C3×C4—182no—
457C2×C3×C4C22×D911yescharacteristic
458C2×C3×C4C22×D911yescharacteristic
459C2×C3×C4C22×D911yescharacteristic
460C2×C3×C4C22×D911yescharacteristic
461C2×C3×C4C22×D911yescharacteristic
462C2×C3×C4C22×D911yescharacteristic
463C2×C3×C4C22×C3×D311yescharacteristic
464C2×C3×C4C22×C3×D311yescharacteristic
465C2×C3×C4C22×C3×D311yescharacteristic
466C2×C3×C4C22×C3×D311yescharacteristic
467C2×C3×C4C22×C3×D311yescharacteristic
468C2×C3×C4C22×C3×D311yescharacteristic
469#67—62no—
470C2×Dic3—31no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—62no—
478C4×D3—62no—
479Dic6—62no—
480Dic6—62no—
481Dic6—62no—
482C2×C32—41no—
483C2×C32D3×#4111yescharacteristic
484C2×C32D3×#4111yescharacteristic
485C2×C32#101011yescharacteristic
486C3×D3—121no—
487C2×C9—21no—
488C2×C9—21no—
489C2×C9—21no—
490C2×C9—41no—
491C2×C9—81no—
492C2×C9C2×C3×#4111yescharacteristic
493C2×C9C2×C3×#4111yescharacteristic
494C2×C9C3×2−1+411yescharacteristic
495D9—41no—
496C2×Q8—91no—
497C2×Q8—91no—
498C2×Q8—91no—
499C2×D4—91no—
500C22×C4—91no—
501C22×C4—91no—
502C4⋊C4—91no—
503C4⋊C4—91no—
504C4⋊C4—91no—
505C4⋊C4—91no—
506C4⋊C4—91no—
507C4⋊C4—91no—
508C4⋊C4—91no—
509C4⋊C4—91no—
510C4⋊C4—91no—
511C4⋊C4C2×C3×D911yescharacteristic
512C4⋊C4C2×C3×D911yescharacteristic
513C4⋊C4C2×C3×D911yescharacteristic
514C22⋊C4—91no—
515C22⋊C4—91no—
516C22⋊C4—91no—
517C22⋊C4—91no—
518C22⋊C4—91no—
519C22⋊C4—91no—
520C22⋊C4—91no—
521C22⋊C4C2×C3×D911yescharacteristic
522C22⋊C4C2×C3×D911yescharacteristic
523C22⋊C4C2×C3×D911yescharacteristic
524C42—91no—
525C42—91no—
526C42—91no—
527C42—91no—
528C42—91no—
529C42—91no—
530C42C2×C3×D911yescharacteristic
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—181no—
542C22×C3—181no—
543C22×C3—181no—
544C22×C3C23×D911yescharacteristic
545C22×C3C23×C3×D311yescharacteristic
546C2×D3—61no—
547C2×D3—61no—
548C2×D3—61no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4—41no—
564C3×C4—41no—
565C3×C4—41no—
566C3×C4—41no—
567C3×C4—92no—
568C3×C4—92no—
569C3×C4—181no—
570C3×C4—181no—
571C3×C4—181no—
572C3×C4—181no—
573C3×C4—181no—
574Dic3—32no—
575Dic3—32no—
576Dic3—61no—
577Dic3—61no—
578Dic3—61no—
579Dic3—61no—
580Dic3—61no—
581C32#570211yescharacteristic
582C9—21no—
583C9C3×#55611yescharacteristic, complemented
584C23—91no—
585C23C22×C3×D911yescharacteristic
586Q8—182no—
587Q8—182no—
588Q8—182no—
589D4—182no—
590C2×C4—91no—
591C2×C4—91no—
592C2×C4—91no—
593C2×C4—91no—
594C2×C4—91no—
595C2×C4—91no—
596C2×C4—91no—
597C2×C4—182no—
598C2×C4—182no—
599C2×C4C22×C3×D911yescharacteristic
600C2×C4C22×C3×D911yescharacteristic
601C2×C4C22×C3×D911yescharacteristic
602C2×C4C22×C3×D911yescharacteristic
603C2×C4C22×C3×D911yescharacteristic
604C2×C4C22×C3×D911yescharacteristic
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—41no—
609C2×C3—41no—
610C2×C3—81no—
611C2×C3—361no—
612C2×C3#41×D911yescharacteristic
613C2×C3#41×D911yescharacteristic
614C2×C3#6371611yescharacteristic
615C2×C3C3×D3×#4111yescharacteristic
616C2×C3C3×D3×#4111yescharacteristic
617C2×C3C3×#101011yescharacteristic
618D3—121no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—181no—
623C22—181no—
624C22—181no—
625C22C23×C3×D911yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—92no—
633C4—92no—
634C4—181no—
635C4—181no—
636C4—181no—
637C4—181no—
638C4—181no—
639C3—21no—
640C3#1058980411yescharacteristic, direct product factor
641C3C3×#570211yescharacteristic
642C2—41no—
643C2—361no—
644C2C3×#41×D911yescharacteristic
645C2C3×#41×D911yescharacteristic
646C2C3×#6371611yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#126C2
socleC22×C32C23×D3
prime radicalC2×C3×#611C22
hypercenterC3×#126D9
hypocenterC9C3×#556
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#126

Complements

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

NH ≅ G/Ntype
1. C3×C9×#126C2semidirect
2. C3×#63460C2semidirect
3. C3×#63460C2semidirect
4. C3×#63458C2semidirect
5. C3×#63450C2semidirect
6. C3×#63449C2semidirect
7. C3×#63449C2semidirect
11. C3×#63441C2semidirect
12. C3×#63440C2semidirect
13. C3×#63439C2semidirect
14. C3×#63434C2semidirect
15. C3×C4×Dic18C2semidirect
17. #10589804C3direct (N × H)
69. C9×#126C2×C3semidirect
70. #63460C2×C3semidirect
71. #63460C2×C3semidirect
72. #63458C2×C3semidirect
73. #63450C2×C3semidirect
74. #63449C2×C3semidirect
75. #63449C2×C3semidirect
79. #63441C2×C3semidirect
80. #63440C2×C3semidirect
81. #63439C2×C3semidirect
82. #63434C2×C3semidirect
83. C4×Dic18C2×C3semidirect
209. C3×#126D9semidirect
421. #126C3×D9semidirect
432. C3×C9#556semidirect
583. C9C3×#556semidirect
640. C3#10589804direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1262
C3×#634602
C3×#634582
C3×#634502
C3×#634492
C3×#634472
C3×#611⋊C42
C3×#634412
C3×#634402
C3×#634392
C3×#634342
C3×C4×Dic182
C3×#57023
#105898043