Finite Group Databasebeta

← C3×#10589795 #13153155

Subgroups — C3×#10589795 #13153155

Order 1728.

698 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#125C211yesmaximal, characteristic, complemented
2C3×#63460C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4C3×#63458C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6C3×#63456C211yesmaximal, characteristic
7C3×#63456C211yesmaximal, characteristic
8C3×#63455C211yesmaximal, characteristic
9C3×#63454C211yesmaximal, characteristic, complemented
10C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
11C3×#63451C211yesmaximal, characteristic, complemented
12C3×#63451C211yesmaximal, characteristic, complemented
13C3×#63449C211yesmaximal, characteristic, complemented
14C3×#63434C211yesmaximal, characteristic, complemented
15C3×#63434C211yesmaximal, characteristic, complemented
16C3×#5693—31nomaximal
17#10589795C311yesmaximal, characteristic, direct product factor
18C2×C3×D36C2211yescharacteristic
19C2×C3×C4×D9C2211yescharacteristic
20C2×C3×C4×D9C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25C3×C9×C4⋊C4C2211yescharacteristic
26C3×C9×C4⋊C4C2211yescharacteristic
27C3×C9×C4⋊C4C2211yescharacteristic
28C3×C9×C4⋊C4C2211yescharacteristic
29C3×C9×C4⋊C4C2211yescharacteristic
30C3×C42×C9C2211yescharacteristic
31C3×(C2×D9)⋊C4C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×C4⋊Dic9C2211yescharacteristic
40C3×C4⋊Dic9C2211yescharacteristic
41C3×Dic9⋊C4C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
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×#125D311yescharacteristic
54C3×#898—31no—
55C3×#898—31no—
56C3×#896—31no—
57C3×#896—31no—
58C3×#894—31no—
59C3×#894—31no—
60C3×#893—31no—
61C3×#892—31no—
62C3×D3×C4⋊C4—31no—
63C3×#889—31no—
64C3×#889—31no—
65C3×#887—31no—
66C3×#872—31no—
67C3×#872—31no—
68C9×#125—21no—
69C9×#125C2×C311yescharacteristic, complemented
70#63460C2×C311yescharacteristic, complemented
71#63460C2×C311yescharacteristic, complemented
72#63458C2×C311yescharacteristic, complemented
73#63458C2×C311yescharacteristic, complemented
74#63456C2×C311yescharacteristic
75#63456C2×C311yescharacteristic
76#63455C2×C311yescharacteristic
77#63454C2×C311yescharacteristic, complemented
78C4⋊C4×D9C2×C311yescharacteristic, complemented
79#63451C2×C311yescharacteristic, complemented
80#63451C2×C311yescharacteristic, complemented
81#63449C2×C311yescharacteristic, complemented
82#63434C2×C311yescharacteristic, complemented
83#63434C2×C311yescharacteristic, complemented
84C22×C3×D9C2311yescharacteristic
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
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×Dic9C2311yescharacteristic
94C2×C3×Dic9C2311yescharacteristic
95C2×C3×Dic9C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C3×D36—22no—
100C3×C4×D9—22no—
101C3×C4×D9—22no—
102C3×C4×D9—22no—
103C3×C4×D9—22no—
104C3×Dic18—22no—
105C3×#552—91no—
106#5693—31no—
107C2×C3×D12—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×Dic6—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D311yescharacteristic
116C32×C4⋊C4C2×D311yescharacteristic
117C32×C4⋊C4C2×D311yescharacteristic
118C32×C4⋊C4C2×D311yescharacteristic
119C32×C42C2×D311yescharacteristic
120C3×(C2×D3)⋊C4—31no—
121C3×(C2×D3)⋊C4—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×(C2×D3)⋊C4—31no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3—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×Dic3⋊C4—31no—
137C3×Dic3⋊C4—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—31no—
142C2×D36C22×C311yescharacteristic
143C2×C4×D9C22×C311yescharacteristic
144C2×C4×D9C22×C311yescharacteristic
145C2×C4×D9C22×C311yescharacteristic
146C2×C4×D9C22×C311yescharacteristic
147C2×Dic18C22×C311yescharacteristic
148C9×C4⋊C4—21no—
149C9×C4⋊C4—21no—
150C9×C4⋊C4—21no—
151C9×C4⋊C4—21no—
152C9×C4⋊C4—21no—
153C9×C4⋊C4—21no—
154C9×C4⋊C4C22×C311yescharacteristic
155C9×C4⋊C4C22×C311yescharacteristic
156C9×C4⋊C4C22×C311yescharacteristic
157C9×C4⋊C4C22×C311yescharacteristic
158C9×C4⋊C4C22×C311yescharacteristic
159C9×C4⋊C4C22×C311yescharacteristic
160C42×C9—21no—
161C42×C9C22×C311yescharacteristic
162(C2×D9)⋊C4C22×C311yescharacteristic
163(C2×D9)⋊C4C22×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
169(C2×D9)⋊C4C22×C311yescharacteristic
170C4⋊Dic9C22×C311yescharacteristic
171C4⋊Dic9C22×C311yescharacteristic
172Dic9⋊C4C22×C311yescharacteristic
173Dic9⋊C4C22×C311yescharacteristic
174Dic9⋊C4C22×C311yescharacteristic
175Dic9⋊C4C22×C311yescharacteristic
176Dic9⋊C4C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178Dic9⋊C4C22×C311yescharacteristic
179Dic9⋊C4C22×C311yescharacteristic
180C4×Dic9C22×C311yescharacteristic
181C4×Dic9C22×C311yescharacteristic
182C4×Dic9C22×C311yescharacteristic
183C4×Dic9C22×C311yescharacteristic
184C22×C3×C9C2411yescharacteristic
185C2×C3×D9—21no—
186C2×C3×D9—21no—
187C2×C3×D9—21no—
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9#4112yes—
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×C4×C9—21no—
198C3×Dic9—21no—
199C3×Dic9—21no—
200C3×Dic9—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9#4112yes—
204C3×#126—91no—
205C3×#126—91no—
206C3×#125—21no—
207C3×#125—91no—
208C3×#125—91no—
209C3×#125D911yescharacteristic, complemented
210C3×#125C3×D311yescharacteristic
211C3×#123—91no—
212C3×#123—91no—
213C3×C22⋊Q8—91no—
214C3×C22⋊Q8—91no—
215C3×C4×Q8—91no—
216C3×C4×D4—91no—
217C3×#117—91no—
218C3×#117—91no—
219C3×#117—91no—
220C2×C3×C4⋊C4—91no—
221#898—31no—
222#898—31no—
223#896—31no—
224#896—31no—
225#894—31no—
226#894—31no—
227#893—31no—
228#892—31no—
229D3×C4⋊C4—31no—
230#889—31no—
231#889—31no—
232#887—31no—
233#872—31no—
234#872—31no—
235C22×C3×D3—31no—
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
243C2×C32×C4C22×D311yescharacteristic
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—31no—
249C2×C3×Dic3—31no—
250C3×D12—62no—
251C3×C4×D3—62no—
252C3×C4×D3—62no—
253C3×C4×D3—62no—
254C3×C4×D3—62no—
255C3×Dic6—62no—
256C22×D9C23×C311yescharacteristic
257C22×D9C23×C311yescharacteristic
258C2×C4×C9—21no—
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
271C2×C4×C9C23×C311yescharacteristic
272C2×Dic9C23×C311yescharacteristic
273C2×Dic9C23×C311yescharacteristic
274C2×Dic9C23×C311yescharacteristic
275C2×Dic9C23×C311yescharacteristic
276C2×Dic9C23×C311yescharacteristic
277C2×Dic9C23×C311yescharacteristic
278D36—22no—
279C4×D9—22no—
280C4×D9—22no—
281C4×D9—22no—
282C4×D9—22no—
283Dic18—22no—
284#552—91noSylow
285C2×C3×C9C2×#4111yescharacteristic
286C2×C3×C9C2×#4111yescharacteristic
287C2×C3×C92−1+411yescharacteristic
288C3×D9—22no—
289C3×D9—41no—
290C2×C3×Q8—91no—
291C2×C3×D4—91no—
292C22×C3×C4—91no—
293C22×C3×C4—91no—
294C22×C3×C4—91no—
295C22×C3×C4—91no—
296C2×D12—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×Dic6—31no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
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⋊C4—91no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4C2×D911yescharacteristic
319C3×C4⋊C4C2×D911yescharacteristic
320C3×C4⋊C4C2×D911yescharacteristic
321C3×C4⋊C4C2×D911yescharacteristic
322C3×C4⋊C4C2×D911yescharacteristic
323C3×C4⋊C4C2×D911yescharacteristic
324C3×C4⋊C4C2×C3×D311yescharacteristic
325C3×C4⋊C4C2×C3×D311yescharacteristic
326C3×C4⋊C4C2×C3×D311yescharacteristic
327C3×C4⋊C4C2×C3×D311yescharacteristic
328C3×C4⋊C4C2×C3×D311yescharacteristic
329C3×C4⋊C4C2×C3×D311yescharacteristic
330C3×C22⋊C4—91no—
331C3×C22⋊C4—91no—
332C3×C22⋊C4—91no—
333C3×C22⋊C4—91no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4—91no—
337C3×C22⋊C4—91no—
338C3×C42—21no—
339C3×C42—91no—
340C3×C42—91no—
341C3×C42—91no—
342C3×C42—91no—
343C3×C42C2×D911yescharacteristic
344C3×C42C2×C3×D311yescharacteristic
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—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—
352(C2×D3)⋊C4—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C22×C32C23×D311yescharacteristic
368C2×C3×D3—32no—
369C2×C3×D3—61no—
370C2×C3×D3—61no—
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—
380C32×C4—21no—
381C3×Dic3—32no—
382C3×Dic3—61no—
383C3×Dic3—61no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C22×C9—21no—
388C22×C9C24×C311yescharacteristic
389C2×D9—21no—
390C2×D9—21no—
391C2×D9—21no—
392C2×D9—21no—
393C2×D9—21no—
394C2×D9C3×#4112yes—
395C4×C9—22no—
396C4×C9—21no—
397C4×C9—21no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—21no—
401C4×C9—21no—
402C4×C9—21no—
403C4×C9—41no—
404C4×C9—41no—
405C4×C9—41no—
406C4×C9—41no—
407C4×C9—41no—
408C4×C9—41no—
409Dic9—21no—
410Dic9—21no—
411Dic9—21no—
412Dic9—21no—
413Dic9—21no—
414Dic9C3×#4112yes—
415#126—91no—
416#126—91no—
417#125—91no—
418#125—91no—
419#125C3×D911yescharacteristic, complemented
420#123—91no—
421#123—91no—
422C22⋊Q8—91no—
423C22⋊Q8—91no—
424C4×Q8—91no—
425C4×D4—91no—
426#117—91no—
427#117—91no—
428#117—91no—
429C2×C4⋊C4—91no—
430C3×C9#55211yescharacteristic, complemented, Sylow
431C23×C3—91no—
432C23×C3—91no—
433C22×D3—31no—
434C22×D3—31no—
435C3×Q8—182no—
436C3×D4—182no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—91no—
445C2×C3×C4—91no—
446C2×C3×C4—91no—
447C2×C3×C4—91no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4—182no—
451C2×C3×C4—182no—
452C2×C3×C4—182no—
453C2×C3×C4—182no—
454C2×C3×C4C22×D911yescharacteristic
455C2×C3×C4C22×D911yescharacteristic
456C2×C3×C4C22×D911yescharacteristic
457C2×C3×C4C22×D911yescharacteristic
458C2×C3×C4C22×D911yescharacteristic
459C2×C3×C4C22×D911yescharacteristic
460C2×C3×C4C22×D911yescharacteristic
461C2×C3×C4C22×C3×D311yescharacteristic
462C2×C3×C4C22×C3×D311yescharacteristic
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×Dic3—31no—
469C2×Dic3—31no—
470C2×Dic3—31no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474D12—62no—
475C4×D3—62no—
476C4×D3—62no—
477C4×D3—62no—
478C4×D3—62no—
479Dic6—62no—
480C2×C32#100711yescharacteristic
481C2×C32D3×#4111yescharacteristic
482C2×C32D3×#4111yescharacteristic
483C3×D3—62no—
484C3×D3—121no—
485C2×C9—21no—
486C2×C9—21no—
487C2×C9—21no—
488C2×C9C2×C3×#4111yescharacteristic
489C2×C9C2×C3×#4111yescharacteristic
490C2×C9C3×2−1+411yescharacteristic
491D9—22no—
492D9—41no—
493C2×Q8—91no—
494C2×D4—91no—
495C22×C4—91no—
496C22×C4—91no—
497C22×C4—91no—
498C22×C4—91no—
499C4⋊C4—91no—
500C4⋊C4—91no—
501C4⋊C4—91no—
502C4⋊C4—91no—
503C4⋊C4—91no—
504C4⋊C4—91no—
505C4⋊C4—91no—
506C4⋊C4—91no—
507C4⋊C4—91no—
508C4⋊C4—91no—
509C4⋊C4C2×C3×D911yescharacteristic
510C4⋊C4C2×C3×D911yescharacteristic
511C4⋊C4C2×C3×D911yescharacteristic
512C4⋊C4C2×C3×D911yescharacteristic
513C4⋊C4C2×C3×D911yescharacteristic
514C4⋊C4C2×C3×D911yescharacteristic
515C22⋊C4—91no—
516C22⋊C4—91no—
517C22⋊C4—91no—
518C22⋊C4—91no—
519C22⋊C4—91no—
520C22⋊C4—91no—
521C22⋊C4—91no—
522C22⋊C4—91no—
523C42—91no—
524C42—91no—
525C42—91no—
526C42—91no—
527C42C2×C3×D911yescharacteristic
528C22×C3—21no—
529C22×C3—92no—
530C22×C3—181no—
531C22×C3—181no—
532C22×C3—181no—
533C22×C3—181no—
534C22×C3—181no—
535C22×C3C23×D911yescharacteristic
536C22×C3C23×C3×D311yescharacteristic
537C2×D3—32no—
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—61no—
541C2×D3—61no—
542C2×D3—61no—
543C3×C4—22no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
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—41no—
559C3×C4—41no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4—41no—
564C3×C4—92no—
565C3×C4—181no—
566C3×C4—181no—
567C3×C4—181no—
568C3×C4—181no—
569C3×C4—181no—
570Dic3—32no—
571Dic3—61no—
572Dic3—61no—
573Dic3—61no—
574Dic3—61no—
575Dic3—61no—
576C32#569311yescharacteristic
577C9—21no—
578C9C3×#55211yescharacteristic, complemented
579C23—91no—
580C23—91no—
581Q8—182no—
582D4—182no—
583C2×C4—91no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—91no—
587C2×C4—91no—
588C2×C4—91no—
589C2×C4—182no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4—182no—
593C2×C4C22×C3×D911yescharacteristic
594C2×C4C22×C3×D911yescharacteristic
595C2×C4C22×C3×D911yescharacteristic
596C2×C4C22×C3×D911yescharacteristic
597C2×C4C22×C3×D911yescharacteristic
598C2×C4C22×C3×D911yescharacteristic
599C2×C4C22×C3×D911yescharacteristic
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—182no—
604C2×C3—361no—
605C2×C3#6371311yescharacteristic
606C2×C3#41×D911yescharacteristic
607C2×C3#41×D911yescharacteristic
608C2×C3C3×#100711yescharacteristic
609C2×C3C3×D3×#4111yescharacteristic
610C2×C3C3×D3×#4111yescharacteristic
611D3—62no—
612D3—121no—
613C22—92no—
614C22—181no—
615C22—181no—
616C22—181no—
617C22—181no—
618C22—181no—
619C22C23×C3×D911yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—92no—
628C4—181no—
629C4—181no—
630C4—181no—
631C4—181no—
632C4—181no—
633C3—21no—
634C3#1058979511yescharacteristic, direct product factor
635C3C3×#569311yescharacteristic
636C2—182no—
637C2—361no—
638C2C3×#6371311yescharacteristic
639C2C3×#41×D911yescharacteristic
640C2C3×#41×D911yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#125C2
socleC22×C32C23×D3
prime radicalC2×C3×D36C22
hypercenterC3×#125D9
hypocenterC9C3×#552
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
1. C3×C9×#125C2semidirect
2. C3×#63460C2semidirect
3. C3×#63460C2semidirect
4. C3×#63458C2semidirect
5. C3×#63458C2semidirect
9. C3×#63454C2semidirect
10. C3×C4⋊C4×D9C2semidirect
11. C3×#63451C2semidirect
12. C3×#63451C2semidirect
13. C3×#63449C2semidirect
14. C3×#63434C2semidirect
15. C3×#63434C2semidirect
17. #10589795C3direct (N × H)
69. C9×#125C2×C3semidirect
70. #63460C2×C3semidirect
71. #63460C2×C3semidirect
72. #63458C2×C3semidirect
73. #63458C2×C3semidirect
77. #63454C2×C3semidirect
78. C4⋊C4×D9C2×C3semidirect
79. #63451C2×C3semidirect
80. #63451C2×C3semidirect
81. #63449C2×C3semidirect
82. #63434C2×C3semidirect
83. #63434C2×C3semidirect
209. C3×#125D9semidirect
419. #125C3×D9semidirect
430. C3×C9#552semidirect
578. C9C3×#552semidirect
634. C3#10589795direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1252
C3×#634602
C3×#634582
C3×#634562
C3×#634552
C3×#634542
C3×C4⋊C4×D92
C3×#634512
C3×#634492
C3×#634342
C3×#56933
#105897953