Finite Group Databasebeta

← C3×#10589717 #13152792

Subgroups — C3×#10589717 #13152792

Order 1728.

814 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#121C211yesmaximal, characteristic, complemented
2C3×#63502C211yesmaximal, characteristic, complemented
3C3×#63501C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5C3×#63501C211yesmaximal, characteristic, complemented
6C3×#63500C211yesmaximal, characteristic, complemented
7C3×#63497C211yesmaximal, characteristic, complemented
8C3×#63491C211yesmaximal, characteristic, complemented
9C3×C4×#611C211yesmaximal, characteristic, complemented
10C3×#63456C211yesmaximal, characteristic, complemented
11C3×#63451C211yesmaximal, characteristic, complemented
12C3×#63446C211yesmaximal, characteristic, complemented
13C3×#63445C211yesmaximal, characteristic, complemented
14C3×#611⋊C4C211yesmaximal, characteristic, complemented
15C3×#63439C211yesmaximal, characteristic, complemented
16C3×#5615—31nomaximal
17#10589717C311yesmaximal, characteristic, direct product factor
18C2×C3×D4×C9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C22×C3×C4×C9C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C22×C3×Dic9C2211yescharacteristic
29C22×C3×Dic9C2211yescharacteristic
30C2×C3×D36C2211yescharacteristic
31C2×C3×C4×D9C2211yescharacteristic
32C2×C3×C4×D9C2211yescharacteristic
33C3×C9×C4⋊C4C2211yescharacteristic
34C3×C9×C22⋊C4C2211yescharacteristic
35C3×C9×C22⋊C4C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×Dic9⋊C4C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#121D311yescharacteristic
54C3×#940—31no—
55C3×#939—31no—
56C3×#939—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#935—31no—
60C3×#929—31no—
61C3×C4×#67—31no—
62C3×#894—31no—
63C3×#889—31no—
64C3×#884—31no—
65C3×#883—31no—
66C3×#67⋊C4—31no—
67C3×#877—31no—
68C9×#121—21no—
69C9×#121C2×C311yescharacteristic, complemented
70#63502C2×C311yescharacteristic, complemented
71#63501C2×C311yescharacteristic, complemented
72#63501C2×C311yescharacteristic, complemented
73#63501C2×C311yescharacteristic, complemented
74#63500C2×C311yescharacteristic, complemented
75#63497C2×C311yescharacteristic, complemented
76#63491C2×C311yescharacteristic, complemented
77C4×#611C2×C311yescharacteristic, complemented
78#63456C2×C311yescharacteristic, complemented
79#63451C2×C311yescharacteristic, complemented
80#63446C2×C311yescharacteristic, complemented
81#63445C2×C311yescharacteristic, complemented
82#611⋊C4C2×C311yescharacteristic, complemented
83#63439C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C23×C3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C3×D4×C9—41no—
90C3×D4×C9—41no—
91C3×D4×C9—41no—
92C2×C3×C4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C3×#611—22no—
98C3×#611—22no—
99C3×#611—41no—
100C3×#611—41no—
101C3×#611—41no—
102C3×#611—41no—
103C2×C3×Dic9—22no—
104C2×C3×Dic9—41no—
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C3×D36—41no—
112C3×C4×D9—41no—
113C3×C4×D9—41no—
114C3×#540—91no—
115#5615—31no—
116C2×C32×D4C2×D311yescharacteristic
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C2×D311yescharacteristic
119C22×C32×C4C2×D311yescharacteristic
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C2×C3×D12—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C32×C4⋊C4C2×D311yescharacteristic
132C32×C22⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C3×#217—31no—
135C3×#217—31no—
136C3×#217—31no—
137C3×#217—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×C4⋊Dic3—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C2×D4×C9—21no—
152C2×D4×C9—21no—
153C2×D4×C9—21no—
154C2×D4×C9C22×C311yescharacteristic
155C2×D4×C9C22×C311yescharacteristic
156C2×D4×C9C22×C311yescharacteristic
157C22×C4×C9—21no—
158C22×C4×C9C22×C311yescharacteristic
159C2×#611C22×C311yescharacteristic
160C2×#611C22×C311yescharacteristic
161C2×#611C22×C311yescharacteristic
162C2×#611C22×C311yescharacteristic
163C2×#611C22×C311yescharacteristic
164C2×#611C22×C311yescharacteristic
165C22×Dic9C22×C311yescharacteristic
166C22×Dic9C22×C311yescharacteristic
167C2×D36C22×C311yescharacteristic
168C2×C4×D9C22×C311yescharacteristic
169C2×C4×D9C22×C311yescharacteristic
170C9×C4⋊C4—21no—
171C9×C4⋊C4C22×C311yescharacteristic
172C9×C22⋊C4—21no—
173C9×C22⋊C4—21no—
174C9×C22⋊C4C22×C311yescharacteristic
175C9×C22⋊C4C22×C311yescharacteristic
176#3676C22×C311yescharacteristic
177#3676C22×C311yescharacteristic
178#3676C22×C311yescharacteristic
179#3676C22×C311yescharacteristic
180(C2×D9)⋊C4C22×C311yescharacteristic
181(C2×D9)⋊C4C22×C311yescharacteristic
182(C2×D9)⋊C4C22×C311yescharacteristic
183(C2×D9)⋊C4C22×C311yescharacteristic
184C4⋊Dic9C22×C311yescharacteristic
185Dic9⋊C4C22×C311yescharacteristic
186Dic9⋊C4C22×C311yescharacteristic
187Dic9⋊C4C22×C311yescharacteristic
188Dic9⋊C4C22×C311yescharacteristic
189Dic9⋊C4C22×C311yescharacteristic
190Dic9⋊C4C22×C311yescharacteristic
191C4×Dic9C22×C311yescharacteristic
192C4×Dic9C22×C311yescharacteristic
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C2411yescharacteristic
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C3×C4×C9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3×C4×C9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9#4112yes—
219C3×#127—91no—
220C3×#125—91no—
221C3×#123—91no—
222C3×#123—91no—
223C3×#123—91no—
224C3×#123—91no—
225C3×#121—21no—
226C3×#121—91no—
227C3×#121—91no—
228C3×#121—91no—
229C3×#121—91no—
230C3×#121—91no—
231C3×#121D911yescharacteristic, complemented
232C3×#121C3×D311yescharacteristic
233C3×C4×D4—91no—
234C3×C4×D4—91no—
235C3×#117—91no—
236#940—31no—
237#939—31no—
238#939—31no—
239#939—31no—
240#938—31no—
241#935—31no—
242#929—31no—
243C4×#67—31no—
244#894—31no—
245#889—31no—
246#884—31no—
247#883—31no—
248#67⋊C4—31no—
249#877—31no—
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C23×C32C22×D311yescharacteristic
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C32×D4—41no—
256C32×D4—41no—
257C32×D4—41no—
258C2×C32×C4—41no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C3×#67—62no—
264C3×#67—62no—
265C3×#67—121no—
266C3×#67—121no—
267C3×#67—121no—
268C3×#67—121no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—121no—
277C3×D12—121no—
278C3×C4×D3—121no—
279C3×C4×D3—121no—
280C23×C9—21no—
281C23×C9—21no—
282C23×C9—21no—
283C23×C9C23×C311yescharacteristic
284C23×C9C23×C311yescharacteristic
285C23×C9C23×C311yescharacteristic
286C22×D9C23×C311yescharacteristic
287C22×D9C23×C311yescharacteristic
288D4×C9—41no—
289D4×C9—41no—
290D4×C9—41no—
291D4×C9—42no—
292D4×C9—42no—
293D4×C9—42no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—21no—
297C2×C4×C9—21no—
298C2×C4×C9—41no—
299C2×C4×C9—42no—
300C2×C4×C9C23×C311yescharacteristic
301C2×C4×C9C23×C311yescharacteristic
302C2×C4×C9C23×C311yescharacteristic
303C2×C4×C9C23×C311yescharacteristic
304#611—22no—
305#611—22no—
306#611—41no—
307#611—41no—
308#611—41no—
309#611—41no—
310C2×Dic9—22no—
311C2×Dic9—41no—
312C2×Dic9C23×C311yescharacteristic
313C2×Dic9C23×C311yescharacteristic
314C2×Dic9C23×C311yescharacteristic
315C2×Dic9C23×C311yescharacteristic
316C2×Dic9C23×C311yescharacteristic
317C2×Dic9C23×C311yescharacteristic
318D36—41no—
319C4×D9—41no—
320C4×D9—41no—
321#540—91noSylow
322C2×C3×C9—41no—
323C2×C3×C9—41no—
324C2×C3×C9—41no—
325C2×C3×C9C2×#4111yescharacteristic
326C2×C3×C9H(5,𝔽2)11yescharacteristic
327C2×C3×C9H(5,𝔽2)11yescharacteristic
328C3×D9—41no—
329C3×D9—41no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4C2×D911yescharacteristic
341C2×C3×D4C2×D911yescharacteristic
342C2×C3×D4C2×D911yescharacteristic
343C2×C3×D4C2×C3×D311yescharacteristic
344C2×C3×D4C2×C3×D311yescharacteristic
345C2×C3×D4C2×C3×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—91no—
348C22×C3×C4—91no—
349C22×C3×C4—91no—
350C22×C3×C4—91no—
351C22×C3×C4C2×D911yescharacteristic
352C22×C3×C4C2×C3×D311yescharacteristic
353C2×#67—31no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—31no—
358C2×#67—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C2×D12—31no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4C2×D911yescharacteristic
373C3×C4⋊C4C2×C3×D311yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4C2×D911yescharacteristic
385C3×C22⋊C4C2×D911yescharacteristic
386C3×C22⋊C4C2×C3×D311yescharacteristic
387C3×C22⋊C4C2×C3×D311yescharacteristic
388C3×C42—91no—
389C3×C42—91no—
390#217—31no—
391#217—31no—
392#217—31no—
393#217—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398C4⋊Dic3—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32C23×D311yescharacteristic
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C3×Dic3—32no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C22×C9—22no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—41no—
445C22×C9—41no—
446C22×C9—41no—
447C22×C9—41no—
448C22×C9—41no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9C24×C311yescharacteristic
453C2×D9—21no—
454C2×D9—21no—
455C2×D9—21no—
456C2×D9—21no—
457C2×D9—21no—
458C2×D9—21no—
459C4×C9—22no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—21no—
463C4×C9—21no—
464C4×C9—41no—
465C4×C9—41no—
466C4×C9—41no—
467Dic9—21no—
468Dic9—21no—
469Dic9—21no—
470Dic9—21no—
471Dic9—21no—
472Dic9C3×#4112yes—
473#127—91no—
474#125—91no—
475#123—91no—
476#123—91no—
477#123—91no—
478#123—91no—
479#121—91no—
480#121—91no—
481#121—91no—
482#121—91no—
483#121—91no—
484#121C3×D911yescharacteristic, complemented
485C4×D4—91no—
486C4×D4—91no—
487#117—91no—
488C3×C9#54011yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—91no—
493C23×C3—91no—
494C23×C3C22×D911yescharacteristic
495C23×C3C22×D911yescharacteristic
496C23×C3C22×D911yescharacteristic
497C23×C3C22×C3×D311yescharacteristic
498C23×C3C22×C3×D311yescharacteristic
499C23×C3C22×C3×D311yescharacteristic
500C22×D3—31no—
501C22×D3—31no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—42no—
509C3×D4—42no—
510C3×D4—42no—
511C3×D4—182no—
512C3×D4—182no—
513C3×D4—361no—
514C3×D4—361no—
515C3×D4—361no—
516C3×D4—361no—
517C3×D4—361no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—42no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—182no—
532C2×C3×C4—361no—
533C2×C3×C4—361no—
534C2×C3×C4—361no—
535C2×C3×C4C22×D911yescharacteristic
536C2×C3×C4C22×D911yescharacteristic
537C2×C3×C4C22×D911yescharacteristic
538C2×C3×C4C22×D911yescharacteristic
539C2×C3×C4C22×C3×D311yescharacteristic
540C2×C3×C4C22×C3×D311yescharacteristic
541C2×C3×C4C22×C3×D311yescharacteristic
542C2×C3×C4C22×C3×D311yescharacteristic
543#67—62no—
544#67—62no—
545#67—121no—
546#67—121no—
547#67—121no—
548#67—121no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—62no—
556C2×Dic3—121no—
557D12—121no—
558C4×D3—121no—
559C4×D3—121no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32#100411yescharacteristic
564C2×C32#100411yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C3×D3—121no—
567C3×D3—121no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—42no—
572C2×C9—41no—
573C2×C9—41no—
574C2×C9—41no—
575C2×C9—81no—
576C2×C9—81no—
577C2×C9C2×C3×#4111yescharacteristic
578C2×C9C3×H(5,𝔽2)11yescharacteristic
579C2×C9C3×H(5,𝔽2)11yescharacteristic
580D9—41no—
581D9—41no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—91no—
585C2×D4—91no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4C2×C3×D911yescharacteristic
590C2×D4C2×C3×D911yescharacteristic
591C2×D4C2×C3×D911yescharacteristic
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4C2×C3×D911yescharacteristic
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4C2×C3×D911yescharacteristic
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—91no—
613C22⋊C4C2×C3×D911yescharacteristic
614C22⋊C4C2×C3×D911yescharacteristic
615C42—91no—
616C42—91no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3C23×D911yescharacteristic
652C22×C3C23×C3×D311yescharacteristic
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—92no—
672C3×C4—181no—
673C3×C4—181no—
674C3×C4—181no—
675C3×C4—181no—
676C3×C4—181no—
677Dic3—32no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683C32#561511yescharacteristic
684C9—21no—
685C9C3×#54011yescharacteristic, complemented
686C23—91no—
687C23—91no—
688C23C22×C3×D911yescharacteristic
689C23C22×C3×D911yescharacteristic
690C23C22×C3×D911yescharacteristic
691D4—41no—
692D4—41no—
693D4—41no—
694D4—182no—
695D4—182no—
696D4—361no—
697D4—361no—
698D4—361no—
699D4—361no—
700D4—361no—
701C2×C4—41no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—182no—
709C2×C4—361no—
710C2×C4—361no—
711C2×C4—361no—
712C2×C4C22×C3×D911yescharacteristic
713C2×C4C22×C3×D911yescharacteristic
714C2×C4C22×C3×D911yescharacteristic
715C2×C4C22×C3×D911yescharacteristic
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—41no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—81no—
728C2×C3—361no—
729C2×C3—361no—
730C2×C3#6371011yescharacteristic
731C2×C3#6371011yescharacteristic
732C2×C3#41×D911yescharacteristic
733C2×C3C3×#100411yescharacteristic
734C2×C3C3×#100411yescharacteristic
735C2×C3C3×D3×#4111yescharacteristic
736D3—121no—
737D3—121no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—181no—
748C22—181no—
749C22—181no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22C23×C3×D911yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—92no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—181no—
763C4—181no—
764C3—21no—
765C3#1058971711yescharacteristic, direct product factor
766C3C3×#561511yescharacteristic
767C2—41no—
768C2—41no—
769C2—41no—
770C2—361no—
771C2—361no—
772C2C3×#6371011yescharacteristic
773C2C3×#6371011yescharacteristic
774C2C3×#41×D911yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#121C2
socleC22×C32C23×D3
hypercenterC3×#121D9
hypocenterC9C3×#540
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
1. C3×C9×#121C2semidirect
2. C3×#63502C2semidirect
3. C3×#63501C2semidirect
4. C3×#63501C2semidirect
5. C3×#63501C2semidirect
6. C3×#63500C2semidirect
7. C3×#63497C2semidirect
8. C3×#63491C2semidirect
9. C3×C4×#611C2semidirect
10. C3×#63456C2semidirect
11. C3×#63451C2semidirect
12. C3×#63446C2semidirect
13. C3×#63445C2semidirect
14. C3×#611⋊C4C2semidirect
15. C3×#63439C2semidirect
17. #10589717C3direct (N × H)
69. C9×#121C2×C3semidirect
70. #63502C2×C3semidirect
71. #63501C2×C3semidirect
72. #63501C2×C3semidirect
73. #63501C2×C3semidirect
74. #63500C2×C3semidirect
75. #63497C2×C3semidirect
76. #63491C2×C3semidirect
77. C4×#611C2×C3semidirect
78. #63456C2×C3semidirect
79. #63451C2×C3semidirect
80. #63446C2×C3semidirect
81. #63445C2×C3semidirect
82. #611⋊C4C2×C3semidirect
83. #63439C2×C3semidirect
231. C3×#121D9semidirect
484. #121C3×D9semidirect
488. C3×C9#540semidirect
685. C9C3×#540semidirect
765. C3#10589717direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1212
C3×#635022
C3×#635012
C3×#635002
C3×#634972
C3×#634912
C3×C4×#6112
C3×#634562
C3×#634512
C3×#634462
C3×#634452
C3×#611⋊C42
C3×#634392
C3×#56153
#105897173