Finite Group Databasebeta

← C3×#10589722 #13152821

Subgroups — C3×#10589722 #13152821

Order 1728.

850 conjugacy classes of subgroups.

The subgroup lattice has 818 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×#63500C211yesmaximal, characteristic, complemented
6C3×#63499C211yesmaximal, characteristic, complemented
7C3×#63499C211yesmaximal, characteristic, complemented
8C3×#63492C211yesmaximal, characteristic, complemented
9C3×#63491C211yesmaximal, characteristic, complemented
10C3×#63460C211yesmaximal, characteristic, complemented
11C3×#63456C211yesmaximal, characteristic, complemented
12C3×#63448C211yesmaximal, characteristic, complemented
13C3×#63446C211yesmaximal, characteristic, complemented
14C3×#63444C211yesmaximal, characteristic, complemented
15C3×#63441C211yesmaximal, characteristic, complemented
16C3×#5620—31nomaximal
17#10589722C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C22×C3×C4×C9C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic, complemented
29C2×C3×#611C2211yescharacteristic, complemented
30C22×C3×Dic9C2211yescharacteristic, complemented
31C2×C3×D36C2211yescharacteristic
32C2×C3×D36C2211yescharacteristic
33C2×C3×C4×D9C2211yescharacteristic, complemented
34C3×C9×C4⋊C4C2211yescharacteristic, complemented
35C3×C9×C22⋊C4C2211yescharacteristic
36C3×C9×C22⋊C4C2211yescharacteristic, complemented
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×#3676C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×C4⋊Dic9C2211yescharacteristic, complemented
48C3×C4⋊Dic9C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51C3×Dic9⋊C4C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#121D311yescharacteristic
54C3×#940—31no—
55C3×#939—31no—
56C3×#939—31no—
57C3×#938—31no—
58C3×#937—31no—
59C3×#937—31no—
60C3×#930—31no—
61C3×#929—31no—
62C3×#898—31no—
63C3×#894—31no—
64C3×#886—31no—
65C3×#884—31no—
66C3×#882—31no—
67C3×#879—31no—
68C9×#121—21no—
69C9×#121C2×C311yescharacteristic, complemented
70#63502C2×C311yescharacteristic, complemented
71#63501C2×C311yescharacteristic, complemented
72#63501C2×C311yescharacteristic, complemented
73#63500C2×C311yescharacteristic, complemented
74#63499C2×C311yescharacteristic, complemented
75#63499C2×C311yescharacteristic, complemented
76#63492C2×C311yescharacteristic, complemented
77#63491C2×C311yescharacteristic, complemented
78#63460C2×C311yescharacteristic, complemented
79#63456C2×C311yescharacteristic, complemented
80#63448C2×C311yescharacteristic, complemented
81#63446C2×C311yescharacteristic, complemented
82#63444C2×C311yescharacteristic, complemented
83#63441C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C23×C3×C9C2311yescharacteristic
87C22×C3×D9—41no—
88C22×C3×D9—41no—
89C22×C3×D9—41no—
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C3×D4×C9—41no—
94C3×D4×C9—41no—
95C3×D4×C9—41no—
96C2×C3×C4×C9—41no—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101C3×#611—41no—
102C3×#611—41no—
103C3×#611—41no—
104C3×#611—41no—
105C3×#611—41no—
106C3×#611—41no—
107C3×#611—41no—
108C2×C3×Dic9—41no—
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C3×D36—41no—
115C3×D36—41no—
116C3×C4×D9—41no—
117C3×#560—91no—
118#5620—31no—
119C23×C3×D3—31no—
120C2×C32×D4C2×D311yescharacteristic
121C2×C32×D4C2×D311yescharacteristic
122C2×C32×D4C2×D311yescharacteristic
123C22×C32×C4C2×D311yescharacteristic
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C22×C3×Dic3—31no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×C4×D3—31no—
135C23×D9C22×C311yescharacteristic
136C32×C4⋊C4C2×D311yescharacteristic
137C32×C22⋊C4C2×D311yescharacteristic
138C32×C22⋊C4C2×D311yescharacteristic
139C3×#217—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×Dic3⋊C4—31no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—31no—
154C3×C4×Dic3—31no—
155C2×D4×C9—21no—
156C2×D4×C9—21no—
157C2×D4×C9—21no—
158C2×D4×C9C22×C311yescharacteristic
159C2×D4×C9C22×C311yescharacteristic
160C2×D4×C9C22×C311yescharacteristic, complemented
161C22×C4×C9—21no—
162C22×C4×C9C22×C311yescharacteristic, complemented
163C2×#611C22×C311yescharacteristic
164C2×#611C22×C311yescharacteristic
165C2×#611C22×C311yescharacteristic
166C2×#611C22×C311yescharacteristic
167C2×#611C22×C311yescharacteristic
168C2×#611C22×C311yescharacteristic, complemented
169C2×#611C22×C311yescharacteristic, complemented
170C22×Dic9C22×C311yescharacteristic, complemented
171C2×D36C22×C311yescharacteristic
172C2×D36C22×C311yescharacteristic
173C2×C4×D9C22×C311yescharacteristic, complemented
174C9×C4⋊C4—21no—
175C9×C4⋊C4C22×C311yescharacteristic, complemented
176C9×C22⋊C4—21no—
177C9×C22⋊C4—21no—
178C9×C22⋊C4C22×C311yescharacteristic
179C9×C22⋊C4C22×C311yescharacteristic, complemented
180#3676C22×C311yescharacteristic
181#3676C22×C311yescharacteristic
182#3676C22×C311yescharacteristic, complemented
183(C2×D9)⋊C4C22×C311yescharacteristic
184(C2×D9)⋊C4C22×C311yescharacteristic
185(C2×D9)⋊C4C22×C311yescharacteristic
186(C2×D9)⋊C4C22×C311yescharacteristic
187(C2×D9)⋊C4C22×C311yescharacteristic
188(C2×D9)⋊C4C22×C311yescharacteristic
189(C2×D9)⋊C4C22×C311yescharacteristic, complemented
190C4⋊Dic9C22×C311yescharacteristic, complemented
191C4⋊Dic9C22×C311yescharacteristic, complemented
192Dic9⋊C4C22×C311yescharacteristic, complemented
193Dic9⋊C4C22×C311yescharacteristic, complemented
194Dic9⋊C4C22×C311yescharacteristic, complemented
195C4×Dic9C22×C311yescharacteristic, complemented
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×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9C2411yescharacteristic
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—44no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3×C4×C9—21no—
219C3×C4×C9—21no—
220C3×Dic9—21no—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#127—91no—
226C3×#126—91no—
227C3×#126—91no—
228C3×#123—91no—
229C3×#123—91no—
230C3×#123—91no—
231C3×#121—21no—
232C3×#121—91no—
233C3×#121—91no—
234C3×#121—91no—
235C3×#121—91no—
236C3×#121—91no—
237C3×#121D911yescharacteristic, complemented
238C3×#121C3×D311yescharacteristic
239C3×#120—91no—
240C3×#120—91no—
241C3×#120—91no—
242#940—31no—
243#939—31no—
244#939—31no—
245#938—31no—
246#937—31no—
247#937—31no—
248#930—31no—
249#929—31no—
250#898—31no—
251#894—31no—
252#886—31no—
253#884—31no—
254#882—31no—
255#879—31no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C23×C32C22×D311yescharacteristic
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3—31no—
262C22×C3×D3—121no—
263C22×C3×D3—121no—
264C22×C3×D3—121no—
265C32×D4—41no—
266C32×D4—41no—
267C32×D4—41no—
268C2×C32×C4—41no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C3×#67—121no—
274C3×#67—121no—
275C3×#67—121no—
276C3×#67—121no—
277C3×#67—121no—
278C3×#67—121no—
279C3×#67—121no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—121no—
286C3×D12—121no—
287C3×D12—121no—
288C3×C4×D3—121no—
289C23×C9—21no—
290C23×C9—21no—
291C23×C9—21no—
292C23×C9C23×C311yescharacteristic
293C23×C9C23×C311yescharacteristic
294C23×C9C23×C311yescharacteristic
295C22×D9—41no—
296C22×D9—41no—
297C22×D9—41no—
298C22×D9C23×C311yescharacteristic
299C22×D9C23×C311yescharacteristic
300C22×D9C23×C311yescharacteristic
301D4×C9—41no—
302D4×C9—41no—
303D4×C9—41no—
304D4×C9—42no—
305D4×C9—42no—
306D4×C9—42no—
307C2×C4×C9—21no—
308C2×C4×C9—21no—
309C2×C4×C9—21no—
310C2×C4×C9—21no—
311C2×C4×C9—41no—
312C2×C4×C9—42no—
313C2×C4×C9C23×C311yescharacteristic
314C2×C4×C9C23×C311yescharacteristic
315C2×C4×C9C23×C311yescharacteristic
316C2×C4×C9C23×C311yescharacteristic
317#611—41no—
318#611—41no—
319#611—41no—
320#611—41no—
321#611—41no—
322#611—41no—
323#611—41no—
324C2×Dic9—41no—
325C2×Dic9C23×C311yescharacteristic
326C2×Dic9C23×C311yescharacteristic
327C2×Dic9C23×C311yescharacteristic
328C2×Dic9C23×C311yescharacteristic
329C2×Dic9C23×C311yescharacteristic
330D36—41no—
331D36—41no—
332C4×D9—41no—
333#560—91noSylow
334C2×C3×C9—41no—
335C2×C3×C9—41no—
336C2×C3×C9—41no—
337C2×C3×C9H(5,𝔽2)11yescharacteristic
338C2×C3×C9H(5,𝔽2)11yescharacteristic
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C3×D9—41no—
341C3×D9—41no—
342C3×D9—41no—
343C24×C3—91no—
344C23×D3—31no—
345C2×C3×D4—21no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4—91no—
356C2×C3×D4—91no—
357C2×C3×D4C2×D911yescharacteristic
358C2×C3×D4C2×D911yescharacteristic
359C2×C3×D4C2×D911yescharacteristic, complemented
360C2×C3×D4C2×C3×D311yescharacteristic
361C2×C3×D4C2×C3×D311yescharacteristic
362C2×C3×D4C2×C3×D311yescharacteristic
363C22×C3×C4—21no—
364C22×C3×C4—91no—
365C22×C3×C4—91no—
366C22×C3×C4C2×D911yescharacteristic, complemented
367C22×C3×C4C2×C3×D311yescharacteristic
368C2×#67—31no—
369C2×#67—31no—
370C2×#67—31no—
371C2×#67—31no—
372C2×#67—31no—
373C2×#67—31no—
374C2×#67—31no—
375C22×Dic3—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×C4×D3—31no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—91no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4—91no—
385C3×C4⋊C4C2×D911yescharacteristic, complemented
386C3×C4⋊C4C2×C3×D311yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4—91no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4C2×D911yescharacteristic
400C3×C22⋊C4C2×D911yescharacteristic, complemented
401C3×C22⋊C4C2×C3×D311yescharacteristic
402C3×C22⋊C4C2×C3×D311yescharacteristic
403C3×C42—91no—
404#217—31no—
405#217—31no—
406#217—31no—
407(C2×D3)⋊C4—31no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—31no—
419C4×Dic3—31no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C23×D311yescharacteristic
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—124no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C22×C9—22no—
450C22×C9—21no—
451C22×C9—21no—
452C22×C9—21no—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—41no—
461C22×C9—41no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—41no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—41no—
468C22×C9C24×C311yescharacteristic
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—21no—
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—21no—
475C2×D9—21no—
476C2×D9—21no—
477C2×D9—21no—
478C2×D9—44no—
479C4×C9—22no—
480C4×C9—21no—
481C4×C9—21no—
482C4×C9—21no—
483C4×C9—21no—
484C4×C9—41no—
485C4×C9—41no—
486C4×C9—41no—
487Dic9—21no—
488Dic9—21no—
489Dic9—21no—
490Dic9—21no—
491Dic9—21no—
492#127—91no—
493#126—91no—
494#126—91no—
495#123—91no—
496#123—91no—
497#123—91no—
498#121—91no—
499#121—91no—
500#121—91no—
501#121—91no—
502#121—91no—
503#121C3×D911yescharacteristic, complemented
504#120—91no—
505#120—91no—
506#120—91no—
507C3×C9#56011yescharacteristic, complemented, Sylow
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—91no—
512C23×C3—91no—
513C23×C3—91no—
514C23×C3—361no—
515C23×C3—361no—
516C23×C3—361no—
517C23×C3C22×D911yescharacteristic
518C23×C3C22×D911yescharacteristic
519C23×C3C22×D911yescharacteristic
520C23×C3C22×C3×D311yescharacteristic
521C23×C3C22×C3×D311yescharacteristic
522C23×C3C22×C3×D311yescharacteristic
523C22×D3—31no—
524C22×D3—31no—
525C22×D3—31no—
526C22×D3—121no—
527C22×D3—121no—
528C22×D3—121no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—42no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—361no—
539C3×D4—361no—
540C3×D4—361no—
541C3×D4—361no—
542C3×D4—361no—
543C3×D4—361no—
544C3×D4—361no—
545C3×D4—361no—
546C3×D4—361no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—91no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—361no—
560C2×C3×C4—361no—
561C2×C3×C4C22×D911yescharacteristic
562C2×C3×C4C22×D911yescharacteristic
563C2×C3×C4C22×D911yescharacteristic
564C2×C3×C4C22×D911yescharacteristic
565C2×C3×C4C22×C3×D311yescharacteristic
566C2×C3×C4C22×C3×D311yescharacteristic
567C2×C3×C4C22×C3×D311yescharacteristic
568C2×C3×C4C22×C3×D311yescharacteristic
569#67—121no—
570#67—121no—
571#67—121no—
572#67—121no—
573#67—121no—
574#67—121no—
575#67—121no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—121no—
582D12—121no—
583D12—121no—
584C4×D3—121no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32#100411yescharacteristic
589C2×C32#100411yescharacteristic
590C2×C32#100911yescharacteristic
591C3×D3—121no—
592C3×D3—121no—
593C3×D3—121no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—42no—
598C2×C9—41no—
599C2×C9—41no—
600C2×C9—41no—
601C2×C9—81no—
602C2×C9—81no—
603C2×C9C3×H(5,𝔽2)11yescharacteristic
604C2×C9C3×H(5,𝔽2)11yescharacteristic
605C2×C9C3×H(5,𝔽2)11yescharacteristic
606D9—41no—
607D9—41no—
608D9—41no—
609C24—91no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—91no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—91no—
618C2×D4—91no—
619C2×D4C2×C3×D911yescharacteristic
620C2×D4C2×C3×D911yescharacteristic
621C2×D4C2×C3×D911yescharacteristic, complemented
622C22×C4—91no—
623C22×C4—91no—
624C22×C4C2×C3×D911yescharacteristic, complemented
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4C2×C3×D911yescharacteristic, complemented
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4C2×C3×D911yescharacteristic
642C22⋊C4C2×C3×D911yescharacteristic, complemented
643C42—91no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—364no—
682C22×C3C23×D911yescharacteristic
683C22×C3C23×C3×D311yescharacteristic
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—124no—
694C3×C4—22no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—181no—
707C3×C4—181no—
708C3×C4—181no—
709C3×C4—181no—
710C3×C4—181no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—61no—
716C32#562011yescharacteristic
717C9—21no—
718C9C3×#56011yescharacteristic, complemented
719C23—91no—
720C23—91no—
721C23—91no—
722C23—361no—
723C23—361no—
724C23—361no—
725C23C22×C3×D911yescharacteristic
726C23C22×C3×D911yescharacteristic
727C23C22×C3×D911yescharacteristic
728D4—41no—
729D4—41no—
730D4—41no—
731D4—361no—
732D4—361no—
733D4—361no—
734D4—361no—
735D4—361no—
736D4—361no—
737D4—361no—
738D4—361no—
739D4—361no—
740C2×C4—41no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—361no—
747C2×C4—361no—
748C2×C4C22×C3×D911yescharacteristic
749C2×C4C22×C3×D911yescharacteristic
750C2×C4C22×C3×D911yescharacteristic
751C2×C4C22×C3×D911yescharacteristic
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—81no—
763C2×C3—81no—
764C2×C3—361no—
765C2×C3—361no—
766C2×C3—361no—
767C2×C3#6371011yescharacteristic
768C2×C3#6371011yescharacteristic
769C2×C3#6371511yescharacteristic
770C2×C3C3×#100411yescharacteristic
771C2×C3C3×#100411yescharacteristic
772C2×C3C3×#100911yescharacteristic
773D3—121no—
774D3—121no—
775D3—121no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—181no—
786C22—181no—
787C22—181no—
788C22—181no—
789C22—181no—
790C22—181no—
791C22—181no—
792C22—181no—
793C22—181no—
794C22—364no—
795C22C23×C3×D911yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—181no—
801C4—181no—
802C4—181no—
803C4—181no—
804C4—181no—
805C3—21no—
806C3#1058972211yescharacteristic, direct product factor
807C3C3×#562011yescharacteristic
808C2—41no—
809C2—41no—
810C2—41no—
811C2—361no—
812C2—361no—
813C2—361no—
814C2C3×#6371011yescharacteristic
815C2C3×#6371011yescharacteristic
816C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#121C2
socleC22×C32C23×D3
hypercenterC3×#121D9
hypocenterC9C3×#560
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×#63500C2semidirect
6. C3×#63499C2semidirect
7. C3×#63499C2semidirect
8. C3×#63492C2semidirect
9. C3×#63491C2semidirect
10. C3×#63460C2semidirect
11. C3×#63456C2semidirect
12. C3×#63448C2semidirect
13. C3×#63446C2semidirect
14. C3×#63444C2semidirect
15. C3×#63441C2semidirect
17. #10589722C3direct (N × H)
21. C2×C3×D4×C9C22semidirect
22. C22×C3×C4×C9C22semidirect
28. C2×C3×#611C22semidirect
29. C2×C3×#611C22semidirect
30. C22×C3×Dic9C22semidirect
33. C2×C3×C4×D9C22semidirect
34. C3×C9×C4⋊C4C22semidirect
36. C3×C9×C22⋊C4C22semidirect
39. C3×#3676C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×C4⋊Dic9C22semidirect
48. C3×C4⋊Dic9C22semidirect
49. C3×Dic9⋊C4C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. C3×Dic9⋊C4C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#121C2×C3semidirect
70. #63502C2×C3semidirect
71. #63501C2×C3semidirect
72. #63501C2×C3semidirect
73. #63500C2×C3semidirect
74. #63499C2×C3semidirect
75. #63499C2×C3semidirect
76. #63492C2×C3semidirect
77. #63491C2×C3semidirect
78. #63460C2×C3semidirect
79. #63456C2×C3semidirect
80. #63448C2×C3semidirect
81. #63446C2×C3semidirect
82. #63444C2×C3semidirect
83. #63441C2×C3semidirect
160. C2×D4×C9C22×C3semidirect
162. C22×C4×C9C22×C3semidirect
168. C2×#611C22×C3semidirect
169. C2×#611C22×C3semidirect
170. C22×Dic9C22×C3semidirect
173. C2×C4×D9C22×C3semidirect
175. C9×C4⋊C4C22×C3semidirect
179. C9×C22⋊C4C22×C3semidirect
182. #3676C22×C3semidirect
189. (C2×D9)⋊C4C22×C3semidirect
190. C4⋊Dic9C22×C3semidirect
191. C4⋊Dic9C22×C3semidirect
192. Dic9⋊C4C22×C3semidirect
193. Dic9⋊C4C22×C3semidirect
194. Dic9⋊C4C22×C3semidirect
195. C4×Dic9C22×C3semidirect
237. C3×#121D9semidirect
359. C2×C3×D4C2×D9semidirect
366. C22×C3×C4C2×D9semidirect
385. C3×C4⋊C4C2×D9semidirect
400. C3×C22⋊C4C2×D9semidirect
503. #121C3×D9semidirect
507. C3×C9#560semidirect
621. C2×D4C2×C3×D9semidirect
624. C22×C4C2×C3×D9semidirect
630. C4⋊C4C2×C3×D9semidirect
642. C22⋊C4C2×C3×D9semidirect
718. C9C3×#560semidirect
806. C3#10589722direct (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×#634992
C3×#634922
C3×#634912
C3×#634602
C3×#634562
C3×#634482
C3×#634462
C3×#634442
C3×#634412
C3×#56203
#105897223