Finite Group Databasebeta

← C3×D3×#560 #11910152

Subgroups — C3×D3×#560 #11910152

Order 1152.

2814 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#560C211yesmaximal, characteristic, complemented
2C3×#5720C211yesmaximal, characteristic, complemented
3C3×D3×#127C211yesmaximal, characteristic, complemented
4C3×#5711C212yesmaximal, complemented
5C3×D3×#126C212yesmaximal, complemented
6C3×#5666C213yesmaximal, complemented
7C3×D3×#123C213yesmaximal, complemented
8C3×#5620C216yesmaximal, complemented
9C3×D3×#121C216yesmaximal, complemented
10C3×#5595C213yesmaximal, complemented
11C3×D3×#120C213yesmaximal, complemented
12C2×C3×#560—31nomaximal
13D3×#560C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C2×C3×D3×D4C2216yes—
16C2×C3×D3×D4C2213yes—
17C2×C3×D3×D4C2213yescomplemented
18C22×C3×C4×D3C2213yescomplemented
19C32×#127C2211yescharacteristic, complemented
20C32×#126C2212yescomplemented
21C32×#123C2213yescomplemented
22C32×#121C2216yescomplemented
23C32×#120C2213yescomplemented
24C3×#953C2213yescomplemented
25C3×#940C2213yescomplemented
26C3×#940C2213yescomplemented
27C3×#939C2216yescomplemented
28C3×#939C2216yescomplemented
29C3×#938C2216yescomplemented
30C3×#937C2216yescomplemented
31C3×#937C2213yescomplemented
32C3×#935C2213yescomplemented
33C3×#930C2216yescomplemented
34C3×#929C2213yescomplemented
35C3×#898C2216yescomplemented
36C3×#895C2216yescomplemented
37C3×#894C2216yescomplemented
38C3×D3×C4⋊C4C2216yescomplemented
39C3×#886C2213yescomplemented
40C3×#884C2216yescomplemented
41C3×#884C2216yescomplemented
42C3×#883C2216yescomplemented
43C3×#882C2216yescomplemented
44C3×#882C2213yescomplemented
45C3×D3×C22⋊C4C2216yes—
46C3×D3×C22⋊C4C2213yes—
47C3×D3×C22⋊C4C2213yescomplemented
48C3×#879C2216yescomplemented
49C3×#876C2212yescomplemented
50C3×#874C2211yescharacteristic, complemented
51C3×C42×D3C2211yescharacteristic, complemented
52C3×#560—21no—
53C3×#560—31no—
54C3×#560—32no—
55C3×#560—33no—
56C3×#560—36no—
57C3×#560—33no—
58C3×#560D311yescharacteristic, direct product factor
59C3×#560C2×C311yescharacteristic, complemented
60C2×C3×#127—31no—
61C2×C3×#126—32no—
62C2×C3×#123—33no—
63C2×C3×#121—36no—
64C2×C3×#120—33no—
65#5720C2×C311yescharacteristic, complemented
66D3×#127C2×C311yescharacteristic, complemented
67#5711C2×C312yescomplemented
68D3×#126C2×C312yescomplemented
69#5666C2×C313yescomplemented
70D3×#123C2×C313yescomplemented
71#5620C2×C316yescomplemented
72D3×#121C2×C316yescomplemented
73#5595C2×C313yescomplemented
74D3×#120C2×C313yescomplemented
75C24×C32C2311yescharacteristic
76C23×C3×D3—46no—
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2313yes—
80C23×C3×D3C2312yes—
81C23×C3×D3C2311yescharacteristic
82C2×C32×D4C2313yes—
83C2×C32×D4C2316yes—
84C2×C32×D4C2313yescomplemented
85C22×C32×C4C2313yescomplemented
86C2×C3×#67C2313yes—
87C2×C3×#67C2316yes—
88C2×C3×#67C2316yes—
89C2×C3×#67C2313yes—
90C2×C3×#67C2316yescomplemented
91C22×C3×Dic3C2313yescomplemented
92C3×D3×D4—412no—
93C3×D3×D4—46no—
94C3×D3×D4—46no—
95C2×C3×D12C2316yes—
96C2×C3×D12C2313yes—
97C2×C3×D12C2313yescomplemented
98C2×C3×C4×D3—46no—
99C2×C3×C4×D3C2316yes—
100C2×C3×C4×D3C2313yes—
101C2×C3×C4×D3C2316yescomplemented
102C32×C4⋊C4C2316yescomplemented
103C32×C22⋊C4C2316yes—
104C32×C22⋊C4C2313yes—
105C32×C22⋊C4C2313yescomplemented
106C32×C42C2311yescharacteristic, complemented
107C3×#217C2316yes—
108C3×#217C2313yes—
109C3×#217C2313yescomplemented
110C3×(C2×D3)⋊C4C2316yes—
111C3×(C2×D3)⋊C4C2316yes—
112C3×(C2×D3)⋊C4C2316yes—
113C3×(C2×D3)⋊C4C2316yescomplemented
114C3×C4⋊Dic3C2316yescomplemented
115C3×Dic3⋊C4C2316yescomplemented
116C3×Dic3⋊C4C2316yescomplemented
117C3×C4×Dic3C2313yescomplemented
118C2×#560—31noSylow
119C25×C3—31no—
120C24×D3C22×C311yescharacteristic
121C22×C3×D4—36no—
122C22×C3×D4—33no—
123C22×C3×D4—33no—
124C23×C3×C4—33no—
125C2×D3×D4C22×C313yes—
126C2×D3×D4C22×C316yes—
127C2×D3×D4C22×C313yescomplemented
128C22×C4×D3C22×C313yescomplemented
129C3×#127—21no—
130C3×#127—33no—
131C3×#127—33no—
132C3×#127—31no—
133C3×#127C2×D311yescharacteristic, complemented
134C3×#127C22×C311yescharacteristic, complemented
135C3×#126—22no—
136C3×#126—36no—
137C3×#126—36no—
138C3×#126—32no—
139C3×#126C2×D312yescomplemented
140C3×#126C22×C312yescomplemented
141C3×#123—23no—
142C3×#123—33no—
143C3×#123—33no—
144C3×#123—36no—
145C3×#123—36no—
146C3×#123—33no—
147C3×#123C2×D313yescomplemented
148C3×#123C22×C313yescomplemented
149C3×#121—26no—
150C3×#121—36no—
151C3×#121—36no—
152C3×#121—36no—
153C3×#121—36no—
154C3×#121—36no—
155C3×#121—36no—
156C3×#121—36no—
157C3×#121C2×D316yescomplemented
158C3×#121C22×C316yescomplemented
159C3×#120—23no—
160C3×#120—33no—
161C3×#120—36no—
162C3×#120—33no—
163C3×#120—33no—
164C3×#120—36no—
165C3×#120C2×D313yescomplemented
166C3×#120C22×C313yescomplemented
167C2×C3×C4⋊C4—36no—
168C2×C3×C22⋊C4—36no—
169C2×C3×C22⋊C4—33no—
170C2×C3×C22⋊C4—33no—
171C2×C3×C42—31no—
172#953C22×C313yescomplemented
173#940C22×C313yescomplemented
174#940C22×C313yescomplemented
175#939C22×C316yescomplemented
176#939C22×C316yescomplemented
177#938C22×C316yescomplemented
178#937C22×C313yescomplemented
179#937C22×C316yescomplemented
180#935C22×C313yescomplemented
181#930C22×C316yescomplemented
182#929C22×C313yescomplemented
183#898C22×C316yescomplemented
184#895C22×C316yescomplemented
185#894C22×C316yescomplemented
186D3×C4⋊C4C22×C316yescomplemented
187#886C22×C313yescomplemented
188#884C22×C316yescomplemented
189#884C22×C316yescomplemented
190#883C22×C316yescomplemented
191#882C22×C313yescomplemented
192#882C22×C316yescomplemented
193D3×C22⋊C4C22×C313yes—
194D3×C22⋊C4C22×C316yes—
195D3×C22⋊C4C22×C313yescomplemented
196#879C22×C316yescomplemented
197#876C22×C312yescomplemented
198#874C22×C311yescharacteristic, complemented
199C42×D3C22×C311yescharacteristic, complemented
200C23×C32—43no—
201C23×C32C2412yes—
202C23×C32C2411yescharacteristic
203C23×C32C2413yes—
204C22×C3×D3—212no—
205C22×C3×D3—26no—
206C22×C3×D3—26no—
207C22×C3×D3—212no—
208C22×C3×D3—46no—
209C22×C3×D3—43no—
210C22×C3×D3—416no—
211C22×C3×D3C2412yes—
212C22×C3×D3C2411yescharacteristic
213C22×C3×D3C2413yes—
214C22×C3×D3C2411yescharacteristic
215C32×D4—46no—
216C32×D4—43no—
217C32×D4—43no—
218C2×C32×C4—43no—
219C2×C32×C4C2413yes—
220C2×C32×C4C2416yes—
221C3×#67—46no—
222C3×#67—46no—
223C3×#67—43no—
224C3×#67—43no—
225C3×#67—46no—
226C2×C3×Dic3—43no—
227C2×C3×Dic3C2413yes—
228C2×C3×Dic3C2416yes—
229C3×D12—46no—
230C3×D12—43no—
231C3×D12—43no—
232C3×C4×D3—212no—
233C3×C4×D3—26no—
234C3×C4×D3—46no—
235#560—31no—
236#560—32no—
237#560—33no—
238#560—36no—
239#560—33no—
240#560C3×D311yescharacteristic, direct product factor
241C2×#127—31no—
242C2×#126—32no—
243C2×#123—33no—
244C2×#121—36no—
245C2×#120—33no—
246C24×C3—21no—
247C24×C3—32no—
248C24×C3—31no—
249C24×C3—33no—
250C24×C3—31no—
251C24×C3—32no—
252C24×C3—126no—
253C24×C3C22×D311yescharacteristic
254C24×C3C23×C311yescharacteristic
255C23×D3—46no—
256C23×D3C23×C311yescharacteristic
257C23×D3C23×C312yes—
258C23×D3C23×C313yes—
259C23×D3C23×C311yescharacteristic
260C23×D3C23×C312yes—
261C2×C3×D4—26no—
262C2×C3×D4—23no—
263C2×C3×D4—23no—
264C2×C3×D4—36no—
265C2×C3×D4—36no—
266C2×C3×D4—33no—
267C2×C3×D4—33no—
268C2×C3×D4—36no—
269C2×C3×D4—36no—
270C2×C3×D4—33no—
271C2×C3×D4—33no—
272C2×C3×D4—1212no—
273C2×C3×D4—126no—
274C2×C3×D4—126no—
275C2×C3×D4C22×D316yes—
276C2×C3×D4C22×D313yes—
277C2×C3×D4C22×D313yescomplemented
278C2×C3×D4C23×C313yes—
279C2×C3×D4C23×C316yes—
280C2×C3×D4C23×C313yescomplemented
281C22×C3×C4—23no—
282C22×C3×C4—33no—
283C22×C3×C4—33no—
284C22×C3×C4—36no—
285C22×C3×C4—36no—
286C22×C3×C4—126no—
287C22×C3×C4C22×D313yescomplemented
288C22×C3×C4C23×C313yescomplemented
289C2×#67C23×C313yes—
290C2×#67C23×C316yes—
291C2×#67C23×C316yes—
292C2×#67C23×C313yes—
293C2×#67C23×C316yescomplemented
294C22×Dic3C23×C313yescomplemented
295D3×D4—412no—
296D3×D4—46no—
297D3×D4—46no—
298C2×D12C23×C313yes—
299C2×D12C23×C316yes—
300C2×D12C23×C313yescomplemented
301C2×C4×D3—46no—
302C2×C4×D3C23×C313yes—
303C2×C4×D3C23×C316yes—
304C2×C4×D3C23×C316yescomplemented
305C3×C4⋊C4—26no—
306C3×C4⋊C4—36no—
307C3×C4⋊C4—36no—
308C3×C4⋊C4—36no—
309C3×C4⋊C4C22×D316yescomplemented
310C3×C4⋊C4C23×C316yescomplemented
311C3×C22⋊C4—26no—
312C3×C22⋊C4—23no—
313C3×C22⋊C4—23no—
314C3×C22⋊C4—36no—
315C3×C22⋊C4—33no—
316C3×C22⋊C4—33no—
317C3×C22⋊C4—36no—
318C3×C22⋊C4—36no—
319C3×C22⋊C4—36no—
320C3×C22⋊C4—36no—
321C3×C22⋊C4C22×D316yes—
322C3×C22⋊C4C22×D313yes—
323C3×C22⋊C4C22×D313yescomplemented
324C3×C22⋊C4C23×C316yes—
325C3×C22⋊C4C23×C313yes—
326C3×C22⋊C4C23×C313yescomplemented
327C3×C42—21no—
328C3×C42—33no—
329C3×C42C22×D311yescharacteristic, complemented
330C3×C42C23×C311yescharacteristic, complemented
331#217C23×C316yes—
332#217C23×C313yes—
333#217C23×C313yescomplemented
334(C2×D3)⋊C4C23×C316yes—
335(C2×D3)⋊C4C23×C316yes—
336(C2×D3)⋊C4C23×C316yes—
337(C2×D3)⋊C4C23×C316yescomplemented
338C4⋊Dic3C23×C316yescomplemented
339Dic3⋊C4C23×C316yescomplemented
340Dic3⋊C4C23×C316yescomplemented
341C4×Dic3C23×C313yescomplemented
342C22×C32—23no—
343C22×C32—26no—
344C22×C32—26no—
345C22×C32—23no—
346C22×C32—44no—
347C22×C32C2511yescharacteristic
348C2×C3×D3—23no—
349C2×C3×D3—26no—
350C2×C3×D3—26no—
351C2×C3×D3—23no—
352C2×C3×D3—48no—
353C2×C3×D3—44no—
354C2×C3×D3—412no—
355C2×C3×D3—48no—
356C2×C3×D3—44no—
357C2×C3×D3H(5,𝔽2)16yes—
358C32×C4—26no—
359C32×C4—23no—
360C3×Dic3—26no—
361C3×Dic3—23no—
362C25—31no—
363C22×D4—36no—
364C22×D4—33no—
365C22×D4—33no—
366C23×C4—33no—
367#127—33no—
368#127—33no—
369#127—31no—
370#127C2×C3×D311yescharacteristic, complemented
371#126—36no—
372#126—36no—
373#126—32no—
374#126C2×C3×D312yescomplemented
375#123—33no—
376#123—33no—
377#123—36no—
378#123—36no—
379#123—33no—
380#123C2×C3×D313yescomplemented
381#121—36no—
382#121—36no—
383#121—36no—
384#121—36no—
385#121—36no—
386#121—36no—
387#121—36no—
388#121C2×C3×D316yescomplemented
389#120—33no—
390#120—36no—
391#120—33no—
392#120—33no—
393#120—36no—
394#120C2×C3×D313yescomplemented
395C2×C4⋊C4—36no—
396C2×C22⋊C4—36no—
397C2×C22⋊C4—33no—
398C2×C22⋊C4—33no—
399C2×C42—31no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—23no—
403C23×C3—31no—
404C23×C3—32no—
405C23×C3—31no—
406C23×C3—33no—
407C23×C3—43no—
408C23×C3—43no—
409C23×C3—66no—
410C23×C3—612no—
411C23×C3—612no—
412C23×C3—66no—
413C23×C3—83no—
414C23×C3—126no—
415C23×C3—123no—
416C23×C3—1216no—
417C23×C3C23×D312yes—
418C23×C3C23×D311yescharacteristic
419C23×C3C23×D313yes—
420C23×C3C24×C312yes—
421C23×C3C24×C311yescharacteristic
422C23×C3C24×C313yes—
423C22×D3—26no—
424C22×D3—212no—
425C22×D3—212no—
426C22×D3—26no—
427C22×D3—43no—
428C22×D3—46no—
429C22×D3—416no—
430C22×D3C24×C312yes—
431C22×D3C24×C311yescharacteristic
432C22×D3C24×C313yes—
433C22×D3C24×C311yescharacteristic
434C3×D4—46no—
435C3×D4—43no—
436C3×D4—43no—
437C3×D4—46no—
438C3×D4—43no—
439C3×D4—43no—
440C3×D4—86no—
441C3×D4—83no—
442C3×D4—83no—
443C3×D4—126no—
444C3×D4—123no—
445C3×D4—123no—
446C3×D4—126no—
447C3×D4—126no—
448C3×D4—123no—
449C3×D4—126no—
450C3×D4—123no—
451C2×C3×C4—23no—
452C2×C3×C4—26no—
453C2×C3×C4—33no—
454C2×C3×C4—36no—
455C2×C3×C4—43no—
456C2×C3×C4—43no—
457C2×C3×C4—612no—
458C2×C3×C4—66no—
459C2×C3×C4—83no—
460C2×C3×C4—126no—
461C2×C3×C4—123no—
462C2×C3×C4C23×D313yes—
463C2×C3×C4C23×D316yes—
464C2×C3×C4C24×C313yes—
465C2×C3×C4C24×C316yes—
466#67—46no—
467#67—46no—
468#67—43no—
469#67—43no—
470#67—46no—
471C2×Dic3—43no—
472C2×Dic3C24×C313yes—
473C2×Dic3C24×C316yes—
474D12—46no—
475D12—43no—
476D12—43no—
477C4×D3—212no—
478C4×D3—26no—
479C4×D3—46no—
480C2×C32—42no—
481C2×C32—41no—
482C2×C32—43no—
483C2×C32C2×H(5,𝔽2)13yes—
484C3×D3—43no—
485C3×D3—42no—
486C3×D3—41no—
487C3×D3#56014yesdirect product factor
488C24—32no—
489C24—31no—
490C24—33no—
491C24—31no—
492C24—32no—
493C24—126no—
494C24C22×C3×D311yescharacteristic
495C2×D4—36no—
496C2×D4—36no—
497C2×D4—33no—
498C2×D4—33no—
499C2×D4—36no—
500C2×D4—36no—
501C2×D4—33no—
502C2×D4—33no—
503C2×D4—1212no—
504C2×D4—126no—
505C2×D4—126no—
506C2×D4C22×C3×D316yes—
507C2×D4C22×C3×D313yes—
508C2×D4C22×C3×D313yescomplemented
509C22×C4—33no—
510C22×C4—33no—
511C22×C4—36no—
512C22×C4—36no—
513C22×C4—126no—
514C22×C4C22×C3×D313yescomplemented
515C4⋊C4—36no—
516C4⋊C4—36no—
517C4⋊C4—36no—
518C4⋊C4C22×C3×D316yescomplemented
519C22⋊C4—36no—
520C22⋊C4—33no—
521C22⋊C4—33no—
522C22⋊C4—36no—
523C22⋊C4—36no—
524C22⋊C4—36no—
525C22⋊C4—36no—
526C22⋊C4C22×C3×D316yes—
527C22⋊C4C22×C3×D313yes—
528C22⋊C4C22×C3×D313yescomplemented
529C42—33no—
530C42C22×C3×D311yescharacteristic, complemented
531C22×C3—23no—
532C22×C3—26no—
533C22×C3—26no—
534C22×C3—23no—
535C22×C3—23no—
536C22×C3—26no—
537C22×C3—26no—
538C22×C3—23no—
539C22×C3—21no—
540C22×C3—36no—
541C22×C3—43no—
542C22×C3—46no—
543C22×C3—46no—
544C22×C3—43no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—63no—
548C22×C3—66no—
549C22×C3—66no—
550C22×C3—63no—
551C22×C3—84no—
552C22×C3—128no—
553C22×C3—124no—
554C22×C3—1212no—
555C22×C3—128no—
556C22×C3—124no—
557C22×C3C24×D311yescharacteristic
558C22×C3C25×C311yescharacteristic
559C2×D3—23no—
560C2×D3—26no—
561C2×D3—26no—
562C2×D3—23no—
563C2×D3—44no—
564C2×D3—48no—
565C2×D3—48no—
566C2×D3—44no—
567C2×D3—412no—
568C2×D3C3×H(5,𝔽2)16yes—
569C3×C4—26no—
570C3×C4—23no—
571C3×C4—26no—
572C3×C4—23no—
573C3×C4—46no—
574C3×C4—43no—
575C3×C4—66no—
576C3×C4—63no—
577Dic3—26no—
578Dic3—23no—
579C32C2×#56011yescharacteristic, complemented, Sylow
580C23—31no—
581C23—32no—
582C23—31no—
583C23—33no—
584C23—43no—
585C23—66no—
586C23—612no—
587C23—612no—
588C23—66no—
589C23—126no—
590C23—123no—
591C23—1216no—
592C23C23×C3×D312yes—
593C23C23×C3×D311yescharacteristic
594C23C23×C3×D313yes—
595D4—46no—
596D4—43no—
597D4—43no—
598D4—126no—
599D4—123no—
600D4—123no—
601D4—126no—
602D4—126no—
603D4—123no—
604D4—126no—
605D4—123no—
606C2×C4—33no—
607C2×C4—36no—
608C2×C4—43no—
609C2×C4—612no—
610C2×C4—66no—
611C2×C4—126no—
612C2×C4—123no—
613C2×C4C23×C3×D313yes—
614C2×C4C23×C3×D316yes—
615C2×C3—23no—
616C2×C3—34no—
617C2×C3—42no—
618C2×C3—41no—
619C2×C3—43no—
620C2×C3—42no—
621C2×C3—41no—
622C2×C3—43no—
623C2×C3—82no—
624C2×C3—81no—
625C2×C3—83no—
626C2×C3—122no—
627C2×C3—121no—
628C2×C3—123no—
629C2×C3D3×H(5,𝔽2)13yes—
630C2×C3C2×C3×H(5,𝔽2)13yes—
631D3—42no—
632D3—41no—
633D3—43no—
634D3C3×#56014yesdirect product factor
635C22—23no—
636C22—26no—
637C22—26no—
638C22—23no—
639C22—36no—
640C22—44no—
641C22—63no—
642C22—66no—
643C22—66no—
644C22—63no—
645C22—128no—
646C22—124no—
647C22—1212no—
648C22—128no—
649C22—124no—
650C22C24×C3×D311yescharacteristic
651C4—26no—
652C4—23no—
653C4—66no—
654C4—63no—
655C3—21no—
656C3D3×#56011yescharacteristic, direct product factor
657C3C2×C3×#56011yescharacteristic, complemented
658C2—34no—
659C2—42no—
660C2—41no—
661C2—43no—
662C2—122no—
663C2—121no—
664C2—123no—
665C2C3×D3×H(5,𝔽2)13yes—
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#560C2
socleC22×C32C25
hypercenterC3×#560D3
hypocenterC3C2×C3×#560
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#560

Complements

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

NH ≅ G/Ntype
1. C32×#560C2semidirect
2. C3×#5720C2semidirect
3. C3×D3×#127C2semidirect
4. C3×#5711C2semidirect
5. C3×D3×#126C2semidirect
6. C3×#5666C2semidirect
7. C3×D3×#123C2semidirect
8. C3×#5620C2semidirect
9. C3×D3×#121C2semidirect
10. C3×#5595C2semidirect
11. C3×D3×#120C2semidirect
13. D3×#560C3direct (N × H)
17. C2×C3×D3×D4C22semidirect
18. C22×C3×C4×D3C22semidirect
19. C32×#127C22semidirect
20. C32×#126C22semidirect
21. C32×#123C22semidirect
22. C32×#121C22semidirect
23. C32×#120C22semidirect
24. C3×#953C22semidirect
25. C3×#940C22semidirect
26. C3×#940C22semidirect
27. C3×#939C22semidirect
28. C3×#939C22semidirect
29. C3×#938C22semidirect
30. C3×#937C22semidirect
31. C3×#937C22semidirect
32. C3×#935C22semidirect
33. C3×#930C22semidirect
34. C3×#929C22semidirect
35. C3×#898C22semidirect
36. C3×#895C22semidirect
37. C3×#894C22semidirect
38. C3×D3×C4⋊C4C22semidirect
39. C3×#886C22semidirect
40. C3×#884C22semidirect
41. C3×#884C22semidirect
42. C3×#883C22semidirect
43. C3×#882C22semidirect
44. C3×#882C22semidirect
47. C3×D3×C22⋊C4C22semidirect
48. C3×#879C22semidirect
49. C3×#876C22semidirect
50. C3×#874C22semidirect
51. C3×C42×D3C22semidirect
58. C3×#560D3direct (N × H)
59. C3×#560C2×C3semidirect
65. #5720C2×C3semidirect
66. D3×#127C2×C3semidirect
67. #5711C2×C3semidirect
68. D3×#126C2×C3semidirect
69. #5666C2×C3semidirect
70. D3×#123C2×C3semidirect
71. #5620C2×C3semidirect
72. D3×#121C2×C3semidirect
73. #5595C2×C3semidirect
74. D3×#120C2×C3semidirect
84. C2×C32×D4C23semidirect
85. C22×C32×C4C23semidirect
90. C2×C3×#67C23semidirect
91. C22×C3×Dic3C23semidirect
97. C2×C3×D12C23semidirect
101. C2×C3×C4×D3C23semidirect
102. C32×C4⋊C4C23semidirect
105. C32×C22⋊C4C23semidirect
106. C32×C42C23semidirect
109. C3×#217C23semidirect
113. C3×(C2×D3)⋊C4C23semidirect
114. C3×C4⋊Dic3C23semidirect
115. C3×Dic3⋊C4C23semidirect
116. C3×Dic3⋊C4C23semidirect
117. C3×C4×Dic3C23semidirect
127. C2×D3×D4C22×C3semidirect
128. C22×C4×D3C22×C3semidirect
133. C3×#127C2×D3semidirect
134. C3×#127C22×C3semidirect
139. C3×#126C2×D3semidirect
140. C3×#126C22×C3semidirect
147. C3×#123C2×D3semidirect
148. C3×#123C22×C3semidirect
157. C3×#121C2×D3semidirect
158. C3×#121C22×C3semidirect
165. C3×#120C2×D3semidirect
166. C3×#120C22×C3semidirect
172. #953C22×C3semidirect
173. #940C22×C3semidirect
174. #940C22×C3semidirect
175. #939C22×C3semidirect
176. #939C22×C3semidirect
177. #938C22×C3semidirect
178. #937C22×C3semidirect
179. #937C22×C3semidirect
180. #935C22×C3semidirect
181. #930C22×C3semidirect
182. #929C22×C3semidirect
183. #898C22×C3semidirect
184. #895C22×C3semidirect
185. #894C22×C3semidirect
186. D3×C4⋊C4C22×C3semidirect
187. #886C22×C3semidirect
188. #884C22×C3semidirect
189. #884C22×C3semidirect
190. #883C22×C3semidirect
191. #882C22×C3semidirect
192. #882C22×C3semidirect
195. D3×C22⋊C4C22×C3semidirect
196. #879C22×C3semidirect
197. #876C22×C3semidirect
198. #874C22×C3semidirect
199. C42×D3C22×C3semidirect
240. #560C3×D3direct (N × H)
277. C2×C3×D4C22×D3semidirect
280. C2×C3×D4C23×C3semidirect
287. C22×C3×C4C22×D3semidirect
288. C22×C3×C4C23×C3semidirect
293. C2×#67C23×C3semidirect
294. C22×Dic3C23×C3semidirect
300. C2×D12C23×C3semidirect
304. C2×C4×D3C23×C3semidirect
309. C3×C4⋊C4C22×D3semidirect
310. C3×C4⋊C4C23×C3semidirect
323. C3×C22⋊C4C22×D3semidirect
326. C3×C22⋊C4C23×C3semidirect
329. C3×C42C22×D3semidirect
330. C3×C42C23×C3semidirect
333. #217C23×C3semidirect
337. (C2×D3)⋊C4C23×C3semidirect
338. C4⋊Dic3C23×C3semidirect
339. Dic3⋊C4C23×C3semidirect
340. Dic3⋊C4C23×C3semidirect
341. C4×Dic3C23×C3semidirect
370. #127C2×C3×D3semidirect
374. #126C2×C3×D3semidirect
380. #123C2×C3×D3semidirect
388. #121C2×C3×D3semidirect
394. #120C2×C3×D3semidirect
487. C3×D3#560direct (N × H)
508. C2×D4C22×C3×D3semidirect
514. C22×C4C22×C3×D3semidirect
518. C4⋊C4C22×C3×D3semidirect
528. C22⋊C4C22×C3×D3semidirect
530. C42C22×C3×D3semidirect
579. C32C2×#560semidirect
634. D3C3×#560direct (N × H)
656. C3D3×#560direct (N × H)
657. C3C2×C3×#560semidirect

Maximal subgroups

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

subgroupindex
C32×#5602
C3×#57202
C3×D3×#1272
C3×#57112
C3×D3×#1262
C3×#56662
C3×D3×#1232
C3×#56202
C3×D3×#1212
C3×#55952
C3×D3×#1202
C2×C3×#5603
D3×#5603