Finite Group Databasebeta

← C3×#10591452 #13158463

Subgroups — C3×#10591452 #13158463

Order 1728.

992 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×#3753C211yesmaximal, characteristic, complemented
3C3×#63909C211yesmaximal, characteristic, complemented
4C2×C3×#3717C211yesmaximal, characteristic, complemented
5C32×#832C211yesmaximal, characteristic, complemented
6C3×#63565C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5238—31nomaximal
9C3×#4781—31nomaximal
10#10591452C311yesmaximal, characteristic, direct product factor
11C2×C33×D4C2211yescharacteristic
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×#67—21no—
14C22×C32×Dic3—21no—
15C32×#237—22no—
16C32×#237—22no—
17C2×C32×C4×D3C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic
19C2×C3×#626—21no—
20C3×#3753—22no—
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C2×C32×C3⋊C8C2211yescharacteristic
24C3×#3722—21no—
25C3×#3717—22no—
26C2×C32×#41—31no—
27C2×C3×#237—21no—
28C2×C3×#237D311yescharacteristic, complemented
29C2×C3×#237C2×C311yescharacteristic, complemented
30C2×#3753C2×C311yescharacteristic, complemented
31C2×C3×#215—31no—
32C2×C3×#213—31no—
33C2×C3×#213—31no—
34C2×C3×#213—61no—
35C3×#930—31no—
36C2×C3×#204—31no—
37C3×#895—31no—
38#63909C2×C311yescharacteristic, complemented
39C2×#3717C2×C311yescharacteristic, complemented
40C32×#102—31no—
41C3×#835—31no—
42C3×#832—21no—
43C3×#832D311yescharacteristic, complemented
44C3×#832C2×C311yescharacteristic, complemented
45C3×#830—31no—
46C3×(C2×D3)⋊C8—31no—
47C3×#810—31no—
48#63565C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C3×C3⋊D3—21no—
52C22×C32×D3D411yescharacteristic
53C33×D4—21no—
54C33×D4D412yescomplemented
55C2×C33×C4C2311yescharacteristic
56C3×C4⋊(C3⋊D3)—21no—
57C3×C4⋊(C3⋊D3)—21no—
58C32×#67—24no—
59C2×C32×Dic3—24no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3D411yescharacteristic
63C32×C4×D3—21no—
64C32×C4×D3—21no—
65C32×Dic6—21no—
66C32×Dic6D412yescomplemented
67C3×#626—42no—
68C3×C3⋊(C3⋊C8)—21no—
69C32×C3⋊C8—21no—
70C3×#449—91no—
71#5238—31no—
72#4781—31no—
73C32×#41—62no—
74C32×#41—62no—
75C2×C32×Q8—31no—
76C2×C32×D4—21no—
77C2×C32×D4—21no—
78C2×C32×D4—21no—
79C2×C32×D4—41no—
80C2×C32×D4—61no—
81C2×C32×D4C2×D311yescharacteristic
82C2×C32×D4C2×D311yescharacteristic
83C2×C32×D4C22×C311yescharacteristic
84C22×C32×C4—31no—
85C22×C32×C4—61no—
86C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
87C2×C3×#67—22no—
88C2×C3×#67—21no—
89C2×C3×#67—21no—
90C2×C3×#67—61no—
91C22×C3×Dic3—22no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C3×#237—24no—
95C3×#237—24no—
96C3×#237—22no—
97C3×#237—22no—
98C3×#237—22no—
99C3×#237—22no—
100C2×C3×D12—31no—
101C2×C3×D12—31no—
102C2×C3×D12—61no—
103C2×C3×D12—61no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×C4×D3C22×C311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2×D311yescharacteristic
109C2×C3×Dic6C22×C311yescharacteristic
110C2×#626—21no—
111C2×C32×C8—31no—
112C32×C4⋊C4—31no—
113#3753—22no—
114C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
115C3×#215—62no—
116C3×#213—64no—
117C3×#213—62no—
118C3×#213—62no—
119C3×(C2×D3)⋊C4—61no—
120C3×(C2×D3)⋊C4—61no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2×D311yescharacteristic
123C3×C4⋊Dic3C22×C311yescharacteristic
124C2×C3×C3⋊C8—21no—
125C2×C3×C3⋊C8—31no—
126C2×C3×C3⋊C8—31no—
127C2×C3×C3⋊C8—61no—
128C2×C3×C3⋊C8C2×D311yescharacteristic
129C2×C3×C3⋊C8C22×C311yescharacteristic
130C3×#204—62no—
131#3722—21no—
132#3717—22no—
133C22×C33—22no—
134C22×C33—41no—
135C22×C33—41no—
136C22×C33C2×D411yescharacteristic
137C2×C3×C3⋊D3—41no—
138C2×C3×C3⋊D3—41no—
139C2×C3×C3⋊D3—41no—
140C2×C32×D3—21no—
141C2×C32×D3—21no—
142C2×C32×D3—21no—
143C33×C4C2×D411yescharacteristic
144C33×C4C2×D411yescharacteristic
145C32×Dic3—22no—
146C32×Dic3—21no—
147C32×Dic3—41no—
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×C3×#41—61no—
151C2×#237C3×D311yescharacteristic, complemented
152C2×C3×SD16—91no—
153C2×C3×D8—91no—
154C3×#121—91no—
155C2×#215—31no—
156C2×#213—31no—
157C2×#213—31no—
158C2×#213—61no—
159#930—31no—
160C2×#204—31no—
161#895—31no—
162C3×#103—91no—
163C3×#102—31no—
164C3×#102—31no—
165C3×#102—61no—
166C3×C22⋊C8—91no—
167#835—31no—
168#832C3×D311yescharacteristic, complemented
169#830—31no—
170(C2×D3)⋊C8—31no—
171#810—31no—
172C23×C32—21no—
173C23×C32—22no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—31no—
177C23×C32—41no—
178C23×C32—41no—
179C23×C32—42no—
180C22×C3⋊D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—61no—
183C22×C3×D3—61no—
184C22×C3×D3—121no—
185C22×C3×D3#6711yescharacteristic
186C22×C3×D3C3×D411yescharacteristic
187C32×Q8—32no—
188C32×Q8—61no—
189C32×D4—21no—
190C32×D4—22no—
191C32×D4—21no—
192C32×D4—21no—
193C32×D4—22no—
194C32×D4—22no—
195C32×D4—22no—
196C32×D4—42no—
197C32×D4—41no—
198C32×D4—41no—
199C32×D4—42no—
200C32×D4—64no—
201C32×D4D1212yescomplemented
202C32×D4#6712yescomplemented
203C32×D4C3×D412yescomplemented
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—31no—
208C2×C32×C4—41no—
209C2×C32×C4—64no—
210C2×C32×C4—61no—
211C2×C32×C4—61no—
212C2×C32×C4—61no—
213C2×C32×C4—61no—
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C22×D311yescharacteristic
216C2×C32×C4C23×C311yescharacteristic
217C4⋊(C3⋊D3)—21no—
218C4⋊(C3⋊D3)—21no—
219C3×#67—28no—
220C3×#67—24no—
221C3×#67—24no—
222C3×#67—122no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—28no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—24no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3#6711yescharacteristic
234C2×C3×Dic3C3×D411yescharacteristic
235C3×D12—62no—
236C3×D12—61no—
237C3×D12—61no—
238C3×D12—61no—
239C3×D12—61no—
240C3×D12—121no—
241C3×D12—122no—
242C3×C4×D3—22no—
243C3×C4×D3—22no—
244C3×C4×D3—21no—
245C3×C4×D3—21no—
246C3×C4×D3—21no—
247C3×C4×D3—21no—
248C3×Dic6—22no—
249C3×Dic6—21no—
250C3×Dic6—21no—
251C3×Dic6—22no—
252C3×Dic6#6712yescomplemented
253C3×Dic6C3×D412yescomplemented
254#626—42no—
255C32×C8—61no—
256C3⋊(C3⋊C8)—21no—
257C3×C3⋊C8—21no—
258C3×C3⋊C8—21no—
259C3×C3⋊C8—41no—
260C3×C3⋊C8—62no—
261C3×C3⋊C8—61no—
262C3×C3⋊C8—61no—
263#449—91noSylow
264C2×C33—42no—
265C2×C33#12011yescharacteristic
266C2×C33#13511yescharacteristic
267C2×C33AGL(1,ℤ/8)11yescharacteristic
268C3×C3⋊D3—81no—
269C32×D3—41no—
270C3×#41—62no—
271C3×#41—62no—
272C3×#41—64no—
273C3×#41—64no—
274C3×#41—62no—
275C3×#41—62no—
276C2×C3×Q8—31no—
277C2×C3×Q8—31no—
278C2×C3×Q8—61no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—41no—
283C2×C3×D4—61no—
284C2×C3×D4—61no—
285C2×C3×D4—62no—
286C2×C3×D4—91no—
287C2×C3×D4—181no—
288C2×C3×D4D3211yescharacteristic
289C2×C3×D4C2×C3×D311yescharacteristic
290C2×C3×D4C2×C3×D311yescharacteristic
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C22×C3×C4—62no—
297C2×#67—21no—
298C2×#67—61no—
299C22×Dic3—21no—
300#237—22no—
301#237—22no—
302C2×D12—31no—
303C2×D12—31no—
304C2×D12—61no—
305C2×D12—61no—
306C2×C4×D3C2×C3×D311yescharacteristic
307C2×Dic6C2×C3×D311yescharacteristic
308C3×SD16—182no—
309C3×D8—182no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—61no—
313C2×C3×C8—91no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—61no—
317C3×C22⋊C4—181no—
318#215—62no—
319#213—64no—
320#213—62no—
321#213—62no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324C4⋊Dic3C2×C3×D311yescharacteristic
325C2×C3⋊C8—31no—
326C2×C3⋊C8—31no—
327C2×C3⋊C8—61no—
328C2×C3⋊C8C2×C3×D311yescharacteristic
329#204—62no—
330C22×C32—22no—
331C22×C32—24no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—41no—
338C22×C32—42no—
339C22×C32—42no—
340C22×C32—44no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—42no—
344C22×C32—42no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32—61no—
350C22×C32—61no—
351C22×C32—61no—
352C22×C32—81no—
353C22×C32—81no—
354C22×C32—81no—
355C22×C32—81no—
356C22×C32—82no—
357C22×C32—82no—
358C22×C32D3×D411yescharacteristic
359C22×C32C2×#6711yescharacteristic
360C22×C32C2×C3×D411yescharacteristic
361C2×C3⋊D3—41no—
362C2×C3⋊D3—41no—
363C2×C3⋊D3—41no—
364C2×C3×D3—22no—
365C2×C3×D3—21no—
366C2×C3×D3—21no—
367C2×C3×D3—21no—
368C2×C3×D3—21no—
369C2×C3×D3—21no—
370C2×C3×D3—21no—
371C2×C3×D3—41no—
372C2×C3×D3—41no—
373C2×C3×D3—122no—
374C2×C3×D3—121no—
375C2×C3×D3—121no—
376C2×C3×D3—121no—
377C2×C3×D3—121no—
378C2×C3×D3—121no—
379C2×C3×D3—121no—
380C2×C3×D3—241no—
381C2×C3×D3—241no—
382C32×C4—21no—
383C32×C4—21no—
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4—61no—
391C32×C4—62no—
392C32×C4—121no—
393C32×C4C2×D1211yescharacteristic
394C32×C4D3×D411yescharacteristic
395C32×C4C2×#6711yescharacteristic
396C32×C4C2×#6711yescharacteristic
397C32×C4C2×C3×D411yescharacteristic
398C32×C4C2×C3×D411yescharacteristic
399C3×Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—21no—
403C3×Dic3—22no—
404C3×Dic3—21no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—81no—
408C2×#41—31no—
409C2×SD16—91no—
410C2×D8—91no—
411#121—91no—
412#103—91no—
413#102—31no—
414C22⋊C8—91no—
415C33#44911yescharacteristic, complemented, Sylow
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—31no—
421C23×C3—31no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—42no—
425C23×C3—61no—
426C23×C3—181no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3—121no—
430C22×D3C3×#6711yescharacteristic
431C3×Q8—32no—
432C3×Q8—32no—
433C3×Q8—62no—
434C3×Q8—62no—
435C3×Q8—61no—
436C3×Q8—61no—
437C3×D4—22no—
438C3×D4—21no—
439C3×D4—21no—
440C3×D4—21no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—22no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—42no—
447C3×D4—42no—
448C3×D4—68no—
449C3×D4—64no—
450C3×D4—64no—
451C3×D4—181no—
452C3×D4—181no—
453C3×D4—362no—
454C3×D4#62612yescomplemented
455C3×D4C3×D1212yescomplemented
456C3×D4C3×#6712yescomplemented
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—41no—
463C2×C3×C4—61no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—68no—
468C2×C3×C4—64no—
469C2×C3×C4—64no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—121no—
479C2×C3×C4C2×D3211yescharacteristic
480C2×C3×C4C22×C3×D311yescharacteristic
481C2×C3×C4C22×C3×D311yescharacteristic
482#67—24no—
483#67—122no—
484C2×Dic3—24no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3C3×#6711yescharacteristic
488D12—62no—
489D12—61no—
490D12—61no—
491D12—61no—
492D12—61no—
493D12—121no—
494D12—122no—
495C4×D3—21no—
496C4×D3—21no—
497Dic6—21no—
498Dic6C3×#6712yescomplemented
499C3×C8—61no—
500C3×C8—61no—
501C3×C8—121no—
502C3×C8—181no—
503C3⋊C8—21no—
504C3⋊C8—62no—
505C3⋊C8—61no—
506C3⋊C8—61no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—41no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—42no—
520C2×C32—44no—
521C2×C32—42no—
522C2×C32—42no—
523C2×C32—82no—
524C2×C32—82no—
525C2×C32—84no—
526C2×C32—121no—
527C2×C32#88211yescharacteristic
528C2×C32#91111yescharacteristic
529C2×C32#91611yescharacteristic
530C2×C32#94911yescharacteristic
531C2×C32#95011yescharacteristic
532C2×C32#95311yescharacteristic
533C2×C32C3×#12011yescharacteristic
534C2×C32C3×#13511yescharacteristic
535C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
536C3⋊D3—81no—
537C3×D3—42no—
538C3×D3—41no—
539C3×D3—41no—
540C3×D3—242no—
541C3×D3—241no—
542C3×D3—241no—
543#41—62no—
544#41—62no—
545C2×Q8—31no—
546C2×D4—61no—
547C2×D4—91no—
548C2×D4—181no—
549C2×D4C3×D3211yescharacteristic
550C22×C4—31no—
551C22×C4—61no—
552SD16—182no—
553D8—182no—
554C2×C8—31no—
555C2×C8—91no—
556C4⋊C4—31no—
557C22⋊C4—181no—
558C22×C3—24no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—44no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—62no—
578C22×C3—61no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—61no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—361no—
593C22×C3—361no—
594C22×C3—361no—
595C22×C3D3×#6711yescharacteristic
596C22×C3C3×D3×D411yescharacteristic
597C22×C3C2×C3×#6711yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—122no—
602C2×D3—121no—
603C2×D3—121no—
604C2×D3—121no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—241no—
609C2×D3—241no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—62no—
619C3×C4—64no—
620C3×C4—61no—
621C3×C4—62no—
622C3×C4—61no—
623C3×C4—62no—
624C3×C4—121no—
625C3×C4—121no—
626C3×C4—241no—
627C3×C4C2×#62611yescharacteristic
628C3×C4D3×#6711yescharacteristic
629C3×C4C2×C3×D1211yescharacteristic
630C3×C4C3×D3×D411yescharacteristic
631C3×C4C2×C3×#6711yescharacteristic
632C3×C4C2×C3×#6711yescharacteristic
633Dic3—22no—
634Dic3—21no—
635Dic3—41no—
636C32—21no—
637C32—21no—
638C32—21no—
639C32—41no—
640C32#478111yescharacteristic, complemented
641C32#523811yescharacteristic, complemented
642C32C3×#44911yescharacteristic, complemented
643C23—21no—
644C23—31no—
645C23—181no—
646Q8—32no—
647Q8—61no—
648D4—21no—
649D4—64no—
650D4—181no—
651D4—181no—
652D4—362no—
653D4C3×#62612yescomplemented
654C2×C4—31no—
655C2×C4—64no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4C2×C3×D3211yescharacteristic
661C8—61no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—44no—
673C2×C3—42no—
674C2×C3—42no—
675C2×C3—42no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—82no—
680C2×C3—82no—
681C2×C3—84no—
682C2×C3—122no—
683C2×C3—121no—
684C2×C3—121no—
685C2×C3—721no—
686C2×C3#6392511yescharacteristic
687C2×C3#6393511yescharacteristic
688C2×C3#6397711yescharacteristic
689C2×C3C3×#88211yescharacteristic
690C2×C3C3×#91111yescharacteristic
691C2×C3C3×#91611yescharacteristic
692C2×C3C3×#94911yescharacteristic
693C2×C3C3×#95011yescharacteristic
694C2×C3C3×#95311yescharacteristic
695D3—41no—
696D3—242no—
697D3—241no—
698D3—241no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—61no—
703C22—61no—
704C22—61no—
705C22—361no—
706C22—361no—
707C22—361no—
708C22C3×D3×#6711yescharacteristic
709C4—61no—
710C4—62no—
711C4—121no—
712C4C2×C3×#62611yescharacteristic
713C4C3×D3×#6711yescharacteristic
714C3—21no—
715C3—21no—
716C3—21no—
717C3—41no—
718C3#1059145211yescharacteristic, direct product factor
719C3C3×#478111yescharacteristic, complemented
720C3C3×#523811yescharacteristic, complemented
721C2—42no—
722C2—121no—
723C2—721no—
724C2C3×#6392511yescharacteristic
725C2C3×#6393511yescharacteristic
726C2C3×#6397711yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C3×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C3×#3753C2semidirect
3. C3×#63909C2semidirect
4. C2×C3×#3717C2semidirect
5. C32×#832C2semidirect
6. C3×#63565C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591452C3direct (N × H)
28. C2×C3×#237D3semidirect
29. C2×C3×#237C2×C3semidirect
30. C2×#3753C2×C3semidirect
38. #63909C2×C3semidirect
39. C2×#3717C2×C3semidirect
43. C3×#832D3semidirect
44. C3×#832C2×C3semidirect
48. #63565C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
54. C33×D4D4semidirect
66. C32×Dic6D4semidirect
151. C2×#237C3×D3semidirect
168. #832C3×D3semidirect
201. C32×D4D12semidirect
202. C32×D4#67semidirect
203. C32×D4C3×D4semidirect
252. C3×Dic6#67semidirect
253. C3×Dic6C3×D4semidirect
415. C33#449semidirect
454. C3×D4#626semidirect
455. C3×D4C3×D12semidirect
456. C3×D4C3×#67semidirect
498. Dic6C3×#67semidirect
640. C32#4781semidirect
641. C32#5238semidirect
642. C32C3×#449semidirect
653. D4C3×#626semidirect
718. C3#10591452direct (N × H)
719. C3C3×#4781semidirect
720. C3C3×#5238semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×#37532
C3×#639092
C2×C3×#37172
C32×#8322
C3×#635652
C3×(C2×D3)⋊(C3⋊C8)2
C3×#52383
C3×#47813
#105914523