Finite Group Databasebeta

← C3×#10590596 #13157613

Subgroups — C3×#10590596 #13157613

Order 1728.

952 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2C32×#897C211yesmaximal, characteristic, complemented
3C2×C3×#3717C211yesmaximal, characteristic, complemented
4C2×C3×#3715C211yesmaximal, characteristic, complemented
5C3×#63636C211yesmaximal, characteristic, complemented
6C32×#809C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5046—31nomaximal
9C3×#4776—31nomaximal
10#10590596C311yesmaximal, characteristic, direct product factor
11C22×C3×D32—21no—
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D12C2211yescharacteristic
14C2×C32×C4×D3C2211yescharacteristic
15C2×C32×Dic6C2211yescharacteristic, complemented
16C2×C3×#626—21no—
17C3×D3×D12—22no—
18C3×D3×D12—22no—
19C33×C4⋊C4C2211yescharacteristic, complemented
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
21C32×(C2×D3)⋊C4—21no—
22C32×C4⋊Dic3—21no—
23C2×C32×C3⋊C8C2211yescharacteristic, complemented
24C3×#3717—22no—
25C3×#3715—22no—
26C2×C3×D3×D4—31no—
27C22×C3×D12—31no—
28C2×D3×D12C2×C311yescharacteristic
29C32×C22⋊Q8—31no—
30C2×C3×#215—31no—
31C2×C3×#215—31no—
32C2×C3×#214—31no—
33C2×C3×#204—31no—
34C3×#897—21no—
35C3×#897D311yescharacteristic, complemented
36C3×#897C2×C311yescharacteristic, complemented
37C2×#3717C2×C311yescharacteristic, complemented
38C2×#3715C2×C311yescharacteristic, complemented
39C32×#102—31no—
40#63636C2×C311yescharacteristic, complemented
41C3×#830—31no—
42C3×(C2×D3)⋊C8—31no—
43C3×#809—21no—
44C3×#809—31no—
45C3×#809—31no—
46C3×#809—61no—
47C3×#809D311yescharacteristic, complemented
48C3×#809C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C22×C3×C3⋊D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3D411yescharacteristic
53C2×C3×D32—24no—
54C2×C3×D32—42no—
55C2×C3×D32—42no—
56C2×C33×C4—21no—
57C2×C33×C4C2311yescharacteristic
58C3×C4⋊(C3⋊D3)—21no—
59C3×C4⋊(C3⋊D3)D412yes—
60C2×C32×Dic3—21no—
61C2×C32×Dic3D411yescharacteristic
62C32×D12—21no—
63C32×D12D412yes—
64C32×C4×D3—21no—
65C32×C4×D3—21no—
66C32×Dic6—21no—
67C32×Dic6—21no—
68C3×#626—24no—
69C3×C3⋊(C3⋊C8)—21no—
70C32×C3⋊C8—21no—
71C3×#450—91no—
72#5046—31no—
73#4776—31no—
74C23×C3×D3—61no—
75C23×C3×D3—61no—
76C22×D32—21no—
77C2×C32×Q8—31no—
78C2×C32×D4—31no—
79C22×C32×C4—31no—
80C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
81C2×C3×#67—61no—
82C3×D3×D4—62no—
83C3×D3×D4—62no—
84C2×C3×D12—21no—
85C2×C3×D12—31no—
86C2×C3×D12—31no—
87C2×C3×D12—62no—
88C2×C3×D12—61no—
89C2×C3×D12—62no—
90C2×C3×D12—61no—
91C2×C3×D12C2×D311yescharacteristic
92C2×C3×D12C22×C311yescharacteristic
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3C2×D311yescharacteristic
95C2×C3×C4×D3C22×C311yescharacteristic
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2×D311yescharacteristic, complemented
98C2×C3×Dic6C22×C311yescharacteristic, complemented
99C2×#626—21no—
100D3×D12—22no—
101D3×D12—22no—
102C2×C32×C8—31no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—41no—
107C32×C4⋊C4—61no—
108C32×C4⋊C4C2×D311yescharacteristic, complemented
109C32×C4⋊C4C2×D311yescharacteristic, complemented
110C32×C4⋊C4C22×C311yescharacteristic, complemented
111C32×C22⋊C4—61no—
112C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
113C3×#215—62no—
114C3×#215—62no—
115C3×#214—62no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—22no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C2×C3×C3⋊C8—21no—
123C2×C3×C3⋊C8—31no—
124C2×C3×C3⋊C8—31no—
125C2×C3×C3⋊C8—61no—
126C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
127C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
128C3×#204—62no—
129#3717—22no—
130#3715—22no—
131C22×C33C2×D411yescharacteristic
132C2×C3×C3⋊D3—22no—
133C2×C3×C3⋊D3—41no—
134C2×C3×C3⋊D3—41no—
135C2×C32×D3—21no—
136C2×C32×D3—21no—
137C2×C32×D3—22no—
138C2×C32×D3—41no—
139C2×C32×D3—41no—
140C2×C32×D3SD1612yescomplemented
141C3×D32—48no—
142C33×C4—41no—
143C33×C4C2×D411yescharacteristic
144C33×C4C2×D411yescharacteristic
145C32×Dic3—21no—
146C32×Dic3—41no—
147C22×C3×D4—91no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C2×C3×SD16—91no—
151C2×C3×SD16—91no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C2×#215—31no—
156C2×#215—31no—
157C2×#214—31no—
158C2×#204—31no—
159#897C3×D311yescharacteristic, complemented
160C3×#102—31no—
161C3×#102—31no—
162C3×#102—61no—
163C3×#102—91no—
164C3×C22⋊C8—91no—
165#830—31no—
166(C2×D3)⋊C8—31no—
167#809—31no—
168#809—31no—
169#809—61no—
170#809C3×D311yescharacteristic, complemented
171C23×C32—31no—
172C23×C32—61no—
173C22×C3⋊D3—21no—
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3—41no—
178C22×C3×D3—64no—
179C22×C3×D3—64no—
180C22×C3×D3—61no—
181C22×C3×D3—61no—
182C22×C3×D3—121no—
183C22×C3×D3—122no—
184C22×C3×D3—122no—
185C22×C3×D3—122no—
186C22×C3×D3—122no—
187C22×C3×D3#6711yescharacteristic
188C22×C3×D3C3×D411yescharacteristic
189C2×D32—24no—
190C2×D32—42no—
191C2×D32—42no—
192C32×Q8—61no—
193C32×Q8—61no—
194C32×D4—32no—
195C32×D4—61no—
196C2×C32×C4—21no—
197C2×C32×C4—22no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—31no—
204C2×C32×C4—41no—
205C2×C32×C4—41no—
206C2×C32×C4—41no—
207C2×C32×C4—42no—
208C2×C32×C4—61no—
209C2×C32×C4—61no—
210C2×C32×C4—61no—
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C22×D311yescharacteristic
213C2×C32×C4C23×C311yescharacteristic
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)C3×D412yes—
216C3×#67—64no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3#6711yescharacteristic
222C2×C3×Dic3C3×D411yescharacteristic
223C3×D12—21no—
224C3×D12—21no—
225C3×D12—22no—
226C3×D12—32no—
227C3×D12—32no—
228C3×D12—41no—
229C3×D12—62no—
230C3×D12—64no—
231C3×D12—61no—
232C3×D12—61no—
233C3×D12—121no—
234C3×D12D1212yes—
235C3×D12C3×D412yes—
236C3×C4×D3—21no—
237C3×C4×D3—21no—
238C3×C4×D3—21no—
239C3×C4×D3—21no—
240C3×C4×D3—41no—
241C3×C4×D3—41no—
242C3×Dic6—21no—
243C3×Dic6—21no—
244C3×Dic6—21no—
245C3×Dic6—21no—
246C3×Dic6—41no—
247C3×Dic6—41no—
248#626—24no—
249C32×C8—61no—
250C3⋊(C3⋊C8)—21no—
251C3×C3⋊C8—21no—
252C3×C3⋊C8—21no—
253C3×C3⋊C8—41no—
254C3×C3⋊C8—61no—
255C3×C3⋊C8—61no—
256C3×C3⋊C8—121no—
257#450—91noSylow
258C2×C33#12011yescharacteristic
259C2×C33C2×SD1611yescharacteristic
260C2×C33AGL(1,ℤ/8)11yescharacteristic
261C3×C3⋊D3—42no—
262C32×D3—22no—
263C32×D3—42no—
264C24×C3—181no—
265C23×D3—61no—
266C23×D3—61no—
267C2×C3×Q8—31no—
268C2×C3×Q8—31no—
269C2×C3×Q8—61no—
270C2×C3×D4—31no—
271C2×C3×D4—31no—
272C2×C3×D4—61no—
273C2×C3×D4—91no—
274C2×C3×D4—181no—
275C2×C3×D4—182no—
276C2×C3×D4—182no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—61no—
280C2×#67—61no—
281D3×D4—62no—
282D3×D4—62no—
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×D12—62no—
287C2×D12—61no—
288C2×D12—62no—
289C2×D12C2×C3×D311yescharacteristic
290C2×C4×D3C2×C3×D311yescharacteristic
291C2×Dic6C2×C3×D311yescharacteristic, complemented
292C3×SD16—182no—
293C3×SD16—182no—
294C2×C3×C8—31no—
295C2×C3×C8—31no—
296C2×C3×C8—61no—
297C2×C3×C8—91no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—41no—
302C3×C4⋊C4—61no—
303C3×C4⋊C4—61no—
304C3×C4⋊C4—62no—
305C3×C4⋊C4D3211yescharacteristic, complemented
306C3×C4⋊C4C2×C3×D311yescharacteristic, complemented
307C3×C4⋊C4C2×C3×D311yescharacteristic, complemented
308C3×C22⋊C4—61no—
309C3×C22⋊C4—61no—
310C3×C22⋊C4—62no—
311#215—62no—
312#215—62no—
313#214—62no—
314(C2×D3)⋊C4—21no—
315C4⋊Dic3—21no—
316C2×C3⋊C8—31no—
317C2×C3⋊C8—31no—
318C2×C3⋊C8—61no—
319C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
320#204—62no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—32no—
325C22×C32—41no—
326C22×C32—61no—
327C22×C32—61no—
328C22×C32—62no—
329C22×C32—121no—
330C22×C32—121no—
331C22×C32D3×D411yescharacteristic
332C22×C32C2×#6711yescharacteristic
333C22×C32C2×C3×D411yescharacteristic
334C2×C3⋊D3—22no—
335C2×C3⋊D3—41no—
336C2×C3⋊D3—41no—
337C2×C3×D3—21no—
338C2×C3×D3—21no—
339C2×C3×D3—21no—
340C2×C3×D3—21no—
341C2×C3×D3—22no—
342C2×C3×D3—22no—
343C2×C3×D3—22no—
344C2×C3×D3—41no—
345C2×C3×D3—41no—
346C2×C3×D3—42no—
347C2×C3×D3—41no—
348C2×C3×D3—41no—
349C2×C3×D3—41no—
350C2×C3×D3—41no—
351C2×C3×D3—62no—
352C2×C3×D3—62no—
353C2×C3×D3—81no—
354C2×C3×D3—81no—
355C2×C3×D3—122no—
356C2×C3×D3—128no—
357C2×C3×D3—128no—
358C2×C3×D3—121no—
359C2×C3×D3—121no—
360C2×C3×D3—121no—
361C2×C3×D3—121no—
362C2×C3×D3—241no—
363C2×C3×D3—241no—
364C2×C3×D3#21512yescomplemented
365C2×C3×D3C3×SD1612yescomplemented
366D32—48no—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—21no—
371C32×C4—21no—
372C32×C4—21no—
373C32×C4—41no—
374C32×C4—41no—
375C32×C4—41no—
376C32×C4—42no—
377C32×C4—41no—
378C32×C4—41no—
379C32×C4—61no—
380C32×C4—81no—
381C32×C4—81no—
382C32×C4—82no—
383C32×C4—121no—
384C32×C4C2×D1211yescharacteristic
385C32×C4D3×D411yescharacteristic
386C32×C4D3×D411yescharacteristic
387C32×C4D3×D411yescharacteristic
388C32×C4C2×C3×D411yescharacteristic
389C32×C4C2×C3×D411yescharacteristic
390C3×Dic3—21no—
391C3×Dic3—21no—
392C3×Dic3—41no—
393C3×Dic3—42no—
394C3×Dic3—41no—
395C3×Dic3—41no—
396C22×D4—91no—
397C2×SD16—91no—
398C2×SD16—91no—
399C22⋊Q8—31no—
400#102—31no—
401#102—91no—
402C22⋊C8—91no—
403C33#45011yescharacteristic, complemented, Sylow
404C23×C3—31no—
405C23×C3—31no—
406C23×C3—61no—
407C23×C3—61no—
408C23×C3—61no—
409C23×C3—121no—
410C23×C3—184no—
411C23×C3—181no—
412C23×C3—362no—
413C23×C3—362no—
414C22×D3—21no—
415C22×D3—64no—
416C22×D3—64no—
417C22×D3—61no—
418C22×D3—61no—
419C22×D3—121no—
420C22×D3—122no—
421C22×D3—122no—
422C22×D3—122no—
423C22×D3—122no—
424C22×D3C3×#6711yescharacteristic
425C3×Q8—61no—
426C3×Q8—61no—
427C3×Q8—61no—
428C3×Q8—61no—
429C3×Q8—121no—
430C3×Q8—121no—
431C3×D4—32no—
432C3×D4—32no—
433C3×D4—62no—
434C3×D4—61no—
435C3×D4—61no—
436C3×D4—92no—
437C3×D4—121no—
438C3×D4—184no—
439C3×D4—181no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—42no—
452C2×C3×C4—41no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—62no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—121no—
462C2×C3×C4—121no—
463C2×C3×C4C2×D3211yescharacteristic
464C2×C3×C4C22×C3×D311yescharacteristic
465C2×C3×C4C22×C3×D311yescharacteristic
466#67—64no—
467C2×Dic3—21no—
468C2×Dic3C3×#6711yescharacteristic
469D12—21no—
470D12—32no—
471D12—32no—
472D12—62no—
473D12—64no—
474D12—61no—
475D12—61no—
476D12—121no—
477D12C3×D1212yes—
478C4×D3—21no—
479C4×D3—21no—
480Dic6—21no—
481Dic6—21no—
482C3×C8—61no—
483C3×C8—61no—
484C3×C8—121no—
485C3×C8—181no—
486C3⋊C8—21no—
487C3⋊C8—61no—
488C3⋊C8—61no—
489C3⋊C8—121no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—41no—
500C2×C32—41no—
501C2×C32—41no—
502C2×C32—62no—
503C2×C32—122no—
504C2×C32#88211yescharacteristic
505C2×C32#91111yescharacteristic
506C2×C32D3×SD1611yescharacteristic
507C2×C32#93711yescharacteristic
508C2×C32C2×#21511yescharacteristic
509C2×C32#94911yescharacteristic
510C2×C32C3×#12011yescharacteristic
511C2×C32C2×C3×SD1611yescharacteristic
512C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
513C3⋊D3—42no—
514C3×D3—22no—
515C3×D3—22no—
516C3×D3—42no—
517C3×D3—42no—
518C3×D3—42no—
519C3×D3—82no—
520C3×D3—122no—
521C3×D3—122no—
522C3×D3—242no—
523C24—181no—
524C2×Q8—31no—
525C2×D4—31no—
526C2×D4—91no—
527C2×D4—181no—
528C2×D4—182no—
529C2×D4—182no—
530C22×C4—31no—
531SD16—182no—
532SD16—182no—
533C2×C8—31no—
534C2×C8—91no—
535C4⋊C4—61no—
536C4⋊C4C3×D3211yescharacteristic, complemented
537C22⋊C4—61no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—32no—
542C22×C3—32no—
543C22×C3—41no—
544C22×C3—62no—
545C22×C3—61no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—61no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—121no—
552C22×C3—121no—
553C22×C3—122no—
554C22×C3—121no—
555C22×C3—121no—
556C22×C3—121no—
557C22×C3—121no—
558C22×C3—182no—
559C22×C3—241no—
560C22×C3—241no—
561C22×C3—368no—
562C22×C3—361no—
563C22×C3—361no—
564C22×C3D3×#6711yescharacteristic
565C22×C3C3×D3×D411yescharacteristic
566C22×C3C2×C3×#6711yescharacteristic
567C2×D3—21no—
568C2×D3—21no—
569C2×D3—22no—
570C2×D3—41no—
571C2×D3—41no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—122no—
575C2×D3—128no—
576C2×D3—128no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—241no—
582C2×D3—241no—
583C2×D3C3×#21512yescomplemented
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—42no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—81no—
599C3×C4—81no—
600C3×C4—82no—
601C3×C4—121no—
602C3×C4—122no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4D3×D1211yescharacteristic
606C3×C4#380211yescharacteristic
607C3×C4C2×C3×D1211yescharacteristic
608C3×C4C3×D3×D411yescharacteristic
609C3×C4C3×D3×D411yescharacteristic
610C3×C4C3×D3×D411yescharacteristic
611Dic3—21no—
612Dic3—41no—
613C32—21no—
614C32—21no—
615C32—21no—
616C32—41no—
617C32#477611yescharacteristic, complemented
618C32#504611yescharacteristic, complemented
619C32C3×#45011yescharacteristic, complemented
620C23—31no—
621C23—61no—
622C23—184no—
623C23—181no—
624C23—362no—
625C23—362no—
626Q8—61no—
627Q8—61no—
628D4—32no—
629D4—61no—
630D4—92no—
631D4—184no—
632D4—181no—
633C2×C4—21no—
634C2×C4—31no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4C2×C3×D3211yescharacteristic
639C8—61no—
640C8—181no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—41no—
651C2×C3—41no—
652C2×C3—41no—
653C2×C3—62no—
654C2×C3—62no—
655C2×C3—122no—
656C2×C3—122no—
657C2×C3—122no—
658C2×C3—242no—
659C2×C3—362no—
660C2×C3#6392211yescharacteristic
661C2×C3#6392511yescharacteristic
662C2×C3D3×#21511yescharacteristic
663C2×C3C3×#88211yescharacteristic
664C2×C3C3×#91111yescharacteristic
665C2×C3C3×D3×SD1611yescharacteristic
666C2×C3C3×#93711yescharacteristic
667C2×C3C2×C3×#21511yescharacteristic
668C2×C3C3×#94911yescharacteristic
669D3—22no—
670D3—42no—
671D3—122no—
672D3—122no—
673D3—242no—
674C22—32no—
675C22—61no—
676C22—61no—
677C22—62no—
678C22—121no—
679C22—121no—
680C22—182no—
681C22—368no—
682C22—361no—
683C22—361no—
684C22C3×D3×#6711yescharacteristic
685C4—41no—
686C4—61no—
687C4—121no—
688C4C3×D3×D1211yescharacteristic
689C4C3×#380211yescharacteristic
690C3—21no—
691C3—21no—
692C3—21no—
693C3—41no—
694C3#1059059611yescharacteristic, direct product factor
695C3C3×#477611yescharacteristic, complemented
696C3C3×#504611yescharacteristic, complemented
697C2—62no—
698C2—122no—
699C2—362no—
700C2C3×#6392211yescharacteristic
701C2C3×#6392511yescharacteristic
702C2C3×D3×#21511yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC2×C3×D3×D12C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×#897C2semidirect
3. C2×C3×#3717C2semidirect
4. C2×C3×#3715C2semidirect
5. C3×#63636C2semidirect
6. C32×#809C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10590596C3direct (N × H)
15. C2×C32×Dic6C22semidirect
19. C33×C4⋊C4C22semidirect
20. C2×C3×C3⋊(C3⋊C8)C22semidirect
23. C2×C32×C3⋊C8C22semidirect
35. C3×#897D3semidirect
36. C3×#897C2×C3semidirect
37. C2×#3717C2×C3semidirect
38. C2×#3715C2×C3semidirect
40. #63636C2×C3semidirect
47. C3×#809D3semidirect
48. C3×#809C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
97. C2×C3×Dic6C2×D3semidirect
98. C2×C3×Dic6C22×C3semidirect
108. C32×C4⋊C4C2×D3semidirect
109. C32×C4⋊C4C2×D3semidirect
110. C32×C4⋊C4C22×C3semidirect
112. C2×C3⋊(C3⋊C8)C22×C3semidirect
126. C2×C3×C3⋊C8C2×D3semidirect
127. C2×C3×C3⋊C8C22×C3semidirect
140. C2×C32×D3SD16semidirect
159. #897C3×D3semidirect
170. #809C3×D3semidirect
291. C2×Dic6C2×C3×D3semidirect
305. C3×C4⋊C4D32semidirect
306. C3×C4⋊C4C2×C3×D3semidirect
307. C3×C4⋊C4C2×C3×D3semidirect
319. C2×C3⋊C8C2×C3×D3semidirect
364. C2×C3×D3#215semidirect
365. C2×C3×D3C3×SD16semidirect
403. C33#450semidirect
536. C4⋊C4C3×D32semidirect
583. C2×D3C3×#215semidirect
617. C32#4776semidirect
618. C32#5046semidirect
619. C32C3×#450semidirect
694. C3#10590596direct (N × H)
695. C3C3×#4776semidirect
696. C3C3×#5046semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C32×#8972
C2×C3×#37172
C2×C3×#37152
C3×#636362
C32×#8092
C3×(C2×D3)⋊(C3⋊C8)2
C3×#50463
C3×#47763
#105905963