Finite Group Databasebeta

← C3×#10591113 #13158144

Subgroups — C3×#10591113 #13158144

Order 1728.

978 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic
2C32×#926C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C3×#63570C214yesmaximal, complemented
5C3×#5139—31nomaximal
6C3×#5005—31nomaximal
7#10591113C311yesmaximal, characteristic, direct product factor
8C22×C33×C4C2211yescharacteristic
9C2×C3×#638—21no—
10C3×#3828—21no—
11C3×#3828—21no—
12C3×#3828C412yescomplemented
13C3×#3828C2212yes—
14C2×C3×C4⋊(C3⋊D3)C411yescharacteristic, complemented
15C2×C3×C4×C3⋊D3—21no—
16C2×C3×#634C411yescharacteristic, complemented
17C32×#217—21no—
18C32×C4⋊Dic3—21no—
19C32×C4×Dic3C2212yescomplemented
20C32×#208—21no—
21C32×#208C2212yescomplemented
22C2×C32×C3⋊C8—21no—
23C2×#3828C2×C311yescharacteristic
24C2×C3×#235—31no—
25C2×C3×#235—31no—
26C2×C3×#235—61no—
27C2×C32×M16—31no—
28C32×#117—31no—
29C3×#926—21no—
30C3×#926D311yescharacteristic, complemented
31C3×#926C2×C311yescharacteristic, complemented
32C2×C3×#208—21no—
33C2×C3×#208D311yescharacteristic, complemented
34C2×C3×#208C2×C311yescharacteristic, complemented
35C3×#825—34no—
36C3×#805—34no—
37#63570C2×C314yescomplemented
38C23×C33D411yescharacteristic
39C22×C3×C3⋊D3—21no—
40C2×C33×C4C2×C411yescharacteristic
41C2×C33×C4C2×C411yescharacteristic
42C2×C33×C4D411yescharacteristic
43C2×C33×C4D411yescharacteristic
44C2×C33×C4D411yescharacteristic
45C2×C33×C4C2311yescharacteristic
46C3×#638—22no—
47C3×#638—22no—
48C2×C3×C3⋊Dic3—21no—
49C3×C4⋊(C3⋊D3)—21no—
50C3×C4⋊(C3⋊D3)C2×C412yes—
51C3×C4×C3⋊D3—22no—
52C3×C4×C3⋊D3—22no—
53C3×#634—21no—
54C3×#634C2×C412yes—
55C2×C32×Dic3—22no—
56C32×C3⋊C8—22no—
57C3×#421—91no—
58#5139—31no—
59#5005—31no—
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—41no—
64C22×C32×C4C2×D311yescharacteristic
65C22×C32×C4C2×D311yescharacteristic
66C22×C32×C4C22×C311yescharacteristic
67C2×#638—21no—
68#3828—21no—
69#3828—21no—
70#3828C3×C412yescomplemented
71#3828C22×C312yes—
72C2×C4⋊(C3⋊D3)C3×C411yescharacteristic, complemented
73C2×C4×C3⋊D3—21no—
74C2×#634C3×C411yescharacteristic, complemented
75C2×C3×#67—62no—
76C2×C3×#67—61no—
77C2×C3×#67—61no—
78C3×#235—32no—
79C3×#235—32no—
80C3×#235—32no—
81C3×#235—32no—
82C3×#235—62no—
83C3×#235—62no—
84C3×#235—62no—
85C3×#235—62no—
86C3×#235—61no—
87C3×#235—61no—
88C3×#235—61no—
89C3×#235—61no—
90C2×C3×D12—31no—
91C2×C3×D12—31no—
92C2×C3×D12—61no—
93C2×C3×C4×D3—62no—
94C2×C3×C4×D3—61no—
95C2×C3×C4×D3—61no—
96C2×C3×Dic6—31no—
97C2×C3×Dic6—31no—
98C2×C3×Dic6—61no—
99C32×M16—32no—
100C32×M16—61no—
101C2×C32×C8—61no—
102C32×C4⋊C4—61no—
103C32×C22⋊C4—61no—
104C32×C42—32no—
105C3×#217—22no—
106C3×#217—21no—
107C3×#217—21no—
108C3×C4⋊Dic3—22no—
109C3×C4⋊Dic3—21no—
110C3×C4⋊Dic3—21no—
111C3×C4×Dic3—22no—
112C3×C4×Dic3C2×D312yescomplemented
113C3×C4×Dic3C22×C312yescomplemented
114C3×#208—22no—
115C3×#208—22no—
116C3×#208—21no—
117C3×#208—21no—
118C3×#208C2×D312yescomplemented
119C3×#208C22×C312yescomplemented
120C2×C3×C3⋊C8—22no—
121C2×C3×C3⋊C8—21no—
122C2×C3×C3⋊C8—21no—
123C22×C33—41no—
124C22×C33C22⋊C411yescharacteristic
125C22×C33C22⋊C411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C2×C3×C3⋊D3—22no—
128C2×C3×C3⋊D3—42no—
129C33×C4C22⋊C411yescharacteristic
130C33×C4C22⋊C411yescharacteristic
131C33×C4C22×C411yescharacteristic
132C33×C4C2×D411yescharacteristic
133C3×C3⋊Dic3—22no—
134C32×Dic3—42no—
135C2×C3×#41—91no—
136C2×#235—31no—
137C2×#235—31no—
138C2×#235—61no—
139C2×C3×M16—31no—
140C2×C3×M16—31no—
141C2×C3×M16—61no—
142C3×#117—31no—
143C3×#117—31no—
144C3×#117—61no—
145#926C3×D311yescharacteristic, complemented
146C2×#208C3×D311yescharacteristic, complemented
147C3×#104—94no—
148#825—34no—
149#805—34no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—41no—
154C23×C32D1211yescharacteristic
155C23×C32#6711yescharacteristic
156C23×C32C3×D411yescharacteristic
157C22×C3⋊D3—21no—
158C22×C3×D3—62no—
159C22×C3×D3—61no—
160C22×C3×D3—61no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—41no—
180C2×C32×C4—41no—
181C2×C32×C4—41no—
182C2×C32×C4—41no—
183C2×C32×C4—41no—
184C2×C32×C4—41no—
185C2×C32×C4—62no—
186C2×C32×C4C4×D311yescharacteristic
187C2×C32×C4C4×D311yescharacteristic
188C2×C32×C4C4×D311yescharacteristic
189C2×C32×C4C4×D311yescharacteristic
190C2×C32×C4D1211yescharacteristic
191C2×C32×C4D1211yescharacteristic
192C2×C32×C4D1211yescharacteristic
193C2×C32×C4#6711yescharacteristic
194C2×C32×C4#6711yescharacteristic
195C2×C32×C4#6711yescharacteristic
196C2×C32×C4C2×C3×C411yescharacteristic
197C2×C32×C4C2×C3×C411yescharacteristic
198C2×C32×C4C3×D411yescharacteristic
199C2×C32×C4C3×D411yescharacteristic
200C2×C32×C4C3×D411yescharacteristic
201C2×C32×C4C22×D311yescharacteristic
202C2×C32×C4C22×D311yescharacteristic
203C2×C32×C4C23×C311yescharacteristic
204#638—22no—
205#638—22no—
206C2×C3⋊Dic3—21no—
207C4⋊(C3⋊D3)—21no—
208C4⋊(C3⋊D3)C2×C3×C412yes—
209C4×C3⋊D3—22no—
210C4×C3⋊D3—22no—
211#634—21no—
212#634C2×C3×C412yes—
213C3×#67—64no—
214C3×#67—64no—
215C3×#67—62no—
216C3×#67—62no—
217C3×#67—62no—
218C3×#67—62no—
219C2×C3×Dic3—24no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—62no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C3×D12—32no—
226C3×D12—32no—
227C3×D12—62no—
228C3×D12—62no—
229C3×D12—61no—
230C3×D12—61no—
231C3×C4×D3—64no—
232C3×C4×D3—64no—
233C3×C4×D3—62no—
234C3×C4×D3—62no—
235C3×C4×D3—62no—
236C3×C4×D3—62no—
237C3×Dic6—32no—
238C3×Dic6—32no—
239C3×Dic6—62no—
240C3×Dic6—62no—
241C3×Dic6—61no—
242C3×Dic6—61no—
243C32×C8—62no—
244C3×C3⋊C8—24no—
245C3×C3⋊C8—22no—
246C3×C3⋊C8—22no—
247#421—91noSylow
248C2×C33—21no—
249C2×C33—21no—
250C2×C33—21no—
251C2×C33C2×C22⋊C411yescharacteristic
252C3×C3⋊D3—42no—
253C3×#41—92no—
254C3×#41—92no—
255C3×#41—181no—
256C3×#41—181no—
257C2×C3×Q8—91no—
258C2×C3×D4—91no—
259C2×C3×D4—181no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—41no—
264C22×C3×C4—181no—
265C22×C3×C4D3211yescharacteristic
266C22×C3×C4C2×C3×D311yescharacteristic
267C22×C3×C4C2×C3×D311yescharacteristic
268C2×#67—62no—
269C2×#67—61no—
270C2×#67—61no—
271#235—32no—
272#235—32no—
273#235—32no—
274#235—32no—
275#235—62no—
276#235—62no—
277#235—62no—
278#235—62no—
279#235—61no—
280#235—61no—
281#235—61no—
282#235—61no—
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×C4×D3—62no—
287C2×C4×D3—61no—
288C2×C4×D3—61no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C3×M16—32no—
293C3×M16—32no—
294C3×M16—62no—
295C3×M16—62no—
296C3×M16—61no—
297C3×M16—61no—
298C2×C3×C8—62no—
299C2×C3×C8—61no—
300C2×C3×C8—61no—
301C3×C4⋊C4—62no—
302C3×C4⋊C4—61no—
303C3×C4⋊C4—61no—
304C3×C22⋊C4—62no—
305C3×C22⋊C4—61no—
306C3×C22⋊C4—61no—
307C3×C42—32no—
308C3×C42—32no—
309C3×C42—62no—
310#217—21no—
311C4⋊Dic3—21no—
312C4×Dic3C2×C3×D312yescomplemented
313#208—21no—
314#208C2×C3×D312yescomplemented
315C2×C3⋊C8—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32—44no—
335C22×C32(C2×D3)⋊C411yescharacteristic
336C22×C32(C2×D3)⋊C411yescharacteristic
337C22×C32(C2×D3)⋊C411yescharacteristic
338C22×C32(C2×D3)⋊C411yescharacteristic
339C22×C32C3×C22⋊C411yescharacteristic
340C22×C32C3×C22⋊C411yescharacteristic
341C22×C32C2×D1211yescharacteristic
342C22×C32C2×#6711yescharacteristic
343C22×C32C2×C3×D411yescharacteristic
344C2×C3⋊D3—22no—
345C2×C3⋊D3—42no—
346C2×C3×D3—64no—
347C2×C3×D3—62no—
348C2×C3×D3—62no—
349C2×C3×D3—124no—
350C2×C3×D3—122no—
351C2×C3×D3—122no—
352C32×C4—21no—
353C32×C4—21no—
354C32×C4—21no—
355C32×C4—21no—
356C32×C4—21no—
357C32×C4—21no—
358C32×C4—21no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—21no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4—122no—
369C32×C4(C2×D3)⋊C411yescharacteristic
370C32×C4(C2×D3)⋊C411yescharacteristic
371C32×C4(C2×D3)⋊C411yescharacteristic
372C32×C4(C2×D3)⋊C411yescharacteristic
373C32×C4C3×C22⋊C411yescharacteristic
374C32×C4C3×C22⋊C411yescharacteristic
375C32×C4C2×C4×D311yescharacteristic
376C32×C4C2×C4×D311yescharacteristic
377C32×C4C2×D1211yescharacteristic
378C32×C4C2×#6711yescharacteristic
379C32×C4C22×C3×C411yescharacteristic
380C32×C4C2×C3×D411yescharacteristic
381C3⋊Dic3—22no—
382C3×Dic3—44no—
383C3×Dic3—42no—
384C3×Dic3—42no—
385C3×Dic3—64no—
386C3×Dic3—62no—
387C3×Dic3—62no—
388C2×#41—91no—
389C2×M16—31no—
390#117—31no—
391#104—94no—
392C33#42111yescharacteristic, complemented, Sylow
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—41no—
397C23×C3—181no—
398C23×C3#62611yescharacteristic
399C23×C3C3×D1211yescharacteristic
400C23×C3C3×#6711yescharacteristic
401C22×D3—62no—
402C22×D3—61no—
403C22×D3—61no—
404C3×Q8—92no—
405C3×Q8—181no—
406C3×D4—92no—
407C3×D4—182no—
408C3×D4—182no—
409C3×D4—181no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—64no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—181no—
438C2×C3×C4—182no—
439C2×C3×C4—182no—
440C2×C3×C4#62411yescharacteristic
441C2×C3×C4#62411yescharacteristic
442C2×C3×C4#62611yescharacteristic
443C2×C3×C4#62611yescharacteristic
444C2×C3×C4#62611yescharacteristic
445C2×C3×C4C3×C4×D311yescharacteristic
446C2×C3×C4C3×C4×D311yescharacteristic
447C2×C3×C4C3×C4×D311yescharacteristic
448C2×C3×C4C3×C4×D311yescharacteristic
449C2×C3×C4C3×D1211yescharacteristic
450C2×C3×C4C3×D1211yescharacteristic
451C2×C3×C4C3×D1211yescharacteristic
452C2×C3×C4C3×#6711yescharacteristic
453C2×C3×C4C3×#6711yescharacteristic
454C2×C3×C4C3×#6711yescharacteristic
455C2×C3×C4C2×D3211yescharacteristic
456C2×C3×C4C22×C3×D311yescharacteristic
457C2×C3×C4C22×C3×D311yescharacteristic
458#67—64no—
459#67—64no—
460#67—62no—
461#67—62no—
462#67—62no—
463#67—62no—
464C2×Dic3—22no—
465C2×Dic3—62no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468D12—32no—
469D12—32no—
470D12—62no—
471D12—62no—
472D12—61no—
473D12—61no—
474C4×D3—64no—
475C4×D3—64no—
476C4×D3—62no—
477C4×D3—62no—
478C4×D3—62no—
479C4×D3—62no—
480Dic6—32no—
481Dic6—32no—
482Dic6—62no—
483Dic6—62no—
484Dic6—61no—
485Dic6—61no—
486C3×C8—64no—
487C3×C8—62no—
488C3×C8—62no—
489C3⋊C8—22no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—22no—
494C2×C32—22no—
495C2×C32—22no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—41no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—41no—
509C2×C32—41no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32—42no—
513C2×C32—42no—
514C2×C32—42no—
515C2×C32C2×(C2×D3)⋊C411yescharacteristic
516C2×C32C2×(C2×D3)⋊C411yescharacteristic
517C2×C32C2×C3×C22⋊C411yescharacteristic
518C3⋊D3—42no—
519C3×D3—124no—
520C3×D3—122no—
521C3×D3—122no—
522#41—92no—
523#41—92no—
524#41—181no—
525#41—181no—
526C2×Q8—91no—
527C2×D4—91no—
528C2×D4—181no—
529C22×C4—181no—
530C22×C4C3×D3211yescharacteristic
531M16—32no—
532M16—61no—
533C2×C8—61no—
534C4⋊C4—61no—
535C22⋊C4—61no—
536C42—32no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—44no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—182no—
557C22×C3—362no—
558C22×C3#372211yescharacteristic
559C22×C3#372211yescharacteristic
560C22×C3C3×(C2×D3)⋊C411yescharacteristic
561C22×C3C3×(C2×D3)⋊C411yescharacteristic
562C22×C3C3×(C2×D3)⋊C411yescharacteristic
563C22×C3C3×(C2×D3)⋊C411yescharacteristic
564C22×C3C2×#62611yescharacteristic
565C22×C3C2×C3×D1211yescharacteristic
566C22×C3C2×C3×#6711yescharacteristic
567C2×D3—64no—
568C2×D3—62no—
569C2×D3—62no—
570C2×D3—124no—
571C2×D3—122no—
572C2×D3—122no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—124no—
590C3×C4—122no—
591C3×C4—122no—
592C3×C4—182no—
593C3×C4#372211yescharacteristic
594C3×C4#372211yescharacteristic
595C3×C4C3×(C2×D3)⋊C411yescharacteristic
596C3×C4C3×(C2×D3)⋊C411yescharacteristic
597C3×C4C3×(C2×D3)⋊C411yescharacteristic
598C3×C4C3×(C2×D3)⋊C411yescharacteristic
599C3×C4C2×#62411yescharacteristic
600C3×C4C2×#62611yescharacteristic
601C3×C4C2×C3×C4×D311yescharacteristic
602C3×C4C2×C3×C4×D311yescharacteristic
603C3×C4C2×C3×D1211yescharacteristic
604C3×C4C2×C3×#6711yescharacteristic
605Dic3—42no—
606Dic3—64no—
607Dic3—62no—
608Dic3—62no—
609C32—21no—
610C32—21no—
611C32—21no—
612C32—41no—
613C32#500511yescharacteristic, complemented
614C32#513911yescharacteristic, complemented
615C32C3×#42111yescharacteristic, complemented
616C23—181no—
617C23C3×#62611yescharacteristic
618Q8—92no—
619Q8—181no—
620D4—92no—
621D4—182no—
622D4—182no—
623D4—181no—
624C2×C4—62no—
625C2×C4—181no—
626C2×C4—182no—
627C2×C4—182no—
628C2×C4C3×#62411yescharacteristic
629C2×C4C3×#62411yescharacteristic
630C2×C4C3×#62611yescharacteristic
631C2×C4C3×#62611yescharacteristic
632C2×C4C3×#62611yescharacteristic
633C2×C4C2×C3×D3211yescharacteristic
634C8—62no—
635C2×C3—22no—
636C2×C3—22no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
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—41no—
654C2×C3—41no—
655C2×C3—41no—
656C2×C3—42no—
657C2×C3—42no—
658C2×C3—42no—
659C2×C3—41no—
660C2×C3—362no—
661C2×C3C2×#372211yescharacteristic
662C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
663C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
664D3—124no—
665D3—122no—
666D3—122no—
667C22—41no—
668C22—182no—
669C22—362no—
670C22C3×#372211yescharacteristic
671C22C3×#372211yescharacteristic
672C22C2×C3×#62611yescharacteristic
673C4—122no—
674C4—182no—
675C4C3×#372211yescharacteristic
676C4C3×#372211yescharacteristic
677C4C2×C3×#62411yescharacteristic
678C4C2×C3×#62611yescharacteristic
679C3—21no—
680C3—21no—
681C3—21no—
682C3—41no—
683C3#1059111311yescharacteristic, direct product factor
684C3C3×#500511yescharacteristic, complemented
685C3C3×#513911yescharacteristic, complemented
686C2—21no—
687C2—21no—
688C2—21no—
689C2—362no—
690C2C2×C3×#372211yescharacteristic
subgroupG/H
centerC3×C4C2×#626
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC2×C33C2×C22⋊C4
prime radicalC2×C3×#3828C2
cosocleC2×C32×C4C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C32×#926C2semidirect
3. C2×C32×#208C2semidirect
4. C3×#63570C2semidirect
7. #10591113C3direct (N × H)
12. C3×#3828C4semidirect
14. C2×C3×C4⋊(C3⋊D3)C4semidirect
16. C2×C3×#634C4semidirect
19. C32×C4×Dic3C22semidirect
21. C32×#208C22semidirect
30. C3×#926D3semidirect
31. C3×#926C2×C3semidirect
33. C2×C3×#208D3semidirect
34. C2×C3×#208C2×C3semidirect
37. #63570C2×C3semidirect
70. #3828C3×C4semidirect
72. C2×C4⋊(C3⋊D3)C3×C4semidirect
74. C2×#634C3×C4semidirect
112. C3×C4×Dic3C2×D3semidirect
113. C3×C4×Dic3C22×C3semidirect
118. C3×#208C2×D3semidirect
119. C3×#208C22×C3semidirect
145. #926C3×D3semidirect
146. C2×#208C3×D3semidirect
312. C4×Dic3C2×C3×D3semidirect
314. #208C2×C3×D3semidirect
392. C33#421semidirect
613. C32#5005semidirect
614. C32#5139semidirect
615. C32C3×#421semidirect
683. C3#10591113direct (N × H)
684. C3C3×#5005semidirect
685. C3C3×#5139semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C32×#9262
C2×C32×#2082
C3×#635702
C3×#51393
C3×#50053
#105911133