Finite Group Databasebeta

← C3×#10591111 #13158142

Subgroups — C3×#10591111 #13158142

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×C32×#235C211yesmaximal, characteristic
2C2×C3×#3748C211yesmaximal, characteristic, complemented
3C32×#926C211yesmaximal, characteristic, complemented
4C3×#63569C214yesmaximal, complemented
5C3×#5236—31nomaximal
6C3×#5005—31nomaximal
7#10591111C311yesmaximal, characteristic, direct product factor
8C22×C33×C4C2211yescharacteristic
9C2×C32×#67—21no—
10C32×#235—21no—
11C32×#235—21no—
12C32×#235C412yescomplemented
13C32×#235C2212yes—
14C2×C32×D12C411yescharacteristic, complemented
15C2×C32×C4×D3—21no—
16C2×C32×Dic6C411yescharacteristic, complemented
17C3×#3748—21no—
18C3×#3748C2212yescomplemented
19C2×C3×C3⋊(C3⋊C8)—21no—
20C32×#217—21no—
21C32×C4⋊Dic3—21no—
22C32×C4×Dic3C2212yescomplemented
23C2×C32×#41—31no—
24C2×C3×#235—21no—
25C2×C3×#235D311yescharacteristic
26C2×C3×#235C2×C311yescharacteristic
27C32×#117—31no—
28C2×#3748C2×C311yescharacteristic, complemented
29C3×#926—21no—
30C3×#926D311yescharacteristic, complemented
31C3×#926C2×C311yescharacteristic, complemented
32C2×C3×#208—31no—
33C2×C3×#208—31no—
34C2×C3×#208—61no—
35C3×#837—34no—
36C3×#805—34no—
37#63569C2×C314yescomplemented
38C23×C33D411yescharacteristic
39C22×C32×D3—21no—
40C2×C33×C4C2×C411yescharacteristic
41C2×C33×C4C2×C411yescharacteristic
42C2×C33×C4D411yescharacteristic
43C2×C33×C4D411yescharacteristic
44C2×C33×C4D411yescharacteristic
45C2×C33×C4C2311yescharacteristic
46C32×#67—22no—
47C32×#67—22no—
48C2×C32×Dic3—21no—
49C2×C32×Dic3—22no—
50C32×D12—21no—
51C32×D12C2×C412yes—
52C32×C4×D3—22no—
53C32×C4×D3—22no—
54C32×Dic6—21no—
55C32×Dic6C2×C412yes—
56C3×C3⋊(C3⋊C8)—22no—
57C3×#421—91no—
58#5236—31no—
59#5005—31no—
60C32×#41—32no—
61C32×#41—32no—
62C32×#41—61no—
63C32×#41—61no—
64C2×C32×Q8—31no—
65C2×C32×D4—31no—
66C2×C32×D4—61no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—41no—
71C22×C32×C4—61no—
72C22×C32×C4C2×D311yescharacteristic
73C22×C32×C4C2×D311yescharacteristic
74C22×C32×C4C22×C311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235—22no—
82C3×#235—21no—
83C3×#235—21no—
84C3×#235—21no—
85C3×#235—21no—
86C3×#235Dic312yescomplemented
87C3×#235C3×C412yescomplemented
88C3×#235C2×D312yes—
89C3×#235C22×C312yes—
90C2×C3×D12—21no—
91C2×C3×D12Dic311yescharacteristic, complemented
92C2×C3×D12C3×C411yescharacteristic, complemented
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6Dic311yescharacteristic, complemented
98C2×C3×Dic6C3×C411yescharacteristic, complemented
99C32×C4⋊C4—61no—
100C32×C22⋊C4—61no—
101C32×C42—32no—
102#3748—21no—
103#3748C22×C312yescomplemented
104C2×C3⋊(C3⋊C8)—21no—
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—32no—
115C3×#208—32no—
116C3×#208—62no—
117C3×#208—62no—
118C3×#208—61no—
119C3×#208—61no—
120C2×C3×C3⋊C8—62no—
121C2×C3×C3⋊C8—61no—
122C2×C3×C3⋊C8—61no—
123C22×C33—41no—
124C22×C33C22⋊C411yescharacteristic
125C22×C33C22⋊C411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C2×C32×D3—22no—
128C2×C32×D3—42no—
129C33×C4C22⋊C411yescharacteristic
130C33×C4C22⋊C411yescharacteristic
131C33×C4C22×C411yescharacteristic
132C33×C4C2×D411yescharacteristic
133C32×Dic3—22no—
134C32×Dic3—42no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—61no—
138C2×#235C3×D311yescharacteristic
139C2×C3×M16—91no—
140C3×#117—31no—
141C3×#117—31no—
142C3×#117—61no—
143#926C3×D311yescharacteristic, complemented
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C3×#104—94no—
148#837—34no—
149#805—34no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—41no—
154C23×C32—61no—
155C23×C32#6711yescharacteristic
156C23×C32#6711yescharacteristic
157C23×C32C3×D411yescharacteristic
158C22×C3×D3—22no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C32×Q8—32no—
162C32×Q8—61no—
163C32×D4—32no—
164C32×D4—62no—
165C32×D4—62no—
166C32×D4—61no—
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—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—41no—
190C2×C32×C4—41no—
191C2×C32×C4—61no—
192C2×C32×C4—62no—
193C2×C32×C4—62no—
194C2×C32×C4—62no—
195C2×C32×C4C4×D311yescharacteristic
196C2×C32×C4C4×D311yescharacteristic
197C2×C32×C4D1211yescharacteristic
198C2×C32×C4D1211yescharacteristic
199C2×C32×C4C2×Dic311yescharacteristic
200C2×C32×C4C2×Dic311yescharacteristic
201C2×C32×C4#6711yescharacteristic
202C2×C32×C4#6711yescharacteristic
203C2×C32×C4#6711yescharacteristic
204C2×C32×C4#6711yescharacteristic
205C2×C32×C4C2×C3×C411yescharacteristic
206C2×C32×C4C2×C3×C411yescharacteristic
207C2×C32×C4C3×D411yescharacteristic
208C2×C32×C4C3×D411yescharacteristic
209C2×C32×C4C3×D411yescharacteristic
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C23×C311yescharacteristic
213C3×#67—24no—
214C3×#67—24no—
215C3×#67—22no—
216C3×#67—22no—
217C3×#67—22no—
218C3×#67—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C3×D12—22no—
226C3×D12—21no—
227C3×D12—21no—
228C3×D12—22no—
229C3×D12C2×Dic312yes—
230C3×D12C2×C3×C412yes—
231C3×C4×D3—24no—
232C3×C4×D3—24no—
233C3×C4×D3—22no—
234C3×C4×D3—22no—
235C3×C4×D3—22no—
236C3×C4×D3—22no—
237C3×Dic6—22no—
238C3×Dic6—21no—
239C3×Dic6—21no—
240C3×Dic6—22no—
241C3×Dic6C2×Dic312yes—
242C3×Dic6C2×C3×C412yes—
243C3⋊(C3⋊C8)—22no—
244C3×C3⋊C8—64no—
245C3×C3⋊C8—62no—
246C3×C3⋊C8—62no—
247#421—91noSylow
248C2×C33—21no—
249C2×C33—21no—
250C2×C33—21no—
251C2×C33C2×C22⋊C411yescharacteristic
252C32×D3—42no—
253C3×#41—32no—
254C3×#41—32no—
255C3×#41—32no—
256C3×#41—32no—
257C3×#41—62no—
258C3×#41—62no—
259C3×#41—62no—
260C3×#41—62no—
261C3×#41—61no—
262C3×#41—61no—
263C3×#41—61no—
264C3×#41—61no—
265C2×C3×Q8—31no—
266C2×C3×Q8—31no—
267C2×C3×Q8—61no—
268C2×C3×D4—31no—
269C2×C3×D4—31no—
270C2×C3×D4—61no—
271C2×C3×D4—62no—
272C2×C3×D4—61no—
273C2×C3×D4—61no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—41no—
278C22×C3×C4—62no—
279C22×C3×C4—61no—
280C22×C3×C4—61no—
281C22×C3×C4D3211yescharacteristic
282C22×C3×C4C2×C3×D311yescharacteristic
283C22×C3×C4C2×C3×D311yescharacteristic
284C2×#67—21no—
285#235—21no—
286#235—21no—
287#235C3×Dic312yescomplemented
288#235C2×C3×D312yes—
289C2×D12C3×Dic311yescharacteristic, complemented
290C2×C4×D3—21no—
291C2×Dic6C3×Dic311yescharacteristic, complemented
292C3×M16—92no—
293C3×M16—181no—
294C2×C3×C8—181no—
295C3×C4⋊C4—62no—
296C3×C4⋊C4—61no—
297C3×C4⋊C4—61no—
298C3×C22⋊C4—62no—
299C3×C22⋊C4—61no—
300C3×C22⋊C4—61no—
301C3×C42—32no—
302C3×C42—32no—
303C3×C42—62no—
304#217—21no—
305C4⋊Dic3—21no—
306C4×Dic3C2×C3×D312yescomplemented
307#208—32no—
308#208—32no—
309#208—62no—
310#208—62no—
311#208—61no—
312#208—61no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—61no—
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—62no—
336C22×C32—122no—
337C22×C32(C2×D3)⋊C411yescharacteristic
338C22×C32(C2×D3)⋊C411yescharacteristic
339C22×C32#21711yescharacteristic
340C22×C32#21711yescharacteristic
341C22×C32C3×C22⋊C411yescharacteristic
342C22×C32C3×C22⋊C411yescharacteristic
343C22×C32C2×#6711yescharacteristic
344C22×C32C2×#6711yescharacteristic
345C22×C32C2×C3×D411yescharacteristic
346C2×C3×D3—24no—
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3—44no—
350C2×C3×D3—42no—
351C2×C3×D3—42no—
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—62no—
369C32×C4—122no—
370C32×C4(C2×D3)⋊C411yescharacteristic
371C32×C4(C2×D3)⋊C411yescharacteristic
372C32×C4#21711yescharacteristic
373C32×C4#21711yescharacteristic
374C32×C4C3×C22⋊C411yescharacteristic
375C32×C4C3×C22⋊C411yescharacteristic
376C32×C4C2×C4×D311yescharacteristic
377C32×C4C2×D1211yescharacteristic
378C32×C4C22×Dic311yescharacteristic
379C32×C4C2×#6711yescharacteristic
380C32×C4C22×C3×C411yescharacteristic
381C32×C4C2×C3×D411yescharacteristic
382C3×Dic3—24no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—44no—
386C3×Dic3—42no—
387C3×Dic3—42no—
388C2×#41—31no—
389C2×M16—91no—
390#117—31no—
391#104—94no—
392C33#42111yescharacteristic, complemented, Sylow
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—41no—
397C23×C3—62no—
398C23×C3—61no—
399C23×C3—61no—
400C23×C3#62511yescharacteristic
401C23×C3C3×#6711yescharacteristic
402C23×C3C3×#6711yescharacteristic
403C22×D3—21no—
404C3×Q8—32no—
405C3×Q8—32no—
406C3×Q8—62no—
407C3×Q8—62no—
408C3×Q8—61no—
409C3×Q8—61no—
410C3×D4—32no—
411C3×D4—32no—
412C3×D4—62no—
413C3×D4—62no—
414C3×D4—64no—
415C3×D4—64no—
416C3×D4—62no—
417C3×D4—62no—
418C3×D4—62no—
419C3×D4—62no—
420C3×D4—61no—
421C3×D4—61no—
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—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—64no—
447C2×C3×C4—64no—
448C2×C3×C4—62no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—64no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4D3×Dic311yescharacteristic
459C2×C3×C4D3×Dic311yescharacteristic
460C2×C3×C4#62511yescharacteristic
461C2×C3×C4#62611yescharacteristic
462C2×C3×C4#62611yescharacteristic
463C2×C3×C4C3×C4×D311yescharacteristic
464C2×C3×C4C3×C4×D311yescharacteristic
465C2×C3×C4C3×D1211yescharacteristic
466C2×C3×C4C3×D1211yescharacteristic
467C2×C3×C4C2×C3×Dic311yescharacteristic
468C2×C3×C4C2×C3×Dic311yescharacteristic
469C2×C3×C4C3×#6711yescharacteristic
470C2×C3×C4C3×#6711yescharacteristic
471C2×C3×C4C3×#6711yescharacteristic
472C2×C3×C4C3×#6711yescharacteristic
473C2×C3×C4C2×D3211yescharacteristic
474C2×C3×C4C22×C3×D311yescharacteristic
475C2×C3×C4C22×C3×D311yescharacteristic
476#67—22no—
477#67—22no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480D12—21no—
481D12C2×C3×Dic312yes—
482C4×D3—22no—
483C4×D3—22no—
484Dic6—21no—
485Dic6C2×C3×Dic312yes—
486C3×C8—182no—
487C3⋊C8—64no—
488C3⋊C8—62no—
489C3⋊C8—62no—
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×C32—122no—
516C2×C32C2×(C2×D3)⋊C411yescharacteristic
517C2×C32C2×#21711yescharacteristic
518C2×C32C2×C3×C22⋊C411yescharacteristic
519C3×D3—44no—
520C3×D3—42no—
521C3×D3—42no—
522#41—32no—
523#41—32no—
524#41—61no—
525#41—61no—
526C2×Q8—31no—
527C2×D4—31no—
528C2×D4—61no—
529C22×C4—61no—
530C22×C4C3×D3211yescharacteristic
531M16—92no—
532M16—181no—
533C2×C8—181no—
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—64no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—124no—
560C22×C3—122no—
561C22×C3—122no—
562C22×C3(C2×D3)⋊Dic311yescharacteristic
563C22×C3(C2×D3)⋊Dic311yescharacteristic
564C22×C3C3×(C2×D3)⋊C411yescharacteristic
565C22×C3C3×(C2×D3)⋊C411yescharacteristic
566C22×C3C3×#21711yescharacteristic
567C22×C3C3×#21711yescharacteristic
568C22×C3C2×#62511yescharacteristic
569C22×C3C2×C3×#6711yescharacteristic
570C22×C3C2×C3×#6711yescharacteristic
571C2×D3—22no—
572C2×D3—42no—
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—64no—
590C3×C4—62no—
591C3×C4—62no—
592C3×C4—124no—
593C3×C4—122no—
594C3×C4—122no—
595C3×C4(C2×D3)⋊Dic311yescharacteristic
596C3×C4(C2×D3)⋊Dic311yescharacteristic
597C3×C4C3×(C2×D3)⋊C411yescharacteristic
598C3×C4C3×(C2×D3)⋊C411yescharacteristic
599C3×C4C3×#21711yescharacteristic
600C3×C4C3×#21711yescharacteristic
601C3×C4C2×D3×Dic311yescharacteristic
602C3×C4C2×#62611yescharacteristic
603C3×C4C2×C3×C4×D311yescharacteristic
604C3×C4C2×C3×D1211yescharacteristic
605C3×C4C22×C3×Dic311yescharacteristic
606C3×C4C2×C3×#6711yescharacteristic
607Dic3—22no—
608Dic3—42no—
609C32—21no—
610C32—21no—
611C32—21no—
612C32—41no—
613C32#500511yescharacteristic, complemented
614C32#523611yescharacteristic, complemented
615C32C3×#42111yescharacteristic, complemented
616C23—61no—
617C23C3×#62511yescharacteristic
618Q8—32no—
619Q8—61no—
620D4—32no—
621D4—62no—
622D4—62no—
623D4—61no—
624C2×C4—61no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4C3×D3×Dic311yescharacteristic
629C2×C4C3×D3×Dic311yescharacteristic
630C2×C4C3×#62511yescharacteristic
631C2×C4C3×#62611yescharacteristic
632C2×C4C3×#62611yescharacteristic
633C2×C4C2×C3×D3211yescharacteristic
634C8—182no—
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—124no—
661C2×C3—122no—
662C2×C3—122no—
663C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
664C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
665C2×C3C2×C3×#21711yescharacteristic
666D3—42no—
667C22—41no—
668C22—62no—
669C22—122no—
670C22C3×(C2×D3)⋊Dic311yescharacteristic
671C22C3×(C2×D3)⋊Dic311yescharacteristic
672C22C2×C3×#62511yescharacteristic
673C4—62no—
674C4—122no—
675C4C3×(C2×D3)⋊Dic311yescharacteristic
676C4C3×(C2×D3)⋊Dic311yescharacteristic
677C4C2×C3×D3×Dic311yescharacteristic
678C4C2×C3×#62611yescharacteristic
679C3—21no—
680C3—21no—
681C3—21no—
682C3—41no—
683C3#1059111111yescharacteristic, direct product factor
684C3C3×#500511yescharacteristic, complemented
685C3C3×#523611yescharacteristic, complemented
686C2—21no—
687C2—21no—
688C2—21no—
689C2—122no—
690C2C2×C3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC3×C4C2×#626
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC2×C33C2×C22⋊C4
prime radicalC2×C32×#235C2
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. C2×C3×#3748C2semidirect
3. C32×#926C2semidirect
4. C3×#63569C2semidirect
7. #10591111C3direct (N × H)
12. C32×#235C4semidirect
14. C2×C32×D12C4semidirect
16. C2×C32×Dic6C4semidirect
18. C3×#3748C22semidirect
22. C32×C4×Dic3C22semidirect
28. C2×#3748C2×C3semidirect
30. C3×#926D3semidirect
31. C3×#926C2×C3semidirect
37. #63569C2×C3semidirect
86. C3×#235Dic3semidirect
87. C3×#235C3×C4semidirect
91. C2×C3×D12Dic3semidirect
92. C2×C3×D12C3×C4semidirect
97. C2×C3×Dic6Dic3semidirect
98. C2×C3×Dic6C3×C4semidirect
103. #3748C22×C3semidirect
112. C3×C4×Dic3C2×D3semidirect
113. C3×C4×Dic3C22×C3semidirect
143. #926C3×D3semidirect
287. #235C3×Dic3semidirect
289. C2×D12C3×Dic3semidirect
291. C2×Dic6C3×Dic3semidirect
306. C4×Dic3C2×C3×D3semidirect
392. C33#421semidirect
613. C32#5005semidirect
614. C32#5236semidirect
615. C32C3×#421semidirect
683. C3#10591111direct (N × H)
684. C3C3×#5005semidirect
685. C3C3×#5236semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C3×#37482
C32×#9262
C3×#635692
C3×#52363
C3×#50053
#105911113