Finite Group Databasebeta

← C3×C4×#932 #11860265

Subgroups — C3×C4×#932 #11860265

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic
3C3×C4×#235C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5C3×#5018C212yesmaximal, complemented
6C3×C4×#214C212yesmaximal, complemented
7C3×#5014C212yesmaximal, complemented
8C3×C4×#213C212yesmaximal, complemented
9C3×#4966C211yesmaximal, characteristic, complemented
10C3×#4964C211yesmaximal, characteristic, complemented
11C3×C4×#208C211yesmaximal, characteristic, complemented
12C3×C4×AGL(1,ℤ/8)—31nomaximal
13C4×#932C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4—21no—
16C2×C3×#235C2211yescharacteristic
17C32×C4×D4—21no—
18C32×C4×D4—21no—
19C32×C4×D4C2212yes—
20C32×C4×D4C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4—21no—
23C2×C32×C42C2211yescharacteristic
24C2×C3×#214C2212yes—
25C3×#932C418yesdirect product factor
26C2×C3×#213C2212yes—
27C3×C4×#67—21no—
28C3×C4×#67—21no—
29C3×#926C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×C4×D12C2211yescharacteristic, complemented
34C3×#872—21no—
35C3×C42×D3—21no—
36C3×C4×Dic6C2211yescharacteristic, complemented
37C3×C4×Dic6C2211yescharacteristic, complemented
38C3×#832C2212yes—
39C3×#832C2212yes—
40C3×#810C2212yescomplemented
41C3×#809C2212yescomplemented
42C3×#808C2212yescomplemented
43C3×#807C2212yescomplemented
44C3×#803C2212yescomplemented
45C3×C4×C3⋊C8C2212yescomplemented
46C2×C3×AGL(1,ℤ/8)—31no—
47C3×C4×#41—31no—
48C2×C3×C4×D4—21no—
49C2×C3×C4×D4D311yescharacteristic, complemented
50C2×C3×C4×D4C2×C311yescharacteristic, complemented
51C2×#932C2×C311yescharacteristic
52C4×#235C2×C311yescharacteristic, complemented
53C3×#442—32no—
54C3×#440—32no—
55C3×C4×SD16—32no—
56C3×C4×D8—32no—
57C3×#428—31no—
58C3×#418—31no—
59C3×#417—31no—
60C3×C4×M16—31no—
61#5215C2×C311yescharacteristic, complemented
62#5018C2×C312yescomplemented
63C4×#214C2×C312yescomplemented
64#5014C2×C312yescomplemented
65C4×#213C2×C312yescomplemented
66#4966C2×C311yescharacteristic, complemented
67#4964C2×C311yescharacteristic, complemented
68C4×#208C2×C311yescharacteristic, complemented
69C24×C32—21no—
70C2×C32×D4—21no—
71C2×C32×D4—22no—
72C2×C32×D4C2×C414yescomplemented
73C2×C32×D4C2312yes—
74C22×C32×C4—21no—
75C22×C32×C4—22no—
76C22×C32×C4—22no—
77C22×C32×C4—44no—
78C22×C32×C4D411yescharacteristic
79C22×C32×C4D411yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×C3×#67—21no—
82C3×#235—22no—
83C3×#235C2×C414yescomplemented
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—21no—
86C2×C3×C4×D3—21no—
87C2×C3×C4×D3—21no—
88C2×C3×Dic6C2311yescharacteristic
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2312yes—
91C32×C22⋊C4—22no—
92C32×C22⋊C4—22no—
93C32×C42D411yescharacteristic
94C32×C42D411yescharacteristic
95C32×C42C2311yescharacteristic
96C32×C42C2311yescharacteristic
97C3×#217—21no—
98C3×#214C2×C418yescomplemented
99C3×#213C2×C418yescomplemented
100C3×(C2×D3)⋊C4—21no—
101C3×(C2×D3)⋊C4—21no—
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4⋊Dic3C2311yescharacteristic
104C3×Dic3⋊C4—21no—
105C3×Dic3⋊C4—21no—
106C3×C4×Dic3—21no—
107C3×C4×Dic3—21no—
108C3×C4×Dic3—21no—
109C3×#208—22no—
110C3×#208C2×C414yescomplemented
111C2×C3×C3⋊C8C2312yes—
112C2×C3×C3⋊C8C2312yes—
113C4×AGL(1,ℤ/8)—31noSylow
114C2×C3×#41—31no—
115C22×C3×D4—21no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C22×C311yescharacteristic
118C23×C3×C4—22no—
119C23×C3×C4—21no—
120C23×C3×C4—21no—
121C2×#235C22×C311yescharacteristic
122C3×AGL(1,ℤ/8)—38no—
123C2×C3×SD16—32no—
124C2×C3×D8—32no—
125C2×C3×M16—31no—
126C2×C3×M16—31no—
127C3×C4×Q8—31no—
128C3×C4×Q8—31no—
129C3×C4×D4—22no—
130C3×C4×D4—22no—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4—22no—
136C3×C4×D4—22no—
137C3×C4×D4—31no—
138C3×C4×D4—31no—
139C3×C4×D4—61no—
140C3×C4×D4—61no—
141C3×C4×D4C2×D312yes—
142C3×C4×D4C2×D312yes—
143C3×C4×D4C22×C312yes—
144C3×C4×D4C22×C312yes—
145C3×#117—31no—
146C3×#117—61no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C22×C311yescharacteristic
150C2×C3×C22⋊C4—22no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C42—21no—
154C2×C3×C42—61no—
155C2×C3×C42C2×D311yescharacteristic
156C2×C3×C42C22×C311yescharacteristic
157C2×#214C22×C312yes—
158#932C3×C418yesdirect product factor
159C2×#213C22×C312yes—
160C4×#67—21no—
161C4×#67—21no—
162#926C22×C311yescharacteristic
163C2×#208C22×C311yescharacteristic
164C2×#208C22×C311yescharacteristic
165C4×D12C22×C311yescharacteristic, complemented
166C4×D12C22×C311yescharacteristic, complemented
167#872—21no—
168C42×D3—21no—
169C4×Dic6C22×C311yescharacteristic, complemented
170C4×Dic6C22×C311yescharacteristic, complemented
171C3×#107—32no—
172C3×#106—32no—
173C3×#103—32no—
174C3×#102—32no—
175C3×#102—32no—
176C3×#102—32no—
177C3×#97—32no—
178C3×C4×C8—32no—
179#832C22×C312yes—
180#832C22×C312yes—
181#810C22×C312yescomplemented
182#809C22×C312yescomplemented
183#808C22×C312yescomplemented
184#807C22×C312yescomplemented
185#803C22×C312yescomplemented
186C4×C3⋊C8C22×C312yescomplemented
187C23×C32—24no—
188C23×C32—22no—
189C23×C32—42no—
190C23×C32—42no—
191C23×C32C2×D411yescharacteristic
192C22×C3×D3—21no—
193C32×D4—24no—
194C32×D4—22no—
195C32×D4C22×C414yes—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4—41no—
199C2×C32×C4—44no—
200C2×C32×C4—42no—
201C2×C32×C4—44no—
202C2×C32×C4C22×C412yes—
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4#4112yes—
209C2×C32×C4C2411yescharacteristic
210C3×#67—24no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C3×D12—21no—
215C3×D12C22×C412yescomplemented
216C3×C4×D3—24no—
217C3×C4×D3—42no—
218C3×C4×D3—42no—
219C3×Dic6—21no—
220C3×Dic6C22×C412yescomplemented
221C3×C3⋊C8—22no—
222C3×C3⋊C8C22×C414yescomplemented
223C2×AGL(1,ℤ/8)—31no—
224C4×#41—31no—
225C2×C4×D4C3×D311yescharacteristic, complemented
226#442—32no—
227#440—32no—
228C4×SD16—32no—
229C4×D8—32no—
230#428—31no—
231#418—31no—
232#417—31no—
233C4×M16—31no—
234C24×C3—22no—
235C24×C3—21no—
236C24×C3—21no—
237C3×#41—34no—
238C3×#41—62no—
239C2×C3×Q8—31no—
240C2×C3×D4—22no—
241C2×C3×D4—24no—
242C2×C3×D4—22no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—22no—
246C2×C3×D4—24no—
247C2×C3×D4—22no—
248C2×C3×D4—31no—
249C2×C3×D4—61no—
250C2×C3×D4C4×D314yescomplemented
251C2×C3×D4C2×C3×C414yescomplemented
252C2×C3×D4C22×D312yes—
253C2×C3×D4C23×C312yes—
254C22×C3×C4—22no—
255C22×C3×C4—24no—
256C22×C3×C4—24no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—48no—
267C22×C3×C4—44no—
268C22×C3×C4—44no—
269C22×C3×C4—61no—
270C22×C3×C4—61no—
271C22×C3×C4—61no—
272C22×C3×C4#6711yescharacteristic
273C22×C3×C4#6711yescharacteristic
274C22×C3×C4C3×D411yescharacteristic
275C22×C3×C4C3×D411yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C23×C311yescharacteristic
278C2×#67—21no—
279#235—22no—
280#235C2×C3×C414yescomplemented
281C2×D12C23×C311yescharacteristic
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×Dic6C23×C311yescharacteristic
286C3×SD16—38no—
287C3×D8—38no—
288C3×M16—34no—
289C3×M16—62no—
290C2×C3×C8—32no—
291C2×C3×C8—32no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—31no—
297C3×C4⋊C4—31no—
298C3×C4⋊C4—61no—
299C3×C4⋊C4—61no—
300C3×C4⋊C4C22×D312yes—
301C3×C4⋊C4C23×C312yes—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—61no—
309C3×C22⋊C4—61no—
310C3×C22⋊C4—61no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—61no—
316C3×C42—61no—
317C3×C42—61no—
318C3×C42#6711yescharacteristic
319C3×C42#6711yescharacteristic
320C3×C42C3×D411yescharacteristic
321C3×C42C3×D411yescharacteristic
322C3×C42C22×D311yescharacteristic
323C3×C42C22×D311yescharacteristic
324C3×C42C23×C311yescharacteristic
325C3×C42C23×C311yescharacteristic
326#217—21no—
327#214C2×C3×C418yescomplemented
328#213C2×C3×C418yescomplemented
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—21no—
331C4⋊Dic3C23×C311yescharacteristic
332C4⋊Dic3C23×C311yescharacteristic
333Dic3⋊C4—21no—
334Dic3⋊C4—21no—
335C4×Dic3—21no—
336C4×Dic3—21no—
337C4×Dic3—21no—
338#208—22no—
339#208C2×C3×C414yescomplemented
340C2×C3⋊C8C23×C312yes—
341C2×C3⋊C8C23×C312yes—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—24no—
345C22×C32—48no—
346C22×C32—42no—
347C22×C32—42no—
348C22×C32C4×D412yes—
349C22×C32C22×D411yescharacteristic
350C2×C3×D3—22no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C32×C4—21no—
354C32×C4—21no—
355C32×C4—21no—
356C32×C4—42no—
357C32×C4C4×D412yes—
358C32×C4AGL(1,ℤ/8)12yescomplemented
359C32×C4C23×C411yescharacteristic
360C32×C4C2×#4111yescharacteristic
361C3×Dic3—22no—
362C3×Dic3—41no—
363C3×Dic3—41no—
364C2×#41—31no—
365C22×D4C2×C3×D311yescharacteristic
366C23×C4—21no—
367AGL(1,ℤ/8)—38no—
368C2×SD16—32no—
369C2×D8—32no—
370C2×M16—31no—
371C2×M16—31no—
372C4×Q8—31no—
373C4×Q8—31no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—31no—
377C4×D4—31no—
378C4×D4—61no—
379C4×D4—61no—
380C4×D4C2×C3×D312yes—
381C4×D4C2×C3×D312yes—
382#117—31no—
383#117—61no—
384C2×C4⋊C4C2×C3×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C42—61no—
387C2×C42C2×C3×D311yescharacteristic
388#107—32no—
389#106—32no—
390#103—32no—
391#102—32no—
392#102—32no—
393#102—32no—
394#97—32no—
395C4×C8—32no—
396C23×C3—24no—
397C23×C3—28no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—44no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—44no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—61no—
410C23×C3C2×#6711yescharacteristic
411C23×C3C2×C3×D411yescharacteristic
412C22×D3—21no—
413C3×Q8—32no—
414C3×Q8—61no—
415C3×D4—28no—
416C3×D4—24no—
417C3×D4—24no—
418C3×D4—24no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—24no—
422C3×D4—32no—
423C3×D4—64no—
424C3×D4—61no—
425C3×D4C2×C4×D314yes—
426C3×D4C22×C3×C414yes—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—48no—
444C2×C3×C4—44no—
445C2×C3×C4—44no—
446C2×C3×C4—48no—
447C2×C3×C4—42no—
448C2×C3×C4—44no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—44no—
452C2×C3×C4—44no—
453C2×C3×C4—61no—
454C2×C3×C4—64no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—122no—
458C2×C3×C4—122no—
459C2×C3×C4C2×C4×D312yes—
460C2×C3×C4#23512yes—
461C2×C3×C4C2×#6711yescharacteristic
462C2×C3×C4C2×#6711yescharacteristic
463C2×C3×C4C2×#6711yescharacteristic
464C2×C3×C4C2×#6711yescharacteristic
465C2×C3×C4C2×#6711yescharacteristic
466C2×C3×C4C22×C3×C412yes—
467C2×C3×C4C2×C3×D411yescharacteristic
468C2×C3×C4C2×C3×D411yescharacteristic
469C2×C3×C4C2×C3×D411yescharacteristic
470C2×C3×C4C2×C3×D411yescharacteristic
471C2×C3×C4C2×C3×D411yescharacteristic
472C2×C3×C4C3×#4112yes—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C24×C311yescharacteristic
475#67—24no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479D12—21no—
480D12C22×C3×C412yescomplemented
481C4×D3—24no—
482C4×D3—42no—
483C4×D3—42no—
484Dic6—21no—
485Dic6C22×C3×C412yescomplemented
486C3×C8—34no—
487C3×C8—62no—
488C3⋊C8—22no—
489C3⋊C8C22×C3×C414yescomplemented
490C2×C32—22no—
491C2×C32—44no—
492C2×C32C2×C4×D411yescharacteristic
493C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
494C2×C32#57511yescharacteristic
495C3×D3—42no—
496C24—21no—
497#41—34no—
498#41—62no—
499C2×Q8—31no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—31no—
503C2×D4—61no—
504C2×D4C3×C4×D314yescomplemented
505C2×D4C22×C3×D312yes—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—44no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4C3×#6711yescharacteristic
514C22×C4C3×#6711yescharacteristic
515C22×C4C22×C3×D311yescharacteristic
516SD16—38no—
517D8—38no—
518M16—34no—
519M16—62no—
520C2×C8—32no—
521C2×C8—32no—
522C4⋊C4—21no—
523C4⋊C4—31no—
524C4⋊C4—31no—
525C4⋊C4—61no—
526C4⋊C4—61no—
527C4⋊C4C22×C3×D312yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—61no—
531C22⋊C4—61no—
532C22⋊C4—61no—
533C42—61no—
534C42—61no—
535C42—61no—
536C42C3×#6711yescharacteristic
537C42C3×#6711yescharacteristic
538C42C22×C3×D311yescharacteristic
539C42C22×C3×D311yescharacteristic
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—28no—
547C22×C3—24no—
548C22×C3—24no—
549C22×C3—22no—
550C22×C3—21no—
551C22×C3—44no—
552C22×C3—416no—
553C22×C3—48no—
554C22×C3—48no—
555C22×C3—44no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—62no—
561C22×C3—121no—
562C22×C3—121no—
563C22×C3C4×#6712yes—
564C22×C3C3×C4×D412yes—
565C22×C3C22×#6711yescharacteristic
566C22×C3C22×C3×D411yescharacteristic
567C2×D3—22no—
568C2×D3—41no—
569C2×D3—41no—
570C3×C4—22no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—22no—
578C3×C4—22no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—44no—
584C3×C4—42no—
585C3×C4—42no—
586C3×C4—62no—
587C3×C4—121no—
588C3×C4—121no—
589C3×C4C4×#6712yes—
590C3×C4#93212yesdirect product factor
591C3×C4C3×C4×D412yes—
592C3×C4C3×AGL(1,ℤ/8)12yescomplemented
593C3×C4C22×C4×D311yescharacteristic
594C3×C4C2×#23511yescharacteristic
595C3×C4C23×C3×C411yescharacteristic
596C3×C4C2×C3×#4111yescharacteristic
597Dic3—22no—
598Dic3—41no—
599Dic3—41no—
600C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
601C23—24no—
602C23—22no—
603C23—42no—
604C23—42no—
605C23—61no—
606C23C2×C3×#6711yescharacteristic
607Q8—32no—
608Q8—61no—
609D4—24no—
610D4—22no—
611D4—32no—
612D4—64no—
613D4—61no—
614D4C2×C3×C4×D314yes—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—44no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—61no—
622C2×C4—64no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4C2×C3×C4×D312yes—
628C2×C4C3×#23512yes—
629C2×C4C2×C3×#6711yescharacteristic
630C2×C4C2×C3×#6711yescharacteristic
631C2×C4C2×C3×#6711yescharacteristic
632C2×C4C2×C3×#6711yescharacteristic
633C2×C4C2×C3×#6711yescharacteristic
634C2×C4C23×C3×D311yescharacteristic
635C8—34no—
636C8—62no—
637C2×C3—24no—
638C2×C3—22no—
639C2×C3—22no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—48no—
644C2×C3—44no—
645C2×C3—44no—
646C2×C3—122no—
647C2×C3C2×C4×#6711yescharacteristic
648C2×C3C2×#93211yescharacteristic
649C2×C3#582211yescharacteristic
650C2×C3C2×C3×C4×D411yescharacteristic
651C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
652C2×C3C3×#57511yescharacteristic
653D3—42no—
654C22—21no—
655C22—21no—
656C22—24no—
657C22—48no—
658C22—42no—
659C22—42no—
660C22—62no—
661C22—121no—
662C22—121no—
663C22C3×C4×#6712yes—
664C22C22×C3×#6711yescharacteristic
665C4—21no—
666C4—21no—
667C4—21no—
668C4—42no—
669C4—62no—
670C4—121no—
671C4—121no—
672C4C3×C4×#6712yes—
673C4C3×#93212yesdirect product factor
674C4C22×C3×C4×D311yescharacteristic
675C4C2×C3×#23511yescharacteristic
676C3—21no—
677C3C4×#93211yescharacteristic, direct product factor
678C3C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented
679C2—22no—
680C2—44no—
681C2—122no—
682C2C2×C3×C4×#6711yescharacteristic
683C2C2×C3×#93211yescharacteristic
684C2C3×#582211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
prime radicalC2×C3×#932C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C3×C4×#235C2semidirect
4. C3×#5215C2semidirect
5. C3×#5018C2semidirect
6. C3×C4×#214C2semidirect
7. C3×#5014C2semidirect
8. C3×C4×#213C2semidirect
9. C3×#4966C2semidirect
10. C3×#4964C2semidirect
11. C3×C4×#208C2semidirect
13. C4×#932C3direct (N × H)
25. C3×#932C4direct (N × H)
32. C3×C4×D12C22semidirect
33. C3×C4×D12C22semidirect
36. C3×C4×Dic6C22semidirect
37. C3×C4×Dic6C22semidirect
40. C3×#810C22semidirect
41. C3×#809C22semidirect
42. C3×#808C22semidirect
43. C3×#807C22semidirect
44. C3×#803C22semidirect
45. C3×C4×C3⋊C8C22semidirect
49. C2×C3×C4×D4D3semidirect
50. C2×C3×C4×D4C2×C3semidirect
52. C4×#235C2×C3semidirect
61. #5215C2×C3semidirect
62. #5018C2×C3semidirect
63. C4×#214C2×C3semidirect
64. #5014C2×C3semidirect
65. C4×#213C2×C3semidirect
66. #4966C2×C3semidirect
67. #4964C2×C3semidirect
68. C4×#208C2×C3semidirect
72. C2×C32×D4C2×C4semidirect
83. C3×#235C2×C4semidirect
98. C3×#214C2×C4semidirect
99. C3×#213C2×C4semidirect
110. C3×#208C2×C4semidirect
158. #932C3×C4direct (N × H)
165. C4×D12C22×C3semidirect
166. C4×D12C22×C3semidirect
169. C4×Dic6C22×C3semidirect
170. C4×Dic6C22×C3semidirect
181. #810C22×C3semidirect
182. #809C22×C3semidirect
183. #808C22×C3semidirect
184. #807C22×C3semidirect
185. #803C22×C3semidirect
186. C4×C3⋊C8C22×C3semidirect
215. C3×D12C22×C4semidirect
220. C3×Dic6C22×C4semidirect
222. C3×C3⋊C8C22×C4semidirect
225. C2×C4×D4C3×D3semidirect
250. C2×C3×D4C4×D3semidirect
251. C2×C3×D4C2×C3×C4semidirect
280. #235C2×C3×C4semidirect
327. #214C2×C3×C4semidirect
328. #213C2×C3×C4semidirect
339. #208C2×C3×C4semidirect
358. C32×C4AGL(1,ℤ/8)semidirect
480. D12C22×C3×C4semidirect
485. Dic6C22×C3×C4semidirect
489. C3⋊C8C22×C3×C4semidirect
504. C2×D4C3×C4×D3semidirect
590. C3×C4#932direct (N × H)
592. C3×C4C3×AGL(1,ℤ/8)semidirect
600. C32C4×AGL(1,ℤ/8)semidirect
673. C4C3×#932direct (N × H)
677. C3C4×#932direct (N × H)
678. C3C3×C4×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9322
C3×C4×#2352
C3×#52152
C3×#50182
C3×C4×#2142
C3×#50142
C3×C4×#2132
C3×#49662
C3×#49642
C3×C4×#2082
C3×C4×AGL(1,ℤ/8)3
C4×#9323