Finite Group Databasebeta

← C3×#78910 #11865842

Subgroups — C3×#78910 #11865842

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic, complemented
4C2×C3×#893C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6C3×#5118C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4819C212yesmaximal, complemented
9C3×#4818C212yesmaximal, complemented
10C3×#4787C212yesmaximal, complemented
11C3×#4786C212yesmaximal, complemented
12C3×#3036—31nomaximal
13#78910C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3—21no—
18C2×C32×M16C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C3×#949—24no—
21C3×#947C2211yescharacteristic, complemented
22C3×#944C2211yescharacteristic, complemented
23C2×C3×#215C2212yes—
24C3×#940C2211yescharacteristic, complemented
25C3×#939—21no—
26C3×#939—21no—
27C3×#936C2211yescharacteristic, complemented
28C2×C3×#213C2212yes—
29C3×C4×#67—21no—
30C3×C4×#67—21no—
31C2×C3×(C2×D3)⋊C4—21no—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C3×#908—24no—
35C2×C3×D24C2212yes—
36C2×C3×#204C2212yes—
37C3×#893—21no—
38C3×#893—21no—
39C3×#893C2212yes—
40C3×#893C2212yes—
41C32×#103C2212yescomplemented
42C32×#102C2212yescomplemented
43C3×Dic3⋊C8C2212yescomplemented
44C3×Dic3⋊C8C2212yescomplemented
45C3×#810C2212yescomplemented
46C3×#809C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C2×C3×AGL(1,ℤ/8)—31no—
49C3×#532—31no—
50C2×C3×C4×D4—31no—
51#5832C2×C311yescharacteristic, complemented
52C2×#949C2×C311yescharacteristic, complemented
53C2×#908C2×C311yescharacteristic, complemented
54C2×#893C2×C311yescharacteristic, complemented
55C3×#463—32no—
56C3×#463—32no—
57C3×#461—32no—
58C3×#459—32no—
59C3×#423—31no—
60C3×#417—21no—
61C3×#417—31no—
62C3×#417D311yescharacteristic, complemented
63C3×#417C2×C311yescharacteristic, complemented
64#5118C2×C311yescharacteristic, complemented
65#4966C2×C311yescharacteristic, complemented
66#4819C2×C312yescomplemented
67#4818C2×C312yescomplemented
68#4787C2×C312yescomplemented
69#4786C2×C312yescomplemented
70C23×C3×D3—21no—
71C32×#41—22no—
72C32×#41—22no—
73C2×C32×Q8C2311yescharacteristic
74C2×C32×D4—21no—
75C2×C32×D4C2311yescharacteristic
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×C3×#67—21no—
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C22×C3×Dic3D411yescharacteristic
83C22×C3×Dic3D411yescharacteristic
84C3×#235—22no—
85C3×#235—22no—
86C2×C3×D12—21no—
87C2×C3×D12—22no—
88C2×C3×D12D414yescomplemented
89C2×C3×D12C2311yescharacteristic
90C2×C3×D12C2312yes—
91C2×C3×C4×D3—21no—
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—44no—
95C2×C3×Dic6C2311yescharacteristic
96C32×M16—22no—
97C2×C32×C8C2312yes—
98C32×C4⋊C4—21no—
99C32×C4⋊C4C2312yes—
100C3×#217—21no—
101C3×#217—21no—
102C3×#215—24no—
103C3×#213—24no—
104C3×(C2×D3)⋊C4—22no—
105C3×(C2×D3)⋊C4—22no—
106C3×(C2×D3)⋊C4—21no—
107C3×(C2×D3)⋊C4—21no—
108C3×Dic3⋊C4—21no—
109C3×Dic3⋊C4—21no—
110C3×C4×Dic3D411yescharacteristic
111C3×C4×Dic3D411yescharacteristic
112C3×C4×Dic3C2311yescharacteristic
113C3×C4×Dic3C2311yescharacteristic
114C3×#208—22no—
115C2×C3×C3⋊C8C2312yes—
116C3×D24—24no—
117C3×#204—24no—
118#3036—31noSylow
119C2×C3×#41—21no—
120C2×C3×#41—31no—
121C2×C3×#41C2×D311yescharacteristic
122C2×C3×#41C22×C311yescharacteristic
123C22×C3×D4—31no—
124C23×C3×C4—61no—
125C2×#235C22×C311yescharacteristic
126C22×D12C22×C311yescharacteristic
127C22×C4×D3—21no—
128C3×AGL(1,ℤ/8)—64no—
129C3×AGL(1,ℤ/8)—64no—
130C2×C3×SD16—32no—
131C2×C3×SD16—32no—
132C2×C3×D8—32no—
133C2×C3×D8—32no—
134C2×C3×M16—21no—
135C2×C3×M16—31no—
136C2×C3×M16C2×D311yescharacteristic
137C2×C3×M16C22×C311yescharacteristic
138C3×C4⋊Q8—31no—
139C3×#127—31no—
140C3×#124—31no—
141C3×#124—31no—
142C3×#121—61no—
143C3×#121—61no—
144C3×C4×D4—32no—
145C3×C4×D4—32no—
146C3×C4×D4—61no—
147C3×C4×D4—61no—
148C3×C4×D4—61no—
149C3×C4×D4—61no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4C2×D311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C22⋊C4—61no—
154C2×C3×C42—31no—
155#949—24no—
156#947C22×C311yescharacteristic, complemented
157#944C22×C311yescharacteristic, complemented
158C2×#215C22×C312yes—
159#940C22×C311yescharacteristic, complemented
160#939—21no—
161#939—21no—
162#936C22×C311yescharacteristic, complemented
163C2×#213C22×C312yes—
164C4×#67—21no—
165C4×#67—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×C4×Dic3C22×C311yescharacteristic
168C2×#208C22×C311yescharacteristic
169#908—24no—
170C2×D24C22×C312yes—
171C2×#204C22×C312yes—
172#893—21no—
173#893—21no—
174#893C22×C312yes—
175#893C22×C312yes—
176C3×C4⋊C8—32no—
177C3×C4⋊C8—32no—
178C3×#103—22no—
179C3×#103—32no—
180C3×#103C2×D312yescomplemented
181C3×#103C22×C312yescomplemented
182C3×#102—22no—
183C3×#102—32no—
184C3×#102C2×D312yescomplemented
185C3×#102C22×C312yescomplemented
186Dic3⋊C8C22×C312yescomplemented
187Dic3⋊C8C22×C312yescomplemented
188#810C22×C312yescomplemented
189#809C22×C312yescomplemented
190C23×C32—21no—
191C23×C32C2×D411yescharacteristic
192C22×C3×D3—24no—
193C22×C3×D3—22no—
194C22×C3×D3—21no—
195C22×C3×D3—42no—
196C22×C3×D3—42no—
197C32×Q8—21no—
198C32×Q8—21no—
199C32×D4—21no—
200C32×D4—21no—
201C32×D4—42no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—42no—
205C2×C32×C4—42no—
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D412yes—
208C2×C32×C4#4112yes—
209C2×C32×C4C2411yescharacteristic
210C3×#67—42no—
211C3×#67—42no—
212C3×#67—42no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—41no—
216C2×C3×Dic3C2×D411yescharacteristic
217C2×C3×Dic3C2×D411yescharacteristic
218C2×C3×Dic3C2×D411yescharacteristic
219C2×C3×Dic3C2×D411yescharacteristic
220C3×D12—24no—
221C3×D12—21no—
222C3×D12—22no—
223C3×D12—21no—
224C3×D12C2×D414yes—
225C3×C4×D3—44no—
226C3×C4×D3—42no—
227C3×C4×D3—44no—
228C3×Dic6—21no—
229C3×Dic6—21no—
230C32×C8—22no—
231C3×C3⋊C8—22no—
232C2×AGL(1,ℤ/8)—31no—
233C2×AGL(1,ℤ/8)—31no—
234#532—31no—
235C2×C4×D4—31no—
236#463—32no—
237#463—32no—
238#461—32no—
239#459—32no—
240#423—31no—
241#417—31no—
242#417C3×D311yescharacteristic, complemented
243C24×C3—61no—
244C23×D3—21no—
245C3×#41—24no—
246C3×#41—22no—
247C3×#41—22no—
248C3×#41—22no—
249C3×#41—22no—
250C3×#41—42no—
251C3×#41—62no—
252C3×#41—62no—
253C2×C3×Q8—21no—
254C2×C3×Q8—31no—
255C2×C3×Q8C22×D311yescharacteristic
256C2×C3×Q8C23×C311yescharacteristic
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—34no—
261C2×C3×D4—32no—
262C2×C3×D4—31no—
263C2×C3×D4—41no—
264C2×C3×D4—61no—
265C2×C3×D4—61no—
266C2×C3×D4—61no—
267C2×C3×D4—62no—
268C2×C3×D4—61no—
269C2×C3×D4C22×D311yescharacteristic
270C2×C3×D4C23×C311yescharacteristic
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—41no—
279C22×C3×C4—41no—
280C22×C3×C4—62no—
281C22×C3×C4—62no—
282C22×C3×C4—61no—
283C22×C3×C4—124no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C23×C311yescharacteristic
286C2×#67—21no—
287C2×#67—21no—
288C2×#67—21no—
289C22×Dic3C3×D411yescharacteristic
290C22×Dic3C3×D411yescharacteristic
291#235—22no—
292#235—22no—
293C2×D12—21no—
294C2×D12—22no—
295C2×D12C3×D414yescomplemented
296C2×D12C23×C311yescharacteristic
297C2×D12C23×C312yes—
298C2×C4×D3—21no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—44no—
302C2×Dic6C23×C311yescharacteristic
303C3×SD16—64no—
304C3×SD16—64no—
305C3×D8—64no—
306C3×D8—64no—
307C3×M16—22no—
308C3×M16—22no—
309C3×M16—42no—
310C3×M16—62no—
311C2×C3×C8—22no—
312C2×C3×C8—32no—
313C2×C3×C8C22×D312yes—
314C2×C3×C8C23×C312yes—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—41no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D312yes—
322C3×C4⋊C4C23×C312yes—
323C3×C22⋊C4—62no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—31no—
332C3×C42—31no—
333#217—21no—
334#217—21no—
335#215—24no—
336#213—24no—
337(C2×D3)⋊C4—22no—
338(C2×D3)⋊C4—22no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343C4×Dic3C3×D411yescharacteristic
344C4×Dic3C3×D411yescharacteristic
345C4×Dic3C23×C311yescharacteristic
346C4×Dic3C23×C311yescharacteristic
347#208—22no—
348C2×C3⋊C8C23×C312yes—
349D24—24no—
350#204—24no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32#12112yes—
357C22×C32C22×D411yescharacteristic
358C2×C3×D3—24no—
359C2×C3×D3—48no—
360C2×C3×D3—42no—
361C2×C3×D3—42no—
362C2×C3×D3—41no—
363C2×C3×D3—41no—
364C2×C3×D3—41no—
365C32×C4—41no—
366C32×C4—42no—
367C32×C4#12112yes—
368C32×C4C22×D411yescharacteristic
369C32×C4C2×#4111yescharacteristic
370C3×Dic3—21no—
371C3×Dic3—21no—
372C3×Dic3—21no—
373C3×Dic3—41no—
374C3×Dic3AGL(1,ℤ/8)12yescomplemented
375C2×#41—31no—
376C2×#41C2×C3×D311yescharacteristic
377C22×D4—31no—
378C23×C4—61no—
379AGL(1,ℤ/8)—64no—
380AGL(1,ℤ/8)—64no—
381C2×SD16—32no—
382C2×SD16—32no—
383C2×D8—32no—
384C2×D8—32no—
385C2×M16—31no—
386C2×M16C2×C3×D311yescharacteristic
387C4⋊Q8—31no—
388#127—31no—
389#124—31no—
390#124—31no—
391#121—61no—
392#121—61no—
393C4×D4—32no—
394C4×D4—32no—
395C4×D4—61no—
396C4×D4—61no—
397C4×D4—61no—
398C4×D4—61no—
399C2×C4⋊C4C2×C3×D311yescharacteristic
400C2×C22⋊C4—61no—
401C2×C42—31no—
402C4⋊C8—32no—
403C4⋊C8—32no—
404#103—32no—
405#103C2×C3×D312yescomplemented
406#102—32no—
407#102C2×C3×D312yescomplemented
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—41no—
412C23×C3—64no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—122no—
416C23×C3—122no—
417C23×C3D3×D411yescharacteristic
418C23×C3C2×C3×D411yescharacteristic
419C22×D3—24no—
420C22×D3—22no—
421C22×D3—21no—
422C22×D3—42no—
423C22×D3—42no—
424C3×Q8—22no—
425C3×Q8—21no—
426C3×Q8—21no—
427C3×Q8—21no—
428C3×Q8—21no—
429C3×Q8—41no—
430C3×Q8—61no—
431C3×Q8—61no—
432C3×D4—22no—
433C3×D4—21no—
434C3×D4—21no—
435C3×D4—21no—
436C3×D4—21no—
437C3×D4—34no—
438C3×D4—41no—
439C3×D4—44no—
440C3×D4—42no—
441C3×D4—42no—
442C3×D4—64no—
443C3×D4—62no—
444C3×D4—61no—
445C3×D4—61no—
446C3×D4—122no—
447C3×D4—122no—
448C3×D4—122no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—41no—
462C2×C3×C4—42no—
463C2×C3×C4—44no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—62no—
469C2×C3×C4—61no—
470C2×C3×C4—82no—
471C2×C3×C4—124no—
472C2×C3×C4—124no—
473C2×C3×C4—121no—
474C2×C3×C4—122no—
475C2×C3×C4#23512yes—
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4D3×D412yes—
478C2×C3×C4C2×C3×D411yescharacteristic
479C2×C3×C4C2×C3×D412yes—
480C2×C3×C4C3×#4112yes—
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C24×C311yescharacteristic
483#67—42no—
484#67—42no—
485#67—42no—
486C2×Dic3—22no—
487C2×Dic3—21no—
488C2×Dic3—41no—
489C2×Dic3C2×C3×D411yescharacteristic
490C2×Dic3C2×C3×D411yescharacteristic
491C2×Dic3C2×C3×D411yescharacteristic
492C2×Dic3C2×C3×D411yescharacteristic
493D12—24no—
494D12—21no—
495D12—22no—
496D12—21no—
497D12C2×C3×D414yes—
498C4×D3—44no—
499C4×D3—42no—
500C4×D3—44no—
501Dic6—21no—
502Dic6—21no—
503C3×C8—22no—
504C3×C8—22no—
505C3×C8—42no—
506C3×C8—62no—
507C3⋊C8—22no—
508C2×C32—22no—
509C2×C32—81no—
510C2×C32C2×#12111yescharacteristic
511C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
512C2×C32#57511yescharacteristic
513C3×D3—44no—
514C3×D3—81no—
515C24—61no—
516#41—22no—
517#41—22no—
518#41—62no—
519#41—62no—
520C2×Q8—31no—
521C2×Q8C22×C3×D311yescharacteristic
522C2×D4—21no—
523C2×D4—32no—
524C2×D4—31no—
525C2×D4—34no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—62no—
530C2×D4—61no—
531C2×D4C22×C3×D311yescharacteristic
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—61no—
539C22×C4—124no—
540C22×C4C22×C3×D311yescharacteristic
541SD16—64no—
542SD16—64no—
543D8—64no—
544D8—64no—
545M16—22no—
546M16—62no—
547C2×C8—32no—
548C2×C8C22×C3×D312yes—
549C4⋊C4—21no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4C22×C3×D312yes—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—61no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C42—31no—
560C42—31no—
561C42—31no—
562C42—31no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—42no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—64no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—128no—
582C22×C3—122no—
583C22×C3—122no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3—121no—
587C22×C3#88412yes—
588C22×C3C3×#12112yes—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C22×C3×D411yescharacteristic
591C2×D3—24no—
592C2×D3—48no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C3×C4—22no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—41no—
605C3×C4—42no—
606C3×C4—41no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—82no—
611C3×C4—121no—
612C3×C4#88412yes—
613C3×C4C3×#12112yes—
614C3×C4C2×#23511yescharacteristic
615C3×C4C2×D3×D411yescharacteristic
616C3×C4C22×C3×D411yescharacteristic
617C3×C4C2×C3×#4111yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—41no—
622Dic3C3×AGL(1,ℤ/8)12yescomplemented
623C32#303611yescharacteristic, complemented, Sylow
624C23—21no—
625C23—64no—
626C23—62no—
627C23—61no—
628C23—122no—
629C23—122no—
630C23C3×D3×D411yescharacteristic
631Q8—21no—
632Q8—21no—
633Q8—61no—
634Q8—61no—
635D4—21no—
636D4—21no—
637D4—34no—
638D4—42no—
639D4—64no—
640D4—62no—
641D4—61no—
642D4—61no—
643D4—122no—
644D4—122no—
645D4—122no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—62no—
655C2×C4—61no—
656C2×C4—124no—
657C2×C4—124no—
658C2×C4—121no—
659C2×C4—122no—
660C2×C4C3×#23512yes—
661C2×C4C3×D3×D411yescharacteristic
662C2×C4C3×D3×D412yes—
663C2×C4C23×C3×D311yescharacteristic
664C8—22no—
665C8—62no—
666C2×C3—22no—
667C2×C3—22no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—42no—
672C2×C3—82no—
673C2×C3—81no—
674C2×C3—81no—
675C2×C3—124no—
676C2×C3—241no—
677C2×C3C2×#88411yescharacteristic
678C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
679C2×C3#577711yescharacteristic
680C2×C3C2×C3×#12111yescharacteristic
681C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
682C2×C3C3×#57511yescharacteristic
683D3—44no—
684D3—81no—
685C22—21no—
686C22—21no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—64no—
691C22—128no—
692C22—122no—
693C22—122no—
694C22—121no—
695C22—121no—
696C22—121no—
697C22C3×#88412yes—
698C22C2×C3×D3×D411yescharacteristic
699C4—32no—
700C4—41no—
701C4—42no—
702C4—61no—
703C4—61no—
704C4—61no—
705C4—121no—
706C4C3×#88412yes—
707C4C2×C3×#23511yescharacteristic
708C4C2×C3×D3×D411yescharacteristic
709C3—21no—
710C3#7891011yescharacteristic, direct product factor
711C3C3×#303611yescharacteristic, complemented
712C2—22no—
713C2—81no—
714C2—124no—
715C2—241no—
716C2C2×C3×#88411yescharacteristic
717C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
718C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenterC3×#417D3
hypocenterC3C3×#3036
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
1. C3×#5832C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#908C2semidirect
4. C2×C3×#893C2semidirect
5. C32×#417C2semidirect
6. C3×#5118C2semidirect
7. C3×#4966C2semidirect
8. C3×#4819C2semidirect
9. C3×#4818C2semidirect
10. C3×#4787C2semidirect
11. C3×#4786C2semidirect
13. #78910C3direct (N × H)
21. C3×#947C22semidirect
22. C3×#944C22semidirect
24. C3×#940C22semidirect
27. C3×#936C22semidirect
41. C32×#103C22semidirect
42. C32×#102C22semidirect
43. C3×Dic3⋊C8C22semidirect
44. C3×Dic3⋊C8C22semidirect
45. C3×#810C22semidirect
46. C3×#809C22semidirect
51. #5832C2×C3semidirect
52. C2×#949C2×C3semidirect
53. C2×#908C2×C3semidirect
54. C2×#893C2×C3semidirect
62. C3×#417D3semidirect
63. C3×#417C2×C3semidirect
64. #5118C2×C3semidirect
65. #4966C2×C3semidirect
66. #4819C2×C3semidirect
67. #4818C2×C3semidirect
68. #4787C2×C3semidirect
69. #4786C2×C3semidirect
88. C2×C3×D12D4semidirect
156. #947C22×C3semidirect
157. #944C22×C3semidirect
159. #940C22×C3semidirect
162. #936C22×C3semidirect
180. C3×#103C2×D3semidirect
181. C3×#103C22×C3semidirect
184. C3×#102C2×D3semidirect
185. C3×#102C22×C3semidirect
186. Dic3⋊C8C22×C3semidirect
187. Dic3⋊C8C22×C3semidirect
188. #810C22×C3semidirect
189. #809C22×C3semidirect
242. #417C3×D3semidirect
295. C2×D12C3×D4semidirect
374. C3×Dic3AGL(1,ℤ/8)semidirect
405. #103C2×C3×D3semidirect
407. #102C2×C3×D3semidirect
622. Dic3C3×AGL(1,ℤ/8)semidirect
623. C32#3036semidirect
710. C3#78910direct (N × H)
711. C3C3×#3036semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
C2×C3×#9492
C2×C3×#9082
C2×C3×#8932
C32×#4172
C3×#51182
C3×#49662
C3×#48192
C3×#48182
C3×#47872
C3×#47862
C3×#30363
#789103