Finite Group Databasebeta

← C3×#78887 #11864674

Subgroups — C3×#78887 #11864674

Order 1152.

1505 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5510C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6C3×#5129C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4809C212yesmaximal, complemented
9C3×#4806C212yesmaximal, complemented
10C3×#4783C212yesmaximal, complemented
11C3×#4781C212yesmaximal, complemented
12C3×#3013—31nomaximal
13#78887C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×#1010—24no—
16C3×#1010—24no—
17C2×C3×D3×Q8C2212yes—
18C2×C3×#237—22no—
19C2×C3×#237C2212yes—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6—21no—
24C22×C3×Dic6C2211yescharacteristic
25C2×C32×M16C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C3×#950—24no—
28C2×C3×#216C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#930—22no—
33C22×C3×C3⋊C8C2211yescharacteristic
34C3×#909—24no—
35C2×C3×Dic12C2212yes—
36C2×C3×#204C2212yes—
37C3×#897—21no—
38C3×#897C2212yes—
39C3×#895—21no—
40C3×#895C2212yes—
41C32×#103C2212yes—
42C32×#102C2212yes—
43C3×(C2×D3)⋊C8C2212yes—
44C3×(C2×D3)⋊C8C2212yes—
45C3×#810C2212yes—
46C3×#810C2212yes—
47C2×C3×2−1+4—31no—
48C2×#1010C2×C311yescharacteristic, complemented
49C2×C3×#137—31no—
50C2×C3×#135—31no—
51C3×#537—31no—
52C2×#950C2×C311yescharacteristic, complemented
53C2×#909C2×C311yescharacteristic, complemented
54#5510C2×C311yescharacteristic, complemented
55C3×#452—32no—
56C3×#451—32no—
57C3×#449—32no—
58C3×#448—32no—
59C3×#417—21no—
60C3×#417D311yescharacteristic, complemented
61C3×#417C2×C311yescharacteristic, complemented
62C2×C3×#103—31no—
63C3×#408—31no—
64#5129C2×C311yescharacteristic, complemented
65C2×#810C2×C311yescharacteristic, complemented
66#4809C2×C312yescomplemented
67#4806C2×C312yescomplemented
68#4783C2×C312yescomplemented
69#4781C2×C312yescomplemented
70C32×#41—22no—
71C32×#41D414yescomplemented
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4—21no—
74C2×C32×D4C2311yescharacteristic
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×C3×#67—22no—
79C2×C3×#67—21no—
80C2×C3×#67D412yes—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—22no—
83C3×D3×Q8—24no—
84C3×D3×Q8—24no—
85C3×#237—216no—
86C3×#237—24no—
87C3×#237—24no—
88C3×#235—28no—
89C3×#235—22no—
90C3×#235—22no—
91C3×#235—22no—
92C3×#235—22no—
93C2×C3×D12—22no—
94C2×C3×D12D411yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2312yes—
99C2×C3×Dic6—28no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—22no—
102C2×C3×Dic6—22no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6D414yescomplemented
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2312yes—
107C32×M16—22no—
108C2×C32×C8C2312yes—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2312yes—
111C3×#216—22no—
112C3×#215—22no—
113C3×#214—22no—
114C3×#213—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×C4⋊Dic3—22no—
118C2×C3×C3⋊C8—22no—
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C3×Dic12—24no—
122C3×#204—24no—
123#3013—31noSylow
124C3×2−1+4—64no—
125C3×2−1+4—64no—
126C2×C3×#41—21no—
127C2×C3×#41—31no—
128C2×C3×#41—32no—
129C2×C3×#41—31no—
130C2×C3×#41—61no—
131C2×C3×#41—62no—
132C2×C3×#41C2×D311yescharacteristic
133C2×C3×#41C22×C311yescharacteristic
134C22×C3×Q8—32no—
135C22×C3×Q8—31no—
136C22×C3×Q8—61no—
137#1010—24no—
138#1010—24no—
139C2×D3×Q8C22×C312yes—
140C2×#237—22no—
141C2×#237C22×C312yes—
142C2×#235—21no—
143C2×#235C22×C311yescharacteristic
144C2×#235C22×C311yescharacteristic
145C22×Dic6—21no—
146C22×Dic6C22×C311yescharacteristic
147C3×#137—64no—
148C3×#135—64no—
149C2×C3×Q16—31no—
150C2×C3×Q16—32no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—32no—
154C2×C3×D8—31no—
155C2×C3×M16—21no—
156C2×C3×M16C2×D311yescharacteristic
157C2×C3×M16C22×C311yescharacteristic
158C22×C3×C8—31no—
159C3×C22⋊Q8—32no—
160C3×C22⋊Q8—61no—
161C3×#121—32no—
162C3×#121—61no—
163C3×#121—62no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4C2×D311yescharacteristic
166C2×C3×C4⋊C4C22×C311yescharacteristic
167#950—24no—
168C2×#216C22×C311yescharacteristic
169C2×#215C22×C311yescharacteristic
170C2×#214C22×C311yescharacteristic
171C2×#213C22×C311yescharacteristic
172#930—22no—
173C22×C3⋊C8C22×C311yescharacteristic
174#909—24no—
175C2×Dic12C22×C312yes—
176C2×#204C22×C312yes—
177#897—21no—
178#897C22×C312yes—
179#895—21no—
180#895C22×C312yes—
181C3×#103—22no—
182C3×#103—32no—
183C3×#103—32no—
184C3×#103C2×D312yes—
185C3×#103C22×C312yes—
186C3×#102—22no—
187C3×#102C2×D312yes—
188C3×#102C22×C312yes—
189C3×C22⋊C8—32no—
190C3×C22⋊C8—32no—
191(C2×D3)⋊C8C22×C312yes—
192(C2×D3)⋊C8C22×C312yes—
193#810C22×C312yes—
194#810C22×C312yes—
195C23×C32—21no—
196C23×C32C2×D411yescharacteristic
197C22×C3×D3—21no—
198C22×C3×D3C2×D412yes—
199C32×Q8—21no—
200C32×Q8C2×D412yes—
201C32×D4—24no—
202C32×D4—21no—
203C32×D4C2×D412yes—
204C2×C32×C4—21no—
205C2×C32×C4—24no—
206C2×C32×C4—22no—
207C2×C32×C4—81no—
208C2×C32×C4C2×D412yes—
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2×D412yes—
211C2×C32×C4C2411yescharacteristic
212C3×#67—28no—
213C3×#67—24no—
214C3×#67—42no—
215C2×C3×Dic3—28no—
216C2×C3×Dic3—24no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3C2×D412yes—
220C3×D12—22no—
221C3×D12—21no—
222C3×D12—21no—
223C3×D12—82no—
224C3×C4×D3—28no—
225C3×C4×D3—22no—
226C3×C4×D3—22no—
227C3×C4×D3—42no—
228C3×Dic6—28no—
229C3×Dic6—22no—
230C3×Dic6—24no—
231C3×Dic6—22no—
232C3×Dic6—21no—
233C3×Dic6—21no—
234C3×Dic6C2×D414yes—
235C32×C8—22no—
236C3×C3⋊C8—21no—
237C3×C3⋊C8—21no—
238C2×2−1+4—31no—
239C2×#137—31no—
240C2×#135—31no—
241#537—31no—
242#452—32no—
243#451—32no—
244#449—32no—
245#448—32no—
246#417C3×D311yescharacteristic, complemented
247C2×#103—31no—
248#408—31no—
249C3×#41—22no—
250C3×#41—22no—
251C3×#41—24no—
252C3×#41—42no—
253C3×#41—68no—
254C3×#41—64no—
255C3×#41—616no—
256C3×#41—64no—
257C3×#41—62no—
258C3×#41—62no—
259C3×#41—62no—
260C3×#41—62no—
261C3×#41D1214yescomplemented
262C3×#41C3×D414yescomplemented
263C2×C3×Q8—21no—
264C2×C3×Q8—31no—
265C2×C3×Q8—34no—
266C2×C3×Q8—32no—
267C2×C3×Q8—31no—
268C2×C3×Q8—62no—
269C2×C3×Q8—68no—
270C2×C3×Q8—64no—
271C2×C3×Q8—64no—
272C2×C3×Q8—62no—
273C2×C3×Q8—61no—
274C2×C3×Q8C22×D311yescharacteristic
275C2×C3×Q8C23×C311yescharacteristic
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—32no—
280C2×C3×D4—31no—
281C2×C3×D4—31no—
282C2×C3×D4—41no—
283C2×C3×D4—62no—
284C2×C3×D4—62no—
285C2×C3×D4—61no—
286C2×C3×D4C22×D311yescharacteristic
287C2×C3×D4C23×C311yescharacteristic
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—32no—
294C22×C3×C4—41no—
295C22×C3×C4—41no—
296C22×C3×C4—62no—
297C22×C3×C4—62no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C2×#67—22no—
303C2×#67—21no—
304C2×#67C3×D412yes—
305C22×Dic3—21no—
306C22×Dic3—22no—
307D3×Q8—24no—
308D3×Q8—24no—
309#237—216no—
310#237—24no—
311#237—24no—
312#235—28no—
313#235—22no—
314#235—22no—
315#235—22no—
316#235—22no—
317C2×D12—22no—
318C2×D12C3×D411yescharacteristic
319C2×D12C23×C311yescharacteristic
320C2×C4×D3—22no—
321C2×C4×D3—21no—
322C2×C4×D3C23×C312yes—
323C2×Dic6—28no—
324C2×Dic6—21no—
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6C3×D411yescharacteristic
328C2×Dic6C3×D414yescomplemented
329C2×Dic6C23×C311yescharacteristic
330C2×Dic6C23×C312yes—
331C3×Q16—64no—
332C3×Q16—62no—
333C3×SD16—64no—
334C3×SD16—62no—
335C3×SD16—62no—
336C3×D8—62no—
337C3×M16—22no—
338C3×M16—22no—
339C3×M16—42no—
340C2×C3×C8—22no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—62no—
344C2×C3×C8C22×D312yes—
345C2×C3×C8C23×C312yes—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—22no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—62no—
351C3×C4⋊C4C22×D312yes—
352C3×C4⋊C4C23×C312yes—
353C3×C22⋊C4—62no—
354C3×C22⋊C4—62no—
355#216—22no—
356#215—22no—
357#214—22no—
358#213—22no—
359(C2×D3)⋊C4—22no—
360(C2×D3)⋊C4—22no—
361C4⋊Dic3—22no—
362C2×C3⋊C8—22no—
363C2×C3⋊C8C23×C311yescharacteristic
364C2×C3⋊C8C23×C311yescharacteristic
365Dic12—24no—
366#204—24no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—22no—
370C22×C32—41no—
371C22×C32—41no—
372C22×C32#12012yes—
373C22×C32C22×D411yescharacteristic
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—22no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C2×C3×D3—41no—
380C32×C4—22no—
381C32×C4—42no—
382C32×C4#12012yes—
383C32×C4C22×D411yescharacteristic
384C32×C4C22×D411yescharacteristic
385C3×Dic3—22no—
386C3×Dic3—24no—
387C3×Dic3—41no—
3882−1+4—64no—
3892−1+4—64no—
390C2×#41—31no—
391C2×#41—32no—
392C2×#41—31no—
393C2×#41—61no—
394C2×#41—62no—
395C2×#41C2×C3×D311yescharacteristic
396C22×Q8—32no—
397C22×Q8—31no—
398C22×Q8—61no—
399#137—64no—
400#135—64no—
401C2×Q16—31no—
402C2×Q16—32no—
403C2×SD16—31no—
404C2×SD16—31no—
405C2×SD16—32no—
406C2×D8—31no—
407C2×M16C2×C3×D311yescharacteristic
408C22×C8—31no—
409C22⋊Q8—32no—
410C22⋊Q8—61no—
411#121—32no—
412#121—61no—
413#121—62no—
414C2×C4⋊C4C2×C3×D311yescharacteristic
415#103—32no—
416#103—32no—
417#103C2×C3×D312yes—
418#102C2×C3×D312yes—
419C22⋊C8—32no—
420C22⋊C8—32no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—32no—
425C23×C3—41no—
426C23×C3—61no—
427C23×C3D3×D411yescharacteristic
428C23×C3C2×C3×D411yescharacteristic
429C22×D3—21no—
430C22×D3C2×C3×D412yes—
431C3×Q8—21no—
432C3×Q8—21no—
433C3×Q8—22no—
434C3×Q8—34no—
435C3×Q8—41no—
436C3×Q8—68no—
437C3×Q8—62no—
438C3×Q8—64no—
439C3×Q8—62no—
440C3×Q8—61no—
441C3×Q8—61no—
442C3×Q8C2×D1212yes—
443C3×Q8C2×C3×D412yes—
444C3×D4—24no—
445C3×D4—24no—
446C3×D4—21no—
447C3×D4—21no—
448C3×D4—22no—
449C3×D4—41no—
450C3×D4—44no—
451C3×D4—68no—
452C3×D4—64no—
453C3×D4—62no—
454C3×D4—61no—
455C3×D4—61no—
456C3×D4—122no—
457C3×D4—242no—
458C3×D4C2×D1212yes—
459C3×D4C2×C3×D412yes—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—32no—
471C2×C3×C4—44no—
472C2×C3×C4—41no—
473C2×C3×C4—42no—
474C2×C3×C4—68no—
475C2×C3×C4—68no—
476C2×C3×C4—64no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—61no—
481C2×C3×C4—81no—
482C2×C3×C4—81no—
483C2×C3×C4—82no—
484C2×C3×C4—122no—
485C2×C3×C4C2×D1212yes—
486C2×C3×C4D3×D411yescharacteristic
487C2×C3×C4D3×D412yes—
488C2×C3×C4C2×C3×D412yes—
489C2×C3×C4C2×C3×D411yescharacteristic
490C2×C3×C4C2×C3×D412yes—
491C2×C3×C4C23×D311yescharacteristic
492C2×C3×C4C24×C311yescharacteristic
493#67—28no—
494#67—24no—
495#67—42no—
496C2×Dic3—28no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3C2×C3×D412yes—
501D12—22no—
502D12—21no—
503D12—21no—
504D12—82no—
505C4×D3—28no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—42no—
509Dic6—28no—
510Dic6—22no—
511Dic6—24no—
512Dic6—22no—
513Dic6—21no—
514Dic6—21no—
515Dic6C2×C3×D414yes—
516C3×C8—22no—
517C3×C8—22no—
518C3×C8—42no—
519C3×C8—61no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C2×C32—22no—
524C2×C32—42no—
525C2×C32C2×#12011yescharacteristic
526C2×C32#57711yescharacteristic
527C2×C32#57811yescharacteristic
528C3×D3—42no—
529C3×D3—81no—
530#41—22no—
531#41—68no—
532#41—64no—
533#41—616no—
534#41—64no—
535#41—62no—
536#41—62no—
537#41—62no—
538#41—62no—
539#41C3×D1214yescomplemented
540C2×Q8—31no—
541C2×Q8—32no—
542C2×Q8—31no—
543C2×Q8—34no—
544C2×Q8—62no—
545C2×Q8—68no—
546C2×Q8—64no—
547C2×Q8—64no—
548C2×Q8—62no—
549C2×Q8—61no—
550C2×Q8C22×C3×D311yescharacteristic
551C2×D4—21no—
552C2×D4—32no—
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—61no—
558C2×D4C22×C3×D311yescharacteristic
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—32no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4C22×C3×D311yescharacteristic
567Q16—64no—
568Q16—62no—
569SD16—64no—
570SD16—62no—
571SD16—62no—
572D8—62no—
573M16—22no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—62no—
577C2×C8C22×C3×D312yes—
578C4⋊C4—21no—
579C4⋊C4—62no—
580C4⋊C4C22×C3×D312yes—
581C22⋊C4—62no—
582C22⋊C4—62no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—21no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—42no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—62no—
599C22×C3—62no—
600C22×C3—62no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3—121no—
606C22×C3#88212yes—
607C22×C3C3×#12012yes—
608C22×C3C2×D3×D411yescharacteristic
609C22×C3C22×C3×D411yescharacteristic
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—62no—
625C3×C4—64no—
626C3×C4—82no—
627C3×C4—121no—
628C3×C4#88212yes—
629C3×C4C3×#12012yes—
630C3×C4C22×D1211yescharacteristic
631C3×C4C2×D3×D411yescharacteristic
632C3×C4C22×C3×D411yescharacteristic
633C3×C4C22×C3×D411yescharacteristic
634Dic3—22no—
635Dic3—24no—
636Dic3—41no—
637C32#301311yescharacteristic, complemented, Sylow
638C23—21no—
639C23—32no—
640C23—61no—
641C23C3×D3×D411yescharacteristic
642Q8—21no—
643Q8—34no—
644Q8—68no—
645Q8—62no—
646Q8—64no—
647Q8—62no—
648Q8—61no—
649Q8—61no—
650Q8C2×C3×D1212yes—
651D4—24no—
652D4—21no—
653D4—68no—
654D4—64no—
655D4—62no—
656D4—61no—
657D4—61no—
658D4—122no—
659D4—242no—
660D4C2×C3×D1212yes—
661C2×C4—21no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—68no—
666C2×C4—68no—
667C2×C4—64no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—81no—
673C2×C4—122no—
674C2×C4C2×C3×D1212yes—
675C2×C4C3×D3×D411yescharacteristic
676C2×C4C3×D3×D412yes—
677C2×C4C23×C3×D311yescharacteristic
678C8—22no—
679C8—61no—
680C8—61no—
681C2×C3—22no—
682C2×C3—22no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3—42no—
689C2×C3—82no—
690C2×C3—122no—
691C2×C3—241no—
692C2×C3C2×#88211yescharacteristic
693C2×C3#577511yescharacteristic
694C2×C3#577911yescharacteristic
695C2×C3C2×C3×#12011yescharacteristic
696C2×C3C3×#57711yescharacteristic
697C2×C3C3×#57811yescharacteristic
698D3—42no—
699D3—81no—
700C22—21no—
701C22—21no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—62no—
706C22—62no—
707C22—62no—
708C22—121no—
709C22—121no—
710C22—121no—
711C22C3×#88212yes—
712C22C2×C3×D3×D411yescharacteristic
713C4—22no—
714C4—42no—
715C4—62no—
716C4—64no—
717C4—121no—
718C4C3×#88212yes—
719C4C22×C3×D1211yescharacteristic
720C4C2×C3×D3×D411yescharacteristic
721C3—21no—
722C3#7888711yescharacteristic, direct product factor
723C3C3×#301311yescharacteristic, complemented
724C2—22no—
725C2—42no—
726C2—122no—
727C2—241no—
728C2C2×C3×#88211yescharacteristic
729C2C3×#577511yescharacteristic
730C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenterC3×#417D3
hypocenterC3C3×#3013
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. C2×C3×#1010C2semidirect
2. C2×C3×#950C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5510C2semidirect
5. C32×#417C2semidirect
6. C3×#5129C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4809C2semidirect
9. C3×#4806C2semidirect
10. C3×#4783C2semidirect
11. C3×#4781C2semidirect
13. #78887C3direct (N × H)
48. C2×#1010C2×C3semidirect
52. C2×#950C2×C3semidirect
53. C2×#909C2×C3semidirect
54. #5510C2×C3semidirect
60. C3×#417D3semidirect
61. C3×#417C2×C3semidirect
64. #5129C2×C3semidirect
65. C2×#810C2×C3semidirect
66. #4809C2×C3semidirect
67. #4806C2×C3semidirect
68. #4783C2×C3semidirect
69. #4781C2×C3semidirect
71. C32×#41D4semidirect
104. C2×C3×Dic6D4semidirect
246. #417C3×D3semidirect
261. C3×#41D12semidirect
262. C3×#41C3×D4semidirect
328. C2×Dic6C3×D4semidirect
539. #41C3×D12semidirect
637. C32#3013semidirect
722. C3#78887direct (N × H)
723. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×#9502
C2×C3×#9092
C3×#55102
C32×#4172
C3×#51292
C2×C3×#8102
C3×#48092
C3×#48062
C3×#47832
C3×#47812
C3×#30133
#788873