Finite Group Databasebeta

← C3×#78795 #11864683

Subgroups — C3×#78795 #11864683

Order 1152.

1505 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3C2×C3×#904C211yesmaximal, characteristic, complemented
4C3×#5510C211yesmaximal, characteristic, complemented
5C2×C32×#103C211yesmaximal, characteristic, complemented
6C3×#5110C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4810C212yesmaximal, complemented
9C3×#4809C212yesmaximal, complemented
10C3×#4808C212yesmaximal, complemented
11C3×#4806C212yesmaximal, complemented
12C3×#3013—31nomaximal
13#78795C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C3×#1007—24no—
16C3×#1007—24no—
17C2×C3×#239—21no—
18C2×C3×#239C2212yes—
19C2×C3×D3×Q8—21no—
20C2×C3×D3×Q8C2212yes—
21C2×C3×#235—22no—
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C22×C32×C8C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C3×#216C2212yes—
28C3×#942—24no—
29C2×C3×#215C2212yes—
30C3×#930—22no—
31C2×C3×#208C2211yescharacteristic
32C2×C3×Dic12C2211yescharacteristic
33C3×#904—24no—
34C2×C3×D24C2211yescharacteristic
35C2×C3×#204C2211yescharacteristic
36C2×C3×#204C2211yescharacteristic
37C3×#897—21no—
38C3×#897C2212yes—
39C3×#895—21no—
40C3×#895C2212yes—
41C32×#103C2212yes—
42C32×#103C2212yes—
43C3×(C2×D3)⋊C8C2212yes—
44C3×(C2×D3)⋊C8C2212yes—
45C3×#810C2212yes—
46C3×#809C2212yes—
47C2×C3×2−1+4—31no—
48C2×#1007C2×C311yescharacteristic, complemented
49C2×C3×#137—31no—
50C2×C3×#135—31no—
51C3×#537—31no—
52C2×#942C2×C311yescharacteristic, complemented
53C2×#904C2×C311yescharacteristic, complemented
54#5510C2×C311yescharacteristic, complemented
55C3×#452—32no—
56C3×#451—32no—
57C3×#449—32no—
58C3×#448—32no—
59C3×#417—31no—
60C2×C3×#103—21no—
61C2×C3×#103D311yescharacteristic, complemented
62C2×C3×#103C2×C311yescharacteristic, complemented
63C3×#408—31no—
64#5110C2×C311yescharacteristic, complemented
65#4966C2×C311yescharacteristic, complemented
66#4810C2×C312yescomplemented
67#4809C2×C312yescomplemented
68#4808C2×C312yescomplemented
69#4806C2×C312yescomplemented
70C2×C32×Q8—21no—
71C2×C32×Q8—22no—
72C2×C32×Q8D414yescomplemented
73C2×C32×Q8C2312yes—
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—21no—
78C2×C3×#67—21no—
79C2×C3×#67D412yes—
80C3×#239—28no—
81C3×#239—24no—
82C3×#239—24no—
83C3×D3×Q8—28no—
84C3×D3×Q8—24no—
85C3×D3×Q8—24no—
86C3×#235—216no—
87C3×#235—22no—
88C3×#235—22no—
89C3×#235—22no—
90C3×#235—22no—
91C3×#235—22no—
92C3×#235D414yescomplemented
93C2×C3×D12—22no—
94C2×C3×D12—22no—
95C2×C3×D12D411yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2312yes—
103C2×C3×Dic6—22no—
104C2×C3×Dic6D411yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C32×C8—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2312yes—
112C3×#216—24no—
113C3×#215—24no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×C4⋊Dic3—22no—
117C3×#208—22no—
118C2×C3×C3⋊C8C2312yes—
119C3×Dic12—22no—
120C3×D24—22no—
121C3×#204—22no—
122C3×#204—22no—
123#3013—31noSylow
124C3×2−1+4—64no—
125C3×2−1+4—64no—
126C2×C3×#41—31no—
127C2×C3×#41—32no—
128C2×C3×#41—31no—
129C2×C3×#41—31no—
130C2×C3×#41—62no—
131C2×C3×#41—61no—
132C22×C3×Q8—21no—
133C22×C3×Q8—32no—
134C22×C3×Q8—61no—
135C22×C3×Q8C2×D311yescharacteristic
136C22×C3×Q8C22×C311yescharacteristic
137#1007—24no—
138#1007—24no—
139C2×#239—21no—
140C2×#239C22×C312yes—
141C2×D3×Q8—21no—
142C2×D3×Q8C22×C312yes—
143C2×#235—22no—
144C2×#235C22×C311yescharacteristic
145C2×#235C22×C311yescharacteristic
146C2×#235C22×C311yescharacteristic
147C3×#137—64no—
148C3×#135—64no—
149C2×C3×Q16—32no—
150C2×C3×Q16—31no—
151C2×C3×SD16—32no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C2×C3×D8—31no—
155C2×C3×M16—31no—
156C22×C3×C8—21no—
157C22×C3×C8C2×D311yescharacteristic
158C22×C3×C8C22×C311yescharacteristic
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
167C2×#216C22×C312yes—
168#942—24no—
169C2×#215C22×C312yes—
170#930—22no—
171C2×#208C22×C311yescharacteristic
172C2×Dic12C22×C311yescharacteristic
173#904—24no—
174C2×D24C22×C311yescharacteristic
175C2×#204C22×C311yescharacteristic
176C2×#204C22×C311yescharacteristic
177#897—21no—
178#897C22×C312yes—
179#895—21no—
180#895C22×C312yes—
181C3×#103—22no—
182C3×#103—22no—
183C3×#103—32no—
184C3×#103C2×D312yes—
185C3×#103C2×D312yes—
186C3×#103C22×C312yes—
187C3×#103C22×C312yes—
188C3×#102—32no—
189C3×C22⋊C8—32no—
190C3×C22⋊C8—32no—
191(C2×D3)⋊C8C22×C312yes—
192(C2×D3)⋊C8C22×C312yes—
193#810C22×C312yes—
194#809C22×C312yes—
195C23×C32C2×D411yescharacteristic
196C22×C3×D3—21no—
197C22×C3×D3—21no—
198C22×C3×D3C2×D412yes—
199C32×Q8—24no—
200C32×Q8—22no—
201C32×Q8C2×D414yes—
202C2×C32×C4—24no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—81no—
206C2×C32×C4C2×D412yes—
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2×D412yes—
209C2×C32×C4C2411yescharacteristic
210C3×#67—24no—
211C3×#67—24no—
212C3×#67—42no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3C2×D412yes—
216C3×D12—28no—
217C3×D12—22no—
218C3×D12—21no—
219C3×D12—21no—
220C3×D12—21no—
221C3×D12—82no—
222C3×D12C2×D412yes—
223C3×C4×D3—28no—
224C3×C4×D3—28no—
225C3×C4×D3—24no—
226C3×C4×D3—22no—
227C3×C4×D3—22no—
228C3×C4×D3—42no—
229C3×Dic6—28no—
230C3×Dic6—22no—
231C3×Dic6—21no—
232C3×Dic6—21no—
233C3×Dic6—21no—
234C3×Dic6C2×D412yes—
235C32×C8—21no—
236C32×C8—21no—
237C3×C3⋊C8—22no—
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#417—31no—
247C2×#103C3×D311yescharacteristic, complemented
248#408—31no—
249C3×#41—34no—
250C3×#41—616no—
251C3×#41—64no—
252C3×#41—68no—
253C3×#41—64no—
254C3×#41—62no—
255C3×#41—62no—
256C3×#41—62no—
257C3×#41—62no—
258C3×#41—62no—
259C2×C3×Q8—21no—
260C2×C3×Q8—22no—
261C2×C3×Q8—21no—
262C2×C3×Q8—22no—
263C2×C3×Q8—24no—
264C2×C3×Q8—22no—
265C2×C3×Q8—31no—
266C2×C3×Q8—31no—
267C2×C3×Q8—31no—
268C2×C3×Q8—41no—
269C2×C3×Q8—42no—
270C2×C3×Q8—62no—
271C2×C3×Q8—64no—
272C2×C3×Q8—68no—
273C2×C3×Q8—64no—
274C2×C3×Q8D1214yescomplemented
275C2×C3×Q8C3×D414yescomplemented
276C2×C3×Q8C22×D312yes—
277C2×C3×Q8C23×C312yes—
278C2×C3×D4—32no—
279C2×C3×D4—31no—
280C2×C3×D4—31no—
281C2×C3×D4—31no—
282C2×C3×D4—62no—
283C2×C3×D4—62no—
284C2×C3×D4—61no—
285C2×C3×D4—61no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—32no—
292C22×C3×C4—41no—
293C22×C3×C4—41no—
294C22×C3×C4—62no—
295C22×C3×C4—62no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C2×#67—21no—
301C2×#67—21no—
302C2×#67C3×D412yes—
303#239—28no—
304#239—24no—
305#239—24no—
306D3×Q8—28no—
307D3×Q8—24no—
308D3×Q8—24no—
309#235—216no—
310#235—22no—
311#235—22no—
312#235—22no—
313#235—22no—
314#235—22no—
315#235C3×D414yescomplemented
316C2×D12—22no—
317C2×D12—22no—
318C2×D12C3×D411yescharacteristic
319C2×D12C23×C311yescharacteristic
320C2×D12C23×C311yescharacteristic
321C2×C4×D3—22no—
322C2×C4×D3—21no—
323C2×C4×D3—22no—
324C2×C4×D3—21no—
325C2×C4×D3C23×C312yes—
326C2×Dic6—22no—
327C2×Dic6C3×D411yescharacteristic
328C2×Dic6C23×C311yescharacteristic
329C2×Dic6C23×C311yescharacteristic
330C3×Q16—62no—
331C3×Q16—64no—
332C3×SD16—62no—
333C3×SD16—62no—
334C3×SD16—64no—
335C3×D8—62no—
336C3×M16—62no—
337C2×C3×C8—22no—
338C2×C3×C8—22no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—32no—
342C2×C3×C8—42no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—22no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—62no—
352C3×C4⋊C4C22×D312yes—
353C3×C4⋊C4C23×C312yes—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356#216—24no—
357#215—24no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4—22no—
360C4⋊Dic3—22no—
361#208—22no—
362C2×C3⋊C8C23×C312yes—
363Dic12—22no—
364D24—22no—
365#204—22no—
366#204—22no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32#12012yes—
370C22×C32C22×D411yescharacteristic
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—41no—
376C2×C3×D3—41no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C2×C3×D3—41no—
380C32×C4—24no—
381C32×C4—42no—
382C32×C4#12012yes—
383C32×C4C22×D411yescharacteristic
384C32×C4C22×D411yescharacteristic
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—41no—
3882−1+4—64no—
3892−1+4—64no—
390C2×#41—31no—
391C2×#41—32no—
392C2×#41—31no—
393C2×#41—31no—
394C2×#41—62no—
395C2×#41—61no—
396C22×Q8—32no—
397C22×Q8—61no—
398C22×Q8C2×C3×D311yescharacteristic
399#137—64no—
400#135—64no—
401C2×Q16—32no—
402C2×Q16—31no—
403C2×SD16—32no—
404C2×SD16—31no—
405C2×SD16—31no—
406C2×D8—31no—
407C2×M16—31no—
408C22×C8C2×C3×D311yescharacteristic
409C22⋊Q8—32no—
410C22⋊Q8—61no—
411#121—32no—
412#121—61no—
413#121—62no—
414C2×C4⋊C4C2×C3×D311yescharacteristic
415#103—32no—
416#103C2×C3×D312yes—
417#103C2×C3×D312yes—
418#102—32no—
419C22⋊C8—32no—
420C22⋊C8—32no—
421C23×C3—21no—
422C23×C3—32no—
423C23×C3—61no—
424C23×C3—61no—
425C23×C3D3×D411yescharacteristic
426C23×C3C2×C3×D411yescharacteristic
427C22×D3—21no—
428C22×D3—21no—
429C22×D3C2×C3×D412yes—
430C3×Q8—24no—
431C3×Q8—24no—
432C3×Q8—22no—
433C3×Q8—22no—
434C3×Q8—24no—
435C3×Q8—32no—
436C3×Q8—44no—
437C3×Q8—42no—
438C3×Q8—68no—
439C3×Q8—62no—
440C3×Q8—61no—
441C3×Q8—61no—
442C3×Q8—61no—
443C3×Q8C2×D1214yes—
444C3×Q8C2×C3×D414yes—
445C3×D4—32no—
446C3×D4—68no—
447C3×D4—64no—
448C3×D4—64no—
449C3×D4—62no—
450C3×D4—61no—
451C3×D4—61no—
452C3×D4—61no—
453C3×D4—122no—
454C3×D4—242no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—32no—
466C2×C3×C4—44no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—68no—
470C2×C3×C4—68no—
471C2×C3×C4—61no—
472C2×C3×C4—64no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—61no—
476C2×C3×C4—81no—
477C2×C3×C4—81no—
478C2×C3×C4—82no—
479C2×C3×C4—122no—
480C2×C3×C4C2×D1212yes—
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4D3×D412yes—
483C2×C3×C4C2×C3×D412yes—
484C2×C3×C4C2×C3×D411yescharacteristic
485C2×C3×C4C2×C3×D412yes—
486C2×C3×C4C23×D311yescharacteristic
487C2×C3×C4C24×C311yescharacteristic
488#67—24no—
489#67—24no—
490#67—42no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3C2×C3×D412yes—
494D12—28no—
495D12—22no—
496D12—21no—
497D12—21no—
498D12—21no—
499D12—82no—
500D12C2×C3×D412yes—
501C4×D3—28no—
502C4×D3—28no—
503C4×D3—24no—
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—42no—
507Dic6—28no—
508Dic6—22no—
509Dic6—21no—
510Dic6—21no—
511Dic6—21no—
512Dic6C2×C3×D412yes—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—41no—
519C3×C8—62no—
520C3⋊C8—22no—
521C2×C32—22no—
522C2×C32C2×#12011yescharacteristic
523C2×C32#57711yescharacteristic
524C2×C32#57811yescharacteristic
525C3×D3—42no—
526C3×D3—42no—
527C3×D3—81no—
528#41—34no—
529#41—616no—
530#41—64no—
531#41—68no—
532#41—64no—
533#41—62no—
534#41—62no—
535#41—62no—
536#41—62no—
537#41—62no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—31no—
541C2×Q8—31no—
542C2×Q8—31no—
543C2×Q8—62no—
544C2×Q8—64no—
545C2×Q8—68no—
546C2×Q8—64no—
547C2×Q8C3×D1214yescomplemented
548C2×Q8C22×C3×D312yes—
549C2×D4—32no—
550C2×D4—31no—
551C2×D4—31no—
552C2×D4—31no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—61no—
556C2×D4—61no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—32no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4C22×C3×D311yescharacteristic
565Q16—62no—
566Q16—64no—
567SD16—62no—
568SD16—62no—
569SD16—64no—
570D8—62no—
571M16—62no—
572C2×C8—22no—
573C2×C8—32no—
574C2×C8C22×C3×D311yescharacteristic
575C2×C8C22×C3×D311yescharacteristic
576C4⋊C4—21no—
577C4⋊C4—62no—
578C4⋊C4C22×C3×D312yes—
579C22⋊C4—62no—
580C22⋊C4—62no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—121no—
594C22×C3—121no—
595C22×C3—121no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3#88212yes—
599C22×C3C3×#12012yes—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C22×C3×D411yescharacteristic
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C3×C4—24no—
612C3×C4—24no—
613C3×C4—22no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—44no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—82no—
622C3×C4—121no—
623C3×C4#88212yes—
624C3×C4C3×#12012yes—
625C3×C4C22×D1211yescharacteristic
626C3×C4C2×D3×D411yescharacteristic
627C3×C4C22×C3×D411yescharacteristic
628C3×C4C22×C3×D411yescharacteristic
629Dic3—22no—
630Dic3—22no—
631Dic3—41no—
632C32#301311yescharacteristic, complemented, Sylow
633C23—32no—
634C23—61no—
635C23—61no—
636C23C3×D3×D411yescharacteristic
637Q8—24no—
638Q8—22no—
639Q8—32no—
640Q8—68no—
641Q8—62no—
642Q8—61no—
643Q8—61no—
644Q8—61no—
645Q8C2×C3×D1214yes—
646D4—32no—
647D4—68no—
648D4—64no—
649D4—64no—
650D4—62no—
651D4—61no—
652D4—61no—
653D4—61no—
654D4—122no—
655D4—242no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—32no—
660C2×C4—68no—
661C2×C4—68no—
662C2×C4—61no—
663C2×C4—64no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—61no—
667C2×C4—81no—
668C2×C4—122no—
669C2×C4C2×C3×D1212yes—
670C2×C4C3×D3×D411yescharacteristic
671C2×C4C3×D3×D412yes—
672C2×C4C23×C3×D311yescharacteristic
673C8—21no—
674C8—21no—
675C8—62no—
676C2×C3—24no—
677C2×C3—22no—
678C2×C3—22no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—122no—
683C2×C3—122no—
684C2×C3—241no—
685C2×C3C2×#88211yescharacteristic
686C2×C3#576211yescharacteristic
687C2×C3#576611yescharacteristic
688C2×C3C2×C3×#12011yescharacteristic
689C2×C3C3×#57711yescharacteristic
690C2×C3C3×#57811yescharacteristic
691D3—42no—
692D3—42no—
693D3—81no—
694C22—21no—
695C22—21no—
696C22—62no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—121no—
701C22—121no—
702C22—121no—
703C22—121no—
704C22—121no—
705C22C3×#88212yes—
706C22C2×C3×D3×D411yescharacteristic
707C4—24no—
708C4—42no—
709C4—62no—
710C4—62no—
711C4—121no—
712C4C3×#88212yes—
713C4C22×C3×D1211yescharacteristic
714C4C2×C3×D3×D411yescharacteristic
715C3—21no—
716C3#7879511yescharacteristic, direct product factor
717C3C3×#301311yescharacteristic, complemented
718C2—22no—
719C2—122no—
720C2—122no—
721C2—241no—
722C2C2×C3×#88211yescharacteristic
723C2C3×#576211yescharacteristic
724C2C3×#576611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC22×C32C22×D4
hypercenterC2×C3×#103D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×C3×#942C2semidirect
3. C2×C3×#904C2semidirect
4. C3×#5510C2semidirect
5. C2×C32×#103C2semidirect
6. C3×#5110C2semidirect
7. C3×#4966C2semidirect
8. C3×#4810C2semidirect
9. C3×#4809C2semidirect
10. C3×#4808C2semidirect
11. C3×#4806C2semidirect
13. #78795C3direct (N × H)
48. C2×#1007C2×C3semidirect
52. C2×#942C2×C3semidirect
53. C2×#904C2×C3semidirect
54. #5510C2×C3semidirect
61. C2×C3×#103D3semidirect
62. C2×C3×#103C2×C3semidirect
64. #5110C2×C3semidirect
65. #4966C2×C3semidirect
66. #4810C2×C3semidirect
67. #4809C2×C3semidirect
68. #4808C2×C3semidirect
69. #4806C2×C3semidirect
72. C2×C32×Q8D4semidirect
92. C3×#235D4semidirect
247. C2×#103C3×D3semidirect
274. C2×C3×Q8D12semidirect
275. C2×C3×Q8C3×D4semidirect
315. #235C3×D4semidirect
547. C2×Q8C3×D12semidirect
632. C32#3013semidirect
716. C3#78795direct (N × H)
717. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×C3×#9422
C2×C3×#9042
C3×#55102
C2×C32×#1032
C3×#51102
C3×#49662
C3×#48102
C3×#48092
C3×#48082
C3×#48062
C3×#30133
#787953