Finite Group Databasebeta

← C3×#78835 #11864343

Subgroups — C3×#78835 #11864343

Order 1152.

1583 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C22×C3×#204C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C32×#416C211yesmaximal, characteristic, complemented
6C3×#5110C211yesmaximal, characteristic, complemented
7C3×#5001C211yesmaximal, characteristic, complemented
8C3×#4808C214yesmaximal, complemented
9C3×#4776C214yesmaximal, complemented
10C3×#3009—31nomaximal
11#78835C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C3×#1009—24no—
14C3×#1009—24no—
15C2×C3×#239C2212yes—
16C2×C3×D3×D4—22no—
17C2×C3×D3×D4C2212yes—
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12—21no—
21C22×C3×D12C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic, complemented
24C32×#117C2211yescharacteristic, complemented
25C3×#951—24no—
26C2×C3×#216C2212yescomplemented
27C2×C3×#214C2212yescomplemented
28C2×C3×#208C2211yescharacteristic, complemented
29C2×C3×#204—24no—
30C2×C3×#204C2214yescomplemented
31C3×#897C2214yescomplemented
32C3×#886—22no—
33C3×#875—21no—
34C3×#869—21no—
35C32×#103C2212yescomplemented
36C32×#102C2212yescomplemented
37C3×(C2×D3)⋊C8C2214yescomplemented
38C3×#809C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1009C2×C311yescharacteristic
41C2×C3×#137—31no—
42C22×C3×SD16—31no—
43C3×#536—31no—
44C2×#951C2×C311yescharacteristic, complemented
45C22×#204C2×C311yescharacteristic, complemented
46#5526C2×C311yescharacteristic, complemented
47C3×#452—34no—
48C3×#450—34no—
49C3×#418—31no—
50C3×#416—21no—
51C3×#416D311yescharacteristic, complemented
52C3×#416C2×C311yescharacteristic, complemented
53C3×#408—31no—
54#5110C2×C311yescharacteristic, complemented
55#5001C2×C311yescharacteristic, complemented
56#4808C2×C314yescomplemented
57#4776C2×C314yescomplemented
58C23×C3×D3—21no—
59C23×C3×D3—22no—
60C32×#41—22no—
61C32×#41D414yes—
62C2×C32×Q8C2311yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2311yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67—22no—
68C2×C3×#67D412yes—
69C22×C3×Dic3—21no—
70C3×#239—24no—
71C3×#239—24no—
72C3×D3×D4—216no—
73C3×D3×D4—24no—
74C3×D3×D4—24no—
75C3×#235—28no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—28no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12—22no—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12D414yes—
84C2×C3×D12C2312yes—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3C2312yes—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6—21no—
90C2×C3×Dic6D411yescharacteristic
91C2×C3×Dic6C2312yes—
92C2×C32×C8—22no—
93C2×C32×C8C2312yes—
94C32×C4⋊C4C2312yes—
95C32×C22⋊C4—21no—
96C32×C42—21no—
97C3×#216—24no—
98C3×#214—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×C4⋊Dic3—24no—
101C3×#208—22no—
102C2×C3×C3⋊C8C2312yes—
103C3×#204—28no—
104#3009—31noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41C2×D311yescharacteristic
112C2×C3×#41C22×C311yescharacteristic
113C22×C3×Q8—31no—
114C22×C3×D4—32no—
115C22×C3×D4—31no—
116C22×C3×D4—61no—
117C22×C3×D4—62no—
118#1009—24no—
119#1009—24no—
120C2×#239C22×C312yes—
121C2×D3×D4—22no—
122C2×D3×D4C22×C312yes—
123C2×#235—21no—
124C2×#235C22×C311yescharacteristic
125C22×D12—21no—
126C22×D12C22×C311yescharacteristic
127C22×Dic6C22×C311yescharacteristic, complemented
128C3×#137—64no—
129C2×C3×Q16—32no—
130C2×C3×SD16—32no—
131C2×C3×SD16—34no—
132C2×C3×SD16—64no—
133C2×C3×M16—31no—
134C22×C3×C8—21no—
135C22×C3×C8C2×D311yescharacteristic, complemented
136C22×C3×C8C22×C311yescharacteristic, complemented
137C3×C4⋊Q8—61no—
138C3×#124—61no—
139C3×#123—62no—
140C3×C22⋊Q8—34no—
141C3×#117—21no—
142C3×#117C2×D311yescharacteristic, complemented
143C3×#117C22×C311yescharacteristic, complemented
144#951—24no—
145C2×#216C22×C312yescomplemented
146C2×#214C22×C312yescomplemented
147C2×#208C22×C311yescharacteristic, complemented
148C2×#204—24no—
149C2×#204C22×C314yescomplemented
150#897C22×C314yescomplemented
151#886—22no—
152#875—21no—
153#869—21no—
154C3×#103—22no—
155C3×#103C2×D312yescomplemented
156C3×#103C22×C312yescomplemented
157C3×#102—22no—
158C3×#102—34no—
159C3×#102C2×D312yescomplemented
160C3×#102C22×C312yescomplemented
161C3×C22⋊C8—34no—
162(C2×D3)⋊C8C22×C314yescomplemented
163#809C22×C314yescomplemented
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—28no—
168C22×C3×D3—24no—
169C22×C3×D3—84no—
170C22×C3×D3—82no—
171C22×C3×D3C2×D412yes—
172C32×Q8—21no—
173C32×Q8C2×D412yes—
174C32×D4—24no—
175C32×D4—21no—
176C32×D4C2×D412yes—
177C2×C32×C4—21no—
178C2×C32×C4—24no—
179C2×C32×C4—22no—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184C3×#67—28no—
185C3×#67—24no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—42no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—28no—
190C3×D12—22no—
191C3×D12—24no—
192C3×D12—22no—
193C3×D12C2×D414yes—
194C3×C4×D3—28no—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—22no—
198C3×Dic6—22no—
199C3×Dic6—22no—
200C3×Dic6—42no—
201C32×C8—22no—
202C3×C3⋊C8—22no—
203C2×H(5,𝔽2)—31no—
204C2×#137—31no—
205C22×SD16—31no—
206#536—31no—
207#452—34no—
208#450—34no—
209#418—31no—
210#416C3×D311yescharacteristic, complemented
211#408—31no—
212C24×C3—62no—
213C24×C3—61no—
214C23×D3—21no—
215C23×D3—22no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—24no—
219C3×#41—42no—
220C3×#41—68no—
221C3×#41—64no—
222C3×#41—64no—
223C3×#41—62no—
224C3×#41—62no—
225C3×#41D1214yes—
226C3×#41C3×D414yes—
227C2×C3×Q8—21no—
228C2×C3×Q8—31no—
229C2×C3×Q8—32no—
230C2×C3×Q8—61no—
231C2×C3×Q8—62no—
232C2×C3×Q8—62no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C23×C311yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—32no—
239C2×C3×D4—34no—
240C2×C3×D4—31no—
241C2×C3×D4—32no—
242C2×C3×D4—41no—
243C2×C3×D4—62no—
244C2×C3×D4—68no—
245C2×C3×D4—62no—
246C2×C3×D4—64no—
247C2×C3×D4—616no—
248C2×C3×D4—64no—
249C2×C3×D4—62no—
250C2×C3×D4—61no—
251C2×C3×D4C22×D311yescharacteristic
252C2×C3×D4C23×C311yescharacteristic
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—32no—
257C22×C3×C4—41no—
258C22×C3×C4—62no—
259C22×C3×C4—61no—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C23×C311yescharacteristic
262C2×#67—22no—
263C2×#67C3×D412yes—
264C22×Dic3—21no—
265#239—24no—
266#239—24no—
267D3×D4—216no—
268D3×D4—24no—
269D3×D4—24no—
270#235—28no—
271#235—22no—
272#235—22no—
273C2×D12—28no—
274C2×D12—22no—
275C2×D12—21no—
276C2×D12—22no—
277C2×D12C3×D411yescharacteristic
278C2×D12C3×D414yes—
279C2×D12C23×C312yes—
280C2×C4×D3—22no—
281C2×C4×D3C23×C312yes—
282C2×Dic6—22no—
283C2×Dic6—22no—
284C2×Dic6—21no—
285C2×Dic6C3×D411yescharacteristic
286C2×Dic6C23×C312yes—
287C3×Q16—64no—
288C3×SD16—68no—
289C3×SD16—64no—
290C3×M16—62no—
291C2×C3×C8—22no—
292C2×C3×C8—22no—
293C2×C3×C8—22no—
294C2×C3×C8—32no—
295C2×C3×C8—42no—
296C2×C3×C8C22×D312yes—
297C2×C3×C8C23×C312yes—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—64no—
300C3×C4⋊C4C22×D312yes—
301C3×C4⋊C4C23×C312yes—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—41no—
305C3×C22⋊C4—64no—
306C3×C42—21no—
307C3×C42—21no—
308C3×C42—41no—
309#216—24no—
310#214—24no—
311(C2×D3)⋊C4—24no—
312C4⋊Dic3—24no—
313#208—22no—
314C2×C3⋊C8C23×C312yes—
315#204—28no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—42no—
319C22×C32#12012yes—
320C22×C32C22×D411yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—24no—
323C2×C3×D3—24no—
324C2×C3×D3—44no—
325C2×C3×D3—84no—
326C2×C3×D3—88no—
327C32×C4—22no—
328C32×C4—42no—
329C32×C4#12012yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3×Dic3—22no—
333C3×Dic3—42no—
334H(5,𝔽2)—64no—
335H(5,𝔽2)—64no—
336C2×#41—31no—
337C2×#41—32no—
338C2×#41—61no—
339C2×#41C2×C3×D311yescharacteristic
340C22×Q8—31no—
341C22×D4—32no—
342C22×D4—31no—
343C22×D4—61no—
344C22×D4—62no—
345#137—64no—
346C2×Q16—32no—
347C2×SD16—32no—
348C2×SD16—34no—
349C2×SD16—64no—
350C2×M16—31no—
351C22×C8C2×C3×D311yescharacteristic, complemented
352C4⋊Q8—61no—
353#124—61no—
354#123—62no—
355C22⋊Q8—34no—
356#117C2×C3×D311yescharacteristic, complemented
357#103C2×C3×D312yescomplemented
358#102—34no—
359#102C2×C3×D312yescomplemented
360C22⋊C8—34no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—41no—
366C23×C3—68no—
367C23×C3—62no—
368C23×C3—64no—
369C23×C3—242no—
370C23×C3—244no—
371C23×C3D3×D411yescharacteristic
372C23×C3C2×C3×D411yescharacteristic
373C22×D3—22no—
374C22×D3—28no—
375C22×D3—24no—
376C22×D3—84no—
377C22×D3—82no—
378C22×D3C2×C3×D412yes—
379C3×Q8—21no—
380C3×Q8—21no—
381C3×Q8—22no—
382C3×Q8—41no—
383C3×Q8—62no—
384C3×Q8—62no—
385C3×Q8—62no—
386C3×Q8—122no—
387C3×Q8C2×D1212yes—
388C3×Q8C2×C3×D412yes—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—22no—
394C3×D4—34no—
395C3×D4—41no—
396C3×D4—44no—
397C3×D4—68no—
398C3×D4—68no—
399C3×D4—64no—
400C3×D4—64no—
401C3×D4—62no—
402C3×D4—62no—
403C3×D4C2×D1212yes—
404C3×D4C2×C3×D412yes—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—44no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—68no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—122no—
424C2×C3×C4C2×D1212yes—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D412yes—
427C2×C3×C4C2×C3×D412yes—
428C2×C3×C4C2×C3×D411yescharacteristic
429C2×C3×C4C2×C3×D412yes—
430C2×C3×C4C23×D311yescharacteristic
431C2×C3×C4C24×C311yescharacteristic
432#67—28no—
433#67—24no—
434C2×Dic3—22no—
435C2×Dic3—42no—
436C2×Dic3C2×C3×D412yes—
437D12—28no—
438D12—22no—
439D12—24no—
440D12—22no—
441D12C2×C3×D414yes—
442C4×D3—28no—
443C4×D3—22no—
444C4×D3—22no—
445Dic6—22no—
446Dic6—22no—
447Dic6—22no—
448Dic6—42no—
449C3×C8—22no—
450C3×C8—22no—
451C3×C8—42no—
452C3×C8—62no—
453C3⋊C8—22no—
454C2×C32—22no—
455C2×C32—42no—
456C2×C32C2×#12011yescharacteristic
457C2×C32#57712yes—
458C3×D3—42no—
459C3×D3—44no—
460C24—62no—
461C24—61no—
462#41—22no—
463#41—68no—
464#41—64no—
465#41—64no—
466#41—62no—
467#41—62no—
468#41C3×D1214yes—
469C2×Q8—31no—
470C2×Q8—32no—
471C2×Q8—61no—
472C2×Q8—62no—
473C2×Q8—62no—
474C2×Q8C22×C3×D311yescharacteristic
475C2×D4—21no—
476C2×D4—32no—
477C2×D4—32no—
478C2×D4—34no—
479C2×D4—31no—
480C2×D4—62no—
481C2×D4—68no—
482C2×D4—62no—
483C2×D4—64no—
484C2×D4—616no—
485C2×D4—64no—
486C2×D4—62no—
487C2×D4—61no—
488C2×D4C22×C3×D311yescharacteristic
489C22×C4—21no—
490C22×C4—32no—
491C22×C4—62no—
492C22×C4—61no—
493C22×C4C22×C3×D311yescharacteristic
494Q16—64no—
495SD16—68no—
496SD16—64no—
497M16—62no—
498C2×C8—22no—
499C2×C8—32no—
500C2×C8C22×C3×D312yes—
501C4⋊C4—64no—
502C4⋊C4C22×C3×D312yes—
503C22⋊C4—21no—
504C22⋊C4—64no—
505C42—21no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—64no—
517C22×C3—62no—
518C22×C3—64no—
519C22×C3—82no—
520C22×C3—124no—
521C22×C3—244no—
522C22×C3—248no—
523C22×C3#88212yes—
524C22×C3C3×#12012yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C22×C3×D411yescharacteristic
527C2×D3—24no—
528C2×D3—22no—
529C2×D3—24no—
530C2×D3—44no—
531C2×D3—84no—
532C2×D3—88no—
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—62no—
542C3×C4—82no—
543C3×C4—122no—
544C3×C4#88212yes—
545C3×C4C3×#12012yes—
546C3×C4C22×D1211yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C22×C3×D411yescharacteristic
549C3×C4C22×C3×D411yescharacteristic
550Dic3—22no—
551Dic3—42no—
552C32#300911yescharacteristic, complemented, Sylow
553C23—21no—
554C23—32no—
555C23—68no—
556C23—62no—
557C23—64no—
558C23—242no—
559C23—244no—
560C23C3×D3×D411yescharacteristic
561Q8—21no—
562Q8—62no—
563Q8—62no—
564Q8—62no—
565Q8—122no—
566Q8C2×C3×D1212yes—
567D4—24no—
568D4—21no—
569D4—34no—
570D4—68no—
571D4—68no—
572D4—64no—
573D4—64no—
574D4—62no—
575D4—62no—
576D4C2×C3×D1212yes—
577C2×C4—21no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—32no—
581C2×C4—68no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—122no—
586C2×C4C2×C3×D1212yes—
587C2×C4C3×D3×D411yescharacteristic
588C2×C4C3×D3×D412yes—
589C2×C4C23×C3×D311yescharacteristic
590C8—22no—
591C8—62no—
592C2×C3—22no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—22no—
596C2×C3—42no—
597C2×C3—42no—
598C2×C3—42no—
599C2×C3—82no—
600C2×C3—122no—
601C2×C3—124no—
602C2×C3C2×#88211yescharacteristic
603C2×C3#577012yes—
604C2×C3C2×C3×#12011yescharacteristic
605C2×C3C3×#57712yes—
606D3—42no—
607D3—44no—
608C22—22no—
609C22—22no—
610C22—42no—
611C22—64no—
612C22—62no—
613C22—64no—
614C22—124no—
615C22—244no—
616C22—248no—
617C22C3×#88212yes—
618C22C2×C3×D3×D411yescharacteristic
619C4—22no—
620C4—42no—
621C4—62no—
622C4—122no—
623C4C3×#88212yes—
624C4C22×C3×D1211yescharacteristic
625C4C2×C3×D3×D411yescharacteristic
626C3—21no—
627C3#7883511yescharacteristic, direct product factor
628C3C3×#300911yescharacteristic, complemented
629C2—22no—
630C2—42no—
631C2—122no—
632C2—124no—
633C2C2×C3×#88211yescharacteristic
634C2C3×#577012yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC2×C3×#1009C2
hypercenterC3×#416D3
hypocenterC3C3×#3009
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C22×C3×#204C2semidirect
4. C3×#5526C2semidirect
5. C32×#416C2semidirect
6. C3×#5110C2semidirect
7. C3×#5001C2semidirect
8. C3×#4808C2semidirect
9. C3×#4776C2semidirect
11. #78835C3direct (N × H)
22. C22×C3×Dic6C22semidirect
23. C22×C32×C8C22semidirect
24. C32×#117C22semidirect
26. C2×C3×#216C22semidirect
27. C2×C3×#214C22semidirect
28. C2×C3×#208C22semidirect
30. C2×C3×#204C22semidirect
31. C3×#897C22semidirect
35. C32×#103C22semidirect
36. C32×#102C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#809C22semidirect
44. C2×#951C2×C3semidirect
45. C22×#204C2×C3semidirect
46. #5526C2×C3semidirect
51. C3×#416D3semidirect
52. C3×#416C2×C3semidirect
54. #5110C2×C3semidirect
55. #5001C2×C3semidirect
56. #4808C2×C3semidirect
57. #4776C2×C3semidirect
127. C22×Dic6C22×C3semidirect
135. C22×C3×C8C2×D3semidirect
136. C22×C3×C8C22×C3semidirect
142. C3×#117C2×D3semidirect
143. C3×#117C22×C3semidirect
145. C2×#216C22×C3semidirect
146. C2×#214C22×C3semidirect
147. C2×#208C22×C3semidirect
149. C2×#204C22×C3semidirect
150. #897C22×C3semidirect
155. C3×#103C2×D3semidirect
156. C3×#103C22×C3semidirect
159. C3×#102C2×D3semidirect
160. C3×#102C22×C3semidirect
162. (C2×D3)⋊C8C22×C3semidirect
163. #809C22×C3semidirect
210. #416C3×D3semidirect
351. C22×C8C2×C3×D3semidirect
356. #117C2×C3×D3semidirect
357. #103C2×C3×D3semidirect
359. #102C2×C3×D3semidirect
552. C32#3009semidirect
627. C3#78835direct (N × H)
628. C3C3×#3009semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×C3×#9512
C22×C3×#2042
C3×#55262
C32×#4162
C3×#51102
C3×#50012
C3×#48082
C3×#47762
C3×#30093
#788353