Finite Group Databasebeta

← C3×#78929 #11864337

Subgroups — C3×#78929 #11864337

Order 1152.

1599 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6C3×#5129C211yesmaximal, characteristic, complemented
7C3×#5002C211yesmaximal, characteristic, complemented
8C3×#4783C214yesmaximal, complemented
9C3×#4776C214yesmaximal, complemented
10C3×#3009—31nomaximal
11#78929C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—22no—
14C3×#1004—24no—
15C3×#1004—24no—
16C2×C3×#237—21no—
17C2×C3×#237C2212yes—
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2212yes—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24C32×#117C2211yescharacteristic, complemented
25C2×C3×#214—24no—
26C2×C3×#214C2214yescomplemented
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C3×#909—24no—
29C2×C3×Dic12C2212yescomplemented
30C2×C3×#204C2212yescomplemented
31C3×#897C2214yescomplemented
32C3×#886—22no—
33C3×#875—21no—
34C3×#869—21no—
35C32×#102C2214yescomplemented
36C3×(C2×D3)⋊C8C2214yescomplemented
37C3×#810C2212yescomplemented
38C3×#809C2212yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1004C2×C311yescharacteristic
41C2×C3×#137—31no—
42C22×C3×SD16—31no—
43C3×#536—31no—
44C22×#214C2×C311yescharacteristic, complemented
45C2×#909C2×C311yescharacteristic, complemented
46#5526C2×C311yescharacteristic, complemented
47C3×#452—34no—
48C3×#450—34no—
49C3×#418—21no—
50C3×#418D311yescharacteristic, complemented
51C3×#418C2×C311yescharacteristic, complemented
52C3×#416—31no—
53C3×#408—31no—
54#5129C2×C311yescharacteristic, complemented
55#5002C2×C311yescharacteristic, complemented
56#4783C2×C314yescomplemented
57#4776C2×C314yescomplemented
58C24×C32—21no—
59C23×C3×D3—22no—
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yes—
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—216no—
66C2×C3×#67—21no—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×#67D412yes—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—21no—
72C3×#237—28no—
73C3×#237—24no—
74C3×#237—24no—
75C3×D3×D4—28no—
76C3×D3×D4—24no—
77C3×D3×D4—24no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235D414yes—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—21no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6C2312yes—
91C2×C3×Dic6C2311yescharacteristic
92C32×M16—22no—
93C2×C32×C8C2312yes—
94C32×C4⋊C4C2312yes—
95C32×C22⋊C4—21no—
96C32×C42—21no—
97C3×#214—28no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3—24no—
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2312yes—
102C3×Dic12—24no—
103C3×#204—24no—
104#3009—31noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—61no—
111C22×C3×Q8—31no—
112C22×C3×D4—21no—
113C22×C3×D4—32no—
114C22×C3×D4—61no—
115C22×C3×D4—62no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C22×C311yescharacteristic
118C22×#67—22no—
119#1004—24no—
120#1004—24no—
121C2×#237—21no—
122C2×#237C22×C312yes—
123C2×D3×D4—21no—
124C2×D3×D4C22×C312yes—
125C2×#235C22×C311yescharacteristic
126C2×#235C22×C311yescharacteristic
127C22×Dic6C22×C311yescharacteristic, complemented
128C3×#137—64no—
129C2×C3×Q16—32no—
130C2×C3×SD16—34no—
131C2×C3×SD16—32no—
132C2×C3×SD16—64no—
133C2×C3×M16—21no—
134C2×C3×M16C2×D311yescharacteristic, complemented
135C2×C3×M16C22×C311yescharacteristic, complemented
136C22×C3×C8—31no—
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
144C2×#214—24no—
145C2×#214C22×C314yescomplemented
146C22×C3⋊C8C22×C311yescharacteristic, complemented
147#909—24no—
148C2×Dic12C22×C312yescomplemented
149C2×#204C22×C312yescomplemented
150#897C22×C314yescomplemented
151#886—22no—
152#875—21no—
153#869—21no—
154C3×#103—32no—
155C3×#102—24no—
156C3×#102—32no—
157C3×#102C2×D314yescomplemented
158C3×#102C22×C314yescomplemented
159C3×C22⋊C8—34no—
160(C2×D3)⋊C8C22×C314yescomplemented
161#810C22×C312yescomplemented
162#809C22×C312yescomplemented
163C23×C32—22no—
164C23×C32—24no—
165C23×C32—82no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—28no—
169C22×C3×D3—84no—
170C22×C3×D3C2×D412yes—
171C32×D4—24no—
172C32×D4—22no—
173C32×D4C2×D414yes—
174C2×C32×C4—22no—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C3×#67—28no—
180C3×#67—28no—
181C3×#67—24no—
182C3×#67—24no—
183C2×C3×Dic3—28no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—42no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×D12—21no—
190C3×D12C2×D412yes—
191C3×C4×D3—24no—
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×Dic6—22no—
195C3×Dic6—21no—
196C3×Dic6—22no—
197C3×Dic6—22no—
198C3×Dic6—42no—
199C3×Dic6C2×D412yes—
200C32×C8—22no—
201C3×C3⋊C8—22no—
202C2×H(5,𝔽2)—31no—
203C2×#137—31no—
204C22×SD16—31no—
205#536—31no—
206#452—34no—
207#450—34no—
208#418C3×D311yescharacteristic, complemented
209#416—31no—
210#408—31no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—41no—
214C24×C3—62no—
215C23×D3—22no—
216C3×#41—34no—
217C3×#41—64no—
218C3×#41—68no—
219C3×#41—64no—
220C3×#41—62no—
221C3×#41—62no—
222C3×#41—62no—
223C2×C3×Q8—31no—
224C2×C3×Q8—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—61no—
227C2×C3×Q8—62no—
228C2×C3×Q8—62no—
229C2×C3×D4—21no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—22no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—32no—
236C2×C3×D4—31no—
237C2×C3×D4—31no—
238C2×C3×D4—41no—
239C2×C3×D4—42no—
240C2×C3×D4—62no—
241C2×C3×D4—64no—
242C2×C3×D4—68no—
243C2×C3×D4—62no—
244C2×C3×D4—616no—
245C2×C3×D4—61no—
246C2×C3×D4—64no—
247C2×C3×D4D1214yes—
248C2×C3×D4C3×D414yes—
249C2×C3×D4C22×D312yes—
250C2×C3×D4C23×C312yes—
251C22×C3×C4—21no—
252C22×C3×C4—32no—
253C22×C3×C4—62no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C23×C311yescharacteristic
258C2×#67—216no—
259C2×#67—21no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67C3×D412yes—
263C22×Dic3—22no—
264C22×Dic3—21no—
265#237—28no—
266#237—24no—
267#237—24no—
268D3×D4—28no—
269D3×D4—24no—
270D3×D4—24no—
271#235—22no—
272#235—22no—
273#235—22no—
274#235C3×D414yes—
275C2×D12C3×D411yescharacteristic
276C2×D12C23×C311yescharacteristic
277C2×C4×D3—21no—
278C2×C4×D3C23×C312yes—
279C2×Dic6—22no—
280C2×Dic6—22no—
281C2×Dic6—21no—
282C2×Dic6C3×D411yescharacteristic
283C2×Dic6C23×C312yes—
284C2×Dic6C23×C311yescharacteristic
285C3×Q16—64no—
286C3×SD16—64no—
287C3×SD16—68no—
288C3×M16—22no—
289C3×M16—22no—
290C3×M16—42no—
291C2×C3×C8—22no—
292C2×C3×C8—32no—
293C2×C3×C8—62no—
294C2×C3×C8C22×D312yes—
295C2×C3×C8C23×C312yes—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—64no—
298C3×C4⋊C4C22×D312yes—
299C3×C4⋊C4C23×C312yes—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—41no—
303C3×C22⋊C4—64no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—41no—
307#214—28no—
308(C2×D3)⋊C4—24no—
309C4⋊Dic3—24no—
310C2×C3⋊C8—22no—
311C2×C3⋊C8C23×C312yes—
312Dic12—24no—
313#204—24no—
314C22×C32—22no—
315C22×C32—24no—
316C22×C32—44no—
317C22×C32—84no—
318C22×C32#12012yes—
319C22×C32C22×D411yescharacteristic
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—24no—
323C2×C3×D3—42no—
324C2×C3×D3—88no—
325C32×C4—42no—
326C32×C4#12012yes—
327C32×C4C22×D411yescharacteristic
328C32×C4C22×D411yescharacteristic
329C3×Dic3—22no—
330C3×Dic3—22no—
331C3×Dic3—42no—
332H(5,𝔽2)—64no—
333H(5,𝔽2)—64no—
334C2×#41—31no—
335C2×#41—32no—
336C2×#41—31no—
337C2×#41—61no—
338C22×Q8—31no—
339C22×D4—32no—
340C22×D4—61no—
341C22×D4—62no—
342C22×D4C2×C3×D311yescharacteristic
343#137—64no—
344C2×Q16—32no—
345C2×SD16—34no—
346C2×SD16—32no—
347C2×SD16—64no—
348C2×M16C2×C3×D311yescharacteristic, complemented
349C22×C8—31no—
350C4⋊Q8—61no—
351#124—61no—
352#123—62no—
353C22⋊Q8—34no—
354#117C2×C3×D311yescharacteristic, complemented
355#103—32no—
356#102—32no—
357#102C2×C3×D314yescomplemented
358C22⋊C8—34no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—42no—
366C23×C3—44no—
367C23×C3—68no—
368C23×C3—61no—
369C23×C3—82no—
370C23×C3—82no—
371C23×C3—84no—
372C23×C3—244no—
373C23×C3D3×D411yescharacteristic
374C23×C3C2×C3×D411yescharacteristic
375C22×D3—21no—
376C22×D3—28no—
377C22×D3—84no—
378C22×D3C2×C3×D412yes—
379C3×Q8—32no—
380C3×Q8—62no—
381C3×Q8—61no—
382C3×Q8—62no—
383C3×Q8—62no—
384C3×Q8—122no—
385C3×D4—24no—
386C3×D4—24no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—24no—
390C3×D4—32no—
391C3×D4—44no—
392C3×D4—42no—
393C3×D4—68no—
394C3×D4—68no—
395C3×D4—64no—
396C3×D4—64no—
397C3×D4—62no—
398C3×D4—61no—
399C3×D4C2×D1214yes—
400C3×D4C2×C3×D414yes—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—32no—
408C2×C3×C4—42no—
409C2×C3×C4—68no—
410C2×C3×C4—61no—
411C2×C3×C4—64no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—122no—
416C2×C3×C4C2×D1212yes—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D412yes—
419C2×C3×C4C2×C3×D412yes—
420C2×C3×C4C2×C3×D411yescharacteristic
421C2×C3×C4C2×C3×D412yes—
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C24×C311yescharacteristic
424#67—28no—
425#67—28no—
426#67—24no—
427#67—24no—
428C2×Dic3—28no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—42no—
432C2×Dic3C2×C3×D412yes—
433D12—22no—
434D12—21no—
435D12C2×C3×D412yes—
436C4×D3—24no—
437C4×D3—22no—
438C4×D3—22no—
439Dic6—22no—
440Dic6—21no—
441Dic6—22no—
442Dic6—22no—
443Dic6—42no—
444Dic6C2×C3×D412yes—
445C3×C8—22no—
446C3×C8—22no—
447C3×C8—42no—
448C3×C8—62no—
449C3⋊C8—22no—
450C2×C32—22no—
451C2×C32—44no—
452C2×C32C2×#12011yescharacteristic
453C2×C32#57712yes—
454C3×D3—42no—
455C3×D3—42no—
456C24—21no—
457C24—62no—
458#41—34no—
459#41—64no—
460#41—68no—
461#41—64no—
462#41—62no—
463#41—62no—
464#41—62no—
465C2×Q8—31no—
466C2×Q8—31no—
467C2×Q8—32no—
468C2×Q8—61no—
469C2×Q8—62no—
470C2×Q8—62no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—32no—
474C2×D4—31no—
475C2×D4—31no—
476C2×D4—62no—
477C2×D4—64no—
478C2×D4—68no—
479C2×D4—62no—
480C2×D4—616no—
481C2×D4—61no—
482C2×D4—64no—
483C2×D4C3×D1214yes—
484C2×D4C22×C3×D312yes—
485C22×C4—32no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4C22×C3×D311yescharacteristic
490Q16—64no—
491SD16—64no—
492SD16—68no—
493M16—22no—
494C2×C8—32no—
495C2×C8—62no—
496C2×C8C22×C3×D312yes—
497C4⋊C4—64no—
498C4⋊C4C22×C3×D312yes—
499C22⋊C4—21no—
500C22⋊C4—64no—
501C42—21no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—42no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—64no—
515C22×C3—84no—
516C22×C3—84no—
517C22×C3—84no—
518C22×C3—88no—
519C22×C3—122no—
520C22×C3—248no—
521C22×C3#88212yes—
522C22×C3C3×#12012yes—
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C22×C3×D411yescharacteristic
525C2×D3—24no—
526C2×D3—22no—
527C2×D3—22no—
528C2×D3—42no—
529C2×D3—88no—
530C3×C4—22no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—42no—
534C3×C4—42no—
535C3×C4—62no—
536C3×C4—62no—
537C3×C4—82no—
538C3×C4—122no—
539C3×C4#88212yes—
540C3×C4C3×#12012yes—
541C3×C4C22×D1211yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C22×C3×D411yescharacteristic
544C3×C4C22×C3×D411yescharacteristic
545Dic3—22no—
546Dic3—22no—
547Dic3—42no—
548C32#300911yescharacteristic, complemented, Sylow
549C23—22no—
550C23—24no—
551C23—32no—
552C23—68no—
553C23—61no—
554C23—82no—
555C23—244no—
556C23C3×D3×D411yescharacteristic
557Q8—32no—
558Q8—62no—
559Q8—61no—
560Q8—62no—
561Q8—62no—
562Q8—122no—
563D4—24no—
564D4—22no—
565D4—32no—
566D4—68no—
567D4—68no—
568D4—64no—
569D4—64no—
570D4—62no—
571D4—61no—
572D4C2×C3×D1214yes—
573C2×C4—22no—
574C2×C4—32no—
575C2×C4—68no—
576C2×C4—61no—
577C2×C4—64no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—122no—
582C2×C4C2×C3×D1212yes—
583C2×C4C3×D3×D411yescharacteristic
584C2×C4C3×D3×D412yes—
585C2×C4C23×C3×D311yescharacteristic
586C8—22no—
587C8—62no—
588C2×C3—22no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—22no—
592C2×C3—42no—
593C2×C3—44no—
594C2×C3—44no—
595C2×C3—84no—
596C2×C3—122no—
597C2×C3—122no—
598C2×C3C2×#88211yescharacteristic
599C2×C3#577512yes—
600C2×C3C2×C3×#12011yescharacteristic
601C2×C3C3×#57712yes—
602D3—42no—
603D3—42no—
604C22—22no—
605C22—24no—
606C22—44no—
607C22—62no—
608C22—62no—
609C22—64no—
610C22—84no—
611C22—122no—
612C22—248no—
613C22C3×#88212yes—
614C22C2×C3×D3×D411yescharacteristic
615C4—42no—
616C4—62no—
617C4—62no—
618C4—122no—
619C4C3×#88212yes—
620C4C22×C3×D1211yescharacteristic
621C4C2×C3×D3×D411yescharacteristic
622C3—21no—
623C3#7892911yescharacteristic, direct product factor
624C3C3×#300911yescharacteristic, complemented
625C2—22no—
626C2—44no—
627C2—122no—
628C2—122no—
629C2C2×C3×#88211yescharacteristic
630C2C3×#577512yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
prime radicalC2×C3×#1004C2
hypercenterC3×#418D3
hypocenterC3C3×#3009
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5526C2semidirect
5. C32×#418C2semidirect
6. C3×#5129C2semidirect
7. C3×#5002C2semidirect
8. C3×#4783C2semidirect
9. C3×#4776C2semidirect
11. #78929C3direct (N × H)
22. C22×C3×Dic6C22semidirect
23. C2×C32×M16C22semidirect
24. C32×#117C22semidirect
26. C2×C3×#214C22semidirect
27. C22×C3×C3⋊C8C22semidirect
29. C2×C3×Dic12C22semidirect
30. C2×C3×#204C22semidirect
31. C3×#897C22semidirect
35. C32×#102C22semidirect
36. C3×(C2×D3)⋊C8C22semidirect
37. C3×#810C22semidirect
38. C3×#809C22semidirect
44. C22×#214C2×C3semidirect
45. C2×#909C2×C3semidirect
46. #5526C2×C3semidirect
50. C3×#418D3semidirect
51. C3×#418C2×C3semidirect
54. #5129C2×C3semidirect
55. #5002C2×C3semidirect
56. #4783C2×C3semidirect
57. #4776C2×C3semidirect
127. C22×Dic6C22×C3semidirect
134. C2×C3×M16C2×D3semidirect
135. C2×C3×M16C22×C3semidirect
142. C3×#117C2×D3semidirect
143. C3×#117C22×C3semidirect
145. C2×#214C22×C3semidirect
146. C22×C3⋊C8C22×C3semidirect
148. C2×Dic12C22×C3semidirect
149. C2×#204C22×C3semidirect
150. #897C22×C3semidirect
157. C3×#102C2×D3semidirect
158. C3×#102C22×C3semidirect
160. (C2×D3)⋊C8C22×C3semidirect
161. #810C22×C3semidirect
162. #809C22×C3semidirect
208. #418C3×D3semidirect
348. C2×M16C2×C3×D3semidirect
354. #117C2×C3×D3semidirect
357. #102C2×C3×D3semidirect
548. C32#3009semidirect
623. C3#78929direct (N × H)
624. C3C3×#3009semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C22×C3×#2142
C2×C3×#9092
C3×#55262
C32×#4182
C3×#51292
C3×#50022
C3×#47832
C3×#47762
C3×#30093
#789293