Finite Group Databasebeta

← C3×#83411 #11864482

Subgroups — C3×#83411 #11864482

Order 1152.

1535 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C32×#536C211yesmaximal, characteristic, complemented
3C22×C3×#216C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6C3×#5050C214yesmaximal, complemented
7C3×#5047C214yesmaximal, complemented
8C3×#5004C211yesmaximal, characteristic, complemented
9C3×#5002C211yesmaximal, characteristic, complemented
10C3×#3011—31nomaximal
11#83411C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8—21no—
17C2×C3×#237—22no—
18C2×C3×#237—21no—
19C2×C3×#235C2212yes—
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C22×C3×Dic6C2211yescharacteristic
23C32×C4⋊Q8—21no—
24C32×#124—21no—
25C32×#123—22no—
26C32×C22⋊Q8C2214yes—
27C32×#117C2211yescharacteristic
28C2×C3×#216—24no—
29C2×C3×#216C2212yes—
30C2×C3×#216C2214yes—
31C3×#942—24no—
32C2×C3×#215C2212yes—
33C2×C3×#208C2211yescharacteristic
34C22×C3×C3⋊C8C2211yescharacteristic
35C3×#830C2214yes—
36C3×#810C2212yes—
37C3×#810C2214yes—
38C3×#809C2212yes—
39C2×C3×2−1+4—31no—
40C2×#1010C2×C311yescharacteristic
41C2×C3×#137—31no—
42C22×C3×Q16—31no—
43C3×#536—21no—
44C3×#536D311yescharacteristic, complemented
45C3×#536C2×C311yescharacteristic, complemented
46C22×#216C2×C311yescharacteristic, complemented
47C2×#942C2×C311yescharacteristic, complemented
48C3×#452—34no—
49C3×#451—34no—
50C3×#419—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5234C2×C311yescharacteristic, complemented
54#5050C2×C314yescomplemented
55#5047C2×C314yescomplemented
56#5004C2×C311yescharacteristic, complemented
57#5002C2×C311yescharacteristic, complemented
58C32×#41—22no—
59C32×#41—22no—
60C2×C32×Q8—21no—
61C2×C32×Q8—22no—
62C2×C32×Q8—22no—
63C2×C32×Q8D411yescharacteristic
64C2×C32×Q8C2312yes—
65C2×C32×D4D412yes—
66C2×C32×D4D411yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67—21no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—21no—
74C3×D3×Q8—28no—
75C3×#237—216no—
76C3×#237—28no—
77C3×#235—22no—
78C3×#235—24no—
79C3×#235—24no—
80C3×#235D414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—24no—
88C2×C3×Dic6—24no—
89C2×C3×Dic6D414yes—
90C2×C3×Dic6C2311yescharacteristic
91C2×C3×Dic6C2312yes—
92C32×C4⋊C4—24no—
93C32×C4⋊C4C2312yes—
94C32×C22⋊C4—21no—
95C32×C22⋊C4—24no—
96C32×C42—21no—
97C3×#216—24no—
98C3×#216—28no—
99C3×#215—24no—
100C3×#208—22no—
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104#3011—31noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C22×C311yescharacteristic
114C22×C3×Q8—21no—
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C3×Q8—61no—
118C22×C3×Q8C2×D311yescharacteristic
119C22×C3×Q8C22×C311yescharacteristic
120#1010—24no—
121#1010—24no—
122C2×D3×Q8—21no—
123C2×#237—22no—
124C2×#237—21no—
125C2×#235C22×C312yes—
126C2×#235C22×C311yescharacteristic
127C22×Dic6C22×C312yes—
128C22×Dic6C22×C311yescharacteristic
129C3×#137—64no—
130C2×C3×Q16—34no—
131C2×C3×Q16—32no—
132C2×C3×Q16—64no—
133C2×C3×SD16—32no—
134C2×C3×M16—31no—
135C22×C3×C8—31no—
136C3×C4⋊Q8—22no—
137C3×C4⋊Q8—21no—
138C3×C4⋊Q8—21no—
139C3×#124—22no—
140C3×#124—21no—
141C3×#124—21no—
142C3×#123—24no—
143C3×#123—22no—
144C3×#123—22no—
145C3×C22⋊Q8—24no—
146C3×C22⋊Q8C2×D314yes—
147C3×C22⋊Q8C22×C314yes—
148C3×#117—21no—
149C3×#117C2×D311yescharacteristic
150C3×#117C22×C311yescharacteristic
151C2×#216—24no—
152C2×#216C22×C312yes—
153C2×#216C22×C314yes—
154#942—24no—
155C2×#215C22×C312yes—
156C2×#208C22×C311yescharacteristic
157C22×C3⋊C8C22×C311yescharacteristic
158C3×#103—32no—
159C3×#103—34no—
160C3×#102—32no—
161C3×C22⋊C8—34no—
162#830C22×C314yes—
163#810C22×C312yes—
164#810C22×C314yes—
165#809C22×C312yes—
166C23×C32C2×D412yes—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—21no—
169C32×Q8—22no—
170C32×Q8—22no—
171C32×Q8—22no—
172C32×Q8—42no—
173C32×D4—24no—
174C32×D4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—42no—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C3×#67—28no—
186C3×#67—24no—
187C2×C3×Dic3—28no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C3×D12—21no—
192C3×D12C2×D412yes—
193C3×C4×D3—28no—
194C3×C4×D3—24no—
195C3×Dic6—28no—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6—21no—
199C3×Dic6C2×D412yes—
200C3×Dic6C2×D414yes—
201C3×C3⋊C8—22no—
202C3×C3⋊C8—22no—
203C2×2−1+4—31no—
204C2×#137—31no—
205C22×Q16—31no—
206#536C3×D311yescharacteristic, complemented
207#452—34no—
208#451—34no—
209#419—31no—
210#416—31no—
211#408—31no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—22no—
216C3×#41—34no—
217C3×#41—42no—
218C3×#41—42no—
219C3×#41—64no—
220C3×#41—64no—
221C3×#41—616no—
222C3×#41—68no—
223C3×#41—62no—
224C2×C3×Q8—22no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—22no—
228C2×C3×Q8—22no—
229C2×C3×Q8—22no—
230C2×C3×Q8—22no—
231C2×C3×Q8—21no—
232C2×C3×Q8—22no—
233C2×C3×Q8—34no—
234C2×C3×Q8—32no—
235C2×C3×Q8—31no—
236C2×C3×Q8—42no—
237C2×C3×Q8—42no—
238C2×C3×Q8—64no—
239C2×C3×Q8—64no—
240C2×C3×Q8—68no—
241C2×C3×Q8—62no—
242C2×C3×Q8—62no—
243C2×C3×Q8—61no—
244C2×C3×Q8#6711yescharacteristic
245C2×C3×Q8C3×D411yescharacteristic
246C2×C3×Q8C22×D312yes—
247C2×C3×Q8C23×C312yes—
248C2×C3×D4—22no—
249C2×C3×D4—21no—
250C2×C3×D4—31no—
251C2×C3×D4—62no—
252C2×C3×D4—61no—
253C2×C3×D4#6712yes—
254C2×C3×D4#6711yescharacteristic
255C2×C3×D4C3×D412yes—
256C2×C3×D4C3×D411yescharacteristic
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—22no—
262C22×C3×C4—62no—
263C22×C3×C4—61no—
264C22×C3×C4—62no—
265C22×C3×C4—61no—
266C22×C3×C4C22×D312yes—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C2×#67—22no—
271C2×#67—21no—
272C22×Dic3—22no—
273C22×Dic3—21no—
274D3×Q8—28no—
275#237—216no—
276#237—28no—
277#235—22no—
278#235—24no—
279#235—24no—
280#235C3×D414yes—
281C2×D12C23×C311yescharacteristic
282C2×C4×D3—22no—
283C2×C4×D3—21no—
284C2×Dic6—22no—
285C2×Dic6—21no—
286C2×Dic6—22no—
287C2×Dic6—24no—
288C2×Dic6—24no—
289C2×Dic6C3×D414yes—
290C2×Dic6C23×C311yescharacteristic
291C2×Dic6C23×C312yes—
292C3×Q16—68no—
293C3×Q16—64no—
294C3×SD16—64no—
295C3×M16—62no—
296C2×C3×C8—32no—
297C2×C3×C8—32no—
298C2×C3×C8—62no—
299C3×C4⋊C4—28no—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4C22×D312yes—
304C3×C4⋊C4C23×C312yes—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—28no—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—24no—
311C3×C42—22no—
312C3×C42—21no—
313C3×C42—21no—
314#216—24no—
315#216—28no—
316#215—24no—
317#208—22no—
318C2×C3⋊C8—22no—
319C2×C3⋊C8C23×C312yes—
320C2×C3⋊C8C23×C312yes—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—24no—
324C22×C32#12012yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—22no—
327C2×C3×D3—42no—
328C32×C4—22no—
329C32×C4—42no—
330C32×C4—42no—
331C32×C4#12012yes—
332C32×C4C22×D411yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3×Dic3—22no—
335C3×Dic3—24no—
3362−1+4—64no—
3372−1+4—64no—
338C2×#41—31no—
339C2×#41—32no—
340C2×#41—62no—
341C2×#41—61no—
342C2×#41C2×C3×D311yescharacteristic
343C22×Q8—31no—
344C22×Q8—32no—
345C22×Q8—61no—
346C22×Q8C2×C3×D311yescharacteristic
347#137—64no—
348C2×Q16—34no—
349C2×Q16—32no—
350C2×Q16—64no—
351C2×SD16—32no—
352C2×M16—31no—
353C22×C8—31no—
354C4⋊Q8—21no—
355#124—21no—
356#123—22no—
357C22⋊Q8C2×C3×D314yes—
358#117C2×C3×D311yescharacteristic
359#103—32no—
360#103—34no—
361#102—32no—
362C22⋊C8—34no—
363C23×C3—21no—
364C23×C3—22no—
365C23×C3—61no—
366C23×C3C2×#6712yes—
367C23×C3C2×#6711yescharacteristic
368C23×C3C2×C3×D412yes—
369C23×C3C2×C3×D411yescharacteristic
370C22×D3—21no—
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8—22no—
375C3×Q8—22no—
376C3×Q8—22no—
377C3×Q8—34no—
378C3×Q8—32no—
379C3×Q8—42no—
380C3×Q8—42no—
381C3×Q8—42no—
382C3×Q8—44no—
383C3×Q8—42no—
384C3×Q8—42no—
385C3×Q8—68no—
386C3×Q8—64no—
387C3×Q8—62no—
388C3×Q8—61no—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—32no—
394C3×D4—42no—
395C3×D4—44no—
396C3×D4—68no—
397C3×D4—64no—
398C3×D4—61no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—44no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—68no—
420C2×C3×C4—68no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4—61no—
424C2×C3×C4—64no—
425C2×C3×C4D3×D412yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×C3×D412yes—
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C2×C3×D412yes—
432C2×C3×C4C2×C3×D411yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434C2×C3×C4C24×C311yescharacteristic
435#67—28no—
436#67—24no—
437C2×Dic3—28no—
438C2×Dic3—24no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441D12—21no—
442D12C2×C3×D412yes—
443C4×D3—28no—
444C4×D3—24no—
445Dic6—28no—
446Dic6—24no—
447Dic6—22no—
448Dic6—21no—
449Dic6C2×C3×D412yes—
450Dic6C2×C3×D414yes—
451C3×C8—62no—
452C3×C8—62no—
453C3⋊C8—22no—
454C3⋊C8—22no—
455C2×C32—22no—
456C2×C32—42no—
457C2×C32C2×#12011yescharacteristic
458C2×C32#57812yes—
459C3×D3—42no—
460#41—22no—
461#41—22no—
462#41—34no—
463#41—64no—
464#41—64no—
465#41—616no—
466#41—68no—
467#41—62no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—32no—
472C2×Q8—31no—
473C2×Q8—34no—
474C2×Q8—64no—
475C2×Q8—64no—
476C2×Q8—68no—
477C2×Q8—62no—
478C2×Q8—62no—
479C2×Q8—61no—
480C2×Q8C3×#6711yescharacteristic
481C2×Q8C22×C3×D312yes—
482C2×D4—31no—
483C2×D4—62no—
484C2×D4—61no—
485C2×D4C3×#6712yes—
486C2×D4C3×#6711yescharacteristic
487C22×C4—21no—
488C22×C4—62no—
489C22×C4—61no—
490C22×C4—62no—
491C22×C4—61no—
492C22×C4C22×C3×D312yes—
493C22×C4C22×C3×D311yescharacteristic
494Q16—68no—
495Q16—64no—
496SD16—64no—
497M16—62no—
498C2×C8—32no—
499C2×C8—32no—
500C2×C8—62no—
501C4⋊C4—24no—
502C4⋊C4C22×C3×D312yes—
503C22⋊C4—21no—
504C22⋊C4—24no—
505C42—21no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—24no—
509C22×C3—22no—
510C22×C3—24no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—44no—
517C22×C3—62no—
518C22×C3—122no—
519C22×C3#93712yes—
520C22×C3C3×#12012yes—
521C22×C3C22×#6711yescharacteristic
522C22×C3C22×C3×D411yescharacteristic
523C2×D3—22no—
524C2×D3—42no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—42no—
531C3×C4—44no—
532C3×C4—44no—
533C3×C4—42no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4—42no—
537C3×C4—64no—
538C3×C4—62no—
539C3×C4#93712yes—
540C3×C4C3×#12012yes—
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C22×C3×D411yescharacteristic
544C3×C4C22×C3×D411yescharacteristic
545Dic3—22no—
546Dic3—24no—
547C32#301111yescharacteristic, complemented, Sylow
548C23—61no—
549C23C2×C3×#6712yes—
550C23C2×C3×#6711yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—22no—
554Q8—34no—
555Q8—32no—
556Q8—42no—
557Q8—68no—
558Q8—64no—
559Q8—62no—
560Q8—61no—
561D4—24no—
562D4—22no—
563D4—32no—
564D4—68no—
565D4—64no—
566D4—61no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—68no—
573C2×C4—68no—
574C2×C4—64no—
575C2×C4—62no—
576C2×C4—61no—
577C2×C4—64no—
578C2×C4C3×D3×D412yes—
579C2×C4C3×D3×D412yes—
580C2×C4C2×C3×#6712yes—
581C2×C4C2×C3×#6711yescharacteristic
582C2×C4C23×C3×D311yescharacteristic
583C8—62no—
584C8—62no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—22no—
589C2×C3—42no—
590C2×C3—42no—
591C2×C3—42no—
592C2×C3—82no—
593C2×C3—122no—
594C2×C3C2×#93711yescharacteristic
595C2×C3#583812yes—
596C2×C3C2×C3×#12011yescharacteristic
597C2×C3C3×#57812yes—
598D3—42no—
599C22—22no—
600C22—22no—
601C22—24no—
602C22—62no—
603C22—122no—
604C22C3×#93712yes—
605C22C22×C3×#6711yescharacteristic
606C4—22no—
607C4—42no—
608C4—42no—
609C4—64no—
610C4—62no—
611C4C3×#93712yes—
612C4C2×C3×D3×D411yescharacteristic
613C4C2×C3×D3×D411yescharacteristic
614C3—21no—
615C3#8341111yescharacteristic, direct product factor
616C3C3×#301111yescharacteristic, complemented
617C2—22no—
618C2—42no—
619C2—122no—
620C2C2×C3×#93711yescharacteristic
621C2C3×#583812yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#536C2
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC3×#536D3
hypocenterC3C3×#3011
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
2. C32×#536C2semidirect
3. C22×C3×#216C2semidirect
4. C2×C3×#942C2semidirect
5. C3×#5234C2semidirect
6. C3×#5050C2semidirect
7. C3×#5047C2semidirect
8. C3×#5004C2semidirect
9. C3×#5002C2semidirect
11. #83411C3direct (N × H)
44. C3×#536D3semidirect
45. C3×#536C2×C3semidirect
46. C22×#216C2×C3semidirect
47. C2×#942C2×C3semidirect
53. #5234C2×C3semidirect
54. #5050C2×C3semidirect
55. #5047C2×C3semidirect
56. #5004C2×C3semidirect
57. #5002C2×C3semidirect
206. #536C3×D3semidirect
547. C32#3011semidirect
615. C3#83411direct (N × H)
616. C3C3×#3011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C32×#5362
C22×C3×#2162
C2×C3×#9422
C3×#52342
C3×#50502
C3×#50472
C3×#50042
C3×#50022
C3×#30113
#834113