Finite Group Databasebeta

← C3×#78679 #11864494

Subgroups — C3×#78679 #11864494

Order 1152.

1479 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C22×C3×Dic12C211yesmaximal, characteristic, complemented
5C32×#408C211yesmaximal, characteristic, complemented
6C3×#5120C211yesmaximal, characteristic, complemented
7C3×#5113C211yesmaximal, characteristic, complemented
8C3×#4739C214yesmaximal, complemented
9C3×#4733C214yesmaximal, complemented
10C3×#3011—31nomaximal
11#78679C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C3×#1010—24no—
14C3×#1010—24no—
15C2×C3×D3×Q8—21no—
16C2×C3×#237—22no—
17C2×C3×#237—21no—
18C2×C3×#235C2212yes—
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C22×C3×Dic6C2211yescharacteristic
23C2×C32×M16C2211yescharacteristic
24C22×C32×C8C2211yescharacteristic
25C3×#944—21no—
26C3×#936—21no—
27C3×#935—22no—
28C3×#926C2211yescharacteristic
29C3×#924C2214yes—
30C3×#909—24no—
31C2×C3×Dic12—24no—
32C2×C3×Dic12C2212yes—
33C2×C3×Dic12C2214yes—
34C2×C3×#204C2212yes—
35C32×C22⋊C8C2214yes—
36C3×#821C2212yes—
37C3×#816C2214yes—
38C3×#816C2212yes—
39C2×C3×2−1+4—31no—
40C2×#1010C2×C311yescharacteristic
41C2×C3×#137—31no—
42C22×C3×Q16—31no—
43C3×#536—31no—
44#5825C2×C311yescharacteristic, complemented
45C2×#909C2×C311yescharacteristic, complemented
46C22×Dic12C2×C311yescharacteristic, complemented
47C3×#452—34no—
48C3×#451—34no—
49C3×#419—31no—
50C3×#416—31no—
51C3×#408—21no—
52C3×#408D311yescharacteristic, complemented
53C3×#408C2×C311yescharacteristic, complemented
54#5120C2×C311yescharacteristic, complemented
55#5113C2×C311yescharacteristic, complemented
56#4739C2×C314yescomplemented
57#4733C2×C314yescomplemented
58C32×#41—22no—
59C32×#41—22no—
60C2×C32×Q8D411yescharacteristic
61C2×C32×D4D412yes—
62C2×C32×D4D411yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—22no—
66C2×C3×#67—21no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C3×D3×Q8—28no—
71C3×#237—216no—
72C3×#237—28no—
73C3×#235—22no—
74C3×#235—24no—
75C3×#235—24no—
76C3×#235D414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—21no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6—24no—
84C2×C3×Dic6—24no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—21no—
88C2×C3×Dic6D414yes—
89C2×C3×Dic6C2312yes—
90C2×C3×Dic6C2311yescharacteristic
91C2×C3×Dic6C2312yes—
92C32×M16—22no—
93C2×C32×C8—22no—
94C2×C32×C8C2312yes—
95C2×C32×C8C2312yes—
96C3×#217—24no—
97C3×#217—21no—
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—24no—
100C3×C4×Dic3—21no—
101C3×Dic12—28no—
102C3×Dic12—24no—
103C3×#204—24no—
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—31no—
115C22×C3×Q8—31no—
116C22×C3×Q8—32no—
117C22×C3×Q8—61no—
118#1010—24no—
119#1010—24no—
120C2×D3×Q8—21no—
121C2×#237—22no—
122C2×#237—21no—
123C2×#235C22×C312yes—
124C2×#235C22×C311yescharacteristic
125C22×Dic6C22×C312yes—
126C22×Dic6C22×C311yescharacteristic
127C22×Dic6C22×C311yescharacteristic
128C3×#137—64no—
129C2×C3×Q16—34no—
130C2×C3×Q16—32no—
131C2×C3×Q16—64no—
132C2×C3×SD16—32no—
133C2×C3×M16—21no—
134C2×C3×M16C2×D311yescharacteristic
135C2×C3×M16C22×C311yescharacteristic
136C22×C3×C8—21no—
137C22×C3×C8C2×D311yescharacteristic
138C22×C3×C8C22×C311yescharacteristic
139C3×C4⋊Q8—61no—
140C3×#124—61no—
141C3×#123—62no—
142C3×C22⋊Q8—34no—
143C3×#117—31no—
144#944—21no—
145#936—21no—
146#935—22no—
147#926C22×C311yescharacteristic
148#924C22×C314yes—
149#909—24no—
150C2×Dic12—24no—
151C2×Dic12C22×C314yes—
152C2×Dic12C22×C312yes—
153C2×#204C22×C312yes—
154C3×#103—32no—
155C3×#103—34no—
156C3×#102—32no—
157C3×C22⋊C8—24no—
158C3×C22⋊C8C2×D314yes—
159C3×C22⋊C8C22×C314yes—
160#821C22×C312yes—
161#816C22×C314yes—
162#816C22×C312yes—
163C23×C32C2×D412yes—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—21no—
166C32×Q8—22no—
167C32×D4—24no—
168C32×D4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2411yescharacteristic
176C3×#67—28no—
177C3×#67—24no—
178C2×C3×Dic3—28no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—42no—
185C3×D12—21no—
186C3×D12C2×D412yes—
187C3×C4×D3—28no—
188C3×C4×D3—24no—
189C3×Dic6—28no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—22no—
194C3×Dic6—22no—
195C3×Dic6—42no—
196C3×Dic6C2×D412yes—
197C3×Dic6C2×D414yes—
198C32×C8—22no—
199C32×C8—22no—
200C2×2−1+4—31no—
201C2×#137—31no—
202C22×Q16—31no—
203#536—31no—
204#452—34no—
205#451—34no—
206#419—31no—
207#416—31no—
208#408C3×D311yescharacteristic, complemented
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—34no—
214C3×#41—42no—
215C3×#41—42no—
216C3×#41—64no—
217C3×#41—64no—
218C3×#41—616no—
219C3×#41—68no—
220C3×#41—62no—
221C2×C3×Q8—21no—
222C2×C3×Q8—34no—
223C2×C3×Q8—32no—
224C2×C3×Q8—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—64no—
227C2×C3×Q8—64no—
228C2×C3×Q8—68no—
229C2×C3×Q8—62no—
230C2×C3×Q8—61no—
231C2×C3×Q8—61no—
232C2×C3×Q8—62no—
233C2×C3×Q8—62no—
234C2×C3×Q8—62no—
235C2×C3×Q8D1211yescharacteristic
236C2×C3×Q8C3×D411yescharacteristic
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—31no—
240C2×C3×D4—62no—
241C2×C3×D4—61no—
242C2×C3×D4D1212yes—
243C2×C3×D4D1211yescharacteristic
244C2×C3×D4C3×D412yes—
245C2×C3×D4C3×D411yescharacteristic
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—62no—
249C22×C3×C4—61no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C23×C312yes—
256C22×C3×C4C23×C311yescharacteristic
257C2×#67—22no—
258C2×#67—21no—
259C22×Dic3—22no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262D3×Q8—28no—
263#237—216no—
264#237—28no—
265#235—22no—
266#235—24no—
267#235—24no—
268#235C3×D414yes—
269C2×D12C23×C311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—21no—
272C2×Dic6—22no—
273C2×Dic6—21no—
274C2×Dic6—22no—
275C2×Dic6—24no—
276C2×Dic6—24no—
277C2×Dic6—22no—
278C2×Dic6—22no—
279C2×Dic6—21no—
280C2×Dic6C3×D414yes—
281C2×Dic6C23×C312yes—
282C2×Dic6C23×C311yescharacteristic
283C2×Dic6C23×C312yes—
284C3×Q16—68no—
285C3×Q16—64no—
286C3×SD16—64no—
287C3×M16—22no—
288C3×M16—22no—
289C3×M16—42no—
290C2×C3×C8—22no—
291C2×C3×C8—22no—
292C2×C3×C8—22no—
293C2×C3×C8—22no—
294C2×C3×C8—42no—
295C2×C3×C8C22×D312yes—
296C2×C3×C8C22×D312yes—
297C2×C3×C8C23×C312yes—
298C2×C3×C8C23×C312yes—
299C3×C4⋊C4—32no—
300C3×C4⋊C4—64no—
301C3×C22⋊C4—61no—
302C3×C22⋊C4—64no—
303C3×C42—61no—
304#217—24no—
305#217—21no—
306C4⋊Dic3C23×C312yes—
307Dic3⋊C4—24no—
308C4×Dic3—21no—
309Dic12—28no—
310Dic12—24no—
311#204—24no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—24no—
315C22×C32#12012yes—
316C22×C32C22×D411yescharacteristic
317C2×C3×D3—22no—
318C2×C3×D3—42no—
319C32×C4—22no—
320C32×C4#12012yes—
321C32×C4C22×D411yescharacteristic
322C32×C4C22×D411yescharacteristic
323C3×Dic3—22no—
324C3×Dic3—24no—
325C3×Dic3—42no—
326C3×Dic3—42no—
3272−1+4—64no—
3282−1+4—64no—
329C2×#41—31no—
330C2×#41—32no—
331C2×#41—62no—
332C2×#41—61no—
333C2×#41C2×C3×D311yescharacteristic
334C22×Q8—31no—
335C22×Q8—31no—
336C22×Q8—32no—
337C22×Q8—61no—
338#137—64no—
339C2×Q16—34no—
340C2×Q16—32no—
341C2×Q16—64no—
342C2×SD16—32no—
343C2×M16C2×C3×D311yescharacteristic
344C22×C8C2×C3×D311yescharacteristic
345C4⋊Q8—61no—
346#124—61no—
347#123—62no—
348C22⋊Q8—34no—
349#117—31no—
350#103—32no—
351#103—34no—
352#102—32no—
353C22⋊C8C2×C3×D314yes—
354C23×C3—21no—
355C23×C3—22no—
356C23×C3—61no—
357C23×C3C2×D1212yes—
358C23×C3C2×D1211yescharacteristic
359C23×C3C2×C3×D412yes—
360C23×C3C2×C3×D411yescharacteristic
361C22×D3—21no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—34no—
365C3×Q8—32no—
366C3×Q8—42no—
367C3×Q8—68no—
368C3×Q8—64no—
369C3×Q8—62no—
370C3×Q8—61no—
371C3×Q8—62no—
372C3×Q8—62no—
373C3×Q8—122no—
374C3×D4—24no—
375C3×D4—24no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—32no—
379C3×D4—42no—
380C3×D4—44no—
381C3×D4—68no—
382C3×D4—64no—
383C3×D4—61no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—68no—
396C2×C3×C4—68no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—64no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—122no—
404C2×C3×C4C2×D1212yes—
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4D3×D412yes—
407C2×C3×C4D3×D412yes—
408C2×C3×C4C2×C3×D412yes—
409C2×C3×C4C2×C3×D411yescharacteristic
410C2×C3×C4C2×C3×D412yes—
411C2×C3×C4C2×C3×D412yes—
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C24×C311yescharacteristic
414#67—28no—
415#67—24no—
416C2×Dic3—28no—
417C2×Dic3—24no—
418C2×Dic3—21no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—42no—
423D12—21no—
424D12C2×C3×D412yes—
425C4×D3—28no—
426C4×D3—24no—
427Dic6—28no—
428Dic6—24no—
429Dic6—22no—
430Dic6—21no—
431Dic6—22no—
432Dic6—22no—
433Dic6—42no—
434Dic6C2×C3×D412yes—
435Dic6C2×C3×D414yes—
436C3×C8—22no—
437C3×C8—22no—
438C3×C8—22no—
439C3×C8—22no—
440C3×C8—42no—
441C3×C8—42no—
442C2×C32—22no—
443C2×C32—42no—
444C2×C32C2×#12011yescharacteristic
445C2×C32#57812yes—
446C3×D3—42no—
447#41—22no—
448#41—22no—
449#41—34no—
450#41—64no—
451#41—64no—
452#41—616no—
453#41—68no—
454#41—62no—
455C2×Q8—32no—
456C2×Q8—31no—
457C2×Q8—32no—
458C2×Q8—34no—
459C2×Q8—64no—
460C2×Q8—64no—
461C2×Q8—68no—
462C2×Q8—62no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—62no—
466C2×Q8—62no—
467C2×Q8—62no—
468C2×Q8C3×D1211yescharacteristic
469C2×D4—31no—
470C2×D4—62no—
471C2×D4—61no—
472C2×D4C3×D1212yes—
473C2×D4C3×D1211yescharacteristic
474C22×C4—62no—
475C22×C4—61no—
476C22×C4—62no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4C22×C3×D312yes—
480C22×C4C22×C3×D311yescharacteristic
481Q16—68no—
482Q16—64no—
483SD16—64no—
484M16—22no—
485C2×C8—22no—
486C2×C8C22×C3×D312yes—
487C2×C8C22×C3×D312yes—
488C4⋊C4—32no—
489C4⋊C4—64no—
490C22⋊C4—61no—
491C22⋊C4—64no—
492C42—61no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—24no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—44no—
504C22×C3—62no—
505C22×C3—122no—
506C22×C3#88212yes—
507C22×C3C3×#12012yes—
508C22×C3C22×D1211yescharacteristic
509C22×C3C22×C3×D411yescharacteristic
510C2×D3—22no—
511C2×D3—42no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—42no—
518C3×C4—64no—
519C3×C4—62no—
520C3×C4—122no—
521C3×C4—122no—
522C3×C4#88212yes—
523C3×C4C3×#12012yes—
524C3×C4C2×D3×D411yescharacteristic
525C3×C4C2×D3×D411yescharacteristic
526C3×C4C22×C3×D411yescharacteristic
527C3×C4C22×C3×D411yescharacteristic
528Dic3—22no—
529Dic3—24no—
530Dic3—42no—
531Dic3—42no—
532C32#301111yescharacteristic, complemented, Sylow
533C23—61no—
534C23C2×C3×D1212yes—
535C23C2×C3×D1211yescharacteristic
536Q8—22no—
537Q8—34no—
538Q8—32no—
539Q8—68no—
540Q8—64no—
541Q8—62no—
542Q8—61no—
543Q8—62no—
544Q8—62no—
545Q8—122no—
546D4—24no—
547D4—22no—
548D4—32no—
549D4—68no—
550D4—64no—
551D4—61no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—68no—
555C2×C4—68no—
556C2×C4—64no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—122no—
563C2×C4C2×C3×D1212yes—
564C2×C4C2×C3×D1211yescharacteristic
565C2×C4C3×D3×D412yes—
566C2×C4C3×D3×D412yes—
567C2×C4C23×C3×D311yescharacteristic
568C8—22no—
569C8—22no—
570C2×C3—22no—
571C2×C3—22no—
572C2×C3—21no—
573C2×C3—22no—
574C2×C3—42no—
575C2×C3—42no—
576C2×C3—42no—
577C2×C3—82no—
578C2×C3—122no—
579C2×C3C2×#88211yescharacteristic
580C2×C3#575312yes—
581C2×C3C2×C3×#12011yescharacteristic
582C2×C3C3×#57812yes—
583D3—42no—
584C22—22no—
585C22—22no—
586C22—24no—
587C22—62no—
588C22—122no—
589C22C3×#88212yes—
590C22C22×C3×D1211yescharacteristic
591C4—22no—
592C4—64no—
593C4—62no—
594C4—122no—
595C4—122no—
596C4C3×#88212yes—
597C4C2×C3×D3×D411yescharacteristic
598C4C2×C3×D3×D411yescharacteristic
599C3—21no—
600C3#7867911yescharacteristic, direct product factor
601C3C3×#301111yescharacteristic, complemented
602C2—22no—
603C2—42no—
604C2—122no—
605C2C2×C3×#88211yescharacteristic
606C2C3×#575312yes—
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#408C2
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC3×#408D3
hypocenterC3C3×#3011
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#408

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. C2×C3×#909C2semidirect
4. C22×C3×Dic12C2semidirect
5. C32×#408C2semidirect
6. C3×#5120C2semidirect
7. C3×#5113C2semidirect
8. C3×#4739C2semidirect
9. C3×#4733C2semidirect
11. #78679C3direct (N × H)
44. #5825C2×C3semidirect
45. C2×#909C2×C3semidirect
46. C22×Dic12C2×C3semidirect
52. C3×#408D3semidirect
53. C3×#408C2×C3semidirect
54. #5120C2×C3semidirect
55. #5113C2×C3semidirect
56. #4739C2×C3semidirect
57. #4733C2×C3semidirect
208. #408C3×D3semidirect
532. C32#3011semidirect
600. C3#78679direct (N × H)
601. 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
C3×#58252
C2×C3×#9092
C22×C3×Dic122
C32×#4082
C3×#51202
C3×#51132
C3×#47392
C3×#47332
C3×#30113
#786793