Finite Group Databasebeta

← C3×#78961 #11864491

Subgroups — C3×#78961 #11864491

Order 1152.

1475 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C32×#419C211yesmaximal, characteristic, complemented
6C3×#5129C211yesmaximal, characteristic, complemented
7C3×#5002C211yesmaximal, characteristic, complemented
8C3×#4809C214yesmaximal, complemented
9C3×#4808C214yesmaximal, complemented
10C3×#3011—31nomaximal
11#78961C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C3×#1007—24no—
14C3×#1007—24no—
15C2×C3×#239—21no—
16C2×C3×#239C2212yes—
17C2×C3×D3×Q8—21no—
18C2×C3×D3×Q8C2212yes—
19C2×C3×#235—22no—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C2×C32×M16C2211yescharacteristic
24C32×#117C2211yescharacteristic
25C2×C3×#216—24no—
26C2×C3×#216C2214yes—
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#909—24no—
29C2×C3×Dic12C2212yes—
30C2×C3×#204C2212yes—
31C3×#897C2214yes—
32C3×#886—22no—
33C3×#875—21no—
34C3×#869—21no—
35C32×#103C2214yes—
36C3×(C2×D3)⋊C8C2214yes—
37C3×#810C2212yes—
38C3×#809C2212yes—
39C2×C3×2−1+4—31no—
40C2×#1007C2×C311yescharacteristic
41C2×C3×#137—31no—
42C22×C3×Q16—31no—
43C3×#536—31no—
44C22×#216C2×C311yescharacteristic, complemented
45C2×#909C2×C311yescharacteristic, complemented
46#5526C2×C311yescharacteristic, complemented
47C3×#452—34no—
48C3×#451—34no—
49C3×#419—21no—
50C3×#419D311yescharacteristic, complemented
51C3×#419C2×C311yescharacteristic, complemented
52C3×#416—31no—
53C3×#408—31no—
54#5129C2×C311yescharacteristic, complemented
55#5002C2×C311yescharacteristic, complemented
56#4809C2×C314yescomplemented
57#4808C2×C314yescomplemented
58C2×C32×Q8—21no—
59C2×C32×Q8—22no—
60C2×C32×Q8D414yes—
61C2×C32×Q8C2312yes—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C2×C3×#67—21no—
65C2×C3×#67D412yes—
66C22×C3×Dic3—21no—
67C3×#239—28no—
68C3×#239—24no—
69C3×#239—24no—
70C3×D3×Q8—28no—
71C3×D3×Q8—24no—
72C3×D3×Q8—24no—
73C3×#235—216no—
74C3×#235—22no—
75C3×#235—22no—
76C3×#235—22no—
77C3×#235D414yes—
78C2×C3×D12—22no—
79C2×C3×D12D411yescharacteristic
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6—22no—
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×#216—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#3011—31noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C22×C3×Q8—21no—
113C22×C3×Q8—32no—
114C22×C3×Q8—31no—
115C22×C3×Q8—61no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C22×C311yescharacteristic
118#1007—24no—
119#1007—24no—
120C2×#239—21no—
121C2×#239C22×C312yes—
122C2×D3×Q8—21no—
123C2×D3×Q8C22×C312yes—
124C2×#235—22no—
125C2×#235C22×C311yescharacteristic
126C2×#235C22×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—31no—
137C3×C4⋊Q8—61no—
138C3×#124—61no—
139C3×#123—62no—
140C3×C22⋊Q8—34no—
141C3×#117—21no—
142C3×#117C2×D311yescharacteristic
143C3×#117C22×C311yescharacteristic
144C2×#216—24no—
145C2×#216C22×C314yes—
146C22×C3⋊C8C22×C311yescharacteristic
147#909—24no—
148C2×Dic12C22×C312yes—
149C2×#204C22×C312yes—
150#897C22×C314yes—
151#886—22no—
152#875—21no—
153#869—21no—
154C3×#103—24no—
155C3×#103—32no—
156C3×#103C2×D314yes—
157C3×#103C22×C314yes—
158C3×#102—32no—
159C3×C22⋊C8—34no—
160(C2×D3)⋊C8C22×C314yes—
161#810C22×C312yes—
162#809C22×C312yes—
163C23×C32C2×D411yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3C2×D412yes—
166C32×Q8—24no—
167C32×Q8—22no—
168C32×Q8C2×D414yes—
169C2×C32×C4—24no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2411yescharacteristic
176C3×#67—24no—
177C3×#67—24no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3C2×D412yes—
182C3×D12—28no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12C2×D412yes—
186C3×C4×D3—28no—
187C3×C4×D3—28no—
188C3×C4×D3—24no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×Dic6—28no—
192C3×Dic6—22no—
193C3×Dic6—21no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196C3×Dic6—42no—
197C3×Dic6C2×D412yes—
198C32×C8—22no—
199C3×C3⋊C8—22no—
200C2×2−1+4—31no—
201C2×#137—31no—
202C22×Q16—31no—
203#536—31no—
204#452—34no—
205#451—34no—
206#419C3×D311yescharacteristic, complemented
207#416—31no—
208#408—31no—
209C3×#41—34no—
210C3×#41—616no—
211C3×#41—64no—
212C3×#41—68no—
213C3×#41—64no—
214C3×#41—62no—
215C3×#41—62no—
216C3×#41—62no—
217C2×C3×Q8—21no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—24no—
222C2×C3×Q8—22no—
223C2×C3×Q8—31no—
224C2×C3×Q8—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—41no—
227C2×C3×Q8—42no—
228C2×C3×Q8—62no—
229C2×C3×Q8—64no—
230C2×C3×Q8—68no—
231C2×C3×Q8—64no—
232C2×C3×Q8—61no—
233C2×C3×Q8—62no—
234C2×C3×Q8—62no—
235C2×C3×Q8D1214yes—
236C2×C3×Q8C3×D414yes—
237C2×C3×Q8C22×D312yes—
238C2×C3×Q8C23×C312yes—
239C2×C3×D4—32no—
240C2×C3×D4—31no—
241C2×C3×D4—31no—
242C2×C3×D4—62no—
243C2×C3×D4—61no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—62no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C23×C311yescharacteristic
255C2×#67—21no—
256C2×#67C3×D412yes—
257C22×Dic3—21no—
258#239—28no—
259#239—24no—
260#239—24no—
261D3×Q8—28no—
262D3×Q8—24no—
263D3×Q8—24no—
264#235—216no—
265#235—22no—
266#235—22no—
267#235—22no—
268#235C3×D414yes—
269C2×D12—22no—
270C2×D12C3×D411yescharacteristic
271C2×D12C23×C311yescharacteristic
272C2×C4×D3—22no—
273C2×C4×D3—21no—
274C2×C4×D3—22no—
275C2×C4×D3C23×C312yes—
276C2×Dic6—22no—
277C2×Dic6—22no—
278C2×Dic6—22no—
279C2×Dic6—21no—
280C2×Dic6C3×D411yescharacteristic
281C2×Dic6C23×C312yes—
282C2×Dic6C23×C311yescharacteristic
283C3×Q16—64no—
284C3×Q16—68no—
285C3×SD16—64no—
286C3×M16—22no—
287C3×M16—22no—
288C3×M16—42no—
289C2×C3×C8—22no—
290C2×C3×C8—32no—
291C2×C3×C8—62no—
292C2×C3×C8C22×D312yes—
293C2×C3×C8C23×C312yes—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—64no—
296C3×C4⋊C4C22×D312yes—
297C3×C4⋊C4C23×C312yes—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—21no—
300C3×C22⋊C4—41no—
301C3×C22⋊C4—64no—
302C3×C42—21no—
303C3×C42—21no—
304C3×C42—41no—
305#216—28no—
306(C2×D3)⋊C4—24no—
307C4⋊Dic3—24no—
308C2×C3⋊C8—22no—
309C2×C3⋊C8C23×C312yes—
310Dic12—24no—
311#204—24no—
312C22×C32—22no—
313C22×C32#12012yes—
314C22×C32C22×D411yescharacteristic
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—24no—
318C2×C3×D3—42no—
319C32×C4—24no—
320C32×C4—42no—
321C32×C4#12012yes—
322C32×C4C22×D411yescharacteristic
323C32×C4C22×D411yescharacteristic
324C3×Dic3—22no—
325C3×Dic3—22no—
326C3×Dic3—42no—
3272−1+4—64no—
3282−1+4—64no—
329C2×#41—31no—
330C2×#41—32no—
331C2×#41—31no—
332C2×#41—62no—
333C2×#41—61no—
334C22×Q8—32no—
335C22×Q8—31no—
336C22×Q8—61no—
337C22×Q8C2×C3×D311yescharacteristic
338#137—64no—
339C2×Q16—34no—
340C2×Q16—32no—
341C2×Q16—64no—
342C2×SD16—32no—
343C2×M16C2×C3×D311yescharacteristic
344C22×C8—31no—
345C4⋊Q8—61no—
346#124—61no—
347#123—62no—
348C22⋊Q8—34no—
349#117C2×C3×D311yescharacteristic
350#103—32no—
351#103C2×C3×D314yes—
352#102—32no—
353C22⋊C8—34no—
354C23×C3—21no—
355C23×C3—32no—
356C23×C3—61no—
357C23×C3D3×D411yescharacteristic
358C23×C3C2×C3×D411yescharacteristic
359C22×D3—21no—
360C22×D3C2×C3×D412yes—
361C3×Q8—24no—
362C3×Q8—24no—
363C3×Q8—22no—
364C3×Q8—22no—
365C3×Q8—24no—
366C3×Q8—32no—
367C3×Q8—44no—
368C3×Q8—42no—
369C3×Q8—68no—
370C3×Q8—62no—
371C3×Q8—61no—
372C3×Q8—62no—
373C3×Q8—62no—
374C3×Q8—122no—
375C3×Q8C2×D1214yes—
376C3×Q8C2×C3×D414yes—
377C3×D4—32no—
378C3×D4—68no—
379C3×D4—64no—
380C3×D4—64no—
381C3×D4—62no—
382C3×D4—61no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—32no—
394C2×C3×C4—44no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—68no—
398C2×C3×C4—68no—
399C2×C3×C4—61no—
400C2×C3×C4—64no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—122no—
405C2×C3×C4C2×D1212yes—
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D412yes—
408C2×C3×C4C2×C3×D412yes—
409C2×C3×C4C2×C3×D411yescharacteristic
410C2×C3×C4C2×C3×D412yes—
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C24×C311yescharacteristic
413#67—24no—
414#67—24no—
415C2×Dic3—21no—
416C2×Dic3—22no—
417C2×Dic3—42no—
418C2×Dic3C2×C3×D412yes—
419D12—28no—
420D12—22no—
421D12—21no—
422D12C2×C3×D412yes—
423C4×D3—28no—
424C4×D3—28no—
425C4×D3—24no—
426C4×D3—22no—
427C4×D3—22no—
428Dic6—28no—
429Dic6—22no—
430Dic6—21no—
431Dic6—22no—
432Dic6—22no—
433Dic6—42no—
434Dic6C2×C3×D412yes—
435C3×C8—22no—
436C3×C8—22no—
437C3×C8—42no—
438C3×C8—62no—
439C3⋊C8—22no—
440C2×C32—22no—
441C2×C32C2×#12011yescharacteristic
442C2×C32#57812yes—
443C3×D3—42no—
444C3×D3—42no—
445#41—34no—
446#41—616no—
447#41—64no—
448#41—68no—
449#41—64no—
450#41—62no—
451#41—62no—
452#41—62no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—31no—
456C2×Q8—31no—
457C2×Q8—32no—
458C2×Q8—62no—
459C2×Q8—64no—
460C2×Q8—68no—
461C2×Q8—64no—
462C2×Q8—61no—
463C2×Q8—62no—
464C2×Q8—62no—
465C2×Q8C3×D1214yes—
466C2×Q8C22×C3×D312yes—
467C2×D4—32no—
468C2×D4—31no—
469C2×D4—31no—
470C2×D4—62no—
471C2×D4—61no—
472C22×C4—21no—
473C22×C4—32no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4C22×C3×D311yescharacteristic
479Q16—64no—
480Q16—68no—
481SD16—64no—
482M16—22no—
483C2×C8—32no—
484C2×C8—62no—
485C2×C8C22×C3×D312yes—
486C4⋊C4—64no—
487C4⋊C4C22×C3×D312yes—
488C22⋊C4—21no—
489C22⋊C4—64no—
490C42—21no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—42no—
496C22×C3—62no—
497C22×C3—62no—
498C22×C3—64no—
499C22×C3—122no—
500C22×C3#88212yes—
501C22×C3C3×#12012yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C22×C3×D411yescharacteristic
504C2×D3—24no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—42no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—22no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—44no—
514C3×C4—42no—
515C3×C4—42no—
516C3×C4—62no—
517C3×C4—62no—
518C3×C4—82no—
519C3×C4—122no—
520C3×C4#88212yes—
521C3×C4C3×#12012yes—
522C3×C4C22×D1211yescharacteristic
523C3×C4C2×D3×D411yescharacteristic
524C3×C4C22×C3×D411yescharacteristic
525C3×C4C22×C3×D411yescharacteristic
526Dic3—22no—
527Dic3—22no—
528Dic3—42no—
529C32#301111yescharacteristic, complemented, Sylow
530C23—32no—
531C23—61no—
532C23C3×D3×D411yescharacteristic
533Q8—24no—
534Q8—22no—
535Q8—32no—
536Q8—68no—
537Q8—62no—
538Q8—61no—
539Q8—62no—
540Q8—62no—
541Q8—122no—
542Q8C2×C3×D1214yes—
543D4—32no—
544D4—68no—
545D4—64no—
546D4—64no—
547D4—62no—
548D4—61no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—32no—
553C2×C4—68no—
554C2×C4—68no—
555C2×C4—61no—
556C2×C4—64no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—122no—
561C2×C4C2×C3×D1212yes—
562C2×C4C3×D3×D411yescharacteristic
563C2×C4C3×D3×D412yes—
564C2×C4C23×C3×D311yescharacteristic
565C8—22no—
566C8—62no—
567C2×C3—22no—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—42no—
572C2×C3—122no—
573C2×C3—122no—
574C2×C3C2×#88211yescharacteristic
575C2×C3#577912yes—
576C2×C3C2×C3×#12011yescharacteristic
577C2×C3C3×#57812yes—
578D3—42no—
579D3—42no—
580C22—22no—
581C22—62no—
582C22—62no—
583C22—64no—
584C22—122no—
585C22C3×#88212yes—
586C22C2×C3×D3×D411yescharacteristic
587C4—24no—
588C4—42no—
589C4—62no—
590C4—62no—
591C4—122no—
592C4C3×#88212yes—
593C4C22×C3×D1211yescharacteristic
594C4C2×C3×D3×D411yescharacteristic
595C3—21no—
596C3#7896111yescharacteristic, direct product factor
597C3C3×#301111yescharacteristic, complemented
598C2—22no—
599C2—122no—
600C2—122no—
601C2C2×C3×#88211yescharacteristic
602C2C3×#577912yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#419C2
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
hypercenterC3×#419D3
hypocenterC3C3×#3011
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5526C2semidirect
5. C32×#419C2semidirect
6. C3×#5129C2semidirect
7. C3×#5002C2semidirect
8. C3×#4809C2semidirect
9. C3×#4808C2semidirect
11. #78961C3direct (N × H)
44. C22×#216C2×C3semidirect
45. C2×#909C2×C3semidirect
46. #5526C2×C3semidirect
50. C3×#419D3semidirect
51. C3×#419C2×C3semidirect
54. #5129C2×C3semidirect
55. #5002C2×C3semidirect
56. #4809C2×C3semidirect
57. #4808C2×C3semidirect
206. #419C3×D3semidirect
529. C32#3011semidirect
596. C3#78961direct (N × H)
597. C3C3×#3011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C3×#2162
C2×C3×#9092
C3×#55262
C32×#4192
C3×#51292
C3×#50022
C3×#48092
C3×#48082
C3×#30113
#789613