Finite Group Databasebeta

← C3×#68677 #11792592

Subgroups — C3×#68677 #11792592

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic
3C2×C3×#875C211yesmaximal, characteristic
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C3×#4929C211yesmaximal, characteristic, complemented
7C32×#336C211yesmaximal, characteristic, complemented
8C3×#2015—31nomaximal
9#68677C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic12—22no—
19C2×C3×Dic12—22no—
20C2×C3×Dic12—22no—
21C2×C3×#204—22no—
22C2×C3×#204—22no—
23C2×C3×#204—22no—
24C3×#875—22no—
25C3×#875—22no—
26C3×C3⋊#95—22no—
27C3×#821—22no—
28C3×#816—22no—
29C22×C3×Q16—31no—
30C22×C3×SD16—31no—
31C2×C3×#124—31no—
32C22×Dic12C2×C311yescharacteristic, complemented
33C22×#204C2×C311yescharacteristic
34C2×#875C2×C311yescharacteristic
35C2×C3×#103—31no—
36C2×C3×#102—31no—
37C3×#391—31no—
38C2×#821C2×C311yescharacteristic
39C2×#816C2×C311yescharacteristic, complemented
40#4929C2×C311yescharacteristic, complemented
41C3×#336—21no—
42C3×#336D311yescharacteristic, complemented
43C3×#336C2×C311yescharacteristic, complemented
44C23×C3×D3—21no—
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D412yes—
67C2×C3×Dic6D412yes—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8—21no—
71C2×C32×C8—21no—
72C2×C32×C8D412yes—
73C2×C32×C8D412yes—
74C32×C42—21no—
75C32×C42—21no—
76C3×(C2×D3)⋊C4—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×Dic12—28no—
80C3×#204—28no—
81#2015—31noSylow
82C22×C3×Q8—31no—
83C22×C3×Q8—31no—
84C22×C3×D4—31no—
85C22×D12C22×C311yescharacteristic
86C22×Dic6C22×C311yescharacteristic
87C22×Dic6C22×C311yescharacteristic
88C2×C3×Q16—62no—
89C2×C3×Q16—62no—
90C2×C3×Q16—62no—
91C2×C3×SD16—62no—
92C2×C3×SD16—62no—
93C2×C3×SD16—62no—
94C22×C3×C8—21no—
95C22×C3×C8—21no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C22×C311yescharacteristic
99C22×C3×C8C22×C311yescharacteristic
100C3×#124—62no—
101C3×#124—62no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—62no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C22×C311yescharacteristic
107C2×(C2×D3)⋊C4—22no—
108C2×C4⋊Dic3C22×C311yescharacteristic
109C2×Dic12—22no—
110C2×Dic12—22no—
111C2×Dic12—22no—
112C2×#204—22no—
113C2×#204—22no—
114C2×#204—22no—
115#875—22no—
116#875—22no—
117C3×#103—62no—
118C3×#102—62no—
119C3×#95—62no—
120C3⋊#95—22no—
121#821—22no—
122#816—22no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—42no—
128C22×C3×D3—42no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—42no—
146C3×D12—22no—
147C3×D12—22no—
148C3×D12—41no—
149C3×D12—41no—
150C3×Dic6—22no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—41no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C3×Dic6—41no—
158C32×C8—22no—
159C32×C8—22no—
160C22×Q16—31no—
161C22×SD16—31no—
162C2×#124—31no—
163C2×#103—31no—
164C2×#102—31no—
165#391—31no—
166#336C3×D311yescharacteristic, complemented
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×Q8—32no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4D1212yes—
193C22×C3×C4C3×D412yes—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C23×C311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12C3×D412yes—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6C3×D412yes—
216C2×Dic6C3×D412yes—
217C3×Q16—68no—
218C3×SD16—68no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—41no—
230C2×C3×C8—41no—
231C2×C3×C8—41no—
232C2×C3×C8—41no—
233C2×C3×C8D1212yes—
234C2×C3×C8D1212yes—
235C2×C3×C8C3×D412yes—
236C2×C3×C8C3×D412yes—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C22⋊C4—68no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—41no—
245C3×C42—41no—
246(C2×D3)⋊C4—28no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249Dic12—28no—
250#204—28no—
251C22×C32#12011yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32#12711yescharacteristic
254C22×C32#13512yes—
255C22×C32#13712yes—
256C2×C3×D3—42no—
257C2×C3×D3—44no—
258C2×C3×D3—82no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4—42no—
262C32×C4#12011yescharacteristic
263C32×C4#12011yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4#12111yescharacteristic
266C3×Dic3—42no—
267C3×Dic3—42no—
268C3×Dic3—81no—
269C22×Q8—31no—
270C22×Q8—31no—
271C22×D4—31no—
272C2×Q16—62no—
273C2×Q16—62no—
274C2×Q16—62no—
275C2×SD16—62no—
276C2×SD16—62no—
277C2×SD16—62no—
278C22×C8C2×C3×D311yescharacteristic
279C22×C8C2×C3×D311yescharacteristic
280#124—62no—
281#124—62no—
282C2×C4⋊C4—31no—
283C2×C22⋊C4—62no—
284C2×C42C2×C3×D311yescharacteristic
285#103—62no—
286#102—62no—
287#95—62no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—122no—
293C23×C3—122no—
294C23×C3C2×D1211yescharacteristic
295C23×C3C2×C3×D411yescharacteristic
296C22×D3—22no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—42no—
300C22×D3—42no—
301C3×Q8—62no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—121no—
306C3×Q8—121no—
307C3×Q8—121no—
308C3×Q8—121no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—122no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4C2×C3×D411yescharacteristic
343C2×C3×C4C2×C3×D411yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C2×C3×D411yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C3×#4111yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—42no—
356D12—22no—
357D12—22no—
358D12—41no—
359D12—41no—
360Dic6—22no—
361Dic6—22no—
362Dic6—22no—
363Dic6—22no—
364Dic6—41no—
365Dic6—41no—
366Dic6—41no—
367Dic6—41no—
368C3×C8—22no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—22no—
372C3×C8—42no—
373C3×C8—42no—
374C2×C32#39211yescharacteristic
375C2×C32#45212yes—
376C2×C32#46412yes—
377C2×C32#49511yescharacteristic
378C2×C32#49711yescharacteristic
379C3×D3—82no—
380C24—61no—
381C2×Q8—32no—
382C2×Q8—32no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×D4—32no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4C3×D1212yes—
403C22×C4C22×C3×D311yescharacteristic
404Q16—68no—
405SD16—68no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8C3×D1212yes—
411C2×C8C3×D1212yes—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C22⋊C4—68no—
415C42—21no—
416C42—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—122no—
423C22×C3—124no—
424C22×C3—241no—
425C22×C3—241no—
426C22×C3—242no—
427C22×C3#87411yescharacteristic
428C22×C3#88211yescharacteristic
429C22×C3#89511yescharacteristic
430C22×C3#90412yes—
431C22×C3#90912yes—
432C22×C3C3×#12011yescharacteristic
433C22×C3C3×#12111yescharacteristic
434C22×C3C3×#12711yescharacteristic
435C22×C3C3×#13512yes—
436C22×C3C3×#13712yes—
437C2×D3—42no—
438C2×D3—44no—
439C2×D3—82no—
440C2×D3—81no—
441C2×D3—81no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—44no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—122no—
450C3×C4—122no—
451C3×C4—241no—
452C3×C4#88211yescharacteristic
453C3×C4#88211yescharacteristic
454C3×C4#89511yescharacteristic
455C3×C4#89511yescharacteristic
456C3×C4C3×#12011yescharacteristic
457C3×C4C3×#12011yescharacteristic
458C3×C4C3×#12111yescharacteristic
459C3×C4C3×#12111yescharacteristic
460Dic3—42no—
461Dic3—42no—
462Dic3—81no—
463C32#201511yescharacteristic, complemented, Sylow
464C23—62no—
465C23—121no—
466C23—122no—
467C23—122no—
468C23—121no—
469C23C2×C3×D1211yescharacteristic
470Q8—62no—
471Q8—62no—
472Q8—62no—
473Q8—62no—
474Q8—121no—
475Q8—121no—
476Q8—121no—
477Q8—121no—
478D4—62no—
479D4—62no—
480D4—121no—
481D4—121no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—122no—
492C2×C4—121no—
493C2×C4C2×C3×D1211yescharacteristic
494C2×C4C2×C3×D1211yescharacteristic
495C2×C4C3×D3×D411yescharacteristic
496C2×C4C3×D3×D411yescharacteristic
497C2×C4C3×D3×D411yescharacteristic
498C2×C4C3×#23911yescharacteristic
499C8—22no—
500C8—22no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—22no—
505C2×C3—22no—
506C2×C3—242no—
507C2×C3#467111yescharacteristic
508C2×C3#469611yescharacteristic
509C2×C3#471511yescharacteristic
510C2×C3#473312yes—
511C2×C3#484512yes—
512C2×C3C3×#39211yescharacteristic
513C2×C3C3×#45212yes—
514C2×C3C3×#46412yes—
515C2×C3C3×#49511yescharacteristic
516C2×C3C3×#49711yescharacteristic
517D3—82no—
518C22—122no—
519C22—124no—
520C22—241no—
521C22—241no—
522C22—242no—
523C22C3×#87411yescharacteristic
524C22C3×#88211yescharacteristic
525C22C3×#89511yescharacteristic
526C22C3×#90412yes—
527C22C3×#90912yes—
528C4—42no—
529C4—122no—
530C4—122no—
531C4—241no—
532C4C3×#88211yescharacteristic
533C4C3×#88211yescharacteristic
534C4C3×#89511yescharacteristic
535C4C3×#89511yescharacteristic
536C3—21no—
537C3#6867711yescharacteristic, direct product factor
538C3C3×#201511yescharacteristic, complemented
539C2—242no—
540C2C3×#467111yescharacteristic
541C2C3×#469611yescharacteristic
542C2C3×#471511yescharacteristic
543C2C3×#473312yes—
544C2C3×#484512yes—
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#336C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#336D3
hypocenterC3C3×#2015
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#336

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic12C2semidirect
5. C2×C3×#816C2semidirect
6. C3×#4929C2semidirect
7. C32×#336C2semidirect
9. #68677C3direct (N × H)
32. C22×Dic12C2×C3semidirect
39. C2×#816C2×C3semidirect
40. #4929C2×C3semidirect
42. C3×#336D3semidirect
43. C3×#336C2×C3semidirect
166. #336C3×D3semidirect
463. C32#2015semidirect
537. C3#68677direct (N × H)
538. C3C3×#2015semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C22×C3×#2042
C2×C3×#8752
C2×C3×#8212
C2×C3×#8162
C3×#49292
C32×#3362
C3×#20153
#686773