Finite Group Databasebeta

← C3×#79202 #11860573

Subgroups — C3×#79202 #11860573

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C3×#5504C211yesmaximal, characteristic
4C32×#428C211yesmaximal, characteristic, complemented
5C3×#5122C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4889C212yesmaximal, complemented
9C3×#4873C212yesmaximal, complemented
10C3×#4853C212yesmaximal, complemented
11C3×#4852C212yesmaximal, complemented
12C3×#2947—31nomaximal
13#79202C311yesmaximal, characteristic, direct product factor
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C3×C4×#67—22no—
20C3×#926C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#909C418yescomplemented
23C2×C3×Dic12C2212yes—
24C2×C3×#204C2212yes—
25C3×#893C2212yes—
26C3×#892—21no—
27C3×D3×C4⋊C4—21no—
28C3×#887C2212yes—
29C3×#887C2212yes—
30C3×#887C2212yes—
31C3×#877—22no—
32C3×C4×Dic6—21no—
33C3×C4×Dic6—21no—
34C32×#107C2212yes—
35C32×#106C2212yes—
36C3×#815C2212yes—
37C3×C8×Dic3C2212yes—
38C3×#810C2212yes—
39C3×#810C2212yes—
40C3×#810C2211yescharacteristic
41C3×#810C2211yescharacteristic
42C3×#809C2211yescharacteristic
43C3×#809C2211yescharacteristic
44C2×C3×#137—31no—
45C3×#520—31no—
46C3×#519—31no—
47C2×#909C2×C311yescharacteristic
48#5516C2×C311yescharacteristic, complemented
49#5504C2×C311yescharacteristic
50C3×#441—32no—
51C3×#440—32no—
52C3×C4×Q16—32no—
53C3×C4×SD16—32no—
54C3×#428—21no—
55C3×#428D311yescharacteristic, complemented
56C3×#428C2×C311yescharacteristic, complemented
57C3×#416—31no—
58C2×C3×#103—31no—
59C3×#405—31no—
60#5122C2×C311yescharacteristic, complemented
61#5002C2×C311yescharacteristic
62C2×#810C2×C311yescharacteristic, complemented
63#4889C2×C312yescomplemented
64#4873C2×C312yescomplemented
65#4853C2×C312yescomplemented
66#4852C2×C312yescomplemented
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—21no—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235C2×C414yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2×C414yescomplemented
79C2×C3×Dic6C2312yes—
80C2×C3×Dic6C2311yescharacteristic
81C32×M16C2×C414yescomplemented
82C2×C32×C8C2312yes—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2312yes—
87C32×C22⋊C4—21no—
88C32×C42—21no—
89C3×#217D412yes—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3D411yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3C2312yes—
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103C3×Dic12C2×C418yescomplemented
104C3×#204C2×C418yescomplemented
105#2947—31noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C22×C311yescharacteristic
109C22×Dic6C22×C311yescharacteristic
110C3×#137—38no—
111C2×C3×Q16—32no—
112C2×C3×SD16—32no—
113C2×C3×M16—21no—
114C2×C3×M16C2×D311yescharacteristic
115C2×C3×M16C22×C311yescharacteristic
116C22×C3×C8—31no—
117C3×C4×Q8—32no—
118C3×C4×Q8—32no—
119C3×C4×Q8—32no—
120C3×C4×Q8—61no—
121C3×C4×Q8—61no—
122C3×C4×D4—32no—
123C3×C4×D4—62no—
124C3×#117—21no—
125C3×#117—31no—
126C3×#117—62no—
127C3×#117—61no—
128C3×#117C2×D311yescharacteristic
129C3×#117C22×C311yescharacteristic
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—61no—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C22×C311yescharacteristic
134C4×#67—22no—
135#926C22×C311yescharacteristic
136C22×C3⋊C8C22×C311yescharacteristic
137#909C3×C418yescomplemented
138C2×Dic12C22×C312yes—
139C2×#204C22×C312yes—
140#893C22×C312yes—
141#892—21no—
142D3×C4⋊C4—21no—
143#887C22×C312yes—
144#887C22×C312yes—
145#887C22×C312yes—
146#877—22no—
147C4×Dic6—21no—
148C4×Dic6—21no—
149C3×#107—22no—
150C3×#107C2×D312yes—
151C3×#107C22×C312yes—
152C3×#106—22no—
153C3×#106C2×D312yes—
154C3×#106C22×C312yes—
155C3×#103—32no—
156C3×#103—32no—
157C3×#103—31no—
158C3×#103—31no—
159C3×#102—31no—
160C3×#102—31no—
161C3×#97—32no—
162C3×C4×C8—32no—
163#815C22×C312yes—
164C8×Dic3C22×C312yes—
165#810C22×C311yescharacteristic
166#810C22×C312yes—
167#810C22×C312yes—
168#810C22×C311yescharacteristic
169#809C22×C311yescharacteristic
170#809C22×C311yescharacteristic
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—81no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4C2411yescharacteristic
181C3×#67—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×C4×D3—24no—
190C3×C4×D3—82no—
191C3×Dic6—24no—
192C3×Dic6—22no—
193C3×Dic6—21no—
194C3×Dic6C22×C414yes—
195C3×Dic6C22×C412yes—
196C32×C8C22×C414yes—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C2×#137—31no—
200#520—31no—
201#519—31no—
202#441—32no—
203#440—32no—
204C4×Q16—32no—
205C4×SD16—32no—
206#428C3×D311yescharacteristic, complemented
207#416—31no—
208C2×#103—31no—
209#405—31no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—61no—
216C2×C3×Q8—62no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—41no—
223C22×C3×C4—62no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C23×C311yescharacteristic
228C2×#67—21no—
229C22×Dic3—21no—
230#235—22no—
231#235C2×C3×C414yes—
232C2×D12C23×C311yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—22no—
235C2×Dic6—21no—
236C2×Dic6—22no—
237C2×Dic6C2×C3×C414yescomplemented
238C2×Dic6C23×C312yes—
239C2×Dic6C23×C311yescharacteristic
240C3×Q16—38no—
241C3×SD16—38no—
242C3×M16—24no—
243C3×M16C4×D314yescomplemented
244C3×M16C2×C3×C414yescomplemented
245C2×C3×C8—22no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C2×C3×C8—62no—
249C2×C3×C8C22×D312yes—
250C2×C3×C8C23×C312yes—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—41no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—62no—
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D312yes—
265C3×C4⋊C4C23×C311yescharacteristic
266C3×C4⋊C4C23×C311yescharacteristic
267C3×C4⋊C4C23×C312yes—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—32no—
271C3×C22⋊C4—41no—
272C3×C22⋊C4—62no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—32no—
276C3×C42—41no—
277C3×C42—62no—
278C3×C42—62no—
279C3×C42—62no—
280#217C3×D412yes—
281(C2×D3)⋊C4—22no—
282C4⋊Dic3C3×D411yescharacteristic
283C4⋊Dic3C3×D411yescharacteristic
284Dic3⋊C4—22no—
285Dic3⋊C4—22no—
286Dic3⋊C4—22no—
287C4×Dic3—22no—
288C4×Dic3—22no—
289C4×Dic3—22no—
290C4×Dic3C23×C312yes—
291C2×C3⋊C8—22no—
292C2×C3⋊C8C23×C311yescharacteristic
293C2×C3⋊C8C23×C311yescharacteristic
294Dic12C2×C3×C418yescomplemented
295#204C2×C3×C418yescomplemented
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C4×D412yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C32×C4—42no—
304C32×C4—41no—
305C32×C4—41no—
306C32×C4C4×D412yes—
307C32×C4C23×C411yescharacteristic
308C32×C4C2×#4111yescharacteristic
309C3×Dic3—24no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C2×#41—31no—
314C22×Q8—31no—
315#137—38no—
316C2×Q16—32no—
317C2×SD16—32no—
318C2×M16C2×C3×D311yescharacteristic
319C22×C8—31no—
320C4×Q8—32no—
321C4×Q8—32no—
322C4×Q8—32no—
323C4×Q8—61no—
324C4×Q8—61no—
325C4×D4—32no—
326C4×D4—62no—
327#117—31no—
328#117—62no—
329#117—61no—
330#117C2×C3×D311yescharacteristic
331C2×C4⋊C4—61no—
332C2×C4⋊C4C2×C3×D311yescharacteristic
333#107C2×C3×D312yes—
334#106C2×C3×D312yes—
335#103—32no—
336#103—32no—
337#103—31no—
338#103—31no—
339#102—31no—
340#102—31no—
341#97—32no—
342C4×C8—32no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3D3×D411yescharacteristic
346C23×C3C2×C3×D411yescharacteristic
347C22×D3—21no—
348C3×Q8—34no—
349C3×Q8—32no—
350C3×Q8—64no—
351C3×Q8—62no—
352C3×Q8—61no—
353C3×D4—32no—
354C3×D4—64no—
355C3×D4—61no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—42no—
371C2×C3×C4—64no—
372C2×C3×C4—61no—
373C2×C3×C4—62no—
374C2×C3×C4—64no—
375C2×C3×C4—81no—
376C2×C3×C4—81no—
377C2×C3×C4—82no—
378C2×C3×C4—242no—
379C2×C3×C4C2×C4×D312yes—
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4#23912yes—
382C2×C3×C4C22×C3×C412yes—
383C2×C3×C4C2×C3×D411yescharacteristic
384C2×C3×C4C3×#4112yes—
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C24×C311yescharacteristic
387#67—24no—
388C2×Dic3—24no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3C2×C3×D412yes—
392C2×Dic3C2×C3×D412yes—
393D12—21no—
394D12C22×C3×C412yes—
395C4×D3—24no—
396C4×D3—82no—
397Dic6—24no—
398Dic6—22no—
399Dic6—21no—
400Dic6C22×C3×C414yes—
401Dic6C22×C3×C412yes—
402C3×C8—24no—
403C3×C8—61no—
404C3×C8—61no—
405C3×C8C2×C4×D314yes—
406C3×C8C22×C3×C414yes—
407C3⋊C8—21no—
408C3⋊C8—21no—
409C2×C32—22no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32#57711yescharacteristic
412C2×C32#57811yescharacteristic
413C3×D3—42no—
414#41—34no—
415#41—62no—
416C2×Q8—32no—
417C2×Q8—31no—
418C2×Q8—34no—
419C2×Q8—61no—
420C2×Q8—62no—
421C2×D4—31no—
422C2×D4—61no—
423C22×C4—21no—
424C22×C4—62no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4C22×C3×D311yescharacteristic
428Q16—38no—
429SD16—38no—
430M16C3×C4×D314yescomplemented
431C2×C8—31no—
432C2×C8—31no—
433C2×C8—62no—
434C2×C8C22×C3×D312yes—
435C4⋊C4—21no—
436C4⋊C4—31no—
437C4⋊C4—31no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—62no—
441C4⋊C4C22×C3×D311yescharacteristic
442C4⋊C4C22×C3×D311yescharacteristic
443C4⋊C4C22×C3×D312yes—
444C22⋊C4—21no—
445C22⋊C4—32no—
446C22⋊C4—62no—
447C42—21no—
448C42—32no—
449C42—62no—
450C42—62no—
451C42—62no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3#89312yes—
464C22×C3C3×C4×D412yes—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C22×C3×D411yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C3×C4—22no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—42no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—42no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—62no—
480C3×C4—64no—
481C3×C4—62no—
482C3×C4—62no—
483C3×C4—82no—
484C3×C4—81no—
485C3×C4—81no—
486C3×C4#89312yes—
487C3×C4C3×C4×D412yes—
488C3×C4C22×C4×D311yescharacteristic
489C3×C4C2×#23911yescharacteristic
490C3×C4C23×C3×C411yescharacteristic
491C3×C4C2×C3×#4111yescharacteristic
492Dic3—22no—
493Dic3—22no—
494Dic3—24no—
495Dic3—22no—
496C32#294711yescharacteristic, complemented, Sylow
497C23—61no—
498C23C3×D3×D411yescharacteristic
499Q8—34no—
500Q8—32no—
501Q8—64no—
502Q8—62no—
503Q8—61no—
504D4—32no—
505D4—64no—
506D4—61no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—32no—
511C2×C4—32no—
512C2×C4—64no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—64no—
516C2×C4—81no—
517C2×C4—242no—
518C2×C4C2×C3×C4×D312yes—
519C2×C4C3×D3×D411yescharacteristic
520C2×C4C3×#23912yes—
521C2×C4C23×C3×D311yescharacteristic
522C8—61no—
523C8—61no—
524C8C2×C3×C4×D314yes—
525C2×C3—22no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—42no—
531C2×C3—122no—
532C2×C3C2×#89311yescharacteristic
533C2×C3#577511yescharacteristic
534C2×C3#577911yescharacteristic
535C2×C3C2×C3×C4×D411yescharacteristic
536C2×C3C3×#57711yescharacteristic
537C2×C3C3×#57811yescharacteristic
538D3—42no—
539C22—21no—
540C22—21no—
541C22—62no—
542C22—121no—
543C22—121no—
544C22C3×#89312yes—
545C22C2×C3×D3×D411yescharacteristic
546C4—42no—
547C4—41no—
548C4—41no—
549C4—62no—
550C4—64no—
551C4—62no—
552C4—62no—
553C4C3×#89312yes—
554C4C22×C3×C4×D311yescharacteristic
555C4C2×C3×#23911yescharacteristic
556C3—21no—
557C3#7920211yescharacteristic, direct product factor
558C3C3×#294711yescharacteristic, complemented
559C2—22no—
560C2—122no—
561C2C2×C3×#89311yescharacteristic
562C2C3×#577511yescharacteristic
563C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#428D3
hypocenterC3C3×#2947
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
4. C32×#428C2semidirect
5. C3×#5122C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4889C2semidirect
9. C3×#4873C2semidirect
10. C3×#4853C2semidirect
11. C3×#4852C2semidirect
13. #79202C3direct (N × H)
22. C3×#909C4semidirect
48. #5516C2×C3semidirect
55. C3×#428D3semidirect
56. C3×#428C2×C3semidirect
60. #5122C2×C3semidirect
62. C2×#810C2×C3semidirect
63. #4889C2×C3semidirect
64. #4873C2×C3semidirect
65. #4853C2×C3semidirect
66. #4852C2×C3semidirect
78. C2×C3×Dic6C2×C4semidirect
81. C32×M16C2×C4semidirect
103. C3×Dic12C2×C4semidirect
104. C3×#204C2×C4semidirect
137. #909C3×C4semidirect
206. #428C3×D3semidirect
237. C2×Dic6C2×C3×C4semidirect
243. C3×M16C4×D3semidirect
244. C3×M16C2×C3×C4semidirect
294. Dic12C2×C3×C4semidirect
295. #204C2×C3×C4semidirect
430. M16C3×C4×D3semidirect
496. C32#2947semidirect
557. C3#79202direct (N × H)
558. C3C3×#2947semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C3×#55162
C3×#55042
C32×#4282
C3×#51222
C3×#50022
C2×C3×#8102
C3×#48892
C3×#48732
C3×#48532
C3×#48522
C3×#29473
#792023