Finite Group Databasebeta

← C3×#79625 #11895919

Subgroups — C3×#79625 #11895919

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5570C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5163C212yesmaximal, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6C3×#5007C211yesmaximal, characteristic, complemented
7C3×#4871C212yesmaximal, complemented
8C3×#4817C212yesmaximal, complemented
9C3×#4764C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3368—31nomaximal
13#79625C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C2×C32×SD16C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C3×#940C2212yes—
21C3×#930—21no—
22C3×#893C2212yes—
23C3×#890—22no—
24C3×#890C2212yes—
25C3×#884—22no—
26C3×#874C2211yescharacteristic
27C3×#869—21no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#832C2212yes—
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5570C2×C311yescharacteristic, complemented
46#5553C2×C311yescharacteristic
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#474—31no—
51C3×#460—32no—
52C3×#460—31no—
53C3×#446—31no—
54C3×#440—32no—
55C3×C4×SD16—21no—
56C3×C4×SD16D311yescharacteristic, complemented
57C3×C4×SD16C2×C311yescharacteristic, complemented
58#5163C2×C312yescomplemented
59#5027C2×C311yescharacteristic, complemented
60#5007C2×C311yescharacteristic, complemented
61#4871C2×C312yescomplemented
62#4817C2×C312yescomplemented
63#4764C2×C312yescomplemented
64#4694C2×C311yescharacteristic, complemented
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6D411yescharacteristic
78C32×SD16—22no—
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42—21no—
86C32×C42C2311yescharacteristic
87C3×#215—24no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4D412yes—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3368—31noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×SD16—21no—
103C2×C3×SD16—32no—
104C2×C3×SD16C2×D311yescharacteristic
105C2×C3×SD16C22×C311yescharacteristic
106C3×C4⋊Q8—31no—
107C3×C4⋊Q8—61no—
108C3×#127—32no—
109C3×#127—31no—
110C3×#125—32no—
111C3×#125—62no—
112C3×#121—62no—
113C3×#121—61no—
114C3×C4×Q8—21no—
115C3×C4×Q8—31no—
116C3×C4×Q8—32no—
117C3×C4×Q8—61no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C22×C311yescharacteristic
120C3×C4×D4—21no—
121C3×C4×D4—32no—
122C3×C4×D4C2×D311yescharacteristic
123C3×C4×D4C22×C311yescharacteristic
124Q8×Dic3C22×C312yes—
125C2×#215C22×C312yes—
126#940C22×C312yes—
127#930—21no—
128#893C22×C312yes—
129#890—22no—
130#890C22×C312yes—
131#884—22no—
132#874C22×C311yescharacteristic
133#869—21no—
134#869C22×C311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C22×C311yescharacteristic
137C3×#107—32no—
138C3×#106—21no—
139C3×#106C2×D311yescharacteristic
140C3×#106C22×C311yescharacteristic
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×#103—21no—
144C3×#103C2×D311yescharacteristic
145C3×#103C22×C311yescharacteristic
146C3×#102—21no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102—32no—
151C3×#102C2×D311yescharacteristic
152C3×#102C22×C311yescharacteristic
153C3×#97—32no—
154C3×C4×C8—21no—
155C3×C4×C8C2×D311yescharacteristic
156C3×C4×C8C22×C311yescharacteristic
157#832C22×C312yes—
158#821C22×C312yes—
159#821C22×C312yes—
160#815C22×C312yes—
161Dic3⋊C8C22×C312yes—
162#809C22×C312yes—
163#807C22×C312yes—
164C4⋊(C3⋊C8)C22×C311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—22no—
167C32×Q8—21no—
168C32×Q8#4112yescomplemented
169C32×D4—21no—
170C32×D4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—42no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C3×#67—44no—
179C3×#67—82no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—81no—
187C3×C4×D3—44no—
188C3×Dic6—22no—
189C3×Dic6—42no—
190C32×C8—21no—
191C32×C8—21no—
192C3×C3⋊C8—22no—
193#557—31no—
194#550—31no—
195#490—32no—
196#486—31no—
197#478—32no—
198#474—31no—
199#460—32no—
200#460—31no—
201#446—31no—
202#440—32no—
203C4×SD16C3×D311yescharacteristic, complemented
204C3×#41—124no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×Q8C23×C311yescharacteristic
210C2×C3×D4—21no—
211C2×C3×D4—32no—
212C2×C3×D4—62no—
213C2×C3×D4—62no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4C22×D311yescharacteristic
217C2×C3×D4C23×C311yescharacteristic
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—41no—
221C22×C3×C4—62no—
222C2×#67—22no—
223C2×#67—22no—
224#235—44no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12C23×C312yes—
228C2×C4×D3—22no—
229C2×Dic6—21no—
230C2×Dic6C3×D411yescharacteristic
231C3×SD16—24no—
232C3×SD16—22no—
233C3×SD16—22no—
234C3×SD16—64no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C23×C311yescharacteristic
241C2×C3×C8C23×C311yescharacteristic
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C4⋊C4C23×C311yescharacteristic
257C3×C4⋊C4C23×C311yescharacteristic
258C3×C22⋊C4—21no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—41no—
261C3×C22⋊C4—62no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—32no—
266C3×C42—41no—
267C3×C42—62no—
268C3×C42C22×D311yescharacteristic
269C3×C42C23×C311yescharacteristic
270#215—24no—
271(C2×D3)⋊C4—22no—
272C4⋊Dic3—21no—
273C4⋊Dic3—22no—
274C4⋊Dic3—22no—
275C4⋊Dic3C3×D411yescharacteristic
276C4⋊Dic3C23×C312yes—
277Dic3⋊C4—22no—
278Dic3⋊C4C3×D412yes—
279C4×Dic3—22no—
280C4×Dic3C23×C312yes—
281C2×C3⋊C8C23×C312yes—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—22no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4AGL(1,ℤ/8)12yes—
294C32×C4C2×#4111yescharacteristic
295C32×C42−1+411yescharacteristic
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C2×#41—61no—
300C2×SD16—32no—
301C2×SD16C2×C3×D311yescharacteristic
302C4⋊Q8—31no—
303C4⋊Q8—61no—
304#127—32no—
305#127—31no—
306#125—32no—
307#125—62no—
308#121—62no—
309#121—61no—
310C4×Q8—31no—
311C4×Q8—32no—
312C4×Q8—61no—
313C4×Q8C2×C3×D311yescharacteristic
314C4×D4—32no—
315C4×D4C2×C3×D311yescharacteristic
316#107—32no—
317#106C2×C3×D311yescharacteristic
318C4⋊C8—32no—
319C4⋊C8—31no—
320#103C2×C3×D311yescharacteristic
321#102—32no—
322#102—32no—
323#102—32no—
324#102—32no—
325#102C2×C3×D311yescharacteristic
326#97—32no—
327C4×C8C2×C3×D311yescharacteristic
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—41no—
331C23×C3—62no—
332C22×D3—22no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—22no—
336C3×Q8—41no—
337C3×Q8—62no—
338C3×Q8—122no—
339C3×Q8#23512yescomplemented
340C3×Q8C3×#4112yescomplemented
341C3×D4—22no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—41no—
347C3×D4—62no—
348C3×D4—62no—
349C3×D4—124no—
350C3×D4—122no—
351C3×D4—241no—
352C3×D4—242no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—62no—
370C2×C3×C4—82no—
371C2×C3×C4—124no—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C2×C3×D411yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C24×C311yescharacteristic
378#67—44no—
379#67—82no—
380C2×Dic3—22no—
381C2×Dic3C2×C3×D412yes—
382C2×Dic3C2×C3×D412yes—
383D12—22no—
384D12—22no—
385D12—42no—
386D12—81no—
387C4×D3—44no—
388Dic6—22no—
389Dic6—42no—
390C3×C8—22no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—41no—
396C3×C8—62no—
397C3⋊C8—22no—
398C2×C32—81no—
399C2×C32#54811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32#57711yescharacteristic
402C3×D3—82no—
403#41—124no—
404C2×Q8—31no—
405C2×Q8—61no—
406C2×Q8C22×C3×D311yescharacteristic
407C2×D4—32no—
408C2×D4—62no—
409C2×D4—62no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4C22×C3×D311yescharacteristic
413C22×C4—21no—
414C22×C4—62no—
415SD16—22no—
416SD16—64no—
417C2×C8—32no—
418C2×C8C22×C3×D311yescharacteristic
419C2×C8C22×C3×D311yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—31no—
422C4⋊C4—32no—
423C4⋊C4—32no—
424C4⋊C4—62no—
425C4⋊C4—62no—
426C4⋊C4—62no—
427C4⋊C4—61no—
428C4⋊C4C22×C3×D311yescharacteristic
429C4⋊C4C22×C3×D311yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—62no—
432C42—21no—
433C42—32no—
434C42—62no—
435C42C22×C3×D311yescharacteristic
436C22×C3—21no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C22×C3×D411yescharacteristic
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—42no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—41no—
462C3×C4—42no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—62no—
468C3×C4—62no—
469C3×C4—81no—
470C3×C4—81no—
471C3×C4—122no—
472C3×C4#91412yes—
473C3×C4C3×AGL(1,ℤ/8)12yes—
474C3×C4C2×#23511yescharacteristic
475C3×C4#101011yescharacteristic
476C3×C4C2×C3×#4111yescharacteristic
477C3×C4C3×2−1+411yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—42no—
481C32#336811yescharacteristic, complemented, Sylow
482C23—21no—
483C23—62no—
484Q8—21no—
485Q8—62no—
486Q8—122no—
487Q8C3×#23512yescomplemented
488D4—21no—
489D4—21no—
490D4—62no—
491D4—62no—
492D4—124no—
493D4—122no—
494D4—241no—
495D4—242no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—32no—
500C2×C4—32no—
501C2×C4—42no—
502C2×C4—62no—
503C2×C4—124no—
504C2×C4C3×D3×D411yescharacteristic
505C2×C4C3×D3×D411yescharacteristic
506C2×C4C23×C3×D311yescharacteristic
507C8—21no—
508C8—21no—
509C8—62no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—82no—
514C2×C3—81no—
515C2×C3—81no—
516C2×C3—242no—
517C2×C3#555211yescharacteristic
518C2×C3C2×#91411yescharacteristic
519C2×C3#577011yescharacteristic
520C2×C3C3×#54811yescharacteristic
521C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
522C2×C3C3×#57711yescharacteristic
523D3—82no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—122no—
528C22—122no—
529C22—122no—
530C22C2×C3×D3×D411yescharacteristic
531C4—21no—
532C4—22no—
533C4—41no—
534C4—41no—
535C4—62no—
536C4—62no—
537C4—122no—
538C4C3×#91412yes—
539C4C2×C3×#23511yescharacteristic
540C4C3×#101011yescharacteristic
541C3—21no—
542C3#7962511yescharacteristic, direct product factor
543C3C3×#336811yescharacteristic, complemented
544C2—81no—
545C2—242no—
546C2C3×#555211yescharacteristic
547C2C2×C3×#91411yescharacteristic
548C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5570C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5163C2semidirect
5. C3×#5027C2semidirect
6. C3×#5007C2semidirect
7. C3×#4871C2semidirect
8. C3×#4817C2semidirect
9. C3×#4764C2semidirect
10. C3×#4694C2semidirect
11. C3×#4679C2semidirect
13. #79625C3direct (N × H)
45. #5570C2×C3semidirect
56. C3×C4×SD16D3semidirect
57. C3×C4×SD16C2×C3semidirect
58. #5163C2×C3semidirect
59. #5027C2×C3semidirect
60. #5007C2×C3semidirect
61. #4871C2×C3semidirect
62. #4817C2×C3semidirect
63. #4764C2×C3semidirect
64. #4694C2×C3semidirect
65. #4679C2×C3semidirect
168. C32×Q8#41semidirect
203. C4×SD16C3×D3semidirect
339. C3×Q8#235semidirect
340. C3×Q8C3×#41semidirect
481. C32#3368semidirect
487. Q8C3×#235semidirect
542. C3#79625direct (N × H)
543. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
C3×#55532
C32×C4×SD162
C3×#51632
C3×#50272
C3×#50072
C3×#48712
C3×#48172
C3×#47642
C3×#46942
C3×#46792
C3×#33683
#796253