Finite Group Databasebeta

← C3×#79622 #11895406

Subgroups — C3×#79622 #11895406

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5163C212yesmaximal, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6C3×#5008C211yesmaximal, characteristic, complemented
7C3×#4870C212yesmaximal, complemented
8C3×#4788C212yesmaximal, complemented
9C3×#4760C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3362—31nomaximal
13#79622C311yesmaximal, 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×#888—22no—
24C3×#888C2212yes—
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×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×Q82—31no—
44C3×#550—31no—
45Q8×Dic6C2×C311yescharacteristic, complemented
46#5553C2×C311yescharacteristic
47C3×#486—32no—
48C3×#486—31no—
49C3×#476—31no—
50C3×#476—32no—
51C3×#460—32no—
52C3×#460—31no—
53C3×C8×Q8—31no—
54C3×C4×SD16—21no—
55C3×C4×SD16—32no—
56C3×C4×SD16D311yescharacteristic, complemented
57C3×C4×SD16C2×C311yescharacteristic, complemented
58#5163C2×C312yescomplemented
59#5027C2×C311yescharacteristic, complemented
60#5008C2×C311yescharacteristic, complemented
61#4870C2×C312yescomplemented
62#4788C2×C312yescomplemented
63#4760C2×C312yescomplemented
64#4694C2×C311yescharacteristic, complemented
65C8×Dic6C2×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×Dic6—22no—
78C2×C3×Dic6D411yescharacteristic
79C32×SD16—22no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C42—21no—
87C32×C42C2311yescharacteristic
88C3×#215—24no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
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#3362—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—32no—
107C3×C4⋊Q8—31no—
108C3×C4⋊Q8—61no—
109C3×C4⋊Q8—62no—
110C3×#127—32no—
111C3×#127—31no—
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#888—22no—
130#888C22×C312yes—
131#884—22no—
132#874C22×C311yescharacteristic
133#869—21no—
134#869C22×C311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C22×C311yescharacteristic
137C3×#106—21no—
138C3×#106—32no—
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×C4×C8—21no—
154C3×C4×C8—32no—
155C3×C4×C8C2×D311yescharacteristic
156C3×C4×C8C22×C311yescharacteristic
157#832C22×C312yes—
158#821C22×C312yes—
159#821C22×C312yes—
160Dic3⋊C8C22×C312yes—
161C8×Dic3C22×C312yes—
162#809C22×C312yes—
163#808C22×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—82no—
189C3×Dic6—81no—
190C3×Dic6SD1614yescomplemented
191C32×C8—21no—
192C32×C8—21no—
193C3×C3⋊C8—22no—
194Q82—31no—
195#550—31no—
196#486—32no—
197#486—31no—
198#476—31no—
199#476—32no—
200#460—32no—
201#460—31no—
202C8×Q8—31no—
203C4×SD16—32no—
204C4×SD16C3×D311yescharacteristic, complemented
205C3×#41—124no—
206C2×C3×Q8—21no—
207C2×C3×Q8—31no—
208C2×C3×Q8—62no—
209C2×C3×Q8—61no—
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×Q8C23×C311yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4—32no—
214C2×C3×D4—62no—
215C2×C3×D4—62no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4C22×D311yescharacteristic
219C2×C3×D4C23×C311yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—41no—
223C22×C3×C4—62no—
224C2×#67—22no—
225C2×#67—22no—
226#235—44no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12C23×C312yes—
230C2×C4×D3—22no—
231C2×Dic6—21no—
232C2×Dic6—22no—
233C2×Dic6C3×D411yescharacteristic
234C3×SD16—24no—
235C3×SD16—22no—
236C3×SD16—22no—
237C3×SD16—64no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—32no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C23×C311yescharacteristic
244C2×C3×C8C23×C311yescharacteristic
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—32no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4C22×D311yescharacteristic
257C3×C4⋊C4C22×D311yescharacteristic
258C3×C4⋊C4C23×C311yescharacteristic
259C3×C4⋊C4C23×C311yescharacteristic
260C3×C22⋊C4—21no—
261C3×C22⋊C4—21no—
262C3×C22⋊C4—41no—
263C3×C22⋊C4—62no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—32no—
268C3×C42—41no—
269C3×C42—62no—
270C3×C42C22×D311yescharacteristic
271C3×C42C23×C311yescharacteristic
272#215—24no—
273(C2×D3)⋊C4—22no—
274C4⋊Dic3—21no—
275C4⋊Dic3—22no—
276C4⋊Dic3C3×D411yescharacteristic
277C4⋊Dic3C23×C312yes—
278Dic3⋊C4—22no—
279Dic3⋊C4C3×D412yes—
280C4×Dic3—22no—
281C4×Dic3C23×C312yes—
282C2×C3⋊C8C23×C312yes—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—22no—
291C32×C4—21no—
292C32×C4—41no—
293C32×C4—41no—
294C32×C4C2×SD1612yes—
295C32×C4C2×#4111yescharacteristic
296C32×C42−1+411yescharacteristic
297C3×Dic3—22no—
298C3×Dic3—42no—
299C3×Dic3C2×SD1614yes—
300C2×#41—61no—
301C2×SD16—32no—
302C2×SD16C2×C3×D311yescharacteristic
303C4⋊Q8—32no—
304C4⋊Q8—31no—
305C4⋊Q8—61no—
306C4⋊Q8—62no—
307#127—32no—
308#127—31no—
309#121—62no—
310#121—61no—
311C4×Q8—31no—
312C4×Q8—32no—
313C4×Q8—61no—
314C4×Q8C2×C3×D311yescharacteristic
315C4×D4—32no—
316C4×D4C2×C3×D311yescharacteristic
317#106—32no—
318#106C2×C3×D311yescharacteristic
319C4⋊C8—32no—
320C4⋊C8—31no—
321#103C2×C3×D311yescharacteristic
322#102—32no—
323#102—32no—
324#102—32no—
325#102—32no—
326#102C2×C3×D311yescharacteristic
327C4×C8—32no—
328C4×C8C2×C3×D311yescharacteristic
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—41no—
332C23×C3—62no—
333C22×D3—22no—
334C3×Q8—21no—
335C3×Q8—21no—
336C3×Q8—22no—
337C3×Q8—34no—
338C3×Q8—41no—
339C3×Q8—241no—
340C3×Q8—242no—
341C3×Q8#23512yescomplemented
342C3×Q8C3×#4112yescomplemented
343C3×D4—22no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—21no—
348C3×D4—41no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—124no—
352C3×D4—122no—
353C3×D4—241no—
354C3×D4—242no—
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—21no—
363C2×C3×C4—21no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—62no—
372C2×C3×C4—82no—
373C2×C3×C4—124no—
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4C2×C3×D411yescharacteristic
377C2×C3×C4C2×C3×D411yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C24×C311yescharacteristic
380#67—44no—
381#67—82no—
382C2×Dic3—22no—
383C2×Dic3C2×C3×D412yes—
384C2×Dic3C2×C3×D412yes—
385D12—22no—
386D12—22no—
387D12—42no—
388D12—81no—
389C4×D3—44no—
390Dic6—82no—
391Dic6—81no—
392Dic6C3×SD1614yescomplemented
393C3×C8—22no—
394C3×C8—21no—
395C3×C8—21no—
396C3×C8—21no—
397C3×C8—21no—
398C3×C8—41no—
399C3×C8—62no—
400C3⋊C8—22no—
401C2×C32—81no—
402C2×C32#54811yescharacteristic
403C2×C32C22×SD1611yescharacteristic
404C2×C32#57611yescharacteristic
405C3×D3—82no—
406#41—124no—
407C2×Q8—31no—
408C2×Q8—62no—
409C2×Q8—61no—
410C2×Q8C22×C3×D311yescharacteristic
411C2×D4—32no—
412C2×D4—62no—
413C2×D4—62no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4C22×C3×D311yescharacteristic
417C22×C4—21no—
418C22×C4—62no—
419SD16—22no—
420SD16—64no—
421C2×C8—32no—
422C2×C8C22×C3×D311yescharacteristic
423C2×C8C22×C3×D311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—32no—
426C4⋊C4—31no—
427C4⋊C4—32no—
428C4⋊C4—62no—
429C4⋊C4—62no—
430C4⋊C4—61no—
431C4⋊C4C22×C3×D311yescharacteristic
432C4⋊C4C22×C3×D311yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—62no—
435C42—21no—
436C42—32no—
437C42—62no—
438C42C22×C3×D311yescharacteristic
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C22×C3×D411yescharacteristic
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—34no—
465C3×C4—41no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—62no—
472C3×C4—81no—
473C3×C4—81no—
474C3×C4—122no—
475C3×C4D3×SD1612yes—
476C3×C4C2×C3×SD1612yes—
477C3×C4C2×#23511yescharacteristic
478C3×C4#101011yescharacteristic
479C3×C4C2×C3×#4111yescharacteristic
480C3×C4C3×2−1+411yescharacteristic
481Dic3—22no—
482Dic3—42no—
483Dic3C2×C3×SD1614yes—
484C32#336211yescharacteristic, complemented, Sylow
485C23—21no—
486C23—62no—
487Q8—21no—
488Q8—34no—
489Q8—241no—
490Q8—242no—
491Q8C3×#23512yescomplemented
492D4—21no—
493D4—21no—
494D4—62no—
495D4—62no—
496D4—124no—
497D4—122no—
498D4—241no—
499D4—242no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—42no—
506C2×C4—62no—
507C2×C4—124no—
508C2×C4C3×D3×D411yescharacteristic
509C2×C4C3×D3×D411yescharacteristic
510C2×C4C23×C3×D311yescharacteristic
511C8—21no—
512C8—21no—
513C8—62no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—82no—
518C2×C3—81no—
519C2×C3—81no—
520C2×C3—242no—
521C2×C3#555211yescharacteristic
522C2×C3C2×D3×SD1611yescharacteristic
523C2×C3#576911yescharacteristic
524C2×C3C3×#54811yescharacteristic
525C2×C3C22×C3×SD1611yescharacteristic
526C2×C3C3×#57611yescharacteristic
527D3—82no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—122no—
532C22—122no—
533C22—122no—
534C22C2×C3×D3×D411yescharacteristic
535C4—21no—
536C4—22no—
537C4—34no—
538C4—41no—
539C4—41no—
540C4—62no—
541C4—122no—
542C4C3×D3×SD1612yes—
543C4C2×C3×#23511yescharacteristic
544C4C3×#101011yescharacteristic
545C3—21no—
546C3#7962211yescharacteristic, direct product factor
547C3C3×#336211yescharacteristic, complemented
548C2—81no—
549C2—242no—
550C2C3×#555211yescharacteristic
551C2C2×C3×D3×SD1611yescharacteristic
552C2C3×#576911yescharacteristic
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×#3362
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×Q8×Dic6C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5163C2semidirect
5. C3×#5027C2semidirect
6. C3×#5008C2semidirect
7. C3×#4870C2semidirect
8. C3×#4788C2semidirect
9. C3×#4760C2semidirect
10. C3×#4694C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79622C3direct (N × H)
45. Q8×Dic6C2×C3semidirect
56. C3×C4×SD16D3semidirect
57. C3×C4×SD16C2×C3semidirect
58. #5163C2×C3semidirect
59. #5027C2×C3semidirect
60. #5008C2×C3semidirect
61. #4870C2×C3semidirect
62. #4788C2×C3semidirect
63. #4760C2×C3semidirect
64. #4694C2×C3semidirect
65. C8×Dic6C2×C3semidirect
168. C32×Q8#41semidirect
190. C3×Dic6SD16semidirect
204. C4×SD16C3×D3semidirect
341. C3×Q8#235semidirect
342. C3×Q8C3×#41semidirect
392. Dic6C3×SD16semidirect
484. C32#3362semidirect
491. Q8C3×#235semidirect
546. C3#79622direct (N × H)
547. C3C3×#3362semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#55532
C32×C4×SD162
C3×#51632
C3×#50272
C3×#50082
C3×#48702
C3×#47882
C3×#47602
C3×#46942
C3×C8×Dic62
C3×#33623
#796223