Finite Group Databasebeta

← C3×#79637 #11898289

Subgroups — C3×#79637 #11898289

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5567C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5175C212yesmaximal, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6C3×#5019C211yesmaximal, characteristic, complemented
7C3×#4852C212yesmaximal, complemented
8C3×#4818C212yesmaximal, complemented
9C3×#4762C212yesmaximal, complemented
10C3×#4693C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3392—31nomaximal
13#79637C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C2×C32×SD16C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#944C2212yes—
19C2×C3×#215C2212yes—
20C3×#940C2212yes—
21C2×C3×#214C2212yes—
22C3×#930—21no—
23C2×C3×#204C2212yes—
24C2×C3×#204C2212yes—
25C3×#893C2212yes—
26C3×#889—22no—
27C3×#887C2212yes—
28C3×#884—22no—
29C3×#874C2211yescharacteristic
30C3×#870—21no—
31C3×#869C2211yescharacteristic
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2211yescharacteristic
34C32×#106C2211yescharacteristic
35C32×#103C2211yescharacteristic
36C32×#102C2211yescharacteristic
37C32×C4×C8C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#809C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5567C2×C311yescharacteristic, complemented
46#5553C2×C311yescharacteristic
47C3×#492—32no—
48C3×#492—31no—
49C3×#461—31no—
50C3×#461—32no—
51C3×#460—31no—
52C3×#460—32no—
53C3×C8×Q8—31no—
54C3×C4×SD16—21no—
55C3×C4×SD16—32no—
56C3×C4×SD16D311yescharacteristic, complemented
57C3×C4×SD16C2×C311yescharacteristic, complemented
58#5175C2×C312yescomplemented
59#5027C2×C311yescharacteristic, complemented
60#5019C2×C311yescharacteristic, complemented
61#4852C2×C312yescomplemented
62#4818C2×C312yescomplemented
63#4762C2×C312yescomplemented
64#4693C2×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×Dic6D411yescharacteristic
77C2×C3×Dic6C2312yes—
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—42no—
88C3×#214—42no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3D411yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4D412yes—
97C3×C4×Dic3—22no—
98C3×C4×Dic3C2312yes—
99C2×C3×C3⋊C8C2312yes—
100C3×#204—24no—
101C3×#204—42no—
102#3392—31noSylow
103C2×C3×#41—61no—
104C2×#235—21no—
105C2×C3×SD16—21no—
106C2×C3×SD16—32no—
107C2×C3×SD16—32no—
108C2×C3×SD16—32no—
109C2×C3×SD16—32no—
110C2×C3×SD16C2×D311yescharacteristic
111C2×C3×SD16C22×C311yescharacteristic
112C3×C4⋊Q8—32no—
113C3×C4⋊Q8—31no—
114C3×#127—32no—
115C3×#127—31no—
116C3×#125—61no—
117C3×#125—62no—
118C3×#121—62no—
119C3×#121—61no—
120C3×C4×Q8—21no—
121C3×C4×Q8—31no—
122C3×C4×Q8—32no—
123C3×C4×Q8—61no—
124C3×C4×Q8C2×D311yescharacteristic
125C3×C4×Q8C22×C311yescharacteristic
126C3×C4×D4—21no—
127C3×C4×D4—32no—
128C3×C4×D4C2×D311yescharacteristic
129C3×C4×D4C22×C311yescharacteristic
130#944C22×C312yes—
131C2×#215C22×C312yes—
132#940C22×C312yes—
133C2×#214C22×C312yes—
134#930—21no—
135C2×#204C22×C312yes—
136C2×#204C22×C312yes—
137#893C22×C312yes—
138#889—22no—
139#887C22×C312yes—
140#884—22no—
141#874C22×C311yescharacteristic
142#870—21no—
143#869C22×C311yescharacteristic
144C4×Dic6—21no—
145C4×Dic6C22×C311yescharacteristic
146C3×#106—21no—
147C3×#106C2×D311yescharacteristic
148C3×#106C22×C311yescharacteristic
149C3×C4⋊C8—32no—
150C3×C4⋊C8—31no—
151C3×#103—21no—
152C3×#103—32no—
153C3×#103C2×D311yescharacteristic
154C3×#103C22×C311yescharacteristic
155C3×#102—21no—
156C3×#102—32no—
157C3×#102C2×D311yescharacteristic
158C3×#102C22×C311yescharacteristic
159C3×C4×C8—21no—
160C3×C4×C8—32no—
161C3×C4×C8C2×D311yescharacteristic
162C3×C4×C8C22×C311yescharacteristic
163Dic3⋊C8C22×C312yes—
164C8×Dic3C22×C312yes—
165#810C22×C312yes—
166#809C22×C312yes—
167C4⋊(C3⋊C8)C22×C311yescharacteristic
168C23×C32—21no—
169C22×C3×D3—22no—
170C32×Q8—21no—
171C32×Q8—21no—
172C32×D4—21no—
173C32×D4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C3×#67—44no—
182C3×#67—82no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—42no—
189C3×D12—81no—
190C3×C4×D3—44no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193C3×Dic6SD1614yescomplemented
194C32×C8—21no—
195C32×C8#4112yescomplemented
196C3×C3⋊C8—22no—
197#557—31no—
198#550—31no—
199#492—32no—
200#492—31no—
201#461—31no—
202#461—32no—
203#460—31no—
204#460—32no—
205C8×Q8—31no—
206C4×SD16—32no—
207C4×SD16C3×D311yescharacteristic, complemented
208C3×#41—124no—
209C2×C3×Q8—21no—
210C2×C3×Q8—31no—
211C2×C3×Q8—32no—
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×Q8C23×C311yescharacteristic
214C2×C3×D4—21no—
215C2×C3×D4—32no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C2×C3×D4C22×D311yescharacteristic
221C2×C3×D4C23×C311yescharacteristic
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—41no—
225C22×C3×C4—62no—
226C2×#67—22no—
227C2×#67—22no—
228#235—44no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12C23×C312yes—
232C2×C4×D3—22no—
233C2×Dic6C3×D411yescharacteristic
234C2×Dic6C23×C312yes—
235C3×SD16—24no—
236C3×SD16—22no—
237C3×SD16—22no—
238C3×SD16—64no—
239C3×SD16—122no—
240C3×SD16—122no—
241C3×SD16—122no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—32no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C23×C311yescharacteristic
248C2×C3×C8C23×C311yescharacteristic
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—41no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C23×C311yescharacteristic
264C3×C4⋊C4C23×C311yescharacteristic
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—62no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—32no—
273C3×C42—41no—
274C3×C42—62no—
275C3×C42C22×D311yescharacteristic
276C3×C42C23×C311yescharacteristic
277#215—42no—
278#214—42no—
279(C2×D3)⋊C4—22no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3C3×D411yescharacteristic
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285Dic3⋊C4—22no—
286Dic3⋊C4C3×D412yes—
287C4×Dic3—22no—
288C4×Dic3C23×C312yes—
289C2×C3⋊C8C23×C312yes—
290#204—24no—
291#204—42no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4—41no—
302C32×C4—41no—
303C32×C4C2×SD1612yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4H(5,𝔽2)11yescharacteristic
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3C2×SD1614yes—
309C2×#41—61no—
310C2×SD16—32no—
311C2×SD16—32no—
312C2×SD16—32no—
313C2×SD16—32no—
314C2×SD16C2×C3×D311yescharacteristic
315C4⋊Q8—32no—
316C4⋊Q8—31no—
317#127—32no—
318#127—31no—
319#125—61no—
320#125—62no—
321#121—62no—
322#121—61no—
323C4×Q8—31no—
324C4×Q8—32no—
325C4×Q8—61no—
326C4×Q8C2×C3×D311yescharacteristic
327C4×D4—32no—
328C4×D4C2×C3×D311yescharacteristic
329#106C2×C3×D311yescharacteristic
330C4⋊C8—32no—
331C4⋊C8—31no—
332#103—32no—
333#103C2×C3×D311yescharacteristic
334#102—32no—
335#102C2×C3×D311yescharacteristic
336C4×C8—32no—
337C4×C8C2×C3×D311yescharacteristic
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—41no—
341C23×C3—62no—
342C22×D3—22no—
343C3×Q8—22no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8—21no—
348C3×Q8—34no—
349C3×Q8—41no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×D4—22no—
353C3×D4—21no—
354C3×D4—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—41no—
358C3×D4—62no—
359C3×D4—62no—
360C3×D4—124no—
361C3×D4—122no—
362C3×D4—241no—
363C3×D4—242no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—62no—
381C2×C3×C4—82no—
382C2×C3×C4—124no—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4C2×C3×D411yescharacteristic
386C2×C3×C4C2×C3×D411yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C24×C311yescharacteristic
389#67—44no—
390#67—82no—
391C2×Dic3—22no—
392C2×Dic3C2×C3×D412yes—
393C2×Dic3C2×C3×D412yes—
394D12—22no—
395D12—22no—
396D12—42no—
397D12—81no—
398C4×D3—44no—
399Dic6—22no—
400Dic6—22no—
401Dic6C3×SD1614yescomplemented
402C3×C8—21no—
403C3×C8—21no—
404C3×C8—22no—
405C3×C8—41no—
406C3×C8—62no—
407C3×C8#23512yescomplemented
408C3×C8C3×#4112yescomplemented
409C3⋊C8—22no—
410C2×C32—81no—
411C2×C32#55011yescharacteristic
412C2×C32C22×SD1611yescharacteristic
413C2×C32#57711yescharacteristic
414C3×D3—82no—
415#41—124no—
416C2×Q8—31no—
417C2×Q8—32no—
418C2×Q8C22×C3×D311yescharacteristic
419C2×D4—32no—
420C2×D4—62no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4C22×C3×D311yescharacteristic
425C22×C4—21no—
426C22×C4—62no—
427SD16—22no—
428SD16—64no—
429SD16—122no—
430SD16—122no—
431SD16—122no—
432C2×C8—32no—
433C2×C8C22×C3×D311yescharacteristic
434C2×C8C22×C3×D311yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—62no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4C22×C3×D311yescharacteristic
444C4⋊C4C22×C3×D311yescharacteristic
445C22⋊C4—21no—
446C22⋊C4—62no—
447C42—21no—
448C42—32no—
449C42—62no—
450C42C22×C3×D311yescharacteristic
451C22×C3—21no—
452C22×C3—42no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—122no—
462C22×C3—122no—
463C22×C3—122no—
464C22×C3C2×D3×D411yescharacteristic
465C22×C3C22×C3×D411yescharacteristic
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—34no—
475C3×C4—41no—
476C3×C4—42no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—62no—
484C3×C4—81no—
485C3×C4—81no—
486C3×C4—122no—
487C3×C4D3×SD1612yes—
488C3×C4C2×C3×SD1612yes—
489C3×C4C2×#23511yescharacteristic
490C3×C4#100911yescharacteristic
491C3×C4C2×C3×#4111yescharacteristic
492C3×C4C3×H(5,𝔽2)11yescharacteristic
493Dic3—22no—
494Dic3—42no—
495Dic3C2×C3×SD1614yes—
496C32#339211yescharacteristic, complemented, Sylow
497C23—21no—
498C23—62no—
499Q8—21no—
500Q8—21no—
501Q8—34no—
502Q8—62no—
503Q8—62no—
504D4—21no—
505D4—21no—
506D4—62no—
507D4—62no—
508D4—124no—
509D4—122no—
510D4—241no—
511D4—242no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—42no—
518C2×C4—62no—
519C2×C4—124no—
520C2×C4C3×D3×D411yescharacteristic
521C2×C4C3×D3×D411yescharacteristic
522C2×C4C23×C3×D311yescharacteristic
523C8—21no—
524C8—62no—
525C8C3×#23512yescomplemented
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—82no—
530C2×C3—81no—
531C2×C3—81no—
532C2×C3—242no—
533C2×C3#555311yescharacteristic
534C2×C3C2×D3×SD1611yescharacteristic
535C2×C3#577011yescharacteristic
536C2×C3C3×#55011yescharacteristic
537C2×C3C22×C3×SD1611yescharacteristic
538C2×C3C3×#57711yescharacteristic
539D3—82no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22C2×C3×D3×D411yescharacteristic
547C4—21no—
548C4—34no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—62no—
553C4—122no—
554C4C3×D3×SD1612yes—
555C4C2×C3×#23511yescharacteristic
556C4C3×#100911yescharacteristic
557C3—21no—
558C3#7963711yescharacteristic, direct product factor
559C3C3×#339211yescharacteristic, complemented
560C2—81no—
561C2—242no—
562C2C3×#555311yescharacteristic
563C2C2×C3×D3×SD1611yescharacteristic
564C2C3×#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×#3392
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×#5567C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5175C2semidirect
5. C3×#5027C2semidirect
6. C3×#5019C2semidirect
7. C3×#4852C2semidirect
8. C3×#4818C2semidirect
9. C3×#4762C2semidirect
10. C3×#4693C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79637C3direct (N × H)
45. #5567C2×C3semidirect
56. C3×C4×SD16D3semidirect
57. C3×C4×SD16C2×C3semidirect
58. #5175C2×C3semidirect
59. #5027C2×C3semidirect
60. #5019C2×C3semidirect
61. #4852C2×C3semidirect
62. #4818C2×C3semidirect
63. #4762C2×C3semidirect
64. #4693C2×C3semidirect
65. C8×Dic6C2×C3semidirect
193. C3×Dic6SD16semidirect
195. C32×C8#41semidirect
207. C4×SD16C3×D3semidirect
401. Dic6C3×SD16semidirect
407. C3×C8#235semidirect
408. C3×C8C3×#41semidirect
496. C32#3392semidirect
525. C8C3×#235semidirect
558. C3#79637direct (N × H)
559. C3C3×#3392semidirect

Maximal subgroups

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

subgroupindex
C3×#55672
C3×#55532
C32×C4×SD162
C3×#51752
C3×#50272
C3×#50192
C3×#48522
C3×#48182
C3×#47622
C3×#46932
C3×C8×Dic62
C3×#33923
#796373