Finite Group Databasebeta

← C3×#79621 #11895305

Subgroups — C3×#79621 #11895305

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic, complemented
2C3×#5543C211yesmaximal, characteristic, complemented
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5165C212yesmaximal, complemented
5C3×#5021C211yesmaximal, characteristic, complemented
6C3×#5015C211yesmaximal, characteristic
7C3×#4871C212yesmaximal, complemented
8C3×#4800C212yesmaximal, complemented
9C3×#4756C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3361—31nomaximal
13#79621C311yesmaximal, characteristic, direct product factor
14C2×C32×SD16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#947C2212yes—
18C3×D4×Dic3C2212yes—
19C2×C3×#213C2212yes—
20C2×C3×C4⋊Dic3—21no—
21C3×#924—21no—
22C3×#894—22no—
23C3×#893C2212yes—
24C3×#890C2212yes—
25C3×#878—22no—
26C3×#875—21no—
27C3×#874C2211yescharacteristic
28C3×C4×D12—21no—
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#835C2212yes—
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#809C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#559—31no—
44C3×#554—31no—
45#5585C2×C311yescharacteristic, complemented
46#5543C2×C311yescharacteristic, complemented
47C3×#488—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#477—31no—
51C3×#463—32no—
52C3×#459—31no—
53C3×C8×Q8—31no—
54C3×C4×SD16—21no—
55C3×C4×SD16D311yescharacteristic, complemented
56C3×C4×SD16C2×C311yescharacteristic, complemented
57C3×C4×D8—32no—
58#5165C2×C312yescomplemented
59#5021C2×C311yescharacteristic, complemented
60#5015C2×C311yescharacteristic
61#4871C2×C312yescomplemented
62#4800C2×C312yescomplemented
63#4756C2×C312yescomplemented
64#4694C2×C311yescharacteristic, complemented
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C3×Dic3—22no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6D411yescharacteristic
76C32×SD16—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C4⋊C4C2311yescharacteristic
82C32×C22⋊C4—21no—
83C32×C42—21no—
84C32×C42C2311yescharacteristic
85C3×#217—22no—
86C3×#213—24no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
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×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98#3361—31noSylow
99C2×C3×SD16—21no—
100C2×C3×SD16C2×D311yescharacteristic
101C2×C3×SD16C22×C311yescharacteristic
102C2×C3×D8—32no—
103C3×C4⋊Q8—31no—
104C3×#127—31no—
105C3×#125—32no—
106C3×#124—32no—
107C3×#124—61no—
108C3×#123—62no—
109C3×C22⋊Q8—62no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C22×C311yescharacteristic
115C3×C4×D4—21no—
116C3×C4×D4—32no—
117C3×C4×D4—32no—
118C3×C4×D4—61no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C22×C311yescharacteristic
121C2×C3×C4⋊C4—61no—
122#947C22×C312yes—
123D4×Dic3C22×C312yes—
124C2×#213C22×C312yes—
125C2×C4⋊Dic3—21no—
126#924—21no—
127#894—22no—
128#893C22×C312yes—
129#890C22×C312yes—
130#878—22no—
131#875—21no—
132#874C22×C311yescharacteristic
133C4×D12—21no—
134#869C22×C311yescharacteristic
135C4×Dic6C22×C311yescharacteristic
136C3×#107—32no—
137C3×#106—21no—
138C3×#106C2×D311yescharacteristic
139C3×#106C22×C311yescharacteristic
140C3×C4⋊C8—32no—
141C3×C4⋊C8—31no—
142C3×#103—21no—
143C3×#103—32no—
144C3×#103C2×D311yescharacteristic
145C3×#103C22×C311yescharacteristic
146C3×#102—21no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102C2×D311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×C4×C8—21no—
153C3×C4×C8—32no—
154C3×C4×C8C2×D311yescharacteristic
155C3×C4×C8C22×C311yescharacteristic
156#835C22×C312yes—
157#821C22×C312yes—
158#821C22×C312yes—
159Dic3⋊C8C22×C312yes—
160C8×Dic3C22×C312yes—
161#809C22×C312yes—
162#807C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164C23×C32—21no—
165C22×C3×D3—22no—
166C32×Q8—21no—
167C32×Q8—21no—
168C32×D4—21no—
169C32×D4#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3×Dic3—22no—
178C2×C3×Dic3—82no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—22no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×C4×D3—82no—
186C3×Dic6—22no—
187C3×Dic6—81no—
188C32×C8—21no—
189C32×C8—21no—
190C3×C3⋊C8—22no—
191#559—31no—
192#554—31no—
193#488—32no—
194#486—31no—
195#478—32no—
196#477—31no—
197#463—32no—
198#459—31no—
199C8×Q8—31no—
200C4×SD16C3×D311yescharacteristic, complemented
201C4×D8—32no—
202C2×C3×Q8—21no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C23×C311yescharacteristic
207C2×C3×D4—21no—
208C2×C3×D4—32no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4C22×D311yescharacteristic
212C2×C3×D4C23×C311yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—41no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×Dic3—22no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12C23×C312yes—
222C2×C4×D3—22no—
223C2×Dic6—21no—
224C2×Dic6C3×D411yescharacteristic
225C3×SD16—24no—
226C3×SD16—22no—
227C3×SD16—22no—
228C3×D8—64no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—32no—
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C23×C311yescharacteristic
235C2×C3×C8C23×C311yescharacteristic
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C23×C311yescharacteristic
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—41no—
254C3×C22⋊C4—62no—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C42—21no—
259C3×C42—21no—
260C3×C42—21no—
261C3×C42—32no—
262C3×C42—41no—
263C3×C42C22×D311yescharacteristic
264C3×C42C23×C311yescharacteristic
265#217—22no—
266#213—24no—
267(C2×D3)⋊C4—22no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—21no—
271C4⋊Dic3—22no—
272C4⋊Dic3C3×D411yescharacteristic
273C4⋊Dic3C23×C312yes—
274Dic3⋊C4—22no—
275Dic3⋊C4C3×D412yes—
276C4×Dic3C23×C312yes—
277C2×C3⋊C8C23×C312yes—
278C22×C32—22no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4#13512yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C2×SD16C2×C3×D311yescharacteristic
296C2×D8—32no—
297C4⋊Q8—31no—
298#127—31no—
299#125—32no—
300#124—32no—
301#124—61no—
302#123—62no—
303C22⋊Q8—62no—
304C22⋊Q8—61no—
305C4×Q8—31no—
306C4×Q8C2×C3×D311yescharacteristic
307C4×D4—32no—
308C4×D4—32no—
309C4×D4—61no—
310C4×D4C2×C3×D311yescharacteristic
311C2×C4⋊C4—61no—
312#107—32no—
313#106C2×C3×D311yescharacteristic
314C4⋊C8—32no—
315C4⋊C8—31no—
316#103—32no—
317#103C2×C3×D311yescharacteristic
318#102—32no—
319#102—32no—
320#102—32no—
321#102C2×C3×D311yescharacteristic
322C4×C8—32no—
323C4×C8C2×C3×D311yescharacteristic
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—41no—
327C23×C3—62no—
328C22×D3—22no—
329C3×Q8—22no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—21no—
333C3×Q8—21no—
334C3×Q8—41no—
335C3×Q8—62no—
336C3×Q8—241no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—122no—
344C3×D4—241no—
345C3×D4#23512yes—
346C3×D4C3×#4112yes—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—62no—
364C2×C3×C4—82no—
365C2×C3×C4—242no—
366C2×C3×C4—242no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C24×C311yescharacteristic
373C2×Dic3—22no—
374C2×Dic3—82no—
375C2×Dic3C2×C3×D412yes—
376C2×Dic3C2×C3×D412yes—
377D12—22no—
378D12—22no—
379D12—42no—
380D12—81no—
381C4×D3—82no—
382Dic6—22no—
383Dic6—81no—
384C3×C8—22no—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—41no—
390C3×C8—62no—
391C3⋊C8—22no—
392C2×C32—42no—
393C2×C32#54811yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C2×C32#57611yescharacteristic
396C3×D3—82no—
397C2×Q8—31no—
398C2×Q8—61no—
399C2×Q8C22×C3×D311yescharacteristic
400C2×D4—32no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4C22×C3×D311yescharacteristic
404C22×C4—21no—
405C22×C4—62no—
406C22×C4—62no—
407SD16—22no—
408D8—64no—
409C2×C8—32no—
410C2×C8C22×C3×D311yescharacteristic
411C2×C8C22×C3×D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C4⋊C4—62no—
417C4⋊C4—62no—
418C4⋊C4—61no—
419C4⋊C4C22×C3×D311yescharacteristic
420C4⋊C4C22×C3×D311yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—62no—
423C22⋊C4—62no—
424C22⋊C4—62no—
425C22⋊C4—62no—
426C42—21no—
427C42—32no—
428C42C22×C3×D311yescharacteristic
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—81no—
438C22×C3—81no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3C2×D3×D411yescharacteristic
443C22×C3C22×C3×D411yescharacteristic
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—42no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—42no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—81no—
464C3×C4—122no—
465C3×C4#91612yes—
466C3×C4C3×#13512yes—
467C3×C4C2×#23511yescharacteristic
468C3×C4#101011yescharacteristic
469C3×C4C2×C3×#4111yescharacteristic
470C3×C4C3×2−1+411yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—42no—
474C32#336111yescharacteristic, complemented, Sylow
475C23—21no—
476C23—62no—
477Q8—21no—
478Q8—21no—
479Q8—62no—
480Q8—241no—
481D4—21no—
482D4—62no—
483D4—62no—
484D4—122no—
485D4—241no—
486D4C3×#23512yes—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—42no—
493C2×C4—62no—
494C2×C4—242no—
495C2×C4—242no—
496C2×C4C3×D3×D411yescharacteristic
497C2×C4C3×D3×D411yescharacteristic
498C2×C4C23×C3×D311yescharacteristic
499C8—21no—
500C8—21no—
501C8—62no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—42no—
506C2×C3—42no—
507C2×C3—82no—
508C2×C3—242no—
509C2×C3#555211yescharacteristic
510C2×C3C2×#91611yescharacteristic
511C2×C3#576911yescharacteristic
512C2×C3C3×#54811yescharacteristic
513C2×C3C2×C3×#13511yescharacteristic
514C2×C3C3×#57611yescharacteristic
515D3—82no—
516C22—22no—
517C22—41no—
518C22—41no—
519C22—122no—
520C22—122no—
521C22—122no—
522C22C2×C3×D3×D411yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—62no—
528C4—62no—
529C4—122no—
530C4C3×#91612yes—
531C4C2×C3×#23511yescharacteristic
532C4C3×#101011yescharacteristic
533C3—21no—
534C3#7962111yescharacteristic, direct product factor
535C3C3×#336111yescharacteristic, complemented
536C2—42no—
537C2—242no—
538C2C3×#555211yescharacteristic
539C2C2×C3×#91611yescharacteristic
540C2C3×#576911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5015C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3361
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×#5585C2semidirect
2. C3×#5543C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5165C2semidirect
5. C3×#5021C2semidirect
7. C3×#4871C2semidirect
8. C3×#4800C2semidirect
9. C3×#4756C2semidirect
10. C3×#4694C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79621C3direct (N × H)
45. #5585C2×C3semidirect
46. #5543C2×C3semidirect
55. C3×C4×SD16D3semidirect
56. C3×C4×SD16C2×C3semidirect
58. #5165C2×C3semidirect
59. #5021C2×C3semidirect
61. #4871C2×C3semidirect
62. #4800C2×C3semidirect
63. #4756C2×C3semidirect
64. #4694C2×C3semidirect
65. C8×Dic6C2×C3semidirect
200. C4×SD16C3×D3semidirect
474. C32#3361semidirect
534. C3#79621direct (N × H)
535. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55432
C32×C4×SD162
C3×#51652
C3×#50212
C3×#50152
C3×#48712
C3×#48002
C3×#47562
C3×#46942
C3×C8×Dic62
C3×#33613
#796213