Finite Group Databasebeta

← C3×#79619 #11895149

Subgroups — C3×#79619 #11895149

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5567C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic
4C3×#5162C212yesmaximal
5C3×#5020C211yesmaximal, characteristic, complemented
6C3×#5019C211yesmaximal, characteristic
7C3×#4854C212yesmaximal, complemented
8C3×#4792C212yesmaximal, complemented
9C3×#4758C212yesmaximal
10C3×#4681C211yesmaximal, characteristic, complemented
11C3×C8×Dic6C211yesmaximal, characteristic, complemented
12C3×#3359—31nomaximal
13#79619C311yesmaximal, characteristic, direct product factor
14C22×C3×Dic6—21no—
15C2×C32×SD16C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#944C2212yes—
19C3×D4×Dic3C2212yes—
20C2×C3×#214C2212yes—
21C3×#924—21no—
22C3×#889—22no—
23C3×#888C2212yes—
24C3×#887C2212yes—
25C3×#878—22no—
26C3×#870—21no—
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31C32×#106C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#835C2212yes—
36C3×#816C2212yes—
37C3×#816C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×#810C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#557—31no—
44C3×D4×Q8—31no—
45#5567C2×C311yescharacteristic, complemented
46D4×Dic6C2×C311yescharacteristic
47C3×#487—32no—
48C3×#487—31no—
49C3×#475—31no—
50C3×#475—32no—
51C3×#461—32no—
52C3×#461—31no—
53C3×C8×Q8—31no—
54C3×C4×SD16—21no—
55C3×C4×SD16—32no—
56C3×C4×SD16D311yescharacteristic
57C3×C4×SD16C2×C311yescharacteristic
58#5162C2×C312yes—
59#5020C2×C311yescharacteristic, complemented
60#5019C2×C311yescharacteristic
61#4854C2×C312yescomplemented
62#4792C2×C312yescomplemented
63#4758C2×C312yes—
64#4681C2×C311yescharacteristic, complemented
65C8×Dic6C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C3×Dic3—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—44no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2312yes—
75C32×SD16—22no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C3×#217—22no—
85C3×#214—24no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4D412yes—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3359—31noSylow
100C22×C3×Q8—61no—
101C22×Dic6—21no—
102C2×C3×SD16—21no—
103C2×C3×SD16—32no—
104C2×C3×SD16C2×D311yescharacteristic
105C2×C3×SD16C22×C311yescharacteristic
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—32no—
108C3×C4⋊Q8—31no—
109C3×C4⋊Q8—31no—
110C3×#125—61no—
111C3×#125—62no—
112C3×C22⋊Q8—62no—
113C3×C22⋊Q8—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
124#944C22×C312yes—
125D4×Dic3C22×C312yes—
126C2×#214C22×C312yes—
127#924—21no—
128#889—22no—
129#888C22×C312yes—
130#887C22×C312yes—
131#878—22no—
132#870—21no—
133#869C22×C311yescharacteristic
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×#103—32no—
145C3×#103—32no—
146C3×#103—32no—
147C3×#103—32no—
148C3×#103C2×D311yescharacteristic
149C3×#103C22×C311yescharacteristic
150C3×#102—21no—
151C3×#102C2×D311yescharacteristic
152C3×#102C22×C311yescharacteristic
153C3×C4×C8—21no—
154C3×C4×C8—32no—
155C3×C4×C8C2×D311yescharacteristic
156C3×C4×C8C22×C311yescharacteristic
157#835C22×C312yes—
158#816C22×C312yes—
159#816C22×C312yes—
160Dic3⋊C8C22×C312yes—
161C8×Dic3C22×C312yes—
162#810C22×C312yes—
163#808C22×C312yes—
164C4⋊(C3⋊C8)C22×C311yescharacteristic
165C23×C32—21no—
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—22no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185C3×Dic6—44no—
186C3×Dic6SD1614yescomplemented
187C32×C8—21no—
188C32×C8—21no—
189C3×C3⋊C8—22no—
190#557—31no—
191D4×Q8—31no—
192#487—32no—
193#487—31no—
194#475—31no—
195#475—32no—
196#461—32no—
197#461—31no—
198C8×Q8—31no—
199C4×SD16—32no—
200C4×SD16C3×D311yescharacteristic
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—62no—
205C2×C3×Q8—61no—
206C2×C3×Q8—124no—
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×Q8C23×C311yescharacteristic
209C2×C3×D4—21no—
210C2×C3×D4C22×D311yescharacteristic
211C2×C3×D4C23×C311yescharacteristic
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—41no—
215C22×C3×C4—62no—
216C22×Dic3—22no—
217C2×Dic6—21no—
218C2×Dic6—22no—
219C2×Dic6—44no—
220C2×Dic6C3×D411yescharacteristic
221C2×Dic6C23×C312yes—
222C3×SD16—24no—
223C3×SD16—22no—
224C3×SD16—22no—
225C3×SD16—64no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—32no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C23×C311yescharacteristic
232C2×C3×C8C23×C311yescharacteristic
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C23×C311yescharacteristic
251C3×C4⋊C4C23×C311yescharacteristic
252C3×C22⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C22⋊C4—41no—
255C3×C22⋊C4—62no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—21no—
259C3×C42—32no—
260C3×C42—41no—
261C3×C42—62no—
262C3×C42C22×D311yescharacteristic
263C3×C42C23×C311yescharacteristic
264#217—22no—
265#214—24no—
266C4⋊Dic3—21no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3C3×D411yescharacteristic
270C4⋊Dic3C23×C312yes—
271Dic3⋊C4—22no—
272Dic3⋊C4—22no—
273Dic3⋊C4—22no—
274Dic3⋊C4—22no—
275Dic3⋊C4C3×D412yes—
276C4×Dic3—22no—
277C4×Dic3C23×C312yes—
278C2×C3⋊C8C23×C312yes—
279C22×C32—22no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C3×Dic3C2×SD1614yes—
294C22×Q8—61no—
295C2×SD16—32no—
296C2×SD16C2×C3×D311yescharacteristic
297C4⋊Q8—32no—
298C4⋊Q8—32no—
299C4⋊Q8—31no—
300C4⋊Q8—31no—
301#125—61no—
302#125—62no—
303C22⋊Q8—62no—
304C22⋊Q8—61no—
305C4×Q8—31no—
306C4×Q8—32no—
307C4×Q8—61no—
308C4×Q8C2×C3×D311yescharacteristic
309C4×D4—32no—
310C4×D4C2×C3×D311yescharacteristic
311#106—32no—
312#106C2×C3×D311yescharacteristic
313C4⋊C8—32no—
314C4⋊C8—31no—
315#103—32no—
316#103—32no—
317#103—32no—
318#103—32no—
319#103C2×C3×D311yescharacteristic
320#102C2×C3×D311yescharacteristic
321C4×C8—32no—
322C4×C8C2×C3×D311yescharacteristic
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—41no—
326C3×Q8—22no—
327C3×Q8—21no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—34no—
332C3×Q8—41no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—124no—
336C3×Q8—122no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4#23512yes—
342C3×D4C3×#4112yes—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—82no—
362C2×C3×C4—124no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C24×C311yescharacteristic
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—44no—
372C2×Dic3C2×C3×D412yes—
373C2×Dic3C2×C3×D412yes—
374Dic6—22no—
375Dic6—22no—
376Dic6—42no—
377Dic6—44no—
378Dic6C3×SD1614yescomplemented
379C3×C8—22no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—41no—
385C3×C8—62no—
386C3⋊C8—22no—
387C2×C32—42no—
388C2×C32#54811yescharacteristic
389C2×C32C22×SD1611yescharacteristic
390C2×C32#57811yescharacteristic
391C2×Q8—31no—
392C2×Q8—32no—
393C2×Q8—62no—
394C2×Q8—61no—
395C2×Q8—124no—
396C2×Q8C22×C3×D311yescharacteristic
397C2×D4C22×C3×D311yescharacteristic
398C22×C4—21no—
399C22×C4—62no—
400SD16—22no—
401SD16—64no—
402C2×C8—32no—
403C2×C8C22×C3×D311yescharacteristic
404C2×C8C22×C3×D311yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—32no—
409C4⋊C4—62no—
410C4⋊C4—62no—
411C4⋊C4—62no—
412C4⋊C4—62no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4C22×C3×D311yescharacteristic
417C4⋊C4C22×C3×D311yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—62no—
420C42—21no—
421C42—32no—
422C42—62no—
423C42C22×C3×D311yescharacteristic
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×C3×D411yescharacteristic
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—34no—
442C3×C4—41no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—62no—
451C3×C4—81no—
452C3×C4—81no—
453C3×C4—122no—
454C3×C4—122no—
455C3×C4D3×SD1612yes—
456C3×C4C2×C3×SD1612yes—
457C3×C4C2×#23511yescharacteristic
458C3×C4#101011yescharacteristic
459C3×C4C2×C3×#4111yescharacteristic
460C3×C4C3×2−1+411yescharacteristic
461Dic3—22no—
462Dic3—42no—
463Dic3—42no—
464Dic3C2×C3×SD1614yes—
465C32#335911yescharacteristic, complemented, Sylow
466C23—21no—
467Q8—21no—
468Q8—21no—
469Q8—34no—
470Q8—62no—
471Q8—62no—
472Q8—124no—
473Q8—122no—
474D4—21no—
475D4C3×#23512yes—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—42no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—124no—
485C2×C4C3×D3×D411yescharacteristic
486C2×C4C3×D3×D411yescharacteristic
487C2×C4C23×C3×D311yescharacteristic
488C8—21no—
489C8—21no—
490C8—62no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3—42no—
496C2×C3—82no—
497C2×C3#555211yescharacteristic
498C2×C3C2×D3×SD1611yescharacteristic
499C2×C3#577111yescharacteristic
500C2×C3C3×#54811yescharacteristic
501C2×C3C22×C3×SD1611yescharacteristic
502C2×C3C3×#57811yescharacteristic
503C22—22no—
504C22—41no—
505C22—41no—
506C22C2×C3×D3×D411yescharacteristic
507C4—21no—
508C4—34no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—62no—
513C4—122no—
514C4—122no—
515C4C3×D3×SD1612yes—
516C4C2×C3×#23511yescharacteristic
517C4C3×#101011yescharacteristic
518C3—21no—
519C3#7961911yescharacteristic, direct product factor
520C3C3×#335911yescharacteristic, complemented
521C2—42no—
522C2C3×#555211yescharacteristic
523C2C2×C3×D3×SD1611yescharacteristic
524C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3359
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
5. C3×#5020C2semidirect
7. C3×#4854C2semidirect
8. C3×#4792C2semidirect
10. C3×#4681C2semidirect
11. C3×C8×Dic6C2semidirect
13. #79619C3direct (N × H)
45. #5567C2×C3semidirect
59. #5020C2×C3semidirect
61. #4854C2×C3semidirect
62. #4792C2×C3semidirect
64. #4681C2×C3semidirect
65. C8×Dic6C2×C3semidirect
186. C3×Dic6SD16semidirect
378. Dic6C3×SD16semidirect
465. C32#3359semidirect
519. C3#79619direct (N × H)
520. C3C3×#3359semidirect

Maximal subgroups

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

subgroupindex
C3×#55672
C3×D4×Dic62
C32×C4×SD162
C3×#51622
C3×#50202
C3×#50192
C3×#48542
C3×#47922
C3×#47582
C3×#46812
C3×C8×Dic62
C3×#33593
#796193