Finite Group Databasebeta

← C3×#81905 #11897534

Subgroups — C3×#81905 #11897534

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2C3×#5727C211yesmaximal, characteristic, complemented
3C32×#498C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5C3×#5084C211yesmaximal, characteristic, complemented
6C3×#4871C212yesmaximal, complemented
7C3×#4870C212yesmaximal, complemented
8C3×#4869C212yesmaximal
9C3×#4856C212yesmaximal, complemented
10C3×C4×D24C211yesmaximal, characteristic
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3384—31nomaximal
13#81905C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C3×#946—21no—
18C3×#946—22no—
19C2×C3×D24C2211yescharacteristic
20C3×#897—21no—
21C3×#896—22no—
22C3×#893C2212yes—
23C3×#893C2212yes—
24C3×D3×C4⋊C4—21no—
25C3×#890C2212yes—
26C3×#888C2212yes—
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C32×#106C2212yes—
31C32×#106C2212yes—
32C32×C4×C8C2211yescharacteristic
33C3×#821C2211yescharacteristic
34C3×#821C2211yescharacteristic
35C3×#818C2211yescharacteristic
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#809C2212yes—
39C3×#809C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5730C2×C311yescharacteristic, complemented
46#5727C2×C311yescharacteristic, complemented
47C3×#501—32no—
48C3×#498—21no—
49C3×#498D311yescharacteristic, complemented
50C3×#498C2×C311yescharacteristic, complemented
51C3×#478—32no—
52C3×#476—31no—
53C3×#476—32no—
54C3×#474—31no—
55C3×#446—31no—
56C3×#442—32no—
57C3×C4×D8—31no—
58#5087C2×C311yescharacteristic, complemented
59#5084C2×C311yescharacteristic, complemented
60#4871C2×C312yescomplemented
61#4870C2×C312yescomplemented
62#4869C2×C312yes—
63#4856C2×C312yescomplemented
64C4×D24C2×C311yescharacteristic
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8—21no—
68C3×D3×Q8—44no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6D411yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C4⋊C4C2312yes—
83C32×C42C2311yescharacteristic
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C3×D24Q814yescomplemented
98#3384—31noSylow
99C22×C3×Q8—61no—
100C2×D3×Q8—21no—
101C2×C3×D8—31no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—32no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×C4⋊Q8C22×C311yescharacteristic
109C3×#125—32no—
110C3×C22⋊Q8—62no—
111C3×C22⋊Q8—61no—
112C3×C22⋊Q8—61no—
113C3×C22⋊Q8—62no—
114C3×C4×Q8—31no—
115C3×C4×D4—32no—
116C3×C4×D4—32no—
117C3×C4×D4—31no—
118C3×C4×D4—31no—
119C2×C3×C4⋊C4—61no—
120#946—21no—
121#946—22no—
122C2×D24C22×C311yescharacteristic
123#897—21no—
124#896—22no—
125#893C22×C312yes—
126#893C22×C312yes—
127D3×C4⋊C4—21no—
128#890C22×C312yes—
129#888C22×C312yes—
130C4×D12C22×C311yescharacteristic
131C4×D12C22×C311yescharacteristic
132C4×Dic6C22×C311yescharacteristic
133C3×#107—31no—
134C3×#107—32no—
135C3×#106—22no—
136C3×#106—22no—
137C3×#106—32no—
138C3×#106C2×D312yes—
139C3×#106C2×D312yes—
140C3×#106C22×C312yes—
141C3×#106C22×C312yes—
142C3×C4⋊C8—32no—
143C3×C4⋊C8—31no—
144C3×#102—31no—
145C3×#102—31no—
146C3×#102—32no—
147C3×#102—32no—
148C3×#97—32no—
149C3×C4×C8—21no—
150C3×C4×C8C2×D311yescharacteristic
151C3×C4×C8C22×C311yescharacteristic
152#821C22×C311yescharacteristic
153#821C22×C311yescharacteristic
154#818C22×C311yescharacteristic
155#815C22×C312yes—
156Dic3⋊C8C22×C312yes—
157#809C22×C312yes—
158#809C22×C312yes—
159#808C22×C312yes—
160#807C22×C312yes—
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C32×Q8—42no—
165C32×Q8—81no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12C2×Q812yes—
178C3×D12C2×Q812yescomplemented
179C3×C4×D3—44no—
180C3×C4×D3—42no—
181C3×C4×D3—42no—
182C3×C4×D3—82no—
183C3×Dic6—22no—
184C3×Dic6—44no—
185C32×C8—21no—
186C32×C8C2×Q812yescomplemented
187C3×C3⋊C8—22no—
188#554—31no—
189D4×Q8—31no—
190#501—32no—
191#498C3×D311yescharacteristic, complemented
192#478—32no—
193#476—31no—
194#476—32no—
195#474—31no—
196#446—31no—
197#442—32no—
198C4×D8—31no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—31no—
204C2×C3×Q8—41no—
205C2×C3×Q8—41no—
206C2×C3×Q8—62no—
207C2×C3×Q8—124no—
208C2×C3×D4—31no—
209C2×C3×D4—31no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214D3×Q8—44no—
215C2×D12C23×C311yescharacteristic
216C2×D12C23×C311yescharacteristic
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×Dic6—22no—
222C2×Dic6C3×D411yescharacteristic
223C3×D8—34no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—32no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C23×C311yescharacteristic
230C2×C3×C8C23×C311yescharacteristic
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4C22×D312yes—
247C3×C4⋊C4C22×D312yes—
248C3×C4⋊C4C23×C312yes—
249C3×C4⋊C4C23×C312yes—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—61no—
253C3×C22⋊C4—61no—
254C3×C42—21no—
255C3×C42—32no—
256C3×C42C22×D311yescharacteristic
257C3×C42C23×C311yescharacteristic
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—21no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—22no—
262C4⋊Dic3—22no—
263C4⋊Dic3C3×D411yescharacteristic
264C4⋊Dic3C23×C311yescharacteristic
265C4⋊Dic3C23×C311yescharacteristic
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268Dic3⋊C4C3×D412yes—
269C4×Dic3C23×C312yes—
270C2×C3⋊C8C23×C312yes—
271D24C3×Q814yescomplemented
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—42no—
281C32×C4—42no—
282C32×C4AGL(1,ℤ/8)12yes—
283C32×C4C22×Q811yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C22×Q8—61no—
290C2×D8—31no—
291C4⋊Q8—32no—
292C4⋊Q8C2×C3×D311yescharacteristic
293C4⋊Q8C2×C3×D311yescharacteristic
294#125—32no—
295C22⋊Q8—62no—
296C22⋊Q8—61no—
297C22⋊Q8—61no—
298C22⋊Q8—62no—
299C4×Q8—31no—
300C4×D4—32no—
301C4×D4—32no—
302C4×D4—31no—
303C4×D4—31no—
304C2×C4⋊C4—61no—
305#107—31no—
306#107—32no—
307#106—32no—
308#106C2×C3×D312yes—
309#106C2×C3×D312yes—
310C4⋊C8—32no—
311C4⋊C8—31no—
312#102—31no—
313#102—31no—
314#102—32no—
315#102—32no—
316#97—32no—
317C4×C8C2×C3×D311yescharacteristic
318C23×C3—61no—
319C23×C3—61no—
320C22×D3—21no—
321C22×D3—21no—
322C3×Q8—42no—
323C3×Q8—42no—
324C3×Q8—62no—
325C3×Q8—82no—
326C3×Q8—81no—
327C3×Q8—81no—
328C3×Q8—82no—
329C3×Q8—124no—
330C3×D4—32no—
331C3×D4—32no—
332C3×D4—61no—
333C3×D4—61no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—124no—
348C2×C3×C4—122no—
349C2×C3×C4—122no—
350C2×C3×C4—242no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C24×C311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3C2×C3×D412yes—
360C2×Dic3C2×C3×D412yes—
361D12—21no—
362D12—21no—
363D12C2×C3×Q812yes—
364D12C2×C3×Q812yescomplemented
365C4×D3—44no—
366C4×D3—42no—
367C4×D3—42no—
368C4×D3—82no—
369Dic6—22no—
370Dic6—44no—
371C3×C8—22no—
372C3×C8—21no—
373C3×C8—21no—
374C3×C8—22no—
375C3×C8—62no—
376C3×C8D3×Q812yescomplemented
377C3×C8C2×C3×Q812yescomplemented
378C3⋊C8—22no—
379C2×C32D4×Q811yescharacteristic
380C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
381C2×C32#57711yescharacteristic
382C3×D3—42no—
383C3×D3—42no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—31no—
387C2×Q8—62no—
388C2×Q8—124no—
389C2×D4—31no—
390C2×D4—31no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—61no—
394C22×C4—61no—
395D8—34no—
396C2×C8—32no—
397C2×C8C22×C3×D311yescharacteristic
398C2×C8C22×C3×D311yescharacteristic
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—31no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4C22×C3×D312yes—
409C4⋊C4C22×C3×D312yes—
410C22⋊C4—62no—
411C22⋊C4—62no—
412C22⋊C4—61no—
413C22⋊C4—61no—
414C42—32no—
415C42C22×C3×D311yescharacteristic
416C22×C3—21no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×C3×D411yescharacteristic
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—41no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4—62no—
443C3×C4—82no—
444C3×C4—82no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4#91412yes—
448C3×C4C3×AGL(1,ℤ/8)12yes—
449C3×C4C2×D3×Q811yescharacteristic
450C3×C4#100711yescharacteristic
451C3×C4C22×C3×Q811yescharacteristic
452C3×C4C3×2−1+411yescharacteristic
453Dic3—22no—
454Dic3—22no—
455Dic3—41no—
456Dic3—41no—
457C32#338411yescharacteristic, complemented, Sylow
458C23—61no—
459C23—61no—
460Q8—42no—
461Q8—62no—
462Q8—81no—
463Q8—124no—
464D4—32no—
465D4—32no—
466D4—61no—
467D4—61no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—124no—
475C2×C4—122no—
476C2×C4—122no—
477C2×C4—242no—
478C2×C4C3×D3×D411yescharacteristic
479C2×C4C3×D3×D411yescharacteristic
480C2×C4C23×C3×D311yescharacteristic
481C8—21no—
482C8—62no—
483C8C3×D3×Q812yescomplemented
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—122no—
488C2×C3—122no—
489C2×C3#572711yescharacteristic
490C2×C3C2×#91411yescharacteristic
491C2×C3#576211yescharacteristic
492C2×C3C3×D4×Q811yescharacteristic
493C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
494C2×C3C3×#57711yescharacteristic
495D3—42no—
496D3—42no—
497C22—62no—
498C22—62no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22C2×C3×D3×D411yescharacteristic
504C4—21no—
505C4—42no—
506C4—42no—
507C4—62no—
508C4—62no—
509C4—121no—
510C4—121no—
511C4C3×#91412yes—
512C4C2×C3×D3×Q811yescharacteristic
513C4C3×#100711yescharacteristic
514C3—21no—
515C3#8190511yescharacteristic, direct product factor
516C3C3×#338411yescharacteristic, complemented
517C2—122no—
518C2—122no—
519C2C3×#572711yescharacteristic
520C2C2×C3×#91411yescharacteristic
521C2C3×#576211yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#498C2
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC3×#498D3
hypocenterC3C3×#3384
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#498

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. C3×#5727C2semidirect
3. C32×#498C2semidirect
4. C3×#5087C2semidirect
5. C3×#5084C2semidirect
6. C3×#4871C2semidirect
7. C3×#4870C2semidirect
9. C3×#4856C2semidirect
11. C3×#4679C2semidirect
13. #81905C3direct (N × H)
45. #5730C2×C3semidirect
46. #5727C2×C3semidirect
49. C3×#498D3semidirect
50. C3×#498C2×C3semidirect
58. #5087C2×C3semidirect
59. #5084C2×C3semidirect
60. #4871C2×C3semidirect
61. #4870C2×C3semidirect
63. #4856C2×C3semidirect
65. #4679C2×C3semidirect
97. C3×D24Q8semidirect
178. C3×D12C2×Q8semidirect
186. C32×C8C2×Q8semidirect
191. #498C3×D3semidirect
271. D24C3×Q8semidirect
364. D12C2×C3×Q8semidirect
376. C3×C8D3×Q8semidirect
377. C3×C8C2×C3×Q8semidirect
457. C32#3384semidirect
483. C8C3×D3×Q8semidirect
515. C3#81905direct (N × H)
516. C3C3×#3384semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#57272
C32×#4982
C3×#50872
C3×#50842
C3×#48712
C3×#48702
C3×#48692
C3×#48562
C3×C4×D242
C3×#46792
C3×#33843
#819053