Finite Group Databasebeta

← C3×#81137 #11897618

Subgroups — C3×#81137 #11897618

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C32×#477C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic
6C3×#4890C212yesmaximal
7C3×#4876C212yesmaximal, complemented
8C3×#4842C211yesmaximal, characteristic
9C3×#4831C211yesmaximal, characteristic, complemented
10C3×#4817C212yesmaximal
11C3×#4799C212yesmaximal, complemented
12C3×#3385—31nomaximal
13#81137C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C3×#946—22no—
17C3×Q8×Dic3C2212yes—
18C2×C3×#215C2211yescharacteristic
19C3×#897—21no—
20C3×#893C2212yes—
21C3×D3×C4⋊C4—21no—
22C3×#890C2212yes—
23C3×#888—22no—
24C3×#888C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×#869—21no—
27C3×#869C2211yescharacteristic
28C3×C4×Dic6—21no—
29C3×C4×Dic6C2211yescharacteristic
30C32×#107C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33C3×#835C2211yescharacteristic
34C3×#821C2212yes—
35C3×#817C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#809C2211yescharacteristic
39C3×#808C2211yescharacteristic
40C3×#807C2212yes—
41C3×#807C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×Q82—31no—
44C3×#554—31no—
45#5730C2×C311yescharacteristic
46Q8×Dic6C2×C311yescharacteristic, complemented
47C3×#501—32no—
48C3×#500—31no—
49C3×#479—32no—
50C3×#477—21no—
51C3×#477D311yescharacteristic, complemented
52C3×#477C2×C311yescharacteristic, complemented
53C3×#476—31no—
54C3×#474—32no—
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×SD16—31no—
58#5078C2×C311yescharacteristic, complemented
59C4×#215C2×C311yescharacteristic
60#4890C2×C312yes—
61#4876C2×C312yescomplemented
62#4842C2×C311yescharacteristic
63#4831C2×C311yescharacteristic, complemented
64#4817C2×C312yes—
65#4799C2×C312yescomplemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C32×C8C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2312yes—
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81C3×#215Q814yescomplemented
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97#3385—31noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C22×C311yescharacteristic
106C3×#125—32no—
107C3×C22⋊Q8—61no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—21no—
110C3×C4×Q8—31no—
111C3×C4×Q8—32no—
112C3×C4×Q8—61no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C22×C311yescharacteristic
115C3×C4×D4—32no—
116C3×C4×D4—31no—
117C2×C3×C4⋊C4—61no—
118#946—22no—
119Q8×Dic3C22×C312yes—
120C2×#215C22×C311yescharacteristic
121#897—21no—
122#893C22×C312yes—
123D3×C4⋊C4—21no—
124#890C22×C312yes—
125#888—22no—
126#888C22×C312yes—
127C4×D12C22×C311yescharacteristic
128#869—21no—
129#869C22×C311yescharacteristic
130C4×Dic6—21no—
131C4×Dic6C22×C311yescharacteristic
132C3×#107—22no—
133C3×#107—32no—
134C3×#107—32no—
135C3×#107C2×D312yes—
136C3×#107C22×C312yes—
137C3×#106—32no—
138C3×#106—31no—
139C3×C4⋊C8—21no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8C2×D311yescharacteristic
142C3×C4⋊C8C22×C311yescharacteristic
143C3×#103—22no—
144C3×#103—31no—
145C3×#103C2×D312yes—
146C3×#103C22×C312yes—
147C3×#102—32no—
148C3×#102—31no—
149C3×#97—32no—
150C3×C4×C8—31no—
151#835C22×C311yescharacteristic
152#821C22×C312yes—
153#817C22×C312yes—
154#815C22×C312yes—
155Dic3⋊C8C22×C312yes—
156#809C22×C311yescharacteristic
157#808C22×C311yescharacteristic
158#807C22×C312yes—
159#807C22×C312yes—
160C4×C3⋊C8C22×C311yescharacteristic
161C22×C3×D3—21no—
162C32×Q8—21no—
163C32×Q8—81no—
164C32×Q8C2×Q812yes—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—21no—
176C3×D12C2×Q812yes—
177C3×C4×D3—42no—
178C3×C4×D3—82no—
179C3×Dic6—22no—
180C3×Dic6—82no—
181C3×Dic6—81no—
182C32×C8—22no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8C2×Q812yes—
185Q82—31no—
186#554—31no—
187#501—32no—
188#500—31no—
189#479—32no—
190#477C3×D311yescharacteristic, complemented
191#476—31no—
192#474—32no—
193#446—31no—
194#440—32no—
195C4×SD16—31no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—41no—
201C2×C3×Q8—62no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×Q8C23×C311yescharacteristic
205C2×C3×D4—31no—
206C22×C3×C4—62no—
207C22×C3×C4—61no—
208C2×D12C23×C311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—22no—
211C2×Dic6—21no—
212C2×Dic6—22no—
213C2×Dic6C3×D411yescharacteristic
214C3×SD16—34no—
215C2×C3×C8—22no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C2×C3×C8C22×D312yes—
219C2×C3×C8C23×C312yes—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D312yes—
239C3×C4⋊C4C23×C312yes—
240C3×C4⋊C4C23×C311yescharacteristic
241C3×C22⋊C4—62no—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42—41no—
248C3×C42—62no—
249C3×C42C22×D311yescharacteristic
250C3×C42C23×C311yescharacteristic
251#215C3×Q814yescomplemented
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—22no—
254C4⋊Dic3—21no—
255C4⋊Dic3—22no—
256C4⋊Dic3—22no—
257C4⋊Dic3C3×D411yescharacteristic
258C4⋊Dic3C23×C312yes—
259C4⋊Dic3C23×C311yescharacteristic
260Dic3⋊C4—22no—
261Dic3⋊C4—22no—
262Dic3⋊C4C3×D412yes—
263C4×Dic3—22no—
264C4×Dic3C23×C312yes—
265C2×C3⋊C8C23×C311yescharacteristic
266C2×C3⋊C8C23×C311yescharacteristic
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—41no—
270C2×C3×D3—41no—
271C32×C4—22no—
272C32×C4—21no—
273C32×C4—41no—
274C32×C4—42no—
275C32×C4#13712yes—
276C32×C4C22×Q811yescharacteristic
277C32×C42−1+411yescharacteristic
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—42no—
282C2×SD16—31no—
283C4⋊Q8—32no—
284C4⋊Q8—31no—
285C4⋊Q8—61no—
286C4⋊Q8—62no—
287C4⋊Q8C2×C3×D311yescharacteristic
288#125—32no—
289C22⋊Q8—61no—
290C22⋊Q8—62no—
291C4×Q8—31no—
292C4×Q8—32no—
293C4×Q8—61no—
294C4×Q8C2×C3×D311yescharacteristic
295C4×D4—32no—
296C4×D4—31no—
297C2×C4⋊C4—61no—
298#107—32no—
299#107—32no—
300#107C2×C3×D312yes—
301#106—32no—
302#106—31no—
303C4⋊C8—32no—
304C4⋊C8C2×C3×D311yescharacteristic
305#103—31no—
306#103C2×C3×D312yes—
307#102—32no—
308#102—31no—
309#97—32no—
310C4×C8—31no—
311C23×C3—61no—
312C22×D3—21no—
313C3×Q8—21no—
314C3×Q8—21no—
315C3×Q8—22no—
316C3×Q8—41no—
317C3×Q8—62no—
318C3×Q8—81no—
319C3×Q8—81no—
320C3×Q8—82no—
321C3×Q8—241no—
322C3×Q8—242no—
323C3×Q8D3×Q812yes—
324C3×Q8C2×C3×Q812yes—
325C3×D4—32no—
326C3×D4—61no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—42no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—122no—
344C2×C3×C4—242no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C24×C311yescharacteristic
351C2×Dic3—22no—
352C2×Dic3—21no—
353C2×Dic3C2×C3×D412yes—
354C2×Dic3C2×C3×D412yes—
355D12—21no—
356D12C2×C3×Q812yes—
357C4×D3—42no—
358C4×D3—82no—
359Dic6—22no—
360Dic6—82no—
361Dic6—81no—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—32no—
365C3×C8—42no—
366C3×C8—61no—
367C3⋊C8—21no—
368C3⋊C8C2×C3×Q812yes—
369C2×C32D4×Q811yescharacteristic
370C2×C32C2×#13711yescharacteristic
371C2×C32#57611yescharacteristic
372C3×D3—42no—
373C2×Q8—21no—
374C2×Q8—31no—
375C2×Q8—62no—
376C2×Q8—61no—
377C2×Q8C22×C3×D311yescharacteristic
378C2×D4—31no—
379C22×C4—62no—
380C22×C4—61no—
381SD16—34no—
382C2×C8—31no—
383C2×C8—31no—
384C2×C8C22×C3×D312yes—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—32no—
390C4⋊C4—31no—
391C4⋊C4—62no—
392C4⋊C4—62no—
393C4⋊C4—62no—
394C4⋊C4—62no—
395C4⋊C4—61no—
396C4⋊C4C22×C3×D311yescharacteristic
397C4⋊C4C22×C3×D312yes—
398C22⋊C4—62no—
399C22⋊C4—61no—
400C42—21no—
401C42—32no—
402C42—62no—
403C42C22×C3×D311yescharacteristic
404C22×C3—21no—
405C22×C3—62no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×C3×D411yescharacteristic
410C2×D3—22no—
411C2×D3—41no—
412C2×D3—41no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—41no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—41no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—82no—
429C3×C4—81no—
430C3×C4—121no—
431C3×C4—122no—
432C3×C4#91812yes—
433C3×C4C3×#13712yes—
434C3×C4C2×D3×Q811yescharacteristic
435C3×C4#101011yescharacteristic
436C3×C4C22×C3×Q811yescharacteristic
437C3×C4C3×2−1+411yescharacteristic
438Dic3—22no—
439Dic3—22no—
440Dic3—41no—
441Dic3—42no—
442C32#338511yescharacteristic, complemented, Sylow
443C23—61no—
444Q8—21no—
445Q8—62no—
446Q8—81no—
447Q8—241no—
448Q8—242no—
449Q8C3×D3×Q812yes—
450D4—32no—
451D4—61no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—122no—
460C2×C4—242no—
461C2×C4C3×D3×D411yescharacteristic
462C2×C4C3×D3×D411yescharacteristic
463C2×C4C23×C3×D311yescharacteristic
464C8—22no—
465C8—32no—
466C8—61no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—122no—
471C2×C3#563211yescharacteristic
472C2×C3C2×#91811yescharacteristic
473C2×C3#577411yescharacteristic
474C2×C3C3×D4×Q811yescharacteristic
475C2×C3C2×C3×#13711yescharacteristic
476C2×C3C3×#57611yescharacteristic
477D3—42no—
478C22—62no—
479C22—121no—
480C22—121no—
481C22C2×C3×D3×D411yescharacteristic
482C4—21no—
483C4—22no—
484C4—42no—
485C4—41no—
486C4—62no—
487C4—62no—
488C4—121no—
489C4—122no—
490C4C3×#91812yes—
491C4C2×C3×D3×Q811yescharacteristic
492C4C3×#101011yescharacteristic
493C3—21no—
494C3#8113711yescharacteristic, direct product factor
495C3C3×#338511yescharacteristic, complemented
496C2—122no—
497C2C3×#563211yescharacteristic
498C2C2×C3×#91811yescharacteristic
499C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#477D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C32×#477C2semidirect
4. C3×#5078C2semidirect
7. C3×#4876C2semidirect
9. C3×#4831C2semidirect
11. C3×#4799C2semidirect
13. #81137C3direct (N × H)
46. Q8×Dic6C2×C3semidirect
51. C3×#477D3semidirect
52. C3×#477C2×C3semidirect
58. #5078C2×C3semidirect
61. #4876C2×C3semidirect
63. #4831C2×C3semidirect
65. #4799C2×C3semidirect
81. C3×#215Q8semidirect
190. #477C3×D3semidirect
251. #215C3×Q8semidirect
442. C32#3385semidirect
494. C3#81137direct (N × H)
495. C3C3×#3385semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×Q8×Dic62
C32×#4772
C3×#50782
C3×C4×#2152
C3×#48902
C3×#48762
C3×#48422
C3×#48312
C3×#48172
C3×#47992
C3×#33853
#811373