Finite Group Databasebeta

← C3×#81954 #11897636

Subgroups — C3×#81954 #11897636

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic
2C3×#5722C211yesmaximal, characteristic, complemented
3C32×#500C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5C3×#5084C211yesmaximal, characteristic
6C3×#4890C212yesmaximal
7C3×#4889C212yesmaximal
8C3×#4877C212yesmaximal, complemented
9C3×#4876C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3385—31nomaximal
13#81954C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C3×#946—22no—
17C3×#944—22no—
18C2×C3×#204C2211yescharacteristic
19C3×#897—21no—
20C3×#893C2212yes—
21C3×D3×C4⋊C4—21no—
22C3×#890C2212yes—
23C3×#888—21no—
24C3×#888C2212yes—
25C3×#887—21no—
26C3×#887C2212yes—
27C3×C4×D12C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C32×#107C2212yes—
31C32×#107C2212yes—
32C32×C4×C8C2211yescharacteristic
33C3×#821C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#816C2211yescharacteristic
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×Q82—31no—
44C3×#554—31no—
45#5730C2×C311yescharacteristic
46#5722C2×C311yescharacteristic, complemented
47C3×#501—32no—
48C3×#500—21no—
49C3×#500D311yescharacteristic, complemented
50C3×#500C2×C311yescharacteristic, complemented
51C3×#479—32no—
52C3×#477—31no—
53C3×#476—31no—
54C3×#474—32no—
55C3×#446—31no—
56C3×#440—32no—
57C3×C4×SD16—31no—
58#5091C2×C311yescharacteristic, complemented
59#5084C2×C311yescharacteristic
60#4890C2×C312yes—
61#4889C2×C312yes—
62#4877C2×C312yescomplemented
63#4876C2×C312yescomplemented
64C4×#204C2×C311yescharacteristic
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—22no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C4⋊C4C2312yes—
80C32×C42C2311yescharacteristic
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96C3×#204Q814yescomplemented
97#3385—31noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8—32no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×C4⋊Q8C22×C311yescharacteristic
108C3×#125—32no—
109C3×C22⋊Q8—61no—
110C3×C22⋊Q8—62no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×Q8—31no—
114C3×C4×Q8—61no—
115C3×C4×D4—32no—
116C3×C4×D4—31no—
117C2×C3×C4⋊C4—61no—
118#946—22no—
119#944—22no—
120C2×#204C22×C311yescharacteristic
121#897—21no—
122#893C22×C312yes—
123D3×C4⋊C4—21no—
124#890C22×C312yes—
125#888—21no—
126#888C22×C312yes—
127#887—21no—
128#887C22×C312yes—
129C4×D12C22×C311yescharacteristic
130C4×Dic6C22×C311yescharacteristic
131C4×Dic6C22×C311yescharacteristic
132C3×#107—22no—
133C3×#107—22no—
134C3×#107—32no—
135C3×#107C2×D312yes—
136C3×#107C2×D312yes—
137C3×#107C22×C312yes—
138C3×#107C22×C312yes—
139C3×#106—31no—
140C3×#106—32no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×#103—31no—
144C3×#103—32no—
145C3×#102—31no—
146C3×#102—32no—
147C3×#97—32no—
148C3×C4×C8—21no—
149C3×C4×C8C2×D311yescharacteristic
150C3×C4×C8C22×C311yescharacteristic
151#821C22×C311yescharacteristic
152#817C22×C311yescharacteristic
153#816C22×C311yescharacteristic
154#815C22×C312yes—
155Dic3⋊C8C22×C312yes—
156#810C22×C312yes—
157#809C22×C312yes—
158#808C22×C312yes—
159#807C22×C312yes—
160C4⋊(C3⋊C8)C22×C311yescharacteristic
161C22×C3×D3—21no—
162C32×Q8—81no—
163C32×Q8—81no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D412yes—
174C3×D12—21no—
175C3×D12C2×Q812yes—
176C3×C4×D3—42no—
177C3×C4×D3—82no—
178C3×Dic6—22no—
179C3×Dic6—21no—
180C3×Dic6—82no—
181C3×Dic6C2×Q812yes—
182C32×C8—21no—
183C32×C8C2×Q812yes—
184C3×C3⋊C8—22no—
185Q82—31no—
186#554—31no—
187#501—32no—
188#500C3×D311yescharacteristic, complemented
189#479—32no—
190#477—31no—
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—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—41no—
203C2×C3×Q8—41no—
204C2×C3×Q8—62no—
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—22no—
212C2×Dic6C3×D411yescharacteristic
213C2×Dic6C23×C311yescharacteristic
214C3×SD16—34no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—32no—
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C23×C311yescharacteristic
221C2×C3×C8C23×C311yescharacteristic
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4C22×D312yes—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C23×C312yes—
242C3×C4⋊C4C23×C312yes—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42—62no—
248C3×C42—61no—
249C3×C42C22×D311yescharacteristic
250C3×C42C23×C311yescharacteristic
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—22no—
253C4⋊Dic3—22no—
254C4⋊Dic3C3×D411yescharacteristic
255C4⋊Dic3C23×C311yescharacteristic
256C4⋊Dic3C23×C311yescharacteristic
257Dic3⋊C4—21no—
258Dic3⋊C4—22no—
259Dic3⋊C4—22no—
260Dic3⋊C4—22no—
261Dic3⋊C4C3×D412yes—
262C4×Dic3—21no—
263C4×Dic3—22no—
264C4×Dic3C23×C312yes—
265C2×C3⋊C8C23×C312yes—
266#204C3×Q814yescomplemented
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—41no—
270C2×C3×D3—41no—
271C32×C4—21no—
272C32×C4—42no—
273C32×C4—42no—
274C32×C4#13712yes—
275C32×C4C22×Q811yescharacteristic
276C32×C42−1+411yescharacteristic
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—41no—
282C2×SD16—31no—
283C4⋊Q8—32no—
284C4⋊Q8—61no—
285C4⋊Q8—62no—
286C4⋊Q8C2×C3×D311yescharacteristic
287C4⋊Q8C2×C3×D311yescharacteristic
288#125—32no—
289C22⋊Q8—61no—
290C22⋊Q8—62no—
291C4×Q8—31no—
292C4×Q8—32no—
293C4×Q8—31no—
294C4×Q8—61no—
295C4×D4—32no—
296C4×D4—31no—
297C2×C4⋊C4—61no—
298#107—32no—
299#107C2×C3×D312yes—
300#107C2×C3×D312yes—
301#106—31no—
302#106—32no—
303C4⋊C8—32no—
304C4⋊C8—31no—
305#103—31no—
306#103—32no—
307#102—31no—
308#102—32no—
309#97—32no—
310C4×C8C2×C3×D311yescharacteristic
311C23×C3—61no—
312C22×D3—21no—
313C3×Q8—32no—
314C3×Q8—62no—
315C3×Q8—61no—
316C3×Q8—81no—
317C3×Q8—81no—
318C3×Q8—81no—
319C3×Q8—81no—
320C3×Q8—82no—
321C3×Q8—82no—
322C3×Q8—242no—
323C3×D4—32no—
324C3×D4—61no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—122no—
340C2×C3×C4—242no—
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C2×C3×D411yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C24×C311yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3C2×C3×D412yes—
351C2×Dic3C2×C3×D412yes—
352D12—21no—
353D12C2×C3×Q812yes—
354C4×D3—42no—
355C4×D3—82no—
356Dic6—22no—
357Dic6—21no—
358Dic6—82no—
359Dic6C2×C3×Q812yes—
360C3×C8—22no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—22no—
364C3×C8—62no—
365C3×C8D3×Q812yes—
366C3×C8C2×C3×Q812yes—
367C3⋊C8—22no—
368C2×C32D4×Q811yescharacteristic
369C2×C32C2×#13711yescharacteristic
370C2×C32#57611yescharacteristic
371C3×D3—42no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—31no—
375C2×Q8—31no—
376C2×Q8—62no—
377C2×D4—31no—
378C22×C4—62no—
379C22×C4—61no—
380SD16—34no—
381C2×C8—32no—
382C2×C8C22×C3×D311yescharacteristic
383C2×C8C22×C3×D311yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—31no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—62no—
393C4⋊C4—62no—
394C4⋊C4—61no—
395C4⋊C4C22×C3×D312yes—
396C4⋊C4C22×C3×D312yes—
397C22⋊C4—62no—
398C22⋊C4—61no—
399C42—32no—
400C42—62no—
401C42—61no—
402C42C22×C3×D311yescharacteristic
403C22×C3—21no—
404C22×C3—62no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3C2×D3×D411yescharacteristic
408C22×C3C22×C3×D411yescharacteristic
409C2×D3—22no—
410C2×D3—41no—
411C2×D3—41no—
412C3×C4—22no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—42no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—62no—
423C3×C4—62no—
424C3×C4—62no—
425C3×C4—82no—
426C3×C4—82no—
427C3×C4—121no—
428C3×C4—121no—
429C3×C4#91812yes—
430C3×C4C3×#13712yes—
431C3×C4C2×D3×Q811yescharacteristic
432C3×C4#100711yescharacteristic
433C3×C4C22×C3×Q811yescharacteristic
434C3×C4C3×2−1+411yescharacteristic
435Dic3—22no—
436Dic3—22no—
437Dic3—22no—
438Dic3—41no—
439Dic3—41no—
440C32#338511yescharacteristic, complemented, Sylow
441C23—61no—
442Q8—32no—
443Q8—62no—
444Q8—61no—
445Q8—81no—
446Q8—81no—
447Q8—242no—
448D4—32no—
449D4—61no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—122no—
458C2×C4—242no—
459C2×C4C3×D3×D411yescharacteristic
460C2×C4C3×D3×D411yescharacteristic
461C2×C4C23×C3×D311yescharacteristic
462C8—21no—
463C8—62no—
464C8C3×D3×Q812yes—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—122no—
469C2×C3#572711yescharacteristic
470C2×C3#575711yescharacteristic
471C2×C3C2×#91811yescharacteristic
472C2×C3C3×D4×Q811yescharacteristic
473C2×C3C2×C3×#13711yescharacteristic
474C2×C3C3×#57611yescharacteristic
475D3—42no—
476C22—62no—
477C22—121no—
478C22—121no—
479C22C2×C3×D3×D411yescharacteristic
480C4—21no—
481C4—42no—
482C4—42no—
483C4—62no—
484C4—62no—
485C4—62no—
486C4—121no—
487C4—121no—
488C4C3×#91812yes—
489C4C2×C3×D3×Q811yescharacteristic
490C4C3×#100711yescharacteristic
491C3—21no—
492C3#8195411yescharacteristic, direct product factor
493C3C3×#338511yescharacteristic, complemented
494C2—122no—
495C2C3×#572711yescharacteristic
496C2C3×#575711yescharacteristic
497C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#500C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#500D3
hypocenterC3C3×#3385
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#500

Complements

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

NH ≅ G/Ntype
2. C3×#5722C2semidirect
3. C32×#500C2semidirect
4. C3×#5091C2semidirect
8. C3×#4877C2semidirect
9. C3×#4876C2semidirect
11. C3×#4679C2semidirect
13. #81954C3direct (N × H)
46. #5722C2×C3semidirect
49. C3×#500D3semidirect
50. C3×#500C2×C3semidirect
58. #5091C2×C3semidirect
62. #4877C2×C3semidirect
63. #4876C2×C3semidirect
65. #4679C2×C3semidirect
96. C3×#204Q8semidirect
188. #500C3×D3semidirect
266. #204C3×Q8semidirect
440. C32#3385semidirect
492. C3#81954direct (N × H)
493. 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×#57222
C32×#5002
C3×#50912
C3×#50842
C3×#48902
C3×#48892
C3×#48772
C3×#48762
C3×C4×#2042
C3×#46792
C3×#33853
#819543