Finite Group Databasebeta

← C3×#81626 #11896041

Subgroups — C3×#81626 #11896041

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic
2C3×#5722C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5C3×#5084C211yesmaximal, characteristic
6C3×#4798C212yesmaximal
7C3×#4794C212yesmaximal
8C3×#4791C212yesmaximal, complemented
9C3×#4789C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3369—31nomaximal
13#81626C311yesmaximal, characteristic, direct product factor
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C3×#947C2212yes—
17C3×Q8×Dic3C2212yes—
18C3×#944—22no—
19C2×C3×#216C2212yes—
20C2×C3×#204C2211yescharacteristic
21C3×#898—22no—
22C3×#897—21no—
23C3×#892—21no—
24C3×#888—21no—
25C3×#888C2212yes—
26C3×#887—21no—
27C3×#887C2212yes—
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#103C2212yes—
32C32×#103C2212yes—
33C32×C4×C8C2211yescharacteristic
34C3×#835C2212yes—
35C3×#821C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#816C2211yescharacteristic
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×Q82—31no—
44C3×#556—31no—
45#5732C2×C311yescharacteristic
46#5722C2×C311yescharacteristic, complemented
47C3×#489—32no—
48C3×#487—21no—
49C3×#487D311yescharacteristic, complemented
50C3×#487C2×C311yescharacteristic, complemented
51C3×#476—31no—
52C3×#475—32no—
53C3×#464—32no—
54C3×#462—31no—
55C3×#446—31no—
56C3×#441—32no—
57C3×C4×SD16—31no—
58#5090C2×C311yescharacteristic, complemented
59#5084C2×C311yescharacteristic
60#4798C2×C312yes—
61#4794C2×C312yes—
62#4791C2×C312yescomplemented
63#4789C2×C312yescomplemented
64C4×#204C2×C311yescharacteristic
65#4679C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C42C2311yescharacteristic
80C3×#216—24no—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C3×#204—22no—
98#3369—31noSylow
99C2×C3×Q16—32no—
100C2×C3×SD16—31no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—61no—
105C3×C4⋊Q8—62no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×C4⋊Q8C22×C311yescharacteristic
109C3×C4⋊Q8C22×C311yescharacteristic
110C3×#126—62no—
111C3×#124—32no—
112C3×C22⋊Q8—61no—
113C3×C4×Q8—31no—
114C3×C4×Q8—32no—
115C3×C4×Q8—32no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×D4—31no—
119C3×#117—61no—
120#947C22×C312yes—
121Q8×Dic3C22×C312yes—
122#944—22no—
123C2×#216C22×C312yes—
124C2×#204C22×C311yescharacteristic
125#898—22no—
126#897—21no—
127#892—21no—
128#888—21no—
129#888C22×C312yes—
130#887—21no—
131#887C22×C312yes—
132C4×D12C22×C311yescharacteristic
133C4×Dic6C22×C311yescharacteristic
134C4×Dic6C22×C311yescharacteristic
135C3×#106—31no—
136C3×#106—32no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#103—22no—
140C3×#103—22no—
141C3×#103—32no—
142C3×#103—31no—
143C3×#103C2×D312yes—
144C3×#103C2×D312yes—
145C3×#103C22×C312yes—
146C3×#103C22×C312yes—
147C3×#102—31no—
148C3×#102—32no—
149C3×#97—32no—
150C3×C4×C8—21no—
151C3×C4×C8C2×D311yescharacteristic
152C3×C4×C8C22×C311yescharacteristic
153#835C22×C312yes—
154#821C22×C311yescharacteristic
155#817C22×C311yescharacteristic
156#816C22×C311yescharacteristic
157#815C22×C312yes—
158Dic3⋊C8C22×C312yes—
159#809C22×C312yes—
160#808C22×C312yes—
161C4⋊(C3⋊C8)C22×C311yescharacteristic
162C22×C3×D3—21no—
163C32×Q8—22no—
164C32×Q8—22no—
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×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×C4×D3—42no—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—82no—
182C3×Dic6#4112yes—
183C32×C8—21no—
184C32×C8—21no—
185C3×C3⋊C8—22no—
186Q82—31no—
187#556—31no—
188#489—32no—
189#487C3×D311yescharacteristic, complemented
190#476—31no—
191#475—32no—
192#464—32no—
193#462—31no—
194#446—31no—
195#441—32no—
196C4×SD16—31no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—41no—
203C2×C3×Q8—62no—
204C2×C3×Q8C22×D312yes—
205C2×C3×Q8C23×C312yes—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C2×D12C23×C311yescharacteristic
209C2×C4×D3—21no—
210C2×Dic6—22no—
211C2×Dic6C3×D411yescharacteristic
212C2×Dic6C23×C311yescharacteristic
213C3×Q16—64no—
214C3×SD16—62no—
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—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C23×C312yes—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42—62no—
248C3×C42—62no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C23×C311yescharacteristic
252#216—24no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—22no—
255(C2×D3)⋊C4—22no—
256C4⋊Dic3—22no—
257C4⋊Dic3C3×D411yescharacteristic
258C4⋊Dic3C23×C311yescharacteristic
259C4⋊Dic3C23×C311yescharacteristic
260Dic3⋊C4—21no—
261Dic3⋊C4—22no—
262Dic3⋊C4—22no—
263Dic3⋊C4C3×D412yes—
264C4×Dic3—21no—
265C4×Dic3—22no—
266C4×Dic3—22no—
267C4×Dic3C23×C312yes—
268C2×C3⋊C8C23×C312yes—
269#204—22no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C32×C4—21no—
275C32×C4—42no—
276C32×C4—42no—
277C32×C4#13712yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C2×Q16—32no—
286C2×SD16—31no—
287C4⋊Q8—32no—
288C4⋊Q8—61no—
289C4⋊Q8—62no—
290C4⋊Q8C2×C3×D311yescharacteristic
291C4⋊Q8C2×C3×D311yescharacteristic
292#126—62no—
293#124—32no—
294C22⋊Q8—61no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—32no—
298C4×Q8—31no—
299C4×Q8—61no—
300C4×D4—31no—
301#117—61no—
302#106—31no—
303#106—32no—
304C4⋊C8—32no—
305C4⋊C8—31no—
306#103—32no—
307#103—31no—
308#103C2×C3×D312yes—
309#103C2×C3×D312yes—
310#102—31no—
311#102—32no—
312#97—32no—
313C4×C8C2×C3×D311yescharacteristic
314C23×C3—61no—
315C22×D3—21no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—32no—
321C3×Q8—42no—
322C3×Q8—42no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×Q8—81no—
326C3×Q8—81no—
327C3×Q8—82no—
328C3×Q8—242no—
329C3×D4—61no—
330C3×D4—61no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—122no—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C24×C311yescharacteristic
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3C2×C3×D412yes—
356C2×Dic3C2×C3×D412yes—
357D12—21no—
358D12—21no—
359C4×D3—42no—
360Dic6—22no—
361Dic6—21no—
362Dic6—82no—
363Dic6C3×#4112yes—
364C3×C8—21no—
365C3×C8—21no—
366C3×C8—21no—
367C3×C8—21no—
368C3×C8—41no—
369C3×C8—41no—
370C3×C8—62no—
371C3⋊C8—22no—
372C2×C32#54811yescharacteristic
373C2×C32C2×#13711yescharacteristic
374C2×C32#57711yescharacteristic
375C3×D3—81no—
376C2×Q8—21no—
377C2×Q8—31no—
378C2×Q8—31no—
379C2×Q8—62no—
380C2×Q8C22×C3×D312yes—
381C2×D4—31no—
382C22×C4—61no—
383Q16—64no—
384SD16—62no—
385C2×C8—32no—
386C2×C8C22×C3×D311yescharacteristic
387C2×C8C22×C3×D311yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—31no—
392C4⋊C4—32no—
393C4⋊C4—31no—
394C4⋊C4—31no—
395C4⋊C4—62no—
396C4⋊C4—62no—
397C4⋊C4—62no—
398C4⋊C4—61no—
399C4⋊C4C22×C3×D312yes—
400C22⋊C4—62no—
401C22⋊C4—62no—
402C22⋊C4—61no—
403C42—32no—
404C42—62no—
405C42—62no—
406C42—61no—
407C42C22×C3×D311yescharacteristic
408C22×C3—21no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3C2×D3×D411yescharacteristic
413C22×C3C22×C3×D411yescharacteristic
414C2×D3—41no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—62no—
428C3×C4—62no—
429C3×C4—62no—
430C3×C4—82no—
431C3×C4—82no—
432C3×C4—121no—
433C3×C4—121no—
434C3×C4#91812yes—
435C3×C4C3×#13712yes—
436C3×C4D3×#4111yescharacteristic
437C3×C4#101011yescharacteristic
438C3×C4C2×C3×#4111yescharacteristic
439C3×C4C3×2−1+411yescharacteristic
440Dic3—22no—
441Dic3—22no—
442Dic3—22no—
443Dic3—41no—
444Dic3—41no—
445C32#336911yescharacteristic, complemented, Sylow
446C23—61no—
447Q8—22no—
448Q8—22no—
449Q8—32no—
450Q8—62no—
451Q8—61no—
452Q8—81no—
453Q8—242no—
454D4—61no—
455D4—61no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—122no—
464C2×C4C3×D3×D411yescharacteristic
465C2×C4C3×D3×D411yescharacteristic
466C2×C4C23×C3×D311yescharacteristic
467C8—21no—
468C8—21no—
469C8—62no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—241no—
474C2×C3#567711yescharacteristic
475C2×C3#576211yescharacteristic
476C2×C3C2×#91811yescharacteristic
477C2×C3C3×#54811yescharacteristic
478C2×C3C2×C3×#13711yescharacteristic
479C2×C3C3×#57711yescharacteristic
480D3—81no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22C2×C3×D3×D411yescharacteristic
485C4—21no—
486C4—42no—
487C4—42no—
488C4—62no—
489C4—62no—
490C4—62no—
491C4—121no—
492C4—121no—
493C4C3×#91812yes—
494C4C3×D3×#4111yescharacteristic
495C4C3×#101011yescharacteristic
496C3—21no—
497C3#8162611yescharacteristic, direct product factor
498C3C3×#336911yescharacteristic, complemented
499C2—241no—
500C2C3×#567711yescharacteristic
501C2C3×#576211yescharacteristic
502C2C2×C3×#91811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC3×#487D3
hypocenterC3C3×#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
2. C3×#5722C2semidirect
3. C32×#487C2semidirect
4. C3×#5090C2semidirect
8. C3×#4791C2semidirect
9. C3×#4789C2semidirect
11. C3×#4679C2semidirect
13. #81626C3direct (N × H)
46. #5722C2×C3semidirect
49. C3×#487D3semidirect
50. C3×#487C2×C3semidirect
58. #5090C2×C3semidirect
62. #4791C2×C3semidirect
63. #4789C2×C3semidirect
65. #4679C2×C3semidirect
189. #487C3×D3semidirect
445. C32#3369semidirect
497. C3#81626direct (N × H)
498. C3C3×#3369semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C3×#57222
C32×#4872
C3×#50902
C3×#50842
C3×#47982
C3×#47942
C3×#47912
C3×#47892
C3×C4×#2042
C3×#46792
C3×#33693
#816263