Finite Group Databasebeta

← C3×#68759 #11787800

Subgroups — C3×#68759 #11787800

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2C2×C3×#875C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic
4C3×#5120C211yesmaximal, characteristic, complemented
5C3×#5004C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1885—31nomaximal
9#68759C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C3×#926C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#893—22no—
19C3×D3×C22⋊C4—22no—
20C3×#875—22no—
21C3×#875C414yescomplemented
22C3×C4×D12—22no—
23C3×#823—22no—
24C3×#816—22no—
25C3×#810—22no—
26C2×C3×#124—31no—
27C3×#518—31no—
28#5521C2×C311yescharacteristic
29C2×#875C2×C311yescharacteristic
30C3×#419—31no—
31C3×#419—31no—
32C2×C3×#100—31no—
33C2×#823C2×C311yescharacteristic
34#5120C2×C311yescharacteristic, complemented
35#5004C2×C311yescharacteristic, complemented
36C3×#339—21no—
37C3×#339—31no—
38C3×#339D311yescharacteristic, complemented
39C3×#339C2×C311yescharacteristic, complemented
40#4523C2×C311yescharacteristic, complemented
41C23×C3×D3D412yes—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C2×C3×D12D412yes—
51C2×C3×C4×D3—24no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6C2×C412yescomplemented
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61C32×C4⋊C4D412yes—
62C32×C22⋊C4—21no—
63C32×C42—21no—
64C32×C42—21no—
65C32×C42C2×C412yescomplemented
66C3×#217—21no—
67C3×(C2×D3)⋊C4—24no—
68C3×(C2×D3)⋊C4—28no—
69C3×C4⋊Dic3D412yes—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8—21no—
74#1885—31noSylow
75C22×C3×Q8—31no—
76C22×C3×D4—31no—
77C22×D12C22×C311yescharacteristic
78C22×Dic6C22×C311yescharacteristic
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C22×C311yescharacteristic
83C3×#124—34no—
84C3×#124—62no—
85C3×C4×D4—62no—
86C3×C4×D4—62no—
87C3×#117—21no—
88C3×#117—31no—
89C3×#117C2×D311yescharacteristic
90C3×#117C22×C311yescharacteristic
91C2×C3×C22⋊C4—62no—
92C2×C3×C22⋊C4—62no—
93C2×C3×C42—21no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C22×C311yescharacteristic
96C2×(C2×D3)⋊C4—22no—
97#926C22×C311yescharacteristic
98C2×#208C22×C311yescharacteristic
99#893—22no—
100D3×C22⋊C4—22no—
101#875—22no—
102#875C3×C414yescomplemented
103C4×D12—22no—
104C3×#103—62no—
105C3×#103—62no—
106C3×#100—62no—
107#823—22no—
108#816—22no—
109#810—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—44no—
114C22×C3×D3C22⋊C414yes—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—42no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C3×D12—22no—
129C3×D12—22no—
130C3×D12—22no—
131C3×D12—22no—
132C3×C4×D3—84no—
133C3×Dic6—22no—
134C3×Dic6—22no—
135C3×Dic6—41no—
136C3×Dic6—41no—
137C32×C8—41no—
138C3×C3⋊C8—41no—
139C2×#124—31no—
140#518—31no—
141#419—31no—
142#419—31no—
143C2×#100—31no—
144#339—31no—
145#339C3×D311yescharacteristic, complemented
146C24×C3—32no—
147C23×D3C3×D412yes—
148C2×C3×Q8—32no—
149C2×C3×Q8—61no—
150C2×C3×Q8—61no—
151C2×C3×Q8—61no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—41no—
164C22×C3×C4—64no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C23×C311yescharacteristic
168C22×Dic3—21no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12C2×C3×C412yes—
174C2×D12C3×D412yes—
175C2×C4×D3—24no—
176C2×Dic6—21no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6C2×C3×C412yescomplemented
182C3×M16—22no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—41no—
188C3×M16—61no—
189C3×M16—61no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—41no—
193C2×C3×C8—61no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4D1212yes—
197C3×C4⋊C4C3×D412yes—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—41no—
201C3×C22⋊C4—68no—
202C3×C22⋊C4—64no—
203C3×C22⋊C4—61no—
204C3×C42—21no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—22no—
209C3×C42—41no—
210C3×C42—41no—
211C3×C42—61no—
212C3×C42C4×D312yescomplemented
213C3×C42C2×C3×C412yescomplemented
214#217—21no—
215(C2×D3)⋊C4—24no—
216(C2×D3)⋊C4—28no—
217C4⋊Dic3C3×D412yes—
218C4×Dic3—21no—
219#208—21no—
220#208—21no—
221C2×C3⋊C8—21no—
222C22×C32—22no—
223C22×C32C2×C22⋊C411yescharacteristic
224C22×C32#12011yescharacteristic
225C22×C32#12311yescharacteristic
226C2×C3×D3—24no—
227C2×C3×D3—44no—
228C2×C3×D3—44no—
229C2×C3×D3—82no—
230C32×C4—42no—
231C32×C4—42no—
232C32×C4C4×D411yescharacteristic
233C32×C4C4×D411yescharacteristic
234C32×C4#12111yescharacteristic
235C32×C4#12111yescharacteristic
236C3×Dic3—42no—
237C3×Dic3—42no—
238C22×Q8—31no—
239C22×D4—31no—
240C2×M16—31no—
241C2×M16C2×C3×D311yescharacteristic
242#124—34no—
243#124—62no—
244C4×D4—62no—
245C4×D4—62no—
246#117—31no—
247#117C2×C3×D311yescharacteristic
248C2×C22⋊C4—62no—
249C2×C22⋊C4—62no—
250C2×C42C2×C3×D311yescharacteristic
251#103—62no—
252#103—62no—
253#100—62no—
254C23×C3—21no—
255C23×C3—34no—
256C23×C3—62no—
257C23×C3—62no—
258C23×C3—124no—
259C23×C3D3×D411yescharacteristic
260C23×C3C2×C3×D411yescharacteristic
261C22×D3—22no—
262C22×D3—22no—
263C22×D3—44no—
264C22×D3C3×C22⋊C414yes—
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—62no—
272C3×D4—62no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—44no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—244no—
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4#23911yescharacteristic
299C2×C3×C4C22×C3×C411yescharacteristic
300C2×C3×C4C2×C3×D411yescharacteristic
301C2×C3×C4C2×C3×D411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C3×#4111yescharacteristic
304C2×C3×C4C3×#4111yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309D12—22no—
310D12—22no—
311D12—22no—
312D12—22no—
313C4×D3—84no—
314Dic6—22no—
315Dic6—22no—
316Dic6—41no—
317Dic6—41no—
318C3×C8—42no—
319C3×C8—41no—
320C3×C8—41no—
321C3×C8—121no—
322C3⋊C8—41no—
323C2×C32—21no—
324C2×C32—21no—
325C2×C32#38611yescharacteristic
326C2×C32#45512yes—
327C3×D3—44no—
328C24—32no—
329C2×Q8—32no—
330C2×Q8—61no—
331C2×Q8—61no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×D4—32no—
336C2×D4—32no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C22×C4—21no—
342C22×C4—64no—
343C22×C4—61no—
344C22×C4C22×C3×D311yescharacteristic
345M16—21no—
346M16—21no—
347M16—61no—
348M16—61no—
349C2×C8—21no—
350C2×C8—61no—
351C4⋊C4—32no—
352C4⋊C4C3×D1212yes—
353C22⋊C4—21no—
354C22⋊C4—68no—
355C22⋊C4—64no—
356C22⋊C4—61no—
357C42—21no—
358C42—21no—
359C42—61no—
360C42C3×C4×D312yescomplemented
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—42no—
367C22×C3—64no—
368C22×C3—124no—
369C22×C3—124no—
370C22×C3—242no—
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3#88211yescharacteristic
373C22×C3#89411yescharacteristic
374C22×C3C2×C3×C22⋊C411yescharacteristic
375C22×C3C3×#12011yescharacteristic
376C22×C3C3×#12311yescharacteristic
377C2×D3—24no—
378C2×D3—44no—
379C2×D3—44no—
380C2×D3—82no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4—44no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—82no—
391C3×C4—122no—
392C3×C4—122no—
393C3×C4C4×D1211yescharacteristic
394C3×C4#88411yescharacteristic
395C3×C4#89311yescharacteristic
396C3×C4#89511yescharacteristic
397C3×C4C3×C4×D411yescharacteristic
398C3×C4C3×C4×D411yescharacteristic
399C3×C4C3×#12111yescharacteristic
400C3×C4C3×#12111yescharacteristic
401Dic3—42no—
402Dic3—42no—
403C32#188511yescharacteristic, complemented, Sylow
404C23—34no—
405C23—62no—
406C23—62no—
407C23—124no—
408C23C3×D3×D411yescharacteristic
409Q8—62no—
410Q8—62no—
411Q8—121no—
412Q8—121no—
413D4—62no—
414D4—62no—
415D4—62no—
416D4—62no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—42no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—244no—
425C2×C4C2×C3×C4×D311yescharacteristic
426C2×C4C2×C3×D1211yescharacteristic
427C2×C4C3×#23511yescharacteristic
428C2×C4C3×D3×D411yescharacteristic
429C2×C4C3×D3×D411yescharacteristic
430C2×C4C3×#23911yescharacteristic
431C8—41no—
432C8—121no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—124no—
442C2×C3#466511yescharacteristic
443C2×C3#482512yes—
444C2×C3C3×#38611yescharacteristic
445C2×C3C3×#45512yes—
446D3—44no—
447C22—22no—
448C22—64no—
449C22—124no—
450C22—124no—
451C22—242no—
452C22C3×D3×C22⋊C411yescharacteristic
453C22C3×#88211yescharacteristic
454C22C3×#89411yescharacteristic
455C4—42no—
456C4—42no—
457C4—122no—
458C4—122no—
459C4C3×C4×D1211yescharacteristic
460C4C3×#88411yescharacteristic
461C4C3×#89311yescharacteristic
462C4C3×#89511yescharacteristic
463C3—21no—
464C3#6875911yescharacteristic, direct product factor
465C3C3×#188511yescharacteristic, complemented
466C2—21no—
467C2—21no—
468C2—124no—
469C2C3×#466511yescharacteristic
470C2C3×#482512yes—
subgroupG/H
centerC22×C3#882
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#339C2
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#339D3
hypocenterC3C3×#1885
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
4. C3×#5120C2semidirect
5. C3×#5004C2semidirect
6. C32×#339C2semidirect
7. C3×#4523C2semidirect
9. #68759C3direct (N × H)
21. C3×#875C4semidirect
34. #5120C2×C3semidirect
35. #5004C2×C3semidirect
38. C3×#339D3semidirect
39. C3×#339C2×C3semidirect
40. #4523C2×C3semidirect
57. C2×C3×Dic6C2×C4semidirect
65. C32×C42C2×C4semidirect
102. #875C3×C4semidirect
145. #339C3×D3semidirect
181. C2×Dic6C2×C3×C4semidirect
212. C3×C42C4×D3semidirect
213. C3×C42C2×C3×C4semidirect
360. C42C3×C4×D3semidirect
403. C32#1885semidirect
464. C3#68759direct (N × H)
465. C3C3×#1885semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C2×C3×#8752
C2×C3×#8232
C3×#51202
C3×#50042
C32×#3392
C3×#45232
C3×#18853
#687593