Finite Group Databasebeta

← C3×#69664 #11792231

Subgroups — C3×#69664 #11792231

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#932C212yesmaximal, complemented
2C3×#5510C211yesmaximal, characteristic, complemented
3C32×#390C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×#2006—31nomaximal
7#69664C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4—22no—
12C2×C32×C42C2211yescharacteristic
13C2×C3×#214—22no—
14C3×#932—24no—
15C3×#932—24no—
16C2×C3×#213—22no—
17C3×#930—22no—
18C2×C3×#208C2212yes—
19C3×#897—22no—
20C3×#895—22no—
21C3×#805—24no—
22C2×C3×AGL(1,ℤ/8)—32no—
23C3×#537—31no—
24C2×#932C2×C312yescomplemented
25#5510C2×C311yescharacteristic, complemented
26C2×C3×#104—32no—
27C3×#390—21no—
28C3×#390D311yescharacteristic, complemented
29C3×#390C2×C311yescharacteristic, complemented
30C2×#805C2×C312yescomplemented
31C3×#343—31no—
32#4530C2×C311yescharacteristic, complemented
33C24×C32—21no—
34C2×C32×D4—22no—
35C2×C32×D4—22no—
36C2×C32×D4—21no—
37C2×C32×D4D412yescomplemented
38C22×C32×C4—21no—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—22no—
42C3×#235—22no—
43C3×#235—22no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12—22no—
47C2×C3×D12D412yes—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yes—
50C32×C4⋊C4—22no—
51C32×C22⋊C4—44no—
52C32×C42—22no—
53C3×#214—28no—
54C3×#213—28no—
55C3×(C2×D3)⋊C4—24no—
56C3×C4⋊Dic3—22no—
57C3×#208—22no—
58C3×#208D414yescomplemented
59C2×C3×C3⋊C8—22no—
60#2006—31noSylow
61C2×C3×#41—32no—
62C22×C3×D4—21no—
63C22×C3×D4C2×D311yescharacteristic
64C22×C3×D4C22×C311yescharacteristic
65C2×#235C22×C312yes—
66C3×AGL(1,ℤ/8)—64no—
67C3×AGL(1,ℤ/8)—64no—
68C2×C3×SD16—62no—
69C2×C3×D8—62no—
70C2×C3×M16—32no—
71C3×C22⋊Q8—62no—
72C3×#121—62no—
73C3×#121—62no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C22×C311yescharacteristic
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—22no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C42—21no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C22×C311yescharacteristic
83C2×#214—22no—
84#932—24no—
85#932—24no—
86C2×#213—22no—
87#930—22no—
88C2×#208C22×C312yes—
89#897—22no—
90#895—22no—
91C3×#104—64no—
92#805—24no—
93C23×C32—22no—
94C23×C32—42no—
95C23×C32—42no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C2×D411yescharacteristic
99C22×C3×D3—22no—
100C32×D4—24no—
101C32×D4—42no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—42no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D412yes—
110C2×C32×C4#4111yescharacteristic
111C3×#67—42no—
112C3×#67—42no—
113C2×C3×Dic3—22no—
114C3×D12—22no—
115C3×D12—22no—
116C3×D12—82no—
117C3×C4×D3—42no—
118C3×C4×D3—42no—
119C3×Dic6—22no—
120C3×Dic6—22no—
121C3×C3⋊C8—24no—
122C2×AGL(1,ℤ/8)—32no—
123#537—31no—
124C2×#104—32no—
125#390C3×D311yescharacteristic, complemented
126#343—31no—
127C24×C3—22no—
128C24×C3—21no—
129C24×C3—21no—
130C3×#41—62no—
131C3×#41—62no—
132C3×#41—62no—
133C3×#41—62no—
134C2×C3×Q8—32no—
135C2×C3×D4—22no—
136C2×C3×D4—21no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4—22no—
141C2×C3×D4—21no—
142C2×C3×D4—22no—
143C2×C3×D4—32no—
144C2×C3×D4—42no—
145C2×C3×D4—42no—
146C2×C3×D4—62no—
147C2×C3×D4—62no—
148C2×C3×D4D1212yescomplemented
149C2×C3×D4C3×D412yescomplemented
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—62no—
156C22×C3×C4#6712yes—
157C22×C3×C4C3×D412yes—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×#67—22no—
161#235—22no—
162#235—22no—
163#235—22no—
164#235—22no—
165C2×D12—22no—
166C2×D12C3×D412yes—
167C2×C4×D3—22no—
168C2×Dic6C3×D412yes—
169C3×SD16—68no—
170C3×D8—68no—
171C3×M16—34no—
172C3×M16—62no—
173C2×C3×C8—62no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—42no—
177C3×C4⋊C4—62no—
178C3×C22⋊C4—44no—
179C3×C22⋊C4—44no—
180C3×C22⋊C4—48no—
181C3×C22⋊C4—64no—
182C3×C42—22no—
183C3×C42—22no—
184C3×C42—42no—
185#214—28no—
186#213—28no—
187(C2×D3)⋊C4—24no—
188C4⋊Dic3—22no—
189#208—22no—
190#208C3×D414yescomplemented
191C2×C3⋊C8—22no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—44no—
195C22×C32—42no—
196C22×C32—82no—
197C22×C32—81no—
198C22×C32—81no—
199C22×C32#12011yescharacteristic
200C22×C32#12111yescharacteristic
201C22×C32#12711yescharacteristic
202C2×C3×D3—42no—
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C32×C4—42no—
206C32×C4—42no—
207C32×C4#12012yes—
208C32×C4#12112yes—
209C3×Dic3—42no—
210C2×#41—32no—
211C22×D4C2×C3×D311yescharacteristic
212AGL(1,ℤ/8)—64no—
213AGL(1,ℤ/8)—64no—
214C2×SD16—62no—
215C2×D8—62no—
216C2×M16—32no—
217C22⋊Q8—62no—
218#121—62no—
219#121—62no—
220C2×C4⋊C4C2×C3×D311yescharacteristic
221C2×C22⋊C4—22no—
222C2×C42C2×C3×D311yescharacteristic
223#104—64no—
224C23×C3—24no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—21no—
228C23×C3—44no—
229C23×C3—42no—
230C23×C3—42no—
231C23×C3—42no—
232C23×C3—42no—
233C23×C3—44no—
234C23×C3—42no—
235C23×C3—42no—
236C23×C3—41no—
237C23×C3—41no—
238C23×C3—41no—
239C23×C3—41no—
240C23×C3—62no—
241C23×C3C2×#6711yescharacteristic
242C23×C3C2×C3×D411yescharacteristic
243C22×D3—22no—
244C3×Q8—62no—
245C3×Q8—62no—
246C3×D4—24no—
247C3×D4—24no—
248C3×D4—44no—
249C3×D4—44no—
250C3×D4—42no—
251C3×D4—42no—
252C3×D4—62no—
253C3×D4—62no—
254C3×D4—122no—
255C3×D4—122no—
256C3×D4—242no—
257C2×C3×C4—24no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—44no—
276C2×C3×C4—62no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4C2×D1211yescharacteristic
280C2×C3×C4#23511yescharacteristic
281C2×C3×C4D3×D412yes—
282C2×C3×C4D3×D412yes—
283C2×C3×C4C2×C3×D411yescharacteristic
284C2×C3×C4C2×C3×D412yes—
285C2×C3×C4C2×C3×D412yes—
286C2×C3×C4C3×#4111yescharacteristic
287#67—42no—
288#67—42no—
289C2×Dic3—22no—
290D12—22no—
291D12—22no—
292D12—82no—
293C4×D3—42no—
294C4×D3—42no—
295Dic6—22no—
296Dic6—22no—
297C3×C8—64no—
298C3⋊C8—24no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—82no—
302C2×C32#39211yescharacteristic
303C2×C32#45311yescharacteristic
304C2×C32#45411yescharacteristic
305C3×D3—82no—
306C24—21no—
307#41—62no—
308#41—62no—
309#41—62no—
310#41—62no—
311C2×Q8—32no—
312C2×D4—21no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—32no—
316C2×D4—62no—
317C2×D4—62no—
318C2×D4C3×D1212yescomplemented
319C22×C4—21no—
320C22×C4—62no—
321C22×C4C3×#6712yes—
322C22×C4C22×C3×D311yescharacteristic
323SD16—68no—
324D8—68no—
325M16—34no—
326M16—62no—
327C2×C8—62no—
328C4⋊C4—22no—
329C4⋊C4—62no—
330C22⋊C4—44no—
331C22⋊C4—64no—
332C42—22no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—44no—
343C22×C3—48no—
344C22×C3—44no—
345C22×C3—44no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—84no—
349C22×C3—82no—
350C22×C3—82no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3—122no—
358C22×C3—122no—
359C22×C3—122no—
360C22×C3#93011yescharacteristic
361C22×C3#93711yescharacteristic
362C22×C3#94011yescharacteristic
363C22×C3C3×#12011yescharacteristic
364C22×C3C3×#12111yescharacteristic
365C22×C3C3×#12711yescharacteristic
366C2×D3—42no—
367C2×D3—42no—
368C2×D3—42no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—44no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—42no—
376C3×C4—82no—
377C3×C4—122no—
378C3×C4#88212yes—
379C3×C4#88412yes—
380C3×C4C3×#12012yes—
381C3×C4C3×#12112yes—
382Dic3—42no—
383C32#200611yescharacteristic, complemented, Sylow
384C23—22no—
385C23—42no—
386C23—42no—
387C23—41no—
388C23—41no—
389C23—62no—
390C23C2×C3×#6711yescharacteristic
391Q8—62no—
392Q8—62no—
393D4—24no—
394D4—42no—
395D4—62no—
396D4—62no—
397D4—122no—
398D4—122no—
399D4—242no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—62no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4C2×C3×D1211yescharacteristic
409C2×C4C3×#23511yescharacteristic
410C2×C4C3×D3×D412yes—
411C2×C4C3×D3×D412yes—
412C8—64no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—84no—
423C2×C3—82no—
424C2×C3—82no—
425C2×C3—242no—
426C2×C3#496011yescharacteristic
427C2×C3#506211yescharacteristic
428C2×C3#507711yescharacteristic
429C2×C3C3×#39211yescharacteristic
430C2×C3C3×#45311yescharacteristic
431C2×C3C3×#45411yescharacteristic
432D3—82no—
433C22—21no—
434C22—21no—
435C22—44no—
436C22—42no—
437C22—82no—
438C22—81no—
439C22—81no—
440C22—122no—
441C22—122no—
442C22—122no—
443C22C3×#93011yescharacteristic
444C22C3×#93711yescharacteristic
445C22C3×#94011yescharacteristic
446C4—42no—
447C4—42no—
448C4—122no—
449C4C3×#88212yes—
450C4C3×#88412yes—
451C3—21no—
452C3#6966411yescharacteristic, direct product factor
453C3C3×#200611yescharacteristic, complemented
454C2—21no—
455C2—21no—
456C2—82no—
457C2—242no—
458C2C3×#496011yescharacteristic
459C2C3×#506211yescharacteristic
460C2C3×#507711yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC22×C32#120
hypercenterC3×#390D3
hypocenterC3C3×#2006
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
1. C2×C3×#932C2semidirect
2. C3×#5510C2semidirect
3. C32×#390C2semidirect
4. C2×C3×#805C2semidirect
5. C3×#4530C2semidirect
7. #69664C3direct (N × H)
24. C2×#932C2×C3semidirect
25. #5510C2×C3semidirect
28. C3×#390D3semidirect
29. C3×#390C2×C3semidirect
30. C2×#805C2×C3semidirect
32. #4530C2×C3semidirect
37. C2×C32×D4D4semidirect
58. C3×#208D4semidirect
125. #390C3×D3semidirect
148. C2×C3×D4D12semidirect
149. C2×C3×D4C3×D4semidirect
190. #208C3×D4semidirect
318. C2×D4C3×D12semidirect
383. C32#2006semidirect
452. C3#69664direct (N × H)
453. C3C3×#2006semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
C3×#55102
C32×#3902
C2×C3×#8052
C3×#45302
C3×#20063
#696643