Finite Group Databasebeta

← C3×#68989 #11783410

Subgroups — C3×#68989 #11783410

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C212yesmaximal
2C2×C3×#892C211yesmaximal, characteristic
3C32×#343C211yesmaximal, characteristic, complemented
4C3×#4554C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C3×#1742—31nomaximal
7#68989C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4C412yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×C4×Dic3C412yes—
14C2×C3×#208C2212yes—
15C3×D3×M16—24no—
16C3×D3×M16C418yescomplemented
17C2×C3×ΓL(1,𝔽25)—22no—
18C2×C3×D3×C8—22no—
19C3×#892—22no—
20C3×#892—22no—
21C22×C3×M16—32no—
22C2×C3×#117—31no—
23C2×D3×M16C2×C312yes—
24C2×#892C2×C311yescharacteristic
25C3×#343—21no—
26C3×#343—32no—
27C3×#343—31no—
28C3×#343D311yescharacteristic, complemented
29C3×#343C2×C311yescharacteristic, complemented
30#4554C2×C312yescomplemented
31#4530C2×C311yescharacteristic, complemented
32C23×C3×D3C2×C411yescharacteristic
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3×Dic3C2×C412yes—
36C22×C3×Dic3C2×C411yescharacteristic
37C2×C3×C4×D3C2×C414yes—
38C2×C3×C4×D3D412yes—
39C2×C3×C4×D3D412yes—
40C2×C3×C4×D3D412yes—
41C2×C3×C4×D3Q812yes—
42C32×M16—22no—
43C32×M16C2×C414yes—
44C2×C32×C8—22no—
45C32×C4⋊C4—22no—
46C3×(C2×D3)⋊C4—24no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3—22no—
49C3×C4×Dic3—22no—
50C3×#208—22no—
51C3×#208C2×C414yes—
52C2×C3×C3⋊C8—22no—
53C3×ΓL(1,𝔽25)—28no—
54C3×D3×C8—28no—
55#1742—31noSylow
56C23×C3×C4—31no—
57C22×C4×D3C22×C311yescharacteristic
58C2×C3×M16—22no—
59C2×C3×M16—32no—
60C2×C3×M16—38no—
61C2×C3×M16—62no—
62C2×C3×M16—64no—
63C2×C3×M16C2×D312yes—
64C2×C3×M16C22×C312yes—
65C22×C3×C8—62no—
66C3×#117—62no—
67C3×#117—62no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—31no—
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C3×C4⋊C4C22×C311yescharacteristic
72C2×C3×C22⋊C4—32no—
73C2×C3×C42—32no—
74C2×(C2×D3)⋊C4C3×C412yes—
75C2×C4⋊Dic3C22×C311yescharacteristic
76C2×C4×Dic3C3×C412yes—
77C2×#208C22×C312yes—
78D3×M16—24no—
79D3×M16C3×C418yescomplemented
80C2×ΓL(1,𝔽25)—22no—
81C2×D3×C8—22no—
82#892—22no—
83#892—22no—
84C23×C32C22×C411yescharacteristic
85C22×C3×D3—41no—
86C22×C3×D3—41no—
87C22×C3×D3C4212yes—
88C22×C3×D3C22⋊C412yes—
89C22×C3×D3C4⋊C412yes—
90C2×C32×C4—22no—
91C2×C32×C4—42no—
92C2×C32×C4C22×C412yes—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×Q811yescharacteristic
96C2×C3×Dic3—22no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3C4212yes—
99C2×C3×Dic3C22⋊C411yescharacteristic
100C2×C3×Dic3C22⋊C411yescharacteristic
101C2×C3×Dic3C4⋊C412yes—
102C3×C4×D3C22⋊C414yes—
103C3×C4×D3C22⋊C414yes—
104C3×C4×D3C4⋊C414yes—
105C3×C4×D3C4⋊C414yes—
106C32×C8—24no—
107C3×C3⋊C8—24no—
108C22×M16—32no—
109C2×#117—31no—
110#343—32no—
111#343—31no—
112#343C3×D311yescharacteristic, complemented
113C24×C3—31no—
114C23×D3C2×C3×C411yescharacteristic
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4—31no—
118C22×C3×C4—34no—
119C22×C3×C4—32no—
120C22×C3×C4—32no—
121C22×C3×C4—32no—
122C22×C3×C4—32no—
123C22×C3×C4—32no—
124C22×C3×C4C4×D312yes—
125C22×C3×C4C2×C3×C412yes—
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C23×C311yescharacteristic
128C22×Dic3C2×C3×C412yes—
129C22×Dic3C2×C3×C411yescharacteristic
130C2×C4×D3C2×C3×C414yes—
131C2×C4×D3C3×D412yes—
132C2×C4×D3C3×D412yes—
133C2×C4×D3C3×D412yes—
134C2×C4×D3C3×Q812yes—
135C3×M16—22no—
136C3×M16—22no—
137C3×M16—24no—
138C3×M16—34no—
139C3×M16—42no—
140C3×M16—68no—
141C3×M16—62no—
142C3×M16C4×D314yes—
143C3×M16C2×C3×C414yes—
144C2×C3×C8—22no—
145C2×C3×C8—22no—
146C2×C3×C8—42no—
147C2×C3×C8—68no—
148C2×C3×C8—62no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—22no—
151C3×C4⋊C4—42no—
152C3×C4⋊C4—62no—
153C3×C22⋊C4—64no—
154C3×C42—62no—
155C3×C42—62no—
156(C2×D3)⋊C4—24no—
157C4⋊Dic3—22no—
158C4×Dic3—22no—
159C4×Dic3—22no—
160#208—22no—
161#208C2×C3×C414yes—
162C2×C3⋊C8—22no—
163ΓL(1,𝔽25)—28no—
164D3×C8—28no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32C2×C4211yescharacteristic
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32C2×C4⋊C411yescharacteristic
170C2×C3×D3—22no—
171C2×C3×D3—22no—
172C2×C3×D3—42no—
173C2×C3×D3—42no—
174C2×C3×D3#9514yes—
175C32×C4—42no—
176C32×C4C2×C22⋊C412yes—
177C32×C4C2×C4⋊C412yes—
178C3×Dic3—42no—
179C3×Dic3#9512yes—
180C3×Dic3#9512yes—
181C23×C4—31no—
182C2×M16—32no—
183C2×M16—38no—
184C2×M16—62no—
185C2×M16—64no—
186C2×M16C2×C3×D312yes—
187C22×C8—62no—
188#117—62no—
189#117—62no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4C2×C3×D311yescharacteristic
192C2×C22⋊C4—32no—
193C2×C42—32no—
194C23×C3—21no—
195C23×C3—32no—
196C23×C3—32no—
197C23×C3—32no—
198C23×C3—121no—
199C23×C3—121no—
200C23×C3C2×C4×D311yescharacteristic
201C23×C3C22×C3×C411yescharacteristic
202C22×D3—41no—
203C22×D3—41no—
204C22×D3C3×C4212yes—
205C22×D3C3×C22⋊C412yes—
206C22×D3C3×C4⋊C412yes—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—32no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—32no—
217C2×C3×C4—34no—
218C2×C3×C4—34no—
219C2×C3×C4—34no—
220C2×C3×C4—34no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—62no—
225C2×C3×C4—82no—
226C2×C3×C4—122no—
227C2×C3×C4C2×C4×D312yes—
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D412yes—
230C2×C3×C4D3×Q811yescharacteristic
231C2×C3×C4C22×C3×C412yes—
232C2×C3×C4C2×C3×D411yescharacteristic
233C2×C3×C4C2×C3×D412yes—
234C2×C3×C4C2×C3×Q811yescharacteristic
235C2×Dic3—22no—
236C2×Dic3—42no—
237C2×Dic3C3×C4212yes—
238C2×Dic3C3×C22⋊C411yescharacteristic
239C2×Dic3C3×C22⋊C411yescharacteristic
240C2×Dic3C3×C4⋊C412yes—
241C4×D3C3×C22⋊C414yes—
242C4×D3C3×C22⋊C414yes—
243C4×D3C3×C4⋊C414yes—
244C4×D3C3×C4⋊C414yes—
245C3×C8—24no—
246C3×C8—24no—
247C3×C8—44no—
248C3×C8—64no—
249C3⋊C8—24no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32C2×#9511yescharacteristic
253C2×C32#41311yescharacteristic
254C2×C32#41311yescharacteristic
255C3×D3—24no—
256C24—31no—
257C22×C4—31no—
258C22×C4—34no—
259C22×C4—32no—
260C22×C4—32no—
261C22×C4—32no—
262C22×C4—32no—
263C22×C4—32no—
264C22×C4C3×C4×D312yes—
265C22×C4C22×C3×D311yescharacteristic
266M16—22no—
267M16—34no—
268M16—68no—
269M16—62no—
270M16C3×C4×D314yes—
271C2×C8—22no—
272C2×C8—68no—
273C2×C8—62no—
274C4⋊C4—22no—
275C4⋊C4—62no—
276C22⋊C4—64no—
277C42—62no—
278C42—62no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—34no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—62no—
290C22×C3—62no—
291C22×C3—122no—
292C22×C3—122no—
293C22×C3C42×D311yescharacteristic
294C22×C3D3×C22⋊C411yescharacteristic
295C22×C3D3×C4⋊C411yescharacteristic
296C22×C3C2×C3×C4211yescharacteristic
297C22×C3C2×C3×C22⋊C411yescharacteristic
298C22×C3C2×C3×C4⋊C411yescharacteristic
299C2×D3—22no—
300C2×D3—22no—
301C2×D3—42no—
302C2×D3—42no—
303C2×D3C3×#9514yes—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—32no—
307C3×C4—32no—
308C3×C4—42no—
309C3×C4—42no—
310C3×C4—82no—
311C3×C4—122no—
312C3×C4D3×C22⋊C412yes—
313C3×C4D3×C4⋊C412yes—
314C3×C4C2×C3×C22⋊C412yes—
315C3×C4C2×C3×C4⋊C412yes—
316Dic3—42no—
317Dic3C3×#9512yes—
318Dic3C3×#9512yes—
319C32#174211yescharacteristic, complemented, Sylow
320C23—32no—
321C23—32no—
322C23—32no—
323C23—121no—
324C23—121no—
325C23C2×C3×C4×D311yescharacteristic
326C2×C4—22no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—32no—
330C2×C4—32no—
331C2×C4—34no—
332C2×C4—34no—
333C2×C4—34no—
334C2×C4—34no—
335C2×C4—42no—
336C2×C4—62no—
337C2×C4—122no—
338C2×C4C2×C3×C4×D312yes—
339C2×C4C3×D3×D411yescharacteristic
340C2×C4C3×D3×D412yes—
341C2×C4C3×D3×Q811yescharacteristic
342C8—24no—
343C8—64no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—64no—
354C2×C3D3×#9511yescharacteristic
355C2×C3#474511yescharacteristic
356C2×C3#475111yescharacteristic
357C2×C3C2×C3×#9511yescharacteristic
358C2×C3C3×#41311yescharacteristic
359C2×C3C3×#41311yescharacteristic
360D3—24no—
361C22—21no—
362C22—21no—
363C22—34no—
364C22—62no—
365C22—62no—
366C22—122no—
367C22—122no—
368C22C3×C42×D311yescharacteristic
369C22C3×D3×C22⋊C411yescharacteristic
370C22C3×D3×C4⋊C411yescharacteristic
371C4—32no—
372C4—32no—
373C4—42no—
374C4—122no—
375C4C3×D3×C22⋊C412yes—
376C4C3×D3×C4⋊C412yes—
377C3—21no—
378C3#6898911yescharacteristic, direct product factor
379C3C3×#174211yescharacteristic, complemented
380C2—21no—
381C2—21no—
382C2—64no—
383C2C3×D3×#9511yescharacteristic
384C2C3×#474511yescharacteristic
385C2C3×#475111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#343D3
hypocenterC3C3×#1742
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
3. C32×#343C2semidirect
4. C3×#4554C2semidirect
5. C3×#4530C2semidirect
7. #68989C3direct (N × H)
16. C3×D3×M16C4semidirect
28. C3×#343D3semidirect
29. C3×#343C2×C3semidirect
30. #4554C2×C3semidirect
31. #4530C2×C3semidirect
79. D3×M16C3×C4semidirect
112. #343C3×D3semidirect
319. C32#1742semidirect
378. C3#68989direct (N × H)
379. C3C3×#1742semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C2×C3×#8922
C32×#3432
C3×#45542
C3×#45302
C3×#17423
#689893