Finite Group Databasebeta

← C3×D3×#343 #11783388

Subgroups — C3×D3×#343 #11783388

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C212yesmaximal
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
3C32×#343C211yesmaximal, characteristic, complemented
4C3×#4554C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6C2×C3×#343—31nomaximal
7D3×#343C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C412yes—
9C22×C3×C4×D3C2211yescharacteristic
10C2×C32×M16C2212yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4C412yes—
14C2×C3×#208C2212yes—
15C3×D3×M16—24no—
16C3×D3×M16C418yescomplemented
17C2×C3×ΓL(1,𝔽25)—22no—
18C2×C3×D3×C8—22no—
19C3×D3×C4⋊C4—22no—
20C3×D3×C4⋊C4—22no—
21C22×C3×M16—32no—
22C22×C3×C4⋊C4—31no—
23C2×D3×M16C2×C312yes—
24C2×D3×C4⋊C4C2×C311yescharacteristic
25C3×#343—21no—
26C3×#343—32no—
27C3×#343—31no—
28C3×#343D311yescharacteristic, direct product factor
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×D3—22no—
38C2×C3×C4×D3—22no—
39C2×C3×C4×D3—44no—
40C2×C3×C4×D3C2×C414yes—
41C2×C3×C4×D3D412yes—
42C2×C3×C4×D3D412yes—
43C2×C3×C4×D3D412yes—
44C2×C3×C4×D3Q812yes—
45C32×M16—22no—
46C32×M16C2×C414yescomplemented
47C2×C32×C8—22no—
48C32×C4⋊C4—22no—
49C3×C4⋊Dic3—22no—
50C3×Dic3⋊C4—24no—
51C3×#208—22no—
52C3×#208C2×C414yescomplemented
53C2×C3×C3⋊C8—22no—
54C3×ΓL(1,𝔽25)—28no—
55C3×D3×C8—28no—
56C2×#343—31noSylow
57C23×C3×C4—31no—
58C23×C3×C4—32no—
59C22×C4×D3C3×C412yes—
60C22×C4×D3C22×C311yescharacteristic
61C2×C3×M16—22no—
62C2×C3×M16—32no—
63C2×C3×M16—38no—
64C2×C3×M16—62no—
65C2×C3×M16—64no—
66C2×C3×M16C2×D312yes—
67C2×C3×M16C22×C312yes—
68C22×C3×C8—62no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—32no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—62no—
73C2×C3×C4⋊C4—62no—
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C22×C311yescharacteristic
76C2×C4⋊Dic3C22×C311yescharacteristic
77C2×Dic3⋊C4C3×C412yes—
78C2×#208C22×C312yes—
79D3×M16—24no—
80D3×M16C3×C418yescomplemented
81C2×ΓL(1,𝔽25)—22no—
82C2×D3×C8—22no—
83D3×C4⋊C4—22no—
84D3×C4⋊C4—22no—
85C23×C32C22×C411yescharacteristic
86C22×C3×D3—22no—
87C22×C3×D3—22no—
88C22×C3×D3C4212yes—
89C22×C3×D3C22⋊C411yescharacteristic
90C22×C3×D3C22⋊C411yescharacteristic
91C22×C3×D3C4⋊C412yes—
92C2×C32×C4—22no—
93C2×C32×C4—42no—
94C2×C32×C4C22×C412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4C2×Q811yescharacteristic
98C2×C3×Dic3—22no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3C4212yes—
101C2×C3×Dic3C22⋊C412yes—
102C2×C3×Dic3C4⋊C412yes—
103C3×C4×D3—44no—
104C3×C4×D3—44no—
105C3×C4×D3C22⋊C414yes—
106C3×C4×D3C22⋊C414yes—
107C3×C4×D3C4⋊C414yes—
108C3×C4×D3C4⋊C414yes—
109C32×C8—24no—
110C3×C3⋊C8—24no—
111C22×M16—32no—
112C22×C4⋊C4—31no—
113#343—32no—
114#343—31no—
115#343C3×D311yescharacteristic, direct product factor
116C24×C3—31no—
117C23×D3C2×C3×C411yescharacteristic
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—31no—
121C22×C3×C4—34no—
122C22×C3×C4—32no—
123C22×C3×C4—32no—
124C22×C3×C4—32no—
125C22×C3×C4—32no—
126C22×C3×C4—32no—
127C22×C3×C4—62no—
128C22×C3×C4—62no—
129C22×C3×C4—124no—
130C22×C3×C4C4×D312yes—
131C22×C3×C4C2×C3×C412yes—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C23×C311yescharacteristic
134C22×Dic3C2×C3×C412yes—
135C22×Dic3C2×C3×C411yescharacteristic
136C2×C4×D3—22no—
137C2×C4×D3—22no—
138C2×C4×D3—44no—
139C2×C4×D3C2×C3×C414yes—
140C2×C4×D3C3×D412yes—
141C2×C4×D3C3×D412yes—
142C2×C4×D3C3×D412yes—
143C2×C4×D3C3×Q812yes—
144C3×M16—22no—
145C3×M16—22no—
146C3×M16—24no—
147C3×M16—34no—
148C3×M16—42no—
149C3×M16—68no—
150C3×M16—62no—
151C3×M16C4×D314yescomplemented
152C3×M16C2×C3×C414yescomplemented
153C2×C3×C8—22no—
154C2×C3×C8—22no—
155C2×C3×C8—42no—
156C2×C3×C8—68no—
157C2×C3×C8—62no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—42no—
161C3×C4⋊C4—64no—
162C3×C4⋊C4—62no—
163C4⋊Dic3—22no—
164Dic3⋊C4—24no—
165#208—22no—
166#208C2×C3×C414yescomplemented
167C2×C3⋊C8—22no—
168ΓL(1,𝔽25)—28no—
169D3×C8—28no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32C2×C4211yescharacteristic
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32C2×C4⋊C411yescharacteristic
175C2×C3×D3—21no—
176C2×C3×D3—21no—
177C2×C3×D3—24no—
178C2×C3×D3—24no—
179C2×C3×D3#9512yes—
180C2×C3×D3#9512yes—
181C2×C3×D3#10012yes—
182C2×C3×D3#10112yes—
183C32×C4—42no—
184C32×C4C2×C22⋊C412yes—
185C32×C4C2×C4⋊C412yes—
186C3×Dic3—42no—
187C3×Dic3#9514yes—
188C23×C4—31no—
189C23×C4—32no—
190C2×M16—32no—
191C2×M16—38no—
192C2×M16—62no—
193C2×M16—64no—
194C2×M16C2×C3×D312yes—
195C22×C8—62no—
196C2×C4⋊C4—32no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—62no—
199C2×C4⋊C4—62no—
200C2×C4⋊C4C2×C3×D311yescharacteristic
201C23×C3—21no—
202C23×C3—31no—
203C23×C3—32no—
204C23×C3—31no—
205C23×C3—32no—
206C23×C3—62no—
207C23×C3—62no—
208C23×C3C2×C4×D311yescharacteristic
209C23×C3C22×C3×C411yescharacteristic
210C22×D3—22no—
211C22×D3—22no—
212C22×D3C3×C4212yes—
213C22×D3C3×C22⋊C411yescharacteristic
214C22×D3C3×C22⋊C411yescharacteristic
215C22×D3C3×C4⋊C412yes—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—32no—
223C2×C3×C4—32no—
224C2×C3×C4—32no—
225C2×C3×C4—34no—
226C2×C3×C4—34no—
227C2×C3×C4—34no—
228C2×C3×C4—34no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—62no—
233C2×C3×C4—82no—
234C2×C3×C4—124no—
235C2×C3×C4—124no—
236C2×C3×C4—122no—
237C2×C3×C4C2×C4×D312yes—
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D412yes—
240C2×C3×C4D3×Q811yescharacteristic
241C2×C3×C4C22×C3×C412yes—
242C2×C3×C4C2×C3×D411yescharacteristic
243C2×C3×C4C2×C3×D412yes—
244C2×C3×C4C2×C3×Q811yescharacteristic
245C2×Dic3—22no—
246C2×Dic3—42no—
247C2×Dic3C3×C4212yes—
248C2×Dic3C3×C22⋊C412yes—
249C2×Dic3C3×C4⋊C412yes—
250C4×D3—44no—
251C4×D3—44no—
252C4×D3C3×C22⋊C414yes—
253C4×D3C3×C22⋊C414yes—
254C4×D3C3×C4⋊C414yes—
255C4×D3C3×C4⋊C414yes—
256C3×C8—24no—
257C3×C8—24no—
258C3×C8—44no—
259C3×C8—64no—
260C3⋊C8—24no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32C2×#9511yescharacteristic
264C2×C32C2×#10011yescharacteristic
265C2×C32C2×#10111yescharacteristic
266C3×D3—22no—
267C3×D3#34314yesdirect product factor
268C24—31no—
269C22×C4—31no—
270C22×C4—34no—
271C22×C4—32no—
272C22×C4—32no—
273C22×C4—32no—
274C22×C4—32no—
275C22×C4—32no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—124no—
279C22×C4C3×C4×D312yes—
280C22×C4C22×C3×D311yescharacteristic
281M16—22no—
282M16—34no—
283M16—68no—
284M16—62no—
285M16C3×C4×D314yescomplemented
286C2×C8—22no—
287C2×C8—68no—
288C2×C8—62no—
289C4⋊C4—22no—
290C4⋊C4—64no—
291C4⋊C4—62no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—32no—
300C22×C3—32no—
301C22×C3—32no—
302C22×C3—32no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—64no—
306C22×C3—64no—
307C22×C3—61no—
308C22×C3—61no—
309C22×C3C42×D311yescharacteristic
310C22×C3D3×C22⋊C411yescharacteristic
311C22×C3D3×C4⋊C411yescharacteristic
312C22×C3C2×C3×C4211yescharacteristic
313C22×C3C2×C3×C22⋊C411yescharacteristic
314C22×C3C2×C3×C4⋊C411yescharacteristic
315C2×D3—21no—
316C2×D3—21no—
317C2×D3—24no—
318C2×D3—24no—
319C2×D3C3×#9512yes—
320C2×D3C3×#9512yes—
321C2×D3C3×#10012yes—
322C2×D3C3×#10112yes—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—34no—
326C3×C4—42no—
327C3×C4—42no—
328C3×C4—82no—
329C3×C4—122no—
330C3×C4D3×C22⋊C412yes—
331C3×C4D3×C4⋊C412yes—
332C3×C4C2×C3×C22⋊C412yes—
333C3×C4C2×C3×C4⋊C412yes—
334Dic3—42no—
335Dic3C3×#9514yes—
336C32C2×#34311yescharacteristic, complemented, Sylow
337C23—31no—
338C23—31no—
339C23—32no—
340C23—32no—
341C23—62no—
342C23—62no—
343C23C2×C3×C4×D311yescharacteristic
344C2×C4—22no—
345C2×C4—32no—
346C2×C4—32no—
347C2×C4—32no—
348C2×C4—34no—
349C2×C4—34no—
350C2×C4—34no—
351C2×C4—34no—
352C2×C4—42no—
353C2×C4—62no—
354C2×C4—124no—
355C2×C4—124no—
356C2×C4—122no—
357C2×C4C2×C3×C4×D312yes—
358C2×C4C3×D3×D411yescharacteristic
359C2×C4C3×D3×D412yes—
360C2×C4C3×D3×Q811yescharacteristic
361C8—24no—
362C8—64no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—34no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—62no—
374C2×C3D3×#9511yescharacteristic
375C2×C3D3×#10011yescharacteristic
376C2×C3D3×#10111yescharacteristic
377C2×C3C2×C3×#9511yescharacteristic
378C2×C3C2×C3×#10011yescharacteristic
379C2×C3C2×C3×#10111yescharacteristic
380D3—22no—
381D3C3×#34314yesdirect product factor
382C22—21no—
383C22—21no—
384C22—32no—
385C22—32no—
386C22—32no—
387C22—32no—
388C22—64no—
389C22—64no—
390C22—61no—
391C22—61no—
392C22C3×C42×D311yescharacteristic
393C22C3×D3×C22⋊C411yescharacteristic
394C22C3×D3×C4⋊C411yescharacteristic
395C4—34no—
396C4—42no—
397C4—122no—
398C4C3×D3×C22⋊C412yes—
399C4C3×D3×C4⋊C412yes—
400C3—21no—
401C3D3×#34311yescharacteristic, direct product factor
402C3C2×C3×#34311yescharacteristic, complemented
403C2—21no—
404C2—21no—
405C2—34no—
406C2—62no—
407C2C3×D3×#9511yescharacteristic
408C2C3×D3×#10011yescharacteristic
409C2C3×D3×#10111yescharacteristic
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
hypocenterC3C2×C3×#343
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. D3×#343C3direct (N × H)
16. C3×D3×M16C4semidirect
28. C3×#343D3direct (N × H)
29. C3×#343C2×C3semidirect
30. #4554C2×C3semidirect
31. #4530C2×C3semidirect
46. C32×M16C2×C4semidirect
52. C3×#208C2×C4semidirect
80. D3×M16C3×C4semidirect
115. #343C3×D3direct (N × H)
151. C3×M16C4×D3semidirect
152. C3×M16C2×C3×C4semidirect
166. #208C2×C3×C4semidirect
267. C3×D3#343direct (N × H)
285. M16C3×C4×D3semidirect
336. C32C2×#343semidirect
381. D3C3×#343direct (N × H)
401. C3D3×#343direct (N × H)
402. C3C2×C3×#343semidirect

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×D3×C4⋊C42
C32×#3432
C3×#45542
C3×#45302
C2×C3×#3433
D3×#3433