Finite Group Databasebeta

← C3×D3×#324 #11773727

Subgroups — C3×D3×#324 #11773727

Order 1152.

695 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C3×D3×C22⋊C8C212yesmaximal
3C32×#324C211yesmaximal, characteristic, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5C3×#4469C212yesmaximal, complemented
6C2×C3×#324—31nomaximal
7D3×#324C311yesmaximal, characteristic, direct product factor
8C22×C3×C4×D3C411yescharacteristic
9C22×C3×C4×D3C411yescharacteristic
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C411yescharacteristic
13C2×C3×Dic3⋊C4C411yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C2×C3×D3×C8—22no—
16C3×D3×C4⋊C4—22no—
17C3×D3×C4⋊C4—22no—
18C32×C22⋊C8C2212yes—
19C3×#830C2212yes—
20C3×(C2×D3)⋊C8—22no—
21C22×C3×C4⋊C4—31no—
22C2×D3×C4⋊C4C2×C311yescharacteristic
23C2×C3×C22⋊C8—32no—
24D3×C22⋊C8C2×C312yes—
25C3×#324—21no—
26C3×#324—31no—
27C3×#324—32no—
28C3×#324D311yescharacteristic, direct product factor
29C3×#324C2×C311yescharacteristic, complemented
30#4528C2×C311yescharacteristic, complemented
31#4469C2×C312yescomplemented
32C23×C3×D3C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3C2×C411yescharacteristic
37C22×C3×Dic3C2×C411yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C2×C3×C4×D3—21no—
40C2×C3×C4×D3—21no—
41C2×C3×C4×D3—22no—
42C2×C3×C4×D3—21no—
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—42no—
45C2×C3×C4×D3—42no—
46C2×C3×C4×D3C814yescomplemented
47C2×C3×C4×D3D412yes—
48C2×C3×C4×D3D412yes—
49C2×C32×C8—22no—
50C32×C4⋊C4—22no—
51C3×C4⋊Dic3—22no—
52C3×Dic3⋊C4—22no—
53C3×Dic3⋊C4—22no—
54C2×C3×C3⋊C8—22no—
55C3×D3×C8—44no—
56C2×#324—31noSylow
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C22×C4×D3C3×C411yescharacteristic
61C22×C4×D3C3×C411yescharacteristic
62C22×C4×D3C22×C311yescharacteristic
63C22×C3×C8—62no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—31no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4—62no—
69C2×C3×C4⋊C4—62no—
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C3×C4⋊C4C22×C311yescharacteristic
72C2×C4⋊Dic3C3×C411yescharacteristic
73C2×Dic3⋊C4C3×C411yescharacteristic
74C2×Dic3⋊C4C22×C311yescharacteristic
75C2×D3×C8—22no—
76D3×C4⋊C4—22no—
77D3×C4⋊C4—22no—
78C3×C22⋊C8—22no—
79C3×C22⋊C8—32no—
80C3×C22⋊C8—62no—
81C3×C22⋊C8C2×D312yes—
82C3×C22⋊C8C22×C312yes—
83#830C22×C312yes—
84(C2×D3)⋊C8—22no—
85C23×C32C22×C411yescharacteristic
86C22×C3×D3—22no—
87C22×C3×D3—22no—
88C22×C3×D3C22⋊C411yescharacteristic
89C22×C3×D3C22⋊C411yescharacteristic
90C22×C3×D3C2×C812yes—
91C22×C3×D3M1612yes—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×C812yescomplemented
98C2×C32×C4C2×D412yes—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3C22⋊C412yes—
105C2×C3×Dic3C2×C812yescomplemented
106C3×C4×D3—24no—
107C3×C4×D3—24no—
108C3×C4×D3—24no—
109C3×C4×D3—42no—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C32×C8—42no—
113C3×C3⋊C8—42no—
114C22×C4⋊C4—31no—
115C2×C22⋊C8—32no—
116#324—31no—
117#324—32no—
118#324C3×D311yescharacteristic, direct product factor
119C24×C3—31no—
120C23×D3C2×C3×C411yescharacteristic
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—31no—
125C22×C3×C4—31no—
126C22×C3×C4—34no—
127C22×C3×C4—32no—
128C22×C3×C4—32no—
129C22×C3×C4—31no—
130C22×C3×C4—61no—
131C22×C3×C4—61no—
132C22×C3×C4—62no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C22×C3×C4—122no—
136C22×C3×C4—122no—
137C22×C3×C4C4×D311yescharacteristic
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4C2×C3×C411yescharacteristic
140C22×C3×C4C2×C3×C411yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C23×C311yescharacteristic
143C22×Dic3C2×C3×C411yescharacteristic
144C22×Dic3C2×C3×C411yescharacteristic
145C22×Dic3C2×C3×C411yescharacteristic
146C2×C4×D3—21no—
147C2×C4×D3—21no—
148C2×C4×D3—22no—
149C2×C4×D3—21no—
150C2×C4×D3—21no—
151C2×C4×D3—42no—
152C2×C4×D3—42no—
153C2×C4×D3C3×C814yescomplemented
154C2×C4×D3C3×D412yes—
155C2×C4×D3C3×D412yes—
156C2×C3×C8—22no—
157C2×C3×C8—22no—
158C2×C3×C8—42no—
159C2×C3×C8—62no—
160C2×C3×C8—124no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—42no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—62no—
166C3×C4⋊C4—62no—
167C4⋊Dic3—22no—
168Dic3⋊C4—22no—
169Dic3⋊C4—22no—
170C2×C3⋊C8—22no—
171D3×C8—44no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32C2×C22⋊C411yescharacteristic
175C22×C32C22×C811yescharacteristic
176C22×C32C2×M1611yescharacteristic
177C2×C3×D3—21no—
178C2×C3×D3—21no—
179C2×C3×D3—24no—
180C2×C3×D3—24no—
181C2×C3×D3C22⋊C812yes—
182C2×C3×D3C22⋊C812yes—
183C2×C3×D3#9912yes—
184C2×C3×D3#10112yes—
185C32×C4—22no—
186C32×C4—22no—
187C32×C4—41no—
188C3×Dic3—22no—
189C3×Dic3—22no—
190C3×Dic3—41no—
191C23×C4—31no—
192C23×C4—31no—
193C23×C4—31no—
194C22×C8—62no—
195C2×C4⋊C4—31no—
196C2×C4⋊C4—31no—
197C2×C4⋊C4—31no—
198C2×C4⋊C4—62no—
199C2×C4⋊C4—62no—
200C2×C4⋊C4C2×C3×D311yescharacteristic
201C22⋊C8—32no—
202C22⋊C8—62no—
203C22⋊C8C2×C3×D312yes—
204C23×C3—21no—
205C23×C3—31no—
206C23×C3—31no—
207C23×C3—32no—
208C23×C3—32no—
209C23×C3—62no—
210C23×C3—62no—
211C23×C3C2×C4×D311yescharacteristic
212C23×C3C22×C3×C411yescharacteristic
213C22×D3—22no—
214C22×D3—22no—
215C22×D3C3×C22⋊C411yescharacteristic
216C22×D3C3×C22⋊C411yescharacteristic
217C22×D3C2×C3×C812yes—
218C22×D3C3×M1612yes—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—32no—
228C2×C3×C4—32no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4—64no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—81no—
243C2×C3×C4—81no—
244C2×C3×C4—122no—
245C2×C3×C4—122no—
246C2×C3×C4—122no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4D3×C812yescomplemented
250C2×C3×C4C2×C3×C812yescomplemented
251C2×C3×C4D3×D412yes—
252C2×C3×C4C2×C3×D412yes—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—41no—
257C2×Dic3—41no—
258C2×Dic3C3×C22⋊C412yes—
259C2×Dic3C2×C3×C812yescomplemented
260C4×D3—24no—
261C4×D3—24no—
262C4×D3—24no—
263C4×D3—42no—
264C4×D3—42no—
265C4×D3—42no—
266C3×C8—42no—
267C3×C8—42no—
268C3×C8—82no—
269C3×C8—122no—
270C3⋊C8—42no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32C2×C22⋊C811yescharacteristic
274C2×C32C2×#9911yescharacteristic
275C2×C32C2×#10111yescharacteristic
276C3×D3—22no—
277C3×D3#32414yesdirect product factor
278C24—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—34no—
282C22×C4—32no—
283C22×C4—32no—
284C22×C4—31no—
285C22×C4—61no—
286C22×C4—61no—
287C22×C4—62no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—122no—
291C22×C4—122no—
292C22×C4C3×C4×D311yescharacteristic
293C22×C4C3×C4×D311yescharacteristic
294C22×C4C22×C3×D311yescharacteristic
295C2×C8—22no—
296C2×C8—62no—
297C2×C8—124no—
298C4⋊C4—22no—
299C4⋊C4—62no—
300C4⋊C4—62no—
301C4⋊C4—62no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—32no—
310C22×C3—32no—
311C22×C3—32no—
312C22×C3—32no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—64no—
316C22×C3—64no—
317C22×C3—61no—
318C22×C3—61no—
319C22×C3D3×C22⋊C411yescharacteristic
320C22×C3C2×D3×C811yescharacteristic
321C22×C3D3×M1611yescharacteristic
322C22×C3C2×C3×C22⋊C411yescharacteristic
323C22×C3C22×C3×C811yescharacteristic
324C22×C3C2×C3×M1611yescharacteristic
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—24no—
328C2×D3—24no—
329C2×D3C3×C22⋊C812yes—
330C2×D3C3×C22⋊C812yes—
331C2×D3C3×#9912yes—
332C2×D3C3×#10112yes—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—42no—
338C3×C4—42no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—62no—
342C3×C4—62no—
343C3×C4—81no—
344C3×C4—121no—
345Dic3—22no—
346Dic3—22no—
347Dic3—41no—
348C32C2×#32411yescharacteristic, complemented, Sylow
349C23—31no—
350C23—31no—
351C23—32no—
352C23—32no—
353C23—62no—
354C23—62no—
355C23C2×C3×C4×D311yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—32no—
360C2×C4—32no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—64no—
364C2×C4—64no—
365C2×C4—64no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—122no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4C3×D3×C812yescomplemented
375C2×C4C3×D3×D412yes—
376C8—42no—
377C8—122no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—34no—
386C2×C3—41no—
387C2×C3—41no—
388C2×C3—62no—
389C2×C3D3×C22⋊C811yescharacteristic
390C2×C3D3×#9911yescharacteristic
391C2×C3D3×#10111yescharacteristic
392C2×C3C2×C3×C22⋊C811yescharacteristic
393C2×C3C2×C3×#9911yescharacteristic
394C2×C3C2×C3×#10111yescharacteristic
395D3—22no—
396D3C3×#32414yesdirect product factor
397C22—21no—
398C22—21no—
399C22—32no—
400C22—32no—
401C22—32no—
402C22—32no—
403C22—64no—
404C22—64no—
405C22—61no—
406C22—61no—
407C22C3×D3×C22⋊C411yescharacteristic
408C22C2×C3×D3×C811yescharacteristic
409C22C3×D3×M1611yescharacteristic
410C4—22no—
411C4—22no—
412C4—41no—
413C4—62no—
414C4—62no—
415C4—121no—
416C3—21no—
417C3D3×#32411yescharacteristic, direct product factor
418C3C2×C3×#32411yescharacteristic, complemented
419C2—21no—
420C2—21no—
421C2—34no—
422C2—62no—
423C2C3×D3×C22⋊C811yescharacteristic
424C2C3×D3×#9911yescharacteristic
425C2C3×D3×#10111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#324D3
hypocenterC3C2×C3×#324
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
3. C32×#324C2semidirect
4. C3×#4528C2semidirect
5. C3×#4469C2semidirect
7. D3×#324C3direct (N × H)
28. C3×#324D3direct (N × H)
29. C3×#324C2×C3semidirect
30. #4528C2×C3semidirect
31. #4469C2×C3semidirect
46. C2×C3×C4×D3C8semidirect
97. C2×C32×C4C2×C8semidirect
105. C2×C3×Dic3C2×C8semidirect
118. #324C3×D3direct (N × H)
153. C2×C4×D3C3×C8semidirect
249. C2×C3×C4D3×C8semidirect
250. C2×C3×C4C2×C3×C8semidirect
259. C2×Dic3C2×C3×C8semidirect
277. C3×D3#324direct (N × H)
348. C32C2×#324semidirect
374. C2×C4C3×D3×C8semidirect
396. D3C3×#324direct (N × H)
417. C3D3×#324direct (N × H)
418. C3C2×C3×#324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C3×D3×C22⋊C82
C32×#3242
C3×#45282
C3×#44692
C2×C3×#3243
D3×#3243