Finite Group Databasebeta

← C3×Dic3×C22⋊C8 #11783553

Subgroups — C3×Dic3×C22⋊C8 #11783553

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×Dic3C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×C3×C8×Dic3C212yesmaximal, complemented
5C3×#4550C212yesmaximal, complemented
6C3×C4×C22⋊C8—31nomaximal
7Dic3×C22⋊C8C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C23×C3×Dic3C412yes—
10C22×C32×C8C2212yes—
11C2×C3×C4×Dic3—24no—
12C2×C3×C4×Dic3C412yes—
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2212yes—
16C32×C22⋊C8C414yescomplemented
17C3×#830C414yescomplemented
18C3×C8×Dic3—24no—
19C22×C3×C42—31no—
20C22×C4×Dic3C2×C311yescharacteristic
21C2×C3×C22⋊C8—21no—
22C2×C3×C22⋊C8—31no—
23C2×C3×C22⋊C8D311yescharacteristic
24C2×C3×C22⋊C8C2×C311yescharacteristic
25C2×C3×C4×C8—32no—
26C2×#830C2×C311yescharacteristic
27C2×C8×Dic3C2×C312yescomplemented
28C3×#336—32no—
29#4550C2×C312yescomplemented
30C24×C32C2×C411yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3—24no—
38C22×C3×Dic3—24no—
39C22×C3×Dic3C818yescomplemented
40C22×C3×Dic3C2×C412yes—
41C22×C3×Dic3C2×C412yes—
42C2×C32×C8—22no—
43C2×C32×C8—22no—
44C2×C32×C8C2×C414yescomplemented
45C3×C4×Dic3—22no—
46C3×C4×Dic3—24no—
47C3×C4×Dic3D414yes—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8C2×C414yescomplemented
51C4×C22⋊C8—31noSylow
52C23×C3×C4—21no—
53C23×C3×C4—32no—
54C23×C3×C4C2×D311yescharacteristic
55C23×C3×C4C22×C311yescharacteristic
56C23×Dic3C3×C412yes—
57C22×C3×C8—22no—
58C22×C3×C8—32no—
59C22×C3×C8C2×D312yes—
60C22×C3×C8C22×C312yes—
61C2×C3×C42—31no—
62C2×C3×C42—32no—
63C2×C3×C42—31no—
64C2×C3×C42—64no—
65C2×C4×Dic3—24no—
66C2×C4×Dic3C3×C412yes—
67C2×C4×Dic3C22×C311yescharacteristic
68C2×C4×Dic3C22×C311yescharacteristic
69C22×C3⋊C8C22×C312yes—
70C3×C22⋊C8—24no—
71C3×C22⋊C8—34no—
72C3×C22⋊C8Dic314yesdirect product factor
73C3×C22⋊C8C3×C414yescomplemented
74C3×C4×C8—64no—
75#830C3×C414yescomplemented
76C8×Dic3—24no—
77C23×C32—21no—
78C23×C32—21no—
79C23×C32—22no—
80C23×C32C4212yes—
81C23×C32C2×C814yes—
82C23×C32C22×C411yescharacteristic
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—24no—
86C2×C32×C4—24no—
87C2×C32×C4C4212yes—
88C2×C32×C4C22×C411yescharacteristic
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D412yes—
91C2×C32×C4#4112yes—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—216no—
95C2×C3×Dic3C22⋊C414yes—
96C2×C3×Dic3C2×C814yes—
97C2×C3×Dic3C2×C814yes—
98C2×C3×Dic3M1614yes—
99C32×C8—24no—
100C3×C3⋊C8—24no—
101C22×C42—31no—
102C2×C22⋊C8—31no—
103C2×C22⋊C8C3×D311yescharacteristic
104C2×C4×C8—32no—
105#336—32no—
106C24×C3—21no—
107C24×C3C4×D311yescharacteristic
108C24×C3C2×C3×C411yescharacteristic
109C22×C3×C4—22no—
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—21no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4—32no—
118C22×C3×C4—38no—
119C22×C3×C4—32no—
120C22×C3×C4—42no—
121C22×C3×C4—42no—
122C22×C3×C4—64no—
123C22×C3×C4—64no—
124C22×C3×C4C4×D311yescharacteristic
125C22×C3×C4C4×D312yes—
126C22×C3×C4C2×Dic312yes—
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C2×C3×C412yes—
129C22×C3×C4C2×C3×C412yes—
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C23×C311yescharacteristic
132C22×Dic3—24no—
133C22×Dic3—24no—
134C22×Dic3C3×C818yescomplemented
135C22×Dic3C2×C3×C412yes—
136C22×Dic3C2×C3×C412yes—
137C2×C3×C8—22no—
138C2×C3×C8—22no—
139C2×C3×C8—22no—
140C2×C3×C8—22no—
141C2×C3×C8—24no—
142C2×C3×C8—34no—
143C2×C3×C8—42no—
144C2×C3×C8—42no—
145C2×C3×C8—62no—
146C2×C3×C8—62no—
147C2×C3×C8C2×Dic314yescomplemented
148C2×C3×C8C2×C3×C414yescomplemented
149C3×C42—34no—
150C3×C42—64no—
151C3×C42—62no—
152C4×Dic3—22no—
153C4×Dic3—24no—
154C4×Dic3C3×D414yes—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157C2×C3⋊C8C2×C3×C414yescomplemented
158C22×C32—22no—
159C22×C32—22no—
160C22×C32—24no—
161C22×C32—24no—
162C22×C32C4×C814yescomplemented
163C22×C32C2×C4211yescharacteristic
164C22×C32C2×C22⋊C411yescharacteristic
165C22×C32#11711yescharacteristic
166C22×C32C22×C812yes—
167C22×C32C2×M1612yes—
168C32×C4—22no—
169C32×C4C4×D412yes—
170C32×C4C4×D412yes—
171C3×Dic3—24no—
172C3×Dic3C22⋊C818yesdirect product factor
173C23×C4—32no—
174C23×C4C2×C3×D311yescharacteristic
175C22×C8—32no—
176C22×C8C2×C3×D312yes—
177C2×C42—31no—
178C2×C42—32no—
179C2×C42—31no—
180C2×C42—64no—
181C22⋊C8—34no—
182C22⋊C8C3×Dic314yesdirect product factor
183C4×C8—64no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—22no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—22no—
190C23×C3—24no—
191C23×C3—22no—
192C23×C3—21no—
193C23×C3—41no—
194C23×C3—41no—
195C23×C3—42no—
196C23×C3D3×C814yes—
197C23×C3C4×Dic312yes—
198C23×C3C3×C4212yes—
199C23×C3C2×C3×C814yes—
200C23×C3C2×C4×D311yescharacteristic
201C23×C3C22×C3×C411yescharacteristic
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—24no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—34no—
216C2×C3×C4—34no—
217C2×C3×C4—34no—
218C2×C3×C4—34no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—616no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4C4×Dic312yes—
227C2×C3×C4C3×C4212yes—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4D3×D412yes—
230C2×C3×C4#23712yes—
231C2×C3×C4C22×Dic311yescharacteristic
232C2×C3×C4C22×C3×C411yescharacteristic
233C2×C3×C4C22×C3×C411yescharacteristic
234C2×C3×C4C2×C3×D412yes—
235C2×C3×C4C3×#4112yes—
236C2×Dic3—22no—
237C2×Dic3—22no—
238C2×Dic3—216no—
239C2×Dic3C3×C22⋊C414yes—
240C2×Dic3C2×C3×C814yes—
241C2×Dic3C2×C3×C814yes—
242C2×Dic3C3×M1614yes—
243C3×C8—24no—
244C3×C8—24no—
245C3×C8—44no—
246C3×C8—64no—
247C3⋊C8—24no—
248C2×C32—24no—
249C2×C32C4×C22⋊C411yescharacteristic
250C2×C32C2×C4×C811yescharacteristic
251C2×C32C4×M1611yescharacteristic
252C2×C32C2×C22⋊C812yes—
253C2×C32#43112yes—
254C24C3×C4×D311yescharacteristic
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—32no—
258C22×C4—38no—
259C22×C4—32no—
260C22×C4—64no—
261C22×C4—64no—
262C22×C4C3×C4×D311yescharacteristic
263C22×C4C3×C4×D312yes—
264C22×C4C2×C3×Dic312yes—
265C22×C4C22×C3×D311yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—34no—
269C2×C8—62no—
270C2×C8—62no—
271C2×C8C2×C3×Dic314yescomplemented
272C42—34no—
273C42—64no—
274C42—62no—
275C22×C3—22no—
276C22×C3—24no—
277C22×C3—24no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—24no—
281C22×C3—24no—
282C22×C3—22no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3—24no—
289C22×C3—42no—
290C22×C3—44no—
291C22×C3—44no—
292C22×C3—42no—
293C22×C3C8×Dic314yescomplemented
294C22×C3C3×C4×C814yescomplemented
295C22×C3#87711yescharacteristic
296C22×C3D3×C22⋊C411yescharacteristic
297C22×C3C2×D3×C812yes—
298C22×C3D3×M1612yes—
299C22×C3C2×C4×Dic311yescharacteristic
300C22×C3C2×C3×C4211yescharacteristic
301C22×C3C2×C3×C22⋊C411yescharacteristic
302C22×C3C3×#11711yescharacteristic
303C22×C3C22×C3×C812yes—
304C22×C3C2×C3×M1612yes—
305C3×C4—22no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—38no—
310C3×C4—42no—
311C3×C4—64no—
312C3×C4#67⋊C412yes—
313C3×C4D4×Dic312yes—
314C3×C4C3×C4×D412yes—
315C3×C4C3×C4×D412yes—
316Dic3—24no—
317Dic3C3×C22⋊C818yesdirect product factor
318C32C4×C22⋊C811yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—22no—
322C23C3×D3×C814yes—
323C23C3×C4×Dic312yes—
324C23C2×C3×C4×D311yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—34no—
330C2×C4—34no—
331C2×C4—34no—
332C2×C4—34no—
333C2×C4—616no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4C3×C4×Dic312yes—
337C2×C4C2×C3×C4×D311yescharacteristic
338C2×C4C3×D3×D412yes—
339C2×C4C3×#23712yes—
340C2×C4C22×C3×Dic311yescharacteristic
341C8—24no—
342C8—64no—
343C2×C3—24no—
344C2×C3—24no—
345C2×C3—21no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—44no—
351C2×C3#471812yes—
352C2×C3D3×C22⋊C812yes—
353C2×C3Dic3×C22⋊C411yescharacteristic
354C2×C3C2×C8×Dic311yescharacteristic
355C2×C3Dic3×M1611yescharacteristic
356C2×C3C3×C4×C22⋊C411yescharacteristic
357C2×C3C2×C3×C4×C811yescharacteristic
358C2×C3C3×C4×M1611yescharacteristic
359C2×C3C2×C3×C22⋊C812yes—
360C2×C3C3×#43112yes—
361C22—22no—
362C22—24no—
363C22—24no—
364C22—22no—
365C22C3×C8×Dic314yescomplemented
366C22C3×#87711yescharacteristic
367C22C3×D3×C22⋊C411yescharacteristic
368C22C2×C3×D3×C812yes—
369C22C3×D3×M1612yes—
370C22C2×C3×C4×Dic311yescharacteristic
371C4—22no—
372C4—38no—
373C4—64no—
374C4C3×#67⋊C412yes—
375C4C3×D4×Dic312yes—
376C3—21no—
377C3Dic3×C22⋊C811yescharacteristic, direct product factor
378C3C3×C4×C22⋊C811yescharacteristic, complemented
379C2—24no—
380C2C3×#471812yes—
381C2C3×D3×C22⋊C812yes—
382C2C3×Dic3×C22⋊C411yescharacteristic
383C2C2×C3×C8×Dic311yescharacteristic
384C2C3×Dic3×M1611yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C2×C3×C4×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×C4×C22⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×C8×Dic3C2semidirect
5. C3×#4550C2semidirect
7. Dic3×C22⋊C8C3direct (N × H)
16. C32×C22⋊C8C4semidirect
17. C3×#830C4semidirect
27. C2×C8×Dic3C2×C3semidirect
29. #4550C2×C3semidirect
39. C22×C3×Dic3C8semidirect
44. C2×C32×C8C2×C4semidirect
50. C2×C3×C3⋊C8C2×C4semidirect
72. C3×C22⋊C8Dic3direct (N × H)
73. C3×C22⋊C8C3×C4semidirect
75. #830C3×C4semidirect
134. C22×Dic3C3×C8semidirect
147. C2×C3×C8C2×Dic3semidirect
148. C2×C3×C8C2×C3×C4semidirect
157. C2×C3⋊C8C2×C3×C4semidirect
162. C22×C32C4×C8semidirect
172. C3×Dic3C22⋊C8direct (N × H)
182. C22⋊C8C3×Dic3direct (N × H)
271. C2×C8C2×C3×Dic3semidirect
293. C22×C3C8×Dic3semidirect
294. C22×C3C3×C4×C8semidirect
317. Dic3C3×C22⋊C8direct (N × H)
318. C32C4×C22⋊C8semidirect
365. C22C3×C8×Dic3semidirect
377. C3Dic3×C22⋊C8direct (N × H)
378. C3C3×C4×C22⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×Dic32
C2×C32×C22⋊C82
C2×C3×#8302
C2×C3×C8×Dic32
C3×#45502
C3×C4×C22⋊C83
Dic3×C22⋊C83