Finite Group Databasebeta

← C3×#69947 #11783640

Subgroups — C3×#69947 #11783640

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊C8C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4C2×C3×C8×Dic3C212yesmaximal, complemented
5C3×#4550C212yesmaximal, complemented
6C3×C8×C22⋊C4—31nomaximal
7#69947C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C32×C8C2212yes—
10C2×C3×#217C412yes—
11C2×C3×C4×Dic3C2212yes—
12C22×C3×C3⋊C8—24no—
13C22×C3×C3⋊C8C414yescomplemented
14C22×C3×C3⋊C8C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C32×C22⋊C8C414yescomplemented
17C3×C3⋊#95C412yes—
18C3×C8×Dic3—24no—
19C23×C3×C8—31no—
20C23×C3⋊C8C2×C311yescharacteristic
21C2×C3×C22⋊C8—21no—
22C2×C3×C22⋊C8D311yescharacteristic
23C2×C3×C22⋊C8C2×C311yescharacteristic
24C2×C3×C4×C8—32no—
25C3×C4×C22⋊C4—31no—
26C4×#217C2×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×Dic3C2×C414yes—
38C2×C32×C8—22no—
39C2×C32×C8—22no—
40C2×C32×C8C2×C414yes—
41C3×#217C818yescomplemented
42C3×C4×Dic3—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—28no—
46C2×C3×C3⋊C8C2×C412yes—
47C2×C3×C3⋊C8C2×C412yes—
48C2×C3×C3⋊C8D414yes—
49C8×C22⋊C4—31noSylow
50C23×C3×C4—21no—
51C23×C3×C4C2×D311yescharacteristic
52C23×C3×C4C22×C311yescharacteristic
53C22×C3×C8—22no—
54C22×C3×C8—31no—
55C22×C3×C8—34no—
56C22×C3×C8—31no—
57C22×C3×C8—64no—
58C22×C3×C8C2×D312yes—
59C22×C3×C8C22×C312yes—
60C2×C3×C22⋊C4—32no—
61C2×C3×C42—32no—
62C2×#217C3×C412yes—
63C2×C4×Dic3C22×C312yes—
64C22×C3⋊C8—24no—
65C22×C3⋊C8C3×C414yescomplemented
66C22×C3⋊C8C22×C311yescharacteristic
67C22×C3⋊C8C22×C311yescharacteristic
68C3×C22⋊C8—24no—
69C3×C22⋊C8Dic314yescomplemented
70C3×C22⋊C8C3×C414yescomplemented
71C3×C4×C8—64no—
72C3×#95—32no—
73C3⋊#95C3×C412yes—
74C8×Dic3—24no—
75C23×C32—22no—
76C23×C32—22no—
77C23×C32C4212yes—
78C23×C32C2×C814yes—
79C23×C32C22×C411yescharacteristic
80C2×C32×C4—22no—
81C2×C32×C4—22no—
82C2×C32×C4—22no—
83C2×C32×C4—24no—
84C2×C32×C4C4212yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D412yes—
88C2×C32×C4#4112yes—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3C2×C818yescomplemented
92C32×C8—24no—
93C3×C3⋊C8—22no—
94C3×C3⋊C8C22⋊C414yescomplemented
95C23×C8—31no—
96C2×C22⋊C8C3×D311yescharacteristic
97C2×C4×C8—32no—
98C4×C22⋊C4—31no—
99#336—32no—
100C24×C3—21no—
101C24×C3C4×D311yescharacteristic
102C24×C3C2×C3×C411yescharacteristic
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—21no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4—34no—
112C22×C3×C4—42no—
113C22×C3×C4—42no—
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D312yes—
116C22×C3×C4C2×Dic312yes—
117C22×C3×C4C2×C3×C411yescharacteristic
118C22×C3×C4C2×C3×C412yes—
119C22×C3×C4C2×C3×C412yes—
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C23×C311yescharacteristic
122C22×Dic3C2×C3×C414yes—
123C2×C3×C8—22no—
124C2×C3×C8—22no—
125C2×C3×C8—22no—
126C2×C3×C8—22no—
127C2×C3×C8—24no—
128C2×C3×C8—32no—
129C2×C3×C8—34no—
130C2×C3×C8—32no—
131C2×C3×C8—42no—
132C2×C3×C8—42no—
133C2×C3×C8—68no—
134C2×C3×C8—62no—
135C2×C3×C8C2×Dic314yes—
136C2×C3×C8C2×C3×C414yes—
137C3×C22⋊C4—38no—
138C3×C42—62no—
139C3×C42—62no—
140#217C3×C818yescomplemented
141C4×Dic3—22no—
142C4×Dic3—22no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8—28no—
145C2×C3⋊C8C2×C3×C412yes—
146C2×C3⋊C8C2×C3×C412yes—
147C2×C3⋊C8C3×D414yes—
148C22×C32—22no—
149C22×C32—22no—
150C22×C32—28no—
151C22×C32C4×C814yescomplemented
152C22×C32C2×C4211yescharacteristic
153C22×C32C4×D412yes—
154C22×C32C22×C812yes—
155C22×C32#13112yes—
156C32×C4—22no—
157C32×C4C2×C22⋊C411yescharacteristic
158C32×C4#11711yescharacteristic
159C32×C4C4×D412yes—
160C3×Dic3—28no—
161C23×C4C2×C3×D311yescharacteristic
162C22×C8—31no—
163C22×C8—34no—
164C22×C8—31no—
165C22×C8—64no—
166C22×C8C2×C3×D312yes—
167C2×C22⋊C4—32no—
168C2×C42—32no—
169C22⋊C8C3×Dic314yescomplemented
170C4×C8—64no—
171#95—32no—
172C23×C3—22no—
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—24no—
177C23×C3—22no—
178C23×C3—21no—
179C23×C3—42no—
180C23×C3—42no—
181C23×C3D3×C814yes—
182C23×C3C4×Dic312yes—
183C23×C3C3×C4212yes—
184C23×C3C2×C3×C814yes—
185C23×C3C2×C4×D311yescharacteristic
186C23×C3C22×C3×C411yescharacteristic
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—24no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—38no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—44no—
204C2×C3×C4—42no—
205C2×C3×C4—64no—
206C2×C3×C4—64no—
207C2×C3×C4C4×Dic312yes—
208C2×C3×C4C3×C4212yes—
209C2×C3×C4C2×C4×D311yescharacteristic
210C2×C3×C4D3×D412yes—
211C2×C3×C4#23712yes—
212C2×C3×C4C22×Dic311yescharacteristic
213C2×C3×C4C22×C3×C411yescharacteristic
214C2×C3×C4C22×C3×C411yescharacteristic
215C2×C3×C4C2×C3×D412yes—
216C2×C3×C4C3×#4112yes—
217C2×Dic3—24no—
218C2×Dic3—24no—
219C2×Dic3C2×C3×C818yescomplemented
220C3×C8—24no—
221C3×C8—24no—
222C3×C8—34no—
223C3×C8—44no—
224C3×C8—62no—
225C3⋊C8—22no—
226C3⋊C8C3×C22⋊C414yescomplemented
227C2×C32—24no—
228C2×C32C4×C22⋊C411yescharacteristic
229C2×C32C2×C4×C811yescharacteristic
230C2×C32#40511yescharacteristic
231C2×C32C8×D414yes—
232C24C3×C4×D311yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—34no—
236C22×C4C3×C4×D311yescharacteristic
237C22×C4C3×C4×D312yes—
238C22×C4C2×C3×Dic312yes—
239C22×C4C22×C3×D311yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—32no—
243C2×C8—34no—
244C2×C8—32no—
245C2×C8—68no—
246C2×C8—62no—
247C2×C8C2×C3×Dic314yes—
248C22⋊C4—38no—
249C42—62no—
250C42—62no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—28no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—28no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—24no—
262C22×C3—42no—
263C22×C3—48no—
264C22×C3—42no—
265C22×C3C8×Dic314yescomplemented
266C22×C3C3×C4×C814yescomplemented
267C22×C3#67⋊C412yes—
268C22×C3C2×D3×C812yes—
269C22×C3#90712yes—
270C22×C3C2×C4×Dic311yescharacteristic
271C22×C3C2×C3×C4211yescharacteristic
272C22×C3C3×C4×D412yes—
273C22×C3C22×C3×C812yes—
274C22×C3C3×#13112yes—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—22no—
280C3×C4—42no—
281C3×C4—68no—
282C3×C4#87711yescharacteristic
283C3×C4D3×C22⋊C411yescharacteristic
284C3×C4D4×Dic312yes—
285C3×C4C2×C3×C22⋊C411yescharacteristic
286C3×C4C3×#11711yescharacteristic
287C3×C4C3×C4×D412yes—
288Dic3—28no—
289C32C8×C22⋊C411yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23C3×D3×C814yes—
293C23C3×C4×Dic312yes—
294C23C2×C3×C4×D311yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—38no—
300C2×C4—64no—
301C2×C4—64no—
302C2×C4C3×C4×Dic312yes—
303C2×C4C2×C3×C4×D311yescharacteristic
304C2×C4C3×D3×D412yes—
305C2×C4C3×#23712yes—
306C2×C4C22×C3×Dic311yescharacteristic
307C8—24no—
308C8—34no—
309C8—62no—
310C2×C3—24no—
311C2×C3—24no—
312C2×C3—21no—
313C2×C3—24no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—44no—
317C2×C3#67⋊C814yes—
318C2×C3Dic3×C22⋊C411yescharacteristic
319C2×C3C2×C8×Dic311yescharacteristic
320C2×C3#512211yescharacteristic
321C2×C3C3×C4×C22⋊C411yescharacteristic
322C2×C3C2×C3×C4×C811yescharacteristic
323C2×C3C3×#40511yescharacteristic
324C2×C3C3×C8×D414yes—
325C22—22no—
326C22—28no—
327C22—22no—
328C22C3×C8×Dic314yescomplemented
329C22C3×#67⋊C412yes—
330C22C2×C3×D3×C812yes—
331C22C3×#90712yes—
332C22C2×C3×C4×Dic311yescharacteristic
333C4—22no—
334C4—68no—
335C4C3×#87711yescharacteristic
336C4C3×D3×C22⋊C411yescharacteristic
337C4C3×D4×Dic312yes—
338C3—21no—
339C3#6994711yescharacteristic, direct product factor
340C3C3×C8×C22⋊C411yescharacteristic, complemented
341C2—24no—
342C2C3×#67⋊C814yes—
343C2C3×Dic3×C22⋊C411yescharacteristic
344C2C2×C3×C8×Dic311yescharacteristic
345C2C3×#512211yescharacteristic
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×C8×C22⋊C4
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. #69947C3direct (N × H)
13. C22×C3×C3⋊C8C4semidirect
16. C32×C22⋊C8C4semidirect
27. C2×C8×Dic3C2×C3semidirect
29. #4550C2×C3semidirect
41. C3×#217C8semidirect
65. C22×C3⋊C8C3×C4semidirect
69. C3×C22⋊C8Dic3semidirect
70. C3×C22⋊C8C3×C4semidirect
91. C2×C3×Dic3C2×C8semidirect
94. C3×C3⋊C8C22⋊C4semidirect
140. #217C3×C8semidirect
151. C22×C32C4×C8semidirect
169. C22⋊C8C3×Dic3semidirect
219. C2×Dic3C2×C3×C8semidirect
226. C3⋊C8C3×C22⋊C4semidirect
265. C22×C3C8×Dic3semidirect
266. C22×C3C3×C4×C8semidirect
289. C32C8×C22⋊C4semidirect
328. C22C3×C8×Dic3semidirect
339. C3#69947direct (N × H)
340. C3C3×C8×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊C82
C2×C32×C22⋊C82
C3×C4×#2172
C2×C3×C8×Dic32
C3×#45502
C3×C8×C22⋊C43
#699473