Finite Group Databasebeta

← C3×Dic3×#101 #11783806

Subgroups — C3×Dic3×#101 #11783806

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic
2C2×C32×#101C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic
4C3×Dic3×M16C212yesmaximal
5C3×#4554C212yesmaximal
6C3×C4×#101—31nomaximal
7Dic3×#101C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C2×C32×M16C2212yes—
10C3×Q8×Dic3—22no—
11C3×Q8×Dic3—22no—
12C2×C3×C4⋊Dic3C412yes—
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C412yes—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2212yes—
17C32×#101C414yescomplemented
18C3×#836C414yescomplemented
19C3×#815—22no—
20C3×C8×Dic3—22no—
21C2×C3×C4×Q8—31no—
22C2×Q8×Dic3C2×C311yescharacteristic
23C2×C3×#101—21no—
24C2×C3×#101—31no—
25C2×C3×#101D311yescharacteristic
26C2×C3×#101C2×C311yescharacteristic
27C3×C4×M16—32no—
28C2×#836C2×C311yescharacteristic
29Dic3×M16C2×C312yes—
30C3×#343—32no—
31#4554C2×C312yes—
32C2×C32×Q8—22no—
33C2×C32×Q8—22no—
34C2×C32×Q8C2×C412yes—
35C2×C32×Q8C2×C412yes—
36C22×C32×C4C2×C412yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3C2×C411yescharacteristic
39C22×C3×Dic3C2×C412yes—
40C22×C3×Dic3C2×C411yescharacteristic
41C32×M16—22no—
42C32×M16C2×C414yes—
43C2×C32×C8—22no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—24no—
46C3×C4×Dic3—22no—
47C3×C4×Dic3—22no—
48C3×C4×Dic3D412yes—
49C3×C4×Dic3D412yes—
50C3×#208—22no—
51C3×#208C2×C414yes—
52C2×C3×C3⋊C8—22no—
53C4×#101—31noSylow
54C22×C3×Q8—21no—
55C22×C3×Q8C2×D311yescharacteristic
56C22×C3×Q8C22×C311yescharacteristic
57C2×C3×M16—22no—
58C2×C3×M16—32no—
59C2×C3×M16C2×D312yes—
60C2×C3×M16C22×C312yes—
61C3×C4×Q8—62no—
62C3×C4×Q8—62no—
63C2×C3×C4⋊C4—32no—
64C2×C3×C4⋊C4—31no—
65C2×C3×C42—31no—
66C2×C3×C42—32no—
67Q8×Dic3—22no—
68Q8×Dic3—22no—
69C2×C4⋊Dic3C3×C412yes—
70C2×C4⋊Dic3C22×C311yescharacteristic
71C2×C4×Dic3C3×C412yes—
72C2×C4×Dic3C22×C311yescharacteristic
73C2×#208C22×C312yes—
74C3×#101—24no—
75C3×#101—34no—
76C3×#101Dic314yesdirect product factor
77C3×#101C3×C414yescomplemented
78C3×#97—62no—
79C3×C4×C8—62no—
80#836C3×C414yescomplemented
81#815—22no—
82C8×Dic3—22no—
83C23×C32C22×C411yescharacteristic
84C32×Q8—24no—
85C32×Q8—24no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4C4214yes—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D412yes—
92C2×C32×C4#4112yes—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3C22⋊C411yescharacteristic
98C2×C3×Dic3C22⋊C412yes—
99C2×C3×Dic3C22⋊C411yescharacteristic
100C32×C8—24no—
101C3×C3⋊C8—24no—
102C2×C4×Q8—31no—
103C2×#101—31no—
104C2×#101C3×D311yescharacteristic
105C4×M16—32no—
106#343—32no—
107C2×C3×Q8—22no—
108C2×C3×Q8—22no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—42no—
114C2×C3×Q8—42no—
115C2×C3×Q8C4×D312yes—
116C2×C3×Q8C2×Dic312yes—
117C2×C3×Q8C2×C3×C412yes—
118C2×C3×Q8C2×C3×C412yes—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—32no—
124C22×C3×C4C4×D312yes—
125C22×C3×C4C2×C3×C412yes—
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C23×C311yescharacteristic
128C22×Dic3C2×C3×C411yescharacteristic
129C22×Dic3C2×C3×C412yes—
130C22×Dic3C2×C3×C411yescharacteristic
131C3×M16—22no—
132C3×M16—22no—
133C3×M16—24no—
134C3×M16—34no—
135C3×M16—42no—
136C3×M16—62no—
137C3×M16C2×Dic314yes—
138C3×M16C2×C3×C414yes—
139C2×C3×C8—22no—
140C2×C3×C8—22no—
141C2×C3×C8—42no—
142C2×C3×C8—62no—
143C3×C4⋊C4—64no—
144C3×C4⋊C4—62no—
145C3×C42—32no—
146C3×C42—32no—
147C3×C42—62no—
148C3×C42—62no—
149C4⋊Dic3—22no—
150C4⋊Dic3—24no—
151C4×Dic3—22no—
152C4×Dic3—22no—
153C4×Dic3C3×D412yes—
154C4×Dic3C3×D412yes—
155#208—22no—
156#208C2×C3×C414yes—
157C2×C3⋊C8—22no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32C2×C4211yescharacteristic
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32#11711yescharacteristic
163C32×C4—24no—
164C32×C4C4×D412yes—
165C32×C4C4×D412yes—
166C3×Dic3—21no—
167C3×Dic3—22no—
168C3×Dic3—42no—
169C3×Dic3#10112yesdirect product factor
170C22×Q8C2×C3×D311yescharacteristic
171C2×M16—32no—
172C2×M16C2×C3×D312yes—
173C4×Q8—62no—
174C4×Q8—62no—
175C2×C4⋊C4—32no—
176C2×C4⋊C4—31no—
177C2×C42—31no—
178C2×C42—32no—
179#101—34no—
180#101C3×Dic314yesdirect product factor
181#97—62no—
182C4×C8—62no—
183C23×C3—21no—
184C23×C3C2×C4×D311yescharacteristic
185C23×C3C22×C3×C411yescharacteristic
186C3×Q8—24no—
187C3×Q8—24no—
188C3×Q8—24no—
189C3×Q8—24no—
190C3×Q8—44no—
191C3×Q8—44no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—24no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—32no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—62no—
207C2×C3×C4—62no—
208C2×C3×C4—121no—
209C2×C3×C4—122no—
210C2×C3×C4C4×Dic314yes—
211C2×C3×C4C3×C4214yes—
212C2×C3×C4C2×C4×D311yescharacteristic
213C2×C3×C4D3×D412yes—
214C2×C3×C4#23712yes—
215C2×C3×C4C22×Dic311yescharacteristic
216C2×C3×C4C22×C3×C411yescharacteristic
217C2×C3×C4C22×C3×C411yescharacteristic
218C2×C3×C4C2×C3×D412yes—
219C2×C3×C4C3×#4112yes—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—41no—
223C2×Dic3—42no—
224C2×Dic3C3×C22⋊C411yescharacteristic
225C2×Dic3C3×C22⋊C412yes—
226C2×Dic3C3×C22⋊C411yescharacteristic
227C3×C8—24no—
228C3×C8—24no—
229C3×C8—44no—
230C3×C8—64no—
231C3⋊C8—24no—
232C2×C32—21no—
233C2×C32—21no—
234C2×C32C4×C22⋊C411yescharacteristic
235C2×C32C2×#10111yescharacteristic
236C2×C32#41311yescharacteristic
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8C3×C4×D312yes—
240C2×Q8C2×C3×Dic312yes—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—32no—
244C22×C4C3×C4×D312yes—
245C22×C4C22×C3×D311yescharacteristic
246M16—22no—
247M16—34no—
248M16—62no—
249M16C2×C3×Dic314yes—
250C2×C8—22no—
251C2×C8—62no—
252C4⋊C4—64no—
253C4⋊C4—62no—
254C42—32no—
255C42—32no—
256C42—62no—
257C42—62no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3#87711yescharacteristic
268C22×C3D3×C22⋊C411yescharacteristic
269C22×C3C2×C4×Dic311yescharacteristic
270C22×C3C2×C3×C4211yescharacteristic
271C22×C3C2×C3×C22⋊C411yescharacteristic
272C22×C3C3×#11711yescharacteristic
273C3×C4—24no—
274C3×C4—24no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—32no—
278C3×C4—44no—
279C3×C4—61no—
280C3×C4—62no—
281C3×C4—122no—
282C3×C4#67⋊C412yes—
283C3×C4D4×Dic312yes—
284C3×C4C3×C4×D412yes—
285C3×C4C3×C4×D412yes—
286Dic3—21no—
287Dic3—22no—
288Dic3—42no—
289Dic3C3×#10112yesdirect product factor
290C32C4×#10111yescharacteristic, complemented, Sylow
291C23C2×C3×C4×D311yescharacteristic
292Q8—24no—
293Q8—24no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—32no—
299C2×C4—62no—
300C2×C4—62no—
301C2×C4—121no—
302C2×C4—122no—
303C2×C4C3×C4×Dic314yes—
304C2×C4C2×C3×C4×D311yescharacteristic
305C2×C4C3×D3×D412yes—
306C2×C4C3×#23712yes—
307C2×C4C22×C3×Dic311yescharacteristic
308C8—24no—
309C8—64no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—41no—
318C2×C3—41no—
319C2×C3D3×#10111yescharacteristic
320C2×C3#475111yescharacteristic
321C2×C3Dic3×C22⋊C411yescharacteristic
322C2×C3C3×C4×C22⋊C411yescharacteristic
323C2×C3C2×C3×#10111yescharacteristic
324C2×C3C3×#41311yescharacteristic
325C22—21no—
326C22—21no—
327C22C3×#87711yescharacteristic
328C22C3×D3×C22⋊C411yescharacteristic
329C22C2×C3×C4×Dic311yescharacteristic
330C4—24no—
331C4—32no—
332C4—61no—
333C4—62no—
334C4—122no—
335C4C3×#67⋊C412yes—
336C4C3×D4×Dic312yes—
337C3—21no—
338C3Dic3×#10111yescharacteristic, direct product factor
339C3C3×C4×#10111yescharacteristic, complemented
340C2—21no—
341C2—21no—
342C2C3×D3×#10111yescharacteristic
343C2C3×#475111yescharacteristic
344C2C3×Dic3×C22⋊C411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#101C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#101D3
hypocenterC3C3×C4×#101
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
7. Dic3×#101C3direct (N × H)
17. C32×#101C4semidirect
18. C3×#836C4semidirect
76. C3×#101Dic3direct (N × H)
77. C3×#101C3×C4semidirect
80. #836C3×C4semidirect
169. C3×Dic3#101direct (N × H)
180. #101C3×Dic3direct (N × H)
289. Dic3C3×#101direct (N × H)
290. C32C4×#101semidirect
338. C3Dic3×#101direct (N × H)
339. C3C3×C4×#101semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×C32×#1012
C2×C3×#8362
C3×Dic3×M162
C3×#45542
C3×C4×#1013
Dic3×#1013