Finite Group Databasebeta

← C3×#67692 #11772628

Subgroups — C3×#67692 #11772628

Order 1152.

403 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#408C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4C3×#1395—31nomaximal
5#67692C311yesmaximal, characteristic, direct product factor
6C2×C32×#41C2211yescharacteristic
7C2×C32×M16C411yescharacteristic, complemented
8C22×C32×C8C411yescharacteristic, complemented
9C3×#926—21no—
10C2×C3×#208—21no—
11C32×C22⋊C8—21no—
12C32×C22⋊C8—21no—
13C3×#836C412yescomplemented
14C3×#834—21no—
15C3×#834C412yes—
16C3×#833—21no—
17C3×#413—31no—
18C3×#410—31no—
19C3×#408—21no—
20C3×#408D311yescharacteristic
21C3×#408C2×C311yescharacteristic
22#5240C2×C311yescharacteristic
23#5237C2×C311yescharacteristic
24C32×#41—41no—
25C32×#41—41no—
26C2×C32×Q8C2×C411yescharacteristic
27C2×C32×D4C2×C411yescharacteristic
28C2×C32×D4D411yescharacteristic
29C2×C32×D4Q811yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C32×M16—41no—
34C2×C32×C8—21no—
35C2×C32×C8—21no—
36C2×C32×C8—41no—
37C3×#217—22no—
38C3×C4⋊Dic3—41no—
39C3×C4×Dic3—41no—
40C3×#208—22no—
41C3×#208—41no—
42C2×C3×C3⋊C8—41no—
43#1395—31noSylow
44C2×C3×#41—21no—
45C2×C3×#41C2×D311yescharacteristic
46C2×C3×#41C22×C311yescharacteristic
47C2×C3×M16—21no—
48C2×C3×M16—61no—
49C2×C3×M16Dic311yescharacteristic, complemented
50C2×C3×M16C3×C411yescharacteristic, complemented
51C22×C3×C8—21no—
52C22×C3×C8Dic311yescharacteristic, complemented
53C22×C3×C8C3×C411yescharacteristic, complemented
54C3×#117—61no—
55#926—21no—
56C2×#208—21no—
57C3×#101—32no—
58C3×#100—61no—
59C3×#99—32no—
60C3×#99—61no—
61C3×C22⋊C8—22no—
62C3×C22⋊C8—22no—
63C3×C22⋊C8—21no—
64C3×C22⋊C8—21no—
65C3×C22⋊C8—21no—
66C3×C22⋊C8—21no—
67#836C3×C412yescomplemented
68#834—21no—
69#834C3×C412yes—
70#833—21no—
71C23×C32C22⋊C411yescharacteristic
72C23×C32C4⋊C411yescharacteristic
73C23×C32C4⋊C411yescharacteristic
74C32×Q8—41no—
75C32×D4—41no—
76C32×D4—41no—
77C32×D4—41no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4C4211yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C4⋊C411yescharacteristic
88C2×C3×Dic3—42no—
89C32×C8—41no—
90C32×C8—41no—
91C3×C3⋊C8—42no—
92#413—31no—
93#410—31no—
94#408C3×D311yescharacteristic
95C3×#41—41no—
96C3×#41—41no—
97C3×#41—41no—
98C3×#41—41no—
99C3×#41—42no—
100C3×#41—42no—
101C2×C3×Q8—21no—
102C2×C3×Q8C4×D311yescharacteristic
103C2×C3×Q8C2×C3×C411yescharacteristic
104C2×C3×D4—21no—
105C2×C3×D4—21no—
106C2×C3×D4—21no—
107C2×C3×D4Dic611yescharacteristic
108C2×C3×D4C4×D311yescharacteristic
109C2×C3×D4D1211yescharacteristic
110C2×C3×D4C2×C3×C411yescharacteristic
111C2×C3×D4C3×D411yescharacteristic
112C2×C3×D4C3×Q811yescharacteristic
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4C2×Dic311yescharacteristic
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4C2×C3×C411yescharacteristic
120C22×C3×C4C3×D411yescharacteristic
121C22×C3×C4C3×D411yescharacteristic
122C3×M16—42no—
123C3×M16—41no—
124C3×M16—41no—
125C3×M16—62no—
126C3×M16—121no—
127C2×C3×C8—22no—
128C2×C3×C8—22no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—42no—
134C2×C3×C8—41no—
135C2×C3×C8—41no—
136C2×C3×C8—121no—
137C3×C4⋊C4—121no—
138C3×C22⋊C4—62no—
139C3×C42—121no—
140#217—22no—
141C4⋊Dic3—41no—
142C4×Dic3—41no—
143#208—22no—
144#208—41no—
145C2×C3⋊C8—41no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32—41no—
150C22×C32—41no—
151C22×C32—41no—
152C22×C32#9511yescharacteristic
153C32×C4—21no—
154C32×C4—21no—
155C32×C4—21no—
156C32×C4#9911yescharacteristic
157C32×C4#9911yescharacteristic
158C3×Dic3—82no—
159C2×#41C2×C3×D311yescharacteristic
160C2×M16—61no—
161C2×M16C3×Dic311yescharacteristic, complemented
162C22×C8C3×Dic311yescharacteristic, complemented
163#117—61no—
164#101—32no—
165#100—61no—
166#99—32no—
167#99—61no—
168C22⋊C8—21no—
169C22⋊C8—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3Dic3⋊C411yescharacteristic
174C23×C3C4⋊Dic311yescharacteristic
175C23×C3(C2×D3)⋊C411yescharacteristic
176C23×C3C3×C22⋊C411yescharacteristic
177C23×C3C3×C4⋊C411yescharacteristic
178C23×C3C3×C4⋊C411yescharacteristic
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—42no—
182C3×D4—41no—
183C3×D4—41no—
184C3×D4—41no—
185C3×D4—41no—
186C3×D4—41no—
187C3×D4—41no—
188C3×D4—42no—
189C3×D4—42no—
190C3×D4—42no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—122no—
214C2×C3×C4C4×Dic311yescharacteristic
215C2×C3×C4Dic3⋊C411yescharacteristic
216C2×C3×C4(C2×D3)⋊C411yescharacteristic
217C2×C3×C4#21711yescharacteristic
218C2×C3×C4C3×C4211yescharacteristic
219C2×C3×C4C3×C22⋊C411yescharacteristic
220C2×C3×C4C3×C22⋊C411yescharacteristic
221C2×C3×C4C3×C4⋊C411yescharacteristic
222C2×Dic3—42no—
223C3×C8—42no—
224C3×C8—42no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—122no—
230C3⋊C8—42no—
231C2×C32—21no—
232C2×C32—41no—
233C2×C32—41no—
234C2×C32—41no—
235C2×C32#34211yescharacteristic
236#41—41no—
237#41—41no—
238C2×Q8C3×C4×D311yescharacteristic
239C2×D4C3×Dic611yescharacteristic
240C2×D4C3×C4×D311yescharacteristic
241C2×D4C3×D1211yescharacteristic
242C22×C4C2×C3×Dic311yescharacteristic
243C22×C4C3×#6711yescharacteristic
244C22×C4C3×#6711yescharacteristic
245M16—41no—
246M16—62no—
247M16—121no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—41no—
251C2×C8—121no—
252C4⋊C4—121no—
253C22⋊C4—62no—
254C42—121no—
255C22×C3—22no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3C3⋊#9511yescharacteristic
275C22×C3C3×#9511yescharacteristic
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—242no—
288C3×C4#83411yescharacteristic
289C3×C4#83411yescharacteristic
290C3×C4C3×#9911yescharacteristic
291C3×C4C3×#9911yescharacteristic
292Dic3—82no—
293C32#139511yescharacteristic, complemented, Sylow
294C23C3×Dic3⋊C411yescharacteristic
295C23C3×C4⋊Dic311yescharacteristic
296C23C3×(C2×D3)⋊C411yescharacteristic
297Q8—41no—
298D4—41no—
299D4—41no—
300D4—41no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—122no—
308C2×C4C3×C4×Dic311yescharacteristic
309C2×C4C3×Dic3⋊C411yescharacteristic
310C2×C4C3×(C2×D3)⋊C411yescharacteristic
311C2×C4C3×#21711yescharacteristic
312C8—41no—
313C8—41no—
314C8—122no—
315C2×C3—22no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—42no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—41no—
324C2×C3—41no—
325C2×C3—41no—
326C2×C3—81no—
327C2×C3—81no—
328C2×C3#452611yescharacteristic
329C2×C3C3×#34211yescharacteristic
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22C3×C3⋊#9511yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—242no—
341C4C3×#83411yescharacteristic
342C4C3×#83411yescharacteristic
343C3—21no—
344C3#6769211yescharacteristic, direct product factor
345C3C3×#139511yescharacteristic, complemented
346C2—21no—
347C2—41no—
348C2—41no—
349C2—41no—
350C2C3×#452611yescharacteristic
subgroupG/H
centerC3×C4#834
commutatorC2×C3×C4C3×C42
FrattiniC2×#41C2×C3×D3
FittingC32×#408C2
socleC2×C32#342
prime radicalC2×C32×#41C22
cosocleC2×C3×#41C22×C3
hypercenterC3×#408D3
hypocenterC3C3×#1395
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#408

Complements

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

NH ≅ G/Ntype
5. #67692C3direct (N × H)
7. C2×C32×M16C4semidirect
8. C22×C32×C8C4semidirect
13. C3×#836C4semidirect
49. C2×C3×M16Dic3semidirect
50. C2×C3×M16C3×C4semidirect
52. C22×C3×C8Dic3semidirect
53. C22×C3×C8C3×C4semidirect
67. #836C3×C4semidirect
161. C2×M16C3×Dic3semidirect
162. C22×C8C3×Dic3semidirect
293. C32#1395semidirect
344. C3#67692direct (N × H)
345. C3C3×#1395semidirect

Maximal subgroups

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

subgroupindex
C32×#4082
C3×#52402
C3×#52372
C3×#13953
#676923