Finite Group Databasebeta

← C3×#67701 #11772631

Subgroups — C3×#67701 #11772631

Order 1152.

399 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#413C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4C3×#1395—31nomaximal
5#67701C311yesmaximal, characteristic, direct product factor
6C2×C32×#41C2211yescharacteristic
7C2×C32×M16—21no—
8C3×#926—21no—
9C2×C3×#208C411yescharacteristic, complemented
10C22×C3×C3⋊C8C411yescharacteristic, complemented
11C32×#101C412yescomplemented
12C32×#100—21no—
13C3×#834—21no—
14C3×#834C412yes—
15C3×#830—21no—
16C3×#830—21no—
17C3×#413—21no—
18C3×#413D311yescharacteristic
19C3×#413C2×C311yescharacteristic
20C3×#410—31no—
21C3×#408—31no—
22#5240C2×C311yescharacteristic
23#5234C2×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—22no—
34C32×M16—41no—
35C2×C32×C8—41no—
36C3×#217—22no—
37C3×C4⋊Dic3—41no—
38C3×C4×Dic3—41no—
39C3×#208—41no—
40C2×C3×C3⋊C8—21no—
41C2×C3×C3⋊C8—21no—
42C2×C3×C3⋊C8—41no—
43#1395—31noSylow
44C2×C3×#41—21no—
45C2×C3×#41C2×D311yescharacteristic
46C2×C3×#41C22×C311yescharacteristic
47C2×C3×M16—22no—
48C2×C3×M16—21no—
49C2×C3×M16—21no—
50C2×C3×M16—31no—
51C22×C3×C8—31no—
52C3×#117—61no—
53#926—21no—
54C2×#208C3×C411yescharacteristic, complemented
55C22×C3⋊C8C3×C411yescharacteristic, complemented
56C3×#101—22no—
57C3×#101Dic312yescomplemented
58C3×#101C3×C412yescomplemented
59C3×#100—22no—
60C3×#100—21no—
61C3×#100—21no—
62C3×#99—32no—
63C3×#99—61no—
64C3×C22⋊C8—61no—
65C3×C22⋊C8—61no—
66#834—21no—
67#834C3×C412yes—
68#830—21no—
69#830—21no—
70C23×C32C22⋊C411yescharacteristic
71C23×C32C4⋊C411yescharacteristic
72C23×C32C4⋊C411yescharacteristic
73C32×Q8—41no—
74C32×D4—41no—
75C32×D4—41no—
76C32×D4—41no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4C4211yescharacteristic
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C4⋊C411yescharacteristic
87C2×C3×Dic3—42no—
88C32×C8—42no—
89C3×C3⋊C8—41no—
90C3×C3⋊C8—41no—
91#413C3×D311yescharacteristic
92#410—31no—
93#408—31no—
94C3×#41—41no—
95C3×#41—41no—
96C3×#41—41no—
97C3×#41—41no—
98C3×#41—42no—
99C3×#41—42no—
100C2×C3×Q8—21no—
101C2×C3×Q8C2×Dic311yescharacteristic
102C2×C3×Q8C2×C3×C411yescharacteristic
103C2×C3×D4—21no—
104C2×C3×D4—21no—
105C2×C3×D4—21no—
106C2×C3×D4Dic611yescharacteristic
107C2×C3×D4C4×D311yescharacteristic
108C2×C3×D4#6711yescharacteristic
109C2×C3×D4C2×C3×C411yescharacteristic
110C2×C3×D4C3×D411yescharacteristic
111C2×C3×D4C3×Q811yescharacteristic
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4D1211yescharacteristic
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4C2×C3×C411yescharacteristic
119C22×C3×C4C3×D411yescharacteristic
120C22×C3×C4C3×D411yescharacteristic
121C3×M16—24no—
122C3×M16—22no—
123C3×M16—22no—
124C3×M16—42no—
125C3×M16—41no—
126C3×M16—41no—
127C3×M16—121no—
128C2×C3×C8—42no—
129C2×C3×C8—41no—
130C2×C3×C8—41no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C2×C3×C8—121no—
134C3×C4⋊C4—121no—
135C3×C22⋊C4—62no—
136C3×C42—121no—
137#217—22no—
138C4⋊Dic3—41no—
139C4×Dic3—41no—
140#208—41no—
141C2×C3⋊C8—21no—
142C2×C3⋊C8—21no—
143C2×C3⋊C8—41no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32—41no—
148C22×C32—41no—
149C22×C32—41no—
150C22×C32#9511yescharacteristic
151C32×C4—21no—
152C32×C4—21no—
153C32×C4—21no—
154C32×C4#9911yescharacteristic
155C32×C4#9911yescharacteristic
156C3×Dic3—82no—
157C2×#41C2×C3×D311yescharacteristic
158C2×M16—21no—
159C2×M16—31no—
160C22×C8—31no—
161#117—61no—
162#101C3×Dic312yescomplemented
163#100—21no—
164#99—32no—
165#99—61no—
166C22⋊C8—61no—
167C22⋊C8—61no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3Dic3⋊C411yescharacteristic
172C23×C3Dic3⋊C411yescharacteristic
173C23×C3(C2×D3)⋊C411yescharacteristic
174C23×C3C3×C22⋊C411yescharacteristic
175C23×C3C3×C4⋊C411yescharacteristic
176C23×C3C3×C4⋊C411yescharacteristic
177C3×Q8—41no—
178C3×Q8—41no—
179C3×Q8—42no—
180C3×D4—41no—
181C3×D4—41no—
182C3×D4—41no—
183C3×D4—41no—
184C3×D4—41no—
185C3×D4—41no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
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—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—122no—
212C2×C3×C4C4×Dic311yescharacteristic
213C2×C3×C4C4⋊Dic311yescharacteristic
214C2×C3×C4(C2×D3)⋊C411yescharacteristic
215C2×C3×C4#21711yescharacteristic
216C2×C3×C4C3×C4211yescharacteristic
217C2×C3×C4C3×C22⋊C411yescharacteristic
218C2×C3×C4C3×C22⋊C411yescharacteristic
219C2×C3×C4C3×C4⋊C411yescharacteristic
220C2×Dic3—42no—
221C3×C8—44no—
222C3×C8—42no—
223C3×C8—42no—
224C3×C8—121no—
225C3×C8—121no—
226C3⋊C8—41no—
227C3⋊C8—41no—
228C2×C32—21no—
229C2×C32—41no—
230C2×C32—41no—
231C2×C32—41no—
232C2×C32#34211yescharacteristic
233#41—41no—
234#41—41no—
235C2×Q8C2×C3×Dic311yescharacteristic
236C2×D4C3×Dic611yescharacteristic
237C2×D4C3×C4×D311yescharacteristic
238C2×D4C3×#6711yescharacteristic
239C22×C4C3×C4×D311yescharacteristic
240C22×C4C3×D1211yescharacteristic
241C22×C4C3×#6711yescharacteristic
242M16—22no—
243M16—41no—
244M16—121no—
245C2×C8—41no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—121no—
249C4⋊C4—121no—
250C22⋊C4—62no—
251C42—121no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3C3⋊#9511yescharacteristic
272C22×C3C3×#9511yescharacteristic
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—242no—
285C3×C4#80611yescharacteristic
286C3×C4#80611yescharacteristic
287C3×C4C3×#9911yescharacteristic
288C3×C4C3×#9911yescharacteristic
289Dic3—82no—
290C32#139511yescharacteristic, complemented, Sylow
291C23C3×Dic3⋊C411yescharacteristic
292C23C3×Dic3⋊C411yescharacteristic
293C23C3×(C2×D3)⋊C411yescharacteristic
294Q8—41no—
295D4—41no—
296D4—41no—
297D4—41no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—122no—
305C2×C4C3×C4×Dic311yescharacteristic
306C2×C4C3×C4⋊Dic311yescharacteristic
307C2×C4C3×(C2×D3)⋊C411yescharacteristic
308C2×C4C3×#21711yescharacteristic
309C8—42no—
310C8—121no—
311C8—121no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—41no—
316C2×C3—42no—
317C2×C3—41no—
318C2×C3—41no—
319C2×C3—41no—
320C2×C3—41no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—81no—
324C2×C3—81no—
325C2×C3#452711yescharacteristic
326C2×C3C3×#34211yescharacteristic
327C22—21no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22C3×C3⋊#9511yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—242no—
338C4C3×#80611yescharacteristic
339C4C3×#80611yescharacteristic
340C3—21no—
341C3#6770111yescharacteristic, direct product factor
342C3C3×#139511yescharacteristic, complemented
343C2—21no—
344C2—41no—
345C2—41no—
346C2—41no—
347C2C3×#452711yescharacteristic
subgroupG/H
centerC3×C4#806
commutatorC2×C3×C4C3×C42
FrattiniC2×#41C2×C3×D3
FittingC32×#413C2
socleC2×C32#342
prime radicalC2×C32×#41C22
cosocleC2×C3×#41C22×C3
hypercenterC3×#413D3
hypocenterC3C3×#1395
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
5. #67701C3direct (N × H)
9. C2×C3×#208C4semidirect
10. C22×C3×C3⋊C8C4semidirect
11. C32×#101C4semidirect
54. C2×#208C3×C4semidirect
55. C22×C3⋊C8C3×C4semidirect
57. C3×#101Dic3semidirect
58. C3×#101C3×C4semidirect
162. #101C3×Dic3semidirect
290. C32#1395semidirect
341. C3#67701direct (N × H)
342. C3C3×#1395semidirect

Maximal subgroups

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

subgroupindex
C32×#4132
C3×#52402
C3×#52342
C3×#13953
#677013