Finite Group Databasebeta

← C3×#71442 #11796943

Subgroups — C3×#71442 #11796943

Order 1152.

485 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×C32×M32C211yesmaximal, characteristic, complemented
3C2×C3×#819C211yesmaximal, characteristic, complemented
4C3×#4517C212yesmaximal, complemented
5C3×#4516C212yesmaximal, complemented
6C3×#2148—31nomaximal
7#71442C311yesmaximal, characteristic, direct product factor
8C2×C3×#235—21no—
9C22×C32×C8C2211yescharacteristic
10C2×C3×#208—21no—
11C2×C3×Dic12C2211yescharacteristic
12C3×#904—21no—
13C3×#904—21no—
14C3×#904C412yes—
15C3×#904C412yes—
16C2×C3×D24C2211yescharacteristic
17C2×C3×#204—21no—
18C32×M32—21no—
19C32×M32C2212yes—
20C2×C32×C16—21no—
21C3×#819—21no—
22C3×#819C2212yes—
23C2×C3×#135—31no—
24C2×#904C2×C311yescharacteristic
25C2×C3×M32—21no—
26C2×C3×M32D311yescharacteristic, complemented
27C2×C3×M32C2×C311yescharacteristic, complemented
28C2×C3×#108—31no—
29C2×#819C2×C311yescharacteristic, complemented
30C3×#362—32no—
31C3×#361—32no—
32#4517C2×C312yescomplemented
33#4516C2×C312yescomplemented
34C22×C32×C4D411yescharacteristic
35C2×C3×#67—41no—
36C3×#235—22no—
37C3×#235—22no—
38C3×#235—41no—
39C3×#235—41no—
40C2×C3×D12—21no—
41C2×C3×C4×D3—41no—
42C2×C3×Dic6—21no—
43C2×C32×C8C2×C411yescharacteristic
44C2×C32×C8C2×C411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C2×C32×C8C2311yescharacteristic
49C3×#208—22no—
50C3×#208—41no—
51C2×C3×C3⋊C8—41no—
52C3×Dic12—21no—
53C3×Dic12C2×C412yes—
54C3×D24—21no—
55C3×D24C2×C412yes—
56C3×#204—22no—
57C3×#204—22no—
58C32×C16—22no—
59#2148—31noSylow
60C2×C3×#41—61no—
61C2×#235—21no—
62C3×#135—32no—
63C3×#135—32no—
64C3×#135—61no—
65C3×#135—61no—
66C2×C3×Q16—31no—
67C2×C3×SD16—61no—
68C2×C3×D8—31no—
69C2×C3×M16—61no—
70C22×C3×C8—21no—
71C22×C3×C8C2×D311yescharacteristic
72C22×C3×C8C22×C311yescharacteristic
73C2×#208—21no—
74C2×Dic12C22×C311yescharacteristic
75#904—21no—
76#904—21no—
77#904C3×C412yes—
78#904C3×C412yes—
79C2×D24C22×C311yescharacteristic
80C2×#204—21no—
81C3×M32—22no—
82C3×M32—21no—
83C3×M32—21no—
84C3×M32—22no—
85C3×M32C2×D312yes—
86C3×M32C22×C312yes—
87C2×C3×C16—22no—
88C2×C3×C16—21no—
89C2×C3×C16—21no—
90C3×#108—32no—
91C3×#108—61no—
92#819—21no—
93#819C22×C312yes—
94C23×C32SD1611yescharacteristic
95C22×C3×D3—41no—
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4D811yescharacteristic
99C2×C32×C4D811yescharacteristic
100C2×C32×C4SD1611yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C3×#67—42no—
103C3×#67—42no—
104C2×C3×Dic3—41no—
105C3×D12—22no—
106C3×D12—41no—
107C3×C4×D3—42no—
108C3×C4×D3—42no—
109C3×Dic6—22no—
110C3×Dic6—41no—
111C32×C8C22⋊C411yescharacteristic
112C32×C8C22⋊C411yescharacteristic
113C32×C8C22×C411yescharacteristic
114C32×C8C2×D411yescharacteristic
115C3×C3⋊C8—42no—
116C2×#135—31no—
117C2×M32C3×D311yescharacteristic, complemented
118C2×#108—31no—
119#362—32no—
120#361—32no—
121C3×#41—62no—
122C3×#41—62no—
123C3×#41—121no—
124C3×#41—121no—
125C2×C3×Q8—61no—
126C2×C3×D4—61no—
127C2×C3×D4—121no—
128C22×C3×C4—21no—
129C22×C3×C4—121no—
130C22×C3×C4D1211yescharacteristic
131C22×C3×C4C3×D411yescharacteristic
132C2×#67—41no—
133#235—22no—
134#235—22no—
135#235—41no—
136#235—41no—
137C2×D12—21no—
138C2×C4×D3—41no—
139C2×Dic6—21no—
140C3×Q16—32no—
141C3×Q16—61no—
142C3×SD16—62no—
143C3×SD16—62no—
144C3×D8—32no—
145C3×D8—61no—
146C3×M16—62no—
147C3×M16—121no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—121no—
155C2×C3×C8C4×D311yescharacteristic
156C2×C3×C8C4×D311yescharacteristic
157C2×C3×C8D1211yescharacteristic
158C2×C3×C8#6711yescharacteristic
159C2×C3×C8#6711yescharacteristic
160C2×C3×C8C2×C3×C411yescharacteristic
161C2×C3×C8C2×C3×C411yescharacteristic
162C2×C3×C8C3×D411yescharacteristic
163C2×C3×C8C3×D411yescharacteristic
164C2×C3×C8C3×D411yescharacteristic
165C2×C3×C8C22×D311yescharacteristic
166C2×C3×C8C23×C311yescharacteristic
167#208—22no—
168#208—41no—
169C2×C3⋊C8—41no—
170Dic12—21no—
171Dic12C2×C3×C412yes—
172D24—21no—
173D24C2×C3×C412yes—
174#204—22no—
175#204—22no—
176C3×C16—24no—
177C3×C16—22no—
178C3×C16—22no—
179C22×C32—41no—
180C22×C32#10211yescharacteristic
181C22×C32#10211yescharacteristic
182C22×C32C2×SD1611yescharacteristic
183C2×C3×D3—42no—
184C2×C3×D3—82no—
185C32×C4#10211yescharacteristic
186C32×C4#10211yescharacteristic
187C32×C4C2×C22⋊C411yescharacteristic
188C32×C4C2×D811yescharacteristic
189C3×Dic3—42no—
190C2×#41—61no—
191#135—32no—
192#135—32no—
193#135—61no—
194#135—61no—
195C2×Q16—31no—
196C2×SD16—61no—
197C2×D8—31no—
198C2×M16—61no—
199C22×C8C2×C3×D311yescharacteristic
200M32—21no—
201M32C2×C3×D312yes—
202C2×C16—21no—
203#108—32no—
204#108—61no—
205C23×C3—21no—
206C23×C3—121no—
207C23×C3#20411yescharacteristic
208C23×C3C3×SD1611yescharacteristic
209C22×D3—41no—
210C3×Q8—62no—
211C3×Q8—121no—
212C3×D4—62no—
213C3×D4—122no—
214C3×D4—122no—
215C3×D4—121no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—121no—
223C2×C3×C4—122no—
224C2×C3×C4—122no—
225C2×C3×C4#20411yescharacteristic
226C2×C3×C4D2411yescharacteristic
227C2×C3×C4D2411yescharacteristic
228C2×C3×C4(C2×D3)⋊C411yescharacteristic
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4C3×C22⋊C411yescharacteristic
231C2×C3×C4C3×C22⋊C411yescharacteristic
232C2×C3×C4C3×D811yescharacteristic
233C2×C3×C4C3×D811yescharacteristic
234C2×C3×C4C3×SD1611yescharacteristic
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237#67—42no—
238#67—42no—
239C2×Dic3—41no—
240D12—22no—
241D12—41no—
242C4×D3—42no—
243C4×D3—42no—
244Dic6—22no—
245Dic6—41no—
246C3×C8—21no—
247C3×C8—21no—
248C3×C8—21no—
249C3×C8—21no—
250C3×C8—122no—
251C3×C8(C2×D3)⋊C411yescharacteristic
252C3×C8(C2×D3)⋊C411yescharacteristic
253C3×C8C3×C22⋊C411yescharacteristic
254C3×C8C3×C22⋊C411yescharacteristic
255C3×C8C2×C4×D311yescharacteristic
256C3×C8C2×#6711yescharacteristic
257C3×C8C22×C3×C411yescharacteristic
258C3×C8C2×C3×D411yescharacteristic
259C3⋊C8—42no—
260C2×C32—21no—
261C2×C32—21no—
262C2×C32—21no—
263C2×C32C2×#10211yescharacteristic
264C3×D3—82no—
265#41—62no—
266#41—62no—
267#41—121no—
268#41—121no—
269C2×Q8—61no—
270C2×D4—61no—
271C2×D4—121no—
272C22×C4—121no—
273C22×C4C3×D1211yescharacteristic
274Q16—32no—
275Q16—61no—
276SD16—62no—
277SD16—62no—
278D8—32no—
279D8—61no—
280M16—62no—
281M16—121no—
282C2×C8—121no—
283C2×C8C3×C4×D311yescharacteristic
284C2×C8C3×C4×D311yescharacteristic
285C2×C8C3×D1211yescharacteristic
286C2×C8C3×#6711yescharacteristic
287C2×C8C3×#6711yescharacteristic
288C2×C8C22×C3×D311yescharacteristic
289C16—22no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—42no—
296C22×C3—122no—
297C22×C3—242no—
298C22×C3#82111yescharacteristic
299C22×C3#82111yescharacteristic
300C22×C3C3×#10211yescharacteristic
301C22×C3C3×#10211yescharacteristic
302C22×C3C2×#20411yescharacteristic
303C22×C3C2×C3×SD1611yescharacteristic
304C2×D3—42no—
305C2×D3—82no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—122no—
311C3×C4#82111yescharacteristic
312C3×C4#82111yescharacteristic
313C3×C4C3×#10211yescharacteristic
314C3×C4C3×#10211yescharacteristic
315C3×C4C2×D2411yescharacteristic
316C3×C4C2×(C2×D3)⋊C411yescharacteristic
317C3×C4C2×C3×C22⋊C411yescharacteristic
318C3×C4C2×C3×D811yescharacteristic
319Dic3—42no—
320C32#214811yescharacteristic, complemented, Sylow
321C23—121no—
322C23C3×#20411yescharacteristic
323Q8—62no—
324Q8—121no—
325D4—62no—
326D4—122no—
327D4—122no—
328D4—121no—
329C2×C4—121no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4C3×#20411yescharacteristic
333C2×C4C3×D2411yescharacteristic
334C2×C4C3×D2411yescharacteristic
335C2×C4C3×(C2×D3)⋊C411yescharacteristic
336C2×C4C3×(C2×D3)⋊C411yescharacteristic
337C2×C4C2×C3×D1211yescharacteristic
338C8—122no—
339C8C3×(C2×D3)⋊C411yescharacteristic
340C8C3×(C2×D3)⋊C411yescharacteristic
341C8C2×C3×C4×D311yescharacteristic
342C8C2×C3×#6711yescharacteristic
343C2×C3—22no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—242no—
354C2×C3C2×#82111yescharacteristic
355C2×C3C2×C3×#10211yescharacteristic
356D3—82no—
357C22—41no—
358C22—122no—
359C22—242no—
360C22C3×#82111yescharacteristic
361C22C3×#82111yescharacteristic
362C22C2×C3×#20411yescharacteristic
363C4—122no—
364C4C3×#82111yescharacteristic
365C4C3×#82111yescharacteristic
366C4C2×C3×D2411yescharacteristic
367C4C2×C3×(C2×D3)⋊C411yescharacteristic
368C3—21no—
369C3#7144211yescharacteristic, direct product factor
370C3C3×#214811yescharacteristic, complemented
371C2—21no—
372C2—21no—
373C2—21no—
374C2—242no—
375C2C2×C3×#82111yescharacteristic
subgroupG/H
centerC3×C4#821
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
FittingC2×C32×M32C2
socleC2×C32C2×#102
prime radicalC2×C3×#904C2
cosocleC2×C3×C8C23×C3
hypercenterC2×C3×M32D3
hypocenterC3C3×#2148
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×M32

Complements

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

NH ≅ G/Ntype
2. C2×C32×M32C2semidirect
3. C2×C3×#819C2semidirect
4. C3×#4517C2semidirect
5. C3×#4516C2semidirect
7. #71442C3direct (N × H)
26. C2×C3×M32D3semidirect
27. C2×C3×M32C2×C3semidirect
29. C2×#819C2×C3semidirect
32. #4517C2×C3semidirect
33. #4516C2×C3semidirect
117. C2×M32C3×D3semidirect
320. C32#2148semidirect
369. C3#71442direct (N × H)
370. C3C3×#2148semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×C32×M322
C2×C3×#8192
C3×#45172
C3×#45162
C3×#21483
#714423