Finite Group Databasebeta

← C3×#71836 #11775172

Subgroups — C3×#71836 #11775172

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic
2C3×#4932C211yesmaximal, characteristic
3C3×#4926C211yesmaximal, characteristic
4C3×#4538C214yesmaximal
5C3×#1506—31nomaximal
6#71836C311yesmaximal, characteristic, direct product factor
7C32×C4⋊Q8C411yescharacteristic, complemented
8C32×C4⋊Q8C411yescharacteristic, complemented
9C32×#125—21no—
10C32×C22⋊Q8—21no—
11C32×C22⋊Q8C2212yes—
12C32×C4×Q8—21no—
13C32×C4×Q8C412yescomplemented
14C32×#117—21no—
15C2×C32×C42C2211yescharacteristic
16C2×C3×C4×Dic3—21no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C3×#533—21no—
23C3×#533D311yescharacteristic
24C3×#533C2×C311yescharacteristic
25C3×#432—31no—
26C3×#376—31no—
27#4932C2×C311yescharacteristic
28#4926C2×C311yescharacteristic
29C3×#328—34no—
30#4538C2×C314yes—
31C2×C32×Q8—21no—
32C2×C32×Q8C2×C412yes—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3—22no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—22no—
41C32×C4⋊C4—22no—
42C32×C4⋊C4C2×C412yes—
43C32×C22⋊C4—22no—
44C32×C42—22no—
45C32×C42C2×C411yescharacteristic
46C32×C42C2×C411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42D411yescharacteristic
49C3×C4×Dic3—24no—
50C2×C3×C3⋊C8—22no—
51#1506—31noSylow
52C3×C4⋊Q8—21no—
53C3×C4⋊Q8—21no—
54C3×C4⋊Q8Dic311yescharacteristic, complemented
55C3×C4⋊Q8Dic311yescharacteristic, complemented
56C3×C4⋊Q8C3×C411yescharacteristic, complemented
57C3×C4⋊Q8C3×C411yescharacteristic, complemented
58C3×#125—22no—
59C3×#125—21no—
60C3×#125—21no—
61C3×C22⋊Q8—22no—
62C3×C22⋊Q8—21no—
63C3×C22⋊Q8—21no—
64C3×C22⋊Q8—22no—
65C3×C22⋊Q8C2×D312yes—
66C3×C22⋊Q8C22×C312yes—
67C3×C4×Q8—22no—
68C3×C4×Q8—21no—
69C3×C4×Q8—21no—
70C3×C4×Q8—22no—
71C3×C4×Q8Dic312yescomplemented
72C3×C4×Q8C3×C412yescomplemented
73C3×#117—22no—
74C3×#117—21no—
75C3×#117—21no—
76C2×C3×C42—21no—
77C2×C3×C42—61no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C22×C311yescharacteristic
80C2×C4×Dic3—21no—
81C3×C4⋊C8—61no—
82C3×C22⋊C8—32no—
83C3×#97—61no—
84C3×#95—32no—
85C3×#95—61no—
86C3⋊#95—21no—
87C3⋊#95C22×C312yes—
88#830C22×C312yes—
89C4⋊(C3⋊C8)—21no—
90#803—21no—
91C23×C32C2×D411yescharacteristic
92C32×Q8—42no—
93C32×Q8—42no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—41no—
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C3×Dic3—24no—
106C2×C3×Dic3—42no—
107C2×C3×Dic3—42no—
108C3×C3⋊C8—42no—
109#533C3×D311yescharacteristic
110#432—31no—
111#376—31no—
112#328—34no—
113C2×C3×Q8—22no—
114C2×C3×Q8—21no—
115C2×C3×Q8—21no—
116C2×C3×Q8—22no—
117C2×C3×Q8C2×Dic312yes—
118C2×C3×Q8C2×C3×C412yes—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4C3×D411yescharacteristic
126C22×C3×C4C3×D411yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C23×C311yescharacteristic
129C22×Dic3—22no—
130C2×C3×C8—62no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4C2×Dic312yes—
148C3×C4⋊C4C2×C3×C412yes—
149C3×C22⋊C4—24no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C42—24no—
153C3×C42—22no—
154C3×C42—22no—
155C3×C42—21no—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—64no—
160C3×C42C2×Dic311yescharacteristic
161C3×C42C2×Dic311yescharacteristic
162C3×C42#6711yescharacteristic
163C3×C42#6711yescharacteristic
164C3×C42C2×C3×C411yescharacteristic
165C3×C42C2×C3×C411yescharacteristic
166C3×C42C3×D411yescharacteristic
167C3×C42C3×D411yescharacteristic
168C4×Dic3—24no—
169C2×C3⋊C8—22no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32C2×C22⋊C411yescharacteristic
173C22×C32#13712yes—
174C32×C4—21no—
175C32×C4—21no—
176C32×C4—21no—
177C32×C4—21no—
178C32×C4—21no—
179C32×C4—42no—
180C32×C4—42no—
181C32×C4#10412yes—
182C3×Dic3—44no—
183C4⋊Q8C3×Dic311yescharacteristic, complemented
184C4⋊Q8C3×Dic311yescharacteristic, complemented
185#125—21no—
186C22⋊Q8—21no—
187C22⋊Q8C2×C3×D312yes—
188C4×Q8—21no—
189C4×Q8C3×Dic312yescomplemented
190#117—21no—
191C2×C42—61no—
192C2×C42C2×C3×D311yescharacteristic
193C4⋊C8—61no—
194C22⋊C8—32no—
195#97—61no—
196#95—32no—
197#95—61no—
198C23×C3—21no—
199C23×C3C2×#6711yescharacteristic
200C23×C3C2×C3×D411yescharacteristic
201C3×Q8—42no—
202C3×Q8—42no—
203C3×Q8—44no—
204C3×Q8—44no—
205C3×Q8—42no—
206C3×Q8—42no—
207C2×C3×C4—24no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—42no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—42no—
228C2×C3×C4—64no—
229C2×C3×C4—122no—
230C2×C3×C4—122no—
231C2×C3×C4#21711yescharacteristic
232C2×C3×C4#21711yescharacteristic
233C2×C3×C4#21711yescharacteristic
234C2×C3×C4#21711yescharacteristic
235C2×C3×C4C3×C22⋊C411yescharacteristic
236C2×C3×C4C3×C22⋊C411yescharacteristic
237C2×C3×C4C3×C22⋊C411yescharacteristic
238C2×C3×C4C3×C22⋊C411yescharacteristic
239C2×C3×C4C22×Dic311yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×C3×C4C22×C3×C411yescharacteristic
242C2×C3×C4C2×C3×D411yescharacteristic
243C2×Dic3—24no—
244C2×Dic3—42no—
245C2×Dic3—42no—
246C3×C8—122no—
247C3⋊C8—42no—
248C2×C32—22no—
249C2×C32#41011yescharacteristic
250C2×C32#41911yescharacteristic
251C2×C32C2×#10411yescharacteristic
252C2×Q8—21no—
253C2×Q8C2×C3×Dic312yes—
254C22×C4—62no—
255C22×C4C3×#6711yescharacteristic
256C22×C4C3×#6711yescharacteristic
257C22×C4C22×C3×D311yescharacteristic
258C2×C8—62no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4C2×C3×Dic312yes—
265C22⋊C4—22no—
266C42—22no—
267C42—64no—
268C42C2×C3×Dic311yescharacteristic
269C42C2×C3×Dic311yescharacteristic
270C42C3×#6711yescharacteristic
271C42C3×#6711yescharacteristic
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—22no—
277C22×C3—21no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3#94212yes—
281C22×C3C2×#21711yescharacteristic
282C22×C3C2×C3×C22⋊C411yescharacteristic
283C22×C3C3×#13712yes—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—22no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—44no—
301C3×C4—44no—
302C3×C4—42no—
303C3×C4—42no—
304C3×C4—42no—
305C3×C4—42no—
306C3×C4—124no—
307C3×C4#83712yes—
308C3×C4C3×#10412yes—
309Dic3—44no—
310C32#150611yescharacteristic, complemented, Sylow
311C23C2×C3×#6711yescharacteristic
312Q8—42no—
313Q8—42no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—64no—
320C2×C4—122no—
321C2×C4—122no—
322C2×C4C3×#21711yescharacteristic
323C2×C4C3×#21711yescharacteristic
324C2×C4C3×#21711yescharacteristic
325C2×C4C3×#21711yescharacteristic
326C2×C4C22×C3×Dic311yescharacteristic
327C2×C4C2×C3×#6711yescharacteristic
328C8—122no—
329C2×C3—22no—
330C2×C3—22no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—42no—
335C2×C3#522511yescharacteristic
336C2×C3C2×#83711yescharacteristic
337C2×C3#524011yescharacteristic
338C2×C3C3×#41011yescharacteristic
339C2×C3C3×#41911yescharacteristic
340C2×C3C2×C3×#10411yescharacteristic
341C22—21no—
342C22—21no—
343C22C3×#94212yes—
344C22C2×C3×#21711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—42no—
352C4—124no—
353C4C3×#83712yes—
354C3—21no—
355C3#7183611yescharacteristic, direct product factor
356C3C3×#150611yescharacteristic, complemented
357C2—22no—
358C2C3×#522511yescharacteristic
359C2C2×C3×#83711yescharacteristic
360C2C3×#524011yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#533C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#533D3
hypocenterC3C3×#1506
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
6. #71836C3direct (N × H)
7. C32×C4⋊Q8C4semidirect
8. C32×C4⋊Q8C4semidirect
13. C32×C4×Q8C4semidirect
54. C3×C4⋊Q8Dic3semidirect
55. C3×C4⋊Q8Dic3semidirect
56. C3×C4⋊Q8C3×C4semidirect
57. C3×C4⋊Q8C3×C4semidirect
71. C3×C4×Q8Dic3semidirect
72. C3×C4×Q8C3×C4semidirect
183. C4⋊Q8C3×Dic3semidirect
184. C4⋊Q8C3×Dic3semidirect
189. C4×Q8C3×Dic3semidirect
310. C32#1506semidirect
355. C3#71836direct (N × H)
356. C3C3×#1506semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
C3×#49322
C3×#49262
C3×#45382
C3×#15063
#718363