Finite Group Databasebeta

← C3×#70851 #11781014

Subgroups — C3×#70851 #11781014

Order 1152.

399 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×D4C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic
3C3×#5008C211yesmaximal, characteristic
4C3×#4680C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1671—31nomaximal
9#70851C311yesmaximal, characteristic, direct product factor
10C22×C32×C8—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#214—21no—
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C22⋊C8—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#832—21no—
19C3×#817—21no—
20C3×#817—21no—
21C3×#810—21no—
22C3×#808—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#498—31no—
26C3×#476—31no—
27C3×#461—31no—
28C3×C8×D4—21no—
29C3×C8×D4D311yescharacteristic
30C3×C8×D4C2×C311yescharacteristic
31#5019C2×C311yescharacteristic
32#5008C2×C311yescharacteristic
33#4680C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#332—31no—
37#4486C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4457C2×C311yescharacteristic, complemented
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C2×C32×C8—42no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×#214—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1671—31noSylow
59C2×C3×SD16—61no—
60C22×C3×C8—22no—
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C3×C4⋊Q8—31no—
64C3×C4⋊Q8—31no—
65C3×C4×D4—21no—
66C3×C4×D4C2×D311yescharacteristic
67C3×C4×D4C22×C311yescharacteristic
68C2×#214—21no—
69#869C22×C311yescharacteristic
70#869C22×C311yescharacteristic
71C3×#106—61no—
72C3×#106—61no—
73C3×#106—61no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×C4⋊C8C2×D311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
79C3×#103—61no—
80C3×#102—61no—
81C3×C22⋊C8—22no—
82C3×C22⋊C8—21no—
83C3×C22⋊C8—21no—
84C3×C4×C8—21no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#832—21no—
88#817—21no—
89#817—21no—
90#810—21no—
91#808—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C23×C32—21no—
95C32×D4—21no—
96C32×D4SD1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—81no—
108C32×C8—21no—
109C32×C8—41no—
110C32×C8SD1612yescomplemented
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#498—31no—
114#476—31no—
115#461—31no—
116C8×D4C3×D311yescharacteristic
117#334—31no—
118#333—31no—
119#332—31no—
120C2×C3×Q8—61no—
121C2×C3×Q8—61no—
122C2×C3×D4—21no—
123C2×C3×D4D1211yescharacteristic
124C2×C3×D4C3×D411yescharacteristic
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C2×Dic6—21no—
129C2×Dic6—21no—
130C3×SD16—122no—
131C2×C3×C8—22no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—44no—
137C2×C3×C8—42no—
138C2×C3×C8—42no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C2×C3×C8#6711yescharacteristic
142C2×C3×C8#6711yescharacteristic
143C2×C3×C8C3×D411yescharacteristic
144C2×C3×C8C3×D411yescharacteristic
145C3×C4⋊C4—21no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4D1211yescharacteristic
151C3×C4⋊C4C3×D411yescharacteristic
152C3×C22⋊C4—22no—
153C3×C22⋊C4—21no—
154C3×C22⋊C4—21no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C23×C311yescharacteristic
158#214—42no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C4⋊Dic3—21no—
162C4⋊Dic3—21no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C22×C32—22no—
166C22×C32—41no—
167C22×C32—41no—
168C22×C32#12111yescharacteristic
169C32×C4—21no—
170C32×C4—41no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13711yescharacteristic
175C3×Dic3—81no—
176C3×Dic3—81no—
177C2×SD16—61no—
178C22×C8—21no—
179C4⋊Q8—31no—
180C4⋊Q8—31no—
181C4×D4C2×C3×D311yescharacteristic
182#106—61no—
183#106—61no—
184#106—61no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8C2×C3×D311yescharacteristic
188#103—61no—
189#102—61no—
190C22⋊C8—21no—
191C4×C8C2×C3×D311yescharacteristic
192C23×C3—22no—
193C23×C3—21no—
194C23×C3—21no—
195C3×Q8—121no—
196C3×Q8—121no—
197C3×Q8—241no—
198C3×D4—22no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—22no—
202C3×D4#20412yes—
203C3×D4C3×SD1612yes—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—121no—
217C2×C3×C4—121no—
218C2×C3×C4C2×D1211yescharacteristic
219C2×C3×C4#23511yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×C3×C4C2×C3×D411yescharacteristic
223C2×C3×C4C3×#4111yescharacteristic
224C2×Dic3—41no—
225C2×Dic3—41no—
226Dic6—41no—
227Dic6—41no—
228Dic6—81no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—22no—
232C3×C8—41no—
233C3×C8—42no—
234C3×C8—41no—
235C3×C8—41no—
236C3×C8—121no—
237C3×C8—121no—
238C3×C8#21412yescomplemented
239C3×C8C3×SD1612yescomplemented
240C3⋊C8—41no—
241C3⋊C8—41no—
242C2×C32—42no—
243C2×C32#46111yescharacteristic
244C2×C32#46511yescharacteristic
245C2×C32#47111yescharacteristic
246C2×Q8—61no—
247C2×Q8—61no—
248C2×D4C3×D1211yescharacteristic
249C22×C4—21no—
250SD16—122no—
251C2×C8—21no—
252C2×C8—42no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8C3×#6711yescharacteristic
256C2×C8C3×#6711yescharacteristic
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4C3×D1211yescharacteristic
262C22⋊C4—21no—
263C42C22×C3×D311yescharacteristic
264C22×C3—24no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3#93011yescharacteristic
275C22×C3C3×#12111yescharacteristic
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—41no—
283C3×C4—42no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—241no—
287C3×C4—241no—
288C3×C4C2×#20411yescharacteristic
289C3×C4#90411yescharacteristic
290C3×C4C2×#21411yescharacteristic
291C3×C4#95111yescharacteristic
292C3×C4C2×C3×SD1611yescharacteristic
293C3×C4C2×C3×SD1611yescharacteristic
294C3×C4C3×#13511yescharacteristic
295C3×C4C3×#13711yescharacteristic
296Dic3—81no—
297Dic3—81no—
298C32#167111yescharacteristic, complemented, Sylow
299C23—21no—
300Q8—121no—
301Q8—121no—
302Q8—241no—
303D4—21no—
304D4C3×#20412yes—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—121no—
309C2×C4—121no—
310C2×C4C2×C3×D1211yescharacteristic
311C2×C4C3×#23511yescharacteristic
312C2×C4C2×C3×#6711yescharacteristic
313C8—21no—
314C8—41no—
315C8—121no—
316C8—121no—
317C8C3×#21412yescomplemented
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—44no—
322C2×C3—42no—
323C2×C3—42no—
324C2×C3#501911yescharacteristic
325C2×C3#511411yescharacteristic
326C2×C3#514111yescharacteristic
327C2×C3C3×#46111yescharacteristic
328C2×C3C3×#46511yescharacteristic
329C2×C3C3×#47111yescharacteristic
330C22—22no—
331C22—41no—
332C22—41no—
333C22C3×#93011yescharacteristic
334C4—21no—
335C4—41no—
336C4—241no—
337C4—241no—
338C4C2×C3×#20411yescharacteristic
339C4C3×#90411yescharacteristic
340C4C2×C3×#21411yescharacteristic
341C4C3×#95111yescharacteristic
342C3—21no—
343C3#7085111yescharacteristic, direct product factor
344C3C3×#167111yescharacteristic, complemented
345C2—42no—
346C2C3×#501911yescharacteristic
347C2C3×#511411yescharacteristic
348C2C3×#514111yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×C8×D4C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×C8×D4D3
hypocenterC3C3×#1671
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
4. C3×#4680C2semidirect
5. C3×#4486C2semidirect
6. C3×#4481C2semidirect
7. C3×#4457C2semidirect
9. #70851C3direct (N × H)
33. #4680C2×C3semidirect
37. #4486C2×C3semidirect
38. #4481C2×C3semidirect
39. #4457C2×C3semidirect
110. C32×C8SD16semidirect
238. C3×C8#214semidirect
239. C3×C8C3×SD16semidirect
298. C32#1671semidirect
317. C8C3×#214semidirect
343. C3#70851direct (N × H)
344. C3C3×#1671semidirect

Maximal subgroups

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

subgroupindex
C32×C8×D42
C3×#50192
C3×#50082
C3×#46802
C3×#44862
C3×#44812
C3×#44572
C3×#16713
#708513