Finite Group Databasebeta

← C3×#70854 #11781333

Subgroups — C3×#70854 #11781333

Order 1152.

399 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×D4C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1679—31nomaximal
9#70854C311yesmaximal, 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×#816—21no—
20C3×#816—21no—
21C3×#810—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#487—31no—
26C3×#474—31no—
27C3×#461—31no—
28C3×C8×D4—21no—
29C3×C8×D4D311yescharacteristic
30C3×C8×D4C2×C311yescharacteristic
31#5019C2×C311yescharacteristic
32#5007C2×C311yescharacteristic
33#4681C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#332—31no—
36C3×#332—31no—
37#4486C2×C311yescharacteristic, complemented
38#4482C2×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#1679—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×#107—61no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#103—61no—
78C3×#103—61no—
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#816—21no—
89#816—21no—
90#810—21no—
91#807—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—41no—
108C3×Dic6—41no—
109C32×C8—21no—
110C32×C8—21no—
111C32×C8—41no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—31no—
115#474—31no—
116#461—31no—
117C8×D4C3×D311yescharacteristic
118#334—31no—
119#332—31no—
120#332—31no—
121C2×C3×Q8—61no—
122C2×C3×Q8—61no—
123C2×C3×D4—21no—
124C2×C3×D4D1211yescharacteristic
125C2×C3×D4C3×D411yescharacteristic
126C22×C3×C4—22no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C2×Dic6—21no—
130C2×Dic6—21no—
131C3×SD16—122no—
132C2×C3×C8—22no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—44no—
138C2×C3×C8—42no—
139C2×C3×C8—42no—
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C2×C3×C8#6711yescharacteristic
143C2×C3×C8#6711yescharacteristic
144C2×C3×C8C3×D411yescharacteristic
145C2×C3×C8C3×D411yescharacteristic
146C3×C4⋊C4—21no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4D1211yescharacteristic
152C3×C4⋊C4C3×D411yescharacteristic
153C3×C22⋊C4—22no—
154C3×C22⋊C4—21no—
155C3×C22⋊C4—21no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C23×C311yescharacteristic
159#214—42no—
160C4⋊Dic3—21no—
161C4⋊Dic3—21no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166C22×C32—22no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32#12111yescharacteristic
170C32×C4—21no—
171C32×C4—41no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4AGL(1,ℤ/8)11yescharacteristic
176C3×Dic3—81no—
177C3×Dic3—81no—
178C2×SD16—61no—
179C22×C8—21no—
180C4⋊Q8—31no—
181C4⋊Q8—31no—
182C4×D4C2×C3×D311yescharacteristic
183#107—61no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8C2×C3×D311yescharacteristic
187#103—61no—
188#103—61no—
189#103—61no—
190#102—61no—
191C22⋊C8—21no—
192C4×C8C2×C3×D311yescharacteristic
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—21no—
196C3×Q8—121no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×Q8—121no—
200C3×D4—22no—
201C3×D4—21no—
202C3×D4—21no—
203C3×D4—22no—
204C3×D4#20412yes—
205C3×D4C3×SD1612yes—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—121no—
219C2×C3×C4—121no—
220C2×C3×C4C2×D1211yescharacteristic
221C2×C3×C4#23511yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×C3×C4C2×C3×D411yescharacteristic
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×C3×C4C3×#4111yescharacteristic
226C2×Dic3—41no—
227C2×Dic3—41no—
228Dic6—41no—
229Dic6—41no—
230Dic6—41no—
231Dic6—41no—
232C3×C8—22no—
233C3×C8—21no—
234C3×C8—21no—
235C3×C8—21no—
236C3×C8—21no—
237C3×C8—41no—
238C3×C8—42no—
239C3×C8—41no—
240C3×C8—41no—
241C3×C8—121no—
242C3×C8—121no—
243C3⋊C8—41no—
244C3⋊C8—41no—
245C2×C32—42no—
246C2×C32#46311yescharacteristic
247C2×C32#46511yescharacteristic
248C2×C32#47311yescharacteristic
249C2×Q8—61no—
250C2×Q8—61no—
251C2×D4C3×D1211yescharacteristic
252C22×C4—21no—
253SD16—122no—
254C2×C8—21no—
255C2×C8—42no—
256C2×C8—61no—
257C2×C8—61no—
258C2×C8C3×#6711yescharacteristic
259C2×C8C3×#6711yescharacteristic
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4C3×D1211yescharacteristic
265C22⋊C4—21no—
266C42C22×C3×D311yescharacteristic
267C22×C3—24no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3#93011yescharacteristic
278C22×C3C3×#12111yescharacteristic
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—42no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—241no—
290C3×C4—241no—
291C3×C4C2×#20411yescharacteristic
292C3×C4#90411yescharacteristic
293C3×C4#93211yescharacteristic
294C3×C4#95011yescharacteristic
295C3×C4C2×C3×SD1611yescharacteristic
296C3×C4C3×#13511yescharacteristic
297C3×C4C3×#13511yescharacteristic
298C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
299Dic3—81no—
300Dic3—81no—
301C32#167911yescharacteristic, complemented, Sylow
302C23—21no—
303Q8—121no—
304Q8—121no—
305Q8—121no—
306Q8—121no—
307D4—21no—
308D4C3×#20412yes—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—121no—
313C2×C4—121no—
314C2×C4C2×C3×D1211yescharacteristic
315C2×C4C3×#23511yescharacteristic
316C2×C4C2×C3×#6711yescharacteristic
317C8—21no—
318C8—21no—
319C8—41no—
320C8—121no—
321C8—121no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—44no—
326C2×C3—42no—
327C2×C3—42no—
328C2×C3#501611yescharacteristic
329C2×C3#511411yescharacteristic
330C2×C3#514311yescharacteristic
331C2×C3C3×#46311yescharacteristic
332C2×C3C3×#46511yescharacteristic
333C2×C3C3×#47311yescharacteristic
334C22—22no—
335C22—41no—
336C22—41no—
337C22C3×#93011yescharacteristic
338C4—21no—
339C4—41no—
340C4—241no—
341C4—241no—
342C4C2×C3×#20411yescharacteristic
343C4C3×#90411yescharacteristic
344C4C3×#93211yescharacteristic
345C4C3×#95011yescharacteristic
346C3—21no—
347C3#7085411yescharacteristic, direct product factor
348C3C3×#167911yescharacteristic, complemented
349C2—42no—
350C2C3×#501611yescharacteristic
351C2C3×#511411yescharacteristic
352C2C3×#514311yescharacteristic
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×#1679
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×#4681C2semidirect
5. C3×#4486C2semidirect
6. C3×#4482C2semidirect
7. C3×#4457C2semidirect
9. #70854C3direct (N × H)
33. #4681C2×C3semidirect
37. #4486C2×C3semidirect
38. #4482C2×C3semidirect
39. #4457C2×C3semidirect
301. C32#1679semidirect
347. C3#70854direct (N × H)
348. C3C3×#1679semidirect

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×#50072
C3×#46812
C3×#44862
C3×#44822
C3×#44572
C3×#16793
#708543