Finite Group Databasebeta

← C3×#70941 #11781473

Subgroups — C3×#70941 #11781473

Order 1152.

383 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×Q8C211yesmaximal, characteristic, complemented
2C3×#5031C211yesmaximal, characteristic, complemented
3C3×#5027C211yesmaximal, characteristic
4C3×#4694C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#70941C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#216—21no—
12C2×C3×#215—21no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8—21no—
16C32×C4⋊C8C2211yescharacteristic
17C32×C4×C8—21no—
18C32×C4×C8C2211yescharacteristic
19C3×#821—21no—
20C3×#821—21no—
21C3×#810—21no—
22C3×#809—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—31no—
26C3×#462—31no—
27C3×#460—31no—
28C3×C8×Q8—21no—
29C3×C8×Q8D311yescharacteristic, complemented
30C3×C8×Q8C2×C311yescharacteristic, complemented
31#5031C2×C311yescharacteristic, complemented
32#5027C2×C311yescharacteristic
33#4694C2×C311yescharacteristic
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4486C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic
39#4458C2×C311yescharacteristic, complemented
40C2×C32×Q8D411yescharacteristic
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52C3×#216—42no—
53C3×#215—42no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1682—31noSylow
59C2×C3×Q16—61no—
60C2×C3×SD16—61no—
61C3×C4⋊Q8—31no—
62C3×#127—31no—
63C3×C4×Q8—21no—
64C3×C4×Q8C2×D311yescharacteristic
65C3×C4×Q8C22×C311yescharacteristic
66C2×#216—21no—
67C2×#215—21no—
68#874C22×C311yescharacteristic
69#869C22×C311yescharacteristic
70C3×C4⋊C8—22no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#103—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×#102—61no—
82C3×C4×C8—22no—
83C3×C4×C8—21no—
84C3×C4×C8—21no—
85C3×C4×C8—21no—
86C3×C4×C8C2×D311yescharacteristic
87C3×C4×C8C22×C311yescharacteristic
88#821—21no—
89#821—21no—
90#810—21no—
91#809—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C22×C3×D3—41no—
95C32×Q8—21no—
96C32×Q8D812yes—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C32×C8—21no—
111C32×C8—21no—
112C32×C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486—31no—
116#462—31no—
117#460—31no—
118C8×Q8C3×D311yescharacteristic, complemented
119#335—31no—
120#332—31no—
121#331—31no—
122C2×C3×Q8—21no—
123C2×C3×Q8—61no—
124C2×C3×Q8D1211yescharacteristic
125C2×C3×Q8C3×D411yescharacteristic
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×Dic6—21no—
133C3×Q16—122no—
134C3×SD16—122no—
135C2×C3×C8—22no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
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—22no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4D1211yescharacteristic
153C3×C4⋊C4C3×D411yescharacteristic
154C3×C42—22no—
155C3×C42—21no—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42C22×D311yescharacteristic
159C3×C42C23×C311yescharacteristic
160#216—42no—
161#215—42no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166C22×C32#12111yescharacteristic
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—22no—
171C32×C4—21no—
172C32×C4—41no—
173C32×C4C2×D811yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4#13711yescharacteristic
177C3×Dic3—81no—
178C2×Q16—61no—
179C2×SD16—61no—
180C4⋊Q8—31no—
181#127—31no—
182C4×Q8C2×C3×D311yescharacteristic
183C4⋊C8—21no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8C2×C3×D311yescharacteristic
187#103—61no—
188#102—61no—
189#102—61no—
190#102—61no—
191C4×C8—21no—
192C4×C8C2×C3×D311yescharacteristic
193C23×C3—121no—
194C22×D3—41no—
195C3×Q8—22no—
196C3×Q8—21no—
197C3×Q8—21no—
198C3×Q8—22no—
199C3×Q8—121no—
200C3×Q8—121no—
201C3×Q8D2412yes—
202C3×Q8C3×D812yes—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—121no—
206C3×D4—121no—
207C3×D4—241no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
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—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—41no—
229D12—81no—
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#46411yescharacteristic
246C2×C32#46611yescharacteristic
247C2×C32#47111yescharacteristic
248C3×D3—161no—
249C2×Q8—61no—
250C2×Q8C3×D1211yescharacteristic
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254Q16—122no—
255SD16—122no—
256C2×C8—21no—
257C2×C8—61no—
258C2×C8—61no—
259C2×C8C3×#6711yescharacteristic
260C2×C8C3×#6711yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4C3×D1211yescharacteristic
265C42—21no—
266C42C22×C3×D311yescharacteristic
267C22×C3—21no—
268C22×C3—241no—
269C22×C3—241no—
270C22×C3—241no—
271C22×C3#93011yescharacteristic
272C22×C3C3×#12111yescharacteristic
273C2×D3—81no—
274C2×D3—81no—
275C2×D3—81no—
276C3×C4—24no—
277C3×C4—21no—
278C3×C4—22no—
279C3×C4—21no—
280C3×C4—22no—
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×C4C2×D2411yescharacteristic
291C3×C4#90411yescharacteristic
292C3×C4#94211yescharacteristic
293C3×C4#95011yescharacteristic
294C3×C4C2×C3×D811yescharacteristic
295C3×C4C3×#13511yescharacteristic
296C3×C4C3×#13511yescharacteristic
297C3×C4C3×#13711yescharacteristic
298Dic3—81no—
299C32#168211yescharacteristic, complemented, Sylow
300C23—121no—
301Q8—21no—
302Q8—121no—
303Q8—121no—
304Q8C3×D2412yes—
305D4—121no—
306D4—121no—
307D4—121no—
308D4—121no—
309D4—241no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—121no—
313C2×C4C2×C3×D1211yescharacteristic
314C2×C4C3×#23511yescharacteristic
315C2×C4C2×C3×#6711yescharacteristic
316C8—21no—
317C8—21no—
318C8—41no—
319C8—121no—
320C8—121no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—481no—
325C2×C3#502811yescharacteristic
326C2×C3#511511yescharacteristic
327C2×C3#514111yescharacteristic
328C2×C3C3×#46411yescharacteristic
329C2×C3C3×#46611yescharacteristic
330C2×C3C3×#47111yescharacteristic
331D3—161no—
332C22—241no—
333C22—241no—
334C22—241no—
335C22C3×#93011yescharacteristic
336C4—22no—
337C4—21no—
338C4—41no—
339C4—241no—
340C4C2×C3×D2411yescharacteristic
341C4C3×#90411yescharacteristic
342C4C3×#94211yescharacteristic
343C4C3×#95011yescharacteristic
344C3—21no—
345C3#7094111yescharacteristic, direct product factor
346C3C3×#168211yescharacteristic, complemented
347C2—481no—
348C2C3×#502811yescharacteristic
349C2C3×#511511yescharacteristic
350C2C3×#514111yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×C8×Q8C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×C8×Q8D3
hypocenterC3C3×#1682
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C32×C8×Q8C2semidirect
2. C3×#5031C2semidirect
5. C3×#4486C2semidirect
7. C3×#4458C2semidirect
9. #70941C3direct (N × H)
29. C3×C8×Q8D3semidirect
30. C3×C8×Q8C2×C3semidirect
31. #5031C2×C3semidirect
37. #4486C2×C3semidirect
39. #4458C2×C3semidirect
118. C8×Q8C3×D3semidirect
299. C32#1682semidirect
345. C3#70941direct (N × H)
346. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C32×C8×Q82
C3×#50312
C3×#50272
C3×#46942
C3×#44862
C3×#44852
C3×#44582
C3×#16823
#709413