Finite Group Databasebeta

← C3×#70940 #11781286

Subgroups — C3×#70940 #11781286

Order 1152.

371 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×Q8C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic
3C3×#5021C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic
5C3×#4485C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1678—31nomaximal
9#70940C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8—21no—
15C32×C4⋊C8C2211yescharacteristic
16C32×C4×C8—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#835—21no—
19C3×#821—21no—
20C3×#821—21no—
21C3×#809—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—31no—
26C3×#477—31no—
27C3×#460—31no—
28C3×C8×Q8—21no—
29C3×C8×Q8D311yescharacteristic, complemented
30C3×C8×Q8C2×C311yescharacteristic, complemented
31#5027C2×C311yescharacteristic
32#5021C2×C311yescharacteristic, complemented
33#4694C2×C311yescharacteristic
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4485C2×C311yescharacteristic
38#4481C2×C311yescharacteristic, complemented
39#4457C2×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×#215—42no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1678—31noSylow
58C2×C3×SD16—61no—
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C22×C311yescharacteristic
64C2×#215—21no—
65#874C22×C311yescharacteristic
66#869C22×C311yescharacteristic
67C3×#107—61no—
68C3×C4⋊C8—22no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#103—61no—
77C3×#102—61no—
78C3×#102—61no—
79C3×#102—61no—
80C3×C4×C8—22no—
81C3×C4×C8—21no—
82C3×C4×C8—21no—
83C3×C4×C8—21no—
84C3×C4×C8C2×D311yescharacteristic
85C3×C4×C8C22×C311yescharacteristic
86#835—21no—
87#821—21no—
88#821—21no—
89#809—21no—
90#807—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C22×C3×D3—41no—
94C32×Q8—21no—
95C32×Q8SD1612yes—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—81no—
107C3×Dic6—81no—
108C32×C8—21no—
109C32×C8—21no—
110C32×C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486—31no—
114#477—31no—
115#460—31no—
116C8×Q8C3×D311yescharacteristic, complemented
117#334—31no—
118#333—31no—
119#331—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—61no—
122C2×C3×Q8D1211yescharacteristic
123C2×C3×Q8C3×D411yescharacteristic
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12—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—61no—
138C2×C3×C8—61no—
139C2×C3×C8#6711yescharacteristic
140C2×C3×C8#6711yescharacteristic
141C2×C3×C8C3×D411yescharacteristic
142C2×C3×C8C3×D411yescharacteristic
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4D1211yescharacteristic
150C3×C4⋊C4C3×D411yescharacteristic
151C3×C42—22no—
152C3×C42—21no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42C22×D311yescharacteristic
156C3×C42C23×C311yescharacteristic
157#215—42no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C32×C4—22no—
167C32×C4—21no—
168C32×C4—41no—
169C32×C4C2×SD1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4#13711yescharacteristic
173C3×Dic3—81no—
174C2×SD16—61no—
175C4⋊Q8—31no—
176#127—31no—
177C4×Q8C2×C3×D311yescharacteristic
178#107—61no—
179C4⋊C8—21no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8C2×C3×D311yescharacteristic
183#103—61no—
184#102—61no—
185#102—61no—
186#102—61no—
187C4×C8—21no—
188C4×C8C2×C3×D311yescharacteristic
189C23×C3—121no—
190C22×D3—41no—
191C3×Q8—22no—
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—22no—
195C3×Q8—241no—
196C3×Q8#20412yes—
197C3×Q8C3×SD1612yes—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—241no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
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—121no—
213C2×C3×C4C2×D1211yescharacteristic
214C2×C3×C4#23511yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×C3×C4C2×C3×D411yescharacteristic
217C2×C3×C4C2×C3×D411yescharacteristic
218C2×C3×C4C3×#4111yescharacteristic
219C2×Dic3—41no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—41no—
224D12—81no—
225Dic6—81no—
226C3×C8—22no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—41no—
232C3×C8—42no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—121no—
236C3×C8—121no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C2×C32#46411yescharacteristic
240C2×C32#46511yescharacteristic
241C2×C32#47211yescharacteristic
242C3×D3—161no—
243C2×Q8—61no—
244C2×Q8C3×D1211yescharacteristic
245C2×D4—61no—
246C2×D4—61no—
247C2×D4—61no—
248SD16—122no—
249C2×C8—21no—
250C2×C8—61no—
251C2×C8—61no—
252C2×C8C3×#6711yescharacteristic
253C2×C8C3×#6711yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4C3×D1211yescharacteristic
258C42—21no—
259C42C22×C3×D311yescharacteristic
260C22×C3—21no—
261C22×C3—241no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3#93011yescharacteristic
265C22×C3C3×#12111yescharacteristic
266C2×D3—81no—
267C2×D3—81no—
268C2×D3—81no—
269C3×C4—24no—
270C3×C4—21no—
271C3×C4—22no—
272C3×C4—21no—
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—42no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—241no—
283C3×C4C2×#20411yescharacteristic
284C3×C4#90411yescharacteristic
285C3×C4#94211yescharacteristic
286C3×C4#95011yescharacteristic
287C3×C4C2×C3×SD1611yescharacteristic
288C3×C4C3×#13511yescharacteristic
289C3×C4C3×#13511yescharacteristic
290C3×C4C3×#13711yescharacteristic
291Dic3—81no—
292C32#167811yescharacteristic, complemented, Sylow
293C23—121no—
294Q8—21no—
295Q8—241no—
296Q8C3×#20412yes—
297D4—121no—
298D4—121no—
299D4—121no—
300D4—121no—
301D4—241no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—121no—
305C2×C4C2×C3×D1211yescharacteristic
306C2×C4C3×#23511yescharacteristic
307C2×C4C2×C3×#6711yescharacteristic
308C8—21no—
309C8—21no—
310C8—41no—
311C8—121no—
312C8—121no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—481no—
317C2×C3#502811yescharacteristic
318C2×C3#511411yescharacteristic
319C2×C3#514211yescharacteristic
320C2×C3C3×#46411yescharacteristic
321C2×C3C3×#46511yescharacteristic
322C2×C3C3×#47211yescharacteristic
323D3—161no—
324C22—241no—
325C22—241no—
326C22—241no—
327C22C3×#93011yescharacteristic
328C4—22no—
329C4—21no—
330C4—41no—
331C4—241no—
332C4C2×C3×#20411yescharacteristic
333C4C3×#90411yescharacteristic
334C4C3×#94211yescharacteristic
335C4C3×#95011yescharacteristic
336C3—21no—
337C3#7094011yescharacteristic, direct product factor
338C3C3×#167811yescharacteristic, complemented
339C2—481no—
340C2C3×#502811yescharacteristic
341C2C3×#511411yescharacteristic
342C2C3×#514211yescharacteristic
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×#1678
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
3. C3×#5021C2semidirect
6. C3×#4481C2semidirect
7. C3×#4457C2semidirect
9. #70940C3direct (N × H)
29. C3×C8×Q8D3semidirect
30. C3×C8×Q8C2×C3semidirect
32. #5021C2×C3semidirect
38. #4481C2×C3semidirect
39. #4457C2×C3semidirect
116. C8×Q8C3×D3semidirect
292. C32#1678semidirect
337. C3#70940direct (N × H)
338. C3C3×#1678semidirect

Maximal subgroups

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

subgroupindex
C32×C8×Q82
C3×#50272
C3×#50212
C3×#46942
C3×#44852
C3×#44812
C3×#44572
C3×#16783
#709403