Finite Group Databasebeta

← C3×#70849 #11781427

Subgroups — C3×#70849 #11781427

Order 1152.

431 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×D4C211yesmaximal, characteristic, complemented
2C3×#5019C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1681—31nomaximal
9#70849C311yesmaximal, characteristic, direct product factor
10C22×C32×C8—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#214—21no—
13C2×C3×#213—21no—
14C3×#874C2211yescharacteristic
15C3×#869C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C22⋊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×#461—31no—
27C3×#459—31no—
28C3×C8×D4—21no—
29C3×C8×D4D311yescharacteristic, complemented
30C3×C8×D4C2×C311yescharacteristic, complemented
31#5019C2×C311yescharacteristic, complemented
32#5015C2×C311yescharacteristic
33#4694C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4486C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic, complemented
39#4458C2×C311yescharacteristic, complemented
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—42no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×#214—42no—
54C3×#213—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59#1681—31noSylow
60C2×C3×SD16—61no—
61C2×C3×D8—61no—
62C22×C3×C8—22no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C3×C4⋊Q8—31no—
66C3×#127—31no—
67C3×C4×D4—21no—
68C3×C4×D4C2×D311yescharacteristic
69C3×C4×D4C22×C311yescharacteristic
70C2×#214—21no—
71C2×#213—21no—
72#874C22×C311yescharacteristic
73#869C22×C311yescharacteristic
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×#102—61no—
82C3×#102—61no—
83C3×C22⋊C8—22no—
84C3×C22⋊C8—21no—
85C3×C22⋊C8—21no—
86C3×C4×C8—21no—
87C3×C4×C8C2×D311yescharacteristic
88C3×C4×C8C22×C311yescharacteristic
89#821—21no—
90#821—21no—
91#810—21no—
92#809—21no—
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4⋊(C3⋊C8)C22×C311yescharacteristic
95C23×C32—21no—
96C22×C3×D3—41no—
97C32×D4—21no—
98C32×D4D812yes—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C3×Dic6—41no—
112C3×Dic6—41no—
113C32×C8—21no—
114C32×C8—21no—
115C32×C8—41no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—31no—
119#461—31no—
120#459—31no—
121C8×D4C3×D311yescharacteristic, complemented
122#335—31no—
123#332—31no—
124#331—31no—
125C2×C3×Q8—61no—
126C2×C3×D4—21no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4D1211yescharacteristic
131C2×C3×D4C3×D411yescharacteristic
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×Dic6—21no—
139C3×SD16—122no—
140C3×D8—122no—
141C2×C3×C8—22no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—44no—
147C2×C3×C8—42no—
148C2×C3×C8—42no—
149C2×C3×C8—61no—
150C2×C3×C8—61no—
151C2×C3×C8#6711yescharacteristic
152C2×C3×C8#6711yescharacteristic
153C2×C3×C8C3×D411yescharacteristic
154C2×C3×C8C3×D411yescharacteristic
155C3×C4⋊C4—21no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4D1211yescharacteristic
159C3×C4⋊C4C3×D411yescharacteristic
160C3×C22⋊C4—22no—
161C3×C22⋊C4—21no—
162C3×C22⋊C4—21no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C23×C311yescharacteristic
166#214—42no—
167#213—42no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C22×C32—22no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32#12111yescharacteristic
176C2×C3×D3—81no—
177C2×C3×D3—81no—
178C2×C3×D3—81no—
179C32×C4—21no—
180C32×C4—41no—
181C32×C4C2×D811yescharacteristic
182C32×C4#13511yescharacteristic
183C32×C4#13511yescharacteristic
184C32×C4AGL(1,ℤ/8)11yescharacteristic
185C3×Dic3—81no—
186C2×SD16—61no—
187C2×D8—61no—
188C22×C8—21no—
189C4⋊Q8—31no—
190#127—31no—
191C4×D4C2×C3×D311yescharacteristic
192C4⋊C8—31no—
193C4⋊C8—31no—
194C4⋊C8C2×C3×D311yescharacteristic
195#103—61no—
196#102—61no—
197#102—61no—
198#102—61no—
199C22⋊C8—21no—
200C4×C8C2×C3×D311yescharacteristic
201C23×C3—22no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—121no—
205C22×D3—41no—
206C3×Q8—121no—
207C3×Q8—121no—
208C3×D4—22no—
209C3×D4—21no—
210C3×D4—21no—
211C3×D4—22no—
212C3×D4—121no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—121no—
216C3×D4—241no—
217C3×D4D2412yes—
218C3×D4C3×D812yes—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—121no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4#23511yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×C3×C4C3×#4111yescharacteristic
238C2×Dic3—41no—
239D12—41no—
240D12—41no—
241D12—41no—
242D12—41no—
243D12—81no—
244Dic6—41no—
245Dic6—41no—
246C3×C8—22no—
247C3×C8—21no—
248C3×C8—21no—
249C3×C8—21no—
250C3×C8—21no—
251C3×C8—41no—
252C3×C8—42no—
253C3×C8—41no—
254C3×C8—41no—
255C3×C8—121no—
256C3×C8—121no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C2×C32—42no—
260C2×C32#46311yescharacteristic
261C2×C32#46611yescharacteristic
262C2×C32#47111yescharacteristic
263C3×D3—161no—
264C2×Q8—61no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—61no—
268C2×D4C3×D1211yescharacteristic
269C22×C4—21no—
270SD16—122no—
271D8—122no—
272C2×C8—21no—
273C2×C8—42no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8C3×#6711yescharacteristic
277C2×C8C3×#6711yescharacteristic
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4C3×D1211yescharacteristic
281C22⋊C4—21no—
282C42C22×C3×D311yescharacteristic
283C22×C3—24no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—21no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—241no—
294C22×C3—241no—
295C22×C3—241no—
296C22×C3#93011yescharacteristic
297C22×C3C3×#12111yescharacteristic
298C2×D3—81no—
299C2×D3—81no—
300C2×D3—81no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—42no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—241no—
312C3×C4C2×D2411yescharacteristic
313C3×C4#90411yescharacteristic
314C3×C4#93211yescharacteristic
315C3×C4#95011yescharacteristic
316C3×C4C2×C3×D811yescharacteristic
317C3×C4C3×#13511yescharacteristic
318C3×C4C3×#13511yescharacteristic
319C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
320Dic3—81no—
321C32#168111yescharacteristic, complemented, Sylow
322C23—21no—
323C23—121no—
324Q8—121no—
325Q8—121no—
326D4—21no—
327D4—121no—
328D4—121no—
329D4—121no—
330D4—121no—
331D4—241no—
332D4C3×D2412yes—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—121no—
337C2×C4C2×C3×D1211yescharacteristic
338C2×C4C3×#23511yescharacteristic
339C2×C4C2×C3×#6711yescharacteristic
340C8—21no—
341C8—21no—
342C8—41no—
343C8—121no—
344C8—121no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—44no—
349C2×C3—42no—
350C2×C3—42no—
351C2×C3—481no—
352C2×C3#501611yescharacteristic
353C2×C3#511511yescharacteristic
354C2×C3#514111yescharacteristic
355C2×C3C3×#46311yescharacteristic
356C2×C3C3×#46611yescharacteristic
357C2×C3C3×#47111yescharacteristic
358D3—161no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—241no—
363C22—241no—
364C22—241no—
365C22C3×#93011yescharacteristic
366C4—21no—
367C4—41no—
368C4—241no—
369C4C2×C3×D2411yescharacteristic
370C4C3×#90411yescharacteristic
371C4C3×#93211yescharacteristic
372C4C3×#95011yescharacteristic
373C3—21no—
374C3#7084911yescharacteristic, direct product factor
375C3C3×#168111yescharacteristic, complemented
376C2—42no—
377C2—481no—
378C2C3×#501611yescharacteristic
379C2C3×#511511yescharacteristic
380C2C3×#514111yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×C8×D4C2
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#1681
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
1. C32×C8×D4C2semidirect
2. C3×#5019C2semidirect
4. C3×#4694C2semidirect
5. C3×#4486C2semidirect
6. C3×#4485C2semidirect
7. C3×#4458C2semidirect
9. #70849C3direct (N × H)
29. C3×C8×D4D3semidirect
30. C3×C8×D4C2×C3semidirect
31. #5019C2×C3semidirect
33. #4694C2×C3semidirect
37. #4486C2×C3semidirect
38. #4485C2×C3semidirect
39. #4458C2×C3semidirect
121. C8×D4C3×D3semidirect
321. C32#1681semidirect
374. C3#70849direct (N × H)
375. C3C3×#1681semidirect

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×#50152
C3×#46942
C3×#44862
C3×#44852
C3×#44582
C3×#16813
#708493