Finite Group Databasebeta

← C3×#83703 #11895412

Subgroups — C3×#83703 #11895412

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×Q82C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic
3C3×#5088C213yesmaximal, complemented
4C3×#5084C213yesmaximal, complemented
5C3×#5027C213yesmaximal, complemented
6C3×C4×#215C213yesmaximal, complemented
7C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#3362—31nomaximal
9#83703C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C32×C4⋊Q8—23no—
12C32×C4⋊Q8C2213yes—
13C32×C4×Q8—21no—
14C32×C4×Q8C2213yes—
15C32×C4×Q8C2211yescharacteristic
16C2×C3×#215C2213yes—
17C3×#895—23no—
18C3×#874C2213yes—
19C3×C4×D12C2213yes—
20C3×#835C2211yescharacteristic
21C3×#809C2213yes—
22C3×#809C2216yes—
23C3×#808C2213yes—
24C3×C4⋊(C3⋊C8)C2213yes—
25C3×C4×C3⋊C8C2213yes—
26C3×Q82—21no—
27C3×Q82D311yescharacteristic, complemented
28C3×Q82C2×C311yescharacteristic, complemented
29C3×#550—31no—
30#5577C2×C311yescharacteristic
31C3×#486—33no—
32C3×#476—33no—
33C3×#460—33no—
34C3×C8×Q8—31no—
35C3×C4×SD16—33no—
36#5088C2×C313yescomplemented
37#5084C2×C313yescomplemented
38#5027C2×C313yescomplemented
39C4×#215C2×C313yescomplemented
40Q8×C3⋊C8C2×C311yescharacteristic, complemented
41C2×C32×Q8—23no—
42C2×C32×Q8D411yescharacteristic
43C2×C32×Q8C2311yescharacteristic
44C3×#239—44no—
45C2×C3×D12—23no—
46C2×C3×D12—23no—
47C2×C3×D12C2313yes—
48C2×C3×C4×D3—23no—
49C32×C4⋊C4—23no—
50C32×C4⋊C4—23no—
51C32×C4⋊C4D413yes—
52C32×C4⋊C4C2313yes—
53C32×C42—23no—
54C32×C42C2313yes—
55C3×#215—26no—
56C3×(C2×D3)⋊C4—23no—
57C3×C4⋊Dic3C2311yescharacteristic
58C2×C3×C3⋊C8C2313yes—
59C2×C3×C3⋊C8C2311yescharacteristic
60#3362—31noSylow
61C2×C3×#41—61no—
62C2×#239—21no—
63C2×C3×SD16—33no—
64C3×C4⋊Q8—26no—
65C3×C4⋊Q8—23no—
66C3×C4⋊Q8—23no—
67C3×C4⋊Q8—23no—
68C3×C4⋊Q8C2×D313yes—
69C3×C4⋊Q8C22×C313yes—
70C3×#127—33no—
71C3×#121—63no—
72C3×C4×Q8—22no—
73C3×C4×Q8—21no—
74C3×C4×Q8—21no—
75C3×C4×Q8—23no—
76C3×C4×Q8—21no—
77C3×C4×Q8C2×D313yes—
78C3×C4×Q8C2×D311yescharacteristic
79C3×C4×Q8C22×C313yes—
80C3×C4×Q8C22×C311yescharacteristic
81C3×C4×D4—33no—
82C2×#215C22×C313yes—
83#895—23no—
84#874C22×C313yes—
85C4×D12C22×C313yes—
86C3×#106—33no—
87C3×C4⋊C8—33no—
88C3×#103—31no—
89C3×#102—33no—
90C3×#102—36no—
91C3×C4×C8—33no—
92#835C22×C311yescharacteristic
93#809C22×C313yes—
94#809C22×C316yes—
95#808C22×C313yes—
96C4⋊(C3⋊C8)C22×C313yes—
97C4×C3⋊C8C22×C313yes—
98C22×C3×D3—23no—
99C32×Q8—21no—
100C32×Q8—83no—
101C32×Q8SD1614yescomplemented
102C32×Q8#4112yescomplemented
103C2×C32×C4—21no—
104C2×C32×C4—23no—
105C2×C32×C4C2×D413yes—
106C2×C32×C4C2×D413yes—
107C2×C32×C4C2411yescharacteristic
108C2×C3×Dic3—21no—
109C3×D12—23no—
110C3×D12—23no—
111C3×D12—46no—
112C3×D12—83no—
113C3×C4×D3—46no—
114C3×C3⋊C8—23no—
115C3×C3⋊C8—21no—
116Q82C3×D311yescharacteristic, complemented
117#550—31no—
118#486—33no—
119#476—33no—
120#460—33no—
121C8×Q8—31no—
122C4×SD16—33no—
123C3×#41—124no—
124C2×C3×Q8—26no—
125C2×C3×Q8—23no—
126C2×C3×Q8—23no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×Q8#6711yescharacteristic
130C2×C3×Q8C3×D411yescharacteristic
131C2×C3×Q8C22×D311yescharacteristic
132C2×C3×Q8C23×C311yescharacteristic
133C2×C3×D4—33no—
134C2×C3×D4—63no—
135C2×C3×D4—63no—
136C22×C3×C4—63no—
137#239—44no—
138C2×D12—23no—
139C2×D12—23no—
140C2×D12C23×C313yes—
141C2×C4×D3—23no—
142C3×SD16—66no—
143C2×C3×C8—31no—
144C2×C3×C8—33no—
145C3×C4⋊C4—26no—
146C3×C4⋊C4—26no—
147C3×C4⋊C4—23no—
148C3×C4⋊C4—23no—
149C3×C4⋊C4—23no—
150C3×C4⋊C4—23no—
151C3×C4⋊C4—23no—
152C3×C4⋊C4—23no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4#6713yes—
155C3×C4⋊C4C3×D413yes—
156C3×C4⋊C4C22×D313yes—
157C3×C4⋊C4C23×C313yes—
158C3×C22⋊C4—63no—
159C3×C42—26no—
160C3×C42—23no—
161C3×C42—23no—
162C3×C42—23no—
163C3×C42C22×D313yes—
164C3×C42C23×C313yes—
165#215—26no—
166(C2×D3)⋊C4—23no—
167C4⋊Dic3C23×C311yescharacteristic
168C2×C3⋊C8C23×C311yescharacteristic
169C2×C3⋊C8C23×C313yes—
170C22×C32C22×D411yescharacteristic
171C2×C3×D3—43no—
172C2×C3×D3—43no—
173C2×C3×D3—43no—
174C32×C4—22no—
175C32×C4—23no—
176C32×C4—43no—
177C32×C4C2×SD1616yes—
178C32×C4C2×#4111yescharacteristic
179C32×C42−1+411yescharacteristic
180C3×Dic3—41no—
181C2×#41—61no—
182C2×SD16—33no—
183C4⋊Q8—23no—
184C4⋊Q8C2×C3×D313yes—
185#127—33no—
186#121—63no—
187C4×Q8—21no—
188C4×Q8C2×C3×D313yes—
189C4×Q8C2×C3×D311yescharacteristic
190C4×D4—33no—
191#106—33no—
192C4⋊C8—33no—
193#103—31no—
194#102—33no—
195#102—36no—
196C4×C8—33no—
197C23×C3—63no—
198C22×D3—23no—
199C3×Q8—22no—
200C3×Q8—21no—
201C3×Q8—21no—
202C3×Q8—24no—
203C3×Q8—22no—
204C3×Q8—83no—
205C3×Q8—83no—
206C3×Q8—86no—
207C3×Q8#21514yescomplemented
208C3×Q8C3×SD1614yescomplemented
209C3×Q8#23912yescomplemented
210C3×Q8C3×#4112yescomplemented
211C3×D4—63no—
212C3×D4—63no—
213C3×D4—126no—
214C3×D4—243no—
215C2×C3×C4—22no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—26no—
219C2×C3×C4—23no—
220C2×C3×C4—23no—
221C2×C3×C4—21no—
222C2×C3×C4—23no—
223C2×C3×C4—23no—
224C2×C3×C4—61no—
225C2×C3×C4—126no—
226C2×C3×C4C2×#6713yes—
227C2×C3×C4C2×#6713yes—
228C2×C3×C4C2×C3×D413yes—
229C2×C3×C4C2×C3×D413yes—
230C2×C3×C4C23×D311yescharacteristic
231C2×C3×C4C24×C311yescharacteristic
232C2×Dic3—21no—
233D12—23no—
234D12—23no—
235D12—46no—
236D12—83no—
237C4×D3—46no—
238C3×C8—63no—
239C3×C8—61no—
240C3⋊C8—23no—
241C3⋊C8—21no—
242C2×C32#54811yescharacteristic
243C2×C32C22×SD1611yescharacteristic
244C2×C32#57611yescharacteristic
245C3×D3—83no—
246#41—124no—
247C2×Q8—23no—
248C2×Q8C3×#6711yescharacteristic
249C2×Q8C22×C3×D311yescharacteristic
250C2×D4—33no—
251C2×D4—63no—
252C2×D4—63no—
253C22×C4—63no—
254SD16—66no—
255C2×C8—31no—
256C2×C8—33no—
257C4⋊C4—23no—
258C4⋊C4—23no—
259C4⋊C4—31no—
260C4⋊C4C3×#6713yes—
261C4⋊C4C22×C3×D313yes—
262C22⋊C4—63no—
263C42—23no—
264C42C22×C3×D313yes—
265C22×C3—21no—
266C22×C3—123no—
267C22×C3—123no—
268C22×C3—123no—
269C22×C3C22×#6711yescharacteristic
270C22×C3C22×C3×D411yescharacteristic
271C2×D3—43no—
272C2×D3—43no—
273C2×D3—43no—
274C3×C4—24no—
275C3×C4—23no—
276C3×C4—22no—
277C3×C4—23no—
278C3×C4—22no—
279C3×C4—26no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—43no—
283C3×C4—46no—
284C3×C4—43no—
285C3×C4—43no—
286C3×C4—121no—
287C3×C4C2×#21516yes—
288C3×C4C2×C3×SD1616yes—
289C3×C4C2×#23911yescharacteristic
290C3×C4#100711yescharacteristic
291C3×C4C2×C3×#4111yescharacteristic
292C3×C4C3×2−1+411yescharacteristic
293Dic3—41no—
294C32#336211yescharacteristic, complemented, Sylow
295C23—63no—
296Q8—21no—
297Q8—83no—
298Q8C3×#21514yescomplemented
299Q8C3×#23912yescomplemented
300D4—63no—
301D4—63no—
302D4—126no—
303D4—243no—
304C2×C4—21no—
305C2×C4—23no—
306C2×C4—61no—
307C2×C4—126no—
308C2×C4C2×C3×#6713yes—
309C2×C4C2×C3×#6713yes—
310C2×C4C23×C3×D311yescharacteristic
311C8—63no—
312C8—61no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—243no—
317C2×C3C22×#21511yescharacteristic
318C2×C3#581711yescharacteristic
319C2×C3#583511yescharacteristic
320C2×C3C3×#54811yescharacteristic
321C2×C3C22×C3×SD1611yescharacteristic
322C2×C3C3×#57611yescharacteristic
323D3—83no—
324C22—123no—
325C22—123no—
326C22—123no—
327C22C22×C3×#6711yescharacteristic
328C4—22no—
329C4—23no—
330C4—43no—
331C4—121no—
332C4C2×C3×#21516yes—
333C4C2×C3×#23911yescharacteristic
334C4C3×#100711yescharacteristic
335C3—21no—
336C3#8370311yescharacteristic, direct product factor
337C3C3×#336211yescharacteristic, complemented
338C2—243no—
339C2C22×C3×#21511yescharacteristic
340C2C3×#581711yescharacteristic
341C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×Q82C2
socleC22×C32C22×D4
prime radicalC3×#5577C2
hypercenterC3×Q82D3
hypocenterC3C3×#3362
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×Q82

Complements

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

NH ≅ G/Ntype
1. C32×Q82C2semidirect
3. C3×#5088C2semidirect
4. C3×#5084C2semidirect
5. C3×#5027C2semidirect
6. C3×C4×#215C2semidirect
7. C3×Q8×C3⋊C8C2semidirect
9. #83703C3direct (N × H)
27. C3×Q82D3semidirect
28. C3×Q82C2×C3semidirect
36. #5088C2×C3semidirect
37. #5084C2×C3semidirect
38. #5027C2×C3semidirect
39. C4×#215C2×C3semidirect
40. Q8×C3⋊C8C2×C3semidirect
101. C32×Q8SD16semidirect
102. C32×Q8#41semidirect
116. Q82C3×D3semidirect
207. C3×Q8#215semidirect
208. C3×Q8C3×SD16semidirect
209. C3×Q8#239semidirect
210. C3×Q8C3×#41semidirect
294. C32#3362semidirect
298. Q8C3×#215semidirect
299. Q8C3×#239semidirect
336. C3#83703direct (N × H)
337. C3C3×#3362semidirect

Maximal subgroups

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

subgroupindex
C32×Q822
C3×#55772
C3×#50882
C3×#50842
C3×#50272
C3×C4×#2152
C3×Q8×C3⋊C82
C3×#33623
#837033