Finite Group Databasebeta

← C3×#83685 #11898283

Subgroups — C3×#83685 #11898283

Order 1152.

908 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic
3C3×#5085C213yesmaximal, complemented
4C3×#5083C213yesmaximal, complemented
5C3×#5027C213yesmaximal, complemented
6C3×C4×#215C213yesmaximal, complemented
7C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#3392—31nomaximal
9#83685C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C32×C4⋊Q8C2213yes—
12C32×#125—23no—
13C32×C4×Q8—21no—
14C32×C4×Q8C2213yes—
15C32×C4×Q8C2211yescharacteristic
16C2×C3×#215C2213yes—
17C2×C3×#215C2216yes—
18C3×#895—23no—
19C3×#874C2213yes—
20C3×C4×D12C2213yes—
21C3×#835C2213yes—
22C3×#809C2213yes—
23C3×#808C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2213yes—
25C3×C4×C3⋊C8C2213yes—
26C3×#557—21no—
27C3×#557D311yescharacteristic, complemented
28C3×#557C2×C311yescharacteristic, complemented
29C3×#550—31no—
30#5577C2×C311yescharacteristic
31C3×#492—33no—
32C3×#461—33no—
33C3×#460—33no—
34C3×C8×Q8—31no—
35C3×C4×SD16—33no—
36#5085C2×C313yescomplemented
37#5083C2×C313yescomplemented
38#5027C2×C313yescomplemented
39C4×#215C2×C313yescomplemented
40Q8×C3⋊C8C2×C311yescharacteristic, complemented
41C2×C32×Q8D411yescharacteristic
42C2×C32×Q8C2313yes—
43C3×#239—44no—
44C2×C3×D12—23no—
45C2×C3×D12—23no—
46C2×C3×D12C2313yes—
47C2×C3×C4×D3—23no—
48C32×C4⋊C4—23no—
49C32×C4⋊C4—23no—
50C32×C4⋊C4—23no—
51C32×C4⋊C4D413yes—
52C32×C4⋊C4C2311yescharacteristic
53C32×C42—23no—
54C32×C42C2313yes—
55C3×#215—26no—
56C3×#215—46no—
57C3×(C2×D3)⋊C4—23no—
58C3×C4⋊Dic3C2311yescharacteristic
59C2×C3×C3⋊C8C2313yes—
60C2×C3×C3⋊C8C2311yescharacteristic
61#3392—31noSylow
62C2×C3×#41—61no—
63C2×#239—21no—
64C2×C3×SD16—33no—
65C2×C3×SD16—36no—
66C3×C4⋊Q8—23no—
67C3×C4⋊Q8C2×D313yes—
68C3×C4⋊Q8C22×C313yes—
69C3×#127—33no—
70C3×#125—26no—
71C3×#125—23no—
72C3×#125—23no—
73C3×#121—63no—
74C3×C4×Q8—22no—
75C3×C4×Q8—21no—
76C3×C4×Q8—21no—
77C3×C4×Q8—23no—
78C3×C4×Q8—21no—
79C3×C4×Q8C2×D313yes—
80C3×C4×Q8C2×D311yescharacteristic
81C3×C4×Q8C22×C313yes—
82C3×C4×Q8C22×C311yescharacteristic
83C3×C4×D4—33no—
84C2×#215C22×C313yes—
85C2×#215C22×C316yes—
86#895—23no—
87#874C22×C313yes—
88C4×D12C22×C313yes—
89C3×#106—31no—
90C3×C4⋊C8—33no—
91C3×#103—33no—
92C3×#102—33no—
93C3×C4×C8—33no—
94#835C22×C313yes—
95#809C22×C313yes—
96#808C22×C311yescharacteristic
97C4⋊(C3⋊C8)C22×C313yes—
98C4×C3⋊C8C22×C313yes—
99C22×C3×D3—23no—
100C32×Q8—23no—
101C32×Q8—23no—
102C32×Q8SD1614yescomplemented
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#4112yescomplemented
116#557C3×D311yescharacteristic, complemented
117#550—31no—
118#492—33no—
119#461—33no—
120#460—33no—
121C8×Q8—31no—
122C4×SD16—33no—
123C3×#41—124no—
124C2×C3×Q8—21no—
125C2×C3×Q8—23no—
126C2×C3×Q8#6711yescharacteristic
127C2×C3×Q8C3×D411yescharacteristic
128C2×C3×Q8C22×D313yes—
129C2×C3×Q8C23×C313yes—
130C2×C3×D4—33no—
131C2×C3×D4—63no—
132C2×C3×D4—63no—
133C22×C3×C4—63no—
134#239—44no—
135C2×D12—23no—
136C2×D12—23no—
137C2×D12C23×C313yes—
138C2×C4×D3—23no—
139C3×SD16—66no—
140C3×SD16—126no—
141C2×C3×C8—31no—
142C2×C3×C8—33no—
143C3×C4⋊C4—26no—
144C3×C4⋊C4—26no—
145C3×C4⋊C4—26no—
146C3×C4⋊C4—23no—
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—21no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4#6713yes—
156C3×C4⋊C4C3×D413yes—
157C3×C4⋊C4C22×D311yescharacteristic
158C3×C4⋊C4C23×C311yescharacteristic
159C3×C22⋊C4—63no—
160C3×C42—26no—
161C3×C42—23no—
162C3×C42—23no—
163C3×C42—23no—
164C3×C42C22×D313yes—
165C3×C42C23×C313yes—
166#215—26no—
167#215—46no—
168(C2×D3)⋊C4—23no—
169C4⋊Dic3C23×C311yescharacteristic
170C2×C3⋊C8C23×C313yes—
171C2×C3⋊C8C23×C311yescharacteristic
172C22×C32C22×D411yescharacteristic
173C2×C3×D3—43no—
174C2×C3×D3—43no—
175C2×C3×D3—43no—
176C32×C4—23no—
177C32×C4—43no—
178C32×C4—41no—
179C32×C4C2×SD1616yes—
180C32×C4C2×#4111yescharacteristic
181C32×C4H(5,𝔽2)11yescharacteristic
182C3×Dic3—41no—
183C2×#41—61no—
184C2×SD16—33no—
185C2×SD16—36no—
186C4⋊Q8C2×C3×D313yes—
187#127—33no—
188#125—23no—
189#121—63no—
190C4×Q8—21no—
191C4×Q8C2×C3×D313yes—
192C4×Q8C2×C3×D311yescharacteristic
193C4×D4—33no—
194#106—31no—
195C4⋊C8—33no—
196#103—33no—
197#102—33no—
198C4×C8—33no—
199C23×C3—63no—
200C22×D3—23no—
201C3×Q8—23no—
202C3×Q8—23no—
203C3×Q8—23no—
204C3×Q8—23no—
205C3×Q8—24no—
206C3×Q8—43no—
207C3×Q8—43no—
208C3×Q8#21514yescomplemented
209C3×Q8C3×SD1614yescomplemented
210C3×D4—63no—
211C3×D4—63no—
212C3×D4—126no—
213C3×D4—243no—
214C2×C3×C4—22no—
215C2×C3×C4—26no—
216C2×C3×C4—21no—
217C2×C3×C4—23no—
218C2×C3×C4—21no—
219C2×C3×C4—23no—
220C2×C3×C4—21no—
221C2×C3×C4—23no—
222C2×C3×C4—23no—
223C2×C3×C4—61no—
224C2×C3×C4—126no—
225C2×C3×C4C2×#6713yes—
226C2×C3×C4C2×#6713yes—
227C2×C3×C4C2×C3×D413yes—
228C2×C3×C4C2×C3×D413yes—
229C2×C3×C4C23×D311yescharacteristic
230C2×C3×C4C24×C311yescharacteristic
231C2×Dic3—21no—
232D12—23no—
233D12—23no—
234D12—46no—
235D12—83no—
236C4×D3—46no—
237C3×C8—32no—
238C3×C8—63no—
239C3⋊C8—23no—
240C3⋊C8C3×#4112yescomplemented
241C2×C32#55011yescharacteristic
242C2×C32C22×SD1611yescharacteristic
243C2×C32#57711yescharacteristic
244C3×D3—83no—
245#41—124no—
246C2×Q8C3×#6711yescharacteristic
247C2×Q8C22×C3×D313yes—
248C2×D4—33no—
249C2×D4—63no—
250C2×D4—63no—
251C22×C4—63no—
252SD16—66no—
253SD16—126no—
254C2×C8—31no—
255C2×C8—33no—
256C4⋊C4—23no—
257C4⋊C4—23no—
258C4⋊C4—23no—
259C4⋊C4—31no—
260C4⋊C4C3×#6713yes—
261C4⋊C4C22×C3×D311yescharacteristic
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—23no—
275C3×C4—23no—
276C3×C4—26no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—43no—
280C3×C4—46no—
281C3×C4—42no—
282C3×C4—41no—
283C3×C4—43no—
284C3×C4—41no—
285C3×C4—43no—
286C3×C4—121no—
287C3×C4C2×#21516yes—
288C3×C4C2×C3×SD1616yes—
289C3×C4D3×#4111yescharacteristic
290C3×C4#100911yescharacteristic
291C3×C4C2×C3×#4111yescharacteristic
292C3×C4C3×H(5,𝔽2)11yescharacteristic
293Dic3—41no—
294C32#339211yescharacteristic, complemented, Sylow
295C23—63no—
296Q8—23no—
297Q8—23no—
298Q8C3×#21514yescomplemented
299D4—63no—
300D4—63no—
301D4—126no—
302D4—243no—
303C2×C4—21no—
304C2×C4—23no—
305C2×C4—61no—
306C2×C4—126no—
307C2×C4C2×C3×#6713yes—
308C2×C4C2×C3×#6713yes—
309C2×C4C23×C3×D311yescharacteristic
310C8—32no—
311C8—63no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—243no—
316C2×C3C22×#21511yescharacteristic
317C2×C3#583411yescharacteristic
318C2×C3#583711yescharacteristic
319C2×C3C3×#55011yescharacteristic
320C2×C3C22×C3×SD1611yescharacteristic
321C2×C3C3×#57711yescharacteristic
322D3—83no—
323C22—123no—
324C22—123no—
325C22—123no—
326C22C22×C3×#6711yescharacteristic
327C4—23no—
328C4—43no—
329C4—41no—
330C4—121no—
331C4C2×C3×#21516yes—
332C4C3×D3×#4111yescharacteristic
333C4C3×#100911yescharacteristic
334C3—21no—
335C3#8368511yescharacteristic, direct product factor
336C3C3×#339211yescharacteristic, complemented
337C2—243no—
338C2C22×C3×#21511yescharacteristic
339C2C3×#583411yescharacteristic
340C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radicalC3×#5577C2
hypercenterC3×#557D3
hypocenterC3C3×#3392
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. C3×#5085C2semidirect
4. C3×#5083C2semidirect
5. C3×#5027C2semidirect
6. C3×C4×#215C2semidirect
7. C3×Q8×C3⋊C8C2semidirect
9. #83685C3direct (N × H)
27. C3×#557D3semidirect
28. C3×#557C2×C3semidirect
36. #5085C2×C3semidirect
37. #5083C2×C3semidirect
38. #5027C2×C3semidirect
39. C4×#215C2×C3semidirect
40. Q8×C3⋊C8C2×C3semidirect
102. C32×Q8SD16semidirect
115. C3×C3⋊C8#41semidirect
116. #557C3×D3semidirect
208. C3×Q8#215semidirect
209. C3×Q8C3×SD16semidirect
240. C3⋊C8C3×#41semidirect
294. C32#3392semidirect
298. Q8C3×#215semidirect
335. C3#83685direct (N × H)
336. C3C3×#3392semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×#55772
C3×#50852
C3×#50832
C3×#50272
C3×C4×#2152
C3×Q8×C3⋊C82
C3×#33923
#836853