Finite Group Databasebeta

← C3×#83813 #11857666

Subgroups — C3×#83813 #11857666

Order 1152.

1641 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C32×#568C211yesmaximal, characteristic, complemented
3C3×#5819C211yesmaximal, characteristic, complemented
4C3×#5132C216yesmaximal, complemented
5C2×C3×#823C216yesmaximal, complemented
6C3×#2888—31nomaximal
7#83813C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2211yescharacteristic
9C3×#1009—24no—
10C3×#1009—24no—
11C2×C3×#239C412yes—
12C2×C3×D3×D4C416yes—
13C2×C3×#235C2213yes—
14C22×C3×D12C2213yes—
15C32×#131—24no—
16C2×C32×M16C2216yescomplemented
17C3×#948—24no—
18C2×C3×#208C2216yescomplemented
19C3×#824C2214yescomplemented
20C3×#823C22112yescomplemented
21C2×C3×H(5,𝔽2)—31no—
22C2×#1009C2×C311yescharacteristic
23C3×#568—21no—
24C3×#568—31no—
25C3×#568D311yescharacteristic, complemented
26C3×#568C2×C311yescharacteristic, complemented
27#5819C2×C311yescharacteristic, complemented
28C3×#413—36no—
29C2×C3×#100—36no—
30#5132C2×C316yescomplemented
31C2×#823C2×C316yescomplemented
32C23×C3×D3C2×C416yes—
33C32×#41D414yes—
34C32×#41D414yes—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C32×D4C2×C413yes—
37C22×C32×C4C2313yes—
38C2×C3×#67C2×C416yes—
39C3×#239—28no—
40C3×D3×D4—224no—
41C3×#235—26no—
42C3×#235—26no—
43C2×C3×D12—26no—
44C2×C3×D12—26no—
45C2×C3×D12C2×C416yes—
46C2×C3×D12C2313yes—
47C2×C3×C4×D3C2×C416yes—
48C2×C3×Dic6C2311yescharacteristic
49C32×M16—26no—
50C32×M16C2314yes—
51C2×C32×C8—26no—
52C3×#208—26no—
53C3×#208C2314yes—
54C2×C3×C3⋊C8—26no—
55#2888—31noSylow
56C3×H(5,𝔽2)—64no—
57C3×H(5,𝔽2)—64no—
58C2×C3×#41—21no—
59C2×C3×#41—32no—
60C2×C3×#41—33no—
61C2×C3×#41C2×D311yescharacteristic
62C2×C3×#41C22×C311yescharacteristic
63C22×C3×D4—36no—
64C22×C3×D4—33no—
65#1009—24no—
66#1009—24no—
67C2×#239C3×C412yes—
68C2×D3×D4C3×C416yes—
69C2×#235C22×C313yes—
70C22×D12C22×C313yes—
71C3×#131—28no—
72C3×#131—24no—
73C3×#131—24no—
74C3×#131—64no—
75C2×C3×M16—26no—
76C2×C3×M16—36no—
77C2×C3×M16C2×D316yescomplemented
78C2×C3×M16C22×C316yescomplemented
79#948—24no—
80C2×#208C22×C316yescomplemented
81C3×#101—34no—
82C3×#100—312no—
83#824C22×C314yescomplemented
84#823C22×C3112yescomplemented
85C23×C32C22×C413yes—
86C22×C3×D3—212no—
87C22×C3×D3—86no—
88C22×C3×D3C22×C416yes—
89C32×Q8C22⋊C414yes—
90C32×D4C22⋊C4112yes—
91C2×C32×C4C22×C413yes—
92C2×C32×C4C2×D416yes—
93C2×C32×C4C2×D416yes—
94C2×C32×C4C2411yescharacteristic
95C3×#67—212no—
96C2×C3×Dic3C22×C412yes—
97C3×D12—212no—
98C3×D12—23no—
99C3×D12—23no—
100C3×C4×D3—212no—
101C3×Dic6—21no—
102C3×Dic6—21no—
103C32×C8—24no—
104C3×C3⋊C8—24no—
105C2×H(5,𝔽2)—31no—
106#568—31no—
107#568C3×D311yescharacteristic, complemented
108#413—36no—
109C2×#100—36no—
110C24×C3—36no—
111C23×D3C2×C3×C416yes—
112C3×#41—24no—
113C3×#41—24no—
114C3×#41—68no—
115C3×#41—66no—
116C3×#41—66no—
117C3×#41D1214yes—
118C3×#41#6714yes—
119C3×#41C3×D414yes—
120C3×#41C3×D414yes—
121C2×C3×Q8—21no—
122C2×C3×Q8—31no—
123C2×C3×Q8C4×D311yescharacteristic
124C2×C3×Q8C2×C3×C411yescharacteristic
125C2×C3×D4—23no—
126C2×C3×D4—36no—
127C2×C3×D4—36no—
128C2×C3×D4—33no—
129C2×C3×D4—624no—
130C2×C3×D4—66no—
131C2×C3×D4—66no—
132C2×C3×D4C4×D313yes—
133C2×C3×D4C2×C3×C413yes—
134C22×C3×C4—23no—
135C22×C3×C4—36no—
136C22×C3×C4C22×D313yes—
137C22×C3×C4C23×C313yes—
138C2×#67C2×C3×C416yes—
139#239—28no—
140D3×D4—224no—
141#235—26no—
142#235—26no—
143C2×D12—26no—
144C2×D12—26no—
145C2×D12C2×C3×C416yes—
146C2×D12C23×C313yes—
147C2×C4×D3C2×C3×C416yes—
148C2×Dic6C23×C311yescharacteristic
149C3×M16—212no—
150C3×M16—26no—
151C3×M16—26no—
152C3×M16—24no—
153C3×M16—34no—
154C3×M16—66no—
155C3×M16C22×D314yes—
156C3×M16C23×C314yes—
157C2×C3×C8—212no—
158C2×C3×C8—26no—
159C2×C3×C8—26no—
160C2×C3×C8—66no—
161#208—26no—
162#208C23×C314yes—
163C2×C3⋊C8—26no—
164C22×C32—43no—
165C22×C32C2×C22⋊C416yes—
166C22×C32C23×C411yescharacteristic
167C2×C3×D3—26no—
168C2×C3×D3—46no—
169C2×C3×D3—812no—
170C32×C4C2×C22⋊C416yes—
171C32×C4C22×D411yescharacteristic
172C32×C4C22×D411yescharacteristic
173C3×Dic3—22no—
174H(5,𝔽2)—64no—
175H(5,𝔽2)—64no—
176C2×#41—32no—
177C2×#41—33no—
178C2×#41C2×C3×D311yescharacteristic
179C22×D4—36no—
180C22×D4—33no—
181#131—24no—
182#131—64no—
183C2×M16—36no—
184C2×M16C2×C3×D316yescomplemented
185#101—34no—
186#100—312no—
187C23×C3—23no—
188C23×C3—36no—
189C23×C3—612no—
190C23×C3—246no—
191C23×C3C2×C4×D313yes—
192C23×C3C22×C3×C413yes—
193C22×D3—212no—
194C22×D3—86no—
195C22×D3C22×C3×C416yes—
196C3×Q8—24no—
197C3×Q8—61no—
198C3×Q8—61no—
199C3×Q8(C2×D3)⋊C414yes—
200C3×Q8C3×C22⋊C414yes—
201C3×D4—212no—
202C3×D4—612no—
203C3×D4—612no—
204C3×D4—63no—
205C3×D4—63no—
206C3×D4(C2×D3)⋊C4112yes—
207C3×D4C3×C22⋊C4112yes—
208C2×C3×C4—21no—
209C2×C3×C4—23no—
210C2×C3×C4—26no—
211C2×C3×C4—26no—
212C2×C3×C4—32no—
213C2×C3×C4—612no—
214C2×C3×C4C2×C4×D313yes—
215C2×C3×C4C2×D1216yes—
216C2×C3×C4C2×#6716yes—
217C2×C3×C4C22×C3×C413yes—
218C2×C3×C4C2×C3×D416yes—
219C2×C3×C4C2×C3×D416yes—
220C2×C3×C4C23×D311yescharacteristic
221C2×C3×C4C24×C311yescharacteristic
222#67—212no—
223C2×Dic3C22×C3×C412yes—
224D12—212no—
225D12—23no—
226D12—23no—
227C4×D3—212no—
228Dic6—21no—
229Dic6—21no—
230C3×C8—28no—
231C3×C8—24no—
232C3×C8—24no—
233C3×C8—64no—
234C3⋊C8—24no—
235C2×C32—21no—
236C2×C32—26no—
237C2×C32C22×C22⋊C411yescharacteristic
238C3×D3—46no—
239C24—36no—
240#41—68no—
241#41—66no—
242#41—66no—
243#41C3×D1214yes—
244#41C3×#6714yes—
245C2×Q8—31no—
246C2×Q8C3×C4×D311yescharacteristic
247C2×D4—36no—
248C2×D4—33no—
249C2×D4—36no—
250C2×D4—624no—
251C2×D4—66no—
252C2×D4—66no—
253C2×D4C3×C4×D313yes—
254C22×C4—36no—
255C22×C4C22×C3×D313yes—
256M16—26no—
257M16—34no—
258M16—66no—
259M16C22×C3×D314yes—
260C2×C8—26no—
261C2×C8—66no—
262C22×C3—26no—
263C22×C3—21no—
264C22×C3—43no—
265C22×C3—43no—
266C22×C3—66no—
267C22×C3—83no—
268C22×C3—126no—
269C22×C3—2412no—
270C22×C3C2×(C2×D3)⋊C416yes—
271C22×C3C2×C3×C22⋊C416yes—
272C22×C3C22×C4×D311yescharacteristic
273C22×C3C23×C3×C411yescharacteristic
274C2×D3—26no—
275C2×D3—46no—
276C2×D3—812no—
277C3×C4—26no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—62no—
281C3×C4C2×(C2×D3)⋊C416yes—
282C3×C4C2×C3×C22⋊C416yes—
283C3×C4C22×D1211yescharacteristic
284C3×C4C22×#6711yescharacteristic
285C3×C4C22×C3×D411yescharacteristic
286C3×C4C22×C3×D411yescharacteristic
287Dic3—22no—
288C32#288811yescharacteristic, complemented, Sylow
289C23—36no—
290C23—612no—
291C23—246no—
292C23C2×C3×C4×D313yes—
293Q8—61no—
294Q8—61no—
295Q8C3×(C2×D3)⋊C414yes—
296D4—612no—
297D4—612no—
298D4—63no—
299D4—63no—
300D4C3×(C2×D3)⋊C4112yes—
301C2×C4—32no—
302C2×C4—612no—
303C2×C4C2×C3×C4×D313yes—
304C2×C4C2×C3×D1216yes—
305C2×C4C2×C3×#6716yes—
306C2×C4C23×C3×D311yescharacteristic
307C8—24no—
308C8—64no—
309C2×C3—21no—
310C2×C3—26no—
311C2×C3—21no—
312C2×C3—26no—
313C2×C3—21no—
314C2×C3—41no—
315C2×C3—46no—
316C2×C3—126no—
317C2×C3C22×(C2×D3)⋊C411yescharacteristic
318C2×C3C22×C3×C22⋊C411yescharacteristic
319D3—46no—
320C22—43no—
321C22—66no—
322C22—126no—
323C22—2412no—
324C22C2×C3×(C2×D3)⋊C416yes—
325C22C22×C3×C4×D311yescharacteristic
326C4—62no—
327C4C2×C3×(C2×D3)⋊C416yes—
328C4C22×C3×D1211yescharacteristic
329C4C22×C3×#6711yescharacteristic
330C3—21no—
331C3#8381311yescharacteristic, direct product factor
332C3C3×#288811yescharacteristic, complemented
333C2—21no—
334C2—26no—
335C2—126no—
336C2C22×C3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C3C22×(C2×D3)⋊C4
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#568C2
socleC2×C32C22×C22⋊C4
prime radicalC2×C3×#1009C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#568D3
hypocenterC3C3×#2888
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×#41 ◁ C3×#568

Complements

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

NH ≅ G/Ntype
2. C32×#568C2semidirect
3. C3×#5819C2semidirect
4. C3×#5132C2semidirect
5. C2×C3×#823C2semidirect
7. #83813C3direct (N × H)
16. C2×C32×M16C22semidirect
18. C2×C3×#208C22semidirect
19. C3×#824C22semidirect
20. C3×#823C22semidirect
25. C3×#568D3semidirect
26. C3×#568C2×C3semidirect
27. #5819C2×C3semidirect
30. #5132C2×C3semidirect
31. C2×#823C2×C3semidirect
77. C2×C3×M16C2×D3semidirect
78. C2×C3×M16C22×C3semidirect
80. C2×#208C22×C3semidirect
83. #824C22×C3semidirect
84. #823C22×C3semidirect
107. #568C3×D3semidirect
184. C2×M16C2×C3×D3semidirect
288. C32#2888semidirect
331. C3#83813direct (N × H)
332. C3C3×#2888semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C32×#5682
C3×#58192
C3×#51322
C2×C3×#8232
C3×#28883
#838133