Finite Group Databasebeta

← C3×#83817 #11858178

Subgroups — C3×#83817 #11858178

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2C32×#568C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4C3×#5139C216yesmaximal, complemented
5C2×C3×#825C216yesmaximal, complemented
6C3×#2901—31nomaximal
7#83817C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2211yescharacteristic
9C3×#1010C414yescomplemented
10C3×#1009C414yescomplemented
11C3×D3×#41—24no—
12C3×#1007—21no—
13C3×#1004—23no—
14C2×C3×#235C2216yes—
15C32×#131—24no—
16C2×C32×M16C2216yescomplemented
17C3×Q8×Dic3—21no—
18C3×D4×Dic3—23no—
19C3×#926C2213yescomplemented
20C2×C3×C4×Dic3C2213yescomplemented
21C3×#825C2214yescomplemented
22C3×#825C22112yescomplemented
23C3×#585—31no—
24#5964C2×C311yescharacteristic
25C3×#568—21no—
26C3×#568D311yescharacteristic, complemented
27C3×#568C2×C311yescharacteristic, complemented
28C3×C4×#41—31no—
29Dic3×#41C2×C311yescharacteristic, complemented
30C3×#421—36no—
31C2×C3×#104—36no—
32#5139C2×C316yescomplemented
33C2×#825C2×C316yescomplemented
34C32×#41C2×C414yes—
35C32×#41D414yes—
36C2×C32×Q8D411yescharacteristic
37C2×C32×D4D413yes—
38C22×C32×C4C2313yes—
39C2×C3×#67—26no—
40C22×C3×Dic3—23no—
41C3×#239—24no—
42C3×D3×Q8—24no—
43C3×#237—212no—
44C3×D3×D4—212no—
45C3×#235—26no—
46C3×#235—26no—
47C3×#235C2×C4112yescomplemented
48C3×#235C2314yes—
49C2×C3×D12C2×C416yescomplemented
50C2×C3×C4×D3—26no—
51C2×C3×Dic6C2×C416yescomplemented
52C32×M16—26no—
53C32×M16C2314yes—
54C2×C32×C8—26no—
55C3×#217—23no—
56C3×C4⋊Dic3—23no—
57C3×C4×Dic3—23no—
58C3×C4×Dic3C2311yescharacteristic
59C3×C4×Dic3C2313yes—
60#2901—31noSylow
61C3×2−1+4—34no—
62C3×2−1+4—61no—
63C3×H(5,𝔽2)—34no—
64C3×H(5,𝔽2)—63no—
65C2×C3×#41—21no—
66C2×C3×#41—36no—
67C2×C3×#41—64no—
68C2×C3×#41C2×D311yescharacteristic
69C2×C3×#41C22×C311yescharacteristic
70#1010C3×C414yescomplemented
71#1009C3×C414yescomplemented
72D3×#41—24no—
73#1007—21no—
74#1004—23no—
75C2×#235C22×C316yes—
76C3×#131—28no—
77C3×#131—24no—
78C3×#131—24no—
79C2×C3×M16—26no—
80C2×C3×M16C2×D316yescomplemented
81C2×C3×M16C22×C316yescomplemented
82C3×C4×Q8—61no—
83C3×C4×D4—63no—
84C3×#117—33no—
85C2×C3×C42—33no—
86Q8×Dic3—21no—
87D4×Dic3—23no—
88#926C22×C313yescomplemented
89C2×C4×Dic3C22×C313yescomplemented
90C3×#104—34no—
91C3×#104—312no—
92#825C22×C314yescomplemented
93#825C22×C3112yescomplemented
94C23×C32C2×D413yes—
95C22×C3×D3—26no—
96C32×Q8C22⋊C414yes—
97C32×D4C22⋊C4112yes—
98C2×C32×C4C22×C416yes—
99C2×C32×C4C2×D413yes—
100C2×C32×C4C2×D416yes—
101C2×C32×C4C2411yescharacteristic
102C3×#67—212no—
103C3×#67—24no—
104C2×C3×Dic3—26no—
105C2×C3×Dic3—21no—
106C2×C3×Dic3—23no—
107C2×C3×Dic3—46no—
108C3×D12—26no—
109C3×D12C22×C414yes—
110C3×C4×D3—212no—
111C3×C4×D3—24no—
112C3×Dic6—26no—
113C3×Dic6C22×C414yes—
114C32×C8—24no—
115#585—31no—
116#568C3×D311yescharacteristic, complemented
117C4×#41—31no—
118#421—36no—
119C2×#104—36no—
120C3×#41—24no—
121C3×#41—24no—
122C3×#41—312no—
123C3×#41—34no—
124C3×#41—64no—
125C3×#41—612no—
126C3×#41—66no—
127C3×#41—66no—
128C3×#41C4×D314yes—
129C3×#41#6714yes—
130C3×#41C2×C3×C414yes—
131C3×#41C3×D414yes—
132C2×C3×Q8—21no—
133C2×C3×Q8—36no—
134C2×C3×Q8—64no—
135C2×C3×Q8D1211yescharacteristic
136C2×C3×Q8C3×D411yescharacteristic
137C2×C3×D4—23no—
138C2×C3×D4—36no—
139C2×C3×D4—66no—
140C2×C3×D4—612no—
141C2×C3×D4D1213yes—
142C2×C3×D4C3×D413yes—
143C22×C3×C4—23no—
144C22×C3×C4—66no—
145C22×C3×C4—63no—
146C22×C3×C4C22×D313yes—
147C22×C3×C4C23×C313yes—
148C2×#67—26no—
149C22×Dic3—23no—
150#239—24no—
151D3×Q8—24no—
152#237—212no—
153D3×D4—212no—
154#235—26no—
155#235—26no—
156#235C2×C3×C4112yescomplemented
157#235C23×C314yes—
158C2×D12C2×C3×C416yescomplemented
159C2×C4×D3—26no—
160C2×Dic6C2×C3×C416yescomplemented
161C3×M16—212no—
162C3×M16—26no—
163C3×M16—26no—
164C3×M16—24no—
165C3×M16C22×D314yes—
166C3×M16C23×C314yes—
167C2×C3×C8—212no—
168C2×C3×C8—26no—
169C2×C3×C8—26no—
170C3×C4⋊C4—63no—
171C3×C22⋊C4—63no—
172C3×C42—31no—
173C3×C42—33no—
174C3×C42—63no—
175#217—23no—
176C4⋊Dic3—23no—
177C4×Dic3—23no—
178C4×Dic3C23×C311yescharacteristic
179C4×Dic3C23×C313yes—
180C22×C32—43no—
181C22×C32C2×C22⋊C416yes—
182C22×C32C22×D411yescharacteristic
183C2×C3×D3—24no—
184C2×C3×D3—86no—
185C32×C4C2×C22⋊C416yes—
186C32×C4C23×C411yescharacteristic
187C32×C4C22×D411yescharacteristic
188C3×Dic3—22no—
189C3×Dic3—24no—
190C3×Dic3—43no—
1912−1+4—34no—
1922−1+4—61no—
193H(5,𝔽2)—34no—
194H(5,𝔽2)—63no—
195C2×#41—36no—
196C2×#41—64no—
197C2×#41C2×C3×D311yescharacteristic
198#131—24no—
199C2×M16C2×C3×D316yescomplemented
200C4×Q8—61no—
201C4×D4—63no—
202#117—33no—
203C2×C42—33no—
204#104—34no—
205#104—312no—
206C23×C3—23no—
207C23×C3—66no—
208C23×C3C2×D1213yes—
209C23×C3C2×C3×D413yes—
210C22×D3—26no—
211C3×Q8—24no—
212C3×Q8—34no—
213C3×Q8—66no—
214C3×Q8(C2×D3)⋊C414yes—
215C3×Q8C3×C22⋊C414yes—
216C3×D4—212no—
217C3×D4—34no—
218C3×D4—612no—
219C3×D4—64no—
220C3×D4—66no—
221C3×D4(C2×D3)⋊C4112yes—
222C3×D4C3×C22⋊C4112yes—
223C2×C3×C4—21no—
224C2×C3×C4—26no—
225C2×C3×C4—23no—
226C2×C3×C4—26no—
227C2×C3×C4—66no—
228C2×C3×C4—61no—
229C2×C3×C4—612no—
230C2×C3×C4—64no—
231C2×C3×C4—63no—
232C2×C3×C4—126no—
233C2×C3×C4C2×C4×D316yes—
234C2×C3×C4C2×D1213yes—
235C2×C3×C4C2×#6716yes—
236C2×C3×C4C22×C3×C416yes—
237C2×C3×C4C2×C3×D413yes—
238C2×C3×C4C2×C3×D416yes—
239C2×C3×C4C23×D311yescharacteristic
240C2×C3×C4C24×C311yescharacteristic
241#67—212no—
242#67—24no—
243C2×Dic3—26no—
244C2×Dic3—21no—
245C2×Dic3—23no—
246C2×Dic3—46no—
247D12—26no—
248D12C22×C3×C414yes—
249C4×D3—212no—
250C4×D3—24no—
251Dic6—26no—
252Dic6C22×C3×C414yes—
253C3×C8—28no—
254C3×C8—24no—
255C3×C8—24no—
256C2×C32—21no—
257C2×C32—26no—
258C2×C32C22×C22⋊C411yescharacteristic
259C3×D3—44no—
260#41—34no—
261#41—312no—
262#41—64no—
263#41—612no—
264#41—66no—
265#41—66no—
266#41C3×C4×D314yes—
267#41C3×#6714yes—
268C2×Q8—36no—
269C2×Q8—64no—
270C2×Q8C3×D1211yescharacteristic
271C2×D4—36no—
272C2×D4—66no—
273C2×D4—612no—
274C2×D4C3×D1213yes—
275C22×C4—66no—
276C22×C4—63no—
277C22×C4C22×C3×D313yes—
278M16—26no—
279M16C22×C3×D314yes—
280C2×C8—26no—
281C4⋊C4—63no—
282C22⋊C4—63no—
283C42—31no—
284C42—33no—
285C42—63no—
286C22×C3—26no—
287C22×C3—21no—
288C22×C3—43no—
289C22×C3—43no—
290C22×C3—64no—
291C22×C3—83no—
292C22×C3—246no—
293C22×C3C2×(C2×D3)⋊C416yes—
294C22×C3C2×C3×C22⋊C416yes—
295C22×C3C22×D1211yescharacteristic
296C22×C3C22×C3×D411yescharacteristic
297C2×D3—24no—
298C2×D3—86no—
299C3×C4—26no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—62no—
303C3×C4—64no—
304C3×C4—123no—
305C3×C4C2×(C2×D3)⋊C416yes—
306C3×C4C2×C3×C22⋊C416yes—
307C3×C4C22×C4×D311yescharacteristic
308C3×C4C22×#6711yescharacteristic
309C3×C4C23×C3×C411yescharacteristic
310C3×C4C22×C3×D411yescharacteristic
311Dic3—22no—
312Dic3—24no—
313Dic3—43no—
314C32#290111yescharacteristic, complemented, Sylow
315C23—66no—
316C23C2×C3×D1213yes—
317Q8—34no—
318Q8—66no—
319Q8C3×(C2×D3)⋊C414yes—
320D4—34no—
321D4—612no—
322D4—64no—
323D4—66no—
324D4C3×(C2×D3)⋊C4112yes—
325C2×C4—66no—
326C2×C4—61no—
327C2×C4—612no—
328C2×C4—64no—
329C2×C4—63no—
330C2×C4—126no—
331C2×C4C2×C3×C4×D316yes—
332C2×C4C2×C3×D1213yes—
333C2×C4C2×C3×#6716yes—
334C2×C4C23×C3×D311yescharacteristic
335C8—24no—
336C2×C3—21no—
337C2×C3—26no—
338C2×C3—21no—
339C2×C3—26no—
340C2×C3—21no—
341C2×C3—41no—
342C2×C3—46no—
343C2×C3—124no—
344C2×C3C22×(C2×D3)⋊C411yescharacteristic
345C2×C3C22×C3×C22⋊C411yescharacteristic
346D3—44no—
347C22—43no—
348C22—64no—
349C22—246no—
350C22C2×C3×(C2×D3)⋊C416yes—
351C22C22×C3×D1211yescharacteristic
352C4—62no—
353C4—64no—
354C4—123no—
355C4C2×C3×(C2×D3)⋊C416yes—
356C4C22×C3×C4×D311yescharacteristic
357C4C22×C3×#6711yescharacteristic
358C3—21no—
359C3#8381711yescharacteristic, direct product factor
360C3C3×#290111yescharacteristic, complemented
361C2—21no—
362C2—26no—
363C2—124no—
364C2C22×C3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC3×C4C22×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#568C2
socleC2×C32C22×C22⋊C4
prime radicalC3×#5964C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#568D3
hypocenterC3C3×#2901
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C2×C3×#41 ◁ C3×#568

Complements

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

NH ≅ G/Ntype
2. C32×#568C2semidirect
3. C3×Dic3×#41C2semidirect
4. C3×#5139C2semidirect
5. C2×C3×#825C2semidirect
7. #83817C3direct (N × H)
9. C3×#1010C4semidirect
10. C3×#1009C4semidirect
16. C2×C32×M16C22semidirect
19. C3×#926C22semidirect
20. C2×C3×C4×Dic3C22semidirect
21. C3×#825C22semidirect
22. C3×#825C22semidirect
26. C3×#568D3semidirect
27. C3×#568C2×C3semidirect
29. Dic3×#41C2×C3semidirect
32. #5139C2×C3semidirect
33. C2×#825C2×C3semidirect
47. C3×#235C2×C4semidirect
49. C2×C3×D12C2×C4semidirect
51. C2×C3×Dic6C2×C4semidirect
70. #1010C3×C4semidirect
71. #1009C3×C4semidirect
80. C2×C3×M16C2×D3semidirect
81. C2×C3×M16C22×C3semidirect
88. #926C22×C3semidirect
89. C2×C4×Dic3C22×C3semidirect
92. #825C22×C3semidirect
93. #825C22×C3semidirect
116. #568C3×D3semidirect
156. #235C2×C3×C4semidirect
158. C2×D12C2×C3×C4semidirect
160. C2×Dic6C2×C3×C4semidirect
199. C2×M16C2×C3×D3semidirect
314. C32#2901semidirect
359. C3#83817direct (N × H)
360. C3C3×#2901semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C32×#5682
C3×Dic3×#412
C3×#51392
C2×C3×#8252
C3×#29013
#838173