Finite Group Databasebeta

← C3×#73132 #11920910

Subgroups — C3×#73132 #11920910

Order 1152.

332 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5923C211yesmaximal, characteristic
2C3×#568⋊C3C211yesmaximal, characteristic, complemented
3C3×#5424C211yesmaximal, characteristic, complemented
4#73132C311yesmaximal, characteristic, direct product factor
5C3×#1881—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#986C411yescharacteristic, complemented
8C3×#985—21no—
9C3×#984C411yescharacteristic, complemented
10C3×#983—21no—
11C3×#131⋊C3—21no—
12C3×#859—21no—
13C3×#825—41nomaximal
14#5923C2×C311yescharacteristic
15C3×#575—31no—
16C3×#568D311yescharacteristic, complemented
17#568⋊C3—21no—
18#568⋊C3C2×C311yescharacteristic, complemented
19#5424C2×C311yescharacteristic, complemented
20C3×#421—31no—
21C3×#416—31no—
22C3×#408—31no—
23C3×#344—31no—
24C3×#341—31no—
25C3×#235—41no—
26C3×#41⋊C3C2×C411yescharacteristic
27C3×#41⋊C3D411yescharacteristic
28C2×C3×SL(2,𝔽3)D411yescharacteristic
29C3×GL(2,𝔽3)—21no—
30C3×#226—21no—
31C32×M16—41no—
32C3×C4×Dic3—41no—
33#1881—31noSylow
34C2×C3×#41—31no—
35C2×C3×#41C2×D311yescharacteristic
36C2×#41⋊C3—21no—
37C2×#41⋊C3C22×C311yescharacteristic
38#986C3×C411yescharacteristic, complemented
39#985—21no—
40#984C3×C411yescharacteristic, complemented
41#983—21no—
42C3×#137—31no—
43C3×#137—31no—
44C3×#137—61no—
45C3×AGL(1,ℤ/8)—31no—
46C3×AGL(1,ℤ/8)—31no—
47C3×AGL(1,ℤ/8)—61no—
48C3×#135—61no—
49C3×#135—61no—
50C3×#131—21no—
51C3×#131—61no—
52C2×C3×M16—31no—
53C2×C3×M16—31no—
54C2×C3×M16—31no—
55C22×C3×C8—31no—
56C3×#117—31no—
57#131⋊C3—22no—
58#131⋊C3—21no—
59#859—21no—
60C3×#104—61no—
61C3×#104—61no—
62C3×#103—61no—
63C3×#102—61no—
64C3×C22⋊C8—62no—
65#825—41no—
66C2×C32×C4—41no—
67C3×#67—81no—
68C2×C3×Dic3—81no—
69C3×D12—41no—
70C3×C4×D3—81no—
71C3×Dic6—41no—
72C3×SL(2,𝔽3)C22⋊C411yescharacteristic
73C32×C8—81no—
74#575—31no—
75#568C3×D311yescharacteristic, complemented
76#421—31no—
77#416—31no—
78#408—31no—
79#344—31no—
80#341—31no—
81C3×#41—31no—
82C3×#41—31no—
83C3×#41—61no—
84C3×#41—61no—
85C3×#41—61no—
86C3×#41—61no—
87C3×#41C4×D311yescharacteristic
88C3×#41#6711yescharacteristic
89C2×C3×Q8—31no—
90C2×C3×Q8D1211yescharacteristic
91C2×C3×D4—31no—
92C2×C3×D4—31no—
93C2×C3×D4—61no—
94C22×C3×C4—31no—
95C22×C3×C4—61no—
96#235—41no—
97#41⋊C3—21no—
98#41⋊C3—21no—
99#41⋊C3C2×C3×C411yescharacteristic
100#41⋊C3C3×D411yescharacteristic
101C2×SL(2,𝔽3)—21no—
102C2×SL(2,𝔽3)C3×D411yescharacteristic
103GL(2,𝔽3)—21no—
104#226—21no—
105C3×Q16—61no—
106C3×Q16—61no—
107C3×SD16—61no—
108C3×SD16—61no—
109C3×SD16—61no—
110C3×SD16—61no—
111C3×D8—61no—
112C3×D8—61no—
113C3×M16—31no—
114C3×M16—31no—
115C3×M16—31no—
116C3×M16—41no—
117C3×M16—61no—
118C3×M16—61no—
119C3×M16—61no—
120C3×M16—81no—
121C3×M16S411yescharacteristic
122C2×C3×C8—32no—
123C2×C3×C8—61no—
124C2×C3×C8—61no—
125C2×C3×C8—61no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C3×C4⋊C4—61no—
129C3×C22⋊C4—61no—
130C3×C42—61no—
131C4×Dic3—41no—
132C22×C32—41no—
133C2×C3×D3—81no—
134C32×C4—41no—
135C32×C4—41no—
136C3×Dic3—81no—
137C3×Dic3—82no—
138C2×#41—31no—
139C2×#41C2×C3×D311yescharacteristic
140#137—31no—
141#137—31no—
142#137—61no—
143AGL(1,ℤ/8)—31no—
144AGL(1,ℤ/8)—31no—
145AGL(1,ℤ/8)—61no—
146#135—61no—
147#135—61no—
148#131—21no—
149#131—61no—
150C2×M16—31no—
151C2×M16—31no—
152C2×M16—31no—
153C22×C8—31no—
154#117—31no—
155#104—61no—
156#104—61no—
157#103—61no—
158#102—61no—
159C22⋊C8—62no—
160C23×C3—31no—
161C23×C3—61no—
162C3×Q8—31no—
163C3×Q8—61no—
164C3×Q8—61no—
165C3×Q8(C2×D3)⋊C411yescharacteristic
166C3×D4—31no—
167C3×D4—31no—
168C3×D4—61no—
169C3×D4—61no—
170C3×D4—61no—
171C3×D4—121no—
172C3×D4—121no—
173C2×C3×C4—31no—
174C2×C3×C4—31no—
175C2×C3×C4—31no—
176C2×C3×C4—31no—
177C2×C3×C4—31no—
178C2×C3×C4—41no—
179C2×C3×C4—61no—
180C2×C3×C4—81no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4—121no—
184C2×C3×C4C2×S411yescharacteristic
185#67—81no—
186C2×Dic3—81no—
187D12—41no—
188C4×D3—81no—
189Dic6—41no—
190SL(2,𝔽3)—21no—
191SL(2,𝔽3)C3×C22⋊C411yescharacteristic
192C3×C8—21no—
193C3×C8—61no—
194C3×C8—61no—
195C3×C8—61no—
196C3×C8—81no—
197C3×C8—82no—
198C3×C8—121no—
199C2×C32—41no—
200C2×C32—81no—
201C3×D3—161no—
202#41—31no—
203#41—31no—
204#41—61no—
205#41—61no—
206#41—61no—
207#41—61no—
208#41C3×C4×D311yescharacteristic
209#41C3×#6711yescharacteristic
210C2×Q8—31no—
211C2×Q8C3×D1211yescharacteristic
212C2×D4—31no—
213C2×D4—31no—
214C2×D4—61no—
215C22×C4—31no—
216C22×C4—61no—
217Q16—61no—
218Q16—61no—
219SD16—61no—
220SD16—61no—
221SD16—61no—
222SD16—61no—
223D8—61no—
224D8—61no—
225M16—31no—
226M16—31no—
227M16—31no—
228M16—61no—
229M16—61no—
230M16—61no—
231M16C3×S411yescharacteristic
232C2×C8—32no—
233C2×C8—61no—
234C2×C8—61no—
235C2×C8—61no—
236C2×C8—61no—
237C2×C8—61no—
238C4⋊C4—61no—
239C22⋊C4—61no—
240C42—61no—
241C22×C3—31no—
242C22×C3—31no—
243C22×C3—41no—
244C22×C3—81no—
245C22×C3—121no—
246C22×C3—122no—
247C22×C3—121no—
248C22×C3C4⋊S411yescharacteristic
249C2×D3—81no—
250C3×C4—31no—
251C3×C4—31no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4—81no—
255C3×C4—81no—
256C3×C4—121no—
257C3×C4—241no—
258C3×C4C4×S411yescharacteristic
259C3×C4GL(2,ℤ/4)11yescharacteristic
260Dic3—81no—
261Dic3—82no—
262C32—41noSylow
263C23—31no—
264C23—61no—
265Q8—31no—
266Q8—61no—
267Q8—61no—
268Q8C3×(C2×D3)⋊C411yescharacteristic
269D4—31no—
270D4—31no—
271D4—61no—
272D4—61no—
273D4—61no—
274D4—121no—
275D4—121no—
276C2×C4—31no—
277C2×C4—31no—
278C2×C4—31no—
279C2×C4—31no—
280C2×C4—31no—
281C2×C4—61no—
282C2×C4—121no—
283C2×C4—121no—
284C2×C4—121no—
285C2×C4C2×C3×S411yescharacteristic
286C8—21no—
287C8—61no—
288C8—61no—
289C8—61no—
290C8—121no—
291C2×C3—21no—
292C2×C3—41no—
293C2×C3—61no—
294C2×C3—61no—
295C2×C3—81no—
296C2×C3—81no—
297C2×C3—161no—
298C2×C3—241no—
299C2×C3(C2×S4)⋊C411yescharacteristic
300D3—161no—
301C22—31no—
302C22—31no—
303C22—121no—
304C22—122no—
305C22—121no—
306C22C3×C4⋊S411yescharacteristic
307C4—31no—
308C4—31no—
309C4—121no—
310C4—241no—
311C4C3×C4×S411yescharacteristic
312C4C3×GL(2,ℤ/4)11yescharacteristic
313C3—41no—
314C3—81no—
315C3#7313211yescharacteristic, direct product factor
316C2—21no—
317C2—61no—
318C2—61no—
319C2—241no—
320C2C3×(C2×S4)⋊C411yescharacteristic
subgroupG/H
centerC3×C4GL(2,ℤ/4)
commutator#41⋊C3C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC3×#568D3
socleC2×C3(C2×S4)⋊C4
prime radicalC3×#5923C2
cosocleC2×#41⋊C3C22×C3
hypercenterC3×M16S4
hypocenterSL(2,𝔽3)C3×C22⋊C4
LCSG ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×M16

Complements

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

NH ≅ G/Ntype
2. C3×#568⋊C3C2semidirect
3. C3×#5424C2semidirect
4. #73132C3direct (N × H)
7. C3×#986C4semidirect
9. C3×#984C4semidirect
16. C3×#568D3semidirect
18. #568⋊C3C2×C3semidirect
19. #5424C2×C3semidirect
38. #986C3×C4semidirect
40. #984C3×C4semidirect
75. #568C3×D3semidirect
315. C3#73132direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#59232
C3×#568⋊C32
C3×#54242
#731323
C3×#18813
C3×#8254