Finite Group Databasebeta

← C3×#73128 #11920906

Subgroups — C3×#73128 #11920906

Order 1152.

359 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 359 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C2×C3×#986C211yesmaximal, characteristic
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3C3×#5426C211yesmaximal, characteristic, complemented
4#73128C311yesmaximal, characteristic, direct product factor
5C3×#1907—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#986—21no—
8C3×#986C412yescomplemented
9C2×C3×GL(2,𝔽3)—21no—
10C3×#131⋊C3—21no—
11C3×#859—21no—
12C3×#821—41nomaximal
13C2×#986C2×C311yescharacteristic
14C2×C3×AGL(1,ℤ/8)—31no—
15C2×C3×#131D311yescharacteristic, complemented
16C2×#131⋊C3—21no—
17C2×#131⋊C3C2×C311yescharacteristic, complemented
18#5426C2×C311yescharacteristic, complemented
19C3×#417—31no—
20C2×C3×#102—31no—
21C2×C3×#100—31no—
22C3×#343—31no—
23C3×#341—31no—
24C2×C3×D12—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3×GL(2,𝔽3)—22no—
29C2×C32×C8—41no—
30C3×C4⋊Dic3—41no—
31#1907—31noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×C3×D4—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C22×C311yescharacteristic
36#986—21no—
37#986C3×C412yescomplemented
38C2×GL(2,𝔽3)—21no—
39C3×AGL(1,ℤ/8)—32no—
40C3×AGL(1,ℤ/8)—32no—
41C3×AGL(1,ℤ/8)—61no—
42C3×AGL(1,ℤ/8)—61no—
43C2×C3×SD16—61no—
44C2×C3×D8—61no—
45C3×#131—21no—
46C3×#131—61no—
47C2×C3×M16—31no—
48C2×C3×M16—31no—
49C2×C3×M16—31no—
50C22×C3×C8—31no—
51C2×C3×C4⋊C4—31no—
52#131⋊C3—22no—
53#131⋊C3—21no—
54#859—21no—
55C3×#103—61no—
56C3×#102—61no—
57C3×#102—61no—
58C3×#102—61no—
59C3×#100—62no—
60#821—41no—
61C22×C3×D3—81no—
62C2×C32×C4—41no—
63C2×C3×Dic3—81no—
64C3×D12—42no—
65C3×D12—81no—
66C3×SL(2,𝔽3)C22⋊C411yescharacteristic
67C32×C8—81no—
68C2×AGL(1,ℤ/8)—31no—
69C2×#131C3×D311yescharacteristic, complemented
70#417—31no—
71C2×#102—31no—
72C2×#100—31no—
73#343—31no—
74#341—31no—
75C24×C3—61no—
76C3×#41—31no—
77C3×#41—31no—
78C3×#41C4×D311yescharacteristic
79C3×#41#6711yescharacteristic
80C2×C3×Q8D1211yescharacteristic
81C2×C3×D4—31no—
82C2×C3×D4—32no—
83C2×C3×D4—61no—
84C2×C3×D4—61no—
85C2×C3×D4—61no—
86C2×C3×D4—61no—
87C2×C3×D4—61no—
88C22×C3×C4—31no—
89C22×C3×C4—61no—
90C2×D12—41no—
91#41⋊C3—21no—
92#41⋊C3—21no—
93#41⋊C3C2×C3×C411yescharacteristic
94#41⋊C3C3×D411yescharacteristic
95C2×SL(2,𝔽3)—21no—
96C2×SL(2,𝔽3)C3×D411yescharacteristic
97GL(2,𝔽3)—22no—
98C3×SD16—62no—
99C3×SD16—62no—
100C3×D8—62no—
101C3×D8—62no—
102C3×M16—32no—
103C3×M16—32no—
104C3×M16—61no—
105C3×M16—61no—
106C3×M16—61no—
107C3×M16—61no—
108C2×C3×C8—31no—
109C2×C3×C8—41no—
110C2×C3×C8—61no—
111C2×C3×C8—61no—
112C2×C3×C8—61no—
113C2×C3×C8—61no—
114C2×C3×C8—81no—
115C2×C3×C8S411yescharacteristic
116C3×C4⋊C4—61no—
117C3×C4⋊C4—61no—
118C4⋊Dic3—41no—
119C22×C32—41no—
120C2×C3×D3—82no—
121C2×C3×D3—161no—
122C2×C3×D3—161no—
123C32×C4—41no—
124C32×C4—41no—
125C3×Dic3—161no—
126C2×#41C2×C3×D311yescharacteristic
127C22×D4—31no—
128AGL(1,ℤ/8)—32no—
129AGL(1,ℤ/8)—32no—
130AGL(1,ℤ/8)—61no—
131AGL(1,ℤ/8)—61no—
132C2×SD16—61no—
133C2×D8—61no—
134#131—21no—
135#131—61no—
136C2×M16—31no—
137C2×M16—31no—
138C2×M16—31no—
139C22×C8—31no—
140C2×C4⋊C4—31no—
141#103—61no—
142#102—61no—
143#102—61no—
144#102—61no—
145#100—62no—
146C23×C3—31no—
147C23×C3—62no—
148C23×C3—121no—
149C23×C3—121no—
150C23×C3—241no—
151C23×C3—241no—
152C22×D3—81no—
153C3×Q8—31no—
154C3×Q8(C2×D3)⋊C411yescharacteristic
155C3×D4—31no—
156C3×D4—31no—
157C3×D4—61no—
158C3×D4—62no—
159C3×D4—62no—
160C3×D4—121no—
161C3×D4—121no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—41no—
168C2×C3×C4—81no—
169C2×C3×C4—121no—
170C2×C3×C4—241no—
171C2×C3×C4C2×S411yescharacteristic
172C2×Dic3—81no—
173D12—42no—
174D12—81no—
175SL(2,𝔽3)—21no—
176SL(2,𝔽3)C3×C22⋊C411yescharacteristic
177C3×C8—21no—
178C3×C8—62no—
179C3×C8—61no—
180C3×C8—81no—
181C3×C8—82no—
182C3×C8—121no—
183C2×C32—41no—
184C2×C32—41no—
185C2×C32—41no—
186C3×D3—162no—
187C24—61no—
188#41—31no—
189#41—31no—
190#41C3×C4×D311yescharacteristic
191#41C3×#6711yescharacteristic
192C2×Q8C3×D1211yescharacteristic
193C2×D4—31no—
194C2×D4—32no—
195C2×D4—61no—
196C2×D4—61no—
197C2×D4—61no—
198C2×D4—61no—
199C2×D4—61no—
200C22×C4—31no—
201C22×C4—61no—
202SD16—62no—
203SD16—62no—
204D8—62no—
205D8—62no—
206M16—32no—
207M16—32no—
208M16—61no—
209M16—61no—
210M16—61no—
211M16—61no—
212C2×C8—31no—
213C2×C8—61no—
214C2×C8—61no—
215C2×C8—61no—
216C2×C8—61no—
217C2×C8C3×S411yescharacteristic
218C4⋊C4—61no—
219C4⋊C4—61no—
220C22×C3—31no—
221C22×C3—31no—
222C22×C3—41no—
223C22×C3—61no—
224C22×C3—61no—
225C22×C3—81no—
226C22×C3—122no—
227C22×C3—242no—
228C22×C3—242no—
229C22×C3—241no—
230C22×C3—241no—
231C22×C3C4⋊S411yescharacteristic
232C2×D3—82no—
233C2×D3—161no—
234C2×D3—161no—
235C3×C4—31no—
236C3×C4—31no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—81no—
240C3×C4—81no—
241C3×C4—241no—
242C3×C4C4×S411yescharacteristic
243C3×C4GL(2,ℤ/4)11yescharacteristic
244Dic3—161no—
245C32—41noSylow
246C23—31no—
247C23—62no—
248C23—121no—
249C23—121no—
250C23—241no—
251C23—241no—
252Q8—31no—
253Q8C3×(C2×D3)⋊C411yescharacteristic
254D4—31no—
255D4—31no—
256D4—61no—
257D4—62no—
258D4—62no—
259D4—121no—
260D4—121no—
261C2×C4—31no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—121no—
267C2×C4—241no—
268C2×C4C2×C3×S411yescharacteristic
269C8—21no—
270C8—62no—
271C8—61no—
272C8—121no—
273C2×C3—41no—
274C2×C3—41no—
275C2×C3—41no—
276C2×C3—61no—
277C2×C3—61no—
278C2×C3—81no—
279C2×C3—81no—
280C2×C3—81no—
281C2×C3—242no—
282C2×C3#540611yescharacteristic
283C2×C3#540711yescharacteristic
284C2×C3(C2×S4)⋊C411yescharacteristic
285D3—162no—
286C22—31no—
287C22—31no—
288C22—61no—
289C22—61no—
290C22—122no—
291C22—242no—
292C22—242no—
293C22—241no—
294C22—241no—
295C22C3×C4⋊S411yescharacteristic
296C4—31no—
297C4—31no—
298C4—241no—
299C4C3×C4×S411yescharacteristic
300C4C3×GL(2,ℤ/4)11yescharacteristic
301C3—41no—
302C3—81no—
303C3#7312811yescharacteristic, direct product factor
304C2—61no—
305C2—61no—
306C2—242no—
307C2C3×#540611yescharacteristic
308C2C3×#540711yescharacteristic
309C2C3×(C2×S4)⋊C411yescharacteristic
subgroupG/H
center, socleC22×C3C4⋊S4
commutator#41⋊C3C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC2×C3×#131D3
prime radicalC2×C3×#986C2
cosocleC2×#41⋊C3C22×C3
hypercenterC2×C3×C8S4
hypocenterSL(2,𝔽3)C3×C22⋊C4
LCSG ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#131⋊C3C2semidirect
3. C3×#5426C2semidirect
4. #73128C3direct (N × H)
8. C3×#986C4semidirect
15. C2×C3×#131D3semidirect
17. C2×#131⋊C3C2×C3semidirect
18. #5426C2×C3semidirect
37. #986C3×C4semidirect
69. C2×#131C3×D3semidirect
303. C3#73128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9862
C2×C3×#131⋊C32
C3×#54262
#731283
C3×#19073
C3×#8214