Finite Group Databasebeta

← C3×#2898⋊C3 #11919546

Subgroups — C3×#2898⋊C3 #11919546

Order 1152.

466 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 94 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×C3×2−1+4⋊C3C211yesmaximal, characteristic
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3C3×#520⋊C3C211yesmaximal, characteristic, complemented
4C3×#2898C311yesmaximal, characteristic, complemented
5#2898⋊C3C313yesmaximal, direct product factor
6C3×2−1+4⋊C3—21no—
7C3×2−1+4⋊C3C412yescomplemented
8C2×C3×#41⋊C3C2211yescharacteristic
9C22×C3×SL(2,𝔽3)—21no—
10C3×#131⋊C3—21no—
11C3×C4×SL(2,𝔽3)—21no—
12C32×#102—41nomaximal
13C2×C3×2−1+4C2×C311yescharacteristic
14C2×2−1+4⋊C3C2×C313yes—
15C2×C3×#131C2×C311yescharacteristic, complemented
16C3×#520C2×C311yescharacteristic, complemented
17C2×#131⋊C3C2×C313yescomplemented
18#520⋊C3C2×C313yescomplemented
19C3×#419—31no—
20C3×#417—31no—
21C3×#416—31no—
22C2×C3×#103—31no—
23C2×C32×D4—41no—
24C3×#41⋊C3C2×C411yescharacteristic
25C3×#41⋊C3D411yescharacteristic
26C2×C3×SL(2,𝔽3)—22no—
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C2×C32×C8—41no—
29C32×C4⋊C4—41no—
30#2898C3211yescharacteristic, complemented, Sylow
31C3×2−1+4—21no—
32C3×2−1+4—32no—
33C3×2−1+4—61no—
34C3×2−1+4C3×C412yescomplemented
35C2×C3×#41—31no—
36C2×C3×#41—61no—
37C2×C3×#41C22×C311yescharacteristic
38C22×C3×Q8—21no—
39C22×C3×Q8—31no—
402−1+4⋊C3—23no—
412−1+4⋊C3C3×C416yescomplemented
42C2×#41⋊C3C22×C313yes—
43C22×SL(2,𝔽3)—23no—
44C3×#131—21no—
45C3×#131—61no—
46C2×C3×M16—31no—
47C22×C3×C8—31no—
48C3×C4×Q8—21no—
49C3×C4×D4—61no—
50C3×#117—31no—
51C2×C3×C4⋊C4—31no—
52#131⋊C3—23no—
53C4×SL(2,𝔽3)—23no—
54C3×#103—32no—
55C3×#103—31no—
56C3×#103—31no—
57C3×#102—31no—
58C3×#102—43no—
59C3×#102A411yescharacteristic
60C23×C32—81no—
61C32×D4—42no—
62C32×D4—81no—
63C2×C32×C4—41no—
64C2×C32×C4—81no—
65C3×SL(2,𝔽3)C22⋊C411yescharacteristic
66C32×C8—81no—
67C2×2−1+4C2×C3211yescharacteristic
68C2×#131C2×C3211yescharacteristic, complemented
69#520C2×C3211yescharacteristic, complemented
70#419—31no—
71#417—31no—
72#416—31no—
73C2×#103—31no—
74C3×#41—31no—
75C3×#41—31no—
76C3×#41—32no—
77C3×#41—32no—
78C3×#41—61no—
79C3×#41—61no—
80C3×#41—64no—
81C3×#41—62no—
82C3×#41—62no—
83C3×#41C2×C3×C411yescharacteristic
84C3×#41C3×D411yescharacteristic
85C2×C3×Q8—22no—
86C2×C3×Q8—32no—
87C2×C3×Q8—32no—
88C2×C3×Q8—31no—
89C2×C3×Q8—61no—
90C2×C3×Q8—61no—
91C2×C3×Q8—61no—
92C2×C3×Q8—62no—
93C2×C3×Q8C3×D411yescharacteristic
94C2×C3×D4—31no—
95C2×C3×D4—43no—
96C2×C3×D4—61no—
97C2×C3×D4C2×A411yescharacteristic
98C22×C3×C4—31no—
99C22×C3×C4—61no—
100C22×C3×C4—61no—
101C22×C3×C4—61no—
102#41⋊C3C2×C3×C413yes—
103#41⋊C3C3×D413yes—
104C2×SL(2,𝔽3)—26no—
105C2×SL(2,𝔽3)C3×D413yes—
106C3×M16—61no—
107C3×M16—61no—
108C2×C3×C8—31no—
109C2×C3×C8—43no—
110C2×C3×C8—61no—
111C2×C3×C8—61no—
112C2×C3×C8C2×A411yescharacteristic
113C3×C4⋊C4—31no—
114C3×C4⋊C4—43no—
115C3×C4⋊C4—61no—
116C3×C4⋊C4C2×A411yescharacteristic
117C3×C22⋊C4—61no—
118C3×C42—61no—
119C22×C32—41no—
120C22×C32—82no—
121C22×C32—161no—
122C22×C32—161no—
123C32×C4—41no—
124C32×C4—41no—
125C32×C4—161no—
1262−1+4—21no—
1272−1+4—32no—
1282−1+4—61no—
1292−1+4C32×C412yescomplemented
130C2×#41—31no—
131C2×#41—61no—
132C2×#41C22×C3211yescharacteristic
133C22×Q8—21no—
134C22×Q8—31no—
135#131—21no—
136#131—61no—
137C2×M16—31no—
138C22×C8—31no—
139C4×Q8—21no—
140C4×D4—61no—
141#117—31no—
142C2×C4⋊C4—31no—
143#103—32no—
144#103—31no—
145#103—31no—
146#102—31no—
147#102C3×A411yescharacteristic
148C23×C3—21no—
149C23×C3—31no—
150C23×C3—83no—
151C3×Q8—31no—
152C3×Q8—32no—
153C3×Q8—62no—
154C3×Q8—62no—
155C3×Q8—61no—
156C3×Q8C3×C22⋊C411yescharacteristic
157C3×D4—21no—
158C3×D4—31no—
159C3×D4—31no—
160C3×D4—32no—
161C3×D4—46no—
162C3×D4—62no—
163C3×D4—62no—
164C3×D4—83no—
165C3×D4C4×A412yes—
166C2×C3×C4—21no—
167C2×C3×C4—31no—
168C2×C3×C4—31no—
169C2×C3×C4—31no—
170C2×C3×C4—31no—
171C2×C3×C4—31no—
172C2×C3×C4—43no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4—62no—
176C2×C3×C4—61no—
177C2×C3×C4—62no—
178C2×C3×C4—61no—
179C2×C3×C4—83no—
180C2×C3×C4—241no—
181C2×C3×C4C22×A411yescharacteristic
182SL(2,𝔽3)C3×C22⋊C413yes—
183C3×C8—21no—
184C3×C8—61no—
185C3×C8—83no—
186C2×C32—41no—
187C2×C32—41no—
188C2×C32—41no—
189C2×C32—162no—
190#41—31no—
191#41—31no—
192#41—32no—
193#41—32no—
194#41—61no—
195#41—61no—
196#41—64no—
197#41—62no—
198#41—62no—
199#41C2×C32×C411yescharacteristic
200#41C32×D411yescharacteristic
201C2×Q8—22no—
202C2×Q8—32no—
203C2×Q8—32no—
204C2×Q8—31no—
205C2×Q8—61no—
206C2×Q8—61no—
207C2×Q8—61no—
208C2×Q8—62no—
209C2×Q8C32×D411yescharacteristic
210C2×D4—31no—
211C2×D4—61no—
212C2×D4C2×C3×A411yescharacteristic
213C22×C4—31no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217M16—61no—
218M16—61no—
219C2×C8—31no—
220C2×C8—61no—
221C2×C8—61no—
222C2×C8C2×C3×A411yescharacteristic
223C4⋊C4—31no—
224C4⋊C4—61no—
225C4⋊C4C2×C3×A411yescharacteristic
226C22⋊C4—61no—
227C42—61no—
228C22×C3—22no—
229C22×C3—31no—
230C22×C3—31no—
231C22×C3—41no—
232C22×C3—41no—
233C22×C3—43no—
234C22×C3—61no—
235C22×C3—61no—
236C22×C3—86no—
237C22×C3—163no—
238C22×C3—163no—
239C22×C3D4×A411yescharacteristic
240C3×C4—31no—
241C3×C4—31no—
242C3×C4—41no—
243C3×C4—43no—
244C3×C4—43no—
245C3×C4—62no—
246C3×C4—121no—
247C3×C4—163no—
248C3×C4C2×C4×A411yescharacteristic
249C3×C4D4×A411yescharacteristic
250C32—41noSylow
251C23—21no—
252C23—31no—
253Q8—31no—
254Q8—32no—
255Q8—62no—
256Q8—62no—
257Q8—61no—
258Q8C32×C22⋊C411yescharacteristic
259D4—21no—
260D4—31no—
261D4—31no—
262D4—32no—
263D4—62no—
264D4—62no—
265D4C3×C4×A412yes—
266C2×C4—21no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—62no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—61no—
276C2×C4—62no—
277C2×C4—61no—
278C2×C4—241no—
279C2×C4C22×C3×A411yescharacteristic
280C8—21no—
281C8—61no—
282C2×C3—42no—
283C2×C3—43no—
284C2×C3—43no—
285C2×C3—43no—
286C2×C3—61no—
287C2×C3—61no—
288C2×C3—166no—
289C2×C3A4×C22⋊C411yescharacteristic
290C2×C3#577⋊C311yescharacteristic
291C2×C3#578⋊C311yescharacteristic
292C22—22no—
293C22—31no—
294C22—31no—
295C22—41no—
296C22—41no—
297C22—61no—
298C22—61no—
299C22C3×D4×A411yescharacteristic
300C4—31no—
301C4—31no—
302C4—41no—
303C4—62no—
304C4—121no—
305C4C2×C3×C4×A411yescharacteristic
306C4C3×D4×A411yescharacteristic
307C3—43no—
308C3#2898⋊C311yescharacteristic, direct product factor
309C2—42no—
310C2—61no—
311C2—61no—
312C2C3×A4×C22⋊C411yescharacteristic
313C2C3×#577⋊C311yescharacteristic
314C2C3×#578⋊C311yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutator#41C2×C32×C4
FrattiniC2×C4C22×C3×A4
FittingC3×#2898C3
prime radicalC2×C3×2−1+4⋊C3C2
cosocleC2×#41C22×C32
hypercenterC3×#102A4
hypocenterQ8C32×C22⋊C4
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#131⋊C3C2semidirect
3. C3×#520⋊C3C2semidirect
4. C3×#2898C3semidirect
5. #2898⋊C3C3direct (N × H)
7. C3×2−1+4⋊C3C4semidirect
15. C2×C3×#131C2×C3semidirect
16. C3×#520C2×C3semidirect
17. C2×#131⋊C3C2×C3semidirect
18. #520⋊C3C2×C3semidirect
30. #2898C32semidirect
34. C3×2−1+4C3×C4semidirect
41. 2−1+4⋊C3C3×C4semidirect
68. C2×#131C2×C32semidirect
69. #520C2×C32semidirect
129. 2−1+4C32×C4semidirect
308. C3#2898⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×2−1+4⋊C32
C2×C3×#131⋊C32
C3×#520⋊C32
C3×#28983
#2898⋊C33
C32×#1024