Finite Group Databasebeta

← C3×#85511 #11922794

Subgroups — C3×#85511 #11922794

Order 1152.

668 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 124 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×A4×#41C211yesmaximal, characteristic
2C3×#5409C213yesmaximal, complemented
3C2×C3×A4⋊C8C213yesmaximal, complemented
4#85511C311yesmaximal, characteristic, direct product factor
5C3×#2880—31nomaximal
6C3×Q8×A4C411yescharacteristic
7C3×D4×A4C413yes—
8C2×C3×C4×A4C2213yes—
9C3×#948—41nomaximal
10C3×A4⋊C8C2211yescharacteristic
11C3×A4⋊C8C2213yes—
12C22×C3×#41D311yescharacteristic
13A4×#41—21no—
14A4×#41C2×C311yescharacteristic
15C2×C3×#131—31no—
16C2×C3×#131—31no—
17#5409C2×C313yescomplemented
18C2×A4⋊C8C2×C313yescomplemented
19C3×#408—33no—
20C3×#408—33no—
21C3×#407—33no—
22C2×C3×C22⋊C8—33no—
23C22×C3×A4C2×C413yes—
24C32×#41—41no—
25C3×C4×A4C2×C413yes—
26C3×C4×A4C2311yescharacteristic
27C3×#208—43no—
28C2×C3×C3⋊C8—43no—
29#2880—31noSylow
30C2×C3×#41—31no—
31C2×C3×#41—33no—
32C2×C3×#41—31no—
33C2×C3×#41—33no—
34C22×C3×Q8Dic311yescharacteristic
35C22×C3×D4Dic313yes—
36C23×C3×C4C2×D313yes—
37Q8×A4—21no—
38Q8×A4C3×C411yescharacteristic
39D4×A4—23no—
40D4×A4C3×C413yes—
41C2×C4×A4—23no—
42C2×C4×A4C22×C313yes—
43C3×#131—61no—
44C3×#131—63no—
45C3×#131—63no—
46C3×#131—61no—
47C2×C3×M16—33no—
48C2×C3×M16—33no—
49C22×C3×C8—33no—
50C22×C3×C8—33no—
51#948—41no—
52A4⋊C8C22×C311yescharacteristic
53A4⋊C8C22×C313yes—
54C3×C22⋊C8—33no—
55C3×C22⋊C8—33no—
56C3×C22⋊C8—36no—
57C3×C22⋊C8—31no—
58C3×C22⋊C8—33no—
59C2×C3×A4—23no—
60C2×C3×A4C22×C411yescharacteristic
61C32×Q8—41no—
62C32×D4—43no—
63C2×C32×C4—43no—
64C3×C3⋊C8—41no—
65C3×C3⋊C8—43no—
66C22×#41C3×D311yescharacteristic
67C2×#131—31no—
68C2×#131—31no—
69#408—33no—
70#408—33no—
71#407—33no—
72C2×C22⋊C8—33no—
73C24×C3C2×Dic313yes—
74C22×A4—23no—
75C22×A4C2×C3×C413yes—
76C3×#41—31no—
77C3×#41—33no—
78C3×#41—33no—
79C3×#41—41no—
80C3×#41—61no—
81C3×#41—63no—
82C3×#41—63no—
83C3×#41—81no—
84C3×#41S411yescharacteristic
85C2×C3×Q8—31no—
86C2×C3×Q8—33no—
87C2×C3×D4—33no—
88C2×C3×D4—33no—
89C2×C3×D4—36no—
90C22×C3×C4—33no—
91C22×C3×C4—33no—
92C22×C3×C4—33no—
93C22×C3×C4—33no—
94C22×C3×C4C2×Dic313yes—
95C22×C3×C4C22×D311yescharacteristic
96C4×A4—23no—
97C4×A4—21no—
98C4×A4C2×C3×C413yes—
99C4×A4C23×C311yescharacteristic
100C3×M16—63no—
101C3×M16—63no—
102C3×M16—63no—
103C3×M16—63no—
104C2×C3×C8—31no—
105C2×C3×C8—31no—
106C2×C3×C8—33no—
107C2×C3×C8—33no—
108C2×C3×C8—63no—
109C2×C3×C8—63no—
110C2×C3×C8—63no—
111C2×C3×C8—63no—
112#208—43no—
113C2×C3⋊C8—43no—
114C22×C32—43no—
115C3×A4#13111yescharacteristic, complemented
116C32×C4—43no—
117C32×C4—41no—
118C2×#41—31no—
119C2×#41—33no—
120C2×#41—33no—
121C2×#41—31no—
122C22×Q8C3×Dic311yescharacteristic
123C22×D4C3×Dic313yes—
124C23×C4C2×C3×D313yes—
125#131—61no—
126#131—63no—
127#131—63no—
128#131—61no—
129C2×M16—33no—
130C2×M16—33no—
131C22×C8—33no—
132C22×C8—33no—
133C22⋊C8—33no—
134C22⋊C8—33no—
135C22⋊C8—36no—
136C22⋊C8—31no—
137C22⋊C8—33no—
138C23×C3—23no—
139C23×C3—33no—
140C23×C3—33no—
141C23×C3—63no—
142C23×C3C22×Dic311yescharacteristic
143C2×A4—23no—
144C2×A4—21no—
145C2×A4—43no—
146C2×A4C22×C3×C411yescharacteristic
147C3×Q8—33no—
148C3×Q8—41no—
149C3×Q8—61no—
150C3×Q8—81no—
151C3×Q8SL(2,ℤ/4)11yescharacteristic
152C3×D4—36no—
153C3×D4—33no—
154C3×D4—43no—
155C3×D4—63no—
156C3×D4—83no—
157C3×D4SL(2,ℤ/4)13yes—
158C2×C3×C4—33no—
159C2×C3×C4—33no—
160C2×C3×C4—33no—
161C2×C3×C4—31no—
162C2×C3×C4—33no—
163C2×C3×C4—31no—
164C2×C3×C4—33no—
165C2×C3×C4—43no—
166C2×C3×C4—63no—
167C2×C3×C4—83no—
168C2×C3×C4C2×S413yes—
169C3×C8—61no—
170C3×C8—63no—
171C3×C8—61no—
172C3×C8—63no—
173C3⋊C8—41no—
174C3⋊C8—43no—
175C2×C32—41no—
176C2×C32—83no—
177C24C2×C3×Dic313yes—
178#41—31no—
179#41—33no—
180#41—33no—
181#41—61no—
182#41—63no—
183#41—63no—
184#41C3×S411yescharacteristic
185C2×Q8—31no—
186C2×Q8—33no—
187C2×D4—33no—
188C2×D4—33no—
189C2×D4—36no—
190C22×C4—33no—
191C22×C4—33no—
192C22×C4—33no—
193C22×C4—33no—
194C22×C4C2×C3×Dic313yes—
195C22×C4C22×C3×D311yescharacteristic
196M16—63no—
197M16—63no—
198M16—63no—
199M16—63no—
200C2×C8—31no—
201C2×C8—31no—
202C2×C8—33no—
203C2×C8—33no—
204C2×C8—63no—
205C2×C8—63no—
206C2×C8—63no—
207C2×C8—63no—
208C22×C3—31no—
209C22×C3—31no—
210C22×C3—33no—
211C22×C3—43no—
212C22×C3—63no—
213C22×C3—63no—
214C22×C3—63no—
215C22×C3—63no—
216C22×C3—83no—
217C22×C3#94811yescharacteristic, complemented
218C22×C3C2×SL(2,ℤ/4)13yes—
219A4—21no—
220A4C3×#13111yescharacteristic, complemented
221C3×C4—31no—
222C3×C4—33no—
223C3×C4—43no—
224C3×C4—41no—
225C3×C4—83no—
226C3×C4—81no—
227C3×C4C2×SL(2,ℤ/4)13yes—
228C3×C4C22×S411yescharacteristic
229C32—41noSylow
230C23—23no—
231C23—33no—
232C23—33no—
233C23—63no—
234C23C22×C3×Dic311yescharacteristic
235Q8—33no—
236Q8—61no—
237Q8C3×SL(2,ℤ/4)11yescharacteristic
238D4—36no—
239D4—33no—
240D4—63no—
241D4C3×SL(2,ℤ/4)13yes—
242C2×C4—33no—
243C2×C4—33no—
244C2×C4—33no—
245C2×C4—31no—
246C2×C4—33no—
247C2×C4—31no—
248C2×C4—33no—
249C2×C4—63no—
250C2×C4C2×C3×S413yes—
251C8—61no—
252C8—63no—
253C8—61no—
254C8—63no—
255C2×C3—23no—
256C2×C3—31no—
257C2×C3—31no—
258C2×C3—41no—
259C2×C3—63no—
260C2×C3—83no—
261C2×C3—81no—
262C2×C3—163no—
263C2×C3C22×SL(2,ℤ/4)11yescharacteristic
264C22—31no—
265C22—31no—
266C22—33no—
267C22—63no—
268C22—63no—
269C22—63no—
270C22—63no—
271C22C3×#94811yescharacteristic, complemented
272C22C2×C3×SL(2,ℤ/4)13yes—
273C4—31no—
274C4—33no—
275C4C2×C3×SL(2,ℤ/4)13yes—
276C4C22×C3×S411yescharacteristic
277C3—41no—
278C3—81no—
279C3#8551111yescharacteristic, direct product factor
280C2—23no—
281C2—31no—
282C2—31no—
283C2—63no—
284C2C22×C3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC3×C4C22×S4
commutatorC2×A4C22×C3×C4
FrattiniC4C22×C3×S4
FittingC22×C3×#41D3
socleC23×C3C22×Dic3
prime radicalC3×A4×#41C2
cosocleC4×A4C23×C3
hypercenterC3×#41S4
hypocenterA4C3×#131
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5409C2semidirect
3. C2×C3×A4⋊C8C2semidirect
4. #85511C3direct (N × H)
17. #5409C2×C3semidirect
18. C2×A4⋊C8C2×C3semidirect
115. C3×A4#131semidirect
217. C22×C3#948semidirect
220. A4C3×#131semidirect
271. C22C3×#948semidirect
279. C3#85511direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×#412
C3×#54092
C2×C3×A4⋊C82
#855113
C3×#28803
C3×#9484