Finite Group Databasebeta

← C3×#68391 #11779301

Subgroups — C3×#68391 #11779301

Order 1152.

670 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 114 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×#5717C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic, complemented
3C3×#4842C212yesmaximal, complemented
4C32×#331C211yesmaximal, characteristic, complemented
5C3×#4483C212yesmaximal, complemented
6C3×#1629—31nomaximal
7#68391C311yesmaximal, characteristic, direct product factor
8C2×C3×D3×D4—22no—
9C32×#127C2211yescharacteristic
10C3×#938—22no—
11C3×#937—22no—
12C2×C3×#214—22no—
13C3×C4×D12C2212yes—
14C3×#869C2211yescharacteristic, complemented
15C32×C4⋊C8C2212yescomplemented
16C3×#821—22no—
17C3×#817—22no—
18C3×C4×C3⋊C8C2211yescharacteristic, complemented
19C3×D42—31no—
20#5717C2×C311yescharacteristic
21C3×#492—31no—
22C3×#476—32no—
23#5076C2×C311yescharacteristic, complemented
24#4842C2×C312yescomplemented
25C3×#331—21no—
26C3×#331D311yescharacteristic, complemented
27C3×#331C2×C311yescharacteristic, complemented
28C3×D4⋊C8—32no—
29#4483C2×C312yescomplemented
30C23×C3×D3—22no—
31C2×C32×D4—22no—
32C2×C32×D4D412yes—
33C2×C3×#67—24no—
34C3×D3×D4—44no—
35C3×D3×D4—44no—
36C2×C3×D12D412yes—
37C2×C3×C4×D3—22no—
38C2×C3×Dic6—21no—
39C2×C32×C8—22no—
40C32×C42C2311yescharacteristic
41C3×#217—22no—
42C3×#214—44no—
43C3×(C2×D3)⋊C4—22no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3D412yes—
46C2×C3×C3⋊C8—21no—
47#1629—31noSylow
48C22×C3×D4—62no—
49C2×D3×D4—22no—
50C2×C3×SD16—62no—
51C3×C4⋊Q8—31no—
52C3×#127—21no—
53C3×#127C2×D311yescharacteristic
54C3×#127C22×C311yescharacteristic
55C3×#121—62no—
56C3×#120—62no—
57C3×C4×D4—32no—
58#938—22no—
59#937—22no—
60C2×#214—22no—
61C4×D12C22×C312yes—
62#869C22×C311yescharacteristic, complemented
63C3×#106—62no—
64C3×C4⋊C8—22no—
65C3×C4⋊C8C2×D312yescomplemented
66C3×C4⋊C8C22×C312yescomplemented
67C3×#102—62no—
68C3×C4×C8—31no—
69#821—22no—
70#817—22no—
71C4×C3⋊C8C22×C311yescharacteristic, complemented
72C23×C32—22no—
73C22×C3×D3—22no—
74C22×C3×D3—48no—
75C22×C3×D3—82no—
76C32×D4—42no—
77C32×D4—42no—
78C32×D4—42no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D412yes—
81C3×#67—48no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—41no—
84C3×D12—22no—
85C3×D12SD1614yescomplemented
86C3×C4×D3—42no—
87C3×C4×D3—42no—
88C3×Dic6—42no—
89C32×C8—42no—
90C3×C3⋊C8—22no—
91D42—31no—
92#492—31no—
93#476—32no—
94#331C3×D311yescharacteristic, complemented
95D4⋊C8—32no—
96C24×C3—62no—
97C23×D3—22no—
98C2×C3×Q8—61no—
99C2×C3×D4—22no—
100C2×C3×D4—22no—
101C2×C3×D4—22no—
102C2×C3×D4—32no—
103C2×C3×D4—42no—
104C2×C3×D4—64no—
105C2×C3×D4—124no—
106C2×C3×D4—124no—
107C2×C3×D4D1212yes—
108C2×C3×D4C3×D412yes—
109C22×C3×C4—62no—
110C2×#67—24no—
111D3×D4—44no—
112D3×D4—44no—
113C2×D12C3×D412yes—
114C2×C4×D3—22no—
115C2×Dic6—21no—
116C3×SD16—124no—
117C2×C3×C8—22no—
118C2×C3×C8—22no—
119C2×C3×C8—42no—
120C2×C3×C8—61no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—62no—
123C3×C22⋊C4—62no—
124C3×C22⋊C4—62no—
125C3×C42—21no—
126C3×C42C22×D311yescharacteristic
127C3×C42C23×C311yescharacteristic
128#217—22no—
129#214—44no—
130(C2×D3)⋊C4—22no—
131C4⋊Dic3—22no—
132C4⋊Dic3C3×D412yes—
133C2×C3⋊C8—21no—
134C22×C32—44no—
135C22×C32—42no—
136C22×C32#12011yescharacteristic
137C2×C3×D3—24no—
138C2×C3×D3—42no—
139C2×C3×D3—42no—
140C2×C3×D3—88no—
141C32×C4—21no—
142C32×C4C2×SD1612yes—
143C32×C4AGL(1,ℤ/8)12yes—
144C3×Dic3—42no—
145C3×Dic3—81no—
146C22×D4—62no—
147C2×SD16—62no—
148C4⋊Q8—31no—
149#127C2×C3×D311yescharacteristic
150#121—62no—
151#120—62no—
152C4×D4—32no—
153#106—62no—
154C4⋊C8C2×C3×D312yescomplemented
155#102—62no—
156C4×C8—31no—
157C23×C3—22no—
158C23×C3—22no—
159C23×C3—42no—
160C23×C3—62no—
161C23×C3—128no—
162C23×C3—242no—
163C22×D3—22no—
164C22×D3—48no—
165C22×D3—82no—
166C3×Q8—122no—
167C3×D4—34no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—42no—
171C3×D4—42no—
172C3×D4—42no—
173C3×D4—42no—
174C3×D4—62no—
175C3×D4—82no—
176C3×D4—82no—
177C3×D4—82no—
178C3×D4—128no—
179C2×C3×C4—21no—
180C2×C3×C4—22no—
181C2×C3×C4—62no—
182C2×C3×C4—122no—
183C2×C3×C4—122no—
184C2×C3×C4—121no—
185C2×C3×C4C2×D1211yescharacteristic
186C2×C3×C4D3×D412yes—
187C2×C3×C4C2×C3×D411yescharacteristic
188C2×C3×C4C2×C3×D412yes—
189#67—48no—
190C2×Dic3—22no—
191C2×Dic3—41no—
192D12—22no—
193D12C3×SD1614yescomplemented
194C4×D3—42no—
195C4×D3—42no—
196Dic6—42no—
197C3×C8—42no—
198C3×C8—42no—
199C3×C8—62no—
200C3×C8—82no—
201C3⋊C8—22no—
202C2×C32—82no—
203C2×C32#45012yes—
204C2×C32#45311yescharacteristic
205C3×D3—44no—
206C24—62no—
207C2×Q8—61no—
208C2×D4—22no—
209C2×D4—32no—
210C2×D4—64no—
211C2×D4—124no—
212C2×D4—124no—
213C2×D4C3×D1212yes—
214C22×C4—62no—
215SD16—124no—
216C2×C8—22no—
217C2×C8—61no—
218C4⋊C4—32no—
219C4⋊C4—62no—
220C22⋊C4—62no—
221C22⋊C4—62no—
222C42C22×C3×D311yescharacteristic
223C22×C3—21no—
224C22×C3—42no—
225C22×C3—44no—
226C22×C3—44no—
227C22×C3—42no—
228C22×C3—64no—
229C22×C3—84no—
230C22×C3—82no—
231C22×C3—122no—
232C22×C3—122no—
233C22×C3—248no—
234C22×C3#88211yescharacteristic
235C22×C3C3×#12011yescharacteristic
236C2×D3—24no—
237C2×D3—42no—
238C2×D3—42no—
239C2×D3—88no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—41no—
245C3×C4—122no—
246C3×C4—241no—
247C3×C4#91112yes—
248C3×C4D3×SD1612yes—
249C3×C4C2×C3×SD1612yes—
250C3×C4C3×AGL(1,ℤ/8)12yes—
251Dic3—42no—
252Dic3—81no—
253C32#162911yescharacteristic, complemented, Sylow
254C23—22no—
255C23—62no—
256C23—128no—
257C23—242no—
258Q8—122no—
259D4—34no—
260D4—42no—
261D4—42no—
262D4—42no—
263D4—62no—
264D4—128no—
265C2×C4—62no—
266C2×C4—122no—
267C2×C4—122no—
268C2×C4—121no—
269C2×C4C2×C3×D1211yescharacteristic
270C2×C4C3×D3×D412yes—
271C8—42no—
272C8—62no—
273C2×C3—21no—
274C2×C3—22no—
275C2×C3—82no—
276C2×C3—82no—
277C2×C3—124no—
278C2×C3—162no—
279C2×C3#474711yescharacteristic
280C2×C3#477612yes—
281C2×C3C3×#45012yes—
282C2×C3C3×#45311yescharacteristic
283D3—44no—
284C22—42no—
285C22—44no—
286C22—64no—
287C22—122no—
288C22—122no—
289C22—248no—
290C22C3×#88211yescharacteristic
291C4—21no—
292C4—122no—
293C4—241no—
294C4C3×#91112yes—
295C4C3×D3×SD1612yes—
296C3—21no—
297C3#6839111yescharacteristic, direct product factor
298C3C3×#162911yescharacteristic, complemented
299C2—82no—
300C2—124no—
301C2C3×#474711yescharacteristic
302C2C3×#477612yes—
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#120
prime radicalC3×#5717C2
hypercenterC3×#331D3
hypocenterC3C3×#1629
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
2. C3×#5076C2semidirect
3. C3×#4842C2semidirect
4. C32×#331C2semidirect
5. C3×#4483C2semidirect
7. #68391C3direct (N × H)
14. C3×#869C22semidirect
15. C32×C4⋊C8C22semidirect
18. C3×C4×C3⋊C8C22semidirect
23. #5076C2×C3semidirect
24. #4842C2×C3semidirect
26. C3×#331D3semidirect
27. C3×#331C2×C3semidirect
29. #4483C2×C3semidirect
62. #869C22×C3semidirect
65. C3×C4⋊C8C2×D3semidirect
66. C3×C4⋊C8C22×C3semidirect
71. C4×C3⋊C8C22×C3semidirect
85. C3×D12SD16semidirect
94. #331C3×D3semidirect
154. C4⋊C8C2×C3×D3semidirect
193. D12C3×SD16semidirect
253. C32#1629semidirect
297. C3#68391direct (N × H)
298. C3C3×#1629semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
C3×#50762
C3×#48422
C32×#3312
C3×#44832
C3×#16293
#683913