Finite Group Databasebeta

← C3×#72985 #11920763

Subgroups — C3×#72985 #11920763

Order 1152.

286 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 26 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×#95⋊C3C211yesmaximal, characteristic, complemented
2C3×#4622C211yesmaximal, characteristic, complemented
3C3×#4621C211yesmaximal, characteristic, complemented
4#72985C311yesmaximal, characteristic, direct product factor
5C3×#1504—31nomaximal
6C3×GL(2,ℤ/4)—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8C3×#525—31no—
9C3×#407—31no—
10C2×C3×#95D311yescharacteristic, complemented
11C2×#95⋊C3—21no—
12C2×#95⋊C3C2×C311yescharacteristic, complemented
13#4622C2×C311yescharacteristic, complemented
14#4621C2×C311yescharacteristic, complemented
15C3×#328—31no—
16C3×#328—31no—
17C3×#327—31no—
18C3×#327—31no—
19C22×C3×A4—41no—
20C2×C3×S4—41no—
21C3×SL(2,ℤ/4)—41no—
22#1504—31noSylow
23C2×C3×#41—31no—
24C23×C3×C4—31no—
25GL(2,ℤ/4)—41no—
26C2×C3×M16—61no—
27C3×#123—61no—
28C3×C22⋊Q8—31no—
29C3×C22⋊Q8—31no—
30C3×#121—31no—
31C3×#121—31no—
32C3×#120—61no—
33C3×C4×D4—61no—
34C3×C4×D4—61no—
35C3×#117—31no—
36C3×C22⋊C8—31no—
37C3×C22⋊C8—31no—
38C3×C22⋊C8—61no—
39C3×#95—31no—
40C3×#95C2×D311yescharacteristic
41#95⋊C3—21no—
42#95⋊C3C22×C311yescharacteristic
43C2×C3×A4—41no—
44C2×C3×A4—81no—
45C3×S4—81no—
46C3×#67—161no—
47#525—31no—
48#407—31no—
49C2×#95C3×D311yescharacteristic, complemented
50#328—31no—
51#328—31no—
52#327—31no—
53#327—31no—
54C24×C3S411yescharacteristic
55C22×A4—41no—
56C22×A4—81no—
57C2×S4—41no—
58C3×#41—122no—
59C2×C3×Q8—31no—
60C2×C3×D4—31no—
61C2×C3×D4—61no—
62C2×C3×D4—61no—
63C2×C3×D4—61no—
64C22×C3×C4—31no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—31no—
70C22×C3×C4—61no—
71C22×C3×C4—122no—
72SL(2,ℤ/4)—41no—
73C3×M16—122no—
74C2×C3×C8—61no—
75C2×C3×C8—61no—
76C3×C4⋊C4—31no—
77C3×C4⋊C4—31no—
78C3×C4⋊C4—61no—
79C3×C4⋊C4—61no—
80C3×C22⋊C4—61no—
81C3×C22⋊C4—61no—
82C3×C22⋊C4—61no—
83C3×C22⋊C4—61no—
84C3×C22⋊C4—61no—
85C3×C42—61no—
86C22×C32—161no—
87C2×C3×D3—161no—
88C3×A4—41no—
89C3×Dic3—161no—
90C2×#41—31no—
91C23×C4—31no—
92C2×M16—61no—
93#123—61no—
94C22⋊Q8—31no—
95C22⋊Q8—31no—
96#121—31no—
97#121—31no—
98#120—61no—
99C4×D4—61no—
100C4×D4—61no—
101#117—31no—
102C22⋊C8—31no—
103C22⋊C8—31no—
104C22⋊C8—61no—
105#95—31no—
106#95C2×C3×D311yescharacteristic
107C23×C3—21no—
108C23×C3—31no—
109C23×C3—31no—
110C23×C3—61no—
111C23×C3—61no—
112C23×C3C2×S411yescharacteristic
113C2×A4—41no—
114C2×A4—81no—
115C2×A4—82no—
116C2×A4—81no—
117S4—81no—
118C3×Q8—121no—
119C3×D4—121no—
120C3×D4—121no—
121C3×D4—121no—
122C3×D4—122no—
123C3×D4—121no—
124C3×D4—121no—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—62no—
130C2×C3×C4—62no—
131C2×C3×C4—61no—
132C2×C3×C4—61no—
133C2×C3×C4—61no—
134C2×C3×C4—121no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×C3×C4—121no—
138C2×C3×C4—122no—
139#67—161no—
140C3×C8—121no—
141C3×C8—121no—
142C2×C32—161no—
143C2×C32—321no—
144C3×D3—321no—
145C24C3×S411yescharacteristic
146#41—122no—
147C2×Q8—31no—
148C2×D4—31no—
149C2×D4—61no—
150C2×D4—61no—
151C2×D4—61no—
152C22×C4—31no—
153C22×C4—31no—
154C22×C4—31no—
155C22×C4—31no—
156C22×C4—31no—
157C22×C4—31no—
158C22×C4—61no—
159C22×C4—122no—
160M16—122no—
161C2×C8—61no—
162C2×C8—61no—
163C4⋊C4—31no—
164C4⋊C4—31no—
165C4⋊C4—61no—
166C4⋊C4—61no—
167C22⋊C4—61no—
168C22⋊C4—61no—
169C22⋊C4—61no—
170C22⋊C4—61no—
171C22⋊C4—61no—
172C42—61no—
173C22×C3—31no—
174C22×C3—31no—
175C22×C3—32no—
176C22×C3—31no—
177C22×C3—61no—
178C22×C3—61no—
179C22×C3—61no—
180C22×C3—121no—
181C22×C3—121no—
182C22×C3—121no—
183C22×C3—161no—
184C22×C3—321no—
185C22×C3#85711yescharacteristic
186C22×C3#98311yescharacteristic
187C2×D3—161no—
188A4—41no—
189A4—81no—
190C3×C4—61no—
191C3×C4—61no—
192C3×C4—61no—
193C3×C4—61no—
194C3×C4—121no—
195C3×C4—121no—
196C3×C4—121no—
197Dic3—161no—
198C32—161noSylow
199C23—21no—
200C23—31no—
201C23—31no—
202C23—61no—
203C23—61no—
204C23C2×C3×S411yescharacteristic
205Q8—121no—
206D4—121no—
207D4—122no—
208D4—121no—
209D4—121no—
210D4—121no—
211D4—121no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—62no—
217C2×C4—62no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—121no—
222C2×C4—121no—
223C2×C4—121no—
224C2×C4—121no—
225C2×C4—122no—
226C8—121no—
227C8—121no—
228C2×C3—21no—
229C2×C3—31no—
230C2×C3—31no—
231C2×C3—61no—
232C2×C3—161no—
233C2×C3—241no—
234C2×C3—321no—
235C2×C3—322no—
236C2×C3—321no—
237C2×C3C2×#85711yescharacteristic
238D3—321no—
239C22—31no—
240C22—31no—
241C22—32no—
242C22—31no—
243C22—61no—
244C22—61no—
245C22—61no—
246C22—121no—
247C22—121no—
248C22—121no—
249C22C3×#85711yescharacteristic
250C22C3×#98311yescharacteristic
251C4—61no—
252C4—61no—
253C4—61no—
254C4—61no—
255C4—121no—
256C4—121no—
257C4—121no—
258C3—161no—
259C3—321no—
260C3#7298511yescharacteristic, direct product factor
261C2—21no—
262C2—31no—
263C2—31no—
264C2—61no—
265C2—241no—
266C2C2×C3×#85711yescharacteristic
subgroupG/H
centerC2×C3C2×#857
commutator, cosocle, hypocenter#95⋊C3C22×C3
FrattiniC23C2×C3×S4
FittingC2×C3×#95D3
socleC23×C3C2×S4
hypercenterC22×C3#857
LCSG ▷ #95⋊C3
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#95⋊C3C2semidirect
2. C3×#4622C2semidirect
3. C3×#4621C2semidirect
4. #72985C3direct (N × H)
10. C2×C3×#95D3semidirect
12. C2×#95⋊C3C2×C3semidirect
13. #4622C2×C3semidirect
14. #4621C2×C3semidirect
49. C2×#95C3×D3semidirect
260. C3#72985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#95⋊C32
C3×#46222
C3×#46212
#729853
C3×#15043
C3×GL(2,ℤ/4)4