Finite Group Databasebeta

← C3×#67773 #11772782

Subgroups — C3×#67773 #11772782

Order 1152.

283 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 283 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×#456C211yesmaximal, characteristic
2C3×#4548C211yesmaximal, characteristic, complemented
3C3×#4546C211yesmaximal, characteristic, complemented
4C3×#1405—31nomaximal
5#67773C311yesmaximal, characteristic, direct product factor
6C32×2−1+4C411yescharacteristic
7C32×#137—21no—
8C32×C4⋊Q8C2211yescharacteristic
9C32×#104—21no—
10C32×#101C411yescharacteristic
11C3×#836—21no—
12C3×C4⋊(C3⋊C8)—21no—
13C3×#456—21no—
14C3×#456D311yescharacteristic
15C3×#456C2×C311yescharacteristic
16C3×#356—31no—
17C3×#333—31no—
18#4548C2×C311yescharacteristic, complemented
19#4546C2×C311yescharacteristic, complemented
20C32×#41—21no—
21C32×#41—41no—
22C32×#41—41no—
23C2×C32×Q8—41no—
24C2×C32×Q8C2×C411yescharacteristic
25C2×C32×Q8D411yescharacteristic
26C32×Q16—41no—
27C32×SD16—41no—
28C32×M16—21no—
29C32×C4⋊C4—41no—
30C32×C42D411yescharacteristic
31C3×#208—41no—
32C2×C3×C3⋊C8—41no—
33#1405—31noSylow
34C3×2−1+4—21no—
35C3×2−1+4Dic311yescharacteristic
36C3×2−1+4C3×C411yescharacteristic
37C3×#137—22no—
38C3×#137—21no—
39C3×#137—21no—
40C3×C4⋊Q8—21no—
41C3×C4⋊Q8C2×D311yescharacteristic
42C3×C4⋊Q8C22×C311yescharacteristic
43C3×C4⋊C8—61no—
44C3×#104—22no—
45C3×#104—21no—
46C3×#104—21no—
47C3×#101—21no—
48C3×#101—61no—
49C3×#101Dic311yescharacteristic
50C3×#101C3×C411yescharacteristic
51#836—21no—
52C4⋊(C3⋊C8)—21no—
53C32×Q8—21no—
54C32×Q8—41no—
55C32×Q8—41no—
56C32×Q8—41no—
57C32×D4—21no—
58C32×D4—41no—
59C32×D4—41no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—41no—
64C2×C32×C4—42no—
65C2×C32×C4C22⋊C411yescharacteristic
66C32×C8—41no—
67C3×C3⋊C8—81no—
68C3×C3⋊C8—81no—
69#456C3×D311yescharacteristic
70#356—31no—
71#333—31no—
72C3×#41—22no—
73C3×#41—21no—
74C3×#41—21no—
75C3×#41—42no—
76C3×#41—41no—
77C3×#41—41no—
78C3×#41—42no—
79C3×#41—41no—
80C3×#41—41no—
81C2×C3×Q8—21no—
82C2×C3×Q8—21no—
83C2×C3×Q8—41no—
84C2×C3×Q8—41no—
85C2×C3×Q8—42no—
86C2×C3×Q8C2×Dic311yescharacteristic
87C2×C3×Q8#6711yescharacteristic
88C2×C3×Q8C2×C3×C411yescharacteristic
89C2×C3×Q8C3×D411yescharacteristic
90C3×Q16—41no—
91C3×Q16—41no—
92C3×Q16—42no—
93C3×SD16—41no—
94C3×SD16—41no—
95C3×SD16—42no—
96C3×M16—22no—
97C3×M16—21no—
98C3×M16—21no—
99C3×M16—121no—
100C2×C3×C8—121no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—41no—
103C3×C4⋊C4—42no—
104C3×C42—21no—
105C3×C42#6711yescharacteristic
106C3×C42C3×D411yescharacteristic
107#208—41no—
108C2×C3⋊C8—41no—
109C22×C32—41no—
110C22×C32#9911yescharacteristic
111C32×C4—21no—
112C32×C4—21no—
113C32×C4—21no—
114C32×C4—41no—
115C32×C4—41no—
116C32×C4—41no—
1172−1+4C3×Dic311yescharacteristic
118#137—21no—
119C4⋊Q8C2×C3×D311yescharacteristic
120C4⋊C8—61no—
121#104—21no—
122#101—61no—
123#101C3×Dic311yescharacteristic
124C3×Q8—22no—
125C3×Q8—21no—
126C3×Q8—21no—
127C3×Q8—41no—
128C3×Q8—41no—
129C3×Q8—41no—
130C3×Q8—41no—
131C3×Q8—42no—
132C3×Q8—42no—
133C3×Q8—41no—
134C3×Q8—41no—
135C3×Q8—42no—
136C3×D4—22no—
137C3×D4—21no—
138C3×D4—21no—
139C3×D4—42no—
140C3×D4—41no—
141C3×D4—41no—
142C3×D4—42no—
143C3×D4—41no—
144C3×D4—41no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—22no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—41no—
154C2×C3×C4—41no—
155C2×C3×C4—42no—
156C2×C3×C4—41no—
157C2×C3×C4—41no—
158C2×C3×C4—44no—
159C2×C3×C4—42no—
160C2×C3×C4—42no—
161C2×C3×C4#21711yescharacteristic
162C2×C3×C4C3×C22⋊C411yescharacteristic
163C3×C8—42no—
164C3×C8—41no—
165C3×C8—41no—
166C3×C8—241no—
167C3×C8—241no—
168C3⋊C8—81no—
169C3⋊C8—81no—
170C2×C32—21no—
171C2×C32—81no—
172C2×C32AΣL(1,𝔽16)11yescharacteristic
173#41—21no—
174#41—41no—
175#41—41no—
176C2×Q8—41no—
177C2×Q8C2×C3×Dic311yescharacteristic
178C2×Q8C3×#6711yescharacteristic
179Q16—41no—
180SD16—41no—
181M16—21no—
182M16—121no—
183C2×C8—121no—
184C4⋊C4—41no—
185C42C3×#6711yescharacteristic
186C22×C3—21no—
187C22×C3—42no—
188C22×C3—41no—
189C22×C3—41no—
190C22×C3#83411yescharacteristic
191C22×C3C3×#9911yescharacteristic
192C3×C4—21no—
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—41no—
200C3×C4—41no—
201C3×C4—42no—
202C3×C4—42no—
203C3×C4—41no—
204C3×C4—41no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—41no—
208C3×C4—41no—
209C3×C4—81no—
210C32#140511yescharacteristic, complemented, Sylow
211Q8—21no—
212Q8—41no—
213Q8—41no—
214Q8—41no—
215D4—21no—
216D4—41no—
217D4—41no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4C3×#21711yescharacteristic
224C8—41no—
225C8—241no—
226C8—241no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—41no—
231C2×C3—82no—
232C2×C3—81no—
233C2×C3—81no—
234C2×C3#453611yescharacteristic
235C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
236C22—41no—
237C22C3×#83411yescharacteristic
238C4—21no—
239C4—21no—
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C3—21no—
245C3#6777311yescharacteristic, direct product factor
246C3C3×#140511yescharacteristic, complemented
247C2—21no—
248C2—81no—
249C2C3×#453611yescharacteristic
subgroupG/H
centerC2×C3#4536
commutatorC2×C3×Q8C2×C3×C4
FrattiniC4⋊Q8C2×C3×D3
FittingC32×#456C2
socleC2×C32AΣL(1,𝔽16)
prime radicalC32×2−1+4C4
cosocleC3×C4⋊Q8C22×C3
hypercenterC3×#456D3
hypocenterC3C3×#1405
LCSG ▷ C2×C3×Q8 ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊Q8 ◁ C3×#456

Complements

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

NH ≅ G/Ntype
2. C3×#4548C2semidirect
3. C3×#4546C2semidirect
5. #67773C3direct (N × H)
18. #4548C2×C3semidirect
19. #4546C2×C3semidirect
210. C32#1405semidirect
245. C3#67773direct (N × H)
246. C3C3×#1405semidirect

Maximal subgroups

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

subgroupindex
C32×#4562
C3×#45482
C3×#45462
C3×#14053
#677733