Finite Group Databasebeta

← C3×#1880 #72595

Subgroups — C3×#1880 #72595

Order 384.

374 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×SD16C211yesmaximal, characteristic
2C2×C3×C4×Q8C211yesmaximal, characteristic, complemented
3C2×C3×#103C211yesmaximal, characteristic, complemented
4C2×C3×#102C211yesmaximal, characteristic
5C3×#390C211yesmaximal, characteristic
6C3×#340C211yesmaximal, characteristic, complemented
7C3×#336C211yesmaximal, characteristic, complemented
8#1880C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×Q8C2211yescharacteristic
10C22×C3×D4C2211yescharacteristic
11C2×C3×SD16—22no—
12C2×C3×SD16—22no—
13C2×C3×SD16C414yescomplemented
14C22×C3×C8C2211yescharacteristic
15C22×C3×C8C2211yescharacteristic
16C3×C4×Q8—22no—
17C3×C4×Q8—22no—
18C2×C3×C4⋊C4—21no—
19C2×C3×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4—21no—
22C2×C3×C22⋊C4—21no—
23C2×C3×C42—21no—
24C2×C3×C42C2211yescharacteristic
25C3×#103—22no—
26C3×#102—22no—
27C22×SD16C2×C311yescharacteristic
28C2×C4×Q8C2×C311yescharacteristic, complemented
29C2×#103C2×C311yescharacteristic, complemented
30C2×#102C2×C311yescharacteristic
31#390C2×C311yescharacteristic
32#340C2×C311yescharacteristic, complemented
33#336C2×C311yescharacteristic, complemented
34C24×C3—21no—
35C2×C3×Q8—21no—
36C2×C3×Q8—21no—
37C2×C3×Q8—21no—
38C2×C3×Q8C2×C412yes—
39C2×C3×Q8D412yes—
40C2×C3×Q8D412yes—
41C2×C3×D4—21no—
42C2×C3×D4—21no—
43C2×C3×D4—21no—
44C2×C3×D4—21no—
45C2×C3×D4—21no—
46C2×C3×D4C2×C412yes—
47C22×C3×C4—21no—
48C22×C3×C4—21no—
49C22×C3×C4—21no—
50C22×C3×C4D411yescharacteristic
51C22×C3×C4D411yescharacteristic
52C22×C3×C4C2311yescharacteristic
53C3×SD16—28no—
54C2×C3×C8—21no—
55C2×C3×C8—21no—
56C2×C3×C8—21no—
57C2×C3×C8—21no—
58C2×C3×C8—21no—
59C2×C3×C8C2×C412yes—
60C3×C4⋊C4—24no—
61C3×C4⋊C4—21no—
62C3×C4⋊C4—21no—
63C3×C4⋊C4—21no—
64C3×C4⋊C4D412yes—
65C3×C22⋊C4—42no—
66C3×C22⋊C4—42no—
67C3×C42—24no—
68C3×C42—21no—
69C3×C42—21no—
70C22×Q8C22×C311yescharacteristic
71C22×D4C22×C311yescharacteristic
72C2×SD16—22no—
73C2×SD16—22no—
74C2×SD16C3×C414yescomplemented
75C22×C8C22×C311yescharacteristic
76C22×C8C22×C311yescharacteristic
77C4×Q8—22no—
78C4×Q8—22no—
79C2×C4⋊C4—21no—
80C2×C4⋊C4C22×C311yescharacteristic
81C2×C4⋊C4C22×C311yescharacteristic
82C2×C22⋊C4—21no—
83C2×C22⋊C4—21no—
84C2×C42—21no—
85C2×C42C22×C311yescharacteristic
86#103—22no—
87#102—22no—
88C23×C3—22no—
89C23×C3—41no—
90C23×C3—41no—
91C23×C3—41no—
92C23×C3—41no—
93C23×C3—41no—
94C23×C3—41no—
95C23×C3C2×D411yescharacteristic
96C3×Q8—22no—
97C3×Q8—22no—
98C3×Q8—22no—
99C3×Q8C22⋊C414yescomplemented
100C3×D4—22no—
101C3×D4—22no—
102C3×D4—41no—
103C3×D4—41no—
104C2×C3×C4—22no—
105C2×C3×C4—21no—
106C2×C3×C4—22no—
107C2×C3×C4—22no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—22no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—41no—
114C2×C3×C4—41no—
115C2×C3×C4—41no—
116C2×C3×C4—41no—
117C2×C3×C4—41no—
118C2×C3×C4SD1612yescomplemented
119C2×C3×C4C22×C411yescharacteristic
120C2×C3×C4C2×D411yescharacteristic
121C2×C3×C4C2×D411yescharacteristic
122C2×C3×C4C2×D411yescharacteristic
123C2×C3×C4#4111yescharacteristic
124C2×C3×C4#4111yescharacteristic
125C3×C8—22no—
126C3×C8—41no—
127C24—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8C2×C3×C412yes—
132C2×Q8C3×D412yes—
133C2×Q8C3×D412yes—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4C2×C3×C412yes—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4C3×D411yescharacteristic
144C22×C4C3×D411yescharacteristic
145C22×C4C23×C311yescharacteristic
146SD16—28no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8C2×C3×C412yes—
153C4⋊C4—24no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4C3×D412yes—
158C22⋊C4—42no—
159C22⋊C4—42no—
160C42—24no—
161C42—21no—
162C42—21no—
163C22×C3—42no—
164C22×C3—42no—
165C22×C3—42no—
166C22×C3—81no—
167C22×C3—81no—
168C22×C3—81no—
169C22×C3—81no—
170C22×C3C4×D411yescharacteristic
171C22×C3#12011yescharacteristic
172C22×C3#12111yescharacteristic
173C22×C3C2×SD1611yescharacteristic
174C22×C3#13511yescharacteristic
175C22×C3AGL(1,ℤ/8)11yescharacteristic
176C22×C3#13711yescharacteristic
177C3×C4—24no—
178C3×C4—22no—
179C3×C4—41no—
180C3×C4—42no—
181C3×C4—81no—
182C3×C4C2×C22⋊C411yescharacteristic
183C3×C4C4×D411yescharacteristic
184C3×C4#12111yescharacteristic
185C3×C4#12311yescharacteristic
186C23—22no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23C2×C3×D411yescharacteristic
194Q8—22no—
195Q8—22no—
196Q8—22no—
197Q8C3×C22⋊C414yescomplemented
198D4—22no—
199D4—22no—
200D4—41no—
201D4—41no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4C3×SD1612yescomplemented
217C2×C4C22×C3×C411yescharacteristic
218C2×C4C2×C3×D411yescharacteristic
219C2×C4C2×C3×D411yescharacteristic
220C2×C4C2×C3×D411yescharacteristic
221C2×C4C3×#4111yescharacteristic
222C2×C4C3×#4111yescharacteristic
223C8—22no—
224C8—41no—
225C2×C3—82no—
226C2×C3#38611yescharacteristic
227C2×C3C4×SD1611yescharacteristic
228C2×C3#44011yescharacteristic
229C2×C3#44811yescharacteristic
230C2×C3#44911yescharacteristic
231C2×C3#46011yescharacteristic
232C2×C3#46411yescharacteristic
233C22—42no—
234C22—42no—
235C22—42no—
236C22—81no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22C3×C4×D411yescharacteristic
241C22C3×#12011yescharacteristic
242C22C3×#12111yescharacteristic
243C22C2×C3×SD1611yescharacteristic
244C22C3×#13511yescharacteristic
245C22C3×AGL(1,ℤ/8)11yescharacteristic
246C22C3×#13711yescharacteristic
247C4—24no—
248C4—22no—
249C4—41no—
250C4—42no—
251C4—81no—
252C4C2×C3×C22⋊C411yescharacteristic
253C4C3×C4×D411yescharacteristic
254C4C3×#12111yescharacteristic
255C4C3×#12311yescharacteristic
256C3#188011yescharacteristic, direct product factor, Sylow
257C2—82no—
258C2C3×#38611yescharacteristic
259C2C3×C4×SD1611yescharacteristic
260C2C3×#44011yescharacteristic
261C2C3×#44811yescharacteristic
262C2C3×#44911yescharacteristic
263C2C3×#46011yescharacteristic
264C2C3×#46411yescharacteristic
subgroupG/H
center, socleC23×C3C2×D4
commutatorC2×C4C22×C3×C4
Frattini, cosocleC22×C4C23×C3
prime radicalC22×C3×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Q8C2semidirect
3. C2×C3×#103C2semidirect
6. C3×#340C2semidirect
7. C3×#336C2semidirect
8. #1880C3direct (N × H)
13. C2×C3×SD16C4semidirect
28. C2×C4×Q8C2×C3semidirect
29. C2×#103C2×C3semidirect
32. #340C2×C3semidirect
33. #336C2×C3semidirect
74. C2×SD16C3×C4semidirect
99. C3×Q8C22⋊C4semidirect
118. C2×C3×C4SD16semidirect
197. Q8C3×C22⋊C4semidirect
216. C2×C4C3×SD16semidirect
256. C3#1880direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×SD162
C2×C3×C4×Q82
C2×C3×#1032
C2×C3×#1022
C3×#3902
C3×#3402
C3×#3362
#18803