Finite Group Databasebeta

← C3×#1879 #72594

Subgroups — C3×#1879 #72594

Order 384.

438 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D8C211yesmaximal, characteristic
2C2×C3×C4×D4C211yesmaximal, characteristic, complemented
3C2×C3×#102C211yesmaximal, characteristic, complemented
4C2×C3×#102C211yesmaximal, characteristic, complemented
5C3×#390C211yesmaximal, characteristic, complemented
6C3×#340C211yesmaximal, characteristic, complemented
7C3×#336C211yesmaximal, characteristic, complemented
8#1879C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×D4C2211yescharacteristic
10C22×C3×D4C2211yescharacteristic
11C23×C3×C4—21no—
12C2×C3×D8—22no—
13C2×C3×D8—22no—
14C2×C3×D8C414yescomplemented
15C22×C3×C8C2211yescharacteristic
16C22×C3×C8C2211yescharacteristic
17C3×C4×D4—22no—
18C3×C4×D4—22no—
19C2×C3×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C22⋊C4—21no—
22C2×C3×C22⋊C4—21no—
23C2×C3×C22⋊C4—21no—
24C2×C3×C42C2211yescharacteristic
25C3×#102—22no—
26C3×#102—22no—
27C22×D8C2×C311yescharacteristic
28C2×C4×D4C2×C311yescharacteristic, complemented
29C2×#102C2×C311yescharacteristic, complemented
30C2×#102C2×C311yescharacteristic, complemented
31#390C2×C311yescharacteristic, complemented
32#340C2×C311yescharacteristic, complemented
33#336C2×C311yescharacteristic, complemented
34C24×C3—21no—
35C24×C3—21no—
36C2×C3×D4—21no—
37C2×C3×D4—21no—
38C2×C3×D4—21no—
39C2×C3×D4—21no—
40C2×C3×D4—21no—
41C2×C3×D4—21no—
42C2×C3×D4—21no—
43C2×C3×D4—21no—
44C2×C3×D4C2×C412yes—
45C2×C3×D4C2×C412yescomplemented
46C2×C3×D4D412yes—
47C2×C3×D4D412yes—
48C22×C3×C4—24no—
49C22×C3×C4—21no—
50C22×C3×C4—21no—
51C22×C3×C4—42no—
52C22×C3×C4—42no—
53C22×C3×C4D411yescharacteristic
54C22×C3×C4D411yescharacteristic
55C22×C3×C4C2311yescharacteristic
56C3×D8—28no—
57C2×C3×C8—21no—
58C2×C3×C8—21no—
59C2×C3×C8—21no—
60C2×C3×C8—21no—
61C2×C3×C8—21no—
62C2×C3×C8C2×C412yescomplemented
63C3×C4⋊C4—21no—
64C3×C4⋊C4—21no—
65C3×C4⋊C4—21no—
66C3×C4⋊C4D412yes—
67C3×C22⋊C4—24no—
68C3×C22⋊C4—42no—
69C3×C22⋊C4—42no—
70C3×C42—21no—
71C3×C42—21no—
72C22×D4C22×C311yescharacteristic
73C22×D4C22×C311yescharacteristic
74C23×C4—21no—
75C2×D8—22no—
76C2×D8—22no—
77C2×D8C3×C414yescomplemented
78C22×C8C22×C311yescharacteristic
79C22×C8C22×C311yescharacteristic
80C4×D4—22no—
81C4×D4—22no—
82C2×C4⋊C4C22×C311yescharacteristic
83C2×C4⋊C4C22×C311yescharacteristic
84C2×C22⋊C4—21no—
85C2×C22⋊C4—21no—
86C2×C22⋊C4—21no—
87C2×C42C22×C311yescharacteristic
88#102—22no—
89#102—22no—
90C23×C3—22no—
91C23×C3—22no—
92C23×C3—22no—
93C23×C3—22no—
94C23×C3—41no—
95C23×C3—41no—
96C23×C3—41no—
97C23×C3—41no—
98C23×C3—41no—
99C23×C3—41no—
100C23×C3—41no—
101C23×C3—41no—
102C23×C3—41no—
103C23×C3—41no—
104C23×C3C2×D411yescharacteristic
105C3×D4—22no—
106C3×D4—22no—
107C3×D4—22no—
108C3×D4—22no—
109C3×D4—22no—
110C3×D4—41no—
111C3×D4—41no—
112C3×D4C22⋊C414yescomplemented
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—22no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—48no—
120C2×C3×C4—41no—
121C2×C3×C4—41no—
122C2×C3×C4—41no—
123C2×C3×C4—41no—
124C2×C3×C4—41no—
125C2×C3×C4D812yescomplemented
126C2×C3×C4C22×C411yescharacteristic
127C2×C3×C4C2×D411yescharacteristic
128C2×C3×C4C2×D411yescharacteristic
129C2×C3×C4C2×D411yescharacteristic
130C2×C3×C4#4111yescharacteristic
131C2×C3×C4#4111yescharacteristic
132C3×C8—22no—
133C3×C8—41no—
134C24—21no—
135C24—21no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4C2×C3×C412yes—
145C2×D4C2×C3×C412yescomplemented
146C2×D4C3×D412yes—
147C2×D4C3×D412yes—
148C22×C4—24no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4C3×D411yescharacteristic
154C22×C4C3×D411yescharacteristic
155C22×C4C23×C311yescharacteristic
156D8—28no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8C2×C3×C412yescomplemented
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4C3×D412yes—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42—21no—
171C42—21no—
172C22×C3—24no—
173C22×C3—42no—
174C22×C3—42no—
175C22×C3—42no—
176C22×C3—42no—
177C22×C3—42no—
178C22×C3—42no—
179C22×C3—42no—
180C22×C3—42no—
181C22×C3—42no—
182C22×C3—81no—
183C22×C3—81no—
184C22×C3—81no—
185C22×C3—81no—
186C22×C3C4×D411yescharacteristic
187C22×C3#12011yescharacteristic
188C22×C3#12111yescharacteristic
189C22×C3C2×D811yescharacteristic
190C22×C3#13511yescharacteristic
191C22×C3AGL(1,ℤ/8)11yescharacteristic
192C22×C3AGL(1,ℤ/8)11yescharacteristic
193C3×C4—22no—
194C3×C4—42no—
195C3×C4—41no—
196C3×C4—81no—
197C3×C4C2×C22⋊C411yescharacteristic
198C3×C4C4×D411yescharacteristic
199C3×C4#12111yescharacteristic
200C3×C4#12311yescharacteristic
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—41no—
206C23—41no—
207C23—41no—
208C23—41no—
209C23—41no—
210C23—41no—
211C23—41no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23C2×C3×D411yescharacteristic
216D4—22no—
217D4—22no—
218D4—22no—
219D4—22no—
220D4—22no—
221D4—41no—
222D4—41no—
223D4C3×C22⋊C414yescomplemented
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—48no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4C3×D812yescomplemented
237C2×C4C22×C3×C411yescharacteristic
238C2×C4C2×C3×D411yescharacteristic
239C2×C4C2×C3×D411yescharacteristic
240C2×C4C2×C3×D411yescharacteristic
241C2×C4C3×#4111yescharacteristic
242C2×C4C3×#4111yescharacteristic
243C8—22no—
244C8—41no—
245C2×C3—44no—
246C2×C3—82no—
247C2×C3#38611yescharacteristic
248C2×C3C4×D811yescharacteristic
249C2×C3#44211yescharacteristic
250C2×C3#44711yescharacteristic
251C2×C3#44911yescharacteristic
252C2×C3#45911yescharacteristic
253C2×C3#46311yescharacteristic
254C22—24no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22C3×C4×D411yescharacteristic
269C22C3×#12011yescharacteristic
270C22C3×#12111yescharacteristic
271C22C2×C3×D811yescharacteristic
272C22C3×#13511yescharacteristic
273C22C3×AGL(1,ℤ/8)11yescharacteristic
274C22C3×AGL(1,ℤ/8)11yescharacteristic
275C4—22no—
276C4—42no—
277C4—41no—
278C4—81no—
279C4C2×C3×C22⋊C411yescharacteristic
280C4C3×C4×D411yescharacteristic
281C4C3×#12111yescharacteristic
282C4C3×#12311yescharacteristic
283C3#187911yescharacteristic, direct product factor, Sylow
284C2—44no—
285C2—82no—
286C2C3×#38611yescharacteristic
287C2C3×C4×D811yescharacteristic
288C2C3×#44211yescharacteristic
289C2C3×#44711yescharacteristic
290C2C3×#44911yescharacteristic
291C2C3×#45911yescharacteristic
292C2C3×#46311yescharacteristic
subgroupG/H
center, socleC23×C3C2×D4
commutatorC2×C4C22×C3×C4
Frattini, cosocleC22×C4C23×C3
prime radicalC22×C3×D8C2
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×D4C2semidirect
3. C2×C3×#102C2semidirect
4. C2×C3×#102C2semidirect
5. C3×#390C2semidirect
6. C3×#340C2semidirect
7. C3×#336C2semidirect
8. #1879C3direct (N × H)
14. C2×C3×D8C4semidirect
28. C2×C4×D4C2×C3semidirect
29. C2×#102C2×C3semidirect
30. C2×#102C2×C3semidirect
31. #390C2×C3semidirect
32. #340C2×C3semidirect
33. #336C2×C3semidirect
45. C2×C3×D4C2×C4semidirect
62. C2×C3×C8C2×C4semidirect
77. C2×D8C3×C4semidirect
112. C3×D4C22⋊C4semidirect
125. C2×C3×C4D8semidirect
145. C2×D4C2×C3×C4semidirect
162. C2×C8C2×C3×C4semidirect
223. D4C3×C22⋊C4semidirect
236. C2×C4C3×D8semidirect
283. C3#1879direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D82
C2×C3×C4×D42
C2×C3×#1022
C3×#3902
C3×#3402
C3×#3362
#18793