Finite Group Databasebeta

← C3×A4×C4⋊C8 #11919552

Subgroups — C3×A4×C4⋊C8 #11919552

Order 1152.

416 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 128 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×C8×A4C212yesmaximal
2C3×C42×A4C211yesmaximal, characteristic
3C22×C3×C4⋊C8C311yesmaximal, characteristic, complemented
4A4×C4⋊C8C313yesmaximal, direct product factor
5C2×C3×C4×A4C411yescharacteristic
6C2×C3×C4×A4C411yescharacteristic
7C2×C3×C4×A4C2211yescharacteristic
8C3×C8×A4—22no—
9C32×C4⋊C8—41nomaximal
10C23×C3×C8C2×C312yes—
11C22×C3×C42C2×C311yescharacteristic
12C2×C8×A4C2×C316yes—
13C42×A4C2×C313yes—
14C2×C3×C4⋊C8—31no—
15C2×C3×C4⋊C8—32no—
16C2×C3×C4⋊C8—31no—
17C22×C3×A4C2×C411yescharacteristic
18C3×C4×A4—21no—
19C3×C4×A4C812yescomplemented
20C3×C4×A4D411yescharacteristic
21C3×C4×A4Q811yescharacteristic
22C2×C32×C8—42no—
23C32×C42—41no—
24C22×C4⋊C8C3211yescharacteristic, complemented, Sylow
25C23×C3×C4C3×C411yescharacteristic
26C23×C3×C4C3×C411yescharacteristic
27C23×C3×C4C22×C311yescharacteristic
28C2×C4×A4C3×C413yes—
29C2×C4×A4C3×C413yes—
30C2×C4×A4C22×C313yes—
31C22×C3×C8—22no—
32C22×C3×C8—32no—
33C22×C3×C8—32no—
34C22×C3×C8—62no—
35C2×C3×C42—31no—
36C2×C3×C42—31no—
37C2×C3×C42—31no—
38C2×C3×C42—31no—
39C8×A4—26no—
40C3×C4⋊C8—32no—
41C3×C4⋊C8—32no—
42C3×C4⋊C8—31no—
43C3×C4⋊C8—43no—
44C3×C4⋊C8A411yescharacteristic, direct product factor
45C2×C3×A4C4⋊C411yescharacteristic
46C2×C3×A4C2×C811yescharacteristic
47C2×C3×A4M1611yescharacteristic
48C2×C32×C4—41no—
49C2×C32×C4—41no—
50C2×C32×C4—41no—
51C32×C8—82no—
52C23×C8C2×C3212yes—
53C22×C42C2×C3211yescharacteristic
54C2×C4⋊C8—31no—
55C2×C4⋊C8—32no—
56C2×C4⋊C8—31no—
57C24×C3C2×C3×C411yescharacteristic
58C22×A4C2×C3×C413yes—
59C22×C3×C4—21no—
60C22×C3×C4—31no—
61C22×C3×C4—31no—
62C22×C3×C4—31no—
63C22×C3×C4—31no—
64C22×C3×C4—31no—
65C22×C3×C4—32no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—61no—
70C22×C3×C4C3×C812yescomplemented
71C22×C3×C4C3×D411yescharacteristic
72C22×C3×C4C3×Q811yescharacteristic
73C4×A4—23no—
74C4×A4C3×C816yescomplemented
75C4×A4C3×D413yes—
76C4×A4C3×Q813yes—
77C2×C3×C8—32no—
78C2×C3×C8—46no—
79C2×C3×C8—62no—
80C2×C3×C8—62no—
81C2×C3×C8—62no—
82C2×C3×C8—62no—
83C2×C3×C8C2×A412yes—
84C3×C42—32no—
85C3×C42—31no—
86C3×C42—31no—
87C3×C42—31no—
88C3×C42—43no—
89C3×C42C2×A411yescharacteristic
90C22×C32—41no—
91C3×A4C4⋊C811yescharacteristic, direct product factor
92C32×C4—42no—
93C32×C4—41no—
94C32×C4—41no—
95C32×C4—81no—
96C23×C4C32×C411yescharacteristic
97C23×C4C32×C411yescharacteristic
98C23×C4C22×C3211yescharacteristic
99C22×C8—22no—
100C22×C8—32no—
101C22×C8—32no—
102C22×C8—62no—
103C2×C42—31no—
104C2×C42—31no—
105C2×C42—31no—
106C2×C42—31no—
107C4⋊C8—32no—
108C4⋊C8—32no—
109C4⋊C8—31no—
110C4⋊C8C3×A411yescharacteristic, direct product factor
111C23×C3—31no—
112C23×C3—31no—
113C23×C3—31no—
114C23×C3—31no—
115C23×C3C3×C4⋊C411yescharacteristic
116C23×C3C2×C3×C811yescharacteristic
117C23×C3C3×M1611yescharacteristic
118C2×A4C3×C4⋊C413yes—
119C2×A4C2×C3×C813yes—
120C2×A4C3×M1613yes—
121C2×C3×C4—32no—
122C2×C3×C4—32no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—32no—
126C2×C3×C4—32no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—31no—
131C2×C3×C4—32no—
132C2×C3×C4—31no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—43no—
136C2×C3×C4—43no—
137C2×C3×C4—43no—
138C2×C3×C4—61no—
139C2×C3×C4—61no—
140C2×C3×C4—61no—
141C2×C3×C4—61no—
142C2×C3×C4C4×A411yescharacteristic
143C2×C3×C4C4×A411yescharacteristic
144C2×C3×C4C22×A411yescharacteristic
145C3×C8—22no—
146C3×C8—62no—
147C3×C8—86no—
148C2×C32—41no—
149C2×C32—41no—
150C2×C32—41no—
151C24C2×C32×C411yescharacteristic
152C22×C4—21no—
153C22×C4—31no—
154C22×C4—31no—
155C22×C4—31no—
156C22×C4—31no—
157C22×C4—31no—
158C22×C4—32no—
159C22×C4—31no—
160C22×C4—31no—
161C22×C4—31no—
162C22×C4—61no—
163C22×C4C32×C812yescomplemented
164C22×C4C32×D411yescharacteristic
165C22×C4C32×Q811yescharacteristic
166C2×C8—32no—
167C2×C8—62no—
168C2×C8—62no—
169C2×C8—62no—
170C2×C8—62no—
171C2×C8C2×C3×A412yes—
172C42—32no—
173C42—31no—
174C42—31no—
175C42—31no—
176C42C2×C3×A411yescharacteristic
177C22×C3—31no—
178C22×C3—31no—
179C22×C3—31no—
180C22×C3—32no—
181C22×C3—31no—
182C22×C3—31no—
183C22×C3—31no—
184C22×C3—31no—
185C22×C3—31no—
186C22×C3—31no—
187C22×C3—43no—
188C22×C3C3×C4⋊C811yescharacteristic, complemented
189C22×C3C2×C4×A411yescharacteristic
190A4C3×C4⋊C813yesdirect product factor
191C3×C4—21no—
192C3×C4—31no—
193C3×C4—31no—
194C3×C4—32no—
195C3×C4—43no—
196C3×C4—43no—
197C3×C4—46no—
198C3×C4—61no—
199C3×C4—83no—
200C3×C4C8×A412yescomplemented
201C3×C4D4×A411yescharacteristic
202C3×C4Q8×A411yescharacteristic
203C32—41noSylow
204C23—31no—
205C23—31no—
206C23—31no—
207C23—31no—
208C23C32×C4⋊C411yescharacteristic
209C23C2×C32×C811yescharacteristic
210C23C32×M1611yescharacteristic
211C2×C4—32no—
212C2×C4—32no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—31no—
218C2×C4—31no—
219C2×C4—32no—
220C2×C4—32no—
221C2×C4—32no—
222C2×C4—31no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—61no—
226C2×C4—61no—
227C2×C4—61no—
228C2×C4—61no—
229C2×C4C3×C4×A411yescharacteristic
230C2×C4C3×C4×A411yescharacteristic
231C2×C4C22×C3×A411yescharacteristic
232C8—22no—
233C8—62no—
234C2×C3—31no—
235C2×C3—31no—
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—43no—
239C2×C3—43no—
240C2×C3—43no—
241C2×C3A4×C4⋊C411yescharacteristic
242C2×C3C2×C8×A411yescharacteristic
243C2×C3A4×M1611yescharacteristic
244C22—31no—
245C22—31no—
246C22—31no—
247C22—32no—
248C22—31no—
249C22—31no—
250C22—31no—
251C22—31no—
252C22—31no—
253C22—31no—
254C22C32×C4⋊C811yescharacteristic, complemented
255C22C2×C3×C4×A411yescharacteristic
256C4—21no—
257C4—31no—
258C4—31no—
259C4—32no—
260C4—61no—
261C4C3×C8×A412yescomplemented
262C4C3×D4×A411yescharacteristic
263C4C3×Q8×A411yescharacteristic
264C3—43no—
265C3A4×C4⋊C811yescharacteristic, direct product factor
266C2—31no—
267C2—31no—
268C2—31no—
269C2—31no—
270C2C3×A4×C4⋊C411yescharacteristic
271C2C2×C3×C8×A411yescharacteristic
272C2C3×A4×M1611yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutatorC23C2×C32×C8
FrattiniC2×C4C22×C3×A4
FittingC22×C3×C4⋊C8C3
socleC24×C3C2×C3×C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C4C22×C32
hypercenterC3×C4⋊C8A4
hypocenterC22C32×C4⋊C8
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3×C4 ◁ C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. C22×C3×C4⋊C8C3semidirect
4. A4×C4⋊C8C3direct (N × H)
19. C3×C4×A4C8semidirect
24. C22×C4⋊C8C32semidirect
44. C3×C4⋊C8A4direct (N × H)
70. C22×C3×C4C3×C8semidirect
74. C4×A4C3×C8semidirect
91. C3×A4C4⋊C8direct (N × H)
110. C4⋊C8C3×A4direct (N × H)
163. C22×C4C32×C8semidirect
188. C22×C3C3×C4⋊C8semidirect
190. A4C3×C4⋊C8direct (N × H)
200. C3×C4C8×A4semidirect
254. C22C32×C4⋊C8semidirect
261. C4C3×C8×A4semidirect
265. C3A4×C4⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C3×C42×A42
C22×C3×C4⋊C83
A4×C4⋊C83
C32×C4⋊C84