Finite Group Databasebeta

← C3×A4×#100 #11919532

Subgroups — C3×A4×#100 #11919532

Order 1152.

576 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 96 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×D4×A4C211yesmaximal, characteristic
2C3×A4×M16C212yesmaximal, complemented
3C22×C3×#100C311yesmaximal, characteristic, complemented
4A4×#100C313yesmaximal, direct product factor
5C23×C3×A4C412yes—
6C3×D4×A4—22no—
7C2×C3×C4×A4C2211yescharacteristic
8C3×C8×A4—22no—
9C32×#100—41nomaximal
10C23×C3×D4C2×C311yescharacteristic
11C2×D4×A4C2×C313yes—
12C22×C3×M16C2×C312yescomplemented
13A4×M16C2×C316yescomplemented
14C2×C3×#100—31no—
15C2×C3×#100—31no—
16C2×C3×#100—32no—
17C22×C3×A4—22no—
18C22×C3×A4—42no—
19C22×C3×A4C2×C411yescharacteristic
20C2×C32×D4—41no—
21C3×C4×A4D412yes—
22C32×M16—42no—
23C22×#100C3211yescharacteristic, complemented, Sylow
24C25×C3C3×C412yes—
25C23×A4C3×C416yes—
26C22×C3×D4—22no—
27C22×C3×D4—31no—
28C22×C3×D4—32no—
29C22×C3×D4—31no—
30C22×C3×D4—62no—
31C23×C3×C4C22×C311yescharacteristic
32D4×A4—26no—
33C2×C4×A4C22×C313yes—
34C2×C3×M16—32no—
35C2×C3×M16—32no—
36C2×C3×M16—62no—
37C22×C3×C8—22no—
38C8×A4—26no—
39C3×#100—32no—
40C3×#100—31no—
41C3×#100—32no—
42C3×#100—43no—
43C3×#100A411yescharacteristic, direct product factor
44C23×C32—42no—
45C2×C3×A4—21no—
46C2×C3×A4—42no—
47C2×C3×A4C22⋊C411yescharacteristic
48C32×D4—82no—
49C2×C32×C4—41no—
50C32×C8—82no—
51C23×D4C2×C3211yescharacteristic
52C22×M16C2×C3212yescomplemented
53C2×#100—31no—
54C2×#100—31no—
55C2×#100—32no—
56C24×C3—22no—
57C24×C3—32no—
58C24×C3—32no—
59C24×C3—42no—
60C24×C3—62no—
61C24×C3—122no—
62C24×C3C2×C3×C411yescharacteristic
63C22×A4—26no—
64C22×A4—46no—
65C22×A4C2×C3×C413yes—
66C2×C3×D4—32no—
67C2×C3×D4—32no—
68C2×C3×D4—31no—
69C2×C3×D4—43no—
70C2×C3×D4—62no—
71C2×C3×D4—62no—
72C2×C3×D4—64no—
73C2×C3×D4—62no—
74C2×C3×D4—64no—
75C2×C3×D4—62no—
76C2×C3×D4C2×A411yescharacteristic
77C22×C3×C4—31no—
78C22×C3×C4—32no—
79C22×C3×C4—31no—
80C22×C3×C4C3×D412yes—
81C4×A4C3×D416yes—
82C3×M16—32no—
83C3×M16—46no—
84C3×M16—62no—
85C3×M16—62no—
86C3×M16C2×A412yescomplemented
87C2×C3×C8—62no—
88C2×C3×C8—62no—
89C22×C32—41no—
90C22×C32—82no—
91C22×C32—162no—
92C3×A4#10011yescharacteristic, direct product factor
93C32×C4—42no—
94C25C32×C412yes—
95C22×D4—22no—
96C22×D4—31no—
97C22×D4—31no—
98C22×D4—32no—
99C22×D4—62no—
100C23×C4C22×C3211yescharacteristic
101C2×M16—32no—
102C2×M16—32no—
103C2×M16—62no—
104C22×C8—22no—
105#100—32no—
106#100—31no—
107#100—32no—
108#100C3×A411yescharacteristic, direct product factor
109C23×C3—21no—
110C23×C3—31no—
111C23×C3—31no—
112C23×C3—32no—
113C23×C3—42no—
114C23×C3—46no—
115C23×C3—62no—
116C23×C3—62no—
117C23×C3—61no—
118C23×C3—62no—
119C23×C3—62no—
120C23×C3—122no—
121C23×C3—122no—
122C23×C3—122no—
123C23×C3—122no—
124C23×C3—122no—
125C23×C3—124no—
126C23×C3—124no—
127C23×C3C3×C22⋊C411yescharacteristic
128C23×C3C4×A412yes—
129C2×A4—23no—
130C2×A4—46no—
131C2×A4C3×C22⋊C413yes—
132C3×D4—22no—
133C3×D4—64no—
134C3×D4—64no—
135C3×D4—62no—
136C3×D4—86no—
137C2×C3×C4—32no—
138C2×C3×C4—31no—
139C2×C3×C4—32no—
140C2×C3×C4—32no—
141C2×C3×C4—32no—
142C2×C3×C4—43no—
143C2×C3×C4C22×A411yescharacteristic
144C3×C8—22no—
145C3×C8—62no—
146C3×C8—86no—
147C2×C32—41no—
148C2×C32—81no—
149C2×C32—162no—
150C24—22no—
151C24—32no—
152C24—32no—
153C24—42no—
154C24—62no—
155C24—122no—
156C24C2×C32×C411yescharacteristic
157C2×D4—32no—
158C2×D4—32no—
159C2×D4—31no—
160C2×D4—62no—
161C2×D4—62no—
162C2×D4—64no—
163C2×D4—62no—
164C2×D4—64no—
165C2×D4—62no—
166C2×D4C2×C3×A411yescharacteristic
167C22×C4—31no—
168C22×C4—32no—
169C22×C4—31no—
170C22×C4C32×D412yes—
171M16—32no—
172M16—62no—
173M16—62no—
174M16C2×C3×A412yescomplemented
175C2×C8—62no—
176C2×C8—62no—
177C22×C3—22no—
178C22×C3—31no—
179C22×C3—31no—
180C22×C3—31no—
181C22×C3—42no—
182C22×C3—43no—
183C22×C3—61no—
184C22×C3—61no—
185C22×C3—61no—
186C22×C3—61no—
187C22×C3—62no—
188C22×C3—86no—
189C22×C3—122no—
190C22×C3—122no—
191C22×C3—122no—
192C22×C3—122no—
193C22×C3—122no—
194C22×C3—124no—
195C22×C3—124no—
196C22×C3—166no—
197C22×C3C3×#10011yescharacteristic, complemented
198C22×C3C2×C4×A411yescharacteristic
199A4C3×#10013yesdirect product factor
200C3×C4—32no—
201C3×C4—46no—
202C3×C4D4×A412yes—
203C32—41noSylow
204C23—21no—
205C23—31no—
206C23—31no—
207C23—32no—
208C23—42no—
209C23—62no—
210C23—62no—
211C23—61no—
212C23—62no—
213C23—62no—
214C23—122no—
215C23—122no—
216C23—122no—
217C23—122no—
218C23—122no—
219C23—124no—
220C23—124no—
221C23C32×C22⋊C411yescharacteristic
222C23C3×C4×A412yes—
223D4—22no—
224D4—64no—
225D4—64no—
226D4—62no—
227C2×C4—32no—
228C2×C4—31no—
229C2×C4—32no—
230C2×C4—32no—
231C2×C4—32no—
232C2×C4C22×C3×A411yescharacteristic
233C8—22no—
234C8—62no—
235C2×C3—21no—
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—42no—
239C2×C3—43no—
240C2×C3—61no—
241C2×C3—83no—
242C2×C3—122no—
243C2×C3—166no—
244C2×C3A4×C22⋊C411yescharacteristic
245C22—22no—
246C22—31no—
247C22—31no—
248C22—31no—
249C22—42no—
250C22—61no—
251C22—61no—
252C22—61no—
253C22—61no—
254C22—62no—
255C22—122no—
256C22—122no—
257C22—122no—
258C22—122no—
259C22—122no—
260C22—124no—
261C22—124no—
262C22C32×#10011yescharacteristic, complemented
263C22C2×C3×C4×A411yescharacteristic
264C4—32no—
265C4C3×D4×A412yes—
266C3—43no—
267C3A4×#10011yescharacteristic, direct product factor
268C2—21no—
269C2—31no—
270C2—31no—
271C2—42no—
272C2—61no—
273C2—122no—
274C2C3×A4×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C3A4×C22⋊C4
commutatorC24C2×C32×C4
FrattiniC2×C4C22×C3×A4
FittingC22×C3×#100C3
socleC23×C3C3×C22⋊C4
prime radicalC2×C3×D4×A4C2
cosocleC23×C4C22×C32
hypercenterC3×#100A4
hypocenterC22C32×#100
LCSG ▷ C24 ▷ C23 ▷ C22
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#100

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. C22×C3×#100C3semidirect
4. A4×#100C3direct (N × H)
12. C22×C3×M16C2×C3semidirect
13. A4×M16C2×C3semidirect
23. C22×#100C32semidirect
43. C3×#100A4direct (N × H)
52. C22×M16C2×C32semidirect
86. C3×M16C2×A4semidirect
92. C3×A4#100direct (N × H)
108. #100C3×A4direct (N × H)
174. M16C2×C3×A4semidirect
197. C22×C3C3×#100semidirect
199. A4C3×#100direct (N × H)
262. C22C32×#100semidirect
267. C3A4×#100direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C3×A4×M162
C22×C3×#1003
A4×#1003
C32×#1004