Finite Group Databasebeta

← #11921006

Subgroups — #11921006

Order 1152.

382 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C3×A4×C4⋊C4C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic
4#73050—33nomaximal
5#71555—31nomaximal
6C2×C3×C4×A4—21no—
7C2×C3×C4×A4C2211yescharacteristic
8C2×C3⋊SL(2,ℤ/4)—21no—
9C3⋊(A4⋊C8)C412yescomplemented
10#63634—41nomaximal
11C22×C3×C4⋊C4D311yescharacteristic
12A4×C4⋊C4D313yes—
13C4⋊SL(2,ℤ/4)—33no—
14C2×A4⋊C8—33no—
15#5212—31no—
16C2×#830—31no—
17C2×#807—31no—
18C2×#807—31no—
19#4529—31no—
20#4529—31no—
21C22×C3×A4D411yescharacteristic
22C3×C4×A4—41no—
23C3×C4×A4C2×C411yescharacteristic
24C3×C4×A4Q811yescharacteristic
25C3⋊SL(2,ℤ/4)—41no—
26C32×C4⋊C4—41no—
27C4⋊(C3⋊Dic3)—41no—
28C2×C3⋊(C3⋊C8)—41no—
29#1852—91noSylow
30C23×C3×C4—21no—
31C23×C3×C4C2×D311yescharacteristic
32C2×C4×A4—23no—
33C2×C4×A4C2×D313yes—
34C2×SL(2,ℤ/4)—63no—
35C2×C3×C4⋊C4—31no—
36C2×C3×C4⋊C4—31no—
37C2×C3×C4⋊C4—61no—
38C2×#217—61no—
39C2×C4⋊Dic3—31no—
40C2×C4⋊Dic3—31no—
41C22×C3⋊C8—31no—
42C22×C3⋊C8—31no—
43A4⋊C8—36no—
44C3⋊#95—61no—
45#830—32no—
46#830—32no—
47#807—62no—
48#807—61no—
49#807—61no—
50#807—123no—
51C2×C3×A4C4⋊C411yescharacteristic
52C2×C3×A4D811yescharacteristic
53C2×C3×A4Q1611yescharacteristic
54C2×C32×C4—41no—
55C2×C32×C4—81no—
56C2×C3⋊Dic3—81no—
57C3⋊(C3⋊C8)—42no—
58C22×C4⋊C4C3⋊D311yescharacteristic
59C2×#107—91no—
60C2×#107—91no—
61C2×C22⋊C8—91no—
62#380—91no—
63#340—91no—
64#340—91no—
65C24×C3#6711yescharacteristic
66C22×A4#6713yes—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—31no—
70C22×C3×C4—31no—
71C22×C3×C4—41no—
72C22×C3×C4—61no—
73C22×C3×C4—61no—
74C22×C3×C4—121no—
75C22×C3×C4Dic611yescharacteristic
76C22×C3×C4C4×D311yescharacteristic
77C22×Dic3—61no—
78C22×Dic3—61no—
79C4×A4—43no—
80C4×A4Dic613yes—
81C4×A4C4×D313yes—
82SL(2,ℤ/4)—123no—
83C3×C4⋊C4—32no—
84C3×C4⋊C4—31no—
85C3×C4⋊C4—43no—
86C3×C4⋊C4—61no—
87C3×C4⋊C4S411yescharacteristic
88#217—121no—
89#217—121no—
90C4⋊Dic3—61no—
91C4⋊Dic3—61no—
92C4⋊Dic3—61no—
93C4⋊Dic3—61no—
94C4⋊Dic3—123no—
95C2×C3⋊C8—32no—
96C2×C3⋊C8—32no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—61no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—123no—
102C22×C32—41no—
103C3×A4#10711yescharacteristic, complemented
104C32×C4—41no—
105C32×C4—41no—
106C32×C4—161no—
107C3⋊Dic3—161no—
108C23×C4—21no—
109C23×C4C2×C3⋊D311yescharacteristic
110C22×C8—91no—
111C22×C8—91no—
112C2×C4⋊C4—31no—
113C2×C4⋊C4—31no—
114C2×C4⋊C4—61no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4—91no—
117C2×C22⋊C4—181no—
118#107—182no—
119#107—181no—
120#107—181no—
121C22⋊C8—92no—
122C22⋊C8—92no—
123#95—181no—
124C23×C3—31no—
125C23×C3—31no—
126C23×C3—31no—
127C23×C3—31no—
128C23×C3Dic3⋊C411yescharacteristic
129C23×C3#21311yescharacteristic
130C23×C3#21611yescharacteristic
131C2×A4Dic3⋊C413yes—
132C2×A4#21313yes—
133C2×A4#21613yes—
134C2×C3×C4—21no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—43no—
143C2×C3×C4—61no—
144C2×C3×C4—61no—
145C2×C3×C4—83no—
146C2×C3×C4—121no—
147C2×C3×C4—121no—
148C2×C3×C4—121no—
149C2×C3×C4—121no—
150C2×C3×C4C2×S411yescharacteristic
151C2×Dic3—121no—
152C2×Dic3—121no—
153C2×Dic3—121no—
154C2×Dic3—121no—
155C2×Dic3—121no—
156C2×Dic3—121no—
157C2×Dic3—243no—
158C3⋊C8—62no—
159C3⋊C8—62no—
160C3⋊C8—126no—
161C2×C32—41no—
162C2×C32—41no—
163C2×C32—41no—
164C24#63811yescharacteristic
165C22×C4—31no—
166C22×C4—31no—
167C22×C4—31no—
168C22×C4—31no—
169C22×C4—41no—
170C22×C4—61no—
171C22×C4—61no—
172C22×C4—121no—
173C22×C4—181no—
174C22×C4—181no—
175C22×C4#63411yescharacteristic
176C22×C4C4×C3⋊D311yescharacteristic
177C2×C8—92no—
178C2×C8—92no—
179C2×C8—181no—
180C2×C8—181no—
181C2×C8—181no—
182C2×C8—181no—
183C4⋊C4—32no—
184C4⋊C4—31no—
185C4⋊C4—61no—
186C4⋊C4—181no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4—181no—
190C4⋊C4C3⋊S411yescharacteristic
191C22⋊C4—361no—
192C22⋊C4—361no—
193C22×C3—31no—
194C22×C3—31no—
195C22×C3—31no—
196C22×C3—31no—
197C22×C3—31no—
198C22×C3—31no—
199C22×C3—31no—
200C22×C3—31no—
201C22×C3—31no—
202C22×C3—43no—
203C22×C3—61no—
204C22×C3#80711yescharacteristic, complemented
205C22×C3GL(2,ℤ/4)11yescharacteristic
206A4#80713yescomplemented
207C3×C4—31no—
208C3×C4—31no—
209C3×C4—41no—
210C3×C4—43no—
211C3×C4—43no—
212C3×C4—121no—
213C3×C4—163no—
214C3×C4A4⋊Q811yescharacteristic
215C3×C4C4×S411yescharacteristic
216Dic3—241no—
217Dic3—241no—
218Dic3—483no—
219C32—41noSylow
220C23—31no—
221C23—31no—
222C23—31no—
223C23—31no—
224C23#375011yescharacteristic
225C23#375311yescharacteristic
226C23#375611yescharacteristic
227C2×C4—21no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—31no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—61no—
236C2×C4—61no—
237C2×C4—121no—
238C2×C4—121no—
239C2×C4—121no—
240C2×C4—121no—
241C2×C4—361no—
242C2×C4—361no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4C2×C3⋊S411yescharacteristic
248C8—182no—
249C8—182no—
250C2×C3—31no—
251C2×C3—31no—
252C2×C3—31no—
253C2×C3—31no—
254C2×C3—43no—
255C2×C3—43no—
256C2×C3—43no—
257C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
258C2×C3#541511yescharacteristic
259C2×C3#541611yescharacteristic
260C22—31no—
261C22—31no—
262C22—31no—
263C22—31no—
264C22—31no—
265C22—31no—
266C22—31no—
267C22—31no—
268C22—31no—
269C22—61no—
270C22#6363411yescharacteristic, complemented
271C22#6426911yescharacteristic
272C4—31no—
273C4—31no—
274C4—41no—
275C4—121no—
276C4—721no—
277C4—721no—
278C4#6425911yescharacteristic
279C4C4×C3⋊S411yescharacteristic
280C3—43no—
281C3#7305011yescharacteristic, complemented
282C2—31no—
283C2—31no—
284C2—31no—
285C2—31no—
286C2#1059364511yescharacteristic
287C2#1059364911yescharacteristic
288C2#1059365011yescharacteristic
subgroupG/H
centerC22#64269
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×C4⋊C4D3
socleC24×C3#67
prime radicalC22×C3×A4D4
cosocleC2×C3×C4×A4C22
hypercenterC4⋊C4C3⋊S4
hypocenterC3×A4#107
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
9. C3⋊(A4⋊C8)C4semidirect
103. C3×A4#107semidirect
204. C22×C3#807semidirect
206. A4#807semidirect
270. C22#63634semidirect
281. C3#73050semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C4⋊C42
C4⋊(C3⋊SL(2,ℤ/4))2
C2×C3⋊(A4⋊C8)2
#730503
#715553
#636344