Finite Group Databasebeta

← #11921063

Subgroups — #11921063

Order 1152.

402 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 79 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×A4C211yesmaximal, characteristic
2C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic
4SL(2,ℤ/4)⋊C8—33nomaximal
5#71974—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)C411yescharacteristic
8C2×C3⋊SL(2,ℤ/4)C411yescharacteristic
9C3×C8×A4—21no—
10C3⋊(A4⋊C8)—21no—
11#63641—41nomaximal
12C23×C3×C8D311yescharacteristic
13C2×C8×A4D313yes—
14C4×SL(2,ℤ/4)—33no—
15C2×A4⋊C8—33no—
16C4×#217—31no—
17C2×#830—31no—
18C2×Dic3⋊C8—31no—
19C2×Dic3⋊C8—31no—
20#4550—31no—
21#4550—31no—
22C22×C3×A4C2×C411yescharacteristic
23C3×C4×A4D411yescharacteristic
24C3×C4×A4Q811yescharacteristic
25C3⋊SL(2,ℤ/4)—21no—
26C3⋊SL(2,ℤ/4)C812yescomplemented
27C2×C32×C8—41no—
28C4×C3⋊Dic3—41no—
29C2×C3⋊(C3⋊C8)—41no—
30#1850—91noSylow
31C23×C3×C4C2×D311yescharacteristic
32C2×C4×A4C2×D313yes—
33C2×SL(2,ℤ/4)—33no—
34C2×SL(2,ℤ/4)—33no—
35C22×C3×C8—21no—
36C22×C3×C8—31no—
37C22×C3×C8—31no—
38C22×C3×C8—61no—
39C2×#217—31no—
40C2×#217—31no—
41C2×C4×Dic3—31no—
42C2×C4×Dic3—31no—
43C22×C3⋊C8—31no—
44C22×C3⋊C8—31no—
45C8×A4—23no—
46A4⋊C8—63no—
47C3⋊#95—31no—
48C3⋊#95—31no—
49#830—61no—
50#830—61no—
51Dic3⋊C8—62no—
52Dic3⋊C8—61no—
53Dic3⋊C8—61no—
54Dic3⋊C8—123no—
55C2×C3×A4C4⋊C411yescharacteristic
56C2×C3×A4C2×C811yescharacteristic
57C2×C3×A4M1611yescharacteristic
58C2×C32×C4—41no—
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3—41no—
61C32×C8—81no—
62C3⋊(C3⋊C8)—81no—
63C23×C8C3⋊D311yescharacteristic
64C2×C4⋊C8—91no—
65C2×C4⋊C8—91no—
66C2×C22⋊C8—91no—
67C4×C22⋊C4—91no—
68#336—91no—
69#336—91no—
70C24×C3C4×D311yescharacteristic
71C22×A4C4×D313yes—
72C22×C3×C4—31no—
73C22×C3×C4—31no—
74C22×C3×C4—31no—
75C22×C3×C4—31no—
76C22×C3×C4Dic611yescharacteristic
77C22×C3×C4#6711yescharacteristic
78C22×Dic3—31no—
79C22×Dic3—31no—
80C22×Dic3—31no—
81C22×Dic3—31no—
82C4×A4Dic613yes—
83C4×A4#6713yes—
84SL(2,ℤ/4)—36no—
85SL(2,ℤ/4)—63no—
86C2×C3×C8—32no—
87C2×C3×C8—31no—
88C2×C3×C8—43no—
89C2×C3×C8—61no—
90C2×C3×C8—61no—
91C2×C3×C8—61no—
92C2×C3×C8S411yescharacteristic
93#217—32no—
94#217—32no—
95#217—61no—
96#217—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C4×Dic3—123no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8—123no—
109C22×C32—41no—
110C3×A4C4⋊C811yescharacteristic, complemented
111C32×C4—41no—
112C32×C4—41no—
113C3⋊Dic3—42no—
114C3⋊Dic3—81no—
115C23×C4C2×C3⋊D311yescharacteristic
116C22×C8—21no—
117C22×C8—31no—
118C22×C8—31no—
119C22×C8—61no—
120C22×C8—91no—
121C22×C8—91no—
122C2×C22⋊C4—91no—
123C2×C22⋊C4—91no—
124C2×C42—91no—
125C2×C42—91no—
126C4⋊C8—182no—
127C4⋊C8—181no—
128C4⋊C8—181no—
129C22⋊C8—181no—
130C22⋊C8—181no—
131#95—91no—
132#95—91no—
133C23×C3—31no—
134C23×C3—31no—
135C23×C3—31no—
136C23×C3—31no—
137C23×C3D3×C811yescharacteristic
138C23×C3ΓL(1,𝔽25)11yescharacteristic
139C23×C3Dic3⋊C411yescharacteristic
140C2×A4D3×C813yes—
141C2×A4ΓL(1,𝔽25)13yes—
142C2×A4Dic3⋊C413yes—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—31no—
150C2×C3×C4—43no—
151C2×C3×C4—61no—
152C2×C3×C4C2×S411yescharacteristic
153C2×Dic3—32no—
154C2×Dic3—32no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—123no—
166C2×Dic3—123no—
167C3×C8—21no—
168C3×C8—61no—
169C3×C8—83no—
170C3⋊C8—121no—
171C3⋊C8—121no—
172C3⋊C8—243no—
173C2×C32—41no—
174C2×C32—41no—
175C2×C32—41no—
176C24C4×C3⋊D311yescharacteristic
177C22×C4—31no—
178C22×C4—31no—
179C22×C4—31no—
180C22×C4—31no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4#63411yescharacteristic
186C22×C4#63811yescharacteristic
187C2×C8—32no—
188C2×C8—31no—
189C2×C8—61no—
190C2×C8—61no—
191C2×C8—61no—
192C2×C8—181no—
193C2×C8—181no—
194C2×C8—181no—
195C2×C8—181no—
196C2×C8—181no—
197C2×C8—181no—
198C2×C8C3⋊S411yescharacteristic
199C22⋊C4—92no—
200C22⋊C4—92no—
201C22⋊C4—181no—
202C22⋊C4—181no—
203C42—181no—
204C42—181no—
205C42—181no—
206C42—181no—
207C22×C3—31no—
208C22×C3—31no—
209C22×C3—31no—
210C22×C3—31no—
211C22×C3—31no—
212C22×C3—31no—
213C22×C3—31no—
214C22×C3—31no—
215C22×C3—31no—
216C22×C3—43no—
217C22×C3—61no—
218C22×C3Dic3⋊C811yescharacteristic, complemented
219C22×C3C4×S411yescharacteristic
220A4Dic3⋊C813yescomplemented
221C3×C4—31no—
222C3×C4—31no—
223C3×C4—43no—
224C3×C4—43no—
225C3×C4A4⋊Q811yescharacteristic
226C3×C4GL(2,ℤ/4)11yescharacteristic
227Dic3—62no—
228Dic3—62no—
229Dic3—126no—
230Dic3—121no—
231Dic3—121no—
232Dic3—243no—
233C32—41noSylow
234C23—31no—
235C23—31no—
236C23—31no—
237C23—31no—
238C23C8×C3⋊D311yescharacteristic
239C23#374311yescharacteristic
240C23#375011yescharacteristic
241C2×C4—31no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—31no—
247C2×C4—31no—
248C2×C4—61no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4C2×C3⋊S411yescharacteristic
262C8—21no—
263C8—61no—
264C8—361no—
265C8—361no—
266C2×C3—31no—
267C2×C3—31no—
268C2×C3—31no—
269C2×C3—31no—
270C2×C3—43no—
271C2×C3—43no—
272C2×C3—43no—
273C2×C3C8×S411yescharacteristic
274C2×C3#540011yescharacteristic
275C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
276C22—31no—
277C22—31no—
278C22—31no—
279C22—31no—
280C22—31no—
281C22—31no—
282C22—31no—
283C22—31no—
284C22—31no—
285C22—61no—
286C22#6364111yescharacteristic, complemented
287C22C4×C3⋊S411yescharacteristic
288C4—31no—
289C4—31no—
290C4—182no—
291C4—182no—
292C4—361no—
293C4—361no—
294C4#6425911yescharacteristic
295C4#6426911yescharacteristic
296C3—43no—
297C3SL(2,ℤ/4)⋊C811yescharacteristic, complemented
298C2—31no—
299C2—31no—
300C2—31no—
301C2—31no—
302C2C8×C3⋊S411yescharacteristic
303C2#1059363411yescharacteristic
304C2#1059364511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×C3⋊S4
commutatorC2×C3×A4C2×C8
FittingC23×C3×C8D3
socleC24×C3C4×D3
prime radicalC22×C3×A4C2×C4
cosocleC2×C3×C4×A4C22
hypercenterC2×C8C3⋊S4
hypocenterC3×A4C4⋊C8
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
26. C3⋊SL(2,ℤ/4)C8semidirect
110. C3×A4C4⋊C8semidirect
218. C22×C3Dic3⋊C8semidirect
220. A4Dic3⋊C8semidirect
286. C22#63641semidirect
297. C3SL(2,ℤ/4)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C4×C3⋊SL(2,ℤ/4)2
C2×C3⋊(A4⋊C8)2
SL(2,ℤ/4)⋊C83
#719743
#636414