Finite Group Databasebeta

← #11921072

Subgroups — #11921072

Order 1152.

488 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 61 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×C4⋊(C3⋊S4)C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic, complemented
3#10593643C211yesmaximal, characteristic, complemented
4#73116—33nomaximal
5#72002—31nomaximal
6C22×C3⋊S4C412yes—
7C2×C3×C4×A4C2211yescharacteristic
8C4⋊(C3⋊S4)—21no—
9C4⋊(C3⋊S4)—21no—
10C3×C8×A4—21no—
11C3⋊(A4⋊C8)—21no—
12#63650—41nomaximal
13C2×C4⋊S4—33no—
14C22×C3×M16D311yescharacteristic, complemented
15C2×#930—31no—
16A4×M16D313yescomplemented
17#5409—33no—
18#5207—31no—
19C2×#823—31no—
20C2×#823—31no—
21#4554—31no—
22#4554—31no—
23C22×C3×A4C2×C411yescharacteristic
24C2×C3⋊S4—22no—
25C2×C3⋊S4—42no—
26C2×C4⋊(C3⋊D3)—41no—
27C3×C4×A4D411yescharacteristic
28C3×C4×A4D411yescharacteristic
29C32×M16—41no—
30#3748—41no—
31#1900—91noSylow
32C22×S4—36no—
33C23×C3×C4C2×D311yescharacteristic
34C22×#67—32no—
35C22×D12—31no—
36C2×C4×A4C2×D313yes—
37C4⋊S4—63no—
38C4⋊S4—63no—
39C2×C3×M16—31no—
40C2×C3×M16—31no—
41C2×C3×M16—61no—
42C22×C3×C8—21no—
43#930—61no—
44#930—61no—
45#930—61no—
46#930—61no—
47C2×(C2×D3)⋊C4—32no—
48C2×C4⋊Dic3—31no—
49C2×#208—31no—
50C2×#208—31no—
51C8×A4—23no—
52A4⋊C8—63no—
53#830—61no—
54#830—61no—
55#823—62no—
56#823—61no—
57#823—61no—
58#823—123no—
59C22×C3⋊D3—42no—
60C2×C3×A4—21no—
61C2×C3×A4C22⋊C411yescharacteristic
62C3⋊S4—42no—
63C2×C32×C4—41no—
64C4⋊(C3⋊D3)—81no—
65C4⋊(C3⋊D3)—81no—
66C32×C8—81no—
67C3⋊(C3⋊C8)—81no—
68C22×M16C3⋊D311yescharacteristic, complemented
69C2×#121—91no—
70C2×#100—91no—
71C2×#100—91no—
72#407—91no—
73#343—91no—
74#343—91no—
75C24×C3C4×D311yescharacteristic
76C23×D3—32no—
77C22×A4C4×D313yes—
78C2×S4—66no—
79C2×S4—126no—
80C22×C3×C4—31no—
81C22×C3×C4—31no—
82C22×C3×C4—31no—
83C22×C3×C4—31no—
84C22×C3×C4D1211yescharacteristic
85C22×C3×C4#6711yescharacteristic
86C2×#67—62no—
87C2×#67—62no—
88C2×#67—122no—
89C2×#67—122no—
90C22×Dic3—32no—
91C2×D12—61no—
92C2×D12—61no—
93C2×D12—61no—
94C2×D12—61no—
95C2×D12—61no—
96C2×D12—61no—
97C2×D12—123no—
98C4×A4D1213yes—
99C4×A4#6713yes—
100C3×M16—32no—
101C3×M16—31no—
102C3×M16—43no—
103C3×M16—61no—
104C3×M16S411yescharacteristic, complemented
105C2×C3×C8—61no—
106C2×C3×C8—61no—
107(C2×D3)⋊C4—62no—
108(C2×D3)⋊C4—62no—
109C4⋊Dic3—61no—
110C4⋊Dic3—61no—
111#208—61no—
112#208—61no—
113#208—61no—
114#208—61no—
115#208—123no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118C22×C32—41no—
119C2×C3⋊D3—82no—
120C2×C3⋊D3—162no—
121C3×A4#10011yescharacteristic, complemented
122C32×C4—41no—
123C32×C4—41no—
124C22×D4—91no—
125C22×D4—92no—
126C23×C4C2×C3⋊D311yescharacteristic
127C2×M16—31no—
128C2×M16—31no—
129C2×M16—61no—
130C2×M16—91no—
131C2×M16—91no—
132C22×C8—21no—
133#121—181no—
134#121—181no—
135#121—181no—
136#121—181no—
137C2×C4⋊C4—91no—
138C2×C22⋊C4—92no—
139#100—182no—
140#100—181no—
141#100—181no—
142C22⋊C8—181no—
143C22⋊C8—181no—
144C23×C3—21no—
145C23×C3—31no—
146C23×C3—31no—
147C23×C3—61no—
148C23×C3(C2×D3)⋊C411yescharacteristic
149C22×D3—62no—
150C22×D3—62no—
151C22×D3—62no—
152C22×D3—126no—
153C22×D3—122no—
154C22×D3—122no—
155C2×A4—23no—
156C2×A4(C2×D3)⋊C413yes—
157S4—126no—
158C2×C3×C4—31no—
159C2×C3×C4—31no—
160C2×C3×C4—31no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—43no—
166C2×C3×C4—61no—
167C2×C3×C4C2×S411yescharacteristic
168#67—122no—
169#67—124no—
170#67—122no—
171C2×Dic3—62no—
172C2×Dic3—122no—
173D12—121no—
174D12—121no—
175D12—121no—
176D12—121no—
177D12—243no—
178D12—243no—
179C3×C8—21no—
180C3×C8—61no—
181C3×C8—83no—
182C3⋊C8—121no—
183C3⋊C8—121no—
184C3⋊C8—243no—
185C2×C32—41no—
186C2×C32—81no—
187C3⋊D3—162no—
188C24—92no—
189C24C4×C3⋊D311yescharacteristic
190C2×D4—181no—
191C2×D4—181no—
192C2×D4—181no—
193C2×D4—181no—
194C2×D4—181no—
195C2×D4—182no—
196C2×D4—182no—
197C2×D4—181no—
198C2×D4—362no—
199C2×D4—362no—
200C22×C4—31no—
201C22×C4—31no—
202C22×C4—31no—
203C22×C4—31no—
204C22×C4—92no—
205C22×C4C4⋊(C3⋊D3)11yescharacteristic
206C22×C4#63811yescharacteristic
207M16—32no—
208M16—31no—
209M16—61no—
210M16—181no—
211M16—181no—
212M16—181no—
213M16—181no—
214M16C3⋊S411yescharacteristic, complemented
215C2×C8—61no—
216C2×C8—61no—
217C2×C8—181no—
218C2×C8—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C22⋊C4—182no—
222C22⋊C4—182no—
223C22×C3—31no—
224C22×C3—31no—
225C22×C3—31no—
226C22×C3—43no—
227C22×C3—61no—
228C22×C3—61no—
229C22×C3—61no—
230C22×C3—61no—
231C22×C3#82311yescharacteristic, complemented
232C22×C3C4×S411yescharacteristic
233C2×D3—122no—
234C2×D3—122no—
235C2×D3—122no—
236C2×D3—246no—
237C2×D3—242no—
238C2×D3—242no—
239C2×D3—486no—
240A4#82313yescomplemented
241C3×C4—31no—
242C3×C4—31no—
243C3×C4—43no—
244C3×C4—43no—
245C3×C4C4⋊S411yescharacteristic
246C3×C4GL(2,ℤ/4)11yescharacteristic
247Dic3—122no—
248C32—41noSylow
249C23—21no—
250C23—31no—
251C23—31no—
252C23—61no—
253C23—182no—
254C23—182no—
255C23—182no—
256C23—362no—
257C23—362no—
258C23#375211yescharacteristic
259D4—361no—
260D4—361no—
261D4—362no—
262D4—364no—
263D4—362no—
264D4—361no—
265D4—361no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—31no—
273C2×C4—61no—
274C2×C4—182no—
275C2×C4—362no—
276C2×C4C2×C3⋊S411yescharacteristic
277C8—21no—
278C8—61no—
279C8—361no—
280C8—361no—
281C2×C3—21no—
282C2×C3—31no—
283C2×C3—31no—
284C2×C3—43no—
285C2×C3—61no—
286C2×C3—83no—
287C2×C3(C2×S4)⋊C411yescharacteristic
288D3—242no—
289D3—486no—
290C22—31no—
291C22—31no—
292C22—31no—
293C22—61no—
294C22—61no—
295C22—61no—
296C22—61no—
297C22—362no—
298C22—362no—
299C22—362no—
300C22—722no—
301C22—722no—
302C22#6365011yescharacteristic, complemented
303C22C4×C3⋊S411yescharacteristic
304C4—31no—
305C4—31no—
306C4—362no—
307C4C4⋊(C3⋊S4)11yescharacteristic
308C4#6426911yescharacteristic
309C3—43no—
310C3#7311611yescharacteristic, complemented
311C2—21no—
312C2—31no—
313C2—31no—
314C2—61no—
315C2—722no—
316C2#1059364711yescharacteristic
subgroupG/H
centerC2#10593647
commutatorC22×C3×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×M16D3
socleC23×C3(C2×D3)⋊C4
prime radicalC2×C4⋊(C3⋊S4)C2
cosocleC2×C3×C4×A4C22
hypercenterM16C3⋊S4
hypocenterC3×A4#100
LCSG ▷ C22×C3×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. #10593643C2semidirect
14. C22×C3×M16D3semidirect
16. A4×M16D3semidirect
68. C22×M16C3⋊D3semidirect
104. C3×M16S4semidirect
121. C3×A4#100semidirect
214. M16C3⋊S4semidirect
231. C22×C3#823semidirect
240. A4#823semidirect
302. C22#63650semidirect
310. C3#73116semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊S4)2
C3×A4×M162
#105936432
#731163
#720023
#636504