Finite Group Databasebeta

← #11921071

Subgroups — #11921071

Order 1152.

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

normal subgroups only

This group has 404 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×#64259C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic
3#10593643C211yesmaximal, characteristic
4#73115—33nomaximal
5#72003—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)C412yes—
8#64259—21no—
9#64259—21no—
10C3×C8×A4—21no—
11C3⋊(A4⋊C8)—21no—
12#63651—41nomaximal
13C2×A4⋊Q8—33no—
14C22×C3×M16D311yescharacteristic
15C2×#924—31no—
16A4×M16D313yes—
17#5409—33no—
18#5207—31no—
19C2×#824—31no—
20C2×#824—31no—
21#4554—31no—
22#4554—31no—
23C22×C3×A4C2×C411yescharacteristic
24C2×#634—41no—
25C3×C4×A4D411yescharacteristic
26C3×C4×A4D411yescharacteristic
27C3⋊SL(2,ℤ/4)—22no—
28C32×M16—41no—
29#3748—41no—
30#1901—91noSylow
31C23×C3×C4C2×D311yescharacteristic
32C22×Dic6—31no—
33C2×C4×A4C2×D313yes—
34C2×SL(2,ℤ/4)—36no—
35A4⋊Q8—63no—
36A4⋊Q8—63no—
37C2×C3×M16—31no—
38C2×C3×M16—31no—
39C2×C3×M16—61no—
40C22×C3×C8—21no—
41C2×#217—32no—
42C2×C4⋊Dic3—31no—
43#924—61no—
44#924—61no—
45#924—61no—
46#924—61no—
47C2×Dic3⋊C4—32no—
48C2×#208—31no—
49C2×#208—31no—
50C8×A4—23no—
51A4⋊C8—63no—
52#830—61no—
53#830—61no—
54#824—62no—
55#824—61no—
56#824—61no—
57#824—123no—
58C2×C3×A4—21no—
59C2×C3×A4C22⋊C411yescharacteristic
60C2×C32×C4—41no—
61C2×C3⋊Dic3—42no—
62#634—81no—
63#634—81no—
64C32×C8—81no—
65C3⋊(C3⋊C8)—81no—
66C22×M16C3⋊D311yescharacteristic
67C2×C22⋊Q8—91no—
68C2×#101—91no—
69C2×#101—91no—
70#407—91no—
71#343—91no—
72#343—91no—
73C24×C3C4×D311yescharacteristic
74C22×A4C4×D313yes—
75C22×C3×C4—31no—
76C22×C3×C4—31no—
77C22×C3×C4—31no—
78C22×C3×C4—31no—
79C22×C3×C4D1211yescharacteristic
80C22×C3×C4#6711yescharacteristic
81C22×Dic3—32no—
82C22×Dic3—32no—
83C2×Dic6—61no—
84C2×Dic6—61no—
85C2×Dic6—61no—
86C2×Dic6—61no—
87C2×Dic6—61no—
88C2×Dic6—61no—
89C2×Dic6—123no—
90C4×A4D1213yes—
91C4×A4#6713yes—
92SL(2,ℤ/4)—66no—
93C3×M16—32no—
94C3×M16—31no—
95C3×M16—43no—
96C3×M16—61no—
97C3×M16S411yescharacteristic
98C2×C3×C8—61no—
99C2×C3×C8—61no—
100#217—62no—
101#217—62no—
102C4⋊Dic3—61no—
103C4⋊Dic3—61no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106#208—61no—
107#208—61no—
108#208—61no—
109#208—61no—
110#208—123no—
111C2×C3⋊C8—61no—
112C2×C3⋊C8—61no—
113C22×C32—41no—
114C3×A4#10111yescharacteristic, complemented
115C32×C4—41no—
116C32×C4—41no—
117C3⋊Dic3—82no—
118C22×Q8—91no—
119C23×C4C2×C3⋊D311yescharacteristic
120C2×M16—31no—
121C2×M16—31no—
122C2×M16—61no—
123C2×M16—91no—
124C2×M16—91no—
125C22×C8—21no—
126C22⋊Q8—181no—
127C22⋊Q8—181no—
128C22⋊Q8—181no—
129C22⋊Q8—181no—
130C2×C4⋊C4—91no—
131C2×C4⋊C4—92no—
132C2×C22⋊C4—92no—
133#101—182no—
134#101—181no—
135#101—181no—
136C22⋊C8—181no—
137C22⋊C8—181no—
138C23×C3—21no—
139C23×C3—31no—
140C23×C3—31no—
141C23×C3—61no—
142C23×C3(C2×D3)⋊C411yescharacteristic
143C2×A4—23no—
144C2×A4(C2×D3)⋊C413yes—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—31no—
150C2×C3×C4—31no—
151C2×C3×C4—31no—
152C2×C3×C4—43no—
153C2×C3×C4—61no—
154C2×C3×C4C2×S411yescharacteristic
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—126no—
160C2×Dic3—122no—
161Dic6—121no—
162Dic6—121no—
163Dic6—121no—
164Dic6—121no—
165Dic6—243no—
166Dic6—243no—
167C3×C8—21no—
168C3×C8—61no—
169C3×C8—83no—
170C3⋊C8—121no—
171C3⋊C8—121no—
172C3⋊C8—243no—
173C2×C32—41no—
174C2×C32—81no—
175C24C4×C3⋊D311yescharacteristic
176C2×Q8—181no—
177C2×Q8—181no—
178C2×Q8—181no—
179C2×Q8—181no—
180C2×Q8—181no—
181C2×Q8—181no—
182C22×C4—31no—
183C22×C4—31no—
184C22×C4—31no—
185C22×C4—31no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4C4⋊(C3⋊D3)11yescharacteristic
189C22×C4#63811yescharacteristic
190M16—32no—
191M16—31no—
192M16—61no—
193M16—181no—
194M16—181no—
195M16—181no—
196M16—181no—
197M16C3⋊S411yescharacteristic
198C2×C8—61no—
199C2×C8—61no—
200C2×C8—181no—
201C2×C8—181no—
202C4⋊C4—182no—
203C4⋊C4—182no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C22⋊C4—182no—
207C22⋊C4—182no—
208C22×C3—31no—
209C22×C3—31no—
210C22×C3—31no—
211C22×C3—43no—
212C22×C3—61no—
213C22×C3—61no—
214C22×C3—61no—
215C22×C3—61no—
216C22×C3#82411yescharacteristic, complemented
217C22×C3C4×S411yescharacteristic
218A4#82413yescomplemented
219C3×C4—31no—
220C3×C4—31no—
221C3×C4—43no—
222C3×C4—43no—
223C3×C4C4⋊S411yescharacteristic
224C3×C4GL(2,ℤ/4)11yescharacteristic
225Dic3—122no—
226Dic3—122no—
227Dic3—246no—
228C32—41noSylow
229C23—21no—
230C23—31no—
231C23—31no—
232C23—61no—
233C23#375211yescharacteristic
234Q8—361no—
235Q8—361no—
236Q8—361no—
237Q8—361no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—31no—
241C2×C4—31no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—31no—
245C2×C4—61no—
246C2×C4—182no—
247C2×C4—182no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—362no—
251C2×C4C2×C3⋊S411yescharacteristic
252C8—21no—
253C8—61no—
254C8—361no—
255C8—361no—
256C2×C3—21no—
257C2×C3—31no—
258C2×C3—31no—
259C2×C3—43no—
260C2×C3—61no—
261C2×C3—83no—
262C2×C3(C2×S4)⋊C411yescharacteristic
263C22—31no—
264C22—31no—
265C22—31no—
266C22—61no—
267C22—61no—
268C22—61no—
269C22—61no—
270C22#6365111yescharacteristic, complemented
271C22C4×C3⋊S411yescharacteristic
272C4—31no—
273C4—31no—
274C4—362no—
275C4—362no—
276C4C4⋊(C3⋊S4)11yescharacteristic
277C4#6426911yescharacteristic
278C3—43no—
279C3#7311511yescharacteristic, complemented
280C2—21no—
281C2—31no—
282C2—31no—
283C2—61no—
284C2#1059364711yescharacteristic
subgroupG/H
centerC2#10593647
commutator, prime radicalC22×C3×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×M16D3
socleC23×C3(C2×D3)⋊C4
cosocleC2×C3×C4×A4C22
hypercenterM16C3⋊S4
hypocenterC3×A4#101
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
114. C3×A4#101semidirect
216. C22×C3#824semidirect
218. A4#824semidirect
270. C22#63651semidirect
279. C3#73115semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C3×A4×M162
#105936432
#731153
#720033
#636514