Finite Group Databasebeta

← #11921067

Subgroups — #11921067

Order 1152.

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

normal subgroups only

This group has 450 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
1C2×#64259C211yesmaximal, characteristic
2C2×C3×C8×A4C211yesmaximal, characteristic
3C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
4#73109—33nomaximal
5#71972—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)—21no—
8C2×C3⋊SL(2,ℤ/4)—21no—
9#64259—21no—
10#64259C412yescomplemented
11C3×C8×A4—21no—
12#63643—41nomaximal
13C2×A4⋊Q8—33no—
14C23×C3×C8D311yescharacteristic
15C2×#924—31no—
16C2×C8×A4D313yes—
17C4⋊SL(2,ℤ/4)—33no—
18#5212—31no—
19C2×#816—31no—
20C2×#816—31no—
21#4551—31no—
22#4551—31no—
23C22×C3×A4D411yescharacteristic
24C2×#634—41no—
25C3×C4×A4C2×C411yescharacteristic
26C3×C4×A4D411yescharacteristic
27C3⋊SL(2,ℤ/4)—22no—
28C3⋊SL(2,ℤ/4)—41no—
29C2×C32×C8—41no—
30C4⋊(C3⋊Dic3)—41no—
31#1892—91noSylow
32C23×C3×C4C2×D311yescharacteristic
33C22×Dic6—31no—
34C2×C4×A4C2×D313yes—
35C2×SL(2,ℤ/4)—63no—
36C2×SL(2,ℤ/4)—63no—
37A4⋊Q8—36no—
38A4⋊Q8—63no—
39C22×C3×C8—21no—
40C22×C3×C8—31no—
41C22×C3×C8—31no—
42C22×C3×C8—61no—
43C2×#217—61no—
44C2×#217—61no—
45C2×C4⋊Dic3—31no—
46C2×C4⋊Dic3—31no—
47C2×C4⋊Dic3—31no—
48#924—32no—
49#924—32no—
50#924—61no—
51#924—61no—
52C2×Dic3⋊C4—61no—
53C8×A4—23no—
54C3⋊#95—61no—
55#816—62no—
56#816—61no—
57#816—61no—
58#816—123no—
59C2×C3×A4C22⋊C411yescharacteristic
60C2×C3×A4SD1611yescharacteristic
61C2×C3×A4Q1611yescharacteristic
62C2×C32×C4—41no—
63C2×C3⋊Dic3—81no—
64C2×C3⋊Dic3—81no—
65#634—42no—
66#634—81no—
67C32×C8—81no—
68C23×C8C3⋊D311yescharacteristic
69C2×C22⋊Q8—91no—
70C2×#103—91no—
71C2×#103—91no—
72#380—91no—
73#340—91no—
74#340—91no—
75C24×C3D1211yescharacteristic
76C22×A4D1213yes—
77C22×C3×C4—31no—
78C22×C3×C4—31no—
79C22×C3×C4—31no—
80C22×C3×C4—31no—
81C22×C3×C4C4×D311yescharacteristic
82C22×C3×C4#6711yescharacteristic
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C2×Dic6—32no—
88C2×Dic6—61no—
89C2×Dic6—61no—
90C2×Dic6—61no—
91C2×Dic6—61no—
92C2×Dic6—61no—
93C2×Dic6—123no—
94C4×A4C4×D313yes—
95C4×A4#6713yes—
96SL(2,ℤ/4)—66no—
97SL(2,ℤ/4)—123no—
98C2×C3×C8—32no—
99C2×C3×C8—31no—
100C2×C3×C8—43no—
101C2×C3×C8—61no—
102C2×C3×C8—61no—
103C2×C3×C8—61no—
104C2×C3×C8S411yescharacteristic
105#217—62no—
106#217—62no—
107#217—121no—
108#217—121no—
109C4⋊Dic3—32no—
110C4⋊Dic3—61no—
111C4⋊Dic3—61no—
112C4⋊Dic3—61no—
113C4⋊Dic3—61no—
114C4⋊Dic3—61no—
115C4⋊Dic3—123no—
116Dic3⋊C4—62no—
117Dic3⋊C4—62no—
118C22×C32—41no—
119C3×A4#10311yescharacteristic, complemented
120C32×C4—41no—
121C32×C4—41no—
122C3⋊Dic3—82no—
123C3⋊Dic3—161no—
124C22×Q8—91no—
125C23×C4C2×C3⋊D311yescharacteristic
126C22×C8—21no—
127C22×C8—31no—
128C22×C8—31no—
129C22×C8—61no—
130C22⋊Q8—92no—
131C22⋊Q8—92no—
132C22⋊Q8—181no—
133C22⋊Q8—181no—
134C2×C4⋊C4—91no—
135C2×C4⋊C4—91no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—181no—
138C2×C22⋊C4—181no—
139C2×C22⋊C4—181no—
140#103—182no—
141#103—181no—
142#103—181no—
143#95—181no—
144C23×C3—31no—
145C23×C3—31no—
146C23×C3—31no—
147C23×C3—31no—
148C23×C3#20411yescharacteristic
149C23×C3Dic1211yescharacteristic
150C23×C3(C2×D3)⋊C411yescharacteristic
151C2×A4#20413yes—
152C2×A4Dic1213yes—
153C2×A4(C2×D3)⋊C413yes—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—31no—
159C2×C3×C4—31no—
160C2×C3×C4—31no—
161C2×C3×C4—43no—
162C2×C3×C4—61no—
163C2×C3×C4C2×S411yescharacteristic
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—121no—
167C2×Dic3—121no—
168C2×Dic3—121no—
169C2×Dic3—121no—
170C2×Dic3—121no—
171C2×Dic3—121no—
172C2×Dic3—121no—
173C2×Dic3—121no—
174C2×Dic3—121no—
175C2×Dic3—121no—
176C2×Dic3—243no—
177C2×Dic3—243no—
178Dic6—62no—
179Dic6—62no—
180Dic6—126no—
181Dic6—121no—
182Dic6—121no—
183Dic6—243no—
184C3×C8—21no—
185C3×C8—61no—
186C3×C8—83no—
187C2×C32—41no—
188C2×C32—41no—
189C2×C32—41no—
190C24C4⋊(C3⋊D3)11yescharacteristic
191C2×Q8—92no—
192C2×Q8—181no—
193C2×Q8—181no—
194C2×Q8—181no—
195C2×Q8—181no—
196C2×Q8—181no—
197C22×C4—31no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—31no—
201C22×C4—181no—
202C22×C4—181no—
203C22×C4—181no—
204C22×C4—181no—
205C22×C4C4×C3⋊D311yescharacteristic
206C22×C4#63811yescharacteristic
207C2×C8—32no—
208C2×C8—31no—
209C2×C8—61no—
210C2×C8—61no—
211C2×C8—61no—
212C2×C8C3⋊S411yescharacteristic
213C4⋊C4—92no—
214C4⋊C4—181no—
215C4⋊C4—182no—
216C4⋊C4—182no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C22⋊C4—182no—
222C22⋊C4—182no—
223C22⋊C4—361no—
224C22⋊C4—361no—
225C22×C3—31no—
226C22×C3—31no—
227C22×C3—31no—
228C22×C3—31no—
229C22×C3—31no—
230C22×C3—31no—
231C22×C3—31no—
232C22×C3—31no—
233C22×C3—31no—
234C22×C3—43no—
235C22×C3—61no—
236C22×C3#81611yescharacteristic, complemented
237C22×C3C4⋊S411yescharacteristic
238A4#81613yescomplemented
239C3×C4—31no—
240C3×C4—31no—
241C3×C4—43no—
242C3×C4—43no—
243C3×C4C4×S411yescharacteristic
244C3×C4GL(2,ℤ/4)11yescharacteristic
245Dic3—122no—
246Dic3—122no—
247Dic3—246no—
248Dic3—241no—
249Dic3—241no—
250Dic3—483no—
251C32—41noSylow
252C23—31no—
253C23—31no—
254C23—31no—
255C23—31no—
256C23#374411yescharacteristic
257C23#374611yescharacteristic
258C23#375211yescharacteristic
259Q8—182no—
260Q8—182no—
261Q8—361no—
262Q8—361no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—61no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—361no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4—361no—
282C2×C4—361no—
283C2×C4C2×C3⋊S411yescharacteristic
284C8—21no—
285C8—61no—
286C2×C3—31no—
287C2×C3—31no—
288C2×C3—31no—
289C2×C3—31no—
290C2×C3—43no—
291C2×C3—43no—
292C2×C3—43no—
293C2×C3#539811yescharacteristic
294C2×C3#540111yescharacteristic
295C2×C3(C2×S4)⋊C411yescharacteristic
296C22—31no—
297C22—31no—
298C22—31no—
299C22—31no—
300C22—31no—
301C22—31no—
302C22—31no—
303C22—31no—
304C22—31no—
305C22—61no—
306C22#6364311yescharacteristic, complemented
307C22C4⋊(C3⋊S4)11yescharacteristic
308C4—31no—
309C4—31no—
310C4—362no—
311C4—362no—
312C4—721no—
313C4—721no—
314C4C4×C3⋊S411yescharacteristic
315C4#6426911yescharacteristic
316C3—43no—
317C3#7310911yescharacteristic, complemented
318C2—31no—
319C2—31no—
320C2—31no—
321C2—31no—
322C2#1059363211yescharacteristic
323C2#1059363511yescharacteristic
324C2#1059364711yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC23×C3×C8D3
socleC24×C3D12
prime radicalC22×C3×A4D4
cosocleC2×C3×C4×A4C22
hypercenterC2×C8C3⋊S4
hypocenterC3×A4#103
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
10. #64259C4semidirect
119. C3×A4#103semidirect
236. C22×C3#816semidirect
238. A4#816semidirect
306. C22#63643semidirect
317. C3#73109semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C2×C3×C8×A42
C4⋊(C3⋊SL(2,ℤ/4))2
#731093
#719723
#636434