Finite Group Databasebeta

← #11774043

Subgroups — #11774043

Order 1152.

612 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 131 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×#64098C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4C32×#324C211yesmaximal, characteristic
5#10589394C211yesmaximal, characteristic
6#10589335C211yesmaximal, characteristic
7#10589335C211yesmaximal, characteristic
8#68128—34nomaximal
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic
11C2×#3750C411yescharacteristic
12C2×#3750C411yescharacteristic
13C2×#3750C411yescharacteristic
14C2×#3750C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64098—21no—
17#64098—21no—
18#64098—21no—
19#64098—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23#63657C2211yescharacteristic
24#63642—21no—
25#63641—21no—
26#63641—21no—
27C8×C3⋊Dic3—21no—
28C2×#889—34no—
29#4719—34no—
30#4718—34no—
31C3×#324D314yes—
32#4528—34no—
33#4469—34no—
34#4469—34no—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3C2×C411yescharacteristic
41C22×C3⋊Dic3C2×C411yescharacteristic
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48#3750—21no—
49#3750—21no—
50#3750—21no—
51#3750—21no—
52#3750—21no—
53#3750—21no—
54#3750—21no—
55#3750—21no—
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1470—91noSylow
63C2×C3×C4⋊C4C2×D314yes—
64C2×C4⋊Dic3—34no—
65C2×Dic3⋊C4—34no—
66C2×Dic3⋊C4—34no—
67C2×Dic3⋊C4—34no—
68C2×Dic3⋊C4—34no—
69C2×C4×Dic3—34no—
70#889—64no—
71#889—64no—
72#889—64no—
73#889—64no—
74C3×C22⋊C8C2×D314yes—
75C3×C22⋊C8C2×D314yes—
76#830—34no—
77#830—34no—
78#815—64no—
79Dic3⋊C8—64no—
80Dic3⋊C8—64no—
81C8×Dic3—64no—
82C23×C32C22×C411yescharacteristic
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C32×C8—41no—
104C32×C8—41no—
105C3⋊(C3⋊C8)—41no—
106C3⋊(C3⋊C8)—41no—
107C2×#125—91no—
108#432—91no—
109#431—91no—
110#324—91no—
111#324—91no—
112#324—91no—
113#324C3⋊D311yescharacteristic
114C22×C3×C4C4×D314yes—
115C22×C3×C4C4×D314yes—
116C22×C3×C4C22×D314yes—
117C22×Dic3—34no—
118C22×Dic3—34no—
119C22×Dic3—34no—
120C22×Dic3—34no—
121C2×C3×C8—24no—
122C2×C3×C8—24no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—24no—
125C4⋊Dic3—64no—
126C4⋊Dic3—64no—
127Dic3⋊C4—64no—
128Dic3⋊C4—64no—
129Dic3⋊C4—64no—
130Dic3⋊C4—64no—
131Dic3⋊C4—64no—
132Dic3⋊C4—64no—
133Dic3⋊C4—64no—
134Dic3⋊C4—64no—
135C4×Dic3—34no—
136C4×Dic3—34no—
137C4×Dic3—34no—
138C4×Dic3—34no—
139C2×C3⋊C8—64no—
140C2×C3⋊C8—64no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32C2×C22⋊C411yescharacteristic
144C22×C32#13111yescharacteristic
145C22×C32#13111yescharacteristic
146C32×C4—21no—
147C32×C4—21no—
148C32×C4—41no—
149C32×C4—41no—
150C3⋊Dic3—21no—
151C3⋊Dic3—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3—41no—
154C3⋊Dic3—41no—
155C3⋊Dic3#10112yes—
156#125—181no—
157#125—181no—
158#125—181no—
159#125—181no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4C2×C3⋊D311yescharacteristic
166C2×C42—91no—
167C4⋊C8—181no—
168C4⋊C8—181no—
169C22⋊C8—91no—
170C22⋊C8—91no—
171C22⋊C8C2×C3⋊D311yescharacteristic
172C22⋊C8C2×C3⋊D311yescharacteristic
173#97—181no—
174C4×C8—181no—
175C23×C3C2×C4×D314yes—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—44no—
181C2×C3×C4—44no—
182C2×C3×C4D3×D414yes—
183C2×C3×C4D3×D414yes—
184C2×Dic3—34no—
185C2×Dic3—34no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—68no—
189C2×Dic3—64no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—124no—
196C3×C8—44no—
197C3×C8—44no—
198C3⋊C8—124no—
199C3⋊C8—124no—
200C2×C32—21no—
201C2×C32—21no—
202C2×C32#40811yescharacteristic
203C2×C32#41011yescharacteristic
204C2×C32C2×#10111yescharacteristic
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4C4×C3⋊D311yescharacteristic
210C22×C4C4×C3⋊D311yescharacteristic
211C22×C4C22×C3⋊D311yescharacteristic
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—181no—
215C2×C8—181no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C42—91no—
229C42—91no—
230C42—91no—
231C42—91no—
232C22×C3—24no—
233C22×C3—24no—
234C22×C3D3×C22⋊C414yes—
235C22×C3#90114yes—
236C22×C3#90714yes—
237C3×C4—24no—
238C3×C4—24no—
239C3×C4—44no—
240C3×C4—44no—
241Dic3—38no—
242Dic3—64no—
243Dic3—64no—
244Dic3—64no—
245Dic3—124no—
246Dic3—124no—
247C32#147011yescharacteristic, complemented, Sylow
248C23C2×C4×C3⋊D311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—182no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—181no—
263C2×C4—181no—
264C2×C4—181no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4D4×C3⋊D311yescharacteristic
268C2×C4D4×C3⋊D311yescharacteristic
269C8—41no—
270C8—41no—
271C8—361no—
272C8—361no—
273C2×C3—24no—
274C2×C3—24no—
275C2×C3#472714yes—
276C2×C3#474014yes—
277C2×C3D3×#10114yes—
278C22—21no—
279C22—21no—
280C22C22⋊C4×C3⋊D311yescharacteristic
281C22#6411011yescharacteristic
282C22#6411611yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—92no—
288C4—181no—
289C4—181no—
290C4—181no—
291C4—361no—
292C4—361no—
293C3#6812814yescomplemented
294C2—21no—
295C2—21no—
296C2#1059242611yescharacteristic
297C2#1059243911yescharacteristic
298C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenter#324C3⋊D3
hypocenterC32#1470
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
247. C32#1470semidirect
293. C3#68128semidirect

Maximal subgroups

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

subgroupindex
C2×#640982
#105924182
#105924172
C32×#3242
#105893942
#105893352
#681283