Finite Group Databasebeta

← #11783146

Subgroups — #11783146

Order 1152.

734 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 125 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×#64283C211yesmaximal, characteristic
2#10594969C212yesmaximal
3#10590073C214yesmaximal, complemented
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3792C2212yes—
6#64283—22no—
7#64283—22no—
8C2×#3788C412yescomplemented
9C2×#3787C412yescomplemented
10C3×#926—22no—
11#63974—22no—
12#63957C2214yes—
13#63900—22no—
14C4×#624C414yescomplemented
15#63874—22no—
16#63849C414yescomplemented
17D3×#117—62no—
18C23×C3⋊D3D411yescharacteristic
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C412yes—
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3D412yes—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3Q811yescharacteristic
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×#624—24no—
30#3792—24no—
31C2×#622C2×C414yescomplemented
32#3788—24no—
33#3787—22no—
34#3787—22no—
35C3×#217—24no—
36C3×C4⋊Dic3—24no—
37C3×C4×Dic3—24no—
38#3724—24no—
39#3722—24no—
40Dic32C2×C418yescomplemented
41C2×H(3,ℤ/4)—91nomaximal, Sylow
42C22×C4×D3—62no—
43C3×#117—62no—
44#926—22no—
45#892—64no—
46D3×C4⋊C4—64no—
47D3×C22⋊C4—64no—
48#877—64no—
49#872—64no—
50C42×D3—64no—
51C23×C32C2×D411yescharacteristic
52C22×C3⋊D3—42no—
53C22×C3⋊D3C22⋊C412yes—
54C22×C3⋊D3C22⋊C412yes—
55C22×C3⋊D3C4⋊C411yescharacteristic
56C22×C3⋊D3C4⋊C411yescharacteristic
57C2×C32×C4C22⋊C412yes—
58C2×C32×C4C22⋊C412yes—
59C2×C32×C4C4⋊C411yescharacteristic
60C2×C32×C4C4⋊C411yescharacteristic
61C2×C3⋊Dic3C22×C411yescharacteristic
62C2×C3⋊Dic3C22×C412yes—
63C2×C3⋊Dic3C2×D412yes—
64C2×C3⋊Dic3C2×Q811yescharacteristic
65C4×C3⋊D3C4211yescharacteristic
66C4×C3⋊D3C4212yes—
67C4×C3⋊D3C4211yescharacteristic
68C4×C3⋊D3C22⋊C411yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3C22⋊C412yes—
71C4×C3⋊D3C4⋊C412yes—
72C4×C3⋊D3C4⋊C412yes—
73C4×C3⋊D3C4⋊C412yes—
74C4×C3⋊D3C4⋊C412yes—
75C2×C3×Dic3—28no—
76#624—48no—
77#622—24no—
78C22×M16—91no—
79C2×#117—92no—
80H(3,ℤ/4)—94no—
81C23×D3—62no—
82C22×C3×C4—22no—
83C22×Dic3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—68no—
97C3×C4⋊C4—64no—
98C3×C22⋊C4—64no—
99C3×C42—64no—
100#217—24no—
101(C2×D3)⋊C4—68no—
102C4⋊Dic3—24no—
103Dic3⋊C4—68no—
104C4×Dic3—24no—
105C4×Dic3—68no—
106C22×C32—41no—
107C22×C32C2×C22⋊C412yes—
108C22×C32C2×C4⋊C411yescharacteristic
109C2×C3⋊D3—24no—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—42no—
112C2×C3⋊D3—41no—
113C2×C3⋊D3#9512yes—
114C2×C3⋊D3#9511yescharacteristic
115C2×C3⋊D3#9511yescharacteristic
116C32×C4#9511yescharacteristic
117C32×C4#9512yes—
118C32×C4#9511yescharacteristic
119C3⋊Dic3C2×C4211yescharacteristic
120C3⋊Dic3C2×C22⋊C411yescharacteristic
121C3⋊Dic3C2×C4⋊C412yes—
122C3×Dic3—48no—
123C23×C4—91no—
124C2×M16—92no—
125C2×M16—92no—
126C2×M16—182no—
127C2×M16—182no—
128C22×C8—92no—
129#117—62no—
130#117—94no—
131#117—94no—
132#117—182no—
133C2×C4⋊C4—182no—
134C2×C22⋊C4—182no—
135C2×C42—94no—
136C23×C3—22no—
137C22×D3—62no—
138C22×D3—62no—
139C22×D3—62no—
140C22×D3—62no—
141C22×D3—62no—
142C22×D3—62no—
143C22×D3—128no—
144C2×C3×C4—22no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—68no—
151C2×Dic3—28no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C4×D3—62no—
159C4×D3—62no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—62no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—1216no—
175C2×C32—22no—
176C2×C32—21no—
177C2×C32C2×#9511yescharacteristic
178C3⋊D3—22no—
179C3⋊D3—21no—
180C3⋊D3H(3,ℤ/4)12yescomplemented
181C24—91no—
182C22×C4—91no—
183C22×C4—92no—
184C22×C4—92no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—184no—
192C22×C4GO+(4,𝔽2)11yescharacteristic
193M16—184no—
194M16—184no—
195C2×C8—94no—
196C2×C8—182no—
197C2×C8—182no—
198C4⋊C4—64no—
199C4⋊C4—184no—
200C22⋊C4—64no—
201C22⋊C4—184no—
202C42—64no—
203C42—98no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—44no—
208C2×D3—62no—
209C2×D3—62no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—68no—
213C2×D3—124no—
214C2×D3—124no—
215C2×D3—124no—
216C2×D3—124no—
217C2×D3—124no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—22no—
222C3×C4—128no—
223Dic3—48no—
224Dic3—62no—
225Dic3—62no—
226Dic3—62no—
227Dic3—62no—
228C32C2×H(3,ℤ/4)11yescharacteristic, complemented, Sylow
229C23—92no—
230C23—91no—
231C23—92no—
232C23—91no—
233C23—362no—
234C23C2×GO+(4,𝔽2)11yescharacteristic
235C2×C4—68no—
236C2×C4—92no—
237C2×C4—92no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—91no—
241C2×C4—92no—
242C2×C4—92no—
243C2×C4—92no—
244C2×C4—92no—
245C2×C4—91no—
246C2×C4—92no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—92no—
250C2×C4—368no—
251C2×C4D32⋊C412yes—
252C2×C4D32⋊C412yes—
253C2×C4#377311yescharacteristic
254C2×C4#377311yescharacteristic
255C8—184no—
256C2×C3—24no—
257C2×C3—22no—
258C2×C3—42no—
259C2×C3—42no—
260D3—64no—
261D3—64no—
262D3—122no—
263D3—122no—
264C22—41no—
265C22—91no—
266C22—92no—
267C22—91no—
268C22—184no—
269C22—182no—
270C22—362no—
271C22—361no—
272C22C2×D32⋊C412yes—
273C22C2×#377311yescharacteristic
274C4—91no—
275C4—91no—
276C4—92no—
277C4—128no—
278C4#6373711yescharacteristic
279C4#6373712yes—
280C4#6373711yescharacteristic
281C3—22no—
282C2—22no—
283C2—21no—
284C2—92no—
285C2—182no—
286C2—181no—
287C2C2×#6373711yescharacteristic
subgroupG/H
centerC4#63737
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#95
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×H(3,ℤ/4)
LCSG ▷ C3⋊Dic3 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10590073C2semidirect
8. C2×#3788C4semidirect
9. C2×#3787C4semidirect
14. C4×#624C4semidirect
16. #63849C4semidirect
31. C2×#622C2×C4semidirect
40. Dic32C2×C4semidirect
180. C3⋊D3H(3,ℤ/4)semidirect
228. C32C2×H(3,ℤ/4)semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
#105949692
#105900732
C2×H(3,ℤ/4)9