Finite Group Databasebeta

← #11783426

Subgroups — #11783426

Order 1152.

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

normal subgroups only

This group has 686 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×#64286C211yesmaximal, characteristic
2C2×#63818C212yesmaximal
3#10590053C214yesmaximal, complemented
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6#64286—22no—
7#64286—22no—
8C2×C4⋊#157C2212yes—
9C2×C4×#157C412yes—
10C2×C3×#208—22no—
11C2×#3712C414yescomplemented
12#63818—22no—
13#63818—22no—
14#63818C414yescomplemented
15#63818C2214yes—
16C2×#3710—22no—
17C2×D3×M16—62no—
18C23×C3⋊D3C2×C411yescharacteristic
19C22×#157C2×C414yes—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C412yes—
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3D412yes—
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C22⋊#157—24no—
31C4⋊#157—24no—
32C4×#157—22no—
33C4×#157—22no—
34C3×#208—24no—
35C3×#208—24no—
36C2×C3×C3⋊C8—24no—
37#3712—24no—
38#3712C2×C418yes—
39#3710—24no—
40#3710—24no—
41#1742—91nomaximal, Sylow
42C22×C4×D3—62no—
43C2×C3×M16—62no—
44C2×#208—22no—
45D3×M16—64no—
46D3×M16—64no—
47D3×M16—64no—
48D3×M16—64no—
49C2×ΓL(1,𝔽25)—64no—
50C2×D3×C8—64no—
51C23×C32C4⋊C411yescharacteristic
52C22×C3⋊D3—42no—
53C22×C3⋊D3C4212yes—
54C22×C3⋊D3C22⋊C412yes—
55C22×C3⋊D3C4⋊C411yescharacteristic
56C22×C3⋊D3C22×C411yescharacteristic
57C2×#157—24no—
58C2×#157—44no—
59C2×C32×C4C22⋊C412yes—
60C2×C32×C4C22⋊C412yes—
61C2×C32×C4C4⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3C4⋊C411yescharacteristic
64C2×C3⋊Dic3C4⋊C412yes—
65C2×C3⋊Dic3C4⋊C412yes—
66C2×C3⋊Dic3C2×Q811yescharacteristic
67C4×C3⋊D3C4211yescharacteristic
68C4×C3⋊D3C4211yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3C22⋊C411yescharacteristic
71C4×C3⋊D3C22⋊C412yes—
72C4×C3⋊D3C22⋊C412yes—
73C4×C3⋊D3C4⋊C412yes—
74C4×C3⋊D3C4⋊C412yes—
75C4×C3⋊D3C22×C412yes—
76C4×C3⋊D3C2×D412yes—
77C3×C3⋊C8—28no—
78C22×M16—92no—
79C2×#117—91no—
80#343—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—
96C3×M16—64no—
97C3×M16—64no—
98C2×C3×C8—64no—
99#208—24no—
100#208—24no—
101C2×C3⋊C8—24no—
102ΓL(1,𝔽25)—68no—
103ΓL(1,𝔽25)—68no—
104D3×C8—68no—
105D3×C8—68no—
106C22×C32—41no—
107C22×C32#9512yes—
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⋊D3C2×C4211yescharacteristic
115C2×C3⋊D3C2×C22⋊C411yescharacteristic
116#157—44no—
117C32×C4#9511yescharacteristic
118C32×C4#9511yescharacteristic
119C32×C4C2×C22⋊C412yes—
120C3⋊Dic3#9511yescharacteristic
121C3⋊Dic3#9511yescharacteristic
122C3⋊Dic3C2×C4⋊C412yes—
123C23×C4—91no—
124C2×M16—62no—
125C2×M16—94no—
126C2×M16—94no—
127C2×M16—94no—
128C2×M16—182no—
129C2×M16—182no—
130C22×C8—182no—
131#117—182no—
132#117—182no—
133C2×C4⋊C4—92no—
134C2×C22⋊C4—92no—
135C2×C42—92no—
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×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C4×D3—62no—
157C4×D3—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—
172C3×C8—68no—
173C3⋊C8—28no—
174C2×C32—22no—
175C2×C32—21no—
176C2×C32C2×#9511yescharacteristic
177C3⋊D3—22no—
178C3⋊D3—21no—
179C3⋊D3#41312yes—
180C24—91no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—92no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4—94no—
191C22×C4GO+(4,𝔽2)11yescharacteristic
192M16—64no—
193M16—64no—
194M16—98no—
195M16—184no—
196C2×C8—64no—
197C2×C8—184no—
198C2×C8—184no—
199C4⋊C4—184no—
200C22⋊C4—184no—
201C42—182no—
202C42—182no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—44no—
207C2×D3—62no—
208C2×D3—62no—
209C2×D3—62no—
210C2×D3—62no—
211C2×D3—68no—
212C2×D3—124no—
213C2×D3—124no—
214C2×D3—124no—
215C2×D3—124no—
216C2×D3—124no—
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—22no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—62no—
225C32#174211yescharacteristic, complemented, Sylow
226C23—91no—
227C23—92no—
228C23—91no—
229C23—92no—
230C23—362no—
231C23#377311yescharacteristic
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—92no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—92no—
238C2×C4—92no—
239C2×C4—92no—
240C2×C4—91no—
241C2×C4—92no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—92no—
245C2×C4—91no—
246C2×C4—184no—
247C2×C4—364no—
248C2×C4D32⋊C412yes—
249C2×C4D32⋊C412yes—
250C2×C4#377311yescharacteristic
251C2×C4C2×GO+(4,𝔽2)11yescharacteristic
252C8—68no—
253C2×C3—24no—
254C2×C3—22no—
255C2×C3—42no—
256C2×C3—42no—
257D3—64no—
258D3—64no—
259D3—122no—
260D3—122no—
261C22—41no—
262C22—91no—
263C22—92no—
264C22—91no—
265C22—182no—
266C22—184no—
267C22—361no—
268C22—362no—
269C22#6373712yes—
270C22C2×#377311yescharacteristic
271C4—92no—
272C4—91no—
273C4—91no—
274C4—364no—
275C4#6373711yescharacteristic
276C4#6373711yescharacteristic
277C4C2×D32⋊C412yes—
278C3—22no—
279C2—21no—
280C2—22no—
281C2—92no—
282C2—182no—
283C2—181no—
284C2C2×#6373711yescharacteristic
subgroupG/H
centerC4#63737
commutatorC2×C3⋊D3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#95
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1742
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10590053C2semidirect
11. C2×#3712C4semidirect
14. #63818C4semidirect
225. C32#1742semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#638182
#105900532
#17429