Finite Group Databasebeta

← #11783083

Subgroups — #11783083

Order 1152.

778 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×C4×#157C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C2×M16×C3⋊D3C211yesmaximal, characteristic
4#10590181C214yesmaximal, complemented
5C23×#157C412yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3792C412yescomplemented
8C2×C4×#157—22no—
9C2×C4×#157—22no—
10C2×C4×#157C412yes—
11C2×C4×#157C2212yes—
12#64283—22no—
13#64283—22no—
14C2×#3788C412yescomplemented
15C2×#3787C2212yes—
16C2×C32×M16C411yescharacteristic, complemented
17C2×#3748C411yescharacteristic, complemented
18M16×C3⋊D3—22no—
19M16×C3⋊D3—22no—
20C2×#3743C412yescomplemented
21C2×C8×C3⋊D3C2212yes—
22C2×D3×M16—62no—
23C23×C3⋊D3C2×C411yescharacteristic
24C22×#157—24no—
25C22×#157—28no—
26C22×#157C2×C414yes—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3Q812yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37#3792—24no—
38C2×#622C2×C414yescomplemented
39C4×#157—24no—
40C4×#157—22no—
41C4×#157—22no—
42#3788—24no—
43#3787—22no—
44#3787—22no—
45C32×M16—22no—
46C2×C32×C8C2×C412yescomplemented
47#3748—22no—
48C2×C3⋊(C3⋊C8)C2×C412yescomplemented
49#3743—24no—
50C8×C3⋊D3—22no—
51C8×C3⋊D3—22no—
52#1728—91nomaximal, Sylow
53C22×C4×D3—62no—
54C2×C3×M16—22no—
55C2×#208—62no—
56D3×M16—68no—
57D3×M16—68no—
58C2×ΓL(1,𝔽25)—64no—
59C2×D3×C8—64no—
60C23×C32C4211yescharacteristic
61C22×C3⋊D3—24no—
62C22×C3⋊D3C4211yescharacteristic
63C22×C3⋊D3C22⋊C412yes—
64C22×C3⋊D3C4⋊C412yes—
65C22×C3⋊D3C22×C411yescharacteristic
66C2×#157—216no—
67C2×#157—24no—
68C2×#157—24no—
69C2×#157M1618yescomplemented
70C2×C32×C4C4211yescharacteristic
71C2×C32×C4C22⋊C412yes—
72C2×C32×C4C4⋊C412yes—
73C2×C32×C4C22×C411yescharacteristic
74C2×C3⋊Dic3C4211yescharacteristic
75C2×C3⋊Dic3C22⋊C412yes—
76C2×C3⋊Dic3C4⋊C412yes—
77C2×C3⋊Dic3C22×C411yescharacteristic
78C4×C3⋊D3C22⋊C412yes—
79C4×C3⋊D3C22⋊C412yes—
80C4×C3⋊D3C22⋊C412yes—
81C4×C3⋊D3C4⋊C412yes—
82C4×C3⋊D3C4⋊C412yes—
83C4×C3⋊D3C4⋊C412yes—
84C4×C3⋊D3C2×D411yescharacteristic
85C4×C3⋊D3C2×D411yescharacteristic
86C4×C3⋊D3C2×D411yescharacteristic
87C4×C3⋊D3C2×Q811yescharacteristic
88#622—24no—
89C32×C8—22no—
90C3⋊(C3⋊C8)—22no—
91C22×M16—91no—
92C22×M16—91no—
93C22×C42—91no—
94#336—94no—
95C23×D3—62no—
96C22×C3×C4—22no—
97C22×Dic3—62no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—64no—
101C2×C4×D3—64no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C3×M16—28no—
107C2×C3×C8—24no—
108#208—68no—
109C2×C3⋊C8—64no—
110ΓL(1,𝔽25)—616no—
111D3×C8—68no—
112D3×C8—68no—
113C22×C32—22no—
114C22×C32#9512yes—
115C22×C32C2×C4211yescharacteristic
116C2×C3⋊D3—22no—
117C2×C3⋊D3—24no—
118C2×C3⋊D3—24no—
119C2×C3⋊D3#9512yes—
120C2×C3⋊D3C2×C22⋊C411yescharacteristic
121C2×C3⋊D3C2×C4⋊C411yescharacteristic
122C2×C3⋊D3C2×M1614yes—
123#157—28no—
124C32×C4#9512yes—
125C32×C4C2×C22⋊C411yescharacteristic
126C32×C4C2×C4⋊C411yescharacteristic
127C3⋊Dic3#9512yes—
128C3⋊Dic3C2×C22⋊C411yescharacteristic
129C3⋊Dic3C2×C4⋊C411yescharacteristic
130C23×C4—91no—
131C23×C4—92no—
132C2×M16—92no—
133C2×M16—92no—
134C2×M16—91no—
135C2×M16—92no—
136C2×M16—182no—
137C2×M16—182no—
138C2×M16—182no—
139C2×M16—182no—
140C2×M16#15711yescharacteristic, complemented
141C22×C8—92no—
142C22×C8—92no—
143C2×C42—92no—
144C2×C42—92no—
145C2×C42—182no—
146C2×C42—182no—
147C23×C3—22no—
148C22×D3—62no—
149C22×D3—62no—
150C22×D3—64no—
151C22×D3—64no—
152C22×D3—128no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—24no—
156C2×C3×C4—24no—
157C2×Dic3—62no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—62no—
161C4×D3—64no—
162C4×D3—64no—
163C4×D3—64no—
164C4×D3—64no—
165C4×D3—64no—
166C4×D3—64no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—62no—
170C4×D3—62no—
171C3×C8—28no—
172C3⋊C8—68no—
173C2×C32—22no—
174C2×C32C2×#9511yescharacteristic
175C2×C32C4×M1612yes—
176C3⋊D3—22no—
177C3⋊D3#40712yes—
178C3⋊D3#42312yes—
179C24—91no—
180C22×C4—91no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—94no—
190C22×C4—188no—
191C22×C4—184no—
192C22×C4C2×#15711yescharacteristic
193M16—22no—
194M16—184no—
195M16—184no—
196M16—184no—
197M16—182no—
198C2×C8—94no—
199C2×C8—92no—
200C2×C8—182no—
201C2×C8—182no—
202C2×C8—182no—
203C2×C8—182no—
204C2×C8C2×#15712yescomplemented
205C42—182no—
206C42—184no—
207C42—182no—
208C22×C3—22no—
209C22×C3—24no—
210C22×C3—44no—
211C2×D3—62no—
212C2×D3—62no—
213C2×D3—68no—
214C2×D3—64no—
215C2×D3—128no—
216C2×D3—128no—
217C2×D3—124no—
218C3×C4—22no—
219C3×C4—24no—
220C3×C4—22no—
221Dic3—64no—
222Dic3—62no—
223Dic3—62no—
224C32#172811yescharacteristic, complemented, Sylow
225C23—91no—
226C23—91no—
227C23—92no—
228C23—92no—
229C23—184no—
230C23C4×#15711yescharacteristic
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—92no—
234C2×C4—92no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—92no—
238C2×C4—92no—
239C2×C4—92no—
240C2×C4—92no—
241C2×C4—92no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—92no—
245C2×C4—98no—
246C2×C4—184no—
247C2×C4—184no—
248C2×C4—1816no—
249C2×C4C4×#15711yescharacteristic
250C2×C4C4⋊#15712yes—
251C2×C4C22⋊#15712yes—
252C2×C4C22×#15711yescharacteristic
253C8—22no—
254C8—184no—
255C8—182no—
256C2×C3—22no—
257C2×C3—24no—
258C2×C3—44no—
259D3—64no—
260D3—64no—
261D3—124no—
262C22—22no—
263C22—91no—
264C22—91no—
265C22—94no—
266C22—92no—
267C22—184no—
268C22—184no—
269C22—182no—
270C22#6378112yes—
271C22C2×C4×#15711yescharacteristic
272C4—91no—
273C4—91no—
274C4—92no—
275C4—188no—
276C4#6378112yes—
277C4C2×C4⋊#15711yescharacteristic
278C4C2×C22⋊#15711yescharacteristic
279C3—22no—
280C2—22no—
281C2—92no—
282C2—92no—
283C2—182no—
284C2M16×#15712yes—
285C2C2×#6378111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C2×C42
FittingC2×C32×M16C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×M16#157
hypocenterC32#1728
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10590181C2semidirect
7. C2×#3792C4semidirect
14. C2×#3788C4semidirect
16. C2×C32×M16C4semidirect
17. C2×#3748C4semidirect
20. C2×#3743C4semidirect
38. C2×#622C2×C4semidirect
46. C2×C32×C8C2×C4semidirect
48. C2×C3⋊(C3⋊C8)C2×C4semidirect
69. C2×#157M16semidirect
140. C2×M16#157semidirect
204. C2×C8C2×#157semidirect
224. C32#1728semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C2×#642832
C2×M16×C3⋊D32
#105901812
#17289