Finite Group Databasebeta

← #11783297

Subgroups — #11783297

Order 1152.

566 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 135 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
2C22×C4⋊#157C211yesmaximal, characteristic
3C2×#64283C211yesmaximal, characteristic
4#10590093C214yesmaximal, complemented
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×#3792C412yescomplemented
9#64286—22no—
10#64286C414yescomplemented
11C2×C4⋊#157—22no—
12C2×C4⋊#157—21no—
13C2×C4⋊#157C414yescomplemented
14C2×C4⋊#157C2212yes—
15C2×C4⋊#157C2212yes—
16C2×C4×#157—21no—
17#64283—22no—
18#64283—22no—
19C2×#3788C412yescomplemented
20C2×#3787C2212yes—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—24no—
23C22×#157—22no—
24C22×#157—22no—
25C22×#157—44no—
26C22×C32×C4Q811yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3Q811yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C22⋊#157—24no—
37#3792—24no—
38C2×#622C2×C414yescomplemented
39C4⋊#157—24no—
40C4⋊#157—22no—
41C4⋊#157—22no—
42C4⋊#157C2×C414yes—
43C4⋊#157C2×C414yescomplemented
44C4×#157—24no—
45#3788—24no—
46#3787—22no—
47#3787—22no—
48#1736—91nomaximal, Sylow
49C22×C4×D3—121no—
50C23×C32C4⋊C411yescharacteristic
51C22×C3⋊D3—22no—
52C22×C3⋊D3—22no—
53C22×C3⋊D3C22⋊C412yes—
54C22×C3⋊D3C22⋊C412yes—
55C22×C3⋊D3C4⋊C411yescharacteristic
56C22×C3⋊D3C2×D411yescharacteristic
57C2×#157—24no—
58C2×#157—24no—
59C2×#157—48no—
60C2×#157—42no—
61C2×#157—44no—
62C2×#157—42no—
63C2×C32×C4C4⋊C411yescharacteristic
64C2×C32×C4C4⋊C412yes—
65C2×C32×C4C4⋊C412yes—
66C2×C32×C4C2×Q811yescharacteristic
67C2×C3⋊Dic3C4212yes—
68C2×C3⋊Dic3C22⋊C412yes—
69C2×C3⋊Dic3C4⋊C411yescharacteristic
70C2×C3⋊Dic3C22×C411yescharacteristic
71C4×C3⋊D3C4212yes—
72C4×C3⋊D3C22⋊C412yes—
73C4×C3⋊D3C22⋊C412yes—
74C4×C3⋊D3C22⋊C412yes—
75C4×C3⋊D3C4⋊C412yes—
76C4×C3⋊D3C4⋊C412yes—
77C4×C3⋊D3C22×C411yescharacteristic
78C4×C3⋊D3C22×C411yescharacteristic
79C4×C3⋊D3C2×D411yescharacteristic
80C4×C3⋊D3C2×D411yescharacteristic
81#622—24no—
82C22×M16—91no—
83C2×#117—91no—
84C22×C4⋊C4—91no—
85#340—94no—
86C23×D3—121no—
87C22×C3×C4—41no—
88C22×Dic3—121no—
89C2×C4×D3—122no—
90C2×C4×D3—122no—
91C2×C4×D3—121no—
92C2×C4×D3—121no—
93C2×C4×D3—122no—
94C2×C4×D3—122no—
95C2×C4×D3—121no—
96C2×C4×D3—121no—
97C22×C32—22no—
98C22×C32#9512yes—
99C22×C32C2×C4⋊C411yescharacteristic
100C2×C3⋊D3—22no—
101C2×C3⋊D3—24no—
102C2×C3⋊D3—22no—
103C2×C3⋊D3—22no—
104C2×C3⋊D3#9512yes—
105C2×C3⋊D3C2×C22⋊C411yescharacteristic
106C2×C3⋊D3C2×C22⋊C411yescharacteristic
107C2×C3⋊D3AGL(1,ℤ/8)12yes—
108C2×C3⋊D3#13712yes—
109#157—44no—
110#157—44no—
111C32×C4#9512yes—
112C32×C4C2×C4⋊C411yescharacteristic
113C32×C4C2×C4⋊C411yescharacteristic
114C3⋊Dic3#9512yes—
115C3⋊Dic3C2×C4211yescharacteristic
116C3⋊Dic3C2×C22⋊C411yescharacteristic
117C23×C4—91no—
118C23×C4—181no—
119C2×M16—92no—
120C2×M16—92no—
121C2×M16—182no—
122C2×M16—182no—
123C22×C8—92no—
124#117—94no—
125#117—182no—
126C2×C4⋊C4—94no—
127C2×C4⋊C4—92no—
128C2×C4⋊C4—92no—
129C2×C4⋊C4—181no—
130C2×C4⋊C4—182no—
131C2×C22⋊C4—181no—
132C2×C42—181no—
133C23×C3—41no—
134C22×D3—122no—
135C22×D3—122no—
136C22×D3—121no—
137C22×D3—121no—
138C22×D3—124no—
139C22×D3—124no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—42no—
143C2×C3×C4—42no—
144C2×Dic3—122no—
145C2×Dic3—122no—
146C2×Dic3—121no—
147C2×Dic3—121no—
148C4×D3—122no—
149C4×D3—122no—
150C4×D3—122no—
151C4×D3—122no—
152C4×D3—122no—
153C4×D3—122no—
154C4×D3—121no—
155C4×D3—121no—
156C4×D3—121no—
157C4×D3—121no—
158C2×C32—22no—
159C2×C32C2×#9511yescharacteristic
160C2×C32#42812yes—
161C3⋊D3—22no—
162C3⋊D3#41712yes—
163C3⋊D3#41811yescharacteristic
164C3⋊D3#41911yescharacteristic
165C24—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—91no—
170C22×C4—92no—
171C22×C4—92no—
172C22×C4—92no—
173C22×C4—92no—
174C22×C4—91no—
175C22×C4—182no—
176C22×C4—182no—
177C22×C4—184no—
178C22×C4—364no—
179C22×C4PSU(3,𝔽2)11yescharacteristic
180M16—184no—
181M16—184no—
182C2×C8—94no—
183C2×C8—182no—
184C2×C8—182no—
185C4⋊C4—94no—
186C4⋊C4—94no—
187C4⋊C4—184no—
188C4⋊C4—182no—
189C4⋊C4—182no—
190C22⋊C4—184no—
191C42—184no—
192C22×C3—44no—
193C22×C3—42no—
194C22×C3—41no—
195C2×D3—122no—
196C2×D3—121no—
197C2×D3—121no—
198C2×D3—122no—
199C2×D3—122no—
200C2×D3—124no—
201C2×D3—128no—
202C2×D3—124no—
203C2×D3—124no—
204C3×C4—42no—
205C3×C4—41no—
206C3×C4—41no—
207Dic3—122no—
208Dic3—121no—
209Dic3—121no—
210C32#173611yescharacteristic, complemented, Sylow
211C23—91no—
212C23—92no—
213C23—92no—
214C23—91no—
215C23—182no—
216C23—182no—
217C23#377711yescharacteristic
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—92no—
223C2×C4—92no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—92no—
231C2×C4—92no—
232C2×C4—184no—
233C2×C4—184no—
234C2×C4—364no—
235C2×C4—362no—
236C2×C4—362no—
237C2×C4—368no—
238C2×C4#377711yescharacteristic
239C2×C4#377712yes—
240C2×C4#377712yes—
241C2×C4C2×PSU(3,𝔽2)11yescharacteristic
242C8—184no—
243C2×C3—44no—
244C2×C3—42no—
245C2×C3—41no—
246D3—122no—
247D3—121no—
248D3—121no—
249D3—124no—
250C22—22no—
251C22—92no—
252C22—92no—
253C22—91no—
254C22—91no—
255C22—92no—
256C22—182no—
257C22—184no—
258C22—182no—
259C22—182no—
260C22#6374712yes—
261C22C2×#377711yescharacteristic
262C4—91no—
263C4—92no—
264C4—91no—
265C4—364no—
266C4—364no—
267C4#6374712yes—
268C4C2×#377711yescharacteristic
269C4C2×#377711yescharacteristic
270C3—41no—
271C2—22no—
272C2—91no—
273C2—92no—
274C2—91no—
275C2—182no—
276C2#1059354412yes—
277C2C2×#6374711yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#1736
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590093C2semidirect
8. C2×#3792C4semidirect
10. #64286C4semidirect
13. C2×C4⋊#157C4semidirect
19. C2×#3788C4semidirect
38. C2×#622C2×C4semidirect
43. C4⋊#157C2×C4semidirect
210. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C22×C4⋊#1572
C2×#642832
#105900932
#17369