Finite Group Databasebeta

← #11786445

Subgroups — #11786445

Order 1152.

478 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 85 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
2#10593812C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4C2×#63746C212yesmaximal, complemented
5#10590093C212yesmaximal, complemented
6C23×#157—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×C4⋊#157—21no—
10C2×C4⋊#157—24no—
11C2×C4⋊#157C2211yescharacteristic
12C2×C4⋊#157C2211yescharacteristic
13C2×C4⋊#157C2212yes—
14C2×#3787C2212yes—
15C22⋊#622C412yescomplemented
16#63781—21no—
17#63778C412yescomplemented
18#63746—24no—
19C23×C3⋊D3D411yescharacteristic
20C22×#157—24no—
21C22×#157—22no—
22C22×#157—21no—
23C22×#157—21no—
24C22×#157—42no—
25C22×#157—42no—
26C22×C32×C4Q811yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3Q811yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C22⋊#157—42no—
35C2×#622C2×C414yescomplemented
36C4⋊#157—24no—
37C4⋊#157—22no—
38C4⋊#157—22no—
39C4⋊#157—22no—
40C4⋊#157D414yes—
41#3787—22no—
42#3787—22no—
43#1852—91nomaximal, Sylow
44C22×C4×D3—121no—
45C23×C32C4⋊C411yescharacteristic
46C22×C3⋊D3—21no—
47C22×C3⋊D3—21no—
48C22×C3⋊D3—21no—
49C22×C3⋊D3—21no—
50C22×C3⋊D3C4⋊C411yescharacteristic
51C22×C3⋊D3D812yes—
52C22×C3⋊D3Q1612yes—
53C22×C3⋊D3C2×D411yescharacteristic
54C2×#157—24no—
55C2×#157—48no—
56C2×#157—42no—
57C2×#157—42no—
58C2×#157—41no—
59C2×#157—41no—
60C2×#157—41no—
61C2×#157—41no—
62C2×#157—41no—
63C2×#157—41no—
64C2×C32×C4—22no—
65C2×C32×C4C4⋊C411yescharacteristic
66C2×C32×C4C2×Q811yescharacteristic
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3C4⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3—22no—
74C4×C3⋊D3C2×D412yes—
75C4×C3⋊D3#4112yes—
76#622—24no—
77C22×C4⋊C4—91no—
78C2×#107—92no—
79C2×C22⋊C8—91no—
80#380—91no—
81#340—92no—
82C23×D3—121no—
83C22×C3×C4—41no—
84C22×Dic3—121no—
85C2×C4×D3—121no—
86C2×C4×D3—121no—
87C2×C4×D3—121no—
88C2×C4×D3—121no—
89C2×C4×D3—124no—
90C2×C4×D3—124no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32#10712yescomplemented
94C22×C32C2×C4⋊C411yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—22no—
98C2×C3⋊D3—22no—
99C2×C3⋊D3—22no—
100C2×C3⋊D3—22no—
101C2×C3⋊D3#10712yescomplemented
102C2×C3⋊D3#12011yescharacteristic
103C2×C3⋊D3#12311yescharacteristic
104C2×C3⋊D3C2×D811yescharacteristic
105C2×C3⋊D3C2×Q1611yescharacteristic
106C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
107C2×C3⋊D3#13711yescharacteristic
108#157—44no—
109#157—81no—
110#157—81no—
111C32×C4—21no—
112C32×C4C22⋊Q812yes—
113C3⋊Dic3—21no—
114C3⋊Dic3C4×D412yes—
115C23×C4—91no—
116C23×C4—181no—
117C22×C8—92no—
118C2×C4⋊C4—92no—
119C2×C4⋊C4—91no—
120C2×C4⋊C4—91no—
121C2×C4⋊C4—184no—
122C2×C4⋊C4—181no—
123C2×C22⋊C4—181no—
124#107—184no—
125C22⋊C8—92no—
126C22⋊C8—92no—
127#95—181no—
128C23×C3—41no—
129C22×D3—121no—
130C22×D3—122no—
131C22×D3—122no—
132C22×D3—121no—
133C22×D3—122no—
134C22×D3—122no—
135C22×D3—122no—
136C22×D3—122no—
137C2×C3×C4—44no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×Dic3—121no—
141C2×Dic3—121no—
142C2×Dic3—124no—
143C4×D3—122no—
144C4×D3—122no—
145C4×D3—124no—
146C4×D3—122no—
147C4×D3—122no—
148C4×D3—124no—
149C2×C32—22no—
150C2×C32#38511yescharacteristic
151C2×C32C2×#10711yescharacteristic
152C2×C32#42811yescharacteristic
153C3⋊D3—22no—
154C3⋊D3#44711yescharacteristic
155C3⋊D3#45111yescharacteristic
156C3⋊D3#48011yescharacteristic
157C3⋊D3#48411yescharacteristic
158C24—91no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—182no—
165C22×C4—182no—
166C22×C4—182no—
167C22×C4—184no—
168C22×C4—181no—
169C22×C4—181no—
170C22×C4—362no—
171C22×C4—362no—
172C22×C4PSU(3,𝔽2)11yescharacteristic
173C2×C8—94no—
174C2×C8—182no—
175C2×C8—182no—
176C4⋊C4—94no—
177C4⋊C4—182no—
178C4⋊C4—182no—
179C4⋊C4—182no—
180C4⋊C4—184no—
181C22⋊C4—362no—
182C22×C3—42no—
183C22×C3—42no—
184C22×C3—42no—
185C22×C3—41no—
186C2×D3—121no—
187C2×D3—121no—
188C2×D3—122no—
189C2×D3—121no—
190C2×D3—121no—
191C2×D3—121no—
192C2×D3—121no—
193C2×D3—122no—
194C2×D3—124no—
195C2×D3—124no—
196C2×D3—124no—
197C2×D3—124no—
198C2×D3—122no—
199C3×C4—42no—
200C3×C4—42no—
201Dic3—122no—
202Dic3—122no—
203C32#185211yescharacteristic, complemented, Sylow
204C23—91no—
205C23—92no—
206C23—92no—
207C23—91no—
208C23—181no—
209C23—181no—
210C23—181no—
211C23—181no—
212C23#377711yescharacteristic
213C2×C4—22no—
214C2×C4—91no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—182no—
219C2×C4—181no—
220C2×C4—181no—
221C2×C4—182no—
222C2×C4—182no—
223C2×C4—184no—
224C2×C4—362no—
225C2×C4—362no—
226C2×C4—368no—
227C2×C4—361no—
228C2×C4—361no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4#377711yescharacteristic
234C2×C4C2×PSU(3,𝔽2)11yescharacteristic
235C8—184no—
236C2×C3—44no—
237C2×C3—41no—
238C2×C3—41no—
239C2×C3—41no—
240D3—121no—
241D3—121no—
242D3—121no—
243D3—121no—
244D3—124no—
245C22—21no—
246C22—21no—
247C22—91no—
248C22—91no—
249C22—91no—
250C22—91no—
251C22—91no—
252C22—91no—
253C22—92no—
254C22—182no—
255C22—182no—
256C22—182no—
257C22—182no—
258C22—181no—
259C22—181no—
260C22#6374612yescomplemented
261C22C2×#377711yescharacteristic
262C4—21no—
263C4—92no—
264C4—181no—
265C4—364no—
266C4—721no—
267C4—721no—
268C4C22⋊PSU(3,𝔽2)12yes—
269C3—41no—
270C2—22no—
271C2—91no—
272C2—91no—
273C2—91no—
274C2—91no—
275C2—182no—
276C2C2×#6374611yescharacteristic
277C2#1059354411yescharacteristic
278C2#1059356911yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
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#1852
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63746C2semidirect
5. #10590093C2semidirect
15. C22⋊#622C4semidirect
17. #63778C4semidirect
35. C2×#622C2×C4semidirect
93. C22×C32#107semidirect
101. C2×C3⋊D3#107semidirect
203. C32#1852semidirect
260. C22#63746semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
#105938122
#105938002
C2×#637462
#105900932
#18529