Finite Group Databasebeta

← #11785110

Subgroups — #11785110

Order 1152.

1008 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 227 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C32×#100C211yesmaximal, characteristic
3C2×#63660C211yesmaximal, characteristic
4#10592817C212yesmaximal, complemented
5#10589420C212yesmaximal, complemented
6#70063—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C23×C3⋊Dic3C412yes—
9C2×C32×M16C2212yes—
10C2×#3757C412yes—
11D4×C3⋊Dic3—22no—
12D4×C3⋊Dic3—22no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2212yes—
16C32×#100—22no—
17#63660—22no—
18#63641—22no—
19#63641—22no—
20C2×D4×Dic3—34no—
21C2×C3×#100D314yes—
22C2×#833—34no—
23#5118—38no—
24#4554—38no—
25C24×C32C2×C412yes—
26C2×C32×D4—22no—
27C2×C32×D4—22no—
28C2×C32×D4D412yes—
29C2×C32×D4Q812yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—22no—
32C22×C3⋊Dic3—22no—
33C22×C3⋊Dic3—44no—
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C412yes—
36C22×C3⋊Dic3C2×C411yescharacteristic
37C32×M16—22no—
38C32×M16—22no—
39C2×C32×C8—22no—
40#3757—24no—
41C4⋊(C3⋊Dic3)—22no—
42C4×C3⋊Dic3D412yes—
43C4×C3⋊Dic3D412yes—
44#3748—22no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—22no—
47#1800—91noSylow
48C22×C3×D4C2×D314yes—
49C23×Dic3—38no—
50C2×C3×M16C2×D318yes—
51C2×#217—38no—
52D4×Dic3—68no—
53D4×Dic3—68no—
54C2×C4⋊Dic3—34no—
55C2×C4×Dic3—34no—
56C2×#208—38no—
57C3×#100—28no—
58#833—68no—
59Dic3⋊C8—68no—
60Dic3⋊C8—68no—
61C23×C32—22no—
62C23×C32—22no—
63C23×C32—42no—
64C23×C32—42no—
65C23×C32C4⋊C414yes—
66C23×C32C22×C411yescharacteristic
67C32×D4—24no—
68C32×D4—24no—
69C2×C32×C4C2×D412yes—
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×Q811yescharacteristic
72C2×C32×C4#4112yes—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—44no—
77C2×C3⋊Dic3—44no—
78C2×C3⋊Dic3—42no—
79C2×C3⋊Dic3C22⋊C412yes—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C32×C8—42no—
83C3⋊(C3⋊C8)—42no—
84C2×C4×D4—91no—
85#423—92no—
86C2×#100—91no—
87C2×#100C3⋊D311yescharacteristic
88#343—92no—
89C24×C3C4×D318yes—
90C2×C3×D4—28no—
91C2×C3×D4—28no—
92C2×C3×D4Dic618yes—
93C2×C3×D4#6718yes—
94C22×C3×C4C22×D314yes—
95C22×Dic3—34no—
96C22×Dic3—34no—
97C22×Dic3—38no—
98C22×Dic3—68no—
99C22×Dic3—68no—
100C22×Dic3—1216no—
101C3×M16—28no—
102C3×M16—28no—
103C2×C3×C8—28no—
104#217—616no—
105C4⋊Dic3—68no—
106C4×Dic3—38no—
107C4×Dic3—38no—
108#208—68no—
109#208—68no—
110C2×C3⋊C8—68no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—24no—
114C22×C32—44no—
115C22×C32—44no—
116C22×C32—42no—
117C22×C32—42no—
118C22×C32C2×C22⋊C411yescharacteristic
119C22×C32C2×C4⋊C411yescharacteristic
120C22×C32#11711yescharacteristic
121C32×C4#12112yes—
122C32×C4C22⋊Q812yes—
123C3⋊Dic3—21no—
124C3⋊Dic3—22no—
125C3⋊Dic3—42no—
126C3⋊Dic3#10012yescomplemented
127C22×D4C2×C3⋊D311yescharacteristic
128C23×C4—92no—
129C2×M16—92no—
130C2×M16C2×C3⋊D312yes—
131C4×D4—182no—
132C4×D4—182no—
133C2×C4⋊C4—91no—
134C2×C22⋊C4—92no—
135C2×C42—91no—
136C4⋊C8—182no—
137C4⋊C8—182no—
138#100—22no—
139#100—182no—
140C23×C3—28no—
141C23×C3—28no—
142C23×C3—48no—
143C23×C3—48no—
144C23×C3Dic3⋊C4116yes—
145C23×C3C2×C4×D314yes—
146C3×D4—216no—
147C3×D4—216no—
148C2×C3×C4C2×Dic614yes—
149C2×C3×C4D3×D418yes—
150C2×C3×C4#23718yes—
151C2×C3×C4C2×#6714yes—
152C2×Dic3—34no—
153C2×Dic3—38no—
154C2×Dic3—34no—
155C2×Dic3—68no—
156C2×Dic3—68no—
157C2×Dic3—1216no—
158C2×Dic3—124no—
159C2×Dic3—1216no—
160C2×Dic3—128no—
161C3×C8—48no—
162C3⋊C8—128no—
163C2×C32—21no—
164C2×C32—21no—
165C2×C32—44no—
166C2×C32#38011yescharacteristic
167C2×C32C2×#10011yescharacteristic
168C2×C32#41311yescharacteristic
169C24C4×C3⋊D312yes—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4#63412yes—
173C2×D4#63812yes—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—92no—
177C22×C4—182no—
178C22×C4—182no—
179C22×C4—364no—
180C22×C4C22×C3⋊D311yescharacteristic
181M16—22no—
182M16—22no—
183M16—182no—
184M16—182no—
185C2×C8—22no—
186C2×C8—182no—
187C4⋊C4—182no—
188C22⋊C4—184no—
189C42—92no—
190C42—92no—
191C22×C3—24no—
192C22×C3—24no—
193C22×C3—216no—
194C22×C3—416no—
195C22×C3—416no—
196C22×C3—48no—
197C22×C3—48no—
198C22×C3#87714yes—
199C22×C3D3×C22⋊C414yes—
200C22×C3C2×Dic3⋊C414yes—
201C3×C4#87818yes—
202C3×C4#93918yes—
203Dic3—38no—
204Dic3—64no—
205Dic3—68no—
206Dic3—128no—
207C32#180011yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—42no—
211C23—42no—
212C23#375014yes—
213C23C2×C4×C3⋊D311yescharacteristic
214D4—24no—
215D4—24no—
216C2×C4—91no—
217C2×C4—92no—
218C2×C4—91no—
219C2×C4—182no—
220C2×C4—182no—
221C2×C4—364no—
222C2×C4—361no—
223C2×C4—364no—
224C2×C4—362no—
225C2×C4C2×#63411yescharacteristic
226C2×C4D4×C3⋊D312yes—
227C2×C4#383012yes—
228C2×C4C2×#63811yescharacteristic
229C8—42no—
230C8—362no—
231C2×C3—24no—
232C2×C3—24no—
233C2×C3—416no—
234C2×C3D3×#10014yes—
235C2×C3#474514yes—
236C2×C3#494214yes—
237C22—21no—
238C22—21no—
239C22—24no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22#6408611yescharacteristic
245C22C22⋊C4×C3⋊D311yescharacteristic
246C22C2×#375011yescharacteristic
247C4—92no—
248C4—181no—
249C4—182no—
250C4—362no—
251C4#6408712yes—
252C4#6414812yes—
253C3#7006314yescomplemented
254C2—21no—
255C2—21no—
256C2—44no—
257C2C3⋊D3×#10011yescharacteristic
258C2#1059244411yescharacteristic
259C2#1059264111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#100C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C22
cosocleC22×C32×C4C23
hypercenterC2×#100C3⋊D3
hypocenterC32#1800
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
4. #10592817C2semidirect
5. #10589420C2semidirect
126. C3⋊Dic3#100semidirect
207. C32#1800semidirect
253. C3#70063semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C32×#1002
C2×#636602
#105928172
#105894202
#700633