Finite Group Databasebeta

← #11775322

Subgroups — #11775322

Order 1152.

822 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 181 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×#64133C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic
3#10592910C211yesmaximal, characteristic
4#10589333C214yesmaximal, complemented
5#69981—34nomaximal
6C23×C32×C4C2211yescharacteristic
7C22×#634C411yescharacteristic, complemented
8C2×C32×M16—21no—
9C2×#3757—21no—
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
12#64133—21no—
13#64133—21no—
14#64133C412yescomplemented
15#64133C2212yes—
16C2×#3750—21no—
17C32×C22⋊C8—21no—
18C32×C22⋊C8C2212yes—
19#63658—21no—
20#63658C2212yes—
21C2×#924—34no—
22C3×#407D314yes—
23#5211—34no—
24#4467—316no—
25C24×C32D411yescharacteristic
26C22×C32×C4—42no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—22no—
36C2×#634—21no—
37C2×#634—42no—
38C2×#634C2×C412yes—
39C32×M16—42no—
40C2×C32×C8—22no—
41#3757—22no—
42#3757—22no—
43#3757—42no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C412yes—
46#3750—22no—
47#3750—22no—
48#1511—91noSylow
49C23×C3×C4C2×D314yes—
50C22×Dic6—34no—
51C2×C3×M16—24no—
52C2×#217—64no—
53C2×#217—64no—
54C2×C4⋊Dic3—34no—
55#924—38no—
56#924—38no—
57#924—64no—
58#924—64no—
59C2×Dic3⋊C4—64no—
60C3×C22⋊C8—24no—
61C3×C22⋊C8C2×D318yes—
62C3⋊#95—38no—
63C3⋊#95—64no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32—41no—
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C2×D411yescharacteristic
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—42no—
83C2×C3⋊Dic3—42no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—42no—
86C2×C3⋊Dic3—42no—
87#634—42no—
88#634—42no—
89C32×C8—42no—
90C2×C22⋊Q8—91no—
91#407C3⋊D311yescharacteristic
92#381—91no—
93#328—94no—
94C24×C3D1214yes—
95C22×C3×C4—48no—
96C22×C3×C4C4×D314yes—
97C22×C3×C4C4×D314yes—
98C22×C3×C4D1214yes—
99C22×C3×C4#6714yes—
100C22×C3×C4#6714yes—
101C22×C3×C4C22×D314yes—
102C22×Dic3—64no—
103C22×Dic3—64no—
104C22×Dic3—68no—
105C2×Dic6—38no—
106C2×Dic6—64no—
107C2×Dic6—128no—
108C3×M16—48no—
109C2×C3×C8—28no—
110#217—68no—
111#217—68no—
112#217—128no—
113C4⋊Dic3—38no—
114C4⋊Dic3—64no—
115Dic3⋊C4—68no—
116Dic3⋊C4—68no—
117C22×C32—21no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—44no—
125C22×C32#9912yes—
126C22×C32C2×C22⋊C411yescharacteristic
127C22×C32#13712yes—
128C32×C4—21no—
129C32×C4—21no—
130C32×C4—21no—
131C32×C4—21no—
132C3⋊Dic3—42no—
133C3⋊Dic3—42no—
134C3⋊Dic3—82no—
135C22×Q8—91no—
136C23×C4C2×C3⋊D311yescharacteristic
137C2×M16—21no—
138C22⋊Q8—92no—
139C22⋊Q8—92no—
140C22⋊Q8—181no—
141C22⋊Q8—181no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—181no—
144C2×C22⋊C4—181no—
145C2×C22⋊C4—181no—
146C22⋊C8—21no—
147C22⋊C8C2×C3⋊D312yes—
148#95—92no—
149#95—181no—
150C23×C3—28no—
151C23×C3—28no—
152C23×C3—44no—
153C23×C3(C2×D3)⋊C414yes—
154C23×C3(C2×D3)⋊C414yes—
155C23×C3C2×D1214yes—
156C2×C3×C4—28no—
157C2×C3×C4—28no—
158C2×C3×C4—44no—
159C2×C3×C4—44no—
160C2×C3×C4—44no—
161C2×C3×C4—44no—
162C2×C3×C4(C2×D3)⋊C414yes—
163C2×C3×C4(C2×D3)⋊C414yes—
164C2×C3×C4C2×C4×D314yes—
165C2×C3×C4C2×#6714yes—
166C2×Dic3—68no—
167C2×Dic3—68no—
168C2×Dic3—128no—
169C2×Dic3—128no—
170C2×Dic3—128no—
171C2×Dic3—128no—
172C2×Dic3—128no—
173Dic6—128no—
174Dic6—128no—
175C3×C8—48no—
176C2×C32—22no—
177C2×C32—22no—
178C2×C32—41no—
179C2×C32C2×#9911yescharacteristic
180C2×C32#41911yescharacteristic
181C2×C32#42111yescharacteristic
182C24C4⋊(C3⋊D3)11yescharacteristic
183C2×Q8—92no—
184C2×Q8—181no—
185C2×Q8—362no—
186C22×C4—42no—
187C22×C4—181no—
188C22×C4—181no—
189C22×C4—182no—
190C22×C4C4×C3⋊D311yescharacteristic
191C22×C4C4×C3⋊D311yescharacteristic
192C22×C4C4⋊(C3⋊D3)11yescharacteristic
193C22×C4#63811yescharacteristic
194C22×C4#63811yescharacteristic
195C22×C4C22×C3⋊D311yescharacteristic
196M16—42no—
197C2×C8—22no—
198C4⋊C4—92no—
199C4⋊C4—181no—
200C4⋊C4—182no—
201C4⋊C4—182no—
202C22⋊C4—182no—
203C22⋊C4—182no—
204C22⋊C4—362no—
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—24no—
208C22×C3—24no—
209C22×C3—24no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—416no—
213C22×C3#80618yes—
214C22×C3#90918yes—
215C22×C3C2×(C2×D3)⋊C414yes—
216C3×C4—24no—
217C3×C4—24no—
218C3×C4—24no—
219C3×C4—24no—
220Dic3—128no—
221Dic3—128no—
222Dic3—248no—
223C32#151111yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—41no—
227C23#375211yescharacteristic
228C23#375211yescharacteristic
229C23C2×C4⋊(C3⋊D3)11yescharacteristic
230Q8—362no—
231Q8—362no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—182no—
239C2×C4—182no—
240C2×C4—362no—
241C2×C4—362no—
242C2×C4—362no—
243C2×C4—362no—
244C2×C4—362no—
245C2×C4#375211yescharacteristic
246C2×C4#375211yescharacteristic
247C2×C4C2×C4×C3⋊D311yescharacteristic
248C2×C4C2×#63811yescharacteristic
249C8—42no—
250C2×C3—28no—
251C2×C3—28no—
252C2×C3—44no—
253C2×C3C2×#80614yes—
254C2×C3#512014yes—
255C2×C3#513914yes—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—44no—
264C22#6363312yes—
265C22#6411812yes—
266C22C2×#375211yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—362no—
272C4—362no—
273C4—722no—
274C3#6998114yescomplemented
275C2—22no—
276C2—22no—
277C2—41no—
278C2C2×#6363311yescharacteristic
279C2#1059281911yescharacteristic
280C2#1059283811yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
4. #10589333C2semidirect
7. C22×#634C4semidirect
11. C2×C4⋊(C3⋊Dic3)C4semidirect
14. #64133C4semidirect
223. C32#1511semidirect
274. C3#69981semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C32×#4072
#105929102
#105893332
#699813