Finite Group Databasebeta

← #11775319

Subgroups — #11775319

Order 1152.

822 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 221 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×C32×C22⋊Q8C211yesmaximal, characteristic
2#10592910C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#10589404C214yesmaximal, complemented
5#71689—34nomaximal
6C22×C32×Q8C411yescharacteristic, complemented
7C23×C32×C4C2211yescharacteristic
8C32×C22⋊Q8—21no—
9C32×C22⋊Q8—21no—
10C32×C22⋊Q8C412yescomplemented
11C32×C22⋊Q8C2212yes—
12C2×C32×C4⋊C4—21no—
13C2×C32×C4⋊C4C411yescharacteristic, complemented
14C2×C32×C22⋊C4—21no—
15C2×#3757—21no—
16C2×#3748—21no—
17#63658—21no—
18#63658C2212yes—
19#63657—21no—
20#63657C2212yes—
21C2×C3×C22⋊Q8D314yes—
22#5211—34no—
23#5207—34no—
24#4538—316no—
25C24×C32D411yescharacteristic
26C2×C32×Q8—21no—
27C2×C32×Q8—42no—
28C2×C32×Q8C2×C412yes—
29C22×C32×C4—21no—
30C22×C32×C4—21no—
31C22×C32×C4—42no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—22no—
39C32×C4⋊C4—22no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—22no—
42C32×C4⋊C4C2×C412yes—
43C32×C22⋊C4—22no—
44C32×C22⋊C4—22no—
45#3757—42no—
46#3748—42no—
47C2×C3⋊(C3⋊C8)—22no—
48#1511—91noSylow
49C22×C3×Q8Dic314yescomplemented
50C23×C3×C4C2×D314yes—
51C3×C22⋊Q8—24no—
52C3×C22⋊Q8—24no—
53C3×C22⋊Q8Dic318yescomplemented
54C3×C22⋊Q8C2×D318yes—
55C2×C3×C4⋊C4—24no—
56C2×C3×C4⋊C4Dic314yescomplemented
57C2×C3×C22⋊C4—24no—
58C2×#217—64no—
59C2×#208—64no—
60C3⋊#95—38no—
61C3⋊#95—64no—
62#830—38no—
63#830—64no—
64C23×C32—22no—
65C23×C32—22no—
66C23×C32—41no—
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C2×D411yescharacteristic
70C32×Q8—42no—
71C32×Q8—42no—
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—42no—
81C2×C32×C4—42no—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3—42no—
89C3⋊(C3⋊C8)—42no—
90C2×C22⋊Q8C3⋊D311yescharacteristic
91#407—91no—
92#381—91no—
93#328—94no—
94C24×C3#6714yes—
95C2×C3×Q8—24no—
96C2×C3×Q8—48no—
97C2×C3×Q8C2×Dic318yes—
98C22×C3×C4—24no—
99C22×C3×C4—24no—
100C22×C3×C4—48no—
101C22×C3×C4C2×Dic314yes—
102C22×C3×C4C2×Dic314yes—
103C22×C3×C4#6714yes—
104C22×C3×C4#6714yes—
105C22×C3×C4#6714yes—
106C22×C3×C4C22×D314yes—
107C22×Dic3—68no—
108C3×C4⋊C4—28no—
109C3×C4⋊C4—24no—
110C3×C4⋊C4—28no—
111C3×C4⋊C4C2×Dic318yes—
112C3×C22⋊C4—28no—
113C3×C22⋊C4—28no—
114#217—128no—
115#208—128no—
116C2×C3⋊C8—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—
132C32×C4—42no—
133C32×C4—42no—
134C3⋊Dic3—82no—
135C22×Q8C3⋊Dic311yescharacteristic, complemented
136C23×C4C2×C3⋊D311yescharacteristic
137C2×M16—181no—
138C22⋊Q8—21no—
139C22⋊Q8—21no—
140C22⋊Q8C3⋊Dic312yescomplemented
141C22⋊Q8C2×C3⋊D312yes—
142C2×C4⋊C4—21no—
143C2×C4⋊C4C3⋊Dic311yescharacteristic, complemented
144C2×C22⋊C4—21no—
145C2×C22⋊C4—181no—
146C22⋊C8—92no—
147C22⋊C8—181no—
148#95—92no—
149#95—181no—
150C23×C3—28no—
151C23×C3—28no—
152C23×C3—44no—
153C23×C3#21714yes—
154C23×C3#21714yes—
155C23×C3C2×#6714yes—
156C3×Q8—48no—
157C3×Q8—48no—
158C2×C3×C4—28no—
159C2×C3×C4—28no—
160C2×C3×C4—28no—
161C2×C3×C4—28no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4—44no—
166C2×C3×C4—48no—
167C2×C3×C4—48no—
168C2×C3×C4#21714yes—
169C2×C3×C4#21714yes—
170C2×C3×C4C22×Dic314yes—
171C2×C3×C4C2×#6714yes—
172C2×Dic3—128no—
173C2×Dic3—128no—
174C2×Dic3—128no—
175C3⋊C8—128no—
176C2×C32—22no—
177C2×C32—22no—
178C2×C32—41no—
179C2×C32C2×#9911yescharacteristic
180C2×C32#41911yescharacteristic
181C2×C32#42111yescharacteristic
182C24#63811yescharacteristic
183C2×Q8—21no—
184C2×Q8—42no—
185C2×Q8C2×C3⋊Dic312yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—42no—
189C22×C4—182no—
190C22×C4C2×C3⋊Dic311yescharacteristic
191C22×C4C2×C3⋊Dic311yescharacteristic
192C22×C4#63811yescharacteristic
193C22×C4#63811yescharacteristic
194C22×C4#63811yescharacteristic
195C22×C4C22×C3⋊D311yescharacteristic
196M16—362no—
197C2×C8—182no—
198C4⋊C4—22no—
199C4⋊C4—21no—
200C4⋊C4—22no—
201C4⋊C4C2×C3⋊Dic312yes—
202C22⋊C4—22no—
203C22⋊C4—22no—
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#83418yes—
214C22×C3#94218yes—
215C22×C3C2×#21714yes—
216C3×C4—24no—
217C3×C4—24no—
218C3×C4—24no—
219C3×C4—24no—
220C3×C4—48no—
221C3×C4—48no—
222Dic3—248no—
223C32#151111yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—41no—
227C23#375711yescharacteristic
228C23#375711yescharacteristic
229C23C2×#63811yescharacteristic
230Q8—42no—
231Q8—42no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—362no—
243C2×C4—362no—
244C2×C4—362no—
245C2×C4#375711yescharacteristic
246C2×C4#375711yescharacteristic
247C2×C4C22×C3⋊Dic311yescharacteristic
248C2×C4C2×#63811yescharacteristic
249C8—362no—
250C2×C3—28no—
251C2×C3—28no—
252C2×C3—44no—
253C2×C3C2×#83414yes—
254C2×C3#522514yes—
255C2×C3#523614yes—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—44no—
264C22#6366112yes—
265C22#6415112yes—
266C22C2×#375711yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—42no—
272C4—42no—
273C4—722no—
274C3#7168914yescomplemented
275C2—22no—
276C2—22no—
277C2—41no—
278C2C2×#6366111yescharacteristic
279C2#1059292411yescharacteristic
280C2#1059293511yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10589404C2semidirect
6. C22×C32×Q8C4semidirect
10. C32×C22⋊Q8C4semidirect
13. C2×C32×C4⋊C4C4semidirect
49. C22×C3×Q8Dic3semidirect
53. C3×C22⋊Q8Dic3semidirect
56. C2×C3×C4⋊C4Dic3semidirect
135. C22×Q8C3⋊Dic3semidirect
140. C22⋊Q8C3⋊Dic3semidirect
143. C2×C4⋊C4C3⋊Dic3semidirect
223. C32#1511semidirect
274. C3#71689semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
#105929102
#105929062
#105894042
#716893