Finite Group Databasebeta

← #11775227

Subgroups — #11775227

Order 1152.

882 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 233 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
2C4×#3757C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#10589404C214yesmaximal, complemented
5#71688—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×C4×C3⋊Dic3—21no—
17C2×#3748—21no—
18#63658C2212yes—
19#63657—21no—
20#63657C2212yes—
21C2×C3×C22⋊Q8D314yes—
22C4×#217—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—24no—
46C4×C3⋊Dic3—42no—
47#3748—42no—
48C2×C3⋊(C3⋊C8)—22no—
49#1508—91noSylow
50C22×C3×Q8Dic314yescomplemented
51C23×C3×C4C2×D314yes—
52C3×C22⋊Q8—24no—
53C3×C22⋊Q8—24no—
54C3×C22⋊Q8Dic318yescomplemented
55C3×C22⋊Q8C2×D318yes—
56C2×C3×C4⋊C4—24no—
57C2×C3×C4⋊C4Dic314yescomplemented
58C2×C3×C22⋊C4—24no—
59C2×#217—64no—
60C2×C4×Dic3—64no—
61C2×#208—64no—
62C3⋊#95—38no—
63#830—38no—
64#830—64no—
65C23×C32—22no—
66C23×C32—22no—
67C23×C32—41no—
68C23×C32C22⋊C411yescharacteristic
69C23×C32C22⋊C411yescharacteristic
70C23×C32C2×D411yescharacteristic
71C32×Q8—42no—
72C32×Q8—42no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4—42no—
82C2×C32×C4—42no—
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3—42no—
90C3⋊(C3⋊C8)—42no—
91C2×C22⋊Q8C3⋊D311yescharacteristic
92#407—91no—
93C4×C22⋊C4—91no—
94#328—94no—
95C24×C3#6714yes—
96C2×C3×Q8—24no—
97C2×C3×Q8—48no—
98C2×C3×Q8C2×Dic318yes—
99C22×C3×C4—24no—
100C22×C3×C4—24no—
101C22×C3×C4—48no—
102C22×C3×C4C2×Dic314yes—
103C22×C3×C4C2×Dic314yes—
104C22×C3×C4#6714yes—
105C22×C3×C4#6714yes—
106C22×C3×C4#6714yes—
107C22×C3×C4C22×D314yes—
108C22×Dic3—68no—
109C3×C4⋊C4—28no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—28no—
112C3×C4⋊C4C2×Dic318yes—
113C3×C22⋊C4—28no—
114C3×C22⋊C4—28no—
115#217—616no—
116C4×Dic3—128no—
117#208—128no—
118C2×C3⋊C8—68no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—44no—
127C22×C32#10412yes—
128C22×C32C2×C22⋊C411yescharacteristic
129C22×C32#13712yes—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—42no—
134C32×C4—42no—
135C32×C4#9912yes—
136C3⋊Dic3—44no—
137C22×Q8C3⋊Dic311yescharacteristic, complemented
138C23×C4C2×C3⋊D311yescharacteristic
139C2×M16—181no—
140C22⋊Q8—21no—
141C22⋊Q8—21no—
142C22⋊Q8C3⋊Dic312yescomplemented
143C22⋊Q8C2×C3⋊D312yes—
144C2×C4⋊C4—21no—
145C2×C4⋊C4C3⋊Dic311yescharacteristic, complemented
146C2×C22⋊C4—21no—
147C2×C22⋊C4—181no—
148C2×C42—181no—
149C22⋊C8—92no—
150C22⋊C8—181no—
151#95—92no—
152C23×C3—28no—
153C23×C3—28no—
154C23×C3—44no—
155C23×C3#21714yes—
156C23×C3#21714yes—
157C23×C3C2×#6714yes—
158C3×Q8—48no—
159C3×Q8—48no—
160C2×C3×C4—28no—
161C2×C3×C4—28no—
162C2×C3×C4—28no—
163C2×C3×C4—28no—
164C2×C3×C4—28no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4—44no—
168C2×C3×C4—48no—
169C2×C3×C4—48no—
170C2×C3×C4#21714yes—
171C2×C3×C4#21714yes—
172C2×C3×C4C22×Dic314yes—
173C2×C3×C4C2×#6714yes—
174C2×Dic3—616no—
175C2×Dic3—128no—
176C2×Dic3—128no—
177C3⋊C8—128no—
178C2×C32—22no—
179C2×C32—22no—
180C2×C32—41no—
181C2×C32C2×#9911yescharacteristic
182C2×C32#41911yescharacteristic
183C2×C32C2×#10411yescharacteristic
184C24#63811yescharacteristic
185C2×Q8—21no—
186C2×Q8—42no—
187C2×Q8C2×C3⋊Dic312yes—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—42no—
191C22×C4—182no—
192C22×C4C2×C3⋊Dic311yescharacteristic
193C22×C4C2×C3⋊Dic311yescharacteristic
194C22×C4#63811yescharacteristic
195C22×C4#63811yescharacteristic
196C22×C4#63811yescharacteristic
197C22×C4C22×C3⋊D311yescharacteristic
198M16—362no—
199C2×C8—182no—
200C4⋊C4—22no—
201C4⋊C4—21no—
202C4⋊C4—22no—
203C4⋊C4C2×C3⋊Dic312yes—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—184no—
207C42—362no—
208C22×C3—24no—
209C22×C3—24no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—24no—
215C22×C3—416no—
216C22×C3#83718yes—
217C22×C3#94218yes—
218C22×C3C2×#21714yes—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—48no—
223C3×C4—48no—
224C3×C4#83418yes—
225Dic3—1216no—
226C32#150811yescharacteristic, complemented, Sylow
227C23—22no—
228C23—22no—
229C23—41no—
230C23#375711yescharacteristic
231C23#375711yescharacteristic
232C23C2×#63811yescharacteristic
233Q8—42no—
234Q8—42no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—184no—
246C2×C4—362no—
247C2×C4—362no—
248C2×C4#375711yescharacteristic
249C2×C4#375711yescharacteristic
250C2×C4C22×C3⋊Dic311yescharacteristic
251C2×C4C2×#63811yescharacteristic
252C8—362no—
253C2×C3—28no—
254C2×C3—28no—
255C2×C3—44no—
256C2×C3C2×#83414yes—
257C2×C3#522514yes—
258C2×C3C2×#83714yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—44no—
267C22#6366412yes—
268C22#6415112yes—
269C22C2×#375711yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—364no—
276C4#6366112yes—
277C3#7168814yescomplemented
278C2—22no—
279C2—22no—
280C2—41no—
281C2C2×#6366111yescharacteristic
282C2#1059292411yescharacteristic
283C2C2×#6366411yescharacteristic
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#1508
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
50. C22×C3×Q8Dic3semidirect
54. C3×C22⋊Q8Dic3semidirect
57. C2×C3×C4⋊C4Dic3semidirect
137. C22×Q8C3⋊Dic3semidirect
142. C22⋊Q8C3⋊Dic3semidirect
145. C2×C4⋊C4C3⋊Dic3semidirect
226. C32#1508semidirect
277. C3#71688semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C4×#37572
#105929062
#105894042
#716883