Finite Group Databasebeta

← #11920435

Subgroups — #11920435

Order 1152.

577 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 577 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×2−1+4⋊C9C211yesmaximal, characteristic, complemented
2C2×#63692C211yesmaximal, characteristic, complemented
3#10589526C211yesmaximal, characteristic, complemented
4#10589523C214yesmaximal, complemented
5#84113—31nomaximal
62−1+4⋊C9—22no—
7C2×#41⋊C9C2211yescharacteristic
8C22×Q8⋊C9C2212yescomplemented
9#63692—22no—
10C2×#3689C2212yes—
11#63502—41nomaximal
12#63421C2212yescomplemented
13C2×C3×2−1+4D311yescharacteristic
14#5830—31no—
15C2×#949—31no—
16C22×#215—31no—
17#5238—34no—
18#5234—31no—
19#5233—31no—
20#5227—34no—
21#5225—31no—
22C2×D4×C9—41no—
23C2×#611—44no—
24C2×D36—41no—
25#41⋊C9D412yescomplemented
26C2×Q8⋊C9—22no—
27C2×Q8⋊C9C2311yescharacteristic
28#3689—22no—
29C4×Dic9—41no—
30#3010—91noSylow
31C3×2−1+4—22no—
32C3×2−1+4—62no—
33C2×C3×#41—31no—
34C2×C3×#41—32no—
35C2×C3×#41C2×D311yescharacteristic
36C22×C3×Q8—31no—
37C22×C3×Q8C2×D312yes—
38C22×D12—31no—
39#949—62no—
40#949—62no—
41#947—61no—
42C2×#215—34no—
43C2×#215—32no—
44C2×#215—64no—
45#940—61no—
46#937—62no—
47C2×#213—32no—
48#930—34no—
49#926—31no—
50C2×#208—31no—
51C22×C3⋊C8—31no—
52#835—34no—
53#835—32no—
54#832—32no—
55#830—34no—
56C23×C9—42no—
57C22×D9—42no—
58D4×C9—82no—
59C2×C4×C9—41no—
60#611—88no—
61C2×Dic9—42no—
62D36—82no—
63Q8⋊C9C2×D411yescharacteristic
64C2×2−1+4D911yescharacteristic, complemented
65C2×AGL(1,ℤ/8)—91no—
66C22×SD16—91no—
67#535—91no—
68#449—94no—
69#448—94no—
70#419—91no—
71#416—91no—
72#408—91no—
73C23×D3—61no—
74C3×#41—32no—
75C3×#41—62no—
76C3×#41—62no—
77C3×#41—64no—
78C3×#41—64no—
79C3×#41#6712yes—
80C2×C3×Q8—22no—
81C2×C3×Q8—31no—
82C2×C3×Q8—32no—
83C2×C3×Q8—34no—
84C2×C3×Q8—62no—
85C2×C3×Q8—62no—
86C2×C3×Q8C22×D311yescharacteristic
87C2×C3×D4—31no—
88C2×C3×D4—32no—
89C2×C3×D4S411yescharacteristic
90C22×C3×C4—31no—
91C22×C3×C4—32no—
92C22×C3×C4—61no—
93C2×#67—64no—
94C2×D12—32no—
95C2×D12—62no—
96C2×D12—62no—
97C2×D12—61no—
98#217—61no—
99#215—68no—
100#215—62no—
101#215—62no—
102#213—64no—
103(C2×D3)⋊C4—64no—
104C4⋊Dic3—32no—
105C4×Dic3—61no—
106#208—62no—
107C2×C3⋊C8—32no—
108C2×C3⋊C8—32no—
109C2×C3⋊C8—62no—
110C22×C9—41no—
111C22×C9—84no—
112C22×C9—82no—
113C2×D9—82no—
114C2×D9—84no—
115C4×C9—42no—
116Dic9—44no—
1172−1+4—22no—
1182−1+4—62no—
119C2×#41—31no—
120C2×#41—32no—
121C2×#41C2×D911yescharacteristic
122C22×Q8—31no—
123C22×Q8C2×D912yes—
124C22×D4—91no—
125AGL(1,ℤ/8)—182no—
126AGL(1,ℤ/8)—182no—
127C2×SD16—94no—
128C2×SD16—92no—
129C2×SD16—184no—
130C2×D8—92no—
131C2×M16—91no—
132C22×C8—91no—
133#127—181no—
134#124—181no—
135#121—94no—
136#120—182no—
137#117—91no—
138#103—94no—
139#103—92no—
140#102—92no—
141C22⋊C8—94no—
142C23×C3—31no—
143C23×C3C2×S412yes—
144C22×D3—62no—
145C22×D3—122no—
146C22×D3—242no—
147C3×Q8—31no—
148C3×Q8—34no—
149C3×Q8—62no—
150C3×Q8—62no—
151C3×Q8C2×#6711yescharacteristic
152C3×D4—22no—
153C3×D4—32no—
154C3×D4—61no—
155C3×D4—64no—
156C2×C3×C4—31no—
157C2×C3×C4—32no—
158C2×C3×C4—32no—
159C2×C3×C4—32no—
160C2×C3×C4—62no—
161C2×C3×C4—62no—
162C2×C3×C4—64no—
163C2×C3×C4C2×S411yescharacteristic
164#67—244no—
165C2×Dic3—62no—
166D12—62no—
167D12—62no—
168D12—122no—
169C3⋊C8—62no—
170C3⋊C8—62no—
171C2×C9—42no—
172C2×C9—41no—
173C2×C9—162no—
174D9—162no—
175C24—181no—
176#41—32no—
177#41—62no—
178#41—62no—
179#41—64no—
180#41—64no—
181#41#61112yescomplemented
182C2×Q8—22no—
183C2×Q8—31no—
184C2×Q8—32no—
185C2×Q8—34no—
186C2×Q8—62no—
187C2×Q8—62no—
188C2×Q8C22×D911yescharacteristic
189C2×D4—31no—
190C2×D4—32no—
191C2×D4—92no—
192C2×D4—182no—
193C2×D4—182no—
194C2×D4—184no—
195C2×D4—181no—
196C2×D4(C22⋊C9)⋊C211yescharacteristic
197C22×C4—31no—
198C22×C4—32no—
199C22×C4—61no—
200SD16—188no—
201SD16—182no—
202SD16—182no—
203D8—184no—
204M16—182no—
205C2×C8—92no—
206C2×C8—92no—
207C2×C8—182no—
208C4⋊C4—92no—
209C22⋊C4—184no—
210C22⋊C4—181no—
211C42—181no—
212C22×C3—24no—
213C22×C3—22no—
214C22×C3—32no—
215C22×C3—62no—
216C22×C3C22×S411yescharacteristic
217C2×D3—124no—
218C2×D3—122no—
219C2×D3—244no—
220C3×C4—31no—
221C3×C4—31no—
222C3×C4—62no—
223C3×C4GL(2,ℤ/4)12yes—
224Dic3—122no—
225C9—41noSylow
226C23—31no—
227C23—182no—
228C23—362no—
229C23—722no—
230C23C2×(C22⋊C9)⋊C212yes—
231Q8—31no—
232Q8—34no—
233Q8—62no—
234Q8—62no—
235Q8C2×#61111yescharacteristic
236D4—22no—
237D4—32no—
238D4—61no—
239D4—64no—
240D4—182no—
241D4—182no—
242D4—362no—
243D4—724no—
244C2×C4—31no—
245C2×C4—32no—
246C2×C4—32no—
247C2×C4—32no—
248C2×C4—62no—
249C2×C4—62no—
250C2×C4—64no—
251C2×C4—182no—
252C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
253C8—182no—
254C8—182no—
255C2×C3—42no—
256C2×C3—62no—
257C2×C3#592612yes—
258C2×C3C2×GL(2,ℤ/4)11yescharacteristic
259D3—242no—
260C22—24no—
261C22—22no—
262C22—32no—
263C22—62no—
264C22—364no—
265C22—362no—
266C22—724no—
267C22C22×(C22⋊C9)⋊C211yescharacteristic
268C4—31no—
269C4—31no—
270C4—62no—
271C4—362no—
272C4#6369412yes—
273C3#8554011yescharacteristic
274C2—42no—
275C2—62no—
276C2—722no—
277C2#1059310112yes—
278C2C2×#6369411yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC2×C3×2−1+4D3
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4⋊C9C2semidirect
2. C2×#63692C2semidirect
3. #10589526C2semidirect
4. #10589523C2semidirect
8. C22×Q8⋊C9C22semidirect
12. #63421C22semidirect
25. #41⋊C9D4semidirect
64. C2×2−1+4D9semidirect
181. #41#611semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
C2×#636922
#105895262
#105895232
#841133
#635024