Finite Group Databasebeta

← #11778215

Subgroups — #11778215

Order 1152.

924 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#10595964C211yesmaximal, characteristic
2#10592646C211yesmaximal, characteristic, complemented
3#10592437C212yesmaximal, complemented
4C32×#323C211yesmaximal, characteristic, complemented
5#10589336C212yesmaximal, complemented
6#68108—34nomaximal
7C22×#638—21no—
8C22×#634C2211yescharacteristic, complemented
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757—21no—
11#64139—21no—
12#64139C2212yes—
13C2×#3744—22no—
14#64095—22no—
15#64091—22no—
16C32×C22⋊C8C2212yescomplemented
17#63658—21no—
18#63658C2211yescharacteristic, complemented
19#63643—22no—
20#5493—34no—
21#4947—34no—
22#4738—38no—
23C3×#323D314yescomplemented
24#4470—38no—
25C24×C32D411yescharacteristic
26C23×C3⋊D3—21no—
27C22×C32×C4D411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C2×#638—22no—
30C2×#638—22no—
31C2×#638—42no—
32C2×#638—42no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)D412yes—
38C2×#634—22no—
39C2×#634—42no—
40C2×C32×C8—22no—
41C32×C22⋊C4—22no—
42#3757—42no—
43#3752—22no—
44#3752—22no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)D412yes—
47#3744—44no—
48#1601—91noSylow
49C22×#67—64no—
50C22×Dic6—34no—
51C2×C3×C22⋊C4C2×D314yes—
52C2×#217—64no—
53#930—38no—
54#930—64no—
55C2×#204—68no—
56#886—68no—
57#882—68no—
58C3×C22⋊C8C2×D318yescomplemented
59C3⋊#95—34no—
60C3⋊#95—64no—
61#816—68no—
62C23×C32—21no—
63C23×C32—21no—
64C23×C32—41no—
65C23×C32—41no—
66C23×C32SD1612yescomplemented
67C23×C32C2×D411yescharacteristic
68C22×C3⋊D3—22no—
69C22×C3⋊D3—42no—
70C22×C3⋊D3—81no—
71C22×C3⋊D3—81no—
72C2×C32×C4—21no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4C2×D412yes—
76#638—44no—
77#638—42no—
78#638—42no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—42no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—81no—
89#634—24no—
90#634—42no—
91C32×C8—42no—
92#534—91no—
93#448—92no—
94#393—91no—
95#327—92no—
96#323C3⋊D311yescharacteristic, complemented
97C24×C3D1214yes—
98C23×D3—64no—
99C22×C3×C4D1214yes—
100C22×C3×C4C22×D314yes—
101C2×#67—68no—
102C2×#67—68no—
103C2×#67—128no—
104C2×#67—128no—
105C22×Dic3—64no—
106C22×Dic3—64no—
107C22×Dic3—64no—
108C2×D12—38no—
109C2×D12—64no—
110C2×Dic6—68no—
111C2×Dic6—128no—
112C2×C3×C8—28no—
113C3×C22⋊C4—28no—
114#217—128no—
115(C2×D3)⋊C4—68no—
116(C2×D3)⋊C4—68no—
117C4⋊Dic3—38no—
118C4⋊Dic3—64no—
119#204—1216no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—22no—
123C22×C32—42no—
124C22×C32—41no—
125C22×C32—41no—
126C22×C32—81no—
127C22×C32#12011yescharacteristic
128C22×C32C2×SD1611yescharacteristic
129C22×C32AGL(1,ℤ/8)11yescharacteristic
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—42no—
133C2×C3⋊D3—84no—
134C32×C4—22no—
135C32×C4—41no—
136C3⋊Dic3—42no—
137C3⋊Dic3—42no—
138C3⋊Dic3—81no—
139C22×Q8—91no—
140C22×D4—181no—
141C2×SD16—182no—
142#123—182no—
143#121—92no—
144#121—181no—
145#120—182no—
146C2×C22⋊C4—181no—
147C2×C22⋊C4C2×C3⋊D311yescharacteristic
148#103—182no—
149C22⋊C8C2×C3⋊D312yescomplemented
150#95—91no—
151#95—181no—
152C23×C3—24no—
153C23×C3—24no—
154C23×C3—44no—
155C23×C3—44no—
156C23×C3#20418yescomplemented
157C23×C3C2×D1214yes—
158C22×D3—68no—
159C22×D3—128no—
160C22×D3—244no—
161C22×D3—244no—
162C2×C3×C4—24no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4D3×D418yes—
166#67—1216no—
167#67—128no—
168#67—128no—
169C2×Dic3—68no—
170C2×Dic3—68no—
171C2×Dic3—124no—
172C2×Dic3—128no—
173C2×Dic3—124no—
174C2×Dic3—124no—
175C2×Dic3—124no—
176C2×Dic3—124no—
177D12—128no—
178D12—244no—
179Dic6—616no—
180Dic6—128no—
181C3×C8—48no—
182C2×C32—21no—
183C2×C32—21no—
184C2×C32—42no—
185C2×C32#45011yescharacteristic
186C2×C32#45511yescharacteristic
187C2×C32B(4,𝔽2)11yescharacteristic
188C3⋊D3—82no—
189C24—181no—
190C24C4⋊(C3⋊D3)11yescharacteristic
191C2×Q8—182no—
192C2×Q8—362no—
193C2×D4—92no—
194C2×D4—181no—
195C2×D4—182no—
196C2×D4—182no—
197C2×D4—362no—
198C2×D4—362no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4—181no—
202C22×C4C4⋊(C3⋊D3)11yescharacteristic
203C22×C4C22×C3⋊D311yescharacteristic
204SD16—364no—
205C2×C8—22no—
206C4⋊C4—92no—
207C4⋊C4—181no—
208C22⋊C4—22no—
209C22⋊C4—182no—
210C22⋊C4—182no—
211C22⋊C4—362no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3—28no—
215C22×C3—48no—
216C22×C3—44no—
217C22×C3—44no—
218C22×C3—84no—
219C22×C3#88214yes—
220C22×C3C2×#20414yes—
221C22×C3#90814yes—
222C2×D3—128no—
223C2×D3—128no—
224C2×D3—128no—
225C2×D3—2416no—
226C3×C4—28no—
227C3×C4—44no—
228Dic3—128no—
229Dic3—128no—
230Dic3—244no—
231C32#160111yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—182no—
237C23—362no—
238C23—721no—
239C23—721no—
240C23#374412yescomplemented
241C23C2×C4⋊(C3⋊D3)11yescharacteristic
242Q8—184no—
243Q8—362no—
244D4—362no—
245D4—364no—
246D4—362no—
247D4—362no—
248D4—721no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—182no—
253C2×C4—182no—
254C2×C4—362no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4D4×C3⋊D312yes—
261C8—42no—
262C2×C3—24no—
263C2×C3—24no—
264C2×C3—48no—
265C2×C3#473114yes—
266C2×C3#474114yes—
267C2×C3#474614yes—
268D3—248no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—81no—
276C22—362no—
277C22—362no—
278C22—362no—
279C22—724no—
280C22#6409111yescharacteristic
281C22C2×#374411yescharacteristic
282C22#6411711yescharacteristic
283C4—22no—
284C4—41no—
285C4—362no—
286C4—362no—
287C4—721no—
288C3#6810814yescomplemented
289C2—21no—
290C2—21no—
291C2—42no—
292C2—722no—
293C2#1059243011yescharacteristic
294C2#1059244011yescharacteristic
295C2#1059244511yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32#120
prime radical#10595964C2
hypercenter#323C3⋊D3
hypocenterC32#1601
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10592646C2semidirect
3. #10592437C2semidirect
4. C32×#323C2semidirect
5. #10589336C2semidirect
8. C22×#634C22semidirect
16. C32×C22⋊C8C22semidirect
18. #63658C22semidirect
23. C3×#323D3semidirect
58. C3×C22⋊C8C2×D3semidirect
66. C23×C32SD16semidirect
96. #323C3⋊D3semidirect
149. C22⋊C8C2×C3⋊D3semidirect
156. C23×C3#204semidirect
231. C32#1601semidirect
240. C23#3744semidirect
288. C3#68108semidirect

Maximal subgroups

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

subgroupindex
#105959642
#105926462
#105924372
C32×#3232
#105893362
#681083