Finite Group Databasebeta

← #11773781

Subgroups — #11773781

Order 1152.

996 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 157 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×#64102C211yesmaximal, characteristic
2C3⋊D3×C22⋊C8C212yesmaximal, complemented
3C32×#324C211yesmaximal, characteristic, complemented
4#10589394C211yesmaximal, characteristic, complemented
5#10589334C212yesmaximal, complemented
6#68143—34nomaximal
7C22×C4⋊(C3⋊D3)C411yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C2×C4×C3⋊Dic3C411yescharacteristic
14C2×C8×C3⋊D3—22no—
15#64102—22no—
16#64102—22no—
17C32×C22⋊C8C2212yes—
18#63657C2212yes—
19#63647—22no—
20C2×#893—34no—
21D3×C22⋊C8—38no—
22C3×#324D314yescomplemented
23#4528—34no—
24#4468—38no—
25C23×C3⋊D3C2×C411yescharacteristic
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C2×C4⋊(C3⋊D3)—22no—
33C2×C4⋊(C3⋊D3)—22no—
34C2×C4⋊(C3⋊D3)C814yescomplemented
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3D412yes—
41C2×C32×C8—22no—
42C32×C4⋊C4—22no—
43#3752—22no—
44#3752—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C2×C3⋊(C3⋊C8)—22no—
48C8×C3⋊D3—44no—
49#1459—91noSylow
50C22×D12—34no—
51C22×C4×D3—34no—
52C22×C4×D3—34no—
53C2×C3×C4⋊C4C2×D314yes—
54C2×(C2×D3)⋊C4—34no—
55C2×(C2×D3)⋊C4—34no—
56C2×C4×Dic3—34no—
57C2×D3×C8—68no—
58#893—68no—
59#893—68no—
60C3×C22⋊C8C2×D318yes—
61#830—38no—
62(C2×D3)⋊C8—68no—
63C23×C32C22×C411yescharacteristic
64C22×C3⋊D3—21no—
65C22×C3⋊D3—21no—
66C22×C3⋊D3—41no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3—41no—
70C22×C3⋊D3C22⋊C412yes—
71C22×C3⋊D3C2×C812yes—
72C22×C3⋊D3C2×C812yescomplemented
73C22×C3⋊D3M1612yes—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4C2×C812yescomplemented
80C2×C32×C4C2×D412yes—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C4⋊(C3⋊D3)—28no—
87C4×C3⋊D3—24no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—42no—
91C32×C8—42no—
92C3⋊(C3⋊C8)—42no—
93C2×C4×D4—91no—
94C2×C22⋊C8—92no—
95#324—91no—
96#324C3⋊D311yescharacteristic, complemented
97#323—92no—
98C23×D3—34no—
99C23×D3—34no—
100C22×C3×C4C4×D314yes—
101C22×C3×C4C4×D314yes—
102C22×C3×C4C22×D314yes—
103C22×Dic3—34no—
104C22×Dic3—34no—
105C2×D12—316no—
106C2×D12—68no—
107C2×D12—68no—
108C2×C4×D3—38no—
109C2×C4×D3—38no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—128no—
113C2×C4×D3—128no—
114C2×C3×C8—28no—
115C3×C4⋊C4—28no—
116(C2×D3)⋊C4—68no—
117(C2×D3)⋊C4—68no—
118C4×Dic3—64no—
119C4×Dic3—64no—
120C2×C3⋊C8—68no—
121D3×C8—1216no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32C2×C22⋊C411yescharacteristic
125C22×C32C22×C811yescharacteristic
126C22×C32C2×M1611yescharacteristic
127C2×C3⋊D3—22no—
128C2×C3⋊D3—22no—
129C2×C3⋊D3—22no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—42no—
133C2×C3⋊D3—41no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—42no—
136C2×C3⋊D3C22⋊C814yes—
137C32×C4—22no—
138C32×C4—22no—
139C32×C4—41no—
140C3⋊Dic3—21no—
141C3⋊Dic3—41no—
142C3⋊Dic3#9912yes—
143C22×D4—91no—
144C23×C4—91no—
145C23×C4—91no—
146C22×C8—182no—
147C4×D4—182no—
148C4×D4—182no—
149C2×C4⋊C4C2×C3⋊D311yescharacteristic
150C2×C22⋊C4—91no—
151C2×C22⋊C4—91no—
152C2×C42—91no—
153C22⋊C8—92no—
154C22⋊C8—182no—
155C22⋊C8C2×C3⋊D312yes—
156C23×C3C2×C4×D314yes—
157C22×D3—38no—
158C22×D3—38no—
159C22×D3—38no—
160C22×D3—38no—
161C22×D3—64no—
162C22×D3—64no—
163C22×D3—124no—
164C22×D3—124no—
165C22×D3—124no—
166C22×D3—124no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—44no—
171C2×C3×C4—44no—
172C2×C3×C4D3×C818yescomplemented
173C2×C3×C4D3×D418yes—
174C2×Dic3—34no—
175C2×Dic3—34no—
176C2×Dic3—68no—
177C2×Dic3—64no—
178C2×Dic3—124no—
179D12—632no—
180C4×D3—616no—
181C4×D3—128no—
182C4×D3—128no—
183C4×D3—128no—
184C3×C8—48no—
185C3⋊C8—128no—
186C2×C32—21no—
187C2×C32—21no—
188C2×C32C2×C22⋊C811yescharacteristic
189C2×C32C2×#9911yescharacteristic
190C2×C32#41311yescharacteristic
191C3⋊D3—24no—
192C3⋊D3—42no—
193C24—91no—
194C24—91no—
195C2×D4—94no—
196C2×D4—182no—
197C2×D4—182no—
198C22×C4—91no—
199C22×C4—92no—
200C22×C4—92no—
201C22×C4—91no—
202C22×C4—181no—
203C22×C4—181no—
204C22×C4—362no—
205C22×C4—362no—
206C22×C4C4×C3⋊D311yescharacteristic
207C22×C4C4×C3⋊D311yescharacteristic
208C22×C4C22×C3⋊D311yescharacteristic
209C2×C8—22no—
210C2×C8—182no—
211C2×C8—364no—
212C4⋊C4—22no—
213C22⋊C4—182no—
214C22⋊C4—182no—
215C42—181no—
216C42—181no—
217C22×C3—24no—
218C22×C3—24no—
219C22×C3D3×C22⋊C414yes—
220C22×C3C2×D3×C814yes—
221C22×C3D3×M1614yes—
222C2×D3—316no—
223C2×D3—68no—
224C2×D3—68no—
225C2×D3—68no—
226C2×D3—128no—
227C2×D3—128no—
228C2×D3—128no—
229C2×D3—124no—
230C2×D3—124no—
231C2×D3—128no—
232C3×C4—28no—
233C3×C4—28no—
234C3×C4—44no—
235Dic3—38no—
236Dic3—64no—
237Dic3—124no—
238C32#145911yescharacteristic, complemented, Sylow
239C23—92no—
240C23—92no—
241C23—92no—
242C23—92no—
243C23—181no—
244C23—181no—
245C23—361no—
246C23—361no—
247C23—361no—
248C23—361no—
249C23C2×C4×C3⋊D311yescharacteristic
250D4—188no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—184no—
259C2×C4—182no—
260C2×C4—181no—
261C2×C4—362no—
262C2×C4—362no—
263C2×C4—362no—
264C2×C4—361no—
265C2×C4C8×C3⋊D312yescomplemented
266C2×C4D4×C3⋊D312yes—
267C8—42no—
268C8—362no—
269C2×C3—24no—
270C2×C3—24no—
271C2×C3D3×C22⋊C814yes—
272C2×C3D3×#9914yes—
273C2×C3#475114yes—
274D3—616no—
275D3—128no—
276C22—21no—
277C22—21no—
278C22—94no—
279C22—182no—
280C22—182no—
281C22—182no—
282C22—362no—
283C22—362no—
284C22—362no—
285C22—362no—
286C22—361no—
287C22—361no—
288C22C22⋊C4×C3⋊D311yescharacteristic
289C22C2×C8×C3⋊D311yescharacteristic
290C22M16×C3⋊D311yescharacteristic
291C4—22no—
292C4—22no—
293C4—41no—
294C4—92no—
295C4—181no—
296C4—361no—
297C3#6814314yescomplemented
298C2—21no—
299C2—21no—
300C2—184no—
301C2—362no—
302C2C3⋊D3×C22⋊C811yescharacteristic
303C2C3⋊D3×#9911yescharacteristic
304C2#1059245011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C32×C4C23
hypercenter#324C3⋊D3
hypocenterC32#1459
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C22⋊C8C2semidirect
3. C32×#324C2semidirect
4. #10589394C2semidirect
5. #10589334C2semidirect
22. C3×#324D3semidirect
34. C2×C4⋊(C3⋊D3)C8semidirect
72. C22×C3⋊D3C2×C8semidirect
79. C2×C32×C4C2×C8semidirect
96. #324C3⋊D3semidirect
172. C2×C3×C4D3×C8semidirect
238. C32#1459semidirect
265. C2×C4C8×C3⋊D3semidirect
297. C3#68143semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C3⋊D3×C22⋊C82
C32×#3242
#105893942
#105893342
#681433