Finite Group Databasebeta

← #11773848

Subgroups — #11773848

Order 1152.

1320 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C22×#3752C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic, complemented
3#10592906C211yesmaximal, characteristic, complemented
4#10589334C214yesmaximal, complemented
5#69967—34nomaximal
6C24×C3⋊D3C411yescharacteristic
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3C411yescharacteristic
9C2×C32×M16—21no—
10C2×#3752—21no—
11C2×#3752—21no—
12C2×#3752—21no—
13C2×#3752—21no—
14C2×#3752C412yes—
15C2×#3752C2212yes—
16C2×#3748—21no—
17C32×C22⋊C8—21no—
18C32×C22⋊C8C2212yescomplemented
19#63657—21no—
20#63657C2212yescomplemented
21C22×(C2×D3)⋊C4—34no—
22C3×#407D314yescomplemented
23#5207—34no—
24#4468—316no—
25C24×C32C2×C411yescharacteristic
26C23×C3⋊D3—21no—
27C23×C3⋊D3—21no—
28C23×C3⋊D3—24no—
29C23×C3⋊D3—42no—
30C23×C3⋊D3—42no—
31C23×C3⋊D3C2×C412yes—
32C22×C32×C4—42no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—42no—
42C22×C3⋊Dic3C2×C412yes—
43C32×M16—42no—
44C2×C32×C8—22no—
45#3752—22no—
46#3752—22no—
47#3752—22no—
48#3752—22no—
49#3748—42no—
50C2×C3⋊(C3⋊C8)—22no—
51#1462—91noSylow
52C24×D3—34no—
53C23×C3×C4C2×D314yes—
54C23×Dic3—34no—
55C2×C3×M16—24no—
56C2×(C2×D3)⋊C4—38no—
57C2×(C2×D3)⋊C4—38no—
58C2×(C2×D3)⋊C4—64no—
59C2×(C2×D3)⋊C4—64no—
60C2×(C2×D3)⋊C4—64no—
61C2×(C2×D3)⋊C4—64no—
62C2×#208—64no—
63C3×C22⋊C8—24no—
64C3×C22⋊C8C2×D318yescomplemented
65#830—38no—
66#830—64no—
67C23×C32—22no—
68C23×C32—22no—
69C23×C32—22no—
70C23×C32C22⋊C411yescharacteristic
71C23×C32C22⋊C411yescharacteristic
72C23×C32C22×C411yescharacteristic
73C22×C3⋊D3—24no—
74C22×C3⋊D3—24no—
75C22×C3⋊D3—22no—
76C22×C3⋊D3—22no—
77C22×C3⋊D3—416no—
78C22×C3⋊D3—42no—
79C22×C3⋊D3—42no—
80C22×C3⋊D3—42no—
81C22×C3⋊D3—42no—
82C22×C3⋊D3—42no—
83C22×C3⋊D3—42no—
84C22×C3⋊D3M1614yescomplemented
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—42no—
98C2×C3⋊Dic3—42no—
99C32×C8—42no—
100C3⋊(C3⋊C8)—42no—
101C22×C22⋊C4—91no—
102#407—91no—
103#407C3⋊D311yescharacteristic, complemented
104#323—94no—
105C24×C3C4×D314yes—
106C23×D3—38no—
107C23×D3—616no—
108C23×D3—64no—
109C23×D3—64no—
110C23×D3—128no—
111C23×D3—128no—
112C22×C3×C4—48no—
113C22×C3×C4C4×D314yes—
114C22×C3×C4D1214yes—
115C22×C3×C4D1214yes—
116C22×C3×C4#6714yes—
117C22×C3×C4#6714yes—
118C22×C3×C4C22×D314yes—
119C22×Dic3—38no—
120C22×Dic3—64no—
121C22×Dic3—64no—
122C22×Dic3—128no—
123C3×M16—48no—
124C2×C3×C8—28no—
125(C2×D3)⋊C4—68no—
126(C2×D3)⋊C4—68no—
127(C2×D3)⋊C4—68no—
128(C2×D3)⋊C4—68no—
129#208—128no—
130C2×C3⋊C8—68no—
131C22×C32—28no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32#9912yes—
139C22×C32#10012yes—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32C2×M1612yes—
142C2×C3⋊D3—24no—
143C2×C3⋊D3—48no—
144C2×C3⋊D3—48no—
145C2×C3⋊D3—44no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3—42no—
148C2×C3⋊D3—44no—
149C32×C4—21no—
150C32×C4—21no—
151C32×C4—21no—
152C32×C4—21no—
153C3⋊Dic3—42no—
154C25—91no—
155C23×C4—91no—
156C23×C4C2×C3⋊D311yescharacteristic
157C2×M16—21no—
158C2×M16—181no—
159C2×C22⋊C4—92no—
160C2×C22⋊C4—92no—
161C2×C22⋊C4—181no—
162C2×C22⋊C4—181no—
163C2×C22⋊C4—181no—
164C2×C22⋊C4—181no—
165C22⋊C8—21no—
166C22⋊C8—92no—
167C22⋊C8—181no—
168C22⋊C8C2×C3⋊D312yescomplemented
169C23×C3—28no—
170C23×C3—28no—
171C23×C3—28no—
172C23×C3(C2×D3)⋊C414yes—
173C23×C3(C2×D3)⋊C414yes—
174C23×C3C2×C4×D314yes—
175C22×D3—316no—
176C22×D3—616no—
177C22×D3—616no—
178C22×D3—68no—
179C22×D3—68no—
180C22×D3—1264no—
181C22×D3—128no—
182C22×D3—128no—
183C22×D3—128no—
184C22×D3—128no—
185C22×D3—128no—
186C22×D3—128no—
187C2×C3×C4—28no—
188C2×C3×C4—28no—
189C2×C3×C4—44no—
190C2×C3×C4—44no—
191C2×C3×C4—44no—
192C2×C3×C4—44no—
193C2×C3×C4(C2×D3)⋊C414yes—
194C2×C3×C4(C2×D3)⋊C414yes—
195C2×C3×C4C2×D1214yes—
196C2×C3×C4C2×#6714yes—
197C2×Dic3—68no—
198C2×Dic3—128no—
199C2×Dic3—128no—
200C2×Dic3—128no—
201C3×C8—48no—
202C3⋊C8—128no—
203C2×C32—22no—
204C2×C32—22no—
205C2×C32—22no—
206C2×C32#40711yescharacteristic
207C2×C32C2×#9911yescharacteristic
208C2×C32C2×#10011yescharacteristic
209C3⋊D3—44no—
210C24—92no—
211C24—184no—
212C24—181no—
213C24—181no—
214C24—362no—
215C24—362no—
216C24C4×C3⋊D311yescharacteristic
217C22×C4—42no—
218C22×C4—92no—
219C22×C4—181no—
220C22×C4—181no—
221C22×C4—362no—
222C22×C4C4×C3⋊D311yescharacteristic
223C22×C4C4⋊(C3⋊D3)11yescharacteristic
224C22×C4C4⋊(C3⋊D3)11yescharacteristic
225C22×C4#63811yescharacteristic
226C22×C4#63811yescharacteristic
227C22×C4C22×C3⋊D311yescharacteristic
228M16—42no—
229M16—362no—
230C2×C8—22no—
231C2×C8—182no—
232C22⋊C4—182no—
233C22⋊C4—182no—
234C22⋊C4—182no—
235C22⋊C4—182no—
236C22×C3—232no—
237C22×C3—24no—
238C22×C3—24no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—24no—
242C22×C3—24no—
243C22×C3#80618yes—
244C22×C3#82318yes—
245C22×C3D3×M1618yes—
246C22×C3C2×(C2×D3)⋊C414yes—
247C2×D3—616no—
248C2×D3—1232no—
249C2×D3—1232no—
250C2×D3—1216no—
251C2×D3—128no—
252C2×D3—128no—
253C2×D3—1216no—
254C3×C4—24no—
255C3×C4—24no—
256C3×C4—24no—
257C3×C4—24no—
258Dic3—128no—
259C32#146211yescharacteristic, complemented, Sylow
260C23—22no—
261C23—22no—
262C23—22no—
263C23—94no—
264C23—184no—
265C23—184no—
266C23—182no—
267C23—182no—
268C23—362no—
269C23—362no—
270C23—3616no—
271C23—362no—
272C23—362no—
273C23—362no—
274C23—362no—
275C23#375211yescharacteristic
276C23#375211yescharacteristic
277C23C2×C4×C3⋊D311yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—182no—
285C2×C4—362no—
286C2×C4—362no—
287C2×C4—362no—
288C2×C4#375211yescharacteristic
289C2×C4#375211yescharacteristic
290C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
291C2×C4C2×#63811yescharacteristic
292C8—42no—
293C8—362no—
294C2×C3—28no—
295C2×C3—28no—
296C2×C3—28no—
297C2×C3C2×#80614yes—
298C2×C3#512614yes—
299C2×C3C2×#82314yes—
300D3—1216no—
301C22—28no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—184no—
309C22—364no—
310C22—364no—
311C22—368no—
312C22—368no—
313C22—362no—
314C22—362no—
315C22#6363312yes—
316C22#6365012yes—
317C22M16×C3⋊D312yes—
318C22C2×#375211yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—362no—
324C3#6996714yescomplemented
325C2—22no—
326C2—22no—
327C2—22no—
328C2—364no—
329C2C2×#6363311yescharacteristic
330C2#1059282511yescharacteristic
331C2C2×#6365011yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C4
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1462
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C32×#407C2semidirect
3. #10592906C2semidirect
4. #10589334C2semidirect
18. C32×C22⋊C8C22semidirect
20. #63657C22semidirect
22. C3×#407D3semidirect
64. C3×C22⋊C8C2×D3semidirect
84. C22×C3⋊D3M16semidirect
103. #407C3⋊D3semidirect
168. C22⋊C8C2×C3⋊D3semidirect
259. C32#1462semidirect
324. C3#69967semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C32×#4072
#105929062
#105893342
#699673