Finite Group Databasebeta

← #11796893

Subgroups — #11796893

Order 1152.

557 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 557 conjugacy classes of subgroups — too many to draw. Only its 92 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×#63797C211yesmaximal, characteristic
2C3⋊D3×M32C211yesmaximal, characteristic, complemented
3#10590913C211yesmaximal, characteristic, complemented
4C3×#4516C212yesmaximal, complemented
5#10589126C212yesmaximal, complemented
6D3×#361—32nomaximal
7C2×#3802—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×D24C2212yes—
10C2×#3713—21no—
11#63818—21no—
12#63797—21no—
13#63797—21no—
14#63797C412yes—
15#63797C412yes—
16C32×M32C2211yescharacteristic, complemented
17#63639C2211yescharacteristic, complemented
18#63625—21no—
19C16×C3⋊D3—21no—
20C3×#819C2212yescomplemented
21#63578—21no—
22C2×D3×D8—32no—
23D3×M32—32no—
24D3×M32—61no—
25D3×#108—32no—
26C3×#361—32no—
27#4563—32no—
28#4516D312yescomplemented
29#4495—32no—
30C22×D32—41no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C3×D12—22no—
33C2×#625—41no—
34#3802—22no—
35#3802—22no—
36#3802—41no—
37#3802—41no—
38C2×C32×C8C2311yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C8×C3⋊D3C2×C411yescharacteristic
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C3×#208—22no—
45C3×D24—22no—
46C3×D24C2×C414yes—
47#3713—22no—
48#3713—22no—
49#3712—41no—
50#3710—41no—
51C32×C16—21no—
52C3⋊(C3⋊C16)—21no—
53C2×#361—91noSylow
54C2×D3×D4—62no—
55C2×C3×D8—32no—
56C2×#213—62no—
57D3×D8—34no—
58D3×D8—34no—
59D3×D8—62no—
60D3×D8—62no—
61D3×M16—62no—
62C2×D24C2×D312yes—
63C2×D3×C8—32no—
64C2×D3×C8—61no—
65C3×M32—21no—
66C3×M32C2×D312yescomplemented
67C3×#108—32no—
68#822—62no—
69#819C2×D312yescomplemented
70#812—32no—
71#812—61no—
72#798—62no—
73#798—62no—
74D3×C16—62no—
75D3×C16—62no—
76C22×C3⋊D3SD1611yescharacteristic
77C22×C3×D3—42no—
78C2×D32—42no—
79C2×D32—42no—
80C2×D32—84no—
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3SD1611yescharacteristic
83C4×C3⋊D3C22⋊C411yescharacteristic
84C4×C3⋊D3C22⋊C411yescharacteristic
85C4×C3⋊D3D811yescharacteristic
86C4×C3⋊D3D811yescharacteristic
87C3×D12—24no—
88C3×D12—42no—
89#625—42no—
90#625—42no—
91C32×C8C22×C411yescharacteristic
92C32×C8C2×D411yescharacteristic
93C3⋊(C3⋊C8)C22⋊C411yescharacteristic
94C3⋊(C3⋊C8)C22⋊C411yescharacteristic
95C3×C3⋊C8—42no—
96C22×D8—91no—
97C2×M32—91no—
98C2×#108—91no—
99#361—32no—
100#361—92no—
101C23×D3—122no—
102C2×C3×D4—62no—
103C2×#67—122no—
104D3×D4—64no—
105D3×D4—64no—
106D3×D4—122no—
107D3×D4—122no—
108C2×D12—22no—
109C2×C4×D3—32no—
110C2×C4×D3—61no—
111C3×D8—34no—
112C3×D8—62no—
113C3×M16—62no—
114C2×C3×C8—21no—
115C2×C3×C8C22×D312yes—
116#213—64no—
117#213—64no—
118#208—22no—
119C2×C3⋊C8—32no—
120C2×C3⋊C8—61no—
121D24—22no—
122D24C4×D314yes—
123ΓL(1,𝔽25)—122no—
124D3×C8—32no—
125D3×C8—32no—
126D3×C8—32no—
127D3×C8—32no—
128D3×C8—61no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—61no—
132D3×C8—122no—
133C3×C16—22no—
134C3×C16—22no—
135C3⋊C16—62no—
136C3⋊C16—62no—
137C22×C32C2×SD1611yescharacteristic
138C2×C3⋊D3—22no—
139C2×C3⋊D3#10211yescharacteristic
140C2×C3⋊D3#10211yescharacteristic
141C2×C3×D3—44no—
142C2×C3×D3—84no—
143D32—84no—
144D32—84no—
145C32×C4C2×C22⋊C411yescharacteristic
146C32×C4C2×D811yescharacteristic
147C3⋊Dic3#10211yescharacteristic
148C3⋊Dic3#10211yescharacteristic
149C22×D4—181no—
150C2×D8—32no—
151C2×D8—92no—
152C2×D8—92no—
153C2×D8—181no—
154C2×D8—181no—
155C2×D8—181no—
156C2×M16—181no—
157C22×C8—91no—
158M32—91no—
159M32—181no—
160M32D3211yescharacteristic, complemented
161C2×C16—181no—
162#108—32no—
163#108—181no—
164C23×C3—122no—
165C22×D3—32no—
166C22×D3—42no—
167C22×D3—61no—
168C22×D3—124no—
169C22×D3—124no—
170C22×D3—248no—
171C3×D4—64no—
172C3×D4—122no—
173C2×C3×C4—21no—
174C2×C3×C4D3×D412yes—
175#67—124no—
176#67—124no—
177C2×Dic3—32no—
178C2×Dic3—61no—
179D12—24no—
180D12—42no—
181C4×D3—32no—
182C4×D3—32no—
183C4×D3—32no—
184C4×D3—32no—
185C4×D3—61no—
186C4×D3—61no—
187C4×D3—61no—
188C4×D3—61no—
189C3×C8—21no—
190C3×C8—21no—
191C3×C8—122no—
192C3×C8C2×C4×D312yes—
193C3×C8D3×D412yes—
194C3⋊C8—32no—
195C3⋊C8—32no—
196C3⋊C8—42no—
197C3⋊C8—61no—
198C3⋊C8—61no—
199C2×C32—21no—
200C2×C32C2×#10211yescharacteristic
201C3⋊D3—21no—
202C3⋊D3#36112yescomplemented
203C3×D3—84no—
204C24—361no—
205C2×D4—62no—
206C2×D4—182no—
207C2×D4—182no—
208C2×D4—361no—
209C2×D4—361no—
210C2×D4—361no—
211C22×C4—91no—
212D8—34no—
213D8—62no—
214D8—182no—
215D8—182no—
216M16—62no—
217M16—361no—
218C2×C8—91no—
219C2×C8—91no—
220C2×C8—91no—
221C2×C8—91no—
222C2×C8—91no—
223C2×C8—361no—
224C2×C8C2×D3211yescharacteristic
225C16—21no—
226C16—181no—
227C22×C3—21no—
228C22×C3—124no—
229C22×C3—244no—
230C22×C3D3×SD1612yes—
231C2×D3—32no—
232C2×D3—32no—
233C2×D3—44no—
234C2×D3—61no—
235C2×D3—61no—
236C2×D3—64no—
237C2×D3—84no—
238C2×D3—122no—
239C2×D3—248no—
240C2×D3—248no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4D3×C22⋊C412yes—
244C3×C4D3×D812yes—
245Dic3—32no—
246Dic3—32no—
247Dic3—61no—
248Dic3—61no—
249C32C2×#36111yescharacteristic, complemented, Sylow
250C23—91no—
251C23—122no—
252C23—362no—
253C23—362no—
254C23—724no—
255D4—64no—
256D4—122no—
257D4—362no—
258D4—362no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4#380211yescharacteristic
265C8—91no—
266C8—91no—
267C8—122no—
268C8C4×D3211yescharacteristic
269C8#381111yescharacteristic
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—41no—
273C2×C3—244no—
274C2×C3D3×#10212yes—
275D3—34no—
276D3—62no—
277D3—62no—
278D3—84no—
279D3—121no—
280C22—91no—
281C22—91no—
282C22—124no—
283C22—182no—
284C22—244no—
285C22—724no—
286C22—724no—
287C22#6379611yescharacteristic
288C4—91no—
289C4—91no—
290C4#6379711yescharacteristic
291C4#6392111yescharacteristic
292C3—21no—
293C3D3×#36112yescomplemented
294C2—21no—
295C2—92no—
296C2—181no—
297C2—244no—
298C2#1059094011yescharacteristic
subgroupG/H
centerC2#10590940
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32C2×#102
prime radicalC2×#63797C2
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32C2×#361
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×M32C2semidirect
3. #10590913C2semidirect
4. C3×#4516C2semidirect
5. #10589126C2semidirect
16. C32×M32C22semidirect
17. #63639C22semidirect
20. C3×#819C22semidirect
28. #4516D3semidirect
66. C3×M32C2×D3semidirect
69. #819C2×D3semidirect
160. M32D32semidirect
202. C3⋊D3#361semidirect
249. C32C2×#361semidirect
293. C3D3×#361semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
C3⋊D3×M322
#105909132
C3×#45162
#105891262
D3×#3613