Finite Group Databasebeta

← #11874887

Subgroups — #11874887

Order 1152.

913 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 913 conjugacy classes of subgroups — too many to draw. Only its 212 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#10594374C212yesmaximal
2C3⋊D3×#106C211yesmaximal, characteristic
3C3×#4855C212yesmaximal, complemented
4#10590889C212yesmaximal, complemented
5#10590685C211yesmaximal, characteristic
6C8×#624C211yesmaximal, characteristic
7#10590575C212yesmaximal
8#10590412C214yesmaximal, complemented
9D3×#498—32nomaximal
10C2×#3797—22no—
11C2×C8×C3⋊D3C2211yescharacteristic
12C4⋊C4×C3⋊D3C2212yes—
13C3×#888C2214yes—
14#63918C2214yes—
15#63900C2212yes—
16#63883—22no—
17C4×#624C2211yescharacteristic
18#63839—24no—
19C2×#3710C2211yescharacteristic
20C32×#106C2211yescharacteristic
21#63644C2211yescharacteristic
22#63635C2212yes—
23C3×#817C2212yes—
24C3×C8×Dic3C2212yes—
25C3×#808C2214yes—
26#63574C2212yes—
27#63573C2214yes—
28Dic3×C3⋊C8C2212yes—
29D3×C4⋊Q8—34no—
30C3×#498—32no—
31#5080—34no—
32D3×#106—32no—
33D3×#106—32no—
34D3×#106—34no—
35D3×#106—61no—
36#4855—34no—
37#4855—32no—
38#4855D312yescomplemented
39C4×D3×C8—32no—
40#4680—32no—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×C3×Dic6—24no—
44C2×#627—24no—
45C2×#624—22no—
46C2×#624D412yes—
47#3797—48no—
48C2×C32×C8C2311yescharacteristic
49C32×C4⋊C4C2312yes—
50C4⋊(C3⋊Dic3)C2312yes—
51#3750—22no—
52C2×C3⋊(C3⋊C8)C2311yescharacteristic
53C8×C3⋊D3Q814yescomplemented
54C3×C4⋊Dic3C2314yes—
55C3×Dic3⋊C4—24no—
56C3×C4×Dic3C2312yes—
57C2×C3×C3⋊C8C2312yes—
58#3724—22no—
59Dic3⋊Dic3—24no—
60Dic32D412yes—
61#3710Q814yescomplemented
62C2×#498—91noSylow
63C2×D3×Q8—64no—
64C3×C4⋊Q8—34no—
65#944—64no—
66C2×D3×C8—32no—
67C2×D3×C8—32no—
68C2×D3×C8—61no—
69D3×C4⋊C4—34no—
70D3×C4⋊C4—34no—
71D3×C4⋊C4—62no—
72D3×C4⋊C4—64no—
73#888—34no—
74#888—64no—
75#888C2×D314yes—
76C42×D3—32no—
77#869—34no—
78C3×#106—21no—
79C3×#106—32no—
80C3×#106—34no—
81C3×#106C2×D312yes—
82C3×C4×C8—32no—
83#817—32no—
84#817—34no—
85#817—61no—
86#817C2×D312yes—
87C8×Dic3—32no—
88C8×Dic3C2×D312yes—
89#808—34no—
90#808—34no—
91#808—34no—
92#808—62no—
93#808C2×D314yes—
94C4×C3⋊C8—32no—
95C22×C3⋊D3C2×D411yescharacteristic
96C2×C32×C4—22no—
97C2×C32×C4C2411yescharacteristic
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C2×D411yescharacteristic
100C4×C3⋊D3—44no—
101C4×C3⋊D3C2×Q812yes—
102C4×C3⋊D3C2×Q812yes—
103C2×C3×Dic3—24no—
104C2×C3×Dic3C2×D414yes—
105C3×Dic6—48no—
106#627—48no—
107#624—44no—
108#624SD1618yes—
109C32×C8C2×Q812yescomplemented
110C3⋊(C3⋊C8)C2×Q812yescomplemented
111C3×C3⋊C8C2×Q814yescomplemented
112C2×C4⋊Q8—92no—
113#498—32no—
114#498—92no—
115#498—94no—
116C2×#106—91no—
117C2×#106—92no—
118C2×#106—91no—
119C2×C4×C8—91no—
120C2×C3×Q8—64no—
121D3×Q8—1216no—
122C2×C4×D3—32no—
123C2×C4×D3—34no—
124C2×C4×D3—61no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—122no—
128C2×Dic6—24no—
129C2×Dic6—64no—
130C2×Dic6—64no—
131C2×C3×C8—21no—
132C2×C3×C8—32no—
133C2×C3×C8C22×D312yes—
134C3×C4⋊C4—22no—
135C3×C4⋊C4—34no—
136C3×C4⋊C4—64no—
137C3×C4⋊C4C22×D314yes—
138C3×C42—32no—
139C4⋊Dic3—34no—
140C4⋊Dic3—62no—
141C4⋊Dic3—64no—
142C4⋊Dic3C22×D314yes—
143Dic3⋊C4—24no—
144Dic3⋊C4—64no—
145Dic3⋊C4—64no—
146Dic3⋊C4—64no—
147Dic3⋊C4—122no—
148C4×Dic3—34no—
149C4×Dic3C22×D312yes—
150C2×C3⋊C8—32no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8C22×D312yes—
153D3×C8—38no—
154D3×C8—38no—
155D3×C8—64no—
156C22×C32C22×D411yescharacteristic
157C2×C3⋊D3C4⋊Q812yes—
158C2×C3⋊D3C2×SD1614yes—
159C32×C4—42no—
160C32×C4C22×Q811yescharacteristic
161C32×C4C22×Q811yescharacteristic
162C3⋊Dic3—42no—
163C3⋊Dic3C4⋊Q812yes—
164C3×Dic3—44no—
165C3×Dic3C2×SD1618yes—
166C22×Q8—182no—
167C22×C8—91no—
168C22×C8—91no—
169C4⋊Q8—34no—
170C4⋊Q8—94no—
171C4⋊Q8—184no—
172C2×C4⋊C4—92no—
173C2×C4⋊C4—92no—
174C2×C4⋊C4—182no—
175C2×C42—91no—
176#106—32no—
177#106—34no—
178#106—92no—
179#106—94no—
180#106—91no—
181#106—92no—
182#106D3211yescharacteristic
183C4×C8—32no—
184C4×C8—92no—
185C22×D3—32no—
186C22×D3—61no—
187C3×Q8—128no—
188C2×C3×C4—24no—
189C2×C3×C4—21no—
190C2×C3×C4—34no—
191C2×C3×C4—42no—
192C2×C3×C4—64no—
193C2×C3×C4C23×D312yes—
194C2×Dic3—24no—
195C2×Dic3—32no—
196C2×Dic3—61no—
197C2×Dic3—64no—
198C2×Dic3—122no—
199C2×Dic3D3×D414yes—
200C4×D3—34no—
201C4×D3—34no—
202C4×D3—316no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—128no—
206C4×D3—128no—
207C4×D3—244no—
208Dic6—48no—
209Dic6—128no—
210Dic6—128no—
211C3×C8—22no—
212C3×C8—34no—
213C3×C8D3×Q814yescomplemented
214C3⋊C8—34no—
215C3⋊C8—62no—
216C3⋊C8D3×Q814yescomplemented
217C2×C32C2×C4⋊Q811yescharacteristic
218C2×C32C22×SD1612yes—
219C3⋊D3#49814yescomplemented
220C2×Q8—64no—
221C2×Q8—184no—
222C2×Q8—368no—
223C22×C4—92no—
224C22×C4—91no—
225C22×C4—182no—
226C22×C4—182no—
227C2×C8—32no—
228C2×C8—94no—
229C2×C8—91no—
230C2×C8—94no—
231C2×C8C2×D3211yescharacteristic
232C4⋊C4—34no—
233C4⋊C4—64no—
234C4⋊C4—92no—
235C4⋊C4—182no—
236C4⋊C4—184no—
237C4⋊C4—182no—
238C4⋊C4C2×D3212yes—
239C42—32no—
240C42—92no—
241C22×C3—21no—
242C22×C3C2×D3×D412yes—
243C2×D3—34no—
244C2×D3—38no—
245C2×D3—62no—
246C2×D3—64no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—38no—
250C3×C4—44no—
251C3×C4—82no—
252C3×C4—124no—
253C3×C4C2×D3×Q812yes—
254C3×C4C2×D3×Q812yes—
255Dic3—34no—
256Dic3—44no—
257Dic3—62no—
258Dic3—124no—
259Dic3—242no—
260Dic3D3×SD1618yes—
261C32C2×#49811yescharacteristic, complemented, Sylow
262C23—91no—
263Q8—128no—
264Q8—368no—
265C2×C4—22no—
266C2×C4—34no—
267C2×C4—64no—
268C2×C4—98no—
269C2×C4—91no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—182no—
273C2×C4—364no—
274C2×C4—364no—
275C2×C4C22×D3211yescharacteristic
276C8—34no—
277C8—92no—
278C8#379712yescomplemented
279C2×C3—21no—
280C2×C3—22no—
281C2×C3D3×C4⋊Q812yes—
282C2×C3C2×D3×SD1614yes—
283D3—38no—
284D3—64no—
285C22—92no—
286C22—94no—
287C22D32×D411yescharacteristic
288C4—38no—
289C4—42no—
290C4—92no—
291C4—124no—
292C4—362no—
293C4C2×#379711yescharacteristic
294C4D32×Q811yescharacteristic
295C3—21no—
296C3D3×#49812yescomplemented
297C2—94no—
298C2#1059437411yescharacteristic
299C2D32×SD1612yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#106D32
hypocenterC32C2×#498
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. C3×#4855C2semidirect
4. #10590889C2semidirect
8. #10590412C2semidirect
38. #4855D3semidirect
53. C8×C3⋊D3Q8semidirect
61. #3710Q8semidirect
109. C32×C8C2×Q8semidirect
110. C3⋊(C3⋊C8)C2×Q8semidirect
111. C3×C3⋊C8C2×Q8semidirect
213. C3×C8D3×Q8semidirect
216. C3⋊C8D3×Q8semidirect
219. C3⋊D3#498semidirect
261. C32C2×#498semidirect
278. C8#3797semidirect
296. C3D3×#498semidirect

Maximal subgroups

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

subgroupindex
#105943742
C3⋊D3×#1062
C3×#48552
#105908892
#105906852
C8×#6242
#105905752
#105904122
D3×#4983