Finite Group Databasebeta

← #11785982

Subgroups — #11785982

Order 1152.

501 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 154 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×#63641C211yesmaximal, characteristic
2#10591222C211yesmaximal, characteristic
3C2×#63572C211yesmaximal, characteristic
4C3×#4550C212yesmaximal
5#10589155C212yesmaximal
6#68606—32nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4×Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12#63641—22no—
13#63579C412yes—
14#63579C411yescharacteristic
15#63579C411yescharacteristic
16#63572—22no—
17C2×Dic3⋊C8—32no—
18C2×Dic3⋊C8—32no—
19C2×Dic3⋊C8—61no—
20#4932—32no—
21C3×#336—32no—
22#4550—32no—
23#4550D312yes—
24#4524—32no—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3×Dic3C2×C412yes—
29C22×C3×Dic3C2×C412yes—
30C2×C32×C8—21no—
31C2×C32×C8—22no—
32C4×C3⋊Dic3D412yes—
33C4×C3⋊Dic3Q812yes—
34C2×C3⋊(C3⋊C8)—21no—
35C2×C3⋊(C3⋊C8)—22no—
36C3×C4×Dic3—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8—22no—
41#1832—91noSylow
42C22×C3×C8—21no—
43C22×C3×C8—32no—
44C22×C3×C8C2×D312yes—
45C2×C3×C42—32no—
46C2×C4×Dic3—32no—
47C2×C4×Dic3—61no—
48C2×C4×Dic3C2×D312yes—
49C22×C3⋊C8—32no—
50C22×C3⋊C8—61no—
51C22×C3⋊C8C2×D312yes—
52C3⋊#95—32no—
53C3⋊#95—32no—
54C3⋊#95—32no—
55C3⋊#95—32no—
56Dic3⋊C8—64no—
57Dic3⋊C8—64no—
58Dic3⋊C8—64no—
59C23×C32C22×C411yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4C2×Q811yescharacteristic
62C2×C32×C4#4112yes—
63C2×C32×C4#4112yes—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3C4⋊C412yes—
68C2×C3⋊Dic3C4⋊C412yes—
69C2×C3×Dic3—22no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—22no—
75C32×C8—41no—
76C3⋊(C3⋊C8)—41no—
77C3×C3⋊C8—42no—
78C2×C4⋊C8—91no—
79C2×C4⋊C8—91no—
80#376—91no—
81#336—32no—
82#336—92no—
83C22×C3×C4—21no—
84C22×C3×C4—32no—
85C22×C3×C4—32no—
86C22×C3×C4C22×D312yes—
87C22×Dic3—32no—
88C22×Dic3—32no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C22×Dic3C4×D312yes—
92C22×Dic3C4×D312yes—
93C2×C3×C8—22no—
94C2×C3×C8—22no—
95C2×C3×C8—22no—
96C2×C3×C8—22no—
97C2×C3×C8—42no—
98C2×C3×C8—62no—
99C2×C3×C8—62no—
100C2×C3×C8—62no—
101C3×C42—62no—
102C3×C42—62no—
103C4×Dic3—22no—
104C4×Dic3—22no—
105C4×Dic3—34no—
106C4×Dic3—34no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C2×C3⋊C8—22no—
110C2×C3⋊C8—22no—
111C2×C3⋊C8—22no—
112C2×C3⋊C8—62no—
113C2×C3⋊C8—62no—
114C2×C3⋊C8—62no—
115C2×C3⋊C8—62no—
116C2×C3⋊C8—122no—
117C22×C32C2×C4⋊C411yescharacteristic
118C22×C32#11712yes—
119C22×C32#13111yescharacteristic
120C22×C32#13112yes—
121C22×C32#13111yescharacteristic
122C32×C4#12411yescharacteristic
123C32×C4#12411yescharacteristic
124C32×C4#12512yes—
125C3⋊Dic3—22no—
126C3⋊Dic3—22no—
127C3×Dic3—42no—
128C3×Dic3—42no—
129C22×C8—32no—
130C22×C8—91no—
131C22×C8D3211yescharacteristic
132C2×C42—32no—
133C2×C42—91no—
134C4⋊C8—182no—
135C4⋊C8—182no—
136#95—91no—
137#95—92no—
138#95—91no—
139C23×C3—21no—
140C23×C3C2×C4×D312yes—
141C2×C3×C4—22no—
142C2×C3×C4—21no—
143C2×C3×C4—22no—
144C2×C3×C4—21no—
145C2×C3×C4—62no—
146C2×C3×C4—62no—
147C2×C3×C4—62no—
148C2×C3×C4—62no—
149C2×C3×C4—62no—
150C2×C3×C4—62no—
151C2×C3×C4#23512yes—
152C2×C3×C4#23512yes—
153C2×C3×C4D3×D412yes—
154C2×C3×C4#23712yes—
155C2×C3×C4#23712yes—
156C2×C3×C4D3×Q812yes—
157C2×Dic3—22no—
158C2×Dic3—22no—
159C2×Dic3—22no—
160C2×Dic3—22no—
161C2×Dic3—22no—
162C2×Dic3—22no—
163C2×Dic3—34no—
164C2×Dic3—34no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—122no—
174C3×C8—42no—
175C3×C8—42no—
176C3×C8—122no—
177C3⋊C8—42no—
178C3⋊C8—122no—
179C3⋊C8—122no—
180C2×C32#38211yescharacteristic
181C2×C32#42411yescharacteristic
182C2×C32#42411yescharacteristic
183C2×C32#43312yes—
184C2×C32#43312yes—
185C22×C4—32no—
186C22×C4—32no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4C2×D3211yescharacteristic
190C2×C8—22no—
191C2×C8—21no—
192C2×C8—62no—
193C2×C8—62no—
194C2×C8—62no—
195C2×C8—182no—
196C2×C8—181no—
197C42—62no—
198C42—62no—
199C42—92no—
200C42—92no—
201C22×C3—21no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—21no—
206C22×C3#87212yes—
207C22×C3#87712yes—
208C22×C3D3×C4⋊C412yes—
209C22×C3#90112yes—
210C22×C3#90112yes—
211C22×C3#90712yes—
212C22×C3#90712yes—
213C3×C4—22no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—122no—
217C3×C4—122no—
218C3×C4#88512yes—
219C3×C4#88512yes—
220C3×C4#88912yes—
221C3×C4#88912yes—
222Dic3—42no—
223Dic3—42no—
224Dic3—64no—
225Dic3—64no—
226Dic3—64no—
227Dic3—122no—
228C32#183211yescharacteristic, complemented, Sylow
229C23C4×D3211yescharacteristic
230C2×C4—62no—
231C2×C4—62no—
232C2×C4—62no—
233C2×C4—62no—
234C2×C4—62no—
235C2×C4—62no—
236C2×C4—92no—
237C2×C4—92no—
238C2×C4—181no—
239C2×C4—182no—
240C2×C4—181no—
241C2×C4#379512yes—
242C2×C4#379711yescharacteristic
243C2×C4#380412yes—
244C2×C4#381111yescharacteristic
245C8—41no—
246C8—122no—
247C8—361no—
248C2×C3—21no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3#465012yes—
254C2×C3#469012yes—
255C2×C3#470912yes—
256C2×C3#472012yes—
257C2×C3#472012yes—
258C2×C3#483912yes—
259C2×C3#483912yes—
260C22#6380311yescharacteristic
261C22#6380412yes—
262C22#6380511yescharacteristic
263C22#6387712yes—
264C22#6388311yescharacteristic
265C4—122no—
266C4—122no—
267C4—182no—
268C4—182no—
269C4#6384712yes—
270C4#6391311yescharacteristic
271C4#6395311yescharacteristic
272C3—21no—
273C3#6860612yescomplemented
274C2#1059069612yes—
275C2#1059069712yes—
276C2#1059070111yescharacteristic
277C2#1059070211yescharacteristic
278C2#1059124711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutator, socle, prime radicalC23×C32C22×C4
FittingC22×C32×C8C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1832
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
228. C32#1832semidirect
273. C3#68606semidirect

Maximal subgroups

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

subgroupindex
C2×#636412
#105912222
C2×#635722
C3×#45502
#105891552
#686063