Finite Group Databasebeta

← #11790506

Subgroups — #11790506

Order 1152.

457 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 457 conjugacy classes of subgroups — too many to draw. Only its 132 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#10592821C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3C2×#63576C211yesmaximal, characteristic
4#10591130C212yesmaximal
5C3×#4554C212yesmaximal
6#68985—32nomaximal
7C2×C32×M16C2211yescharacteristic
8#64135C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12#63642—21no—
13C8×C3⋊Dic3—21no—
14#63578C414yescomplemented
15#63576—21no—
16#63576—21no—
17#63575—22no—
18#63573—22no—
19C2×#822—32no—
20#5122—32no—
21#5122—61no—
22#5121—32no—
23#4964—32no—
24C2×#807—32no—
25C3×#343—32no—
26#4554D312yes—
27C22×C32×C4C2311yescharacteristic
28C22×C3×Dic3—22no—
29C32×M16—21no—
30C32×M16Q812yes—
31C2×C32×C8—21no—
32#3757—21no—
33C4⋊(C3⋊Dic3)D411yescharacteristic
34C4⋊(C3⋊Dic3)D411yescharacteristic
35C4×C3⋊Dic3—21no—
36C2×C3⋊(C3⋊C8)C2×C412yes—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C2×C3⋊(C3⋊C8)Q812yes—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3—22no—
42C3×#208—22no—
43C3×#208C2×C414yes—
44C2×C3×C3⋊C8—22no—
45#1952—91noSylow
46C2×C3×M16—21no—
47C2×C3×M16—32no—
48C2×C3×M16C2×D312yes—
49C2×C3×C4⋊C4—32no—
50#926—32no—
51#926—61no—
52C2×C4⋊Dic3C2×D312yes—
53C2×#208C2×D312yes—
54C22×C3⋊C8—32no—
55C22×C3⋊C8—61no—
56#822—38no—
57#818—62no—
58#817—62no—
59#815—62no—
60#815—62no—
61C8×Dic3—62no—
62C8×Dic3—62no—
63#808—62no—
64#807—62no—
65#807—62no—
66#807—62no—
67C23×C32#4111yescharacteristic
68C2×C32×C4C22×C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×Q811yescharacteristic
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4#4111yescharacteristic
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—21no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—82no—
78C32×C8—22no—
79C3⋊(C3⋊C8)C4⋊C412yes—
80C3⋊(C3⋊C8)C4⋊C412yes—
81C3×C3⋊C8—24no—
82C2×#108—91no—
83#428—92no—
84C2×#107—91no—
85#405—91no—
86#343—32no—
87C22×C3×C4—21no—
88C22×C3×C4—62no—
89C22×C3×C4C22×D312yes—
90C22×Dic3—22no—
91C3×M16—22no—
92C3×M16—22no—
93C3×M16—22no—
94C3×M16—34no—
95C3×M16—62no—
96C3×M16Dic614yes—
97C2×C3×C8—22no—
98C2×C3×C8—22no—
99C2×C3×C8—62no—
100C3×C4⋊C4—62no—
101C3×C4⋊C4—62no—
102#217—62no—
103#217—62no—
104C4⋊Dic3—22no—
105C4⋊Dic3—22no—
106C4⋊Dic3—32no—
107C4⋊Dic3—32no—
108C4⋊Dic3—61no—
109C4⋊Dic3—61no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112#208—22no—
113#208C4×D314yes—
114C2×C3⋊C8—22no—
115C2×C3⋊C8—34no—
116C2×C3⋊C8—32no—
117C2×C3⋊C8—32no—
118C2×C3⋊C8—34no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—62no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32C4×Q811yescharacteristic
126C22×C32#12111yescharacteristic
127C22×C32#12511yescharacteristic
128C32×C4C2×C4⋊C411yescharacteristic
129C32×C4C4×D411yescharacteristic
130C32×C4C22⋊Q811yescharacteristic
131C32×C4C4⋊Q811yescharacteristic
132C3⋊Dic3—41no—
133C3⋊Dic3—41no—
134C3×Dic3—82no—
135C2×M16—32no—
136C2×M16D3211yescharacteristic
137C22×C8—91no—
138#117—91no—
139C2×C4⋊C4—32no—
140#108—94no—
141#107—181no—
142#107—181no—
143#107—182no—
144#106—182no—
145#97—181no—
146C4×C8—181no—
147C23×C3—21no—
148C23×C3#23512yes—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—122no—
156C2×C3×C4—242no—
157C2×C3×C4C2×Dic612yes—
158C2×C3×C4C2×C4×D312yes—
159C2×C3×C4D3×D412yes—
160C2×C3×C4D3×D412yes—
161C2×C3×C4#23712yes—
162C2×C3×C4D3×Q812yes—
163C2×Dic3—42no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—82no—
169C3×C8—24no—
170C3×C8—24no—
171C3×C8—64no—
172C3⋊C8—24no—
173C3⋊C8—34no—
174C3⋊C8—34no—
175C3⋊C8—62no—
176C3⋊C8—62no—
177C2×C32—21no—
178C2×C32—21no—
179C2×C32#38911yescharacteristic
180C2×C32#47211yescharacteristic
181C2×C32#47311yescharacteristic
182C22×C4—62no—
183C22×C4C2×D3211yescharacteristic
184M16—21no—
185M16—34no—
186M16—62no—
187M16#62712yes—
188C2×C8—21no—
189C2×C8—62no—
190C2×C8—92no—
191C2×C8—92no—
192C2×C8—91no—
193C2×C8—91no—
194C4⋊C4—62no—
195C4⋊C4—62no—
196C4⋊C4—91no—
197C4⋊C4—91no—
198C22⋊C4—181no—
199C42—181no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—41no—
206C22×C3—41no—
207C22×C3C4×Dic612yes—
208C22×C3#88412yes—
209C22×C3#88912yes—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—242no—
215C3×C4#87812yes—
216C3×C4#67⋊C412yes—
217C3×C4#88812yes—
218C3×C4D3×C4⋊C412yes—
219Dic3—82no—
220Dic3—122no—
221Dic3—122no—
222Dic3—122no—
223Dic3—122no—
224C32#195211yescharacteristic, complemented, Sylow
225C23#379811yescharacteristic
226C2×C4—122no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—242no—
230C2×C4#379711yescharacteristic
231C2×C4C4×D3211yescharacteristic
232C2×C4#380211yescharacteristic
233C2×C4#380511yescharacteristic
234C2×C4C2×#62711yescharacteristic
235C2×C4#381111yescharacteristic
236C8—22no—
237C8—64no—
238C8—92no—
239C8—92no—
240C2×C3—22no—
241C2×C3—22no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—41no—
246C2×C3—41no—
247C2×C3#464712yes—
248C2×C3#474912yes—
249C2×C3#475512yes—
250C22—21no—
251C22—21no—
252C22#6387011yescharacteristic
253C22#6391211yescharacteristic
254C22C4×#62711yescharacteristic
255C4—242no—
256C4—361no—
257C4—361no—
258C4#6388311yescharacteristic
259C4#6390211yescharacteristic
260C4#6391911yescharacteristic
261C4#6398211yescharacteristic
262C3—21no—
263C3#6898512yescomplemented
264C2—21no—
265C2—21no—
266C2#1059098811yescharacteristic
267C2#1059099311yescharacteristic
268C2#1059132811yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC23×C32#41
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1952
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
14. #63578C4semidirect
224. C32#1952semidirect
263. C3#68985semidirect

Maximal subgroups

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

subgroupindex
#105928212
C2×#635782
C2×#635762
#105911302
C3×#45542
#689853