Finite Group Databasebeta

← #11795314

Subgroups — #11795314

Order 1152.

409 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 409 conjugacy classes of subgroups — too many to draw. Only its 112 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#10592818C211yesmaximal, characteristic
2C2×#63576C211yesmaximal, characteristic
3#10591130C212yesmaximal
4C3×#4554C212yesmaximal
5#10589165C211yesmaximal, characteristic
6#68980—32nomaximal
7C2×C32×M16C2211yescharacteristic
8#64135C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12#63641—22no—
13#63576—22no—
14#63575—22no—
15#63573—22no—
16#5121—32no—
17#5119—32no—
18#5119—61no—
19#4964—32no—
20C2×#807—32no—
21C3×#343—32no—
22#4558—32no—
23#4554D312yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3×Dic3—22no—
26C32×M16—22no—
27C2×C32×C8—21no—
28#3757—21no—
29C4⋊(C3⋊Dic3)D411yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31C4×C3⋊Dic3—21no—
32C2×C3⋊(C3⋊C8)—22no—
33C2×C3⋊(C3⋊C8)D412yes—
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—22no—
36C3×#208—22no—
37C3×#208Q814yes—
38C2×C3×C3⋊C8—22no—
39#2089—91noSylow
40C2×C3×M16—21no—
41C2×C3×M16—32no—
42C2×C3×M16C2×D312yes—
43C2×C3×C4⋊C4—32no—
44#926—32no—
45#926—61no—
46C2×C4⋊Dic3C2×D312yes—
47C2×#208C2×D312yes—
48C22×C3⋊C8—32no—
49C22×C3⋊C8—61no—
50#818—62no—
51#817—62no—
52Dic3⋊C8—64no—
53Dic3⋊C8—64no—
54#808—62no—
55#807—62no—
56#807—64no—
57C23×C32#4111yescharacteristic
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×Q812yes—
61C2×C32×C4#4112yes—
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—82no—
66C32×C8—41no—
67C3⋊(C3⋊C8)—22no—
68C3×C3⋊C8—24no—
69#428—92no—
70C2×#107—91no—
71#424—91no—
72#343—32no—
73#341—91no—
74C22×C3×C4—21no—
75C22×C3×C4—62no—
76C22×C3×C4C22×D312yes—
77C22×Dic3—22no—
78C3×M16—22no—
79C3×M16—22no—
80C3×M16—34no—
81C3×M16—42no—
82C3×M16—62no—
83C2×C3×C8—22no—
84C2×C3×C8—22no—
85C2×C3×C8—62no—
86C3×C4⋊C4—62no—
87C3×C4⋊C4—62no—
88#217—62no—
89#217—62no—
90C4⋊Dic3—22no—
91C4⋊Dic3—22no—
92C4⋊Dic3—32no—
93C4⋊Dic3—32no—
94C4⋊Dic3—61no—
95C4⋊Dic3—61no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98#208—22no—
99#208Dic614yes—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—34no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—122no—
106C22×C32—21no—
107C22×C32—21no—
108C22×C32#12111yescharacteristic
109C22×C32#12512yes—
110C32×C4C22⋊Q812yes—
111C32×C4#12311yescharacteristic
112C32×C4C4⋊Q811yescharacteristic
113C3⋊Dic3—41no—
114C3⋊Dic3—41no—
115C3×Dic3—82no—
116C2×M16—32no—
117C2×M16D3211yescharacteristic
118C22×C8—91no—
119#117—91no—
120C2×C4⋊C4—32no—
121#107—182no—
122#107—182no—
123#106—182no—
124C4⋊C8—182no—
125C23×C3—21no—
126C23×C3#23512yes—
127C2×C3×C4—22no—
128C2×C3×C4—21no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—122no—
132C2×C3×C4—242no—
133C2×C3×C4C2×Dic612yes—
134C2×C3×C4#23512yes—
135C2×C3×C4D3×D412yes—
136C2×C3×C4D3×D412yes—
137C2×C3×C4#23712yes—
138C2×C3×C4D3×Q812yes—
139C2×Dic3—42no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—82no—
145C3×C8—42no—
146C3×C8—42no—
147C3×C8—64no—
148C3⋊C8—24no—
149C3⋊C8—64no—
150C3⋊C8—122no—
151C2×C32—22no—
152C2×C32#39811yescharacteristic
153C2×C32#47211yescharacteristic
154C2×C32#47311yescharacteristic
155C22×C4—62no—
156C22×C4C2×D3211yescharacteristic
157M16—22no—
158M16—34no—
159M16—62no—
160C2×C8—21no—
161C2×C8—62no—
162C2×C8—92no—
163C2×C8—182no—
164C4⋊C4—62no—
165C4⋊C4—62no—
166C4⋊C4—91no—
167C4⋊C4—91no—
168C22⋊C4—181no—
169C42—181no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—22no—
173C22×C3—21no—
174C22×C3—41no—
175C22×C3—41no—
176C22×C3#87012yes—
177C22×C3#88412yes—
178C22×C3#88912yes—
179C3×C4—21no—
180C3×C4—22no—
181C3×C4—21no—
182C3×C4—242no—
183C3×C4#87812yes—
184C3×C4#88312yes—
185C3×C4#88812yes—
186C3×C4#89612yes—
187Dic3—82no—
188Dic3—122no—
189Dic3—122no—
190Dic3—122no—
191Dic3—122no—
192C32#208911yescharacteristic, complemented, Sylow
193C23#379811yescharacteristic
194C2×C4—122no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4—242no—
198C2×C4D3×Dic612yes—
199C2×C4#380211yescharacteristic
200C2×C4#380412yes—
201C2×C4#381111yescharacteristic
202C8—41no—
203C8—64no—
204C8—182no—
205C2×C3—22no—
206C2×C3—22no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—42no—
211C2×C3#465712yes—
212C2×C3#474912yes—
213C2×C3#475512yes—
214C22—21no—
215C22—21no—
216C22#6386712yes—
217C22#6391211yescharacteristic
218C4—242no—
219C4—361no—
220C4—361no—
221C4#6384011yescharacteristic
222C4#6389912yes—
223C4#6397511yescharacteristic
224C3—21no—
225C3#6898012yescomplemented
226C2—22no—
227C2#1059098811yescharacteristic
228C2#1059099311yescharacteristic
229C2#1059135611yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC23×C32#41
hypercenterC2×M16D32
hypocenterC32#2089
LCSG ▷ C22×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
192. C32#2089semidirect
225. C3#68980semidirect

Maximal subgroups

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

subgroupindex
#105928182
C2×#635762
#105911302
C3×#45542
#105891652
#689803