Finite Group Databasebeta

← #11787796

Subgroups — #11787796

Order 1152.

1080 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 221 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#10596269C211yesmaximal, characteristic
2C2×#64145C211yesmaximal, characteristic
3C2×C32×#100C211yesmaximal, characteristic
4#10592819C212yesmaximal, complemented
5#10589421C212yesmaximal, complemented
6#70069—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×#3757—22no—
11C2×#3757—22no—
12#64145—22no—
13#64145C414yescomplemented
14D4×C3⋊Dic3—24no—
15#64135C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C32×#100—22no—
18#63643—24no—
19#5798—34no—
20C2×#936—34no—
21C2×C3×#100D314yes—
22#5120—38no—
23#4555—38no—
24C24×C32D412yes—
25C2×C32×D4—22no—
26C2×C32×D4—22no—
27C2×C32×D4C2×C412yes—
28C2×C32×D4D412yes—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—24no—
33C2×#634—22no—
34C2×#634—22no—
35C2×#634—21no—
36C2×#634C2×C412yescomplemented
37C32×M16—22no—
38C32×M16—22no—
39C2×C32×C8—22no—
40#3757—24no—
41#3757—28no—
42#3757—22no—
43C4⋊(C3⋊Dic3)D414yes—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3—22no—
46C4×C3⋊Dic3C2×C412yescomplemented
47#1885—91noSylow
48C22×C3×D4C2×D314yes—
49C22×Dic6—34no—
50C2×C3×M16C2×D318yes—
51C2×#217—68no—
52C2×#217—68no—
53#936—316no—
54#936—68no—
55D4×Dic3—616no—
56#926—38no—
57C2×C4×Dic3—34no—
58C3×#100—28no—
59#816—616no—
60C23×C32—22no—
61C23×C32—22no—
62C23×C32—44no—
63C23×C32C22⋊C414yes—
64C23×C32C2×D411yescharacteristic
65C32×D4—24no—
66C32×D4—24no—
67C2×C32×C4C22×C411yescharacteristic
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4#4112yes—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3—42no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—84no—
78#634—24no—
79#634—42no—
80C32×C8—42no—
81C2×#124—91no—
82#518—91no—
83#419—92no—
84C2×#100C3⋊D311yescharacteristic
85#339—92no—
86C24×C3D1218yes—
87C2×C3×D4—28no—
88C2×C3×D4—28no—
89C2×C3×D4C4×D318yes—
90C2×C3×D4#6718yes—
91C22×C3×C4C22×D314yes—
92C22×Dic3—64no—
93C22×Dic3—64no—
94C22×Dic3—616no—
95C2×Dic6—38no—
96C2×Dic6—68no—
97C2×Dic6—68no—
98C2×Dic6—64no—
99C3×M16—28no—
100C3×M16—28no—
101C2×C3×C8—28no—
102#217—616no—
103#217—632no—
104#217—68no—
105C4⋊Dic3—316no—
106C4×Dic3—38no—
107C4×Dic3—68no—
108C4×Dic3—64no—
109C22×C32—22no—
110C22×C32—24no—
111C22×C32—44no—
112C22×C32—44no—
113C22×C32—82no—
114C22×C32C2×C22⋊C411yescharacteristic
115C22×C32#12011yescharacteristic
116C22×C32#12311yescharacteristic
117C32×C4C4×D412yes—
118C32×C4#12112yes—
119C3⋊Dic3—42no—
120C3⋊Dic3—42no—
121C3⋊Dic3—44no—
122C22×Q8—91no—
123C22×D4C2×C3⋊D311yescharacteristic
124C2×M16C2×C3⋊D312yes—
125#124—94no—
126#124—182no—
127C4×D4—184no—
128#117—92no—
129C2×C22⋊C4—182no—
130C2×C22⋊C4—182no—
131C2×C42—91no—
132#103—184no—
133#100—22no—
134C23×C3—28no—
135C23×C3—28no—
136C23×C3—416no—
137C23×C3(C2×D3)⋊C4116yes—
138C23×C3C2×D1214yes—
139C3×D4—216no—
140C3×D4—216no—
141C2×C3×C4C2×C4×D314yes—
142C2×C3×C4D3×D418yes—
143C2×C3×C4#23718yes—
144C2×C3×C4C2×#6714yes—
145C2×Dic3—616no—
146C2×Dic3—68no—
147C2×Dic3—68no—
148C2×Dic3—128no—
149C2×Dic3—124no—
150C2×Dic3—124no—
151C2×Dic3—2416no—
152Dic6—616no—
153Dic6—128no—
154C3×C8—48no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—44no—
158C2×C32#38611yescharacteristic
159C2×C32#45512yes—
160C24C4⋊(C3⋊D3)12yes—
161C2×Q8—92no—
162C2×Q8—181no—
163C2×Q8—182no—
164C2×Q8—182no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4C4×C3⋊D312yes—
168C2×D4#63812yes—
169C22×C4—181no—
170C22×C4—181no—
171C22×C4—184no—
172C22×C4C22×C3⋊D311yescharacteristic
173M16—22no—
174M16—22no—
175C2×C8—22no—
176C4⋊C4—94no—
177C22⋊C4—184no—
178C22⋊C4—188no—
179C22⋊C4—182no—
180C42—92no—
181C42—182no—
182C42—181no—
183C22×C3—28no—
184C22×C3—216no—
185C22×C3—416no—
186C22×C3—416no—
187C22×C3—88no—
188C22×C3#88214yes—
189C22×C3#88614yes—
190C22×C3C2×(C2×D3)⋊C414yes—
191C3×C4#67⋊C418yes—
192C3×C4#93918yes—
193Dic3—128no—
194Dic3—128no—
195Dic3—1216no—
196C32#188511yescharacteristic, complemented, Sylow
197C23—22no—
198C23—22no—
199C23—44no—
200C23#375214yes—
201C23C2×C4⋊(C3⋊D3)11yescharacteristic
202Q8—184no—
203Q8—362no—
204D4—24no—
205D4—24no—
206C2×C4—184no—
207C2×C4—182no—
208C2×C4—182no—
209C2×C4—362no—
210C2×C4—361no—
211C2×C4—361no—
212C2×C4—724no—
213C2×C4C2×C4×C3⋊D311yescharacteristic
214C2×C4D4×C3⋊D312yes—
215C2×C4#383012yes—
216C2×C4C2×#63811yescharacteristic
217C8—42no—
218C2×C3—24no—
219C2×C3—24no—
220C2×C3—416no—
221C2×C3#474618yes—
222C2×C3#495814yes—
223C22—22no—
224C22—24no—
225C22—44no—
226C22—44no—
227C22—82no—
228C22#6409111yescharacteristic
229C22#6409511yescharacteristic
230C22C2×#375211yescharacteristic
231C4—362no—
232C4—362no—
233C4—364no—
234C4#6409012yes—
235C4#6414812yes—
236C3#7006914yescomplemented
237C2—21no—
238C2—21no—
239C2—44no—
240C2#1059244512yes—
241C2#1059265711yescharacteristic
subgroupG/H
centerC22#64091
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#100C2
socleC22×C32#120
prime radicalC22×C32×D4C22
cosocleC22×C32×C4C23
hypercenterC2×#100C3⋊D3
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
4. #10592819C2semidirect
5. #10589421C2semidirect
13. #64145C4semidirect
36. C2×#634C2×C4semidirect
46. C4×C3⋊Dic3C2×C4semidirect
196. C32#1885semidirect
236. C3#70069semidirect

Maximal subgroups

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

subgroupindex
#105962692
C2×#641452
C2×C32×#1002
#105928192
#105894212
#700693