Finite Group Databasebeta

← #11860842

Subgroups — #11860842

Order 1152.

722 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 151 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×#64228C211yesmaximal, characteristic
2#10594347C212yesmaximal
3#10593748C211yesmaximal, characteristic
4#10593445C212yesmaximal, complemented
5C4×#3776C212yesmaximal, complemented
6#10593389C211yesmaximal, characteristic
7#10593374C212yesmaximal
8#10593369C214yesmaximal, complemented
9C2×#3797C2212yes—
10C2×#3788C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3776C2212yes—
13C2×#3776C2212yes—
14#64228C418yescomplemented
15#64101C2211yescharacteristic
16C3×#887—22no—
17C4×#627C2214yes—
18#63874C2212yes—
19Dic3×Dic6—22no—
20#63838C2214yes—
21#63836—24no—
22#63777C2212yes—
23C4×#622C2212yes—
24#63743C2211yescharacteristic
25#63743C2211yescharacteristic
26#63742C2212yes—
27#63740C2214yes—
28#63740C2214yes—
29#5572—62no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×Dic6—22no—
32C2×#627C2314yes—
33C2×#624—22no—
34#3797—24no—
35#3797C2×C418yes—
36C2×#622C2312yes—
37C2×#622C2311yescharacteristic
38C2×#622C2311yescharacteristic
39#3788—22no—
40#3787C2×C414yes—
41#3776C2×C418yes—
42#3776C2×C418yes—
43C32×C4⋊C4D411yescharacteristic
44#3752D412yes—
45C4⋊(C3⋊Dic3)D411yescharacteristic
46C4×C3⋊Dic3C2312yes—
47C3×Dic3⋊C4—24no—
48C3×C4×Dic3—24no—
49C3×C4×Dic3—22no—
50#3724C2312yes—
51#3724C2312yes—
52Dic3⋊Dic3—24no—
53#3722—22no—
54Dic32—24no—
55#2950—91nomaximal, Sylow
56C2×D3×Q8—62no—
57C3×C4×Q8—62no—
58Q8×Dic3—62no—
59#892—62no—
60#892—64no—
61#887—22no—
62#887—64no—
63#872—62no—
64#872—64no—
65C4×Dic6—64no—
66C4×Dic6—62no—
67C22×C3⋊D3C2×D411yescharacteristic
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C2×D412yes—
71C2×C3⋊Dic3C2411yescharacteristic
72C4×C3⋊D3C22×C412yes—
73C4×C3⋊D3#4112yes—
74C2×C3×Dic3—24no—
75C2×C3×Dic3—22no—
76C2×C3×Dic3—22no—
77C3×Dic6—28no—
78#627—24no—
79#627C22×C418yes—
80#624—28no—
81#622—22no—
82#622C22×C412yes—
83#622C22×C412yes—
84C22×Q16—91no—
85#519—92no—
86#441—94no—
87C4×Q16—92no—
88C4×Q16—92no—
89#427—91no—
90#419—92no—
91#405—91no—
92C2×C3×Q8—62no—
93D3×Q8—68no—
94D3×Q8—68no—
95C2×C4×D3—62no—
96C2×C4×D3—64no—
97C2×Dic6—22no—
98C2×Dic6—64no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—64no—
101C3×C42—62no—
102C3×C42—64no—
103(C2×D3)⋊C4—64no—
104(C2×D3)⋊C4—62no—
105(C2×D3)⋊C4—62no—
106C4⋊Dic3—62no—
107C4⋊Dic3—64no—
108Dic3⋊C4—24no—
109Dic3⋊C4—62no—
110Dic3⋊C4—62no—
111Dic3⋊C4—64no—
112C4×Dic3—24no—
113C4×Dic3—22no—
114C4×Dic3—64no—
115C4×Dic3—64no—
116C4×Dic3—64no—
117C22×C32C22×D411yescharacteristic
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3C4×D412yes—
121C32×C4—22no—
122C32×C4C4×D412yes—
123C3⋊Dic3—22no—
124C3⋊Dic3C23×C411yescharacteristic
125C3⋊Dic3C2×#4111yescharacteristic
126C3×Dic3—28no—
127C3×Dic3—42no—
128C3×Dic3—42no—
129C22×Q8—92no—
130C2×Q16—92no—
131C2×Q16—92no—
132C2×Q16—98no—
133C2×M16—91no—
134C22×C8—91no—
135C4×Q8—62no—
136C4×Q8—94no—
137C4×Q8—94no—
138C4×Q8—182no—
139#117—92no—
140#117—91no—
141#117—184no—
142#107—91no—
143#107—91no—
144#106—92no—
145#103—94no—
146#103—94no—
147#97—92no—
148C4×C8—92no—
149C22×D3—62no—
150C3×Q8—68no—
151C2×C3×C4—22no—
152C2×C3×C4—24no—
153C2×C3×C4—64no—
154C2×C3×C4—62no—
155C2×C3×C4—62no—
156C2×Dic3—24no—
157C2×Dic3—22no—
158C2×Dic3—22no—
159C2×Dic3—62no—
160C2×Dic3—64no—
161C4×D3—64no—
162C4×D3—64no—
163C4×D3—616no—
164Dic6—28no—
165Dic6—68no—
166Dic6—68no—
167C2×C32C2×C4×D411yescharacteristic
168C2×C32#57811yescharacteristic
169C2×C32#57811yescharacteristic
170C3⋊D3—22no—
171C2×Q8—62no—
172C2×Q8—94no—
173C2×Q8—98no—
174C2×Q8—184no—
175C22×C4—91no—
176C22×C4—182no—
177Q16—98no—
178Q16—98no—
179M16—182no—
180C2×C8—91no—
181C2×C8—91no—
182C2×C8—94no—
183C2×C8—92no—
184C4⋊C4—64no—
185C4⋊C4—92no—
186C4⋊C4—92no—
187C4⋊C4—91no—
188C4⋊C4—184no—
189C4⋊C4GO+(4,𝔽2)11yescharacteristic
190C22⋊C4—92no—
191C22⋊C4—182no—
192C42—62no—
193C42—64no—
194C42—92no—
195C42—184no—
196C22×C3—22no—
197C2×D3—64no—
198C2×D3—122no—
199C2×D3—122no—
200C3×C4—24no—
201C3×C4—44no—
202C3×C4—68no—
203C3×C4—122no—
204C3×C4—122no—
205Dic3—28no—
206Dic3—42no—
207Dic3—42no—
208Dic3—62no—
209Dic3—62no—
210Dic3—124no—
211C32#295011yescharacteristic, complemented, Sylow
212C23—91no—
213Q8—68no—
214Q8—98no—
215Q8—184no—
216C2×C4—64no—
217C2×C4—62no—
218C2×C4—62no—
219C2×C4—91no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—188no—
224C2×C4C2×GO+(4,𝔽2)12yes—
225C2×C4C2×GO+(4,𝔽2)11yescharacteristic
226C8—92no—
227C8—92no—
228C8—182no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232D3—124no—
233C22—92no—
234C22—181no—
235C22—181no—
236C22C22×GO+(4,𝔽2)11yescharacteristic
237C4—22no—
238C4—68no—
239C4—91no—
240C4—91no—
241C4—122no—
242C4—122no—
243C4—182no—
244C4C4×GO+(4,𝔽2)12yes—
245C3—22no—
246C2—182no—
247C2C2×C4×GO+(4,𝔽2)11yescharacteristic
248C2#1059651611yescharacteristic
249C2#1059652011yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2950
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10593445C2semidirect
5. C4×#3776C2semidirect
8. #10593369C2semidirect
14. #64228C4semidirect
211. C32#2950semidirect

Maximal subgroups

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

subgroupindex
C2×#642282
#105943472
#105937482
#105934452
C4×#37762
#105933892
#105933742
#105933692
#29509