Finite Group Databasebeta

← #11858446

Subgroups — #11858446

Order 1152.

842 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 199 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
1C22×#3787C211yesmaximal, characteristic
2#10594969C212yesmaximal
3#10593511C214yesmaximal, complemented
4#10593396C212yesmaximal, complemented
5#10593389C214yesmaximal, complemented
6#10593387C212yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#622C2212yes—
9C2×#3787C418yescomplemented
10C2×#3787C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3787C2212yes—
13C3×#926—22no—
14#63974—22no—
15#63957C2214yes—
16#63900C2214yes—
17C4×#624—22no—
18#63874C2214yes—
19#63849—22no—
20#63743C2218yescomplemented
21#63742C2218yescomplemented
22D3×#117—62no—
23C23×C3⋊D3D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3C2×C414yes—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3Q814yes—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×#624—24no—
33C2×#622C2×C418yescomplemented
34C2×#622C2312yes—
35C2×#622C2312yes—
36#3787C2×C414yes—
37#3787C2×C414yes—
38#3787C2×C418yescomplemented
39C3×#217—24no—
40C3×C4⋊Dic3—24no—
41C3×C4×Dic3—24no—
42#3724C2318yes—
43#3722—24no—
44Dic32—24no—
45C2×#427—91nomaximal, Sylow
46C22×C4×D3—62no—
47C3×#117—62no—
48#926—22no—
49#892—64no—
50D3×C4⋊C4—64no—
51D3×C22⋊C4—64no—
52#877—64no—
53#872—64no—
54C42×D3—64no—
55C23×C32C2×D411yescharacteristic
56C22×C3⋊D3—24no—
57C22×C3⋊D3C4⋊C414yes—
58C22×C3⋊D3C2×D411yescharacteristic
59C22×C3⋊D3C2×D411yescharacteristic
60C2×C32×C4C4⋊C414yes—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3C22×C412yes—
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3C2×Q812yes—
66C2×C3⋊Dic3C2411yescharacteristic
67C4×C3⋊D3C4⋊C414yes—
68C4×C3⋊D3C4⋊C414yes—
69C4×C3⋊D3C22×C412yes—
70C4×C3⋊D3C22×C412yes—
71C4×C3⋊D3C2×Q812yes—
72C4×C3⋊D3C2×Q812yes—
73C2×C3×Dic3—28no—
74#624—48no—
75#622C22×C414yes—
76#622C22×C414yes—
77C23×C8—91no—
78C2×#117—92no—
79#427—94no—
80#427—94no—
81C2×#107—92no—
82C2×#106—92no—
83C23×D3—62no—
84C22×C3×C4—22no—
85C22×Dic3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—68no—
91C2×C4×D3—68no—
92C2×C4×D3—68no—
93C3×C4⋊C4—64no—
94C3×C22⋊C4—64no—
95C3×C42—64no—
96#217—24no—
97(C2×D3)⋊C4—68no—
98C4⋊Dic3—24no—
99Dic3⋊C4—68no—
100C4×Dic3—24no—
101C4×Dic3—68no—
102C22×C32—22no—
103C22×C32C2×C4⋊C412yes—
104C22×C32C22×D411yescharacteristic
105C2×C3⋊D3—22no—
106C2×C3⋊D3—28no—
107C2×C3⋊D3C2×C4⋊C412yes—
108C2×C3⋊D3C2×C4⋊C412yes—
109C2×C3⋊D3#13514yes—
110C32×C4C2×C4⋊C412yes—
111C32×C4C2×C4⋊C412yes—
112C3⋊Dic3C2×C4⋊C412yes—
113C3⋊Dic3C23×C411yescharacteristic
114C3⋊Dic3C22×Q811yescharacteristic
115C3×Dic3—48no—
116C23×C4—91no—
117C22×C8—98no—
118C22×C8—91no—
119C22×C8—91no—
120C22×C8—92no—
121C22×C8—92no—
122#117—62no—
123#117—94no—
124#117—94no—
125#117—182no—
126C2×C4⋊C4—94no—
127C2×C22⋊C4—182no—
128C2×C42—182no—
129#107—98no—
130#106—98no—
131C23×C3—22no—
132C22×D3—62no—
133C22×D3—68no—
134C22×D3—62no—
135C22×D3—128no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×C3×C4—28no—
139C2×C3×C4—68no—
140C2×Dic3—28no—
141C2×Dic3—64no—
142C2×Dic3—62no—
143C2×Dic3—64no—
144C2×Dic3—62no—
145C4×D3—68no—
146C4×D3—68no—
147C4×D3—64no—
148C4×D3—64no—
149C4×D3—64no—
150C4×D3—64no—
151C4×D3—1216no—
152C2×C32—22no—
153C2×C32C22×C4⋊C411yescharacteristic
154C2×C32C2×#13512yes—
155C3⋊D3—22no—
156C3⋊D3#42714yescomplemented
157C24—91no—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—94no—
164C22×C4—94no—
165C22×C4—184no—
166C22×C4GO+(4,𝔽2)11yescharacteristic
167C2×C8—92no—
168C2×C8—92no—
169C2×C8—94no—
170C2×C8—94no—
171C2×C8—98no—
172C2×C8—98no—
173C4⋊C4—64no—
174C4⋊C4—98no—
175C22⋊C4—64no—
176C22⋊C4—184no—
177C42—64no—
178C42—184no—
179C22×C3—22no—
180C22×C3—24no—
181C22×C3—44no—
182C2×D3—64no—
183C2×D3—68no—
184C2×D3—64no—
185C2×D3—1216no—
186C2×D3—124no—
187C3×C4—24no—
188C3×C4—24no—
189C3×C4—128no—
190Dic3—48no—
191Dic3—64no—
192Dic3—62no—
193Dic3—62no—
194C32C2×#42711yescharacteristic, complemented, Sylow
195C23—91no—
196C23—91no—
197C23—94no—
198C23—184no—
199C23C2×GO+(4,𝔽2)11yescharacteristic
200C2×C4—68no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—92no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—94no—
209C2×C4—94no—
210C2×C4—92no—
211C2×C4—368no—
212C2×C4#377314yes—
213C2×C4C2×GO+(4,𝔽2)11yescharacteristic
214C2×C4C2×GO+(4,𝔽2)11yescharacteristic
215C8—94no—
216C8—94no—
217C2×C3—24no—
218C2×C3—22no—
219C2×C3—44no—
220D3—68no—
221D3—124no—
222C22—22no—
223C22—94no—
224C22—92no—
225C22—92no—
226C22—188no—
227C22—182no—
228C22C2×#377312yes—
229C22C22×GO+(4,𝔽2)11yescharacteristic
230C4—91no—
231C4—92no—
232C4—91no—
233C4—128no—
234C4C2×#377312yes—
235C4C2×#377312yes—
236C3—22no—
237C2—22no—
238C2—94no—
239C2—182no—
240C2#1059650012yes—
241C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#427
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593511C2semidirect
4. #10593396C2semidirect
5. #10593389C2semidirect
6. #10593387C2semidirect
9. C2×#3787C4semidirect
20. #63743C22semidirect
21. #63742C22semidirect
33. C2×#622C2×C4semidirect
38. #3787C2×C4semidirect
156. C3⋊D3#427semidirect
194. C32C2×#427semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
#105949692
#105935112
#105933962
#105933892
#105933872
C2×#4279