Finite Group Databasebeta

← #11874323

Subgroups — #11874323

Order 1152.

882 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 882 conjugacy classes of subgroups — too many to draw. Only its 125 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×#64223C214yesmaximal, complemented
2#10593972C212yesmaximal, complemented
3C4×#3787C211yesmaximal, characteristic, complemented
4#10593450C211yesmaximal, characteristic, complemented
5#10593442C212yesmaximal, complemented
6#10593424C214yesmaximal, complemented
7#10593418C211yesmaximal, characteristic, complemented
8C2×#3798C2214yes—
9C2×#3787C2212yes—
10C2×#3776C2214yes—
11C2×#3775C2218yes—
12C2×#3774C2214yes—
13#64223—216no—
14C42×C3⋊D3C2211yescharacteristic
15C3×C4×D12—22no—
16#63919C2212yes—
17#63916—22no—
18#63915C2214yes—
19#63914C2212yes—
20#63912—22no—
21C4×#625—22no—
22C4×#622C2211yescharacteristic
23C4×#622C2212yes—
24C4×#622C2211yescharacteristic
25#5548—62no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×D12—22no—
30C2×C3×C4×D3—24no—
31C2×#627C2314yes—
32C2×#626—24no—
33C2×#625—22no—
34C2×#625C2314yes—
35#3798—216no—
36C2×#622C2312yes—
37C2×#622C2312yes—
38#3787D418yescomplemented
39#3776—28no—
40#3775—216no—
41#3774—28no—
42C32×C42D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3C2311yescharacteristic
45C4×C3⋊Dic3C2311yescharacteristic
46C3×(C2×D3)⋊C4—24no—
47C3×C4⋊Dic3—22no—
48#3724—22no—
49(C2×D3)⋊Dic3—24no—
50#3147—91nomaximal, Sylow
51C2×#235—64no—
52C3×C4×D4—62no—
53#940—62no—
54#938—62no—
55C4×#67—64no—
56#895—62no—
57#888—62no—
58#885—64no—
59#884—64no—
60C4×D12—22no—
61C42×D3—62no—
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3×D3—24no—
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C4×C3⋊D3C2×D414yes—
73C2×C3×Dic3—24no—
74C3×D12—44no—
75C3×C4×D3—48no—
76#627—28no—
77#626—48no—
78#625—28no—
79#625—44no—
80#622C2×D414yes—
81#622C2×D414yes—
82C2×#135—94no—
83#532—92no—
84#495—94no—
85#494—91no—
86#493—91no—
87#492—92no—
88C2×C4×C8—91no—
89C2×C3×D4—62no—
90C22×C3×C4—64no—
91C2×#67—64no—
92C2×#67—64no—
93C2×#67—64no—
94#235—1216no—
95C2×D12—22no—
96C2×D12—64no—
97C2×C4×D3—24no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×Dic6—64no—
102C3×C4⋊C4—62no—
103C3×C22⋊C4—64no—
104C3×C42—22no—
105#217—64no—
106(C2×D3)⋊C4—24no—
107(C2×D3)⋊C4—64no—
108C4⋊Dic3—22no—
109Dic3⋊C4—64no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C22×C32C22×D411yescharacteristic
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C2×C3⋊D3#12712yes—
117C2×C3×D3—44no—
118C2×C3×D3—44no—
119C2×C3×D3—44no—
120C32×C4—21no—
121C32×C4#12712yes—
122C32×C4#13512yescomplemented
123C3⋊Dic3—21no—
124C3⋊Dic3#13512yescomplemented
125C3⋊Dic3C22×D412yes—
126C3×Dic3—44no—
127C2×#41—94no—
128#135—1816no—
129C2×Q16—94no—
130C2×SD16—98no—
131C2×D8—94no—
132C22×C8—92no—
133C4⋊Q8—92no—
134#127—92no—
135#124—94no—
136#121—182no—
137#121—182no—
138C4×D4—62no—
139C4×D4—182no—
140C2×C42—91no—
141C4×C8—91no—
142C4×C8—91no—
143C4×C8—92no—
144C23×C3—64no—
145C22×D3—24no—
146C22×D3—62no—
147C3×D4—124no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—64no—
152C2×C3×C4—128no—
153#67—128no—
154#67—128no—
155#67—128no—
156C2×Dic3—24no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160D12—44no—
161D12—128no—
162C4×D3—48no—
163C4×D3—68no—
164C4×D3—124no—
165C4×D3—124no—
166Dic6—128no—
167C2×C32C2×#12711yescharacteristic
168C2×C32C2×#13511yescharacteristic
169C2×C32C2×#13511yescharacteristic
170C3⋊D3—22no—
171C3×D3—84no—
172#41—1816no—
173C2×Q8—94no—
174C2×D4—62no—
175C2×D4—94no—
176C2×D4—184no—
177C2×D4—182no—
178C22×C4—64no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4—91no—
182Q16—188no—
183SD16—1816no—
184D8—188no—
185C2×C8—92no—
186C2×C8—92no—
187C2×C8—98no—
188C4⋊C4—62no—
189C4⋊C4—182no—
190C22⋊C4—64no—
191C22⋊C4—184no—
192C42—91no—
193C42—91no—
194C42—91no—
195C42GO+(4,𝔽2)11yescharacteristic
196C22×C3—22no—
197C22×C3—124no—
198C22×C3—124no—
199C22×C3—124no—
200C2×D3—44no—
201C2×D3—44no—
202C2×D3—44no—
203C2×D3—64no—
204C2×D3—122no—
205C2×D3—122no—
206C3×C4—24no—
207C3×C4—24no—
208C3×C4—42no—
209C3×C4—124no—
210Dic3—44no—
211Dic3—64no—
212Dic3—64no—
213Dic3—122no—
214C32#314711yescharacteristic, complemented, Sylow
215C23—64no—
216C23—91no—
217Q8—188no—
218D4—124no—
219D4—188no—
220D4—364no—
221D4—368no—
222C2×C4—64no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—94no—
226C2×C4—91no—
227C2×C4—128no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4C2×GO+(4,𝔽2)11yescharacteristic
231C2×C4C2×GO+(4,𝔽2)11yescharacteristic
232C2×C4C2×GO+(4,𝔽2)11yescharacteristic
233C8—94no—
234C8—94no—
235C2×C3—22no—
236C2×C3—22no—
237C2×C3—22no—
238C2×C3—244no—
239D3—84no—
240D3—124no—
241C22—92no—
242C22—124no—
243C22—124no—
244C22—124no—
245C22—181no—
246C22—181no—
247C22C22×GO+(4,𝔽2)11yescharacteristic
248C4—21no—
249C4—92no—
250C4—92no—
251C4—124no—
252C4—181no—
253C4#6422312yescomplemented
254C4#6423112yes—
255C3—22no—
256C2—182no—
257C2—244no—
258C2C2×#6422311yescharacteristic
259C2#1059650011yescharacteristic
260C2C2×#6423111yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3147
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#64223C2semidirect
2. #10593972C2semidirect
3. C4×#3787C2semidirect
4. #10593450C2semidirect
5. #10593442C2semidirect
6. #10593424C2semidirect
7. #10593418C2semidirect
38. #3787D4semidirect
122. C32×C4#135semidirect
124. C3⋊Dic3#135semidirect
214. C32#3147semidirect
253. C4#64223semidirect

Maximal subgroups

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

subgroupindex
C2×#642232
#105939722
C4×#37872
#105934502
#105934422
#105934242
#105934182
#31479