Finite Group Databasebeta

← #11776173

Subgroups — #11776173

Order 1152.

636 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 149 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#10596199C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic
3C3⋊D3×C4⋊C8C211yesmaximal, characteristic
4C32×#333C211yesmaximal, characteristic, complemented
5#10589412C211yesmaximal, characteristic, complemented
6#10589352C211yesmaximal, characteristic, complemented
7#10589348C211yesmaximal, characteristic, complemented
8#68481—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10#64155C412yes—
11Q8×C3⋊Dic3C412yes—
12C2×C8×C3⋊D3—21no—
13#64106—21no—
14#64101—21no—
15#64099—21no—
16#64096—21no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21#63647—21no—
22#63641—21no—
23C8×C3⋊Dic3—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26#5728—34no—
27#4833—34no—
28D3×C4⋊C8—34no—
29C3×#333D314yescomplemented
30#4546—34no—
31#4486—34no—
32#4482—34no—
33C2×C32×Q8C2×C412yes—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×#634—21no—
38C2×C32×C8—21no—
39C2×C32×C8—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C42C2311yescharacteristic
43#3752—22no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—22no—
46C4⋊(C3⋊Dic3)C2×C412yes—
47#3750—22no—
48C4×C3⋊Dic3—22no—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C8×C3⋊D3—42no—
55#1542—91noSylow
56C3×C4⋊Q8C2×D314yes—
57#946—38no—
58Q8×Dic3—38no—
59C2×D3×C8—64no—
60#897—64no—
61#892—64no—
62#890—64no—
63#887—64no—
64C42×D3—34no—
65#869—34no—
66C3×C4⋊C8C2×D314yes—
67C3×C4⋊C8C2×D314yes—
68(C2×D3)⋊C8—64no—
69Dic3⋊C8—64no—
70C8×Dic3—64no—
71C4⋊(C3⋊C8)—34no—
72C4⋊(C3⋊C8)—34no—
73C22×C3⋊D3C22⋊C411yescharacteristic
74C32×Q8—42no—
75C2×C32×C4—22no—
76C2×C32×C4C22×C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C4×C3⋊D3—21no—
84C4×C3⋊D3—21no—
85C4×C3⋊D3—41no—
86C4×C3⋊D3SD1612yes—
87C4×C3⋊D3Q1612yes—
88#634—41no—
89#634—41no—
90C32×C8—41no—
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93C3⋊(C3⋊C8)—41no—
94#533—91no—
95#431—91no—
96C2×C4⋊C8—91no—
97#333—91no—
98#333C3⋊D311yescharacteristic, complemented
99#332—91no—
100#332—91no—
101C2×C3×Q8C4×D318yes—
102C2×C4×D3—34no—
103C2×C4×D3—34no—
104C2×C4×D3—34no—
105C2×Dic6—64no—
106C2×C3×C8—24no—
107C2×C3×C8—24no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4—24no—
110C3×C42C22×D314yes—
111(C2×D3)⋊C4—68no—
112C4⋊Dic3—38no—
113C4⋊Dic3—68no—
114C4⋊Dic3—64no—
115Dic3⋊C4—68no—
116C4×Dic3—34no—
117C4×Dic3—34no—
118C4×Dic3—34no—
119C4×Dic3—68no—
120C2×C3⋊C8—64no—
121C2×C3⋊C8—64no—
122D3×C8—128no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3#10312yes—
127C32×C4—21no—
128C32×C4—42no—
129C32×C4C2×SD1611yescharacteristic
130C32×C4C2×Q1611yescharacteristic
131C32×C4#13511yescharacteristic
132C32×C4#13511yescharacteristic
133C3⋊Dic3—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3—42no—
136C3⋊Dic3#10312yes—
137C22×C8—181no—
138C4⋊Q8—91no—
139C4⋊Q8C2×C3⋊D311yescharacteristic
140#125—181no—
141C22⋊Q8—92no—
142C22⋊Q8—181no—
143C4×Q8—92no—
144C4×Q8—181no—
145#117—181no—
146C2×C42—91no—
147C4⋊C8—91no—
148C4⋊C8—91no—
149C4⋊C8—181no—
150C4⋊C8C2×C3⋊D311yescharacteristic
151C4⋊C8C2×C3⋊D311yescharacteristic
152C22⋊C8—181no—
153C4×C8—181no—
154C22×D3—34no—
155C3×Q8—48no—
156C2×C3×C4—28no—
157C2×C3×C4C2×C4×D314yes—
158C2×C3×C4D3×D414yes—
159C2×C3×C4D3×D414yes—
160C2×Dic3—34no—
161C2×Dic3—34no—
162C2×Dic3—34no—
163C2×Dic3—68no—
164C4×D3—38no—
165C4×D3—38no—
166C4×D3—64no—
167C4×D3—64no—
168C4×D3—124no—
169Dic6—124no—
170Dic6—124no—
171C3×C8—44no—
172C3×C8—44no—
173C3⋊C8—124no—
174C3⋊C8—124no—
175C2×C32#41311yescharacteristic
176C2×C32C2×#10311yescharacteristic
177C2×C32#41611yescharacteristic
178C3⋊D3—22no—
179C2×Q8—181no—
180C2×Q8C4×C3⋊D312yes—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—91no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—181no—
187C2×C8—181no—
188C2×C8—362no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—92no—
192C4⋊C4—182no—
193C4⋊C4—182no—
194C4⋊C4—181no—
195C22⋊C4—182no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42—182no—
200C42C22×C3⋊D311yescharacteristic
201C22×C3D3×C22⋊C414yes—
202C2×D3—38no—
203C2×D3—64no—
204C2×D3—64no—
205C3×C4—24no—
206C3×C4—48no—
207C3×C4D3×SD1614yes—
208C3×C4#91614yes—
209C3×C4D3×Q1614yes—
210C3×C4#91914yes—
211Dic3—38no—
212Dic3—64no—
213Dic3—64no—
214Dic3—128no—
215C32#154211yescharacteristic, complemented, Sylow
216C23—91no—
217Q8—42no—
218Q8—361no—
219Q8—361no—
220C2×C4—22no—
221C2×C4—91no—
222C2×C4—92no—
223C2×C4—92no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—182no—
229C2×C4—361no—
230C2×C4C2×C4×C3⋊D311yescharacteristic
231C2×C4D4×C3⋊D311yescharacteristic
232C2×C4D4×C3⋊D311yescharacteristic
233C8—41no—
234C8—41no—
235C8—361no—
236C8—361no—
237C2×C3#474514yes—
238C2×C3D3×#10314yes—
239C2×C3#480414yes—
240D3—68no—
241C22—92no—
242C22—181no—
243C22—181no—
244C22C22⋊C4×C3⋊D311yescharacteristic
245C4—21no—
246C4—42no—
247C4—92no—
248C4—181no—
249C4—181no—
250C4—362no—
251C4SD16×C3⋊D311yescharacteristic
252C4#6412511yescharacteristic
253C4Q16×C3⋊D311yescharacteristic
254C4#6412811yescharacteristic
255C3#6848114yescomplemented
256C2—182no—
257C2#1059244411yescharacteristic
258C2C3⋊D3×#10311yescharacteristic
259C2#1059250311yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#333C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenter#333C3⋊D3
hypocenterC32#1542
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. C32×#333C2semidirect
5. #10589412C2semidirect
6. #10589352C2semidirect
7. #10589348C2semidirect
29. C3×#333D3semidirect
98. #333C3⋊D3semidirect
215. C32#1542semidirect
255. C3#68481semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105925322
C3⋊D3×C4⋊C82
C32×#3332
#105894122
#105893522
#105893482
#684813