Finite Group Databasebeta

← #19139546

Subgroups — #19139546

Order 5504.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×#13063324C211yesmaximal, characteristic, complemented
2C2×#13063302C214yesmaximal, complemented
3C2×D4×Dic43C211yesmaximal, characteristic
4#14582835C214yesmaximal, complemented
5#14582802C211yesmaximal, characteristic
6#14582769C211yesmaximal, characteristic, complemented
7#14582768C211yesmaximal, characteristic, complemented
8C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
9C43×#390C211yesmaximal, characteristic
10C22×Dic86C2212yes—
11C23×Dic43C2212yes—
12#13063324—24no—
13#13063302—216no—
14D4×Dic43—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2214yes—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2214yes—
20C2×Dic43⋊C4C2212yes—
21C2×C22⋊Dic43C2214yes—
22C2×C22⋊Dic43C2212yes—
23C2×C4×Dic43C2211yescharacteristic
24C2×C4×Dic43C2211yescharacteristic
25C43⋊#95C2212yes—
26C22×D4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C4×C43C2214yes—
29C2×C42×C43C2211yescharacteristic
30C24×C43C2312yes—
31C2×D4×C43—22no—
32C2×D4×C43—22no—
33C2×D4×C43Q814yescomplemented
34C22×C4×C43C2312yes—
35C22×C4×C43C2312yes—
36C22×C4×C43C2311yescharacteristic
37C22×Dic43—24no—
38C22×Dic43—28no—
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2311yescharacteristic
42C22×Dic43C2312yes—
43C22×Dic43C2311yescharacteristic
44C2×Dic86—28no—
45C2×Dic86—24no—
46C4⋊C4×C43—22no—
47C22⋊C4×C43—28no—
48C42×C43—22no—
49C22⋊Dic43—24no—
50C22⋊Dic43—28no—
51C4⋊Dic43—22no—
52C4⋊Dic43—28no—
53C4⋊Dic43—22no—
54Dic43⋊C4—28no—
55Dic43⋊C4—24no—
56Dic43⋊C4D418yescomplemented
57C4×Dic43—22no—
58C4×Dic43D414yes—
59C23×C43—24no—
60C23×C43—22no—
61C23×C43—22no—
62C23×C43—24no—
63C23×C43C2×Q814yes—
64C23×C43C2411yescharacteristic
65D4×C43—28no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—24no—
69C2×C4×C43—22no—
70C2×C4×C43C2×D414yes—
71C2×C4×C43C2×D412yes—
72C2×C4×C43C2×Q812yes—
73C2×C4×C43#4112yes—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—24no—
79C2×Dic43—24no—
80C2×Dic43—22no—
81C2×Dic43—48no—
82C2×Dic43C2×D412yes—
83C2×Dic43C2×D414yes—
84C2×Dic43C2×D412yes—
85C2×Dic43C2×D414yes—
86Dic86—48no—
87C22×C43—24no—
88C22×C43—28no—
89C22×C43—42no—
90C22×C43—42no—
91C22×C43—44no—
92C22×C43C22×D411yescharacteristic
93C22×C43C22×D412yes—
94C22×C43C22×Q811yescharacteristic
95C22×C43C2×#4111yescharacteristic
96C22×C432−1+412yes—
97C4×C43—24no—
98C4×C43—42no—
99C4×C43C22⋊Q814yescomplemented
100Dic43—22no—
101Dic43—24no—
102Dic43—42no—
103Dic43—42no—
104Dic43#12714yes—
105#2542—431nomaximal, Sylow
106C2×C43—44no—
107C2×C43C2×C22⋊Q811yescharacteristic
108C2×C43C2×#12711yescharacteristic
109C2×C43#53611yescharacteristic
110C2×C43#54712yes—
111C2×C43D4×Q812yes—
112C2×C4⋊Q8—431no—
113C2×C22⋊Q8—434no—
114C2×C4×D4—431no—
115#399—434no—
116#390—431no—
117#390D4311yescharacteristic
118#384—431no—
119#384—431no—
120C4×C4⋊C4—431no—
121C43#254211yescharacteristic, complemented, Sylow
122C22×Q8—432no—
123C22×D4C2×D4311yescharacteristic
124C23×C4—432no—
125C4⋊Q8—864no—
126C22⋊Q8—8616no—
127C4×D4—864no—
128C2×C4⋊C4—432no—
129C2×C4⋊C4—431no—
130C2×C4⋊C4—434no—
131C2×C4⋊C4—434no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4C2×D4311yescharacteristic
135C2×C22⋊C4—432no—
136C2×C22⋊C4—434no—
137C2×C22⋊C4C2×D4314yes—
138C2×C42—431no—
139C2×C42—431no—
140C2×C42C2×D4311yescharacteristic
141#95—432no—
142C24C22×D4312yes—
143C2×Q8—868no—
144C2×Q8—864no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4Dic8614yescomplemented
148C22×C4—431no—
149C22×C4—431no—
150C22×C4—432no—
151C22×C4—432no—
152C22×C4—432no—
153C22×C4—864no—
154C22×C4—868no—
155C22×C4C22×D4312yes—
156C22×C4C22×D4312yes—
157C22×C4C22×D4311yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—438no—
160C4⋊C4—868no—
161C4⋊C4—864no—
162C4⋊C4—862no—
163C4⋊C4—868no—
164C4⋊C4—862no—
165C22⋊C4—28no—
166C22⋊C4—864no—
167C22⋊C4—868no—
168C42—22no—
169C42—434no—
170C42—862no—
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic8614yes—
176C23C23×D4311yescharacteristic
177Q8—1728no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—432no—
184C2×C4—434no—
185C2×C4—432no—
186C2×C4—434no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—862no—
191C2×C4—864no—
192C2×C4—864no—
193C2×C4—862no—
194C2×C4—1728no—
195C2×C4C2×Dic8612yes—
196C2×C4D4×D4314yes—
197C2×C4D4×D4312yes—
198C2×C4#1062190012yes—
199C22—28no—
200C22—24no—
201C22—42no—
202C22—42no—
203C22—44no—
204C22C2×D4×D4312yes—
205C22C2×D4×D4311yescharacteristic
206C22C22×Dic8611yescharacteristic
207C22C2×#1062190011yescharacteristic
208C22#1306337212yes—
209C4—24no—
210C4—42no—
211C4—434no—
212C4—862no—
213C4—864no—
214C4—1722no—
215C4—1722no—
216C4#1306330214yescomplemented
217C2—44no—
218C2C2×#1306330211yescharacteristic
219C2#127×D4311yescharacteristic
220C2#1458346911yescharacteristic
221C2#1458354912yes—
222C2D4×Dic8612yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#390C2
hypercenter#390D43
hypocenterC43#2542
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
2. C2×#13063302C2semidirect
4. #14582835C2semidirect
6. #14582769C2semidirect
7. #14582768C2semidirect
8. C4×Dic43⋊C4C2semidirect
33. C2×D4×C43Q8semidirect
56. Dic43⋊C4D4semidirect
99. C4×C43C22⋊Q8semidirect
121. C43#2542semidirect
147. C2×D4Dic86semidirect
216. C4#13063302semidirect