Finite Group Databasebeta

← #19139799

Subgroups — #19139799

Order 5504.

500 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 171 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×#13063323C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic
3#14582820C211yesmaximal, characteristic
4#14582819C211yesmaximal, characteristic
5#14582818C211yesmaximal, characteristic
6#14582803C212yesmaximal
7#14582796C212yesmaximal
8#14582794C212yesmaximal
9#14582768C212yesmaximal
10#14582750C211yesmaximal, characteristic
11C43×#395C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14#13063323—24no—
15#13063290—24no—
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2212yes—
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C2×Q8×C43—22no—
38C2×Q8×C43—42no—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2312yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C2×Dic86—22no—
51C2×Dic86—22no—
52C2×Dic86—22no—
53C2×Dic86—42no—
54C2×Dic86Q814yescomplemented
55C4⋊C4×C43—22no—
56C4⋊C4×C43—42no—
57C4⋊Dic43—42no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—24no—
61Dic43⋊C4—24no—
62Dic43⋊C4—42no—
63Dic43⋊C4—42no—
64Dic43⋊C4Q818yescomplemented
65C4×Dic43—22no—
66C4×Dic43—22no—
67C4×Dic43—24no—
68C4×Dic43D414yes—
69C23×C43C2411yescharacteristic
70Q8×C43—44no—
71C2×C4×C43—21no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2×Q814yes—
83C2×C4×C43C2×Q812yes—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87C2×Dic43—22no—
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43C2×D412yes—
94C2×Dic43C2×D412yes—
95C2×Dic43C2×Q814yes—
96C2×Dic43C2×Q812yes—
97C2×Dic43C2×Q812yes—
98C2×Dic43C2×Q814yes—
99C2×Dic43#4112yes—
100Dic86—28no—
101Dic86—44no—
102C22×C43C22×D411yescharacteristic
103C22×C43C22×Q811yescharacteristic
104C22×C43C22×Q812yes—
105C22×C43C2×#4111yescharacteristic
106C22×C43H(5,𝔽2)12yes—
107C4×C43—22no—
108C4×C43—22no—
109C4×C43—24no—
110C4×C43—41no—
111C4×C43—42no—
112Dic43—22no—
113Dic43—24no—
114Dic43—42no—
115Dic43—41no—
116Dic43C22⋊Q814yes—
117Dic43C4⋊Q814yes—
118#2567—431nomaximal, Sylow
119C2×C43C2×C22⋊Q811yescharacteristic
120C2×C43C2×C4⋊Q811yescharacteristic
121C2×C43#53511yescharacteristic
122C2×C43#55412yes—
123C2×C43Q8212yes—
124C2×C4⋊Q8—431no—
125C2×C4×Q8—431no—
126#395—431no—
127#395—431no—
128#395—431no—
129#395D4311yescharacteristic
130#391—432no—
131#389—432no—
132#389—432no—
133#384—432no—
134C4×C4⋊C4—431no—
135C43#256711yescharacteristic, complemented, Sylow
136C22×Q8—431no—
137C22×Q8—431no—
138C22×Q8C2×D4311yescharacteristic
139C4⋊Q8—864no—
140C4×Q8—864no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—431no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4—432no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4C2×D4311yescharacteristic
150C2×C4⋊C4C2×D4312yes—
151C2×C42—431no—
152C2×C42—431no—
153C2×C42—431no—
154C2×C42—432no—
155#95—431no—
156#95—432no—
157#95—432no—
158#95—432no—
159#95C2×D4311yescharacteristic
160#95C2×D4312yes—
161C2×Q8—22no—
162C2×Q8—42no—
163C2×Q8—434no—
164C2×Q8—862no—
165C2×Q8—862no—
166C2×Q8—862no—
167C2×Q8—1722no—
168C22×C4—431no—
169C22×C4—431no—
170C22×C4—431no—
171C22×C4—432no—
172C22×C4—432no—
173C22×C4—431no—
174C22×C4C22×D4312yes—
175C22×C4C22×D4311yescharacteristic
176C22×C4C22×D4311yescharacteristic
177C22×C4C22×D4311yescharacteristic
178C22×C4C22×D4312yes—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—438no—
182C4⋊C4—862no—
183C4⋊C4—864no—
184C4⋊C4—864no—
185C4⋊C4—862no—
186C4⋊C4—1722no—
187C4⋊C4—1722no—
188C4⋊C4—1722no—
189C42—434no—
190C42—862no—
191C42—862no—
192C42—864no—
193C23C23×D4311yescharacteristic
194Q8—44no—
195Q8—868no—
196Q8—1724no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—432no—
208C2×C4—432no—
209C2×C4—434no—
210C2×C4—432no—
211C2×C4—432no—
212C2×C4—434no—
213C2×C4—432no—
214C2×C4—861no—
215C2×C4—862no—
216C2×C4—861no—
217C2×C4—862no—
218C2×C4—861no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4D4×D4312yes—
224C2×C4Q8×D4314yes—
225C2×C4Q8×D4312yes—
226C22C2×D4×D4311yescharacteristic
227C22C2×Q8×D4312yes—
228C22C2×Q8×D4311yescharacteristic
229C22#41×D4311yescharacteristic
230C22#1306337012yes—
231C4—24no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—434no—
237C4—434no—
238C4—864no—
239C4—862no—
240C4—1722no—
241C4—1721no—
242C2C22⋊Q8×D4311yescharacteristic
243C2C4⋊Q8×D4311yescharacteristic
244C2#1458346411yescharacteristic
245C2#1458360312yes—
246C2#1458362912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2567
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×Dic86Q8semidirect
64. Dic43⋊C4Q8semidirect
135. C43#2567semidirect