Finite Group Databasebeta

← #19135693

Subgroups — #19135693

Order 5504.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10621885C211yesmaximal, characteristic
2C2×#13063323C211yesmaximal, characteristic
3C2×#13063250C211yesmaximal, characteristic
4C2×#13063249C211yesmaximal, characteristic
5#14582806C211yesmaximal, characteristic
6#14582653C211yesmaximal, characteristic
7C22×Q16×C43C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C2×#10621885—22no—
10C2×#10621885—22no—
11C2×#10621885—22no—
12C22×C43⋊C8C2211yescharacteristic
13#13063323—22no—
14#13063323—22no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4—22no—
17C2×C4×Dic43C2211yescharacteristic
18#13063250—22no—
19#13063249—22no—
20C43⋊#95—22no—
21C22×Q8×C43C2211yescharacteristic
22C22×Q8×C43C2211yescharacteristic
23C2×Q16×C43—22no—
24C2×Q16×C43—22no—
25C2×Q16×C43—22no—
26C22×C8×C43C2211yescharacteristic
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43—21no—
31C2×Q8×C43—21no—
32C2×Q8×C43—21no—
33C2×Q8×C43—21no—
34C2×Q8×C43—21no—
35C2×Q8×C43—21no—
36C2×Q8×C43—21no—
37C2×Q8×C43D412yes—
38C2×Q8×C43D412yes—
39C22×C4×C43—21no—
40C22×C4×C43—21no—
41C22×C4×C43C2311yescharacteristic
42C22×Dic43—21no—
43C22×Dic43—21no—
44C22×Dic43D412yes—
45C2×Dic86—21no—
46C2×Dic86—21no—
47C2×Dic86—21no—
48C2×Dic86—21no—
49C2×Dic86—21no—
50C2×Dic86D412yes—
51Q16×C43—28no—
52C2×C8×C43—21no—
53C2×C8×C43—21no—
54C2×C8×C43D412yes—
55#10621885—28no—
56C4⋊Dic43—21no—
57C4⋊Dic43—21no—
58Dic43⋊C4—28no—
59C4×Dic43—21no—
60C4×Dic43—21no—
61C2×C43⋊C8—21no—
62C2×C43⋊C8—21no—
63C2×C43⋊C8D412yes—
64C23×C43C2×D411yescharacteristic
65Q8×C43—22no—
66Q8×C43—22no—
67Q8×C43—22no—
68Q8×C43—22no—
69Q8×C43—41no—
70Q8×C43—41no—
71Q8×C43—41no—
72Q8×C43—41no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43#4111yescharacteristic
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—41no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91C2×Dic43—42no—
92C2×Dic43Q1614yescomplemented
93Dic86—22no—
94Dic86—22no—
95Dic86—41no—
96Dic86—41no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43#12011yescharacteristic
100C22×C43#12111yescharacteristic
101C22×C43#12711yescharacteristic
102C22×C43C2×Q1612yes—
103C22×C43#13712yes—
104C4×C43—42no—
105C4×C43—42no—
106C4×C43#12011yescharacteristic
107C4×C43#12011yescharacteristic
108C4×C43#12111yescharacteristic
109C4×C43#12111yescharacteristic
110Dic43—24no—
111Dic43—42no—
112Dic43—81no—
113#2016—431nomaximal, Sylow
114C2×C43#39211yescharacteristic
115C2×C43#45112yes—
116C2×C43#46212yes—
117C2×C43#49411yescharacteristic
118C2×C43#49711yescharacteristic
119C22×Q16—431no—
120C22×Q16D4311yescharacteristic
121C2×C4⋊Q8—431no—
122C2×#103—431no—
123C2×#103—431no—
124#391—431no—
125#336—431no—
126C43#201611yescharacteristic, complemented, Sylow
127C22×Q8—431no—
128C22×Q8C2×D4311yescharacteristic
129C22×Q8C2×D4311yescharacteristic
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16—22no—
133C2×Q16—862no—
134C2×Q16—862no—
135C2×Q16—862no—
136C22×C8—431no—
137C22×C8C2×D4311yescharacteristic
138C4⋊Q8—862no—
139C4⋊Q8—862no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—862no—
142C2×C42—431no—
143#103—862no—
144#103—862no—
145#95—862no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—432no—
157C2×Q8—861no—
158C2×Q8—861no—
159C2×Q8—861no—
160C2×Q8—861no—
161C2×Q8—861no—
162C2×Q8C22⋊D4312yes—
163C2×Q8C22⋊D4312yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—432no—
167C22×C4—861no—
168C22×C4—861no—
169C22×C4C22×D4311yescharacteristic
170Q16—28no—
171Q16—868no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—432no—
175C2×C8—861no—
176C2×C8—861no—
177C2×C8C22⋊D4312yes—
178C4⋊C4—868no—
179C4⋊C4—861no—
180C4⋊C4—861no—
181C42—861no—
182C42—861no—
183C23D4×D4311yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192Q8—862no—
193Q8—862no—
194Q8—1721no—
195Q8—1721no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—434no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—1721no—
207C2×C4—1722no—
208C2×C4—1721no—
209C2×C4—1721no—
210C2×C4D4×D4311yescharacteristic
211C2×C4D4×D4311yescharacteristic
212C2×C4#1062190011yescharacteristic
213C2×C4C2×C22⋊D4311yescharacteristic
214C2×C4C2×C22⋊D4311yescharacteristic
215C2×C4C2×C22⋊D4311yescharacteristic
216C8—22no—
217C8—862no—
218C22#1306329311yescharacteristic
219C22#1306329711yescharacteristic
220C22#1306332111yescharacteristic
221C22Q16×D4312yes—
222C22#1306335712yes—
223C4—42no—
224C4—42no—
225C4—864no—
226C4—3441no—
227C4—1722no—
228C4#1306329311yescharacteristic
229C4#1306329411yescharacteristic
230C4#1306329611yescharacteristic
231C4#1306329711yescharacteristic
232C2#1458280711yescharacteristic
233C2#1458305312yes—
234C2#1458310712yes—
235C2#1458327711yescharacteristic
236C2#1458329211yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC22×Q16×C43C2
socleC23×C43C2×D4
hypercenterC22×Q16D43
hypocenterC43#2016
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
92. C2×Dic43Q16semidirect
126. C43#2016semidirect