Finite Group Databasebeta

← #19135631

Subgroups — #19135631

Order 5504.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#13063356C211yesmaximal, characteristic
2#14583473C211yesmaximal, characteristic
3C2×#13063253C211yesmaximal, characteristic
4#14582908C211yesmaximal, characteristic, complemented
5C2×#13063244C211yesmaximal, characteristic, complemented
6#14582659C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C43C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—22no—
10#13063356—22no—
11C2×#10621885—21no—
12C2×#10621884—21no—
13C2×#10621877C2211yescharacteristic
14C2×#10621877C2211yescharacteristic
15#13063323—21no—
16#13063314—21no—
17#13063308—22no—
18#13063301—22no—
19#13063284C2211yescharacteristic
20#13063253—22no—
21#13063249—22no—
22#13063244—22no—
23C22×Q8×C43C2211yescharacteristic
24C22×Q8×C43C2211yescharacteristic
25C4⋊Q8×C43—22no—
26C4⋊Q8×C43—22no—
27C2×C4⋊C4×C43—22no—
28C2×C42×C43C2211yescharacteristic
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×C43—21no—
38C2×Q8×C43—21no—
39C2×Q8×C43—21no—
40C2×Q8×C43D412yes—
41C22×C4×C43—21no—
42C22×C4×C43—21no—
43C22×C4×C43D412yes—
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—21no—
46#10621898—21no—
47#10621898—21no—
48#10621898—21no—
49#10621898—21no—
50C2×D172D411yescharacteristic
51C2×C4×D43—21no—
52C2×Dic86D411yescharacteristic
53C4⋊C4×C43—28no—
54C42×C43—21no—
55C42×C43D412yes—
56C22⋊Dic43—21no—
57#10621885—24no—
58#10621884—24no—
59(C2×D43)⋊C4—24no—
60C4⋊Dic43D412yes—
61Dic43⋊C4—24no—
62C4×Dic43—21no—
63#10621877—21no—
64#10621877—21no—
65#10621877—21no—
66#10621877D412yes—
67C2×C43⋊C8—21no—
68C2×C43⋊C8—21no—
69C23×C43C2×D411yescharacteristic
70C22×D43—21no—
71Q8×C43—22no—
72Q8×C43—22no—
73Q8×C43—41no—
74Q8×C43—41no—
75Q8×C43—41no—
76Q8×C43—41no—
77Q8×C43—41no—
78Q8×C43—41no—
79C2×C4×C43—24no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D411yescharacteristic
89C2×C4×C43C2×D411yescharacteristic
90C2×C4×C43C2×D411yescharacteristic
91C2×C4×C43C2×D411yescharacteristic
92C2×C4×C43#4111yescharacteristic
93C22⋊D43—41no—
94C22⋊D43—41no—
95C2×Dic43—22no—
96C2×Dic43—21no—
97D172—21no—
98D172—21no—
99C4×D43—41no—
100C4×D43—41no—
101Dic86—21no—
102Dic86—21no—
103C43⋊C8—22no—
104C43⋊C8—41no—
105C22×C43—22no—
106C22×C43#12011yescharacteristic
107C22×C43#12011yescharacteristic
108C22×C43#12111yescharacteristic
109C2×D43—41no—
110C2×D43—42no—
111C4×C43—24no—
112C4×C43—42no—
113C4×C43—42no—
114C4×C43#12011yescharacteristic
115C4×C43#12111yescharacteristic
116C4×C43#12111yescharacteristic
117C4×C43#12711yescharacteristic
118Dic43—41no—
119Dic43—42no—
120#2005—431nomaximal, Sylow
121C2×C43—21no—
122C2×C43—21no—
123C2×C43#39211yescharacteristic
124C2×C43#45612yes—
125D43—81no—
126C2×#137—431no—
127#536—431no—
128C2×C4⋊Q8D4311yescharacteristic, complemented
129C2×#104—431no—
130#419—431no—
131C2×#101—431no—
132#339—431no—
133C43#200511yescharacteristic, complemented, Sylow
134C2×#41—431no—
135C22×Q8C2×D4311yescharacteristic
136C22×Q8C2×D4311yescharacteristic
137#137—862no—
138#137—862no—
139C2×Q16—861no—
140C2×SD16—861no—
141C2×M16—431no—
142C2×M16—431no—
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4⋊Q8—861no—
146#124—861no—
147#123—862no—
148C22⋊Q8—862no—
149#117—431no—
150C2×C4⋊C4—22no—
151C2×C42C2×D4311yescharacteristic
152#104—862no—
153#103—862no—
154#101—862no—
155#41—861no—
156#41—861no—
157#41—861no—
158#41—861no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—431no—
171C2×Q8C22⋊D4312yes—
172C2×D4—431no—
173C2×D4—861no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—861no—
177C22×C4C22⋊D4312yes—
178C22×C4C22×D4311yescharacteristic
179Q16—864no—
180SD16—864no—
181M16—432no—
182M16—861no—
183M16—861no—
184M16—861no—
185C2×C8—861no—
186C2×C8—861no—
187C4⋊C4—28no—
188C4⋊C4—432no—
189C4⋊C4—864no—
190C22⋊C4—864no—
191C22⋊C4—861no—
192C42—21no—
193C42—861no—
194C42C22⋊D4312yes—
195C23—861no—
196C23C2×C22⋊D4311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—41no—
202Q8—41no—
203Q8—41no—
204Q8—41no—
205Q8—861no—
206Q8—861no—
207D4—861no—
208D4—861no—
209D4—1721no—
210D4—1721no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—862no—
220C2×C4—861no—
221C2×C4—1721no—
222C2×C4—1721no—
223C2×C4D4×D4311yescharacteristic
224C2×C4D4×D4311yescharacteristic
225C2×C4D4×D4311yescharacteristic
226C2×C4#1062190011yescharacteristic
227C2×C4C2×C22⋊D4311yescharacteristic
228C2×C4C2×C22⋊D4311yescharacteristic
229C8—862no—
230C8—1721no—
231C22—22no—
232C22—1721no—
233C22—1722no—
234C22#1306329311yescharacteristic
235C22#1306329411yescharacteristic
236C22#1306329711yescharacteristic
237C4—24no—
238C4—42no—
239C4—42no—
240C4—1721no—
241C4—1722no—
242C4#1306329311yescharacteristic
243C4#1306329611yescharacteristic
244C4#1306329711yescharacteristic
245C4#1306332111yescharacteristic
246C2—21no—
247C2—21no—
248C2—3441no—
249C2#1458280711yescharacteristic
250C2#1458308112yes—
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC2×C4⋊Q8×C43C2
socleC22×C43#120
hypercenterC2×C4⋊Q8D43
hypocenterC43#2005
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #14582908C2semidirect
5. C2×#13063244C2semidirect
6. #14582659C2semidirect
7. C2×C4⋊Q8×C43C2semidirect
128. C2×C4⋊Q8D43semidirect
133. C43#2005semidirect