Finite Group Databasebeta

← #19133651

Subgroups — #19133651

Order 5504.

336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D172C211yesmaximal, characteristic, complemented
2#14583276C211yesmaximal, characteristic, complemented
3#14583095C211yesmaximal, characteristic, complemented
4#14583094C211yesmaximal, characteristic, complemented
5#14582642C211yesmaximal, characteristic, complemented
6#14582628C211yesmaximal, characteristic, complemented
7C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×D172—21no—
9C2×D4×D43—21no—
10C2×D344—21no—
11C2×D344—22no—
12C2×#10621882—21no—
13#13063322C2211yescharacteristic
14#13063322C2211yescharacteristic, complemented
15#13063300—21no—
16#13063299—21no—
17#13063295—22no—
18C4×D172C2211yescharacteristic
19C4⋊(C43⋊C8)C2211yescharacteristic, complemented
20#13063247—21no—
21#13063245—21no—
22C4×D4×C43C2211yescharacteristic
23C4⋊C8×C43C2211yescharacteristic, complemented
24C4×C8×C43C2211yescharacteristic, complemented
25C23×D43—22no—
26C2×D4×C43D411yescharacteristic
27C22×C4×C43—21no—
28C2×C22⋊D43—22no—
29D4×D43—42no—
30D4×D43—42no—
31C2×D172—22no—
32C2×D172—21no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172—21no—
36C2×D172—21no—
37C2×D172—42no—
38C2×D172—42no—
39C2×D172D411yescharacteristic
40C2×D172D412yes—
41C2×C4×D43—21no—
42C2×C8×C43—21no—
43C2×C8×C43—21no—
44C4⋊C4×C43D411yescharacteristic
45C22⋊C4×C43—21no—
46C42×C43C2311yescharacteristic
47#10621882—42no—
48(C2×D43)⋊C4—22no—
49(C2×D43)⋊C4—21no—
50C4⋊Dic43D411yescharacteristic
51C2×C43⋊C8—21no—
52D344—44no—
53D344—42no—
54C23×C43—21no—
55C22×D43—21no—
56C22×D43—22no—
57C22×D43—44no—
58C22×D43—44no—
59C22×D43—41no—
60C22×D43—82no—
61D4×C43—21no—
62D4×C43D812yescomplemented
63C2×C4×C43—21no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C22⋊D43—44no—
70C2×Dic43—21no—
71D172—21no—
72D172—42no—
73D172—42no—
74D172—44no—
75D172—41no—
76D172—41no—
77D172—41no—
78D172—41no—
79D172—41no—
80D172—41no—
81D172—41no—
82D172—41no—
83D172D812yescomplemented
84C4×D43—41no—
85C4×D43—41no—
86C8×C43—22no—
87C8×C43—41no—
88C43⋊C8—41no—
89C22×C43—22no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43#12011yescharacteristic
93C2×D43—22no—
94C2×D43—41no—
95C2×D43—41no—
96C2×D43—42no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—88no—
100C2×D43—81no—
101C2×D43—81no—
102C2×D43—81no—
103C4×C43—21no—
104C4×C43—41no—
105C4×C43C2×D811yescharacteristic
106C4×C43C2×D811yescharacteristic
107C4×C43AGL(1,ℤ/8)11yescharacteristic
108C4×C43AGL(1,ℤ/8)11yescharacteristic
109Dic43—41no—
110#1619—431nomaximal, Sylow
111C2×C43—42no—
112C2×C43#44711yescharacteristic
113C2×C43#44711yescharacteristic
114C2×C43#45311yescharacteristic
115D43—42no—
116D43—82no—
117D43—161no—
118D42—431no—
119#493—431no—
120#459—431no—
121#459—431no—
122#331—431no—
123D4⋊C8—431no—
124D4⋊C8D4311yescharacteristic, complemented
125C43#161911yescharacteristic, complemented, Sylow
126C22×D4—861no—
127C22×D4—861no—
128C2×D8—861no—
129C2×D8—862no—
130C2×D8—861no—
131#127—431no—
132#127—431no—
133#121—861no—
134#121—861no—
135#120—862no—
136C4×D4—431no—
137C4×D4C2×D4311yescharacteristic
138C4⋊C8—431no—
139C4⋊C8C2×D4311yescharacteristic, complemented
140#102—861no—
141#102—861no—
142C4×C8C2×D4311yescharacteristic, complemented
143C24—862no—
144C2×D4—431no—
145C2×D4—432no—
146C2×D4—862no—
147C2×D4—862no—
148C2×D4—861no—
149C2×D4—861no—
150C2×D4—861no—
151C2×D4—861no—
152C2×D4—861no—
153C2×D4—1722no—
154C2×D4—1722no—
155C2×D4—1722no—
156C2×D4—1722no—
157C2×D4D17211yescharacteristic
158C22×C4—21no—
159C22×C4—861no—
160D8—1724no—
161D8—1722no—
162D8—1722no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—861no—
166C4⋊C4—431no—
167C4⋊C4D17211yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—862no—
170C22⋊C4—861no—
171C42C22×D4311yescharacteristic
172C23—21no—
173C23—861no—
174C23—862no—
175C23—3442no—
176C23—1724no—
177C23—1724no—
178C23—1721no—
179D4—21no—
180D4—432no—
181D4—861no—
182D4—1722no—
183D4—1722no—
184D4—1724no—
185D4—1724no—
186D4—1721no—
187D4—1721no—
188D4—1721no—
189D4—1721no—
190D4—1721no—
191D4—1721no—
192D4—1721no—
193D4—1721no—
194D4D34412yescomplemented
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—861no—
199C2×C4—1721no—
200C2×C4—1721no—
201C2×C4C2×D17211yescharacteristic
202C2×C4D4×D4311yescharacteristic
203C2×C4D4×D4311yescharacteristic
204C8—22no—
205C8—41no—
206C8—1721no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—862no—
211C22—3448no—
212C22—3441no—
213C22—3441no—
214C22—3441no—
215C22—1722no—
216C22—1722no—
217C22—1722no—
218C22—1721no—
219C22—1721no—
220C22#1306329511yescharacteristic
221C4—21no—
222C4—41no—
223C4—1721no—
224C4D8×D4311yescharacteristic
225C4C2×D34411yescharacteristic
226C4#1306335211yescharacteristic
227C4#1306335311yescharacteristic
228C2—42no—
229C2—3442no—
230C2—1722no—
231C2—6881no—
232C2#1458303411yescharacteristic
233C2#1458303511yescharacteristic
234C2#1458306811yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×D4⋊C8C2
socleC22×C43#120
hypercenterD4⋊C8D43
hypocenterC43#1619
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. D4×D172C2semidirect
2. #14583276C2semidirect
3. #14583095C2semidirect
4. #14583094C2semidirect
5. #14582642C2semidirect
6. #14582628C2semidirect
7. C43×D4⋊C8C2semidirect
14. #13063322C22semidirect
19. C4⋊(C43⋊C8)C22semidirect
23. C4⋊C8×C43C22semidirect
24. C4×C8×C43C22semidirect
62. D4×C43D8semidirect
83. D172D8semidirect
124. D4⋊C8D43semidirect
125. C43#1619semidirect
139. C4⋊C8C2×D43semidirect
142. C4×C8C2×D43semidirect
194. D4D344semidirect