Finite Group Databasebeta

← #19135877

Subgroups — #19135877

Order 5504.

254 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13063358C211yesmaximal, characteristic
2#14582915C211yesmaximal, characteristic
3#14582909C211yesmaximal, characteristic, complemented
4#14582881C211yesmaximal, characteristic
5C2×#13063243C211yesmaximal, characteristic, complemented
6#14582671C211yesmaximal, characteristic, complemented
7C43×#430C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×Dic86C2211yescharacteristic
10#13063358—22no—
11#13063358—22no—
12C2×Dic172—21no—
13C2×#10621873—21no—
14C2×#10621877C2211yescharacteristic
15#13063284C2211yescharacteristic
16#13063251—22no—
17#13063250—22no—
18#13063243—21no—
19#13063243—22no—
20#13063241—21no—
21C2×M16×C43C2211yescharacteristic
22C2×M16×C43C2211yescharacteristic
23C2×M16×C43C2211yescharacteristic
24#108×C43—22no—
25C22×C4×C43C2311yescharacteristic
26C2×C22⋊D43—21no—
27C22×Dic43—21no—
28#10621898—21no—
29#10621898—21no—
30#10621898—21no—
31#10621898—21no—
32C2×D172D411yescharacteristic
33C2×C4×D43—21no—
34C2×Dic86—21no—
35C2×Dic86—21no—
36C2×Dic86—21no—
37C2×Dic86—21no—
38C2×Dic86—21no—
39C2×Dic86D411yescharacteristic
40C2×Dic86D412yes—
41M16×C43—21no—
42M16×C43—21no—
43M16×C43—21no—
44M16×C43—21no—
45M16×C43D412yes—
46M16×C43D412yes—
47C2×C8×C43—21no—
48C2×C8×C43—21no—
49C2×C8×C43—21no—
50C22⋊Dic43—21no—
51C4⋊Dic43—21no—
52C4×Dic43—21no—
53#10621877—21no—
54#10621877—21no—
55C2×C43⋊C8—21no—
56Dic172—24no—
57#10621873—24no—
58C23×C43#4111yescharacteristic
59C22×D43—21no—
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43#4111yescharacteristic
65C2×C4×C43#4111yescharacteristic
66C22⋊D43—41no—
67C22⋊D43—41no—
68C2×Dic43—22no—
69C2×Dic43—21no—
70C2×Dic43—41no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73D172—21no—
74D172—21no—
75C4×D43—41no—
76C4×D43—41no—
77Dic86—22no—
78Dic86—21no—
79Dic86—21no—
80Dic86—22no—
81Dic86—41no—
82Dic86—41no—
83C8×C43—22no—
84C8×C43—22no—
85C8×C43—41no—
86C43⋊C8—41no—
87C22×C43—41no—
88C22×C43#12111yescharacteristic
89C22×C43#12311yescharacteristic
90C22×C43#12411yescharacteristic
91C2×D43—41no—
92C2×D43—81no—
93C4×C43#12011yescharacteristic
94C4×C43#12111yescharacteristic
95C4×C43#12111yescharacteristic
96C4×C43#12311yescharacteristic
97Dic43—42no—
98Dic43—41no—
99Dic43—81no—
100#2049—431nomaximal, Sylow
101C2×C43—21no—
102C2×C43—21no—
103C2×C43—21no—
104C2×C43#39411yescharacteristic
105D43—81no—
106C2×#137—431no—
107#430D4311yescharacteristic, complemented
108#421—431no—
109#419—431no—
110#413—431no—
111C2×#101—431no—
112#344—431no—
113C43#204911yescharacteristic, complemented, Sylow
114C2×#41—431no—
115C22×Q8—431no—
116#137—862no—
117#137—862no—
118C2×Q16—861no—
119C2×SD16—861no—
120C2×M16—431no—
121C2×M16C2×D4311yescharacteristic
122C2×M16C2×D4311yescharacteristic
123C2×M16C2×D4311yescharacteristic
124#117—431no—
125#108—22no—
126#104—862no—
127#103—862no—
128#101—861no—
129#101—862no—
130#100—861no—
131#41—861no—
132#41—861no—
133#41—861no—
134#41—861no—
135C2×Q8—431no—
136C2×Q8—432no—
137C2×Q8—861no—
138C2×Q8—861no—
139C2×Q8—861no—
140C2×Q8—861no—
141C2×Q8—861no—
142C2×D4—431no—
143C2×D4—861no—
144C22×C4—861no—
145C22×C4—861no—
146C22×C4C22×D4311yescharacteristic
147Q16—864no—
148SD16—864no—
149M16—21no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—861no—
154M16—861no—
155M16D17212yes—
156M16C22⋊D4312yes—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—861no—
161C4⋊C4—861no—
162C22⋊C4—861no—
163C42—861no—
164C23—861no—
165C23#1062190211yescharacteristic
166Q8—862no—
167Q8—861no—
168Q8—861no—
169Q8—862no—
170Q8—1721no—
171Q8—1721no—
172D4—861no—
173D4—861no—
174D4—1721no—
175D4—1721no—
176C2×C4—862no—
177C2×C4—861no—
178C2×C4—1721no—
179C2×C4—1721no—
180C2×C4—1721no—
181C2×C4—1721no—
182C2×C4—1721no—
183C2×C4C2×D17211yescharacteristic
184C2×C4#1062189811yescharacteristic
185C2×C4D4×D4311yescharacteristic
186C2×C4D4×D4311yescharacteristic
187C2×C4#1062190211yescharacteristic
188C2×C4C2×C22⋊D4311yescharacteristic
189C8—22no—
190C8—22no—
191C8—41no—
192C8—1721no—
193C22—41no—
194C22—3441no—
195C22—1721no—
196C22#1306330011yescharacteristic
197C22#1306331011yescharacteristic
198C22#1306331411yescharacteristic
199C4—3441no—
200C4—1721no—
201C4—1722no—
202C4#1306329311yescharacteristic
203C4#1306329911yescharacteristic
204C4#1306330011yescharacteristic
205C4#1306331011yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—3441no—
210C2#1458281611yescharacteristic
subgroupG/H
centerC2#14582816
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#430C2
socleC2×C43#394
hypercenter#430D43
hypocenterC43#2049
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
3. #14582909C2semidirect
5. C2×#13063243C2semidirect
6. #14582671C2semidirect
7. C43×#430C2semidirect
107. #430D43semidirect
113. C43#2049semidirect