Finite Group Databasebeta

← #19135248

Subgroups — #19135248

Order 5504.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#14582939C211yesmaximal, characteristic
2#14582909C211yesmaximal, characteristic
3C2×#13063248C211yesmaximal, characteristic
4C2×#13063243C211yesmaximal, characteristic
5#14582857C211yesmaximal, characteristic
6#14582663C211yesmaximal, characteristic
7C43×#343C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C22×C43⋊C8C2211yescharacteristic
11#13063284C2211yescharacteristic
12#13063258—21no—
13#13063256—21no—
14#13063250—21no—
15#13063250—21no—
16#13063248—21no—
17#13063248—21no—
18#13063243C414yescomplemented
19#13063235—21no—
20C8×Dic43—21no—
21C2×M16×C43C2211yescharacteristic
22C2×M16×C43C2211yescharacteristic
23C2×C4⋊C4×C43C2211yescharacteristic
24C22×C4×C43—21no—
25C22×C4×C43C2311yescharacteristic
26C22×Dic43—21no—
27C2×Dic86—21no—
28C2×Dic86—21no—
29C2×Dic86—21no—
30C2×Dic86—21no—
31C2×Dic86—21no—
32C2×Dic86C2×C412yes—
33M16×C43—21no—
34M16×C43—21no—
35M16×C43—21no—
36M16×C43C2×C412yes—
37C2×C8×C43—21no—
38C2×C8×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C22⋊Dic43—21no—
42C4⋊Dic43D411yescharacteristic
43C4⋊Dic43D411yescharacteristic
44C4×Dic43—21no—
45#10621877—21no—
46#10621877C2×C412yes—
47C2×C43⋊C8—21no—
48C2×C43⋊C8—21no—
49C2×C43⋊C8—21no—
50C2×C43⋊C8D411yescharacteristic
51C2×C43⋊C8D411yescharacteristic
52C23×C43#4111yescharacteristic
53C2×C4×C43—41no—
54C2×C4×C43—81no—
55C2×C4×C43C22×C411yescharacteristic
56C2×C4×C43C2×D411yescharacteristic
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43#4111yescharacteristic
59C2×C4×C43#4111yescharacteristic
60C2×C4×C43#4111yescharacteristic
61C2×Dic43—22no—
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—41no—
65C2×Dic43—41no—
66Dic86—22no—
67Dic86—22no—
68Dic86—41no—
69Dic86—41no—
70C8×C43—22no—
71C8×C43—41no—
72C43⋊C8—22no—
73C43⋊C8—21no—
74C43⋊C8—21no—
75C22×C43—21no—
76C22×C43—21no—
77C22×C43#11711yescharacteristic
78C22×C43#12111yescharacteristic
79C22×C43#12611yescharacteristic
80C4×C43—81no—
81C4×C43C4×D411yescharacteristic
82C4×C43C4×D411yescharacteristic
83C4×C43#12311yescharacteristic
84C4×C43#12411yescharacteristic
85Dic43—42no—
86Dic43—41no—
87Dic43—41no—
88#1930—431nomaximal, Sylow
89C2×C43—21no—
90C2×C43—21no—
91C2×C43#38811yescharacteristic
92C2×C43#47111yescharacteristic
93C2×C43#47311yescharacteristic
94#428—431no—
95#419—431no—
96C2×#103—431no—
97C2×#101—431no—
98#405—431no—
99#343D4311yescharacteristic
100#341—431no—
101C43#193011yescharacteristic, complemented, Sylow
102C22×Q8—431no—
103C2×M16—431no—
104C2×M16C2×D4311yescharacteristic
105C2×M16C2×D4311yescharacteristic
106C22×C8—431no—
107#117—431no—
108C2×C4⋊C4C2×D4311yescharacteristic
109#107—861no—
110#106—861no—
111#103—861no—
112#103—861no—
113#103—861no—
114#103—861no—
115#101—434no—
116#97—861no—
117C4×C8—861no—
118C2×Q8—432no—
119C2×Q8—861no—
120C2×Q8—861no—
121C2×Q8—861no—
122C2×Q8—861no—
123C2×Q8—861no—
124C22×C4—21no—
125C22×C4—861no—
126C22×C4C22×D4311yescharacteristic
127M16—21no—
128M16—21no—
129M16—21no—
130M16—432no—
131M16—861no—
132M16C4×D4312yes—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—431no—
136C2×C8—431no—
137C2×C8—861no—
138C2×C8—861no—
139C2×C8—861no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—431no—
143C4⋊C4—431no—
144C22⋊C4—861no—
145C42—861no—
146C23#1062189811yescharacteristic
147Q8—862no—
148Q8—862no—
149Q8—1721no—
150Q8—1721no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—862no—
154C2×C4—861no—
155C2×C4—861no—
156C2×C4—1721no—
157C2×C4—1721no—
158C2×C4C2×C4×D4311yescharacteristic
159C2×C4#1062189811yescharacteristic
160C2×C4D4×D4311yescharacteristic
161C2×C4D4×D4311yescharacteristic
162C2×C4#1062190011yescharacteristic
163C2×C4#1062190211yescharacteristic
164C8—22no—
165C8—41no—
166C8—862no—
167C8—861no—
168C8—861no—
169C22—21no—
170C22—21no—
171C22#1306328211yescharacteristic
172C22#1306329811yescharacteristic
173C22#1306332011yescharacteristic
174C4—81no—
175C4—1722no—
176C4—1721no—
177C4—1721no—
178C4(C22⋊D43)⋊C411yescharacteristic
179C4#1306328711yescharacteristic
180C4#1306331011yescharacteristic
181C4#1306331111yescharacteristic
182C2—21no—
183C2—21no—
184C2#1458278811yescharacteristic
185C2#1458316111yescharacteristic
186C2#1458317311yescharacteristic
subgroupG/H
centerC22#13063298
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#343C2
socleC22×C43#121
hypercenter#343D43
hypocenterC43#1930
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
18. #13063243C4semidirect
101. C43#1930semidirect