Finite Group Databasebeta

← #19135586

Subgroups — #19135586

Order 5504.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13063316C211yesmaximal, characteristic
2#14582922C211yesmaximal, characteristic
3M16×Dic43C211yesmaximal, characteristic
4#14582668C211yesmaximal, characteristic
5#14582667C211yesmaximal, characteristic
6#14582667C211yesmaximal, characteristic
7C43×#343C211yesmaximal, characteristic
8C2×#10621877C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10#13063316—21no—
11#13063316—21no—
12#13063316—21no—
13#13063316—21no—
14C2×C4⋊Dic43C412yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C412yes—
17C2×C4×Dic43C2211yescharacteristic
18Dic43⋊C8—21no—
19Dic43⋊C8—21no—
20#13063235—21no—
21C8×Dic43—21no—
22C2×M16×C43C2211yescharacteristic
23C2×M16×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2211yescharacteristic
25C22×C4×C43C2×C412yes—
26C22×C4×C43C2311yescharacteristic
27C22×Dic43C2×C412yes—
28C22×Dic43C2×C411yescharacteristic
29C22×Dic43C2×C411yescharacteristic
30M16×C43—21no—
31M16×C43—21no—
32M16×C43—21no—
33M16×C43Q812yes—
34C2×C8×C43—21no—
35C2×C8×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊Dic43—21no—
39C4⋊Dic43—21no—
40C4⋊Dic43—22no—
41C4⋊Dic43—22no—
42Dic43⋊C4—22no—
43Dic43⋊C4—22no—
44C4×Dic43D411yescharacteristic
45C4×Dic43D411yescharacteristic
46C4×Dic43D411yescharacteristic
47C4×Dic43D411yescharacteristic
48#10621877—21no—
49#10621877—21no—
50#10621877—21no—
51#10621877Q812yes—
52C2×C43⋊C8—21no—
53C2×C43⋊C8—21no—
54C23×C43C22×C411yescharacteristic
55C2×C4×C43—22no—
56C2×C4×C43—42no—
57C2×C4×C43C2×D411yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×Q811yescharacteristic
60C2×C4×C43C2×Q811yescharacteristic
61C2×C4×C43#4111yescharacteristic
62C2×C4×C43#4111yescharacteristic
63C2×Dic43—22no—
64C2×Dic43—41no—
65C2×Dic43—41no—
66C2×Dic43—42no—
67C2×Dic43C22⋊C411yescharacteristic
68C2×Dic43C22⋊C411yescharacteristic
69C2×Dic43C22⋊C411yescharacteristic
70C2×Dic43C22⋊C411yescharacteristic
71C8×C43—22no—
72C8×C43—41no—
73C43⋊C8—22no—
74C43⋊C8—41no—
75C22×C43—21no—
76C22×C43—21no—
77C22×C43C2×C22⋊C411yescharacteristic
78C22×C43C4×Q811yescharacteristic
79C22×C43C4×Q811yescharacteristic
80C4×C43—42no—
81C4×C43C22⋊Q811yescharacteristic
82C4×C43C22⋊Q811yescharacteristic
83C4×C43#12411yescharacteristic
84C4×C43C4⋊Q811yescharacteristic
85Dic43—21no—
86Dic43—21no—
87Dic43—21no—
88Dic43—21no—
89Dic43—42no—
90#1998—431nomaximal, Sylow
91C2×C43—21no—
92C2×C43—21no—
93C2×C43#39111yescharacteristic
94C2×C43#41311yescharacteristic
95C2×C43#41311yescharacteristic
96C2×#125—431no—
97#423—431no—
98C4×M16—431no—
99#343—431no—
100#343—431no—
101#343—431no—
102#343D4311yescharacteristic
103C43#199811yescharacteristic, complemented, Sylow
104C2×M16—431no—
105C2×M16—431no—
106C2×M16C2×D4311yescharacteristic
107C2×M16C2×D4311yescharacteristic
108#125—861no—
109#125—861no—
110#125—861no—
111#125—861no—
112C2×C4⋊C4—431no—
113C2×C4⋊C4—432no—
114C2×C4⋊C4—432no—
115C2×C4⋊C4C2×D4311yescharacteristic
116C2×C42—431no—
117C4⋊C8—861no—
118C4⋊C8—861no—
119#97—861no—
120C4×C8—861no—
121C22×C4—431no—
122C22×C4—431no—
123C22×C4—432no—
124C22×C4C4×D4312yes—
125C22×C4C22×D4311yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—432no—
130M16—861no—
131M16—861no—
132M16—861no—
133M16Dic8612yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—861no—
137C2×C8—861no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—862no—
141C4⋊C4—862no—
142C4⋊C4—862no—
143C4⋊C4—862no—
144C4⋊C4—861no—
145C4⋊C4—861no—
146C42—431no—
147C42—431no—
148C42—431no—
149C42—431no—
150C23C2×C4×D4311yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—431no—
154C2×C4—431no—
155C2×C4—431no—
156C2×C4—431no—
157C2×C4—862no—
158C2×C4—1721no—
159C2×C4—1721no—
160C2×C4—1722no—
161C2×C4C2×Dic8611yescharacteristic
162C2×C4#1062189811yescharacteristic
163C2×C4D4×D4311yescharacteristic
164C2×C4D4×D4311yescharacteristic
165C2×C4#1062190011yescharacteristic
166C2×C4Q8×D4311yescharacteristic
167C8—22no—
168C8—41no—
169C8—862no—
170C8—1721no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D4311yescharacteristic
174C22#1306329011yescharacteristic
175C22C4×Dic8611yescharacteristic
176C4—42no—
177C4—861no—
178C4—861no—
179C4—861no—
180C4—861no—
181C4—1722no—
182C4#1306330211yescharacteristic
183C4#1306330311yescharacteristic
184C4#1306331111yescharacteristic
185C4#1306332411yescharacteristic
186C2—21no—
187C2—21no—
188C2#1458280311yescharacteristic
189C2#1458288011yescharacteristic
190C2#1458288211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#343C2
socleC22×C43C2×C22⋊C4
hypercenter#343D43
hypocenterC43#1998
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
103. C43#1998semidirect