Finite Group Databasebeta

← #19133638

Subgroups — #19133638

Order 5504.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#14583528C211yesmaximal, characteristic
2#14583235C211yesmaximal, characteristic
3#14583232C211yesmaximal, characteristic
4#14582839C211yesmaximal, characteristic
5#14582635C211yesmaximal, characteristic
6#14582624C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic
8#13063324—21no—
9#13063323—21no—
10#13063315—21no—
11#13063315—21no—
12#13063304C2211yescharacteristic
13#13063302—21no—
14#13063281—21no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C2211yescharacteristic
17#13063259—21no—
18#13063258—21no—
19#13063250—21no—
20#13063249—21no—
21C22⋊(C43⋊C8)C2211yescharacteristic
22C43⋊#95—21no—
23C43⋊#95—21no—
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C22×Dic43—21no—
31C22×Dic43D411yescharacteristic
32C22×Dic43D411yescharacteristic
33C2×Dic86—21no—
34C2×Dic86D411yescharacteristic
35C2×C8×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C22⋊C4×C43—21no—
39C22⋊Dic43—21no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43D411yescharacteristic
44Dic43⋊C4—21no—
45Dic43⋊C4—21no—
46Dic43⋊C4—21no—
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51C4×Dic43—21no—
52C4×Dic43—21no—
53C2×C43⋊C8—21no—
54C23×C43C2×D411yescharacteristic
55Q8×C43—41no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×Dic43—21no—
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—41no—
70C2×Dic43—42no—
71C2×Dic43—41no—
72C2×Dic43Q1612yes—
73Dic86—41no—
74Dic86—81no—
75C8×C43—41no—
76C43⋊C8—41no—
77C22×C43—21no—
78C22×C43—21no—
79C22×C43#12011yescharacteristic
80C22×C43C2×Q1611yescharacteristic
81C22×C43#13711yescharacteristic
82C4×C43—21no—
83C4×C43—21no—
84C4×C43—41no—
85C4×C43—41no—
86C4×C43—81no—
87Dic43—22no—
88Dic43—41no—
89Dic43—41no—
90Dic43—41no—
91Dic43—81no—
92#1617—431nomaximal, Sylow
93C2×C43—21no—
94C2×C43—21no—
95C2×C43#45111yescharacteristic
96C2×C43#45411yescharacteristic
97C2×C43#45811yescharacteristic
98#544—431no—
99#484—431no—
100#484—431no—
101#400—431no—
102#328—431no—
103#328D4311yescharacteristic
104#324—431no—
105C43#161711yescharacteristic, complemented, Sylow
106C4⋊Q8—861no—
107C4⋊Q8—861no—
108#125—861no—
109#125—861no—
110C22⋊Q8—431no—
111C22⋊Q8—861no—
112C22⋊Q8C2×D4311yescharacteristic
113#117—861no—
114C2×C4⋊C4—431no—
115C2×C4⋊C4—431no—
116#107—861no—
117#107—861no—
118#103—861no—
119#103—861no—
120C22⋊C8—431no—
121C22⋊C8C2×D4311yescharacteristic
122#95—861no—
123#95—861no—
124#95C2×D4311yescharacteristic
125C2×Q8—431no—
126C2×Q8—861no—
127C2×Q8D17211yescharacteristic
128C22×C4—21no—
129C22×C4—431no—
130C22×C4—431no—
131C22×C4—861no—
132C22×C4C22×D4311yescharacteristic
133C2×C8—21no—
134C2×C8—861no—
135C4⋊C4—21no—
136C4⋊C4—431no—
137C4⋊C4—861no—
138C4⋊C4—861no—
139C4⋊C4—861no—
140C4⋊C4—861no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4D17211yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—861no—
150C42—861no—
151C42—861no—
152C23D4×D4311yescharacteristic
153Q8—41no—
154Q8—3441no—
155Q8—1721no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—432no—
163C2×C4—861no—
164C2×C4—861no—
165C2×C4—861no—
166C2×C4—861no—
167C2×C4—861no—
168C2×C4—1722no—
169C2×C4—1721no—
170C2×C4—1721no—
171C2×C4C2×D17211yescharacteristic
172C2×C4D4×D4311yescharacteristic
173C8—41no—
174C8—1721no—
175C22—21no—
176C22—21no—
177C22#1306329511yescharacteristic
178C22Q16×D4311yescharacteristic
179C22#1306335411yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—862no—
186C4—3441no—
187C4—1721no—
188C4—1721no—
189C4—1721no—
190C2—21no—
191C2—21no—
192C2#1458305611yescharacteristic
193C2#1458307311yescharacteristic
194C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1617
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
105. C43#1617semidirect