Finite Group Databasebeta

← #19149285

Subgroups — #19149285

Order 5504.

950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 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#14583647C213yesmaximal, complemented
2#14583602C216yesmaximal, complemented
3#14583581C216yesmaximal, complemented
4#14583505C216yesmaximal, complemented
5#14583497C216yesmaximal, complemented
6#14583434C213yesmaximal, complemented
7C43×#564C211yesmaximal, characteristic, complemented
8#13063322C2212yes—
9#13063320C2216yes—
10#13063320C2216yes—
11#13063319C2212yes—
12#13063315C2216yes—
13#13063313C2213yes—
14#13063310C2216yes—
15#13063310C2216yes—
16#13063310C2216yes—
17#13063310C2216yes—
18#13063310C2216yes—
19#13063305C2213yes—
20#13063303C2216yes—
21#13063303C2216yes—
22#13063300C2216yes—
23#13063300C2216yes—
24#13063300C2216yes—
25#13063300C2213yes—
26#13063300C2216yes—
27#13063290C2213yes—
28C4×D172C2216yes—
29#13063287C2216yes—
30#13063287C2213yes—
31#13063287C2216yes—
32#13063283C2216yes—
33#13063282C2216yes—
34C4⋊C4×D43C2216yes—
35C42×D43C2211yescharacteristic
36#125×C43C2216yes—
37#125×C43C2216yes—
38#125×C43C2213yes—
39C2×D172C2313yes—
40C2×D172C2316yes—
41C2×D172C2316yes—
42C2×D172C2316yes—
43C2×C4×D43C2313yes—
44C2×C4×D43C2316yes—
45C2×C4×D43C2316yes—
46C2×C4×D43C2316yes—
47C2×Dic86C2313yes—
48C4⋊C4×C43C2316yes—
49C4⋊C4×C43C2316yes—
50C4⋊C4×C43C2316yes—
51C4⋊C4×C43C2316yes—
52C4⋊C4×C43C2313yes—
53C4⋊C4×C43C2313yes—
54C42×C43C2311yescharacteristic
55C42×C43C2312yes—
56C42×C43C2312yes—
57(C2×D43)⋊C4C2316yes—
58(C2×D43)⋊C4C2316yes—
59(C2×D43)⋊C4C2316yes—
60(C2×D43)⋊C4C2316yes—
61(C2×D43)⋊C4C2316yes—
62(C2×D43)⋊C4C2316yes—
63(C2×D43)⋊C4C2316yes—
64C4⋊Dic43C2316yes—
65Dic43⋊C4C2316yes—
66Dic43⋊C4C2316yes—
67Dic43⋊C4C2316yes—
68C4×Dic43C2313yes—
69C4×Dic43C2316yes—
70C22×D43C2416yes—
71C22×D43C2411yescharacteristic
72C2×C4×C43C2416yes—
73C2×C4×C43C2413yes—
74C2×C4×C43C2416yes—
75C2×Dic43C2413yes—
76C2×Dic43C2416yes—
77D172—43no—
78D172—46no—
79D172—46no—
80D172—46no—
81C4×D43—46no—
82C4×D43—46no—
83C4×D43—43no—
84C4×D43—46no—
85Dic86—43no—
86C22×C43C2511yescharacteristic
87C2×D43—26no—
88C2×D43—26no—
89C2×D43—23no—
90C2×D43—26no—
91C4×C43—23no—
92C4×C43—26no—
93C4×C43—26no—
94Dic43—26no—
95Dic43—23no—
96#3567—431nomaximal, Sylow
97C2×C43#58513yes—
98D43—46no—
99D43—41no—
100#564D4311yescharacteristic, complemented
101#562—433no—
102#553—436no—
103#552—436no—
104#540—436no—
105#539—436no—
106#529—433no—
107C43#356711yescharacteristic, complemented, Sylow
108#127—432no—
109#126—436no—
110#126—436no—
111#126—432no—
112#125—436no—
113#125C2×D4313yes—
114#125C2×D4316yes—
115#125C2×D4316yes—
116#124—433no—
117#123—436no—
118#123—436no—
119#123—436no—
120#123—436no—
121#123—436no—
122C22⋊Q8—433no—
123C22⋊Q8—436no—
124C22⋊Q8—436no—
125#121—433no—
126#121—436no—
127#121—436no—
128#121—436no—
129#121—436no—
130C4×Q8—433no—
131C4×D4—436no—
132C4×D4—433no—
133C4×D4—436no—
134C4×D4—436no—
135#117—436no—
136#117—436no—
137C2×C4⋊C4—436no—
138C2×C42—431no—
139C2×Q8—433no—
140C2×D4—436no—
141C2×D4—433no—
142C2×D4—436no—
143C2×D4—436no—
144C22×C4—433no—
145C22×C4—436no—
146C22×C4—436no—
147C22×C4—436no—
148C4⋊C4—436no—
149C4⋊C4—436no—
150C4⋊C4—436no—
151C4⋊C4—436no—
152C4⋊C4C22×D4316yes—
153C4⋊C4C22×D4316yes—
154C4⋊C4C22×D4316yes—
155C4⋊C4C22×D4316yes—
156C4⋊C4C22×D4313yes—
157C4⋊C4C22×D4313yes—
158C22⋊C4—436no—
159C22⋊C4—436no—
160C22⋊C4—436no—
161C22⋊C4—436no—
162C22⋊C4—436no—
163C22⋊C4—436no—
164C22⋊C4—436no—
165C42—433no—
166C42—436no—
167C42C22×D4311yescharacteristic
168C42C22×D4312yes—
169C42C22×D4312yes—
170C23—436no—
171C23—431no—
172Q8—1723no—
173D4—1726no—
174D4—1726no—
175D4—1726no—
176D4—1723no—
177C2×C4—433no—
178C2×C4—436no—
179C2×C4—1726no—
180C2×C4—1726no—
181C2×C4—1726no—
182C2×C4—1723no—
183C2×C4C23×D4313yes—
184C2×C4C23×D4316yes—
185C2×C4C23×D4316yes—
186C22—866no—
187C22—866no—
188C22—863no—
189C22—866no—
190C22C24×D4311yescharacteristic
191C4—26no—
192C4—26no—
193C4—23no—
194C4—863no—
195C4—866no—
196C2—1726no—
197C2—1721no—
198C2#1458373613yes—
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#564C2
hypercenter#564D43
hypocenterC43#3567
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. #14583647C2semidirect
2. #14583602C2semidirect
3. #14583581C2semidirect
4. #14583505C2semidirect
5. #14583497C2semidirect
6. #14583434C2semidirect
7. C43×#564C2semidirect
100. #564D43semidirect
107. C43#3567semidirect