Finite Group Databasebeta

← #19136617

Subgroups — #19136617

Order 5504.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#14583648C211yesmaximal, characteristic, complemented
2#14583084C211yesmaximal, characteristic, complemented
3#14583081C211yesmaximal, characteristic, complemented
4#14583074C211yesmaximal, characteristic
5#14582697C211yesmaximal, characteristic, complemented
6#14582695C211yesmaximal, characteristic, complemented
7C43×#356C211yesmaximal, characteristic, complemented
8#13063373C2211yescharacteristic
9#13063358—21no—
10#13063356—21no—
11#13063353—21no—
12#13063323C2211yescharacteristic
13#13063320—21no—
14#13063319—21no—
15#13063315—21no—
16#13063314C2211yescharacteristic
17#13063310—21no—
18#13063303—21no—
19#13063301—21no—
20#13063253—21no—
21#13063251—21no—
22#13063251—21no—
23#13063244C2211yescharacteristic
24C4⋊Q8×C43C2211yescharacteristic
25#101×C43C2211yescharacteristic
26#101×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C2×Q8×C43C2311yescharacteristic
29#10621902—41no—
30Q8×D43—41no—
31#10621898—21no—
32#10621898—21no—
33#10621898—21no—
34C2×D172D411yescharacteristic
35C2×C4×D43—21no—
36C2×Dic86D411yescharacteristic
37M16×C43—21no—
38M16×C43—21no—
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C42×C43D411yescharacteristic
42#10621885—41no—
43#10621884—41no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55C4×Dic43D411yescharacteristic
56C4×Dic43D411yescharacteristic
57#10621877—21no—
58Dic172—41no—
59D344—41no—
60#10621873—41no—
61#10621873—41no—
62C22×D43—21no—
63Q8×C43—41no—
64Q8×C43—41no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C22⋊D43—41no—
71C2×Dic43—21no—
72C2×Dic43—21no—
73C2×Dic43—21no—
74D172—21no—
75D172—21no—
76D172—21no—
77D172—41no—
78C4×D43—41no—
79C4×D43—41no—
80C4×D43—41no—
81C4×D43—81no—
82Dic86—21no—
83Dic86—21no—
84Dic86—21no—
85Dic86—41no—
86C8×C43—41no—
87C8×C43—41no—
88C43⋊C8—41no—
89C22×C43#12011yescharacteristic
90C2×D43—42no—
91C2×D43—41no—
92C2×D43—41no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—21no—
96C4×C43—41no—
97C4×C43—41no—
98Dic43—41no—
99Dic43—41no—
100Dic43—41no—
101Dic43—41no—
102#2203—431nomaximal, Sylow
103C2×C43—21no—
104C2×C43B(4,𝔽2)11yescharacteristic
105D43—81no—
106D43—81no—
107#563—431no—
108#456—431no—
109#456—431no—
110#454—431no—
111#356—431no—
112#356D4311yescharacteristic, complemented
113#355—431no—
114C43#220311yescharacteristic, complemented, Sylow
1152−1+4—431no—
116#137—861no—
117#137—861no—
118AGL(1,ℤ/8)—861no—
119C4⋊Q8—431no—
120C4⋊Q8C2×D4311yescharacteristic
121#126—861no—
122#126—861no—
123#125—861no—
124#124—431no—
125#123—861no—
126C22⋊Q8—861no—
127C22⋊Q8—861no—
128#104—861no—
129#104—861no—
130#104—861no—
131#101—431no—
132#101C2×D4311yescharacteristic
133#101C2×D4311yescharacteristic
134#41—861no—
135#41—861no—
136#41—861no—
137#41—1721no—
138C2×Q8—431no—
139C2×Q8—1721no—
140C2×Q8D17211yescharacteristic
141C2×Q8C22×D4311yescharacteristic
142C2×D4—431no—
143C22×C4—861no—
144Q16—1721no—
145Q16—1721no—
146SD16—1721no—
147SD16—1721no—
148SD16—1721no—
149D8—1721no—
150M16—21no—
151M16—21no—
152M16—861no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C22⋊C4—861no—
165C22⋊C4—861no—
166C42—431no—
167C42—431no—
168C42D17211yescharacteristic
169C23—861no—
170Q8—41no—
171Q8—41no—
172Q8—861no—
173Q8—861no—
174Q8—861no—
175Q8—1721no—
176D4—861no—
177D4—861no—
178D4—861no—
179D4—1721no—
180D4—1721no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—861no—
184C2×C4—861no—
185C2×C4—861no—
186C2×C4—3441no—
187C2×C4—1721no—
188C2×C4—1721no—
189C2×C4—1721no—
190C2×C4C2×D17211yescharacteristic
191C2×C4D4×D4311yescharacteristic
192C2×C4D4×D4311yescharacteristic
193C8—41no—
194C8—41no—
195C8—1721no—
196C22—1722no—
197C22—1721no—
198C22—1721no—
199C22#1306329511yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—1721no—
206C4—1721no—
207C4—1721no—
208C4—1721no—
209C2—21no—
210C2—3441no—
211C2—3441no—
212C2#1458308711yescharacteristic
subgroupG/H
centerC2#14583087
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#356C2
socleC2×C43B(4,𝔽2)
hypercenter#356D43
hypocenterC43#2203
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #14583648C2semidirect
2. #14583084C2semidirect
3. #14583081C2semidirect
5. #14582697C2semidirect
6. #14582695C2semidirect
7. C43×#356C2semidirect
112. #356D43semidirect
114. C43#2203semidirect