Finite Group Databasebeta

← #19136278

Subgroups — #19136278

Order 5504.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583445C211yesmaximal, characteristic
2#14582883C211yesmaximal, characteristic, complemented
3#14582697C212yesmaximal, complemented
4#14582695C212yesmaximal, complemented
5C43×#413C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic
7C2×#10621877—21no—
8#13063323C2211yescharacteristic
9#13063321C411yescharacteristic
10#13063314C2211yescharacteristic
11#13063312C411yescharacteristic
12#13063297—21no—
13#13063297—21no—
14C4×C22⋊D43—21no—
15C4×C22⋊D43—21no—
16C2×C4×Dic43C411yescharacteristic
17#13063244C2212yes—
18#13063242—21no—
19C2×#41×C43C2211yescharacteristic
20C2×M16×C43—21no—
21#101×C43C2212yes—
22#100×C43—21no—
23#41×C43—41no—
24#41×C43—41no—
25C2×Q8×C43C2311yescharacteristic
26C2×D4×C43C2×C411yescharacteristic
27C2×D4×C43D411yescharacteristic
28C2×D4×C43D411yescharacteristic
29C22×C4×C43C2×C411yescharacteristic
30C22×C4×C43D411yescharacteristic
31C22×C4×C43D411yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C22×Dic43—21no—
36#10621898—41no—
37#10621898—41no—
38C2×D172C2×C411yescharacteristic
39C2×C4×D43—21no—
40C2×Dic86C2×C411yescharacteristic
41M16×C43—22no—
42M16×C43—41no—
43C2×C8×C43—41no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46(C2×D43)⋊C4—21no—
47(C2×D43)⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50C4×Dic43—21no—
51C4×Dic43C2×C411yescharacteristic
52C4×Dic43C2×C411yescharacteristic
53#10621877—22no—
54#10621877—41no—
55C2×C43⋊C8—41no—
56C23×C43C22⋊C411yescharacteristic
57C23×C43C22⋊C411yescharacteristic
58C23×C43C22⋊C411yescharacteristic
59C22×D43—21no—
60Q8×C43—41no—
61D4×C43—41no—
62D4×C43—41no—
63D4×C43—41no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43C22⋊C411yescharacteristic
71C2×C4×C43C22×C411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C22⋊D43—42no—
75C22⋊D43—42no—
76C22⋊D43—42no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—42no—
81D172—41no—
82C4×D43—41no—
83C4×D43—41no—
84Dic86—41no—
85C8×C43—42no—
86C43⋊C8—42no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43C2×C22⋊C411yescharacteristic
94C2×D43—41no—
95C2×D43—41no—
96C2×D43—41no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43#9911yescharacteristic
101C4×C43#9911yescharacteristic
102Dic43—22no—
103Dic43—41no—
104Dic43—41no—
105#2132—431nomaximal, Sylow
106C2×C43—21no—
107C2×C43—41no—
108C2×C43—41no—
109C2×C43—41no—
110C2×C43C2×#9911yescharacteristic
111D43—81no—
112#532—431no—
113#413—431no—
114#413D4311yescharacteristic, complemented
115#356—432no—
116#355—432no—
117C43#213211yescharacteristic, complemented, Sylow
118C2×#41—431no—
119C2×#41C2×D4311yescharacteristic
120C2×M16—21no—
121C2×M16—861no—
122C4⋊Q8—431no—
123#127—431no—
124#124—431no—
125#124—431no—
126#121—861no—
127#121—861no—
128C4×D4—861no—
129C4×D4—861no—
130C2×C42—431no—
131#101—432no—
132#101C2×D4312yes—
133#100—21no—
134#100—861no—
135#41—41no—
136#41—41no—
137#41—1721no—
138#41—1721no—
139C2×Q8—431no—
140C2×Q8C22×D4311yescharacteristic
141C2×D4—431no—
142C2×D4—861no—
143C2×D4—861no—
144C2×D4—861no—
145C2×D4C4×D4311yescharacteristic
146C2×D4D17211yescharacteristic
147C2×D4C22⋊D4311yescharacteristic
148C22×C4—861no—
149C22×C4—861no—
150C22×C4C4×D4311yescharacteristic
151C22×C4D17211yescharacteristic
152C22×C4C22⋊D4311yescharacteristic
153M16—22no—
154M16—41no—
155M16—862no—
156M16—1721no—
157C2×C8—41no—
158C2×C8—1721no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C22⋊C4—861no—
165C42—431no—
166C42—431no—
167C42—861no—
168C23—861no—
169C23(C2×D43)⋊C411yescharacteristic
170C23(C2×D43)⋊C411yescharacteristic
171C23(C2×D43)⋊C411yescharacteristic
172Q8—41no—
173Q8—1721no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—1721no—
178D4—1722no—
179D4—1722no—
180D4—1722no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—861no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—1722no—
191C2×C4—1721no—
192C2×C4—1721no—
193C2×C4(C2×D43)⋊C411yescharacteristic
194C2×C4C2×C4×D4311yescharacteristic
195C2×C4C2×D17211yescharacteristic
196C2×C4C2×C22⋊D4311yescharacteristic
197C8—42no—
198C8—1722no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—1721no—
206C22—1721no—
207C22—1721no—
208C22C2×(C2×D43)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—862no—
213C4—1721no—
214C4—1721no—
215C4#1306323911yescharacteristic
216C4#1306323911yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—3441no—
222C2C2×#1306323911yescharacteristic
subgroupG/H
centerC4#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC43×#413C2
socleC2×C43C2×#99
hypercenter#413D43
hypocenterC43#2132
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14582883C2semidirect
3. #14582697C2semidirect
4. #14582695C2semidirect
5. C43×#413C2semidirect
114. #413D43semidirect
117. C43#2132semidirect