Finite Group Databasebeta

← #19134957

Subgroups — #19134957

Order 5504.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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#14583697C211yesmaximal, characteristic
2#14582915C211yesmaximal, characteristic, complemented
3#14582895C211yesmaximal, characteristic, complemented
4#14582867C211yesmaximal, characteristic, complemented
5#14582670C211yesmaximal, characteristic, complemented
6#14582663C211yesmaximal, characteristic, complemented
7C43×#568C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—21no—
10#13063355C412yescomplemented
11#13063351—21no—
12#13063350C412yescomplemented
13#13063345—22no—
14C2×#10621877C2211yescharacteristic
15C22×C43⋊C8C2211yescharacteristic
16#13063284C2211yescharacteristic
17#13063251—22no—
18#13063249—21no—
19#13063246—21no—
20(C2×D43)⋊C8—22no—
21C2×#41×C43C2211yescharacteristic
22#131×C43—22no—
23#131×C43—22no—
24C2×M16×C43—22no—
25C2×M16×C43C2211yescharacteristic
26C2×M16×C43C2211yescharacteristic
27#41×C43—21no—
28#41×C43—21no—
29#41×C43C2×C412yes—
30#41×C43D412yes—
31C2×Q8×C43D411yescharacteristic
32C2×D4×C43—21no—
33C2×D4×C43D411yescharacteristic
34C22×C4×C43—21no—
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—21no—
37#10621898—21no—
38#10621898—21no—
39#10621898—21no—
40#10621898—21no—
41C2×D172C2×C411yescharacteristic
42C2×C4×D43—21no—
43C2×Dic86C2×C411yescharacteristic
44M16×C43—24no—
45M16×C43—21no—
46M16×C43—21no—
47M16×C43—21no—
48M16×C43D412yes—
49C2×C8×C43—24no—
50C2×C8×C43—21no—
51C2×C8×C43D412yes—
52C22⋊Dic43—21no—
53#10621885—22no—
54#10621884—22no—
55#10621883—22no—
56#10621882—22no—
57C4⋊Dic43—21no—
58C4×Dic43—21no—
59#10621877—21no—
60#10621877C2×C412yes—
61C2×C43⋊C8—21no—
62C2×C43⋊C8—21no—
63C2×C43⋊C8—21no—
64C2×C43⋊C8—21no—
65C23×C43—21no—
66C23×C43#4111yescharacteristic
67C22×D43—21no—
68Q8×C43—21no—
69Q8×C43C22⋊C412yes—
70D4×C43—22no—
71D4×C43—22no—
72D4×C43—21no—
73D4×C43C22⋊C412yes—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43C22×C411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43#4111yescharacteristic
83C22⋊D43—41no—
84C22⋊D43—41no—
85C2×Dic43—21no—
86C2×Dic43—41no—
87D172—21no—
88D172—21no—
89C4×D43—41no—
90C4×D43—41no—
91Dic86—21no—
92Dic86—21no—
93C8×C43—22no—
94C8×C43—22no—
95C43⋊C8—22no—
96C43⋊C8—41no—
97C22×C43—22no—
98C22×C43—41no—
99C22×C43—81no—
100C22×C43C4×D411yescharacteristic
101C22×C43#12111yescharacteristic
102C22×C43#12311yescharacteristic
103C2×D43—42no—
104C2×D43—41no—
105C4×C43—22no—
106C4×C43C2×C22⋊C411yescharacteristic
107C4×C43C4×D411yescharacteristic
108C4×C43#12011yescharacteristic
109C4×C43#12111yescharacteristic
110Dic43—41no—
111Dic43—81no—
112#1881—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—42no—
117C2×C43#38611yescharacteristic
118D43—81no—
119#575—431no—
120#568D4311yescharacteristic, complemented
121#421—431no—
122#416—431no—
123#408—431no—
124#344—431no—
125#341—431no—
126C43#188111yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C2×#41C2×D4311yescharacteristic
129#137—432no—
130#137—861no—
131AGL(1,ℤ/8)—432no—
132AGL(1,ℤ/8)—861no—
133#135—862no—
134#131—22no—
135#131—22no—
136C2×M16—22no—
137C2×M16—431no—
138C2×M16C2×D4311yescharacteristic
139C2×M16C2×D4311yescharacteristic
140C22×C8—431no—
141#117—431no—
142#104—862no—
143#103—861no—
144#102—861no—
145C22⋊C8—862no—
146#41—21no—
147#41—21no—
148#41—861no—
149#41—861no—
150#41—861no—
151#41—861no—
152#41C4×D4312yes—
153#41C22⋊D4312yes—
154C2×Q8—431no—
155C2×Q8D17211yescharacteristic
156C2×D4—21no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4D17211yescharacteristic
160C22×C4—21no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163Q16—862no—
164SD16—862no—
165SD16—862no—
166D8—862no—
167M16—24no—
168M16—21no—
169M16—21no—
170M16—21no—
171M16—432no—
172M16—861no—
173M16C22⋊D4312yes—
174C2×C8—24no—
175C2×C8—21no—
176C2×C8—861no—
177C2×C8—861no—
178C2×C8—861no—
179C2×C8—861no—
180C2×C8C22⋊D4312yes—
181C4⋊C4—861no—
182C22⋊C4—861no—
183C42—861no—
184C23—21no—
185C23—861no—
186C23#1062189811yescharacteristic
187Q8—21no—
188Q8—861no—
189Q8—861no—
190Q8(C2×D43)⋊C412yes—
191D4—22no—
192D4—22no—
193D4—21no—
194D4—861no—
195D4—861no—
196D4—1721no—
197D4—1721no—
198D4(C2×D43)⋊C412yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—861no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4C2×C4×D4311yescharacteristic
207C2×C4C2×D17211yescharacteristic
208C2×C4#1062189811yescharacteristic
209C2×C4C2×C22⋊D4311yescharacteristic
210C2×C4C2×C22⋊D4311yescharacteristic
211C2×C4C2×C22⋊D4311yescharacteristic
212C8—22no—
213C8—22no—
214C8—862no—
215C8—1721no—
216C22—22no—
217C22—41no—
218C22—81no—
219C22—1722no—
220C22—1721no—
221C22C4×C22⋊D4311yescharacteristic
222C22#1306329911yescharacteristic
223C22#1306330811yescharacteristic
224C4—22no—
225C4—3441no—
226C4—1721no—
227C4C2×(C2×D43)⋊C411yescharacteristic
228C4C4×C22⋊D4311yescharacteristic
229C4#1306329411yescharacteristic
230C4#1306329911yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—3441no—
236C2#1458277811yescharacteristic
subgroupG/H
centerC4#13063294
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#568C2
socleC2×C43#386
hypercenter#568D43
hypocenterC43#1881
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #14582915C2semidirect
3. #14582895C2semidirect
4. #14582867C2semidirect
5. #14582670C2semidirect
6. #14582663C2semidirect
7. C43×#568C2semidirect
10. #13063355C4semidirect
12. #13063350C4semidirect
120. #568D43semidirect
126. C43#1881semidirect