Finite Group Databasebeta

← #19134956

Subgroups — #19134956

Order 5504.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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#14583699C211yesmaximal, characteristic
2#14583665C211yesmaximal, characteristic, complemented
3#14582917C211yesmaximal, characteristic, complemented
4#14582893C211yesmaximal, characteristic, complemented
5#14582867C211yesmaximal, characteristic, complemented
6#14582663C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621898C2211yescharacteristic
10#13063358—21no—
11#13063358C412yescomplemented
12#13063353—21no—
13#13063353C412yescomplemented
14#13063347—22no—
15#13063333—22no—
16#13063331—22no—
17C2×#10621877C2211yescharacteristic
18M16×D43—22no—
19C22×C43⋊C8C2211yescharacteristic
20#13063253—22no—
21#13063248—21no—
22#13063245—21no—
23(C2×D43)⋊C8—22no—
24C2×M16×C43C2211yescharacteristic
25C2×M16×C43C2211yescharacteristic
26#117×C43C2211yescharacteristic
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—21no—
29C2×C22⋊D43—21no—
30#10621898—21no—
31#10621898—21no—
32#10621898—21no—
33#10621898—21no—
34#10621898—21no—
35#10621898—21no—
36#10621898C2×C412yes—
37#10621898D412yes—
38C2×D172C2×C411yescharacteristic
39C2×D172D411yescharacteristic
40C2×C4×D43—21no—
41C2×C4×D43—21no—
42C2×Dic86C2×C411yescharacteristic
43C2×Dic86D411yescharacteristic
44M16×C43—21no—
45M16×C43—21no—
46M16×C43—21no—
47M16×C43C2×C412yes—
48C2×C8×C43—21no—
49C2×C8×C43D412yes—
50C4⋊C4×C43—21no—
51C22⋊C4×C43—21no—
52C42×C43—21no—
53#10621877—21no—
54#10621877D412yes—
55C2×C43⋊C8—21no—
56C2×C43⋊C8—21no—
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59Dic172—22no—
60D344—22no—
61#10621873—22no—
62#10621873—22no—
63#10621872—24no—
64C8×D43—24no—
65C23×C43#4111yescharacteristic
66C22×D43—21no—
67C22×D43—21no—
68C2×C4×C43—41no—
69C2×C4×C43C22×C411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43#4111yescharacteristic
75C22⋊D43—22no—
76C22⋊D43—22no—
77C22⋊D43—41no—
78C22⋊D43—41no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81D172—21no—
82D172—21no—
83D172—21no—
84D172C22⋊C412yes—
85C4×D43—22no—
86C4×D43—22no—
87C4×D43—41no—
88C4×D43—41no—
89Dic86—21no—
90Dic86—21no—
91Dic86—21no—
92Dic86C22⋊C412yes—
93C8×C43—22no—
94C8×C43—22no—
95C43⋊C8—22no—
96C43⋊C8—41no—
97C22×C43—41no—
98C22×C43C4×D411yescharacteristic
99C22×C43#12111yescharacteristic
100C22×C43#12311yescharacteristic
101C2×D43—22no—
102C2×D43—42no—
103C2×D43—41no—
104C2×D43—81no—
105C4×C43—81no—
106C4×C43C2×C22⋊C411yescharacteristic
107C4×C43C4×D411yescharacteristic
108C4×C43#12011yescharacteristic
109C4×C43#12111yescharacteristic
110Dic43—22no—
111Dic43—41no—
112#1881—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43#38611yescharacteristic
117D43—42no—
118D43—81no—
119#575—431no—
120#568—431no—
121#421—431no—
122#416—431no—
123#408—431no—
124#344D4311yescharacteristic, complemented
125#341—431no—
126C43#188111yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C2×#41—431no—
129#137—432no—
130#137—861no—
131AGL(1,ℤ/8)—432no—
132AGL(1,ℤ/8)—861no—
133#135—862no—
134#131—862no—
135#131—862no—
136C2×M16—431no—
137C2×M16—862no—
138C2×M16C2×D4311yescharacteristic
139C2×M16C2×D4311yescharacteristic
140C22×C8—431no—
141#117C2×D4311yescharacteristic
142#104—862no—
143#103—861no—
144#102—861no—
145C22⋊C8—862no—
146#41—432no—
147#41—432no—
148#41—861no—
149#41—861no—
150#41—861no—
151#41—861no—
152#41—861no—
153#41—861no—
154C2×Q8—431no—
155C2×Q8—431no—
156C2×D4—431no—
157C2×D4—431no—
158C2×D4—861no—
159C2×D4—861no—
160C22×C4—861no—
161C22×C4—861no—
162C22×C4C22×D4311yescharacteristic
163Q16—862no—
164SD16—862no—
165SD16—862no—
166D8—862no—
167M16—21no—
168M16—21no—
169M16—21no—
170M16—432no—
171M16—864no—
172M16—861no—
173M16C4×D4312yes—
174C2×C8—21no—
175C2×C8—864no—
176C2×C8—861no—
177C2×C8—861no—
178C2×C8—861no—
179C2×C8—861no—
180C2×C8D17212yes—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—861no—
185C23—861no—
186C23#1062189811yescharacteristic
187Q8—432no—
188Q8—861no—
189Q8—861no—
190Q8—861no—
191D4—432no—
192D4—862no—
193D4—862no—
194D4—861no—
195D4—861no—
196D4—861no—
197D4—1721no—
198D4—1721no—
199C2×C4—41no—
200C2×C4—861no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—861no—
204C2×C4—1721no—
205C2×C4—1721no—
206C2×C4C2×C4×D4311yescharacteristic
207C2×C4C2×D17211yescharacteristic
208C2×C4D4×D4311yescharacteristic
209C2×C4D4×D4311yescharacteristic
210C2×C4D4×D4311yescharacteristic
211C2×C4#1062190211yescharacteristic
212C8—22no—
213C8—22no—
214C8—862no—
215C8—1721no—
216C22—41no—
217C22—862no—
218C22—3441no—
219C22—1722no—
220C22—1721no—
221C22C4×D17211yescharacteristic
222C22#1306329811yescharacteristic
223C22#1306331011yescharacteristic
224C4—81no—
225C4—862no—
226C4—1721no—
227C4C22⋊C4×D4311yescharacteristic
228C4#1306328711yescharacteristic
229C4#1306329511yescharacteristic
230C4#1306330011yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—3441no—
235C2—1722no—
236C2#1458277711yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1881
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #14583665C2semidirect
3. #14582917C2semidirect
4. #14582893C2semidirect
5. #14582867C2semidirect
6. #14582663C2semidirect
7. C43×#344C2semidirect
11. #13063358C4semidirect
13. #13063353C4semidirect
124. #344D43semidirect
126. C43#1881semidirect