Finite Group Databasebeta

← #19135141

Subgroups — #19135141

Order 5504.

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

normal subgroups only

This group has 340 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#14583665C211yesmaximal, characteristic, complemented
2#14583468C211yesmaximal, characteristic
3#14582881C211yesmaximal, characteristic, complemented
4C2×#13063241C211yesmaximal, characteristic, complemented
5C2×#13063241C211yesmaximal, characteristic, complemented
6#14582669C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×D172C2211yescharacteristic
10#13063333—22no—
11#13063331—22no—
12C2×#10621877C2211yescharacteristic
13C2×#10621877C2211yescharacteristic
14M16×D43—22no—
15#13063322—21no—
16#13063313—21no—
17#13063300—22no—
18#13063295C414yes—
19#13063243—21no—
20#13063241—21no—
21#13063241—22no—
22#13063241—22no—
23C2×M16×C43C2211yescharacteristic
24C2×M16×C43C2211yescharacteristic
25#117×C43C2211yescharacteristic
26C23×D43C2×C412yes—
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43C2×C412yes—
29#10621898—21no—
30#10621898—21no—
31#10621898—21no—
32#10621898—21no—
33C2×D172—21no—
34C2×D172—21no—
35C2×D172—21no—
36C2×D172—21no—
37C2×D172—21no—
38C2×D172—21no—
39C2×D172—24no—
40C2×D172D411yescharacteristic
41C2×C4×D43D412yes—
42C2×Dic86D411yescharacteristic
43M16×C43—21no—
44M16×C43—21no—
45M16×C43—21no—
46M16×C43D412yescomplemented
47C2×C8×C43—21no—
48C2×C8×C43—21no—
49C4⋊C4×C43—21no—
50C22⋊C4×C43C2×C412yes—
51C42×C43—21no—
52(C2×D43)⋊C4—24no—
53#10621877—21no—
54#10621877—21no—
55#10621877—21no—
56#10621877D412yescomplemented
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59#10621872—24no—
60C8×D43—24no—
61C23×C43C22×C411yescharacteristic
62C22×D43—22no—
63C22×D43—22no—
64C22×D43—22no—
65C22×D43—82no—
66C22×D43C22⋊C412yes—
67C2×C4×C43—22no—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C2×C4×C43#4111yescharacteristic
74C22⋊D43—22no—
75C22⋊D43—22no—
76C2×Dic43C22⋊C412yes—
77D172—21no—
78D172—21no—
79D172—41no—
80D172—41no—
81D172—41no—
82D172—41no—
83D172—84no—
84C4×D43—22no—
85C4×D43—22no—
86Dic86—21no—
87Dic86—21no—
88C8×C43—22no—
89C8×C43—41no—
90C43⋊C8—22no—
91C43⋊C8—41no—
92C22×C43—41no—
93C22×C43C2×C22⋊C411yescharacteristic
94C22×C43C4×D411yescharacteristic
95C22×C43C4×D411yescharacteristic
96C2×D43—22no—
97C2×D43—42no—
98C2×D43—44no—
99C2×D43—42no—
100C2×D43—82no—
101C2×D43—82no—
102C4×C43—42no—
103C4×C43#12011yescharacteristic
104C4×C43#12111yescharacteristic
105C4×C43#12111yescharacteristic
106C4×C43#12311yescharacteristic
107Dic43—22no—
108#1914—431nomaximal, Sylow
109C2×C43—21no—
110C2×C43—21no—
111C2×C43—21no—
112C2×C43#38611yescharacteristic
113D43—42no—
114D43—82no—
115#568—431no—
116#535—431no—
117#413—431no—
118C2×#100—431no—
119C2×#100—431no—
120#344—431no—
121#344D4311yescharacteristic, complemented
122C43#191411yescharacteristic, complemented, Sylow
123C2×#41—431no—
124C22×D4—431no—
125#131—862no—
126#131—862no—
127C2×M16—431no—
128C2×M16—431no—
129C2×M16—862no—
130C2×M16C2×D4311yescharacteristic
131C2×M16C2×D4311yescharacteristic
132#127—861no—
133#124—861no—
134#121—862no—
135#120—434no—
136#117C2×D4311yescharacteristic
137#101—861no—
138#100—862no—
139#100—861no—
140#100—862no—
141C24—432no—
142#41—861no—
143#41—861no—
144#41—861no—
145#41—861no—
146C2×Q8—431no—
147C2×D4—432no—
148C2×D4—431no—
149C2×D4—864no—
150C2×D4—861no—
151C2×D4—861no—
152C2×D4—861no—
153C2×D4—861no—
154C2×D4—861no—
155C2×D4—861no—
156C22×C4—432no—
157C22×C4C22×D4311yescharacteristic
158M16—21no—
159M16—21no—
160M16—21no—
161M16—432no—
162M16—864no—
163M16—861no—
164M16—861no—
165M16—861no—
166M16D17212yescomplemented
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—864no—
170C2×C8—861no—
171C2×C8—861no—
172C4⋊C4—21no—
173C22⋊C4—864no—
174C22⋊C4C4×D4312yes—
175C42—21no—
176C23—432no—
177C23—862no—
178C23—862no—
179C23—862no—
180C23—3442no—
181C23C2×C4×D4311yescharacteristic
182Q8—861no—
183Q8—861no—
184D4—862no—
185D4—862no—
186D4—861no—
187D4—861no—
188D4—3444no—
189D4—1721no—
190D4—1721no—
191D4—1721no—
192D4—1721no—
193C2×C4—22no—
194C2×C4—432no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4C2×D17211yescharacteristic
198C2×C4#1062189811yescharacteristic
199C2×C4D4×D4311yescharacteristic
200C2×C4D4×D4311yescharacteristic
201C2×C4D4×D4311yescharacteristic
202C2×C4#1062190211yescharacteristic
203C8—22no—
204C8—41no—
205C8—862no—
206C8—1721no—
207C22—41no—
208C22—862no—
209C22—3442no—
210C22—3442no—
211C22—1724no—
212C22—1722no—
213C22—1722no—
214C22C22⋊C4×D4311yescharacteristic
215C22#1306328711yescharacteristic
216C22C4×D17211yescharacteristic
217C4—42no—
218C4—862no—
219C4#1306329511yescharacteristic
220C4#1306329811yescharacteristic
221C4#1306330011yescharacteristic
222C4#1306331011yescharacteristic
223C2—21no—
224C2—21no—
225C2—21no—
226C2—3442no—
227C2—1722no—
228C2#1458277711yescharacteristic
subgroupG/H
centerC2#14582777
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1914
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #14583665C2semidirect
3. #14582881C2semidirect
4. C2×#13063241C2semidirect
5. C2×#13063241C2semidirect
6. #14582669C2semidirect
7. C43×#344C2semidirect
46. M16×C43D4semidirect
56. #10621877D4semidirect
121. #344D43semidirect
122. C43#1914semidirect
166. M16D172semidirect