Finite Group Databasebeta

← #19135146

Subgroups — #19135146

Order 5504.

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

normal subgroups only

This group has 308 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
2#14583475C211yesmaximal, characteristic
3#14582881C211yesmaximal, characteristic
4C2×#13063243C211yesmaximal, characteristic, complemented
5C2×#13063243C211yesmaximal, characteristic, complemented
6#14582669C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×Dic86C2211yescharacteristic
10#13063333—22no—
11#13063331—22no—
12C2×#10621877C2211yescharacteristic
13C2×#10621877C2211yescharacteristic
14M16×D43—22no—
15#13063325—21no—
16#13063313—21no—
17#13063309C414yes—
18#13063305—22no—
19#13063243—21no—
20#13063243—22no—
21#13063243—22no—
22#13063241—21no—
23C2×M16×C43C2211yescharacteristic
24C2×M16×C43C2211yescharacteristic
25#117×C43C2211yescharacteristic
26C22×C4×C43C2311yescharacteristic
27C2×C22⋊D43C2×C412yes—
28C22×Dic43C2×C412yes—
29#10621898—21no—
30#10621898—21no—
31#10621898—21no—
32#10621898—21no—
33C2×D172D411yescharacteristic
34C2×C4×D43D412yes—
35C2×Dic86—21no—
36C2×Dic86—21no—
37C2×Dic86—21no—
38C2×Dic86—21no—
39C2×Dic86—21no—
40C2×Dic86—21no—
41C2×Dic86D411yescharacteristic
42M16×C43—21no—
43M16×C43—21no—
44M16×C43—21no—
45M16×C43D412yes—
46C2×C8×C43—21no—
47C2×C8×C43—21no—
48C4⋊C4×C43—21no—
49C22⋊C4×C43C2×C412yes—
50C42×C43—21no—
51(C2×D43)⋊C4—24no—
52C4⋊Dic43—24no—
53#10621877—21no—
54#10621877—21no—
55#10621877—21no—
56#10621877D412yes—
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59#10621872—24no—
60C8×D43—24no—
61C23×C43C22×C411yescharacteristic
62C22×D43C22⋊C412yes—
63C2×C4×C43—22no—
64C2×C4×C43C2×D411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43#4111yescharacteristic
69C2×C4×C43#4111yescharacteristic
70C22⋊D43—22no—
71C22⋊D43—22no—
72C2×Dic43—22no—
73C2×Dic43—22no—
74C2×Dic43—22no—
75C2×Dic43C22⋊C412yes—
76D172—21no—
77D172—21no—
78C4×D43—22no—
79C4×D43—22no—
80Dic86—21no—
81Dic86—21no—
82Dic86—41no—
83Dic86—41no—
84Dic86—41no—
85Dic86—41no—
86C8×C43—22no—
87C8×C43—41no—
88C43⋊C8—22no—
89C43⋊C8—41no—
90C22×C43—41no—
91C22×C43C2×C22⋊C411yescharacteristic
92C22×C43C4×D411yescharacteristic
93C22×C43C4×D411yescharacteristic
94C2×D43—22no—
95C2×D43—42no—
96C4×C43—42no—
97C4×C43#12011yescharacteristic
98C4×C43#12111yescharacteristic
99C4×C43#12111yescharacteristic
100C4×C43#12311yescharacteristic
101Dic43—22no—
102Dic43—42no—
103#1915—431nomaximal, Sylow
104C2×C43—21no—
105C2×C43—21no—
106C2×C43—21no—
107C2×C43#38611yescharacteristic
108D43—42no—
109#568—431no—
110#536—431no—
111#413—431no—
112C2×#101—431no—
113C2×#101—431no—
114#344—431no—
115#344D4311yescharacteristic, complemented
116C43#191511yescharacteristic, complemented, Sylow
117C2×#41—431no—
118C22×Q8—431no—
119#131—862no—
120#131—862no—
121C2×M16—431no—
122C2×M16—431no—
123C2×M16—862no—
124C2×M16C2×D4311yescharacteristic
125C2×M16C2×D4311yescharacteristic
126C4⋊Q8—861no—
127#124—861no—
128#123—434no—
129C22⋊Q8—862no—
130#117C2×D4311yescharacteristic
131#101—862no—
132#101—861no—
133#101—862no—
134#100—861no—
135#41—861no—
136#41—861no—
137#41—861no—
138#41—861no—
139C2×Q8—431no—
140C2×Q8—861no—
141C2×Q8—861no—
142C2×Q8—861no—
143C2×Q8—861no—
144C2×Q8—861no—
145C2×Q8—861no—
146C2×D4—432no—
147C2×D4—431no—
148C22×C4—432no—
149C22×C4—432no—
150C22×C4C22×D4311yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—432no—
155M16—864no—
156M16—861no—
157M16—861no—
158M16—861no—
159M16D17212yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—864no—
163C2×C8—861no—
164C2×C8—861no—
165C4⋊C4—21no—
166C4⋊C4—864no—
167C22⋊C4—864no—
168C22⋊C4C4×D4312yes—
169C42—21no—
170C23—432no—
171C23C2×C4×D4311yescharacteristic
172Q8—861no—
173Q8—861no—
174Q8—1721no—
175Q8—1721no—
176Q8—1721no—
177Q8—1721no—
178D4—862no—
179D4—862no—
180D4—861no—
181D4—861no—
182C2×C4—22no—
183C2×C4—432no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4C2×D17211yescharacteristic
190C2×C4#1062189811yescharacteristic
191C2×C4D4×D4311yescharacteristic
192C2×C4D4×D4311yescharacteristic
193C2×C4D4×D4311yescharacteristic
194C2×C4#1062190211yescharacteristic
195C8—22no—
196C8—41no—
197C8—862no—
198C8—1721no—
199C22—41no—
200C22—862no—
201C22—1722no—
202C22C22⋊C4×D4311yescharacteristic
203C22#1306328711yescharacteristic
204C22C4×D17211yescharacteristic
205C4—42no—
206C4—862no—
207C4—1722no—
208C4#1306329511yescharacteristic
209C4#1306329811yescharacteristic
210C4#1306330011yescharacteristic
211C4#1306331011yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—1722no—
216C2#1458277711yescharacteristic
subgroupG/H
centerC2#14582777
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#386
hypercenter#344D43
hypocenterC43#1915
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
4. C2×#13063243C2semidirect
5. C2×#13063243C2semidirect
6. #14582669C2semidirect
7. C43×#344C2semidirect
115. #344D43semidirect
116. C43#1915semidirect