Finite Group Databasebeta

← #19134648

Subgroups — #19134648

Order 5504.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×#13063333C211yesmaximal, characteristic
2C2×#13063260C211yesmaximal, characteristic, complemented
3#14582935C211yesmaximal, characteristic, complemented
4#14582917C211yesmaximal, characteristic
5#14582915C211yesmaximal, characteristic
6#14582671C211yesmaximal, characteristic, complemented
7C43×#344C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063333—21no—
10#13063333—21no—
11#13063333C412yescomplemented
12#13063333C412yescomplemented
13C2×#10621877C2211yescharacteristic
14C2×#10621872—21no—
15C22×C43⋊C8C2211yescharacteristic
16C2×C8×D43—21no—
17#13063284C2211yescharacteristic
18#13063260—21no—
19#13063260—21no—
20#13063258—21no—
21#13063256—21no—
22#13063253—22no—
23#13063251—22no—
24C2×M16×C43C2211yescharacteristic
25C2×M16×C43C2211yescharacteristic
26#117×C43C2211yescharacteristic
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—21no—
29#10621898—21no—
30#10621898—21no—
31#10621898C2×C412yes—
32#10621898D412yes—
33C2×D172Q811yescharacteristic
34C2×C4×D43—21no—
35C2×Dic86Q811yescharacteristic
36M16×C43—21no—
37M16×C43—21no—
38M16×C43—21no—
39M16×C43C2×C412yes—
40C2×C8×C43—21no—
41C2×C8×C43—21no—
42C4⋊C4×C43—21no—
43C22⋊C4×C43—21no—
44C42×C43—21no—
45C22⋊Dic43—21no—
46C4⋊Dic43—21no—
47C4×Dic43—21no—
48#10621877—21no—
49#10621877—21no—
50C2×C43⋊C8—21no—
51C2×C43⋊C8C2×C411yescharacteristic
52C2×C43⋊C8C2×C411yescharacteristic
53C2×C43⋊C8D411yescharacteristic
54C2×C43⋊C8D411yescharacteristic
55C2×C43⋊C8D411yescharacteristic
56C2×C43⋊C8D411yescharacteristic
57#10621872—22no—
58#10621872—22no—
59C8×D43—22no—
60C8×D43—22no—
61C23×C43#4111yescharacteristic
62C22×D43—21no—
63C2×C4×C43—41no—
64C2×C4×C43C22×C411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×Q811yescharacteristic
69C2×C4×C43#4111yescharacteristic
70C22⋊D43—22no—
71C22⋊D43—22no—
72C2×Dic43—21no—
73C2×Dic43—41no—
74D172—21no—
75D172C4⋊C412yes—
76C4×D43—22no—
77C4×D43—22no—
78Dic86—21no—
79Dic86C4⋊C412yes—
80C8×C43—22no—
81C8×C43—41no—
82C43⋊C8—41no—
83C43⋊C8C22⋊C411yescharacteristic
84C43⋊C8C22⋊C411yescharacteristic
85C43⋊C8C22⋊C411yescharacteristic
86C43⋊C8C22⋊C411yescharacteristic
87C22×C43—41no—
88C22×C43#11711yescharacteristic
89C22×C43#12111yescharacteristic
90C22×C43C22⋊Q811yescharacteristic
91C2×D43—22no—
92C2×D43—42no—
93C4×C43—81no—
94C4×C43C2×C22⋊C411yescharacteristic
95C4×C43C2×C4⋊C411yescharacteristic
96C4×C43#12111yescharacteristic
97C4×C43C22⋊Q811yescharacteristic
98Dic43—22no—
99Dic43—81no—
100#1814—431nomaximal, Sylow
101C2×C43—21no—
102C2×C43—21no—
103C2×C43—21no—
104C2×C43#38011yescharacteristic
105D43—42no—
106C2×#131—431no—
107C2×#108—431no—
108#427—431no—
109#421—431no—
110#421—431no—
111#344—431no—
112#344D4311yescharacteristic, complemented
113C43#181411yescharacteristic, complemented, Sylow
114C2×#41—431no—
115#131—432no—
116#131—432no—
117#131—861no—
118#131—861no—
119C2×M16—431no—
120C2×M16—861no—
121C2×M16C2×D4311yescharacteristic
122C2×M16C2×D4311yescharacteristic
123C22×C8—431no—
124C22×C8—861no—
125#117—431no—
126#117C2×D4311yescharacteristic
127#108—861no—
128#108—861no—
129#107—861no—
130#106—861no—
131#104—862no—
132#104—862no—
133#41—432no—
134#41—432no—
135#41—861no—
136#41—861no—
137C2×Q8—431no—
138C2×D4—431no—
139C2×D4—861no—
140C22×C4—861no—
141C22×C4C22×D4311yescharacteristic
142M16—21no—
143M16—21no—
144M16—21no—
145M16—862no—
146M16—862no—
147M16—861no—
148M16—861no—
149M16C4×D4312yes—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—431no—
153C2×C8—431no—
154C2×C8—431no—
155C2×C8—431no—
156C2×C8—431no—
157C2×C8—431no—
158C2×C8—862no—
159C2×C8—862no—
160C2×C8—861no—
161C4⋊C4—21no—
162C4⋊C4—861no—
163C22⋊C4—21no—
164C22⋊C4—861no—
165C42—21no—
166C42—861no—
167C23—861no—
168C23#1062189811yescharacteristic
169Q8—432no—
170Q8—861no—
171D4—432no—
172D4—862no—
173D4—862no—
174D4—861no—
175C2×C4—41no—
176C2×C4—861no—
177C2×C4—862no—
178C2×C4—862no—
179C2×C4—1721no—
180C2×C4C2×C4×D4311yescharacteristic
181C2×C4#1062189811yescharacteristic
182C2×C4D4×D4311yescharacteristic
183C2×C4D4×D4311yescharacteristic
184C2×C4D4×D4311yescharacteristic
185C2×C4Q8×D4311yescharacteristic
186C8—22no—
187C8—41no—
188C8—431no—
189C8—431no—
190C8—431no—
191C8—431no—
192C8—1721no—
193C22—41no—
194C22—862no—
195C22—1722no—
196C22#1306328211yescharacteristic
197C22#1306329811yescharacteristic
198C22#1306330311yescharacteristic
199C4—81no—
200C4—862no—
201C4—3441no—
202C4C22⋊C4×D4311yescharacteristic
203C4C4⋊C4×D4311yescharacteristic
204C4#1306329811yescharacteristic
205C4#1306330311yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—1722no—
210C2#1458275811yescharacteristic
subgroupG/H
centerC4#13063298
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#344C2
socleC2×C43#380
hypercenter#344D43
hypocenterC43#1814
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. C2×#13063260C2semidirect
3. #14582935C2semidirect
6. #14582671C2semidirect
7. C43×#344C2semidirect
11. #13063333C4semidirect
12. #13063333C4semidirect
112. #344D43semidirect
113. C43#1814semidirect