Finite Group Databasebeta

← #25016919

Subgroups — #25016919

Order 11008.

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

normal subgroups only

This group has 406 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#19136260C212yesmaximal
2#19132760C214yesmaximal, complemented
3C43×#3152C211yesmaximal, characteristic
4#14582873—22no—
5#14582694—22no—
6#14582692C2214yes—
7C2×#137×C43—22no—
8C43×#532C2211yescharacteristic
9C2×C4⋊Q8×C43C411yescharacteristic, complemented
10C43×#497—22no—
11C43×#494C412yescomplemented
12C43×#492C2212yes—
13C4×M16×C43C411yescharacteristic, complemented
14#13063284—42no—
15#13063240—24no—
16#13063240—42no—
17C2×#41×C43D412yes—
18C22×Q8×C43—21no—
19#137×C43—44no—
20#137×C43—44no—
21C2×Q16×C43—24no—
22C2×SD16×C43—24no—
23C2×M16×C43—21no—
24C4⋊Q8×C43—21no—
25C4⋊Q8×C43—41no—
26C4⋊Q8×C43C2×C412yes—
27C4⋊Q8×C43C2×C411yescharacteristic
28#127×C43C2311yescharacteristic
29#124×C43D412yes—
30#121×C43—41no—
31C4×D4×C43—41no—
32C2×C4⋊C4×C43—41no—
33C2×C42×C43C2×C411yescharacteristic
34#97×C43—21no—
35C4×C8×C43C2×C412yes—
36#41×C43—42no—
37#41×C43—42no—
38C2×Q8×C43—22no—
39C2×Q8×C43—42no—
40C2×Q8×C43—42no—
41C2×Q8×C43—41no—
42C2×Q8×C43C22⋊C412yes—
43C2×D4×C43—22no—
44C2×D4×C43—41no—
45C2×D4×C43C2×D412yes—
46C22×C4×C43—22no—
47C22×C4×C43—21no—
48C22×C4×C43—41no—
49C22×C4×C43C22⋊C411yescharacteristic
50Q16×C43—48no—
51SD16×C43—48no—
52M16×C43—24no—
53C2×C8×C43—22no—
54C4⋊C4×C43—41no—
55C4⋊C4×C43—42no—
56C4⋊C4×C43—42no—
57C22⋊C4×C43—42no—
58C42×C43—21no—
59C42×C43C22⋊C411yescharacteristic
60C42×C43C22×C411yescharacteristic
61C22⋊Dic43—44no—
62C4⋊Dic43—82no—
63C4×Dic43—82no—
64C23×C43—22no—
65C23×C43#9911yescharacteristic
66Q8×C43—42no—
67Q8×C43—44no—
68Q8×C43—82no—
69D4×C43—42no—
70D4×C43—82no—
71D4×C43—82no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—42no—
77C2×C4×C43—42no—
78C2×C4×C43—42no—
79C2×C4×C43—42no—
80C2×C4×C43—81no—
81C2×C4×C43—81no—
82C2×C4×C43#9911yescharacteristic
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C2×Dic43—84no—
85C8×C43—24no—
86#13586—431nomaximal, Sylow
87C22×C43—21no—
88C22×C43—41no—
89C22×C43—42no—
90C22×C43—82no—
91C22×C43C2×#9911yescharacteristic
92C4×C43—22no—
93C4×C43—21no—
94C4×C43—41no—
95C4×C43—42no—
96C4×C43—82no—
97C4×C43#35312yes—
98Dic43—164no—
99#3152D4311yescharacteristic
100#2126—432no—
101#1409—434no—
102C2×C43—21no—
103C2×C43—41no—
104C2×C43—82no—
105C2×C43C2×#35311yescharacteristic
106C2×#137—22no—
107#532C2×D4311yescharacteristic
108C2×C4⋊Q8Dic4311yescharacteristic, complemented
109#497—22no—
110#494Dic4312yescomplemented
111#492C2×D4312yes—
112#410—862no—
113C4×M16Dic4311yescharacteristic, complemented
114#354—862no—
115#353—434no—
116C43#1358611yescharacteristic, complemented, Sylow
117C2×#41C22⋊D4312yes—
118C22×Q8—21no—
119#137—44no—
120#137—44no—
121C2×Q16—24no—
122C2×SD16—24no—
123C2×M16—21no—
124C4⋊Q8—21no—
125C4⋊Q8—41no—
126C4⋊Q8C2×Dic4312yes—
127C4⋊Q8C2×Dic4311yescharacteristic
128#127C22×D4311yescharacteristic
129#124C22⋊D4312yes—
130#121—41no—
131C4×D4—41no—
132#117—1722no—
133C2×C4⋊C4—41no—
134C2×C42C2×Dic4311yescharacteristic
135#99—864no—
136#99—1722no—
137#97—21no—
138C4×C8C2×Dic4312yes—
139#41—42no—
140#41—42no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8C22⋊Dic4312yes—
146C2×D4—22no—
147C2×D4—41no—
148C2×D4C2×C22⋊D4312yes—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C22⋊Dic4311yescharacteristic
153Q16—48no—
154SD16—48no—
155M16—24no—
156C2×C8—22no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—3442no—
161C22⋊C4—42no—
162C22⋊C4—1724no—
163C42—21no—
164C42—3442no—
165C42C22⋊Dic4311yescharacteristic
166C42C22×Dic4311yescharacteristic
167C23—22no—
168C23#1306324011yescharacteristic
169Q8—42no—
170Q8—44no—
171Q8—82no—
172D4—42no—
173D4—82no—
174D4—82no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—3444no—
186C2×C4#1306324011yescharacteristic
187C2×C4C2×C22⋊Dic4311yescharacteristic
188C8—24no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—82no—
193C22C2×#1306324011yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—42no—
198C4—82no—
199C4—6884no—
200C4#1458269212yes—
201C2—21no—
202C2—41no—
203C2—82no—
204C2C2×#1458269211yescharacteristic
subgroupG/H
centerC2C2×#14582692
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#3152C2
socleC2×C43C2×#353
prime radicalC43×#532C22
cosocle#127×C43C23
hypercenter#3152D43
hypocenterC43#13586
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #19132760C2semidirect
9. C2×C4⋊Q8×C43C4semidirect
11. C43×#494C4semidirect
13. C4×M16×C43C4semidirect
108. C2×C4⋊Q8Dic43semidirect
110. #494Dic43semidirect
113. C4×M16Dic43semidirect
116. C43#13586semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191362602
#191327602
C43×#31522
#1358643