Finite Group Databasebeta

← #25010005

Subgroups — #25010005

Order 11008.

356 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136676C212yesmaximal, complemented
2#19134211C211yesmaximal, characteristic, complemented
3#19132634C211yesmaximal, characteristic, complemented
4#19132568C212yesmaximal, complemented
5C43×#3293C211yesmaximal, characteristic
6#14583339—22no—
7#14583302—22no—
8#14583279C2211yescharacteristic
9#14582720C2212yes—
10#14582714—22no—
11C8×C43⋊C8C2211yescharacteristic
12C43×#578—22no—
13C43×#494C2211yescharacteristic
14C43×#473—22no—
15C43×#456—22no—
16C43×#443C2212yes—
17C2×Dic172—22no—
18#13063325—21no—
19#13063271—42no—
20#13063269—42no—
21#13063265—22no—
22#13063258—44no—
23C4×C43⋊C8—21no—
242−1+4×C43—22no—
25#137×C43—24no—
26#137×C43—44no—
27#135×C43—42no—
28#135×C43D412yes—
29C2×Q16×C43—22no—
30C2×Q16×C43—42no—
31#131×C43—22no—
32C4⋊Q8×C43D412yes—
33#108×C43D412yes—
34#104×C43—22no—
35#101×C43—22no—
36C4×C8×C43C2311yescharacteristic
37#41×C43—22no—
38#41×C43—44no—
39#41×C43—82no—
40C2×Q8×C43—22no—
41C2×Q8×C43—44no—
42C2×Dic86—41no—
43Q16×C43—44no—
44Q16×C43—42no—
45Q16×C43—42no—
46Q16×C43D812yes—
47SD16×C43—22no—
48SD16×C43—44no—
49D8×C43D812yes—
50M16×C43—22no—
51M16×C43—42no—
52C2×C8×C43—42no—
53C2×C8×C43C2×D412yes—
54C4⋊C4×C43—42no—
55C42×C43C2×D411yescharacteristic
56C4⋊Dic43—42no—
57C2×C43⋊C8—22no—
58Dic172—42no—
59Dic172—42no—
60C43⋊C16—42no—
61Q8×C43—22no—
62Q8×C43—44no—
63Q8×C43—82no—
64D4×C43—22no—
65D4×C43—42no—
66D4×C43—82no—
67C2×C4×C43—21no—
68C2×C4×C43—42no—
69C2×C4×C43—42no—
70C2×C4×C43—84no—
71C2×C4×C43#12011yescharacteristic
72C2×Dic43—81no—
73Dic86—82no—
74C8×C43—42no—
75C8×C43C2×D812yes—
76C8×C43AGL(1,ℤ/8)12yes—
77C43⋊C8—24no—
78#12313—431nomaximal, Sylow
79C22×C43—42no—
80C22×C43#45311yescharacteristic
81C4×C43—22no—
82C4×C43—42no—
83C4×C43—82no—
84C4×C43#44712yes—
85Dic43—161no—
86#3293D4311yescharacteristic
87#2214—432no—
88#1713—431no—
89#1358—431no—
90#1335—432no—
91C2×C43—21no—
92C2×C43—82no—
93C2×C43#161911yescharacteristic
94#578—22no—
95#510—862no—
96#500—862no—
97#494—431no—
98#494C2×D4311yescharacteristic
99#473—22no—
100#456—22no—
101#443C2×D4312yes—
102#364—432no—
103#362—862no—
104C82—431no—
105C43#1231311yescharacteristic, complemented, Sylow
1062−1+4—22no—
107#137—24no—
108#137—44no—
109#135—42no—
110#135C22⋊D4312yes—
111C2×Q16—22no—
112C2×Q16—42no—
113C2×Q16—862no—
114#131—22no—
115C4⋊Q8—861no—
116C4⋊Q8C22⋊D4312yes—
117Q32—1722no—
118SD32—1722no—
119M32—862no—
120#108C22⋊D4312yes—
121#107—1724no—
122#104—22no—
123#101—22no—
124C4×C8—861no—
125C4×C8C22×D4311yescharacteristic
126#41—22no—
127#41—44no—
128#41—82no—
129C2×Q8—22no—
130C2×Q8—44no—
131C2×Q8—1721no—
132Q16—44no—
133Q16—42no—
134Q16—42no—
135Q16—1722no—
136Q16—1722no—
137Q16#1062188212yes—
138SD16—22no—
139SD16—44no—
140D8#1062188212yes—
141M16—22no—
142M16—42no—
143C2×C8—42no—
144C2×C8—862no—
145C2×C8C2×C22⋊D4312yes—
146C4⋊C4—42no—
147C4⋊C4—1722no—
148C42C2×C22⋊D4311yescharacteristic
149C16—1722no—
150Q8—22no—
151Q8—44no—
152Q8—82no—
153Q8—3442no—
154D4—22no—
155D4—42no—
156D4—82no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—84no—
161C2×C4—3441no—
162C2×C4#1306329411yescharacteristic
163C8—42no—
164C8—864no—
165C8C2×#1062188212yes—
166C8#1306335112yes—
167C22—42no—
168C22#1458306711yescharacteristic
169C4—22no—
170C4—42no—
171C4—82no—
172C4—6881no—
173C4#1458303312yes—
174C2—21no—
175C2—82no—
176C2#1913364911yescharacteristic
subgroupG/H
centerC2#19133649
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3293C2
socleC2×C43#1619
hypercenter#3293D43
hypocenterC43#12313
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3293

Complements

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

NH ≅ G/Ntype
1. #19136676C2semidirect
2. #19134211C2semidirect
3. #19132634C2semidirect
4. #19132568C2semidirect
105. C43#12313semidirect

Maximal subgroups

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

subgroupindex
#191366762
#191342112
#191326342
#191325682
C43×#32932
#1231343