Finite Group Databasebeta

← #27195669

Subgroups — #27195669

Order 13184.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#20268558C211yesmaximal, characteristic, complemented
2#20268355C211yesmaximal, characteristic
3#20267795C212yesmaximal, complemented
4#20267547C212yesmaximal, complemented
5#410×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7#15693028—24no—
8C2×#13110089—22no—
9C2×#13110089C2212yes—
10#15693017C412yescomplemented
11#15693010C412yescomplemented
12#15692995—22no—
13#15692989—22no—
14#15692980C2211yescharacteristic
15#15692941—24no—
16C2×#41×C103C2211yescharacteristic
17#117×C103C2212yes—
18#99×C103—22no—
19C23×D103—21no—
20C2×D412—22no—
21C2×D412—22no—
22C2×D412—21no—
23C2×D412C2×C412yes—
24C2×C22⋊D103—24no—
25#13110089—24no—
26#13110089—22no—
27#13110089—22no—
28C2×C103⋊C8—24no—
29C2×C103⋊C8D414yescomplemented
30C4⋊Dic103—21no—
31C22⋊Dic103—21no—
32(C2×D103)⋊C4—24no—
33C4×Dic103C2×C412yes—
34#41×C103—22no—
35#41×C103—22no—
36C2×Q8×C103C2×C411yescharacteristic
37C2×D4×C103C2×C411yescharacteristic
38C2×D4×C103D412yes—
39C22×C4×C103D412yes—
40C22×C4×C103C2311yescharacteristic
41C4⋊C4×C103—22no—
42C22⋊C4×C103—22no—
43C42×C103—22no—
44C23×C103C22⋊C412yes—
45C23×C103C2×D411yescharacteristic
46C22×D103—22no—
47C22×D103—42no—
48C22×D103—82no—
49Q8×C103—22no—
50D4×C103—24no—
51D4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103—42no—
55C2×C4×C103C22⋊C412yes—
56C2×C4×C103C22×C411yescharacteristic
57C2×C4×C103C2×D412yes—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103#4112yes—
60C22⋊D103—84no—
61C2×Dic103—22no—
62D412—24no—
63D412—41no—
64D412—41no—
65C103⋊C8—24no—
66C22×C103—22no—
67C22×C103—41no—
68C22×C103—42no—
69C22×C103C2×C22⋊C411yescharacteristic
70C22×C103#12112yes—
71C2×D103—44no—
72C2×D103—42no—
73C2×D103—84no—
74C4×C103—22no—
75C4×C103—82no—
76C4×C103C4×D412yes—
77C4×C103#12011yescharacteristic
78C4×C103#12311yescharacteristic
79Dic103—42no—
80C2×C103—21no—
81C2×C103—22no—
82C2×C103—42no—
83C2×C103#38611yescharacteristic
84D103—82no—
85#1910—1031nomaximal, Sylow
86C103#191011yescharacteristic, complemented, Sylow
87#568—1031no—
88#535—1031no—
89#418—1032no—
90#410D10311yescharacteristic, complemented
91H(3,ℤ/4)—1032no—
92C2×#41C2×D10311yescharacteristic
93C22×D4—1031no—
94#131—2064no—
95C2×M16—1032no—
96C2×M16—2062no—
97#127—1032no—
98#124—1032no—
99#121—2062no—
100#120—2062no—
101#117—1031no—
102#117C2×D10312yes—
103#102—2064no—
104#99—22no—
105C24—2061no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D10311yescharacteristic
109C2×D4—1032no—
110C2×D4—2064no—
111C2×D4—2062no—
112C2×D4—2061no—
113C2×D4—2062no—
114C2×D4C4×D10311yescharacteristic
115C2×D4C22⋊D10312yes—
116C22×C4D41212yes—
117C22×C4C22×D10311yescharacteristic
118M16—2064no—
119M16—2062no—
120M16—2062no—
121C2×C8—1034no—
122C2×C8—2064no—
123C4⋊C4—22no—
124C4⋊C4—2061no—
125C22⋊C4—22no—
126C22⋊C4—2061no—
127C22⋊C4—2064no—
128C42—22no—
129C42—1032no—
130C23—8242no—
131C23—4122no—
132C23—2062no—
133C23(C2×D103)⋊C412yes—
134C23C2×C22⋊D10311yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—8244no—
139D4—4121no—
140D4—4121no—
141D4—2064no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—2062no—
146C2×C4(C2×D103)⋊C412yes—
147C2×C4C2×C4×D10311yescharacteristic
148C2×C4D4×D10312yes—
149C2×C4C2×D41211yescharacteristic
150C2×C4#1311010412yes—
151C8—2064no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—8244no—
156C22—4124no—
157C22—4122no—
158C22C2×(C2×D103)⋊C411yescharacteristic
159C22#1569299312yes—
160C4—22no—
161C4—82no—
162C4—4122no—
163C4(C22⋊D103)⋊C412yes—
164C4#1569299111yescharacteristic
165C4#1569300511yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—8242no—
170C2#2026766811yescharacteristic
subgroupG/H
centerC2#20267668
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#410×C103C2
socleC2×C103#386
prime radical#20268355C2
cosocleC22×C4×C103C23
hypercenter#410D103
hypocenterC103#1910
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #20268558C2semidirect
3. #20267795C2semidirect
4. #20267547C2semidirect
5. #410×C103C2semidirect
10. #15693017C4semidirect
11. #15693010C4semidirect
29. C2×C103⋊C8D4semidirect
86. C103#1910semidirect
90. #410D103semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202683552
#202677952
#202675472
#410×C1032
#1910103