Finite Group Databasebeta

← #27196390

Subgroups — #27196390

Order 13184.

298 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15693021C211yesmaximal, characteristic
2C2×#15692944C212yesmaximal
3C2×#15692944C212yesmaximal
4#20267546C211yesmaximal, characteristic
5#389×C103C211yesmaximal, characteristic
6C22×Dic206C2212yes—
7C22×C103⋊C8C2212yes—
8#15693021—24no—
9C2×C4⋊Dic103—21no—
10C2×C4⋊Dic103—21no—
11#15692944—24no—
12#15692944—24no—
13C2×C4⋊C4×C103—21no—
14C2×C4⋊C4×C103C2211yescharacteristic
15C2×C4⋊C4×C103C2211yescharacteristic
16C2×C42×C103C2211yescharacteristic
17#95×C103—21no—
18C2×Dic206—22no—
19C2×Dic206—22no—
20C2×Dic206—22no—
21C2×Dic206—22no—
22C2×Dic206—22no—
23C2×Dic206D414yes—
24C22×Dic103—22no—
25C2×C103⋊C8—22no—
26C2×C103⋊C8—22no—
27C2×C103⋊C8—22no—
28C4⋊Dic103—24no—
29C4⋊Dic103—24no—
30C22×C4×C103—21no—
31C22×C4×C103—21no—
32C22×C4×C103D411yescharacteristic
33C22×C4×C103D411yescharacteristic
34C22×C4×C103C2311yescharacteristic
35C4⋊C4×C103—21no—
36C4⋊C4×C103—22no—
37C4⋊C4×C103—42no—
38C4⋊C4×C103D412yes—
39C42×C103—22no—
40C23×C103C2×D411yescharacteristic
41C2×C4×C103—21no—
42C2×C4×C103—21no—
43C2×C4×C103—21no—
44C2×C4×C103—21no—
45C2×C4×C103—22no—
46C2×C4×C103—41no—
47C2×C4×C103—41no—
48C2×C4×C103—41no—
49C2×C4×C103—41no—
50C2×C4×C103—41no—
51C2×C4×C103SD1612yes—
52C2×C4×C103Q1612yes—
53C2×C4×C103C2×D412yes—
54C2×C4×C103C2×D411yescharacteristic
55C2×C4×C103#4111yescharacteristic
56C2×C4×C103#4112yes—
57C2×Dic103—24no—
58C2×Dic103—42no—
59C2×Dic103—42no—
60Dic206—24no—
61Dic206—24no—
62Dic206—42no—
63Dic206—42no—
64C103⋊C8—42no—
65C22×C103#12011yescharacteristic
66C22×C103#12111yescharacteristic
67C22×C103#12411yescharacteristic
68C22×C103C2×SD1611yescharacteristic
69C22×C103C2×Q1611yescharacteristic
70C22×C103#13711yescharacteristic
71C22×C103#13711yescharacteristic
72C4×C103—22no—
73C4×C103—22no—
74C4×C103—42no—
75C4×C103—81no—
76C4×C103#12112yes—
77C4×C103#12312yes—
78Dic103—44no—
79C2×C103#39411yescharacteristic
80C2×C103#44811yescharacteristic
81C2×C103#45111yescharacteristic
82C2×C103#46111yescharacteristic
83C2×C103#46211yescharacteristic
84C2×C103#48711yescharacteristic
85C2×C103#49111yescharacteristic
86#2043—1031nomaximal, Sylow
87C103#204311yescharacteristic, complemented, Sylow
88C2×C4⋊Q8—1031no—
89C2×#103—1032no—
90C2×#103—1032no—
91#389D10311yescharacteristic
92#336—1031no—
93C22×Q8—1032no—
94C22×C8—1032no—
95C4⋊Q8—2064no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—2061no—
98C2×C4⋊C4—2061no—
99C2×C4⋊C4C2×D10311yescharacteristic
100C2×C4⋊C4C2×D10311yescharacteristic
101C2×C42C2×D10311yescharacteristic
102#103—2064no—
103#103—2064no—
104#95—21no—
105C2×Q8—1034no—
106C2×Q8—2062no—
107C2×Q8—2062no—
108C2×Q8—2062no—
109C2×Q8—2062no—
110C2×Q8—2062no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—2062no—
114C22×C4C22⋊D10311yescharacteristic
115C22×C4C22⋊D10311yescharacteristic
116C22×C4C22×D10311yescharacteristic
117C2×C8—2062no—
118C2×C8—2062no—
119C2×C8—2062no—
120C4⋊C4—21no—
121C4⋊C4—22no—
122C4⋊C4—42no—
123C4⋊C4—2064no—
124C4⋊C4—2064no—
125C4⋊C4D41212yes—
126C42—22no—
127C23C2×C22⋊D10311yescharacteristic
128Q8—4122no—
129Q8—4122no—
130Q8—2064no—
131Q8—2064no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—4122no—
143C2×C4—4122no—
144C2×C4—2064no—
145C2×C4#1311009312yes—
146C2×C4#1311009512yes—
147C2×C4D4×D10312yes—
148C2×C4C2×D41211yescharacteristic
149C2×C4#1311010511yescharacteristic
150C2×C4#1311010612yes—
151C8—4122no—
152C22#1569298911yescharacteristic
153C22#1569299511yescharacteristic
154C22#1569301011yescharacteristic
155C22C2×#1311009311yescharacteristic
156C22C2×#1311009511yescharacteristic
157C22#1569305111yescharacteristic
158C22#1569305111yescharacteristic
159C4—22no—
160C4—22no—
161C4—42no—
162C4—81no—
163C4—4124no—
164C4#1569299612yes—
165C4#1569300612yes—
166C2#2026770811yescharacteristic
167C2#2026792911yescharacteristic
168C2#2026794611yescharacteristic
169C2#2026799611yescharacteristic
170C2#2026800111yescharacteristic
171C2#2026814311yescharacteristic
172C2#2026816111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#389×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#389D103
hypocenterC103#2043
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
87. C103#2043semidirect

Maximal subgroups

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

subgroupindex
C2×#156930212
C2×#156929442
#202675462
#389×C1032
#2043103