Finite Group Databasebeta

← #27196509

Subgroups — #27196509

Order 13184.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15692957C211yesmaximal, characteristic
2#20267831C211yesmaximal, characteristic
3#20267817C211yesmaximal, characteristic
4#20267800C211yesmaximal, characteristic
5C2×#15692940C211yesmaximal, characteristic
6#20267560C211yesmaximal, characteristic
7C2×#103×C103C211yesmaximal, characteristic
8C2×#13110089C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10C2×#13110089C2211yescharacteristic
11#15692980C2211yescharacteristic
12#15692957—22no—
13#15692954—21no—
14#15692952—21no—
15Dic103⋊C8—22no—
16#15692945—21no—
17#15692945—21no—
18#15692940—22no—
19C22×Q8×C103C2211yescharacteristic
20C22×C8×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22#103×C103—22no—
23#13110089—21no—
24#13110089—21no—
25#13110089—21no—
26#13110089—21no—
27#13110089—21no—
28#13110089D412yes—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C4⋊Dic103D411yescharacteristic
33C4⋊Dic103D411yescharacteristic
34C22⋊Dic103—21no—
35C4×Dic103—21no—
36C2×Q8×C103—21no—
37C2×Q8×C103—21no—
38C2×Q8×C103—21no—
39C2×Q8×C103—21no—
40C2×Q8×C103—21no—
41C2×Q8×C103Q812yes—
42C22×C4×C103—21no—
43C22×C4×C103—21no—
44C22×C4×C103C2311yescharacteristic
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C2×C8×C103D412yes—
48C4⋊C4×C103—21no—
49C4⋊C4×C103—21no—
50C23×C103#4111yescharacteristic
51Q8×C103—22no—
52Q8×C103—22no—
53Q8×C103—41no—
54Q8×C103—41no—
55C2×C4×C103—22no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103—81no—
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103C2×Q811yescharacteristic
64C2×C4×C103#4111yescharacteristic
65C2×C4×C103#4111yescharacteristic
66C2×Dic103—21no—
67C2×Dic103—21no—
68C8×C103—22no—
69C103⋊C8—22no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103#12111yescharacteristic
75C22×C103C22⋊Q811yescharacteristic
76C22×C103#12611yescharacteristic
77C4×C103—42no—
78C4×C103—81no—
79C4×C103#12111yescharacteristic
80C4×C103#12111yescharacteristic
81C4×C103C22⋊Q811yescharacteristic
82C4×C103C22⋊Q811yescharacteristic
83Dic103—41no—
84Dic103—41no—
85C2×C103—21no—
86C2×C103—21no—
87C2×C103#39611yescharacteristic
88C2×C103#47111yescharacteristic
89C2×C103#47311yescharacteristic
90#2064—1031nomaximal, Sylow
91C103#206411yescharacteristic, complemented, Sylow
92C2×#108—1031no—
93#428—1031no—
94#424—1031no—
95#419—1031no—
96C2×#103D10311yescharacteristic
97C2×#101—1031no—
98#343—1031no—
99C22×Q8C2×D10311yescharacteristic
100C2×M16—1031no—
101C2×M16—1031no—
102C2×M16—1031no—
103C22×C8C2×D10311yescharacteristic
104#117—1031no—
105C2×C4⋊C4C2×D10311yescharacteristic
106#108—2062no—
107#107—2061no—
108#106—2061no—
109C4⋊C8—2062no—
110#103—22no—
111#103—2061no—
112#103—2061no—
113#101—2062no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic20612yes—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4C22×D10311yescharacteristic
123M16—1032no—
124M16—2061no—
125M16—2061no—
126M16—2061no—
127M16—2061no—
128M16—2061no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—2061no—
132C2×C8—2061no—
133C2×C8—2061no—
134C2×C8C22⋊D10312yes—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—1031no—
138C4⋊C4—1031no—
139C22⋊C4—2061no—
140C42—2061no—
141C23#1311010411yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—2061no—
152C2×C4—2061no—
153C2×C4D4×D10311yescharacteristic
154C2×C4D4×D10311yescharacteristic
155C2×C4C2×C22⋊D10311yescharacteristic
156C2×C4C2×Dic20611yescharacteristic
157C2×C4#1311010411yescharacteristic
158C2×C4#1311010511yescharacteristic
159C8—22no—
160C8—4121no—
161C8—4121no—
162C8—2062no—
163C22—21no—
164C22—21no—
165C22#1569299211yescharacteristic
166C22#1569299811yescharacteristic
167C22#1569301411yescharacteristic
168C4—42no—
169C4—81no—
170C4—4121no—
171C4—4121no—
172C4#1569299311yescharacteristic
173C4#1569299411yescharacteristic
174C4#1569299811yescharacteristic
175C4#1569300011yescharacteristic
176C2—21no—
177C2—21no—
178C2#2026771411yescharacteristic
179C2#2026805111yescharacteristic
180C2#2026806311yescharacteristic
subgroupG/H
centerC22#15692992
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#103×C103C2
socleC22×C103#121
prime radicalC23×C103#41
hypercenterC2×#103D103
hypocenterC103#2064
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
91. C103#2064semidirect

Maximal subgroups

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

subgroupindex
C2×#156929572
#202678312
#202678172
#202678002
C2×#156929402
#202675602
C2×#103×C1032
#2064103