Finite Group Databasebeta

← #27196506

Subgroups — #27196506

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
1#20267833C211yesmaximal, characteristic
2#20267817C211yesmaximal, characteristic
3#20267801C211yesmaximal, characteristic
4C2×#15692946C211yesmaximal, characteristic
5C2×#15692939C211yesmaximal, characteristic
6#20267559C211yesmaximal, characteristic
7C2×#108×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15692980C2211yescharacteristic
11C2×C4⋊Dic103C2211yescharacteristic
12#15692955—21no—
13#15692953—21no—
14Dic103⋊C8—22no—
15#15692946—21no—
16#15692946—21no—
17#15692946—22no—
18#15692939—22no—
19C2×M16×C103C2211yescharacteristic
20C2×M16×C103C2211yescharacteristic
21C22×C8×C103C2211yescharacteristic
22#108×C103—22no—
23C2×Dic206—21no—
24C2×Dic206—21no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206Q812yes—
29C22×Dic103—21no—
30C22×Dic103—21no—
31#13110089—21no—
32#13110089—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103D411yescharacteristic
37C4⋊Dic103D411yescharacteristic
38C22⋊Dic103—21no—
39C4×Dic103—21no—
40C22×C4×C103C2311yescharacteristic
41M16×C103—21no—
42M16×C103—21no—
43M16×C103—21no—
44M16×C103D412yes—
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C2×C8×C103—21no—
48C2×C8×C103—21no—
49C2×C8×C103D412yes—
50C23×C103#4111yescharacteristic
51C2×C4×C103C2×D411yescharacteristic
52C2×C4×C103C2×D411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×Q811yescharacteristic
55C2×C4×C103#4111yescharacteristic
56C2×C4×C103#4111yescharacteristic
57C2×Dic103—21no—
58C2×Dic103—21no—
59C2×Dic103—22no—
60C2×Dic103—41no—
61C2×Dic103—41no—
62C2×Dic103—41no—
63C2×Dic103—81no—
64Dic206—22no—
65Dic206—22no—
66Dic206—41no—
67Dic206—41no—
68C8×C103—22no—
69C8×C103—22no—
70C8×C103—41no—
71C103⋊C8—41no—
72C22×C103—21no—
73C22×C103—21no—
74C22×C103#12111yescharacteristic
75C22×C103C22⋊Q811yescharacteristic
76C22×C103#12611yescharacteristic
77C4×C103#12111yescharacteristic
78C4×C103#12111yescharacteristic
79C4×C103C22⋊Q811yescharacteristic
80C4×C103C22⋊Q811yescharacteristic
81Dic103—42no—
82Dic103—41no—
83Dic103—41no—
84Dic103—81no—
85C2×C103—21no—
86C2×C103—21no—
87C2×C103#39611yescharacteristic
88C2×C103#47111yescharacteristic
89C2×C103#47311yescharacteristic
90#2064—1031nomaximal, Sylow
91C103#206411yescharacteristic, complemented, Sylow
92C2×#108D10311yescharacteristic
93#428—1031no—
94#424—1031no—
95#419—1031no—
96C2×#103—1031no—
97C2×#101—1031no—
98#343—1031no—
99C22×Q8—1031no—
100C2×M16—1031no—
101C2×M16C2×D10311yescharacteristic
102C2×M16C2×D10311yescharacteristic
103C22×C8C2×D10311yescharacteristic
104#117—1031no—
105C2×C4⋊C4—1031no—
106#108—22no—
107#107—2061no—
108#106—2061no—
109C4⋊C8—2062no—
110#103—2061no—
111#103—2061no—
112#103—2062no—
113#101—2062no—
114C2×Q8—1032no—
115C2×Q8—2061no—
116C2×Q8—2061no—
117C2×Q8—2061no—
118C2×Q8—2061no—
119C2×Q8—2061no—
120C22×C4—2061no—
121C22×C4—2061no—
122C22×C4C22×D10311yescharacteristic
123M16—21no—
124M16—21no—
125M16—21no—
126M16—2061no—
127M16—2061no—
128M16C22⋊D10312yes—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2061no—
134C2×C8D41212yes—
135C4⋊C4—1031no—
136C4⋊C4—1031no—
137C4⋊C4—2061no—
138C4⋊C4—2061no—
139C22⋊C4—2061no—
140C42—2061no—
141C23#1311010611yescharacteristic
142Q8—4121no—
143Q8—4121no—
144Q8—2062no—
145Q8—2062no—
146C2×C4—8241no—
147C2×C4—4121no—
148C2×C4—4121no—
149C2×C4—4121no—
150C2×C4—2061no—
151C2×C4—2061no—
152C2×C4—2062no—
153C2×C4D4×D10311yescharacteristic
154C2×C4C2×C22⋊D10311yescharacteristic
155C2×C4C2×D41211yescharacteristic
156C2×C4Q8×D10311yescharacteristic
157C2×C4#1311010411yescharacteristic
158C2×C4#1311010511yescharacteristic
159C8—22no—
160C8—22no—
161C8—41no—
162C8—4121no—
163C22—21no—
164C22—21no—
165C22#1569299611yescharacteristic
166C22#1569299711yescharacteristic
167C22#1569301611yescharacteristic
168C4—8241no—
169C4—4121no—
170C4—4121no—
171C4—4122no—
172C4#1569299311yescharacteristic
173C4#1569299511yescharacteristic
174C4#1569299911yescharacteristic
175C4#1569300111yescharacteristic
176C2—21no—
177C2—21no—
178C2#2026771311yescharacteristic
179C2#2026805511yescharacteristic
180C2#2026806711yescharacteristic
subgroupG/H
centerC22#15692996
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#108×C103C2
socleC22×C103#121
prime radicalC23×C103#41
hypercenterC2×#108D103
hypocenterC103#2064
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

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
#202678332
#202678172
#202678012
C2×#156929462
C2×#156929392
#202675592
C2×#108×C1032
#2064103