Finite Group Databasebeta

← #27195357

Subgroups — #27195357

Order 13184.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#20268268C211yesmaximal, characteristic
2#20267831C211yesmaximal, characteristic
3C2×#15692939C211yesmaximal, characteristic
4#20267696C211yesmaximal, characteristic
5#20267552C211yesmaximal, characteristic
6#20267550C211yesmaximal, characteristic
7#428×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10C4×Dic206—21no—
11C4×Dic206—21no—
12#15692986—21no—
13#15692986—21no—
14#15692980C2211yescharacteristic
15#15692977—22no—
16C2×C4×Dic103C2211yescharacteristic
17#15692954—21no—
18#15692952—21no—
19#15692939C414yescomplemented
20C103⋊#95—22no—
21C2×M16×C103C2211yescharacteristic
22#117×C103C2211yescharacteristic
23C2×C4⋊C4×C103C2211yescharacteristic
24#107×C103—21no—
25#106×C103—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206C2×C412yes—
31C2×Dic206Q812yes—
32C22×Dic103—21no—
33C22×Dic103D412yes—
34#13110089—21no—
35#13110089C2×C412yes—
36C2×C103⋊C8—21no—
37C4⋊Dic103D411yescharacteristic
38C4⋊Dic103D411yescharacteristic
39Dic103⋊C4—22no—
40Dic103⋊C4—22no—
41C22⋊Dic103—21no—
42C4×Dic103—22no—
43C4×Dic103—22no—
44C4×Dic103—21no—
45C4×Dic103—21no—
46C4×Dic103—21no—
47C22×C4×C103—21no—
48C22×C4×C103C2311yescharacteristic
49M16×C103—21no—
50M16×C103C2×C412yes—
51C2×C8×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103—21no—
54C4⋊C4×C103D411yescharacteristic
55C4⋊C4×C103D411yescharacteristic
56C22⋊C4×C103—21no—
57C42×C103—21no—
58C23×C103C2×D411yescharacteristic
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—42no—
62C2×C4×C103—41no—
63C2×C4×C103C22×C411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×C4×C103C2×Q811yescharacteristic
67C2×C4×C103#4111yescharacteristic
68C2×C4×C103#4111yescharacteristic
69C2×Dic103—22no—
70C2×Dic103—22no—
71C2×Dic103—22no—
72C2×Dic103—21no—
73C2×Dic103—21no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103C4⋊C414yes—
77Dic206—22no—
78Dic206—22no—
79Dic206—22no—
80Dic206—22no—
81C8×C103—22no—
82C103⋊C8—22no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103C2×C4⋊C411yescharacteristic
86C22×C103#12011yescharacteristic
87C22×C103#12311yescharacteristic
88C4×C103—41no—
89C4×C103—41no—
90C4×C103—81no—
91C4×C103C4×D411yescharacteristic
92C4×C103C4×D411yescharacteristic
93C4×C103C22⋊Q811yescharacteristic
94C4×C103C22⋊Q811yescharacteristic
95Dic103—24no—
96Dic103—42no—
97Dic103—41no—
98Dic103—41no—
99C2×C103—21no—
100C2×C103—21no—
101C2×C103#38511yescharacteristic
102C2×C103#45411yescharacteristic
103C2×C103#45611yescharacteristic
104#1857—1031nomaximal, Sylow
105C103#185711yescharacteristic, complemented, Sylow
106#519—1031no—
107#428—1031no—
108#428D10311yescharacteristic
109C2×#101—1031no—
110#391—1031no—
111#339—1031no—
112#339—1031no—
113C22×Q8—1031no—
114C2×M16—1031no—
115C2×M16C2×D10311yescharacteristic
116C4×Q8—2061no—
117C4×Q8—2061no—
118C4×Q8—2061no—
119C4×Q8—2061no—
120#117—1031no—
121#117—2062no—
122#117C2×D10311yescharacteristic
123C2×C4⋊C4C2×D10311yescharacteristic
124C2×C42—1031no—
125#107—21no—
126#107—2061no—
127#106—21no—
128#106—2061no—
129#101—1034no—
130#95—2062no—
131C2×Q8—1032no—
132C2×Q8—1032no—
133C2×Q8—2061no—
134C2×Q8—2061no—
135C2×Q8—2061no—
136C2×Q8—2061no—
137C22×C4—21no—
138C22×C4—1032no—
139C22×C4—2061no—
140C22×C4C22×D10311yescharacteristic
141M16—21no—
142M16—1032no—
143M16—2061no—
144M16C4×D10312yes—
145C2×C8—21no—
146C2×C8—2061no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—1031no—
150C4⋊C4—1031no—
151C4⋊C4—2062no—
152C4⋊C4—2062no—
153C4⋊C4C22⋊D10311yescharacteristic
154C4⋊C4C22⋊D10311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2061no—
157C42—21no—
158C42—2062no—
159C42—2062no—
160C42—2061no—
161C42—2061no—
162C42—2061no—
163C23D4×D10311yescharacteristic
164Q8—2062no—
165Q8—2062no—
166Q8—2062no—
167Q8—2062no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—1034no—
173C2×C4—4121no—
174C2×C4—4121no—
175C2×C4—2062no—
176C2×C4—2061no—
177C2×C4—2061no—
178C2×C4—2062no—
179C2×C4—2062no—
180C2×C4C2×C4×D10311yescharacteristic
181C2×C4D4×D10311yescharacteristic
182C2×C4C2×C22⋊D10311yescharacteristic
183C2×C4Q8×D10311yescharacteristic
184C2×C4#1311010511yescharacteristic
185C2×C4#1311010611yescharacteristic
186C8—22no—
187C8—2062no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D10311yescharacteristic
191C22#1569298911yescharacteristic
192C22#1569300611yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—4122no—
197C4—4121no—
198C4—4121no—
199C4—2064no—
200C4C4×C22⋊D10311yescharacteristic
201C4#1569298311yescharacteristic
202C4#1569299711yescharacteristic
203C4#1569299911yescharacteristic
204C2—21no—
205C2—21no—
206C2#2026766211yescharacteristic
207C2#2026796211yescharacteristic
208C2#2026797211yescharacteristic
subgroupG/H
centerC22#15692989
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#428×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenter#428D103
hypocenterC103#1857
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
19. #15692939C4semidirect
105. C103#1857semidirect

Maximal subgroups

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

subgroupindex
#202682682
#202678312
C2×#156929392
#202676962
#202675522
#202675502
#428×C1032
#1857103