Finite Group Databasebeta

← #27194288

Subgroups — #27194288

Order 13184.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268506C211yesmaximal, characteristic
2#20268170C211yesmaximal, characteristic, complemented
3#20268078C211yesmaximal, characteristic, complemented
4#20267539C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic, complemented
7#476×C103C211yesmaximal, characteristic, complemented
8C2×#13110095—22no—
9#15693021C2211yescharacteristic
10#15693007—22no—
11#15692995—21no—
12#15692992—21no—
13C4×D412C2211yescharacteristic
14#15692980—21no—
15#15692979—21no—
16#15692952—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18#15692941—21no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×D4×C103C2211yescharacteristic
22#106×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206D412yes—
26C2×D412D411yescharacteristic
27C2×C22⋊D103—22no—
28C2×C4×D103—21no—
29#13110095—44no—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103D411yescharacteristic
35C22⋊Dic103—22no—
36(C2×D103)⋊C4—22no—
37(C2×D103)⋊C4—21no—
38C4×Dic103—22no—
39C2×Q8×C103—21no—
40C2×D4×C103D411yescharacteristic
41C22×C4×C103—21no—
42C2×C8×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103D411yescharacteristic
46C22⋊C4×C103—21no—
47C42×C103C2311yescharacteristic
48C23×C103—21no—
49C22×D103—21no—
50Q8×C103—42no—
51D4×C103—21no—
52D4×C103—21no—
53C2×C4×C103—21no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C22⋊D103—82no—
61C2×Dic103—21no—
62C2×Dic103—22no—
63D412—21no—
64D412—21no—
65C4×D103—41no—
66C4×D103—41no—
67Dic206—42no—
68C8×C103—41no—
69C103⋊C8—22no—
70C103⋊C8—41no—
71C22×C103—41no—
72C22×C103—41no—
73C22×C103—41no—
74C22×C103#12011yescharacteristic
75C2×D103—41no—
76C2×D103—41no—
77C2×D103—41no—
78C4×C103—21no—
79C4×C103—41no—
80C4×C103—81no—
81C4×C103#13511yescharacteristic
82C4×C103#13511yescharacteristic
83C4×C103#13711yescharacteristic
84C4×C103#13711yescharacteristic
85Dic103—41no—
86Dic103—42no—
87C2×C103—81no—
88C2×C103#45211yescharacteristic
89C2×C103#45211yescharacteristic
90C2×C103#45311yescharacteristic
91D103—81no—
92#1634—1031nomaximal, Sylow
93C103#163411yescharacteristic, complemented, Sylow
94#555—1031no—
95#494—1031no—
96#476—1031no—
97#476D10311yescharacteristic, complemented
98#333—1031no—
99D4⋊C8—1031no—
100D4⋊C8—1031no—
101C2×Q16—2062no—
102C4⋊Q8—1031no—
103C4⋊Q8C2×D10311yescharacteristic
104#124—2062no—
105#121—2061no—
106#121—2061no—
107C4×D4—1031no—
108C4×D4C2×D10311yescharacteristic
109#117—2061no—
110#117—2061no—
111#106—21no—
112#106—2061no—
113C4⋊C8—1031no—
114C4⋊C8C2×D10311yescharacteristic
115#102—21no—
116#102—2061no—
117C4×C8—1031no—
118C2×Q8—21no—
119C2×Q8—1032no—
120C2×D4—1031no—
121C2×D4—2062no—
122C2×D4C22⋊D10311yescharacteristic
123C22×C4—21no—
124C22×C4—2061no—
125Q16—4124no—
126C2×C8—21no—
127C2×C8—2061no—
128C2×C8—2061no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1031no—
132C4⋊C4—2061no—
133C4⋊C4—2061no—
134C4⋊C4C22⋊D10311yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2062no—
137C22⋊C4—2062no—
138C22⋊C4—2061no—
139C42—2062no—
140C42C22×D10311yescharacteristic
141C23—21no—
142C23—2061no—
143Q8—42no—
144Q8—4122no—
145D4—21no—
146D4—21no—
147D4—8242no—
148D4—2061no—
149D4—2061no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—4121no—
155C2×C4—4121no—
156C2×C4—2061no—
157C2×C4—2062no—
158C2×C4D4×D10311yescharacteristic
159C2×C4D4×D10311yescharacteristic
160C2×C4C2×C22⋊D10311yescharacteristic
161C8—41no—
162C8—4121no—
163C8—2062no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—4121no—
168C22—4121no—
169C22—4121no—
170C22#1569298911yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—4121no—
175C4—4122no—
176C4#1569304111yescharacteristic
177C4#1569304211yescharacteristic
178C4#1569305011yescharacteristic
179C4#1569305211yescharacteristic
180C2—81no—
181C2—8241no—
182C2#2026795011yescharacteristic
183C2#2026795111yescharacteristic
184C2#2026795711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#476×C103C2
socleC22×C103#120
prime radical#20268506C2
hypercenter#476D103
hypocenterC103#1634
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20268170C2semidirect
3. #20268078C2semidirect
4. #20267539C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. #20267518C2semidirect
7. #476×C103C2semidirect
93. C103#1634semidirect
97. #476D103semidirect

Maximal subgroups

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

subgroupindex
#202685062
#202681702
#202680782
#202675392
D4⋊(C103⋊C8)2
#202675182
#476×C1032
#1634103