Finite Group Databasebeta

← #27194371

Subgroups — #27194371

Order 13184.

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

normal subgroups only

This group has 212 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#20268143C211yesmaximal, characteristic, complemented
3#20267993C211yesmaximal, characteristic, complemented
4#20267539C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic, complemented
7#474×C103C211yesmaximal, characteristic, complemented
8C2×#13110092—21no—
9#15693021C2211yescharacteristic
10#15693007—22no—
11#15692995—21no—
12#15692992—21no—
13C4×D412C2211yescharacteristic
14#15692980—21no—
15#15692979—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692945—21no—
18#15692944—22no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×D4×C103C2211yescharacteristic
22#107×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#102×C103—21no—
25C2×Dic206D412yes—
26C2×D412D411yescharacteristic
27C2×C22⋊D103—22no—
28C2×C4×D103—21no—
29#13110092—42no—
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—41no—
51Q8×C103—41no—
52D4×C103—21no—
53D4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C22⋊D103—82no—
62C2×Dic103—21no—
63C2×Dic103—22no—
64D412—21no—
65D412—21no—
66C4×D103—41no—
67C4×D103—41no—
68Dic206—42no—
69C8×C103—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103—41no—
73C22×C103—41no—
74C22×C103—41no—
75C22×C103#12011yescharacteristic
76C2×D103—41no—
77C2×D103—41no—
78C2×D103—41no—
79C4×C103—21no—
80C4×C103—41no—
81C4×C103—81no—
82C4×C103#13511yescharacteristic
83C4×C103#13511yescharacteristic
84C4×C103AGL(1,ℤ/8)11yescharacteristic
85C4×C103#13711yescharacteristic
86Dic103—41no—
87Dic103—42no—
88C2×C103—81no—
89C2×C103#44911yescharacteristic
90C2×C103#45211yescharacteristic
91C2×C103#45511yescharacteristic
92D103—81no—
93#1646—1031nomaximal, Sylow
94C103#164611yescharacteristic, complemented, Sylow
95#555—1031no—
96#487—1031no—
97#474D10311yescharacteristic, complemented
98#461—1031no—
99#333—1031no—
100D4⋊C8—1031no—
101D4⋊C8—1031no—
102C2×SD16—2061no—
103C4⋊Q8—1031no—
104C4⋊Q8C2×D10311yescharacteristic
105#124—2062no—
106#121—2061no—
107#121—2061no—
108C4×D4—1031no—
109C4×D4C2×D10311yescharacteristic
110#117—2061no—
111#117—2061no—
112#107—21no—
113C4⋊C8—1031no—
114C4⋊C8C2×D10311yescharacteristic
115#103—2062no—
116#103—2061no—
117#102—21no—
118C4×C8—1031no—
119C2×Q8—21no—
120C2×Q8—1032no—
121C2×D4—1031no—
122C2×D4—2062no—
123C2×D4C22⋊D10311yescharacteristic
124C22×C4—21no—
125C22×C4—2061no—
126SD16—4122no—
127C2×C8—21no—
128C2×C8—2061no—
129C2×C8—2061no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—1031no—
133C4⋊C4—2061no—
134C4⋊C4—2061no—
135C4⋊C4C22⋊D10311yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—2062no—
138C22⋊C4—2062no—
139C22⋊C4—2061no—
140C42—2062no—
141C42C22×D10311yescharacteristic
142C23—21no—
143C23—2061no—
144Q8—41no—
145Q8—41no—
146Q8—4122no—
147D4—21no—
148D4—21no—
149D4—8242no—
150D4—2061no—
151D4—2061no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—4121no—
157C2×C4—4121no—
158C2×C4—2061no—
159C2×C4—2062no—
160C2×C4D4×D10311yescharacteristic
161C2×C4D4×D10311yescharacteristic
162C2×C4C2×C22⋊D10311yescharacteristic
163C8—41no—
164C8—4121no—
165C8—4121no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—4121no—
170C22—4121no—
171C22—4121no—
172C22#1569298911yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—4121no—
177C4—4122no—
178C4#1569304011yescharacteristic
179C4#1569304111yescharacteristic
180C4#1569304511yescharacteristic
181C4#1569305211yescharacteristic
182C2—81no—
183C2—8241no—
184C2#2026793311yescharacteristic
185C2#2026795111yescharacteristic
186C2#2026796711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#474×C103C2
socleC22×C103#120
prime radical#20268506C2
hypercenter#474D103
hypocenterC103#1646
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #20268143C2semidirect
3. #20267993C2semidirect
4. #20267539C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. #20267518C2semidirect
7. #474×C103C2semidirect
94. C103#1646semidirect
97. #474D103semidirect

Maximal subgroups

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

subgroupindex
#202685062
#202681432
#202679932
#202675392
D4⋊(C103⋊C8)2
#202675182
#474×C1032
#1646103