Finite Group Databasebeta

← #27194173

Subgroups — #27194173

Order 13184.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#20268388C211yesmaximal, characteristic
2#20268126C211yesmaximal, characteristic, complemented
3#20268109C211yesmaximal, characteristic
4#20267527C211yesmaximal, characteristic, complemented
5#20267524C211yesmaximal, characteristic
6#20267517C211yesmaximal, characteristic, complemented
7#400×C103C211yesmaximal, characteristic, complemented
8#15693016—21no—
9#15693011—21no—
10#15693006—21no—
11#15693004—21no—
12#15693000C2211yescharacteristic
13#15692999—21no—
14#15692995C2211yescharacteristic
15C4×C22⋊D103—21no—
16#15692954—21no—
17#15692952—21no—
18#15692944—21no—
19#15692941—21no—
20C22⋊(C103⋊C8)C2211yescharacteristic
21C22⋊(C103⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23C2×C4⋊C4×C103C2211yescharacteristic
24#95×C103—21no—
25#95×C103—21no—
26#95×C103C2211yescharacteristic
27C2×Dic206D411yescharacteristic
28C2×D412D411yescharacteristic
29C2×C22⋊D103—21no—
30C2×C4×D103—21no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8—21no—
33C4⋊Dic103D411yescharacteristic
34C4⋊Dic103D411yescharacteristic
35Dic103⋊C4—21no—
36Dic103⋊C4—21no—
37Dic103⋊C4—21no—
38Dic103⋊C4—21no—
39C22⋊Dic103—21no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42(C2×D103)⋊C4—21no—
43(C2×D103)⋊C4—21no—
44C4×Dic103—21no—
45C22×C4×C103—21no—
46C22×C4×C103—21no—
47C22×C4×C103D411yescharacteristic
48C22×C4×C103D411yescharacteristic
49C22×C4×C103C2311yescharacteristic
50C4⋊C4×C103—21no—
51C4⋊C4×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103—21no—
54C23×C103C2×D411yescharacteristic
55C22×D103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—41no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—42no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C22⋊D103—41no—
70C22⋊D103—41no—
71C2×Dic103—21no—
72C2×Dic103—21no—
73C2×Dic103—21no—
74D412—41no—
75C4×D103—81no—
76Dic206—41no—
77C103⋊C8—41no—
78C103⋊C8—41no—
79C22×C103—21no—
80C22×C103—21no—
81C22×C103#12011yescharacteristic
82C22×C103#13511yescharacteristic
83C22×C103#13711yescharacteristic
84C2×D103—41no—
85C2×D103—41no—
86C2×D103—41no—
87C4×C103—21no—
88C4×C103—21no—
89C4×C103—41no—
90C4×C103—41no—
91C4×C103—81no—
92C4×C103—81no—
93Dic103—41no—
94Dic103—41no—
95Dic103—41no—
96C2×C103—21no—
97C2×C103—21no—
98C2×C103#45211yescharacteristic
99C2×C103#45411yescharacteristic
100C2×C103#45811yescharacteristic
101D103—81no—
102#1615—1031nomaximal, Sylow
103C103#161511yescharacteristic, complemented, Sylow
104#539—1031no—
105#484—1031no—
106#481—1031no—
107#400D10311yescharacteristic, complemented
108#328—1031no—
109#327—1031no—
110#324—1031no—
111#126—2061no—
112#125—2061no—
113#123—2061no—
114#123—2061no—
115C22⋊Q8—1031no—
116C22⋊Q8—2061no—
117#121—1031no—
118C4×D4—2061no—
119C2×C4⋊C4C2×D10311yescharacteristic
120C2×C4⋊C4C2×D10311yescharacteristic
121#107—2061no—
122#106—2061no—
123#103—2061no—
124#102—2061no—
125C22⋊C8—1031no—
126C22⋊C8—1031no—
127#95—21no—
128#95—21no—
129#95C2×D10311yescharacteristic
130C2×Q8—1031no—
131C2×D4—1031no—
132C2×D4—2061no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—2061no—
136C22×C4C22⋊D10311yescharacteristic
137C22×C4C22⋊D10311yescharacteristic
138C22×C4C22×D10311yescharacteristic
139C2×C8—2061no—
140C2×C8—2061no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—1031no—
146C4⋊C4—1031no—
147C4⋊C4—2061no—
148C4⋊C4—2061no—
149C4⋊C4—2061no—
150C4⋊C4—2061no—
151C22⋊C4—2061no—
152C22⋊C4—2061no—
153C22⋊C4—2061no—
154C22⋊C4—2061no—
155C22⋊C4—2061no—
156C42—2061no—
157C23—2061no—
158C23C2×C22⋊D10311yescharacteristic
159Q8—4121no—
160D4—4121no—
161D4—4121no—
162D4—4121no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—8241no—
175C2×C4—2061no—
176C2×C4—2061no—
177C2×C4—2061no—
178C2×C4D4×D10311yescharacteristic
179C2×C4D4×D10311yescharacteristic
180C8—4121no—
181C8—4121no—
182C22—21no—
183C22—21no—
184C22—4121no—
185C22—4121no—
186C22—4121no—
187C22#1569298911yescharacteristic
188C22#1569304111yescharacteristic
189C22#1569305211yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—4121no—
197C4—4121no—
198C4—4121no—
199C2—21no—
200C2—21no—
201C2—8241no—
202C2#2026795111yescharacteristic
203C2#2026796311yescharacteristic
204C2#2026798011yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#400×C103C2
socleC22×C103#120
prime radical#15692995C22
hypercenter#400D103
hypocenterC103#1615
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #20268126C2semidirect
4. #20267527C2semidirect
6. #20267517C2semidirect
7. #400×C103C2semidirect
103. C103#1615semidirect
107. #400D103semidirect

Maximal subgroups

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

subgroupindex
#202683882
#202681262
#202681092
#202675272
#202675242
#202675172
#400×C1032
#1615103