Finite Group Databasebeta

← #27194139

Subgroups — #27194139

Order 13184.

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

normal subgroups only

This group has 216 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#20268121C211yesmaximal, characteristic, complemented
3#20268104C211yesmaximal, characteristic
4#20267527C211yesmaximal, characteristic, complemented
5#20267524C211yesmaximal, characteristic
6#20267517C211yesmaximal, characteristic, complemented
7#398×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×C103—21no—
23C2×C4⋊C4×C103C2211yescharacteristic
24C2×C4⋊C4×C103C2211yescharacteristic
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—
54C4⋊C4×C103—42no—
55C23×C103C2×D411yescharacteristic
56C22×D103—21no—
57C2×C4×C103—22no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C22⋊D103—41no—
72C22⋊D103—41no—
73C2×Dic103—21no—
74C2×Dic103—21no—
75C2×Dic103—21no—
76D412—41no—
77C4×D103—81no—
78Dic206—41no—
79C103⋊C8—41no—
80C103⋊C8—41no—
81C22×C103—21no—
82C22×C103—21no—
83C22×C103#12011yescharacteristic
84C22×C103#13511yescharacteristic
85C22×C103AGL(1,ℤ/8)11yescharacteristic
86C2×D103—41no—
87C2×D103—41no—
88C2×D103—41no—
89C4×C103—21no—
90C4×C103—21no—
91C4×C103—42no—
92C4×C103—41no—
93C4×C103—41no—
94C4×C103—81no—
95Dic103—41no—
96Dic103—41no—
97Dic103—41no—
98C2×C103—21no—
99C2×C103—21no—
100C2×C103#44911yescharacteristic
101C2×C103#45611yescharacteristic
102C2×C103#45811yescharacteristic
103D103—81no—
104#1609—1031nomaximal, Sylow
105C103#160911yescharacteristic, complemented, Sylow
106#539—1031no—
107#483—1031no—
108#480—1031no—
109#398D10311yescharacteristic, complemented
110#328—1031no—
111#327—1031no—
112#324—1031no—
113#126—2061no—
114#125—2061no—
115#123—2061no—
116#123—2061no—
117C22⋊Q8—1031no—
118C22⋊Q8—2061no—
119#121—1031no—
120C4×D4—2061no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D10311yescharacteristic
123C2×C4⋊C4C2×D10311yescharacteristic
124#107—2061no—
125#106—2061no—
126#103—2061no—
127#102—2061no—
128C22⋊C8—1031no—
129C22⋊C8—1031no—
130#95—21no—
131#95C2×D10311yescharacteristic
132C2×Q8—1031no—
133C2×D4—1031no—
134C2×D4—2061no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—2061no—
138C22×C4C22⋊D10311yescharacteristic
139C22×C4C22⋊D10311yescharacteristic
140C22×C4C22×D10311yescharacteristic
141C2×C8—2061no—
142C2×C8—2061no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—1031no—
149C4⋊C4—1031no—
150C4⋊C4—2061no—
151C4⋊C4—2061no—
152C4⋊C4—2061no—
153C4⋊C4—2061no—
154C22⋊C4—2061no—
155C22⋊C4—2061no—
156C22⋊C4—2061no—
157C22⋊C4—2061no—
158C22⋊C4—2061no—
159C42—2061no—
160C23—2061no—
161C23C2×C22⋊D10311yescharacteristic
162Q8—4121no—
163D4—4121no—
164D4—4121no—
165D4—4121no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—8241no—
179C2×C4—2061no—
180C2×C4—2061no—
181C2×C4—2061no—
182C2×C4D4×D10311yescharacteristic
183C2×C4D4×D10311yescharacteristic
184C8—4121no—
185C8—4121no—
186C22—21no—
187C22—21no—
188C22—4121no—
189C22—4121no—
190C22—4121no—
191C22#1569298911yescharacteristic
192C22#1569304111yescharacteristic
193C22#1569304711yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—4121no—
201C4—4121no—
202C4—4121no—
203C2—21no—
204C2—21no—
205C2—8241no—
206C2#2026793411yescharacteristic
207C2#2026797311yescharacteristic
208C2#2026798011yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#398×C103C2
socleC22×C103#120
prime radical#15692995C22
hypercenter#398D103
hypocenterC103#1609
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #20268121C2semidirect
4. #20267527C2semidirect
6. #20267517C2semidirect
7. #398×C103C2semidirect
105. C103#1609semidirect
109. #398D103semidirect

Maximal subgroups

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

subgroupindex
#202683882
#202681212
#202681042
#202675272
#202675242
#202675172
#398×C1032
#1609103