Finite Group Databasebeta

← #27194133

Subgroups — #27194133

Order 13184.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#20268416C211yesmaximal, characteristic
2#20268121C211yesmaximal, characteristic, complemented
3#20267717C211yesmaximal, characteristic
4#20267529C211yesmaximal, characteristic, complemented
5#20267528C211yesmaximal, characteristic, complemented
6#20267514C211yesmaximal, characteristic
7#483×C103C211yesmaximal, characteristic, complemented
8#15693001—21no—
9#15693000C2211yescharacteristic
10#15692999—21no—
11#15692999—21no—
12#15692998—21no—
13#15692997—21no—
14C2×(C2×D103)⋊C4—21no—
15C2×(C2×D103)⋊C4C2211yescharacteristic
16C22⋊C4×D103—21no—
17#15692952—21no—
18#15692944—21no—
19C22⋊(C103⋊C8)C2211yescharacteristic
20C103⋊#95—21no—
21C103⋊#95C2211yescharacteristic
22C22⋊Q8×C103C2211yescharacteristic
23C2×C4⋊C4×C103C2211yescharacteristic
24#106×C103—21no—
25#103×C103—21no—
26C22⋊C8×C103C2211yescharacteristic
27C23×D103D411yescharacteristic
28C2×Dic206—21no—
29C2×Dic206D411yescharacteristic
30C22×Dic103—21no—
31C22×Dic103D411yescharacteristic
32C2×C4×D103—21no—
33C2×C4×D103—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103D411yescharacteristic
37Dic103⋊C4—21no—
38Dic103⋊C4—21no—
39Dic103⋊C4—21no—
40C22⋊Dic103—21no—
41(C2×D103)⋊C4—21no—
42(C2×D103)⋊C4—21no—
43(C2×D103)⋊C4—21no—
44(C2×D103)⋊C4—21no—
45(C2×D103)⋊C4—42no—
46C2×Q8×C103D411yescharacteristic
47C22×C4×C103—21no—
48C22×C4×C103C2311yescharacteristic
49C2×C8×C103—21no—
50C4⋊C4×C103—21no—
51C4⋊C4×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103D411yescharacteristic
54C22⋊C4×C103—21no—
55C23×C103C2×D411yescharacteristic
56C22×D103—21no—
57C22×D103—21no—
58C22×D103—41no—
59C22×D103—41no—
60C22×D103SD1612yes—
61Q8×C103—41no—
62C2×C4×C103—21no—
63C2×C4×C103—21no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103C2×D411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×Dic103—21no—
71C2×Dic103—21no—
72C2×Dic103—21no—
73C2×Dic103—41no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77C4×D103—81no—
78C4×D103—81no—
79Dic206—41no—
80Dic206—81no—
81C8×C103—41no—
82C103⋊C8—41no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103#12011yescharacteristic
86C22×C103C2×SD1611yescharacteristic
87C22×C103#13711yescharacteristic
88C2×D103—22no—
89C2×D103—41no—
90C2×D103—41no—
91C2×D103—42no—
92C2×D103—81no—
93C4×C103—21no—
94C4×C103—21no—
95C4×C103—41no—
96C4×C103—41no—
97C4×C103—81no—
98Dic103—41no—
99Dic103—41no—
100Dic103—41no—
101Dic103—81no—
102C2×C103—21no—
103C2×C103—21no—
104C2×C103#44811yescharacteristic
105C2×C103#45511yescharacteristic
106C2×C103#45811yescharacteristic
107D103—42no—
108#1608—1031nomaximal, Sylow
109C103#160811yescharacteristic, complemented, Sylow
110#543—1031no—
111#483—1031no—
112#483D10311yescharacteristic, complemented
113#397—1031no—
114#328—1031no—
115#328—1031no—
116#323—1031no—
117C22⋊Q8—1031no—
118C22⋊Q8—2061no—
119C22⋊Q8—2061no—
120C22⋊Q8—2061no—
121C22⋊Q8—2061no—
122C22⋊Q8—2061no—
123C22⋊Q8C2×D10311yescharacteristic
124C2×C4⋊C4C2×D10311yescharacteristic
125C2×C22⋊C4—1031no—
126C2×C22⋊C4—2061no—
127C2×C22⋊C4—2061no—
128#106—21no—
129#106—2061no—
130#103—21no—
131#103—2061no—
132C22⋊C8—1031no—
133C22⋊C8C2×D10311yescharacteristic
134#95—1031no—
135#95—2061no—
136C24—1031no—
137C2×Q8—1031no—
138C2×Q8—2061no—
139C2×Q8C22⋊D10311yescharacteristic
140C22×C4—21no—
141C22×C4—1031no—
142C22×C4—2061no—
143C22×C4—2061no—
144C22×C4—2061no—
145C22×C4C22×D10311yescharacteristic
146C2×C8—21no—
147C2×C8—2061no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—1031no—
152C4⋊C4—2061no—
153C4⋊C4—2061no—
154C4⋊C4—2061no—
155C4⋊C4—2061no—
156C4⋊C4C22⋊D10311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—4122no—
159C22⋊C4—2061no—
160C22⋊C4—2061no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C22⋊C4—2061no—
164C23—1032no—
165C23—4121no—
166C23—4121no—
167C23—2061no—
168C23—2061no—
169C23D4×D10311yescharacteristic
170Q8—41no—
171Q8—8241no—
172Q8—4121no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—8241no—
180C2×C4—8241no—
181C2×C4—4121no—
182C2×C4—4121no—
183C2×C4—4121no—
184C2×C4—4121no—
185C2×C4—2061no—
186C2×C4—2061no—
187C2×C4—2061no—
188C2×C4D4×D10311yescharacteristic
189C2×C4C2×C22⋊D10311yescharacteristic
190C8—41no—
191C8—4121no—
192C22—21no—
193C22—21no—
194C22—8241no—
195C22—4122no—
196C22—4121no—
197C22—4121no—
198C22—2062no—
199C22#1569298911yescharacteristic
200C22SD16×D10311yescharacteristic
201C22#1569305011yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—8241no—
208C4—4121no—
209C4—4121no—
210C4—4121no—
211C2—21no—
212C2—21no—
213C2—4122no—
214C2#2026792811yescharacteristic
215C2#2026796711yescharacteristic
216C2#2026798011yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#483×C103C2
socleC22×C103#120
prime radicalC23×D103D4
hypercenter#483D103
hypocenterC103#1608
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #20268121C2semidirect
4. #20267529C2semidirect
5. #20267528C2semidirect
7. #483×C103C2semidirect
109. C103#1608semidirect
112. #483D103semidirect

Maximal subgroups

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

subgroupindex
#202684162
#202681212
#202677172
#202675292
#202675282
#202675142
#483×C1032
#1608103