Finite Group Databasebeta

← #27193688

Subgroups — #27193688

Order 13184.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#20268302C211yesmaximal, characteristic
2#20267651C211yesmaximal, characteristic, complemented
3#20267529C212yesmaximal, complemented
4#20267526C212yesmaximal, complemented
5#407×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C411yescharacteristic, complemented
7#15693004—21no—
8#15693000C411yescharacteristic, complemented
9#15693000C2211yescharacteristic
10#15692995C411yescharacteristic, complemented
11#15692995C2211yescharacteristic
12#15692990—21no—
13C4×C22⋊D103—21no—
14C4×C22⋊D103—21no—
15#15692980C411yescharacteristic, complemented
16C2×C4⋊Dic103—21no—
17C2×C22⋊Dic103—21no—
18C103⋊#95C2212yes—
19C23×C4×C103C2211yescharacteristic
20C2×M16×C103—21no—
21C22⋊C8×C103—21no—
22C22⋊C8×C103C2212yes—
23#13110105—42no—
24C2×Dic206C2×C411yescharacteristic
25C2×D412C2×C411yescharacteristic
26C2×C22⋊D103—21no—
27C2×C22⋊D103—21no—
28C2×C22⋊D103—21no—
29C22×Dic103—22no—
30C2×C4×D103—21no—
31C4⋊Dic103—42no—
32C4⋊Dic103C2×C411yescharacteristic
33C4⋊Dic103C2×C411yescharacteristic
34Dic103⋊C4—21no—
35Dic103⋊C4—21no—
36C22⋊Dic103—21no—
37C22⋊Dic103—21no—
38C22⋊Dic103—21no—
39C22⋊Dic103—42no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42C4×Dic103—21no—
43C24×C103D411yescharacteristic
44C22×C4×C103—42no—
45C22×C4×C103C2×C411yescharacteristic
46C22×C4×C103C2×C411yescharacteristic
47C22×C4×C103D411yescharacteristic
48C22×C4×C103D411yescharacteristic
49C22×C4×C103D411yescharacteristic
50C22×C4×C103C2311yescharacteristic
51M16×C103—42no—
52C2×C8×C103—22no—
53C23×C103—21no—
54C23×C103—21no—
55C23×C103—41no—
56C23×C103—41no—
57C23×C103C22⋊C411yescharacteristic
58C23×C103C22⋊C411yescharacteristic
59C23×C103C2×D411yescharacteristic
60C22×D103—21no—
61C2×C4×C103—22no—
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103C22⋊C411yescharacteristic
68C2×C4×C103C22⋊C411yescharacteristic
69C2×C4×C103C22×C411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C22⋊D103—42no—
72C22⋊D103—42no—
73C22⋊D103—41no—
74C22⋊D103—41no—
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—21no—
78C2×Dic103—42no—
79C2×Dic103—42no—
80C2×Dic103—42no—
81D412—41no—
82C4×D103—42no—
83Dic206—41no—
84C8×C103—42no—
85C22×C103—21no—
86C22×C103—21no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—21no—
90C22×C103—21no—
91C22×C103—21no—
92C22×C103—21no—
93C22×C103—42no—
94C22×C103—42no—
95C22×C103C2×C22⋊C411yescharacteristic
96C22×C103AGL(1,ℤ/8)11yescharacteristic
97C22×C103#13711yescharacteristic
98C2×D103—41no—
99C2×D103—41no—
100C2×D103—41no—
101C4×C103—21no—
102C4×C103—21no—
103C4×C103—21no—
104C4×C103#9912yes—
105Dic103—41no—
106Dic103—41no—
107Dic103—41no—
108Dic103—82no—
109C2×C103—21no—
110C2×C103—21no—
111C2×C103—41no—
112C2×C103—41no—
113C2×C103C2×#9911yescharacteristic
114C2×C103#41711yescharacteristic
115C2×C103#42111yescharacteristic
116D103—81no—
117#1513—1031nomaximal, Sylow
118C103#151311yescharacteristic, complemented, Sylow
119#525—1031no—
120#407D10311yescharacteristic, complemented
121#380—1031no—
122#328—1032no—
123#327—1032no—
124C2×#41—1031no—
125C23×C4C2×D10311yescharacteristic
126C2×M16—21no—
127#123—2061no—
128C22⋊Q8—1031no—
129C22⋊Q8—1031no—
130#121—1031no—
131#121—1031no—
132#120—2061no—
133C4×D4—2061no—
134C4×D4—2061no—
135#117—1031no—
136C2×C4⋊C4—2061no—
137C2×C22⋊C4—2061no—
138C22⋊C8—21no—
139C22⋊C8C2×D10312yes—
140#95—1032no—
141C24D41211yescharacteristic
142#41—4122no—
143C2×Q8—1031no—
144C2×D4—1031no—
145C2×D4—2061no—
146C2×D4—2061no—
147C2×D4—2061no—
148C22×C4—42no—
149C22×C4—2062no—
150C22×C4—2061no—
151C22×C4C4×D10311yescharacteristic
152C22×C4C4×D10311yescharacteristic
153C22×C4D41211yescharacteristic
154C22×C4C22⋊D10311yescharacteristic
155C22×C4C22⋊D10311yescharacteristic
156C22×C4C22×D10311yescharacteristic
157M16—42no—
158C2×C8—22no—
159C4⋊C4—1031no—
160C4⋊C4—1031no—
161C4⋊C4—4122no—
162C4⋊C4—2061no—
163C4⋊C4—2061no—
164C22⋊C4—4122no—
165C22⋊C4—2061no—
166C22⋊C4—2061no—
167C22⋊C4—2061no—
168C22⋊C4—2061no—
169C22⋊C4—2061no—
170C42—2061no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—2061no—
176C23(C2×D103)⋊C411yescharacteristic
177C23(C2×D103)⋊C411yescharacteristic
178C23C2×D41211yescharacteristic
179Q8—4121no—
180D4—4121no—
181D4—4122no—
182D4—4122no—
183D4—4121no—
184D4—4121no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—4122no—
192C2×C4—4122no—
193C2×C4—4122no—
194C2×C4—4122no—
195C2×C4—2061no—
196C2×C4—2061no—
197C2×C4—2061no—
198C2×C4(C2×D103)⋊C411yescharacteristic
199C2×C4(C2×D103)⋊C411yescharacteristic
200C2×C4C2×C4×D10311yescharacteristic
201C2×C4C2×C22⋊D10311yescharacteristic
202C8—42no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—4121no—
214C22—4121no—
215C22—4121no—
216C22C2×(C2×D103)⋊C411yescharacteristic
217C22#1569304911yescharacteristic
218C22#1569305411yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—8242no—
223C4—4121no—
224C4—4121no—
225C4—4121no—
226C4#1569293512yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—8241no—
232C2C2×#1569293511yescharacteristic
233C2#2026779311yescharacteristic
234C2#2026780711yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#407×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenter#407D103
hypocenterC103#1513
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #20267651C2semidirect
3. #20267529C2semidirect
4. #20267526C2semidirect
5. #407×C103C2semidirect
6. C2×#13110105C4semidirect
8. #15693000C4semidirect
10. #15692995C4semidirect
15. #15692980C4semidirect
118. C103#1513semidirect
120. #407D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
#202676512
#202675292
#202675262
#407×C1032
#1513103