Finite Group Databasebeta

← #27196288

Subgroups — #27196288

Order 13184.

294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#15693012C211yesmaximal, characteristic, complemented
2C2×#15692942C211yesmaximal, characteristic
3#20267694C211yesmaximal, characteristic
4#20267554C211yesmaximal, characteristic, complemented
5#20267553C211yesmaximal, characteristic, complemented
6#20267545C211yesmaximal, characteristic, complemented
7C2×#102×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9#15693012—22no—
10#15693012—22no—
11C2×C4⋊Dic103—21no—
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×Dic103⋊C4—21no—
15C2×C22⋊Dic103—21no—
16C2×C22⋊Dic103—21no—
17C2×C4×Dic103C2211yescharacteristic
18#15692942—22no—
19C22×D4×C103C2211yescharacteristic
20C22×C8×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22#102×C103—22no—
23C22×Dic103—21no—
24C22×Dic103—21no—
25C22×Dic103D411yescharacteristic
26C22×Dic103D411yescharacteristic
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—24no—
31C4⋊Dic103—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103D412yes—
35Dic103⋊C4—24no—
36C22⋊Dic103—42no—
37C22⋊Dic103—42no—
38C4×Dic103—21no—
39C4×Dic103—21no—
40C24×C103—21no—
41C2×D4×C103—21no—
42C2×D4×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103—21no—
45C2×D4×C103—21no—
46C2×D4×C103Q812yes—
47C22×C4×C103—21no—
48C22×C4×C103C2311yescharacteristic
49C2×C8×C103—21no—
50C2×C8×C103—21no—
51C2×C8×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103D412yes—
54C23×C103—22no—
55C23×C103—41no—
56C23×C103—41no—
57C23×C103—41no—
58C23×C103—41no—
59C23×C103—41no—
60C23×C103—41no—
61C23×C103C2×D411yescharacteristic
62D4×C103—22no—
63D4×C103—22no—
64D4×C103—41no—
65D4×C103—41no—
66C2×C4×C103—22no—
67C2×C4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2×Q811yescharacteristic
72C2×C4×C103#4111yescharacteristic
73C2×C4×C103#4111yescharacteristic
74C2×C4×C103#4111yescharacteristic
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—22no—
78C2×Dic103—21no—
79C2×Dic103—21no—
80C2×Dic103—21no—
81C2×Dic103—21no—
82C2×Dic103—41no—
83C2×Dic103—41no—
84C2×Dic103—41no—
85C2×Dic103—41no—
86C2×Dic103—41no—
87C8×C103—41no—
88C103⋊C8—41no—
89C22×C103—42no—
90C22×C103—42no—
91C22×C103—42no—
92C22×C103—81no—
93C22×C103—81no—
94C22×C103—81no—
95C22×C103—81no—
96C22×C103#12011yescharacteristic
97C22×C103C22⋊Q811yescharacteristic
98C22×C103#12411yescharacteristic
99C22×C103#13511yescharacteristic
100C22×C103#13511yescharacteristic
101C22×C103AGL(1,ℤ/8)11yescharacteristic
102C22×C103AGL(1,ℤ/8)11yescharacteristic
103C4×C103—42no—
104C4×C103C22⋊Q811yescharacteristic
105C4×C103C22⋊Q811yescharacteristic
106C4×C103#12411yescharacteristic
107C4×C103#12411yescharacteristic
108Dic103—41no—
109Dic103—41no—
110Dic103—42no—
111Dic103—81no—
112C2×C103—82no—
113C2×C103#39311yescharacteristic
114C2×C103#44911yescharacteristic
115C2×C103#44911yescharacteristic
116C2×C103#47811yescharacteristic
117C2×C103#47811yescharacteristic
118C2×C103#48811yescharacteristic
119C2×C103#49011yescharacteristic
120#2025—1031nomaximal, Sylow
121C103#202511yescharacteristic, complemented, Sylow
122C2×#125—1031no—
123C2×#102—1031no—
124C2×#102D10311yescharacteristic
125#390—1031no—
126#340—1031no—
127#340—1031no—
128#336—1031no—
129C22×D4C2×D10311yescharacteristic
130C22×C8—1031no—
131C22×C8C2×D10311yescharacteristic
132#125—2062no—
133#125—2062no—
134C2×C4⋊C4—1031no—
135C2×C4⋊C4—1031no—
136C2×C4⋊C4—2061no—
137C2×C4⋊C4—2061no—
138C2×C4⋊C4C2×D10311yescharacteristic
139C2×C22⋊C4—2061no—
140C2×C22⋊C4—2061no—
141C2×C42—1031no—
142#102—22no—
143#102—2062no—
144C24—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4Dic20612yes—
151C22×C4—21no—
152C22×C4—1031no—
153C22×C4—1031no—
154C22×C4—2061no—
155C22×C4—2061no—
156C22×C4C22×D10311yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—2061no—
161C2×C8—2061no—
162C2×C8—2061no—
163C4⋊C4—21no—
164C4⋊C4—1032no—
165C4⋊C4—2064no—
166C4⋊C4—2064no—
167C4⋊C4—2061no—
168C4⋊C4—2061no—
169C4⋊C4—2061no—
170C4⋊C4C22⋊D10312yes—
171C22⋊C4—4122no—
172C22⋊C4—4122no—
173C42—2061no—
174C42—2061no—
175C23—22no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23D4×D10311yescharacteristic
183D4—22no—
184D4—22no—
185D4—41no—
186D4—41no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—4121no—
191C2×C4—4121no—
192C2×C4—4121no—
193C2×C4—4121no—
194C2×C4—4121no—
195C2×C4—2061no—
196C2×C4—2061no—
197C2×C4—2062no—
198C2×C4—2061no—
199C2×C4—2061no—
200C2×C4—2061no—
201C2×C4—2061no—
202C2×C4D4×D10311yescharacteristic
203C2×C4C2×C22⋊D10311yescharacteristic
204C2×C4C2×Dic20611yescharacteristic
205C2×C4#1311010411yescharacteristic
206C2×C4#1311010411yescharacteristic
207C2×C4#1311010511yescharacteristic
208C8—41no—
209C8—4121no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—81no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22#1569298911yescharacteristic
218C22#1569299811yescharacteristic
219C22#1569300711yescharacteristic
220C22#1569304011yescharacteristic
221C22#1569304211yescharacteristic
222C22#1569304511yescharacteristic
223C22#1569304811yescharacteristic
224C4—42no—
225C4—8241no—
226C4—4121no—
227C4—4122no—
228C4—4121no—
229C4#1569299811yescharacteristic
230C4#1569300011yescharacteristic
231C4#1569300711yescharacteristic
232C4#1569300811yescharacteristic
233C2—82no—
234C2#2026770311yescharacteristic
235C2#2026793311yescharacteristic
236C2#2026793511yescharacteristic
237C2#2026808911yescharacteristic
238C2#2026809311yescharacteristic
239C2#2026814411yescharacteristic
240C2#2026815411yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#102×C103C2
socleC23×C103C2×D4
prime radicalC22×D4×C103C22
hypercenterC2×#102D103
hypocenterC103#2025
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#15693012C2semidirect
4. #20267554C2semidirect
5. #20267553C2semidirect
6. #20267545C2semidirect
121. C103#2025semidirect

Maximal subgroups

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

subgroupindex
C2×#156930122
C2×#156929422
#202676942
#202675542
#202675532
#202675452
C2×#102×C1032
#2025103