Finite Group Databasebeta

← #27195175

Subgroups — #27195175

Order 13184.

316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C22×#13110089C211yesmaximal, characteristic
2C2×#15692954C211yesmaximal, characteristic, complemented
3C2×#15692952C211yesmaximal, characteristic, complemented
4#20267651C211yesmaximal, characteristic
5#20267553C211yesmaximal, characteristic, complemented
6#20267553C211yesmaximal, characteristic, complemented
7#380×C103C211yesmaximal, characteristic
8C2×#13110089—22no—
9C2×#13110089—22no—
10C2×#13110089C414yescomplemented
11C22×C103⋊C8C2211yescharacteristic
12C22×C103⋊C8C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×C4⋊Dic103C2211yescharacteristic
15C2×C22⋊Dic103—21no—
16#15692954—22no—
17#15692952—22no—
18C103⋊#95—21no—
19C23×C4×C103C2211yescharacteristic
20C2×C4⋊C4×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22C2×C22⋊C4×C103—21no—
23#95×C103—21no—
24C22×Dic103—21no—
25C22×Dic103—21no—
26#13110089—28no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8C2×C412yes—
30C2×C103⋊C8C2×C412yes—
31C2×C103⋊C8D412yes—
32C2×C103⋊C8D412yes—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103—21no—
37C22⋊Dic103—42no—
38C24×C103D411yescharacteristic
39C22×C4×C103—21no—
40C22×C4×C103—21no—
41C22×C4×C103—21no—
42C22×C4×C103—21no—
43C22×C4×C103—21no—
44C22×C4×C103—21no—
45C22×C4×C103C2×C412yes—
46C22×C4×C103D411yescharacteristic
47C22×C4×C103Q812yes—
48C22×C4×C103C2311yescharacteristic
49C4⋊C4×C103—21no—
50C4⋊C4×C103—21no—
51C4⋊C4×C103—21no—
52C4⋊C4×C103—21no—
53C22⋊C4×C103—42no—
54C23×C103—21no—
55C23×C103—21no—
56C23×C103—21no—
57C23×C103—21no—
58C23×C103—21no—
59C23×C103—21no—
60C23×C103C4⋊C412yes—
61C23×C103C2×D411yescharacteristic
62C2×C4×C103—21no—
63C2×C4×C103—21no—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—22no—
67C2×C4×C103—22no—
68C2×C4×C103—41no—
69C2×C4×C103—41no—
70C2×C4×C103—41no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103—41no—
74C2×C4×C103C4⋊C412yes—
75C2×C4×C103C22×C411yescharacteristic
76C2×C4×C103C2×D411yescharacteristic
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2×Q811yescharacteristic
79C2×C4×C103#4111yescharacteristic
80C2×C4×C103#4111yescharacteristic
81C2×Dic103—41no—
82C2×Dic103—41no—
83C2×Dic103—41no—
84C2×Dic103—41no—
85C2×Dic103—41no—
86C2×Dic103—41no—
87C103⋊C8—22no—
88C103⋊C8C22⋊C414yescomplemented
89C22×C103—22no—
90C22×C103—22no—
91C22×C103—22no—
92C22×C103—41no—
93C22×C103—41no—
94C22×C103—41no—
95C22×C103—41no—
96C22×C103C2×C4⋊C411yescharacteristic
97C22×C103#12111yescharacteristic
98C22×C103#12111yescharacteristic
99C22×C103AGL(1,ℤ/8)11yescharacteristic
100C22×C103AGL(1,ℤ/8)11yescharacteristic
101C22×C103#13711yescharacteristic
102C22×C103#13711yescharacteristic
103C4×C103—22no—
104C4×C103—81no—
105C4×C103—81no—
106C4×C103C2×C22⋊C411yescharacteristic
107C4×C103#11711yescharacteristic
108C4×C103C22⋊Q811yescharacteristic
109C4×C103C22⋊Q811yescharacteristic
110Dic103—81no—
111Dic103—81no—
112C2×C103—42no—
113C2×C103#38011yescharacteristic
114C2×C103#42811yescharacteristic
115C2×C103#42811yescharacteristic
116C2×C103#46811yescharacteristic
117C2×C103#46811yescharacteristic
118C2×C103#46911yescharacteristic
119C2×C103#47011yescharacteristic
120#1809—1031nomaximal, Sylow
121C103#180911yescharacteristic, complemented, Sylow
122C22×M16—1031no—
123C2×#107—1031no—
124C2×#106—1031no—
125#380—1031no—
126#380D10311yescharacteristic
127#340—1031no—
128#340—1031no—
129C23×C4C2×D10311yescharacteristic
130C2×M16—1034no—
131C2×M16—2062no—
132C2×M16—2062no—
133C22×C8—1031no—
134C22×C8—1031no—
135C2×C4⋊C4—1031no—
136C2×C4⋊C4—1031no—
137C2×C4⋊C4C2×D10311yescharacteristic
138C2×C4⋊C4C2×D10311yescharacteristic
139C2×C22⋊C4—21no—
140C2×C22⋊C4—2061no—
141#107—2062no—
142#106—2062no—
143#95—21no—
144#95—2061no—
145C24C22⋊D10311yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—2061no—
153C22×C4—2061no—
154C22×C4Dic20612yes—
155C22×C4C4×D10312yes—
156C22×C4C22⋊D10311yescharacteristic
157C22×C4C22×D10311yescharacteristic
158M16—2068no—
159C2×C8—1032no—
160C2×C8—1032no—
161C2×C8—1032no—
162C2×C8—1032no—
163C2×C8—2061no—
164C2×C8—2061no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—2061no—
170C4⋊C4—2061no—
171C4⋊C4—2061no—
172C4⋊C4—2061no—
173C22⋊C4—42no—
174C22⋊C4—4122no—
175C23—21no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23Dic103⋊C412yes—
182C23C2×C22⋊D10311yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—4121no—
196C2×C4—4121no—
197C2×C4—4121no—
198C2×C4—4121no—
199C2×C4—4121no—
200C2×C4—4121no—
201C2×C4Dic103⋊C412yes—
202C2×C4C2×C4×D10311yescharacteristic
203C2×C4D4×D10311yescharacteristic
204C2×C4D4×D10311yescharacteristic
205C2×C4C2×Dic20611yescharacteristic
206C2×C4#1311010411yescharacteristic
207C2×C4#1311010411yescharacteristic
208C8—1034no—
209C8—2062no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22C2×Dic103⋊C411yescharacteristic
218C22#1569299311yescharacteristic
219C22#1569299311yescharacteristic
220C22#1569304611yescharacteristic
221C22#1569304711yescharacteristic
222C22#1569305111yescharacteristic
223C22#1569305211yescharacteristic
224C4—22no—
225C4—81no—
226C4—81no—
227C4—8241no—
228C4—8241no—
229C4C22⋊C4×D10311yescharacteristic
230C4#1569297711yescharacteristic
231C4#1569299811yescharacteristic
232C4#1569299811yescharacteristic
233C2—42no—
234C2#2026764911yescharacteristic
235C2#2026783111yescharacteristic
236C2#2026783411yescharacteristic
237C2#2026803511yescharacteristic
238C2#2026803911yescharacteristic
239C2#2026804211yescharacteristic
240C2#2026804711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#380×C103C2
socleC23×C103C2×D4
prime radicalC24×C103D4
cosocleC22×C4×C103C23
hypercenter#380D103
hypocenterC103#1809
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#15692954C2semidirect
3. C2×#15692952C2semidirect
5. #20267553C2semidirect
6. #20267553C2semidirect
10. C2×#13110089C4semidirect
88. C103⋊C8C22⋊C4semidirect
121. C103#1809semidirect

Maximal subgroups

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

subgroupindex
C22×#131100892
C2×#156929542
C2×#156929522
#202676512
#202675532
#380×C1032
#1809103