Finite Group Databasebeta

← #27195444

Subgroups — #27195444

Order 13184.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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, complemented
2#20268302C211yesmaximal, characteristic
3C2×#15692949C212yesmaximal, complemented
4#20267551C212yesmaximal, complemented
5C4×C22⋊C4×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7C2×#13110089—24no—
8C2×#13110089—21no—
9C2×#13110089C2212yes—
10C22×C103⋊C8—21no—
11#15693004—21no—
12#15693000C411yescharacteristic, complemented
13#15693000C411yescharacteristic, complemented
14#15692995C411yescharacteristic, complemented
15#15692995C411yescharacteristic, complemented
16#15692990—21no—
17C4×C22⋊D103—21no—
18C4×C22⋊D103—21no—
19#15692980C2211yescharacteristic
20#15692949—24no—
21C23×C4×C103C2211yescharacteristic
22C2×C22⋊C4×C103—21no—
23C2×C42×C103C2212yes—
24#95×C103—21no—
25#13110105—22no—
26#13110105—22no—
27C2×Dic206C2×C411yescharacteristic
28C2×D412C2×C411yescharacteristic
29C2×C22⋊D103—21no—
30C2×C22⋊D103—21no—
31C2×C22⋊D103—21no—
32C2×C4×D103—21no—
33#13110089—24no—
34#13110089—22no—
35#13110089D414yescomplemented
36C2×C103⋊C8—24no—
37C2×C103⋊C8—22no—
38C4⋊Dic103C2×C411yescharacteristic
39C4⋊Dic103C2×C411yescharacteristic
40Dic103⋊C4—21no—
41Dic103⋊C4—21no—
42C22⋊Dic103—21no—
43C22⋊Dic103—21no—
44C22⋊Dic103—21no—
45(C2×D103)⋊C4—21no—
46(C2×D103)⋊C4—21no—
47C4×Dic103—21no—
48C24×C103D411yescharacteristic
49C22×C4×C103—22no—
50C22×C4×C103—22no—
51C22×C4×C103—22no—
52C22×C4×C103C2×C411yescharacteristic
53C22×C4×C103C2×C411yescharacteristic
54C22×C4×C103D411yescharacteristic
55C22×C4×C103D411yescharacteristic
56C22×C4×C103D411yescharacteristic
57C22×C4×C103C2311yescharacteristic
58C22⋊C4×C103—24no—
59C42×C103—22no—
60C42×C103—22no—
61C23×C103—22no—
62C23×C103—22no—
63C23×C103—41no—
64C23×C103C22⋊C411yescharacteristic
65C23×C103C22⋊C411yescharacteristic
66C23×C103C2×D411yescharacteristic
67C22×D103—21no—
68C2×C4×C103—22no—
69C2×C4×C103—22no—
70C2×C4×C103—22no—
71C2×C4×C103—21no—
72C2×C4×C103—21no—
73C2×C4×C103—21no—
74C2×C4×C103—21no—
75C2×C4×C103—24no—
76C2×C4×C103—42no—
77C2×C4×C103—42no—
78C2×C4×C103C22⋊C411yescharacteristic
79C2×C4×C103C22⋊C411yescharacteristic
80C2×C4×C103C22×C411yescharacteristic
81C2×C4×C103C2×D412yes—
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103#4112yes—
84C22⋊D103—42no—
85C22⋊D103—42no—
86C22⋊D103—42no—
87C2×Dic103—21no—
88C2×Dic103—21no—
89C2×Dic103—21no—
90D412—22no—
91C4×D103—41no—
92C4×D103—41no—
93Dic206—22no—
94C103⋊C8—24no—
95C22×C103—21no—
96C22×C103—21no—
97C22×C103—21no—
98C22×C103—21no—
99C22×C103—21no—
100C22×C103—21no—
101C22×C103—21no—
102C22×C103—44no—
103C22×C103#10412yescomplemented
104C22×C103C2×C22⋊C411yescharacteristic
105C22×C103#12112yes—
106C2×D103—41no—
107C2×D103—41no—
108C2×D103—41no—
109C4×C103—21no—
110C4×C103—21no—
111C4×C103—44no—
112C4×C103C4×D412yes—
113C4×C103#12011yescharacteristic
114C4×C103#12311yescharacteristic
115Dic103—41no—
116Dic103—41no—
117Dic103—41no—
118C2×C103—22no—
119C2×C103—22no—
120C2×C103—41no—
121C2×C103#38611yescharacteristic
122C2×C103C2×#10411yescharacteristic
123C2×C103#42111yescharacteristic
124D103—81no—
125#1871—1031nomaximal, Sylow
126C103#187111yescharacteristic, complemented, Sylow
127C22×M16—1031no—
128#525—1031no—
129C2×#104—1032no—
130C4×C22⋊C4D10311yescharacteristic, complemented
131#339—1032no—
132C2×#41—1031no—
133C23×C4C2×D10311yescharacteristic
134C2×M16—1032no—
135C2×M16—2064no—
136C2×M16—2061no—
137C22×C8—2061no—
138#123—2061no—
139C22⋊Q8—1031no—
140C22⋊Q8—1031no—
141#121—1031no—
142#121—1031no—
143#120—2061no—
144C4×D4—2061no—
145C4×D4—2061no—
146#117—1031no—
147C2×C22⋊C4—21no—
148C2×C42C2×D10312yes—
149#104—2064no—
150#95—21no—
151C24C22⋊D10311yescharacteristic
152#41—2062no—
153#41—2062no—
154C2×Q8—1031no—
155C2×D4—1031no—
156C2×D4—2061no—
157C2×D4—2061no—
158C2×D4—2061no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—2061no—
163C22×C4C4×D10311yescharacteristic
164C22×C4C4×D10311yescharacteristic
165C22×C4D41211yescharacteristic
166C22×C4D41211yescharacteristic
167C22×C4C22⋊D10311yescharacteristic
168C22×C4C22×D10311yescharacteristic
169M16—1034no—
170M16—2064no—
171M16—2062no—
172C2×C8—2064no—
173C2×C8—2062no—
174C4⋊C4—1031no—
175C4⋊C4—1031no—
176C4⋊C4—2061no—
177C4⋊C4—2061no—
178C22⋊C4—24no—
179C22⋊C4—2061no—
180C22⋊C4—2061no—
181C22⋊C4—2061no—
182C22⋊C4—2061no—
183C22⋊C4—2061no—
184C42—22no—
185C42—22no—
186C42—2061no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—2061no—
191C23(C2×D103)⋊C411yescharacteristic
192C23(C2×D103)⋊C411yescharacteristic
193C23C2×C22⋊D10311yescharacteristic
194Q8—2062no—
195D4—4122no—
196D4—4122no—
197D4—4122no—
198D4—2062no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—4121no—
210C2×C4—4121no—
211C2×C4—2061no—
212C2×C4—2061no—
213C2×C4—2061no—
214C2×C4(C2×D103)⋊C411yescharacteristic
215C2×C4(C2×D103)⋊C411yescharacteristic
216C2×C4C2×C4×D10311yescharacteristic
217C2×C4D4×D10312yes—
218C2×C4C2×D41211yescharacteristic
219C2×C4#1311010412yes—
220C8—2064no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—4121no—
230C22—4121no—
231C22—4121no—
232C22#1569294912yescomplemented
233C22C2×(C2×D103)⋊C411yescharacteristic
234C22#1569299312yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—4121no—
239C4—4121no—
240C4—4121no—
241C4(C22⋊D103)⋊C412yes—
242C4#1569299111yescharacteristic
243C4#1569300511yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—8241no—
248C2#2026766811yescharacteristic
249C2C2×#1569294911yescharacteristic
250C2#2026780911yescharacteristic
subgroupG/H
centerC2×C4C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC4×C22⋊C4×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenterC4×C22⋊C4D103
hypocenterC103#1871
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#13110089C2semidirect
3. C2×#15692949C2semidirect
4. #20267551C2semidirect
5. C4×C22⋊C4×C103C2semidirect
12. #15693000C4semidirect
13. #15693000C4semidirect
14. #15692995C4semidirect
15. #15692995C4semidirect
35. #13110089D4semidirect
103. C22×C103#104semidirect
126. C103#1871semidirect
130. C4×C22⋊C4D103semidirect
232. C22#15692949semidirect

Maximal subgroups

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

subgroupindex
C22×#131100892
#202683022
C2×#156929492
#202675512
C4×C22⋊C4×C1032
#1871103