Finite Group Databasebeta

← #27205744

Subgroups — #27205744

Order 13184.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268325C211yesmaximal, characteristic
2#20268197C211yesmaximal, characteristic, complemented
3#20268183C211yesmaximal, characteristic, complemented
4#20268159C211yesmaximal, characteristic, complemented
5#20268153C211yesmaximal, characteristic, complemented
6#20268047C212yesmaximal, complemented
7#20268039C212yesmaximal
8C4×#13110095C212yesmaximal, complemented
9C4×#13110092C212yesmaximal, complemented
10C4×#13110089C211yesmaximal, characteristic, complemented
11#533×C103C211yesmaximal, characteristic, complemented
12C2×#13110095C2212yes—
13C2×#13110092C2212yes—
14C2×#13110089C2212yes—
15#15693015—21no—
16#15693013C2211yescharacteristic
17#15693009C2211yescharacteristic
18#15693004—21no—
19#15693000C2211yescharacteristic
20#15692995C2211yescharacteristic
21C4×Dic206C2211yescharacteristic
22C4×D412C2211yescharacteristic
23C4×C22⋊D103—21no—
24#15692978—21no—
25#15692954C2212yes—
26#15692952C2212yes—
27#15692945C2212yes—
28#15692945C2212yes—
29#15692944C2212yes—
30#15692941C2212yes—
31#15692932C2211yescharacteristic
32#15692932C2211yescharacteristic
33C4×C103⋊C8C2212yes—
34C4⋊Q8×C103C2211yescharacteristic
35C4⋊Q8×C103C2211yescharacteristic
36#125×C103—21no—
37C22⋊Q8×C103—21no—
38C22⋊Q8×C103C2212yes—
39C4×Q8×C103—21no—
40C4×Q8×C103C2212yes—
41#117×C103—21no—
42C2×C42×C103C2211yescharacteristic
43C2×Dic206C2311yescharacteristic
44C2×D412C2311yescharacteristic
45C2×C22⋊D103—21no—
46C2×C4×D103—21no—
47#13110095—24no—
48#13110092—24no—
49#13110089—24no—
50C2×C103⋊C8C2312yes—
51C2×C103⋊C8C2312yes—
52C4⋊Dic103C2311yescharacteristic
53C4⋊Dic103C2311yescharacteristic
54Dic103⋊C4—21no—
55Dic103⋊C4—21no—
56Dic103⋊C4—21no—
57Dic103⋊C4—21no—
58C22⋊Dic103—21no—
59(C2×D103)⋊C4—21no—
60(C2×D103)⋊C4—21no—
61(C2×D103)⋊C4—21no—
62(C2×D103)⋊C4—21no—
63C4×Dic103—21no—
64C2×Q8×C103—21no—
65C2×Q8×C103C2312yes—
66C22×C4×C103D411yescharacteristic
67C22×C4×C103D411yescharacteristic
68C22×C4×C103C2311yescharacteristic
69C4⋊C4×C103—21no—
70C4⋊C4×C103—21no—
71C4⋊C4×C103—21no—
72C4⋊C4×C103—22no—
73C4⋊C4×C103—22no—
74C4⋊C4×C103C2312yes—
75C22⋊C4×C103—22no—
76C42×C103—22no—
77C42×C103D411yescharacteristic
78C42×C103D411yescharacteristic
79C42×C103C2311yescharacteristic
80C42×C103C2311yescharacteristic
81C23×C103C2×D411yescharacteristic
82C22×D103—21no—
83Q8×C103—22no—
84Q8×C103—22no—
85Q8×C103—42no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103—22no—
89C2×C4×C103—22no—
90C2×C4×C103—41no—
91C2×C4×C103C2×D411yescharacteristic
92C2×C4×C103C2×D411yescharacteristic
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2×D411yescharacteristic
96C2×C4×C103C2411yescharacteristic
97C22⋊D103—42no—
98C2×Dic103—21no—
99C2×Dic103—21no—
100C2×Dic103—21no—
101D412—22no—
102C4×D103—42no—
103Dic206—22no—
104C103⋊C8—22no—
105C103⋊C8#4114yes—
106C22×C103—21no—
107C22×C103—21no—
108C22×C103—21no—
109C22×C103C22×D411yescharacteristic
110C2×D103—41no—
111C2×D103—41no—
112C2×D103—41no—
113C4×C103—21no—
114C4×C103—21no—
115C4×C103—21no—
116C4×C103—21no—
117C4×C103—42no—
118C4×C103—42no—
119C4×C103#13712yes—
120C4×C103C2×#4112yes—
121Dic103—41no—
122Dic103—41no—
123Dic103—41no—
124C2×C103—41no—
125C2×C103#53211yescharacteristic
126C2×C103C2×#13711yescharacteristic
127C2×C103#57511yescharacteristic
128D103—81no—
129#3172—1031nomaximal, Sylow
130C103#317211yescharacteristic, complemented, Sylow
131#533D10311yescharacteristic, complemented
132#529—1031no—
133#501—1031no—
134#497—1031no—
135#491—1031no—
136#489—1031no—
137#470—1032no—
138#468—1032no—
139C4×Q16—1032no—
140C4×SD16—1032no—
141C4×M16—1031no—
142C2×Q16—1032no—
143C2×SD16—1032no—
144C2×M16—1032no—
145C4⋊Q8C2×D10311yescharacteristic
146C4⋊Q8C2×D10311yescharacteristic
147#126—2061no—
148#125—21no—
149#125—1031no—
150#124—1031no—
151#123—2061no—
152C22⋊Q8—21no—
153C22⋊Q8—1031no—
154C22⋊Q8C2×D10312yes—
155#121—1031no—
156C4×Q8—21no—
157C4×Q8—1031no—
158C4×Q8C2×D10312yes—
159C4×D4—1031no—
160C4×D4—2061no—
161#117—21no—
162#117—2061no—
163C2×C42C2×D10311yescharacteristic
164#107—1032no—
165#106—1032no—
166#103—1032no—
167#103—1032no—
168#103—1032no—
169#102—1032no—
170#97—1031no—
171#97—1031no—
172C4×C8—1032no—
173C2×Q8—21no—
174C2×Q8—1031no—
175C2×Q8C22×D10312yes—
176C2×D4—1031no—
177C2×D4—2061no—
178C22×C4—2061no—
179C22×C4C22⋊D10311yescharacteristic
180C22×C4C22⋊D10311yescharacteristic
181C22×C4C22×D10311yescharacteristic
182Q16—2064no—
183SD16—2064no—
184M16—2064no—
185C2×C8—1032no—
186C2×C8—1032no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—1031no—
193C4⋊C4—1031no—
194C4⋊C4—2061no—
195C4⋊C4—2061no—
196C4⋊C4—2061no—
197C4⋊C4—2061no—
198C4⋊C4C22×D10312yes—
199C22⋊C4—22no—
200C22⋊C4—2061no—
201C22⋊C4—2061no—
202C22⋊C4—2061no—
203C22⋊C4—2061no—
204C22⋊C4—2061no—
205C42—22no—
206C42—2061no—
207C42C22⋊D10311yescharacteristic
208C42C22⋊D10311yescharacteristic
209C42C22×D10311yescharacteristic
210C42C22×D10311yescharacteristic
211C23—2061no—
212C23C2×C22⋊D10311yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—2062no—
217D4—4122no—
218D4—2062no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—4122no—
225C2×C4—2061no—
226C2×C4—2061no—
227C2×C4—2061no—
228C2×C4C2×C22⋊D10311yescharacteristic
229C2×C4C2×C22⋊D10311yescharacteristic
230C2×C4C2×C22⋊D10311yescharacteristic
231C2×C4C2×C22⋊D10311yescharacteristic
232C2×C4C2×C22⋊D10311yescharacteristic
233C2×C4C23×D10311yescharacteristic
234C8—1034no—
235C8—2062no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—4121no—
240C22—4121no—
241C22—4121no—
242C22C22×C22⋊D10311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—4121no—
250C4—4121no—
251C4—4121no—
252C4#1569305212yes—
253C4#41×D10312yes—
254C2—41no—
255C2—8241no—
256C2#2026833711yescharacteristic
257C2C2×#1569305211yescharacteristic
258C2#2026858911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#533×C103C2
socleC22×C103C22×D4
prime radical#15692995C22
hypercenter#533D103
hypocenterC103#3172
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #20268197C2semidirect
3. #20268183C2semidirect
4. #20268159C2semidirect
5. #20268153C2semidirect
6. #20268047C2semidirect
8. C4×#13110095C2semidirect
9. C4×#13110092C2semidirect
10. C4×#13110089C2semidirect
11. #533×C103C2semidirect
130. C103#3172semidirect
131. #533D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202681972
#202681832
#202681592
#202681532
#202680472
#202680392
C4×#131100952
C4×#131100922
C4×#131100892
#533×C1032
#3172103