Finite Group Databasebeta

← #27205854

Subgroups — #27205854

Order 13184.

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

normal subgroups only

This group has 366 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#20268348C211yesmaximal, characteristic, complemented
2#20268201C211yesmaximal, characteristic, complemented
3#20268186C211yesmaximal, characteristic, complemented
4#20268161C211yesmaximal, characteristic, complemented
5#20268150C211yesmaximal, characteristic, complemented
6#20268030C212yesmaximal, complemented
7#20268018C212yesmaximal
8#20267896C212yesmaximal, complemented
9#20267891C212yesmaximal, complemented
10C2×#15692932C211yesmaximal, characteristic, complemented
11#529×C103C211yesmaximal, characteristic
12C2×#13110095C2212yes—
13C2×#13110093C2212yes—
14C22×C103⋊C8C2212yes—
15#15693021C2211yescharacteristic
16#15693021C2211yescharacteristic
17#15693013—21no—
18#15693000—21no—
19#15693000C2212yes—
20C4×Dic206—21no—
21C4×Dic206C2212yes—
22#15692980—21no—
23#15692954C2212yes—
24#15692952C2212yes—
25#15692945C2212yes—
26#15692944C2212yes—
27#15692944C2212yes—
28#15692942C2212yes—
29#15692932C2212yes—
30#15692932C2211yescharacteristic
31#15692932C2211yescharacteristic
32#126×C103—21no—
33#125×C103C2211yescharacteristic
34#124×C103C2211yescharacteristic
35#123×C103—21no—
36C22⋊Q8×C103C2211yescharacteristic
37#121×C103C2211yescharacteristic
38C4×Q8×C103C2211yescharacteristic
39C4×D4×C103—21no—
40C4×D4×C103C2211yescharacteristic
41#117×C103—21no—
42C2×C42×C103C2211yescharacteristic
43C2×Dic206—21no—
44C2×Dic206C2312yes—
45#13110095—24no—
46#13110093—24no—
47C2×C103⋊C8—24no—
48C2×C103⋊C8C2312yes—
49C2×C103⋊C8C2312yes—
50C4⋊Dic103—21no—
51C4⋊Dic103—21no—
52C4⋊Dic103—21no—
53C4⋊Dic103C2312yes—
54Dic103⋊C4—22no—
55Dic103⋊C4—22no—
56C22⋊Dic103—22no—
57C4×Dic103—22no—
58C2×Q8×C103C2311yescharacteristic
59C2×D4×C103—21no—
60C2×D4×C103C2311yescharacteristic
61C22×C4×C103—21no—
62C22×C4×C103D411yescharacteristic
63C22×C4×C103D411yescharacteristic
64C22×C4×C103C2311yescharacteristic
65C4⋊C4×C103—21no—
66C4⋊C4×C103—21no—
67C4⋊C4×C103—21no—
68C4⋊C4×C103—21no—
69C4⋊C4×C103C2311yescharacteristic
70C4⋊C4×C103C2311yescharacteristic
71C22⋊C4×C103—21no—
72C22⋊C4×C103—21no—
73C22⋊C4×C103—21no—
74C22⋊C4×C103—21no—
75C22⋊C4×C103—21no—
76C42×C103—21no—
77C42×C103D411yescharacteristic
78C42×C103D411yescharacteristic
79C42×C103C2311yescharacteristic
80C42×C103C2311yescharacteristic
81C23×C103—21no—
82C23×C103C2×D411yescharacteristic
83Q8×C103—22no—
84D4×C103—22no—
85D4×C103—42no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103—21no—
89C2×C4×C103—21no—
90C2×C4×C103—21no—
91C2×C4×C103—41no—
92C2×C4×C103—42no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2×D411yescharacteristic
96C2×C4×C103C2×D411yescharacteristic
97C2×C4×C103C2×D411yescharacteristic
98C2×C4×C103C2411yescharacteristic
99C2×Dic103—22no—
100C2×Dic103—22no—
101Dic206—22no—
102Dic206—22no—
103Dic206—42no—
104C103⋊C8—22no—
105C103⋊C8#4114yes—
106C22×C103—21no—
107C22×C103—21no—
108C22×C103—41no—
109C22×C103—41no—
110C22×C103—41no—
111C22×C103#13712yes—
112C22×C103C22×D411yescharacteristic
113C4×C103—21no—
114C4×C103—21no—
115C4×C103—21no—
116C4×C103—21no—
117C4×C103—21no—
118C4×C103—41no—
119C4×C103—41no—
120C4×C103—41no—
121C4×C103C2×#4112yes—
122Dic103—42no—
123Dic103—42no—
124C2×C103—22no—
125C2×C103—81no—
126C2×C103#53211yescharacteristic
127C2×C103C2×#13711yescharacteristic
128C2×C103#57511yescharacteristic
129#3181—1031nomaximal, Sylow
130C103#318111yescharacteristic, complemented, Sylow
131#533—1031no—
132#529D10311yescharacteristic
133#501—1031no—
134#497—1031no—
135#491—1031no—
136#489—1031no—
137#467—1032no—
138#465—1032no—
139#441—1032no—
140#440—1032no—
141C2×#97—1031no—
142C2×Q16—1032no—
143C2×SD16—1032no—
144C22×C8—1032no—
145C4⋊Q8—1031no—
146C4⋊Q8—1031no—
147#126—21no—
148#125—2061no—
149#125C2×D10311yescharacteristic
150#124C2×D10311yescharacteristic
151#123—21no—
152C22⋊Q8—1032no—
153C22⋊Q8—2061no—
154C22⋊Q8C2×D10311yescharacteristic
155#121C2×D10311yescharacteristic
156C4×Q8—1032no—
157C4×Q8—2061no—
158C4×Q8C2×D10311yescharacteristic
159C4×D4—21no—
160C4×D4C2×D10311yescharacteristic
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—1032no—
171#97—1031no—
172#97—1031no—
173C2×Q8—1032no—
174C2×Q8—2061no—
175C2×Q8C22×D10311yescharacteristic
176C2×D4—21no—
177C2×D4C22×D10311yescharacteristic
178C22×C4—21no—
179C22×C4C22⋊D10311yescharacteristic
180C22×C4C22⋊D10311yescharacteristic
181C22×C4C22×D10311yescharacteristic
182Q16—2064no—
183SD16—2064no—
184C2×C8—1032no—
185C2×C8—1032no—
186C2×C8—2064no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—1032no—
192C4⋊C4—2062no—
193C4⋊C4—2062no—
194C4⋊C4—2061no—
195C4⋊C4—2061no—
196C4⋊C4—2061no—
197C4⋊C4C22×D10311yescharacteristic
198C4⋊C4C22×D10311yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—2062no—
205C42—21no—
206C42—2062no—
207C42C22⋊D10311yescharacteristic
208C42C22⋊D10311yescharacteristic
209C42C22×D10311yescharacteristic
210C42C22×D10311yescharacteristic
211C23—21no—
212C23C2×C22⋊D10311yescharacteristic
213Q8—22no—
214Q8—4122no—
215Q8—2062no—
216Q8—2062no—
217D4—22no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—2062no—
227C2×C4—2062no—
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—41no—
239C22—41no—
240C22—41no—
241C22#1569305112yes—
242C22C22×C22⋊D10311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—4122no—
252C4—4122no—
253C4#41×D10312yes—
254C2—22no—
255C2—81no—
256C2#2026833711yescharacteristic
257C2C2×#1569305111yescharacteristic
258C2#2026858911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#529×C103C2
socleC22×C103C22×D4
prime radical#121×C103C22
hypercenter#529D103
hypocenterC103#3181
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20268348C2semidirect
2. #20268201C2semidirect
3. #20268186C2semidirect
4. #20268161C2semidirect
5. #20268150C2semidirect
6. #20268030C2semidirect
8. #20267896C2semidirect
9. #20267891C2semidirect
10. C2×#15692932C2semidirect
130. C103#3181semidirect

Maximal subgroups

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

subgroupindex
#202683482
#202682012
#202681862
#202681612
#202681502
#202680302
#202680182
#202678962
#202678912
C2×#156929322
#529×C1032
#3181103