Finite Group Databasebeta

← #27204835

Subgroups — #27204835

Order 13184.

472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15693054C211yesmaximal, characteristic, complemented
2#20268369C211yesmaximal, characteristic
3#20268362C211yesmaximal, characteristic, complemented
4#20268049C212yesmaximal, complemented
5#20268037C212yesmaximal, complemented
6#20268032C212yesmaximal, complemented
7#20268020C212yesmaximal, complemented
8#20267833C211yesmaximal, characteristic, complemented
9#20267788C211yesmaximal, characteristic, complemented
10C2×#15692946C211yesmaximal, characteristic, complemented
11C2×#131×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C22×Dic206C2211yescharacteristic
14#15693054—24no—
15C2×Dic412C2212yes—
16C2×#13110094C2212yes—
17#15693019—21no—
18#15693008—21no—
19#15693002—22no—
20#15693000C2212yes—
21#15693000C2212yes—
22#15693000C2212yes—
23#15692997—21no—
24#15692995C2212yes—
25#15692993—22no—
26#15692992—21no—
27#15692980C2211yescharacteristic
28C2×C4⋊Dic103C2211yescharacteristic
29#15692955C2212yes—
30#15692953C2212yes—
31#15692946C2211yescharacteristic
32#15692946C2212yes—
33#15692946C2212yes—
34#15692946C2211yescharacteristic
35#15692943C2211yescharacteristic
36#15692943C2211yescharacteristic
37C2×#41×C103C2211yescharacteristic
38#131×C103—24no—
39C2×M16×C103C2212yes—
40C2×M16×C103C2211yescharacteristic
41C22×C8×C103C2212yes—
42C22×C8×C103C2211yescharacteristic
43#13110105—22no—
44#13110105—22no—
45C2×Dic206—22no—
46C2×Dic206—22no—
47C2×Dic206—21no—
48C2×Dic206C2312yes—
49C2×Dic206C2311yescharacteristic
50C2×D412C2311yescharacteristic
51C2×C22⋊D103—21no—
52C2×C22⋊D103—22no—
53C22×Dic103—21no—
54C22×Dic103—21no—
55C2×C4×D103—21no—
56Dic412—24no—
57#13110094—24no—
58C4⋊Dic103—21no—
59C4⋊Dic103C2311yescharacteristic
60C4⋊Dic103C2311yescharacteristic
61C4⋊Dic103C2312yes—
62Dic103⋊C4—22no—
63Dic103⋊C4—22no—
64Dic103⋊C4—22no—
65C22⋊Dic103—21no—
66C22⋊Dic103—22no—
67C22⋊Dic103—22no—
68C22⋊Dic103—22no—
69(C2×D103)⋊C4—22no—
70C4×Dic103—21no—
71#41×C103—22no—
72#41×C103—22no—
73C2×Q8×C103D411yescharacteristic
74C2×D4×C103D411yescharacteristic
75C2×D4×C103D412yes—
76C22×C4×C103C2312yes—
77C22×C4×C103C2311yescharacteristic
78M16×C103—24no—
79M16×C103D414yescomplemented
80C2×C8×C103—22no—
81C2×C8×C103—24no—
82C2×C8×C103C2311yescharacteristic
83C2×C8×C103C2311yescharacteristic
84C2×C8×C103C2312yes—
85C23×C103C2×D412yes—
86C23×C103C2×D411yescharacteristic
87C22×D103—21no—
88Q8×C103—22no—
89D4×C103—24no—
90D4×C103—22no—
91C2×C4×C103—22no—
92C2×C4×C103—22no—
93C2×C4×C103C2×D412yes—
94C2×C4×C103C2×D412yes—
95C2×C4×C103C2×D411yescharacteristic
96C2×C4×C103#4112yes—
97C2×C4×C103C2411yescharacteristic
98C22⋊D103—42no—
99C22⋊D103—82no—
100C2×Dic103—21no—
101C2×Dic103—21no—
102C2×Dic103—22no—
103C2×Dic103—21no—
104C2×Dic103—22no—
105C2×Dic103—42no—
106C2×Dic103—81no—
107D412—21no—
108D412—21no—
109C4×D103—42no—
110Dic206—22no—
111Dic206—21no—
112Dic206—22no—
113Dic206—21no—
114Dic206—42no—
115C8×C103—21no—
116C8×C103—21no—
117C8×C103C2×D414yes—
118C22×C103—21no—
119C22×C103—21no—
120C22×C103—22no—
121C22×C103—22no—
122C22×C103—22no—
123C22×C103#12112yes—
124C22×C103C22×D411yescharacteristic
125C2×D103—41no—
126C2×D103—41no—
127C2×D103—41no—
128C4×C103—22no—
129C4×C103#12112yes—
130C4×C103C22×D411yescharacteristic
131C4×C103C2×#4111yescharacteristic
132Dic103—42no—
133Dic103—41no—
134Dic103—41no—
135Dic103—42no—
136Dic103—41no—
137C2×C103—22no—
138C2×C103—42no—
139C2×C103C2×#12111yescharacteristic
140C2×C103#57711yescharacteristic
141C2×C103#57811yescharacteristic
142D103—81no—
143#3063—1031nomaximal, Sylow
144C103#306311yescharacteristic, complemented, Sylow
145C2×#137—1031no—
146C2×#131D10311yescharacteristic, complemented
147#537—1031no—
148#536—1031no—
149#470—1032no—
150#468—1032no—
151#467—1032no—
152#465—1032no—
153#428—1031no—
154#416—1031no—
155C2×#103—1031no—
156C2×#41—1031no—
157C2×#41C2×D10311yescharacteristic
158C22×Q8—1031no—
159#137—2064no—
160C2×Q16—1032no—
161C2×SD16—1032no—
162#131—24no—
163C2×M16C2×D10312yes—
164C2×M16C2×D10311yescharacteristic
165C22×C8C2×D10311yescharacteristic
166C22×C8C2×D10312yes—
167C4⋊Q8—2061no—
168#124—2061no—
169#123—2062no—
170C22⋊Q8—1032no—
171C22⋊Q8—1032no—
172C22⋊Q8—1032no—
173C22⋊Q8—2061no—
174#121—1032no—
175#121—2061no—
176#121—2062no—
177#117—1031no—
178C2×C4⋊C4—1031no—
179#107—1032no—
180#106—1032no—
181#103—1032no—
182#103—1032no—
183#103—1031no—
184#103—1031no—
185#102—1031no—
186#102—1031no—
187#41—22no—
188#41—22no—
189#41—2062no—
190#41—2062no—
191C2×Q8—1032no—
192C2×Q8—1031no—
193C2×Q8—2062no—
194C2×Q8—2062no—
195C2×Q8—2061no—
196C2×Q8D41211yescharacteristic
197C2×D4—1031no—
198C2×D4—2062no—
199C2×D4—2061no—
200C2×D4D41212yes—
201C2×D4D41211yescharacteristic
202C22×C4—2061no—
203C22×C4—2061no—
204C22×C4—2061no—
205C22×C4C22×D10312yes—
206C22×C4C22×D10311yescharacteristic
207Q16—2064no—
208SD16—2064no—
209M16—24no—
210M16C22⋊D10314yescomplemented
211C2×C8—22no—
212C2×C8—24no—
213C2×C8C22×D10311yescharacteristic
214C2×C8C22×D10311yescharacteristic
215C2×C8C22×D10312yes—
216C4⋊C4—1031no—
217C4⋊C4—1031no—
218C4⋊C4—1032no—
219C4⋊C4—2062no—
220C4⋊C4—2062no—
221C4⋊C4—2062no—
222C4⋊C4—2061no—
223C22⋊C4—2061no—
224C22⋊C4—2062no—
225C22⋊C4—2062no—
226C22⋊C4—2062no—
227C22⋊C4—2062no—
228C42—2061no—
229C23—2061no—
230C23C2×D41212yes—
231C23C2×D41211yescharacteristic
232Q8—22no—
233Q8—4122no—
234Q8—2062no—
235Q8—2061no—
236Q8—2062no—
237Q8—2061no—
238D4—24no—
239D4—22no—
240D4—8242no—
241D4—4122no—
242D4—2061no—
243D4—2061no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—8241no—
247C2×C4—4122no—
248C2×C4—4122no—
249C2×C4—2061no—
250C2×C4—2061no—
251C2×C4—2062no—
252C2×C4—2061no—
253C2×C4—2062no—
254C2×C4C2×C22⋊D10312yes—
255C2×C4C2×D41212yes—
256C2×C4C2×D41211yescharacteristic
257C2×C4#1311010512yes—
258C2×C4C23×D10311yescharacteristic
259C8—21no—
260C8—21no—
261C8C2×C22⋊D10314yes—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—4121no—
268C22—4121no—
269C22—4121no—
270C22#1569299512yes—
271C22C22×D41211yescharacteristic
272C4—22no—
273C4—4122no—
274C4—4121no—
275C4—4121no—
276C4—4121no—
277C4—4122no—
278C4#1569299512yes—
279C4C22×C22⋊D10311yescharacteristic
280C4C2×#1311010511yescharacteristic
281C2—22no—
282C2—42no—
283C2—8241no—
284C2C2×#1569299511yescharacteristic
285C2#2026860311yescharacteristic
286C2#2026860811yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#131×C103C2
socleC22×C103C22×D4
prime radical#20268369C2
hypercenterC2×#131D103
hypocenterC103#3063
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#15693054C2semidirect
3. #20268362C2semidirect
4. #20268049C2semidirect
5. #20268037C2semidirect
6. #20268032C2semidirect
7. #20268020C2semidirect
8. #20267833C2semidirect
9. #20267788C2semidirect
10. C2×#15692946C2semidirect
11. C2×#131×C103C2semidirect
79. M16×C103D4semidirect
144. C103#3063semidirect
146. C2×#131D103semidirect
210. M16C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930542
#202683692
#202683622
#202680492
#202680372
#202680322
#202680202
#202678332
#202677882
C2×#156929462
C2×#131×C1032
#3063103