Finite Group Databasebeta

← #27204687

Subgroups — #27204687

Order 13184.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15693041C211yesmaximal, characteristic, complemented
2#20268358C211yesmaximal, characteristic, complemented
3#20268274C211yesmaximal, characteristic, complemented
4#20268011C212yesmaximal, complemented
5#20268004C212yesmaximal, complemented
6#20267989C212yesmaximal, complemented
7#20267984C212yesmaximal, complemented
8#20267819C211yesmaximal, characteristic, complemented
9#20267793C211yesmaximal, characteristic, complemented
10C2×#15692942C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13#15693041—24no—
14C2×#13110095C2211yescharacteristic, complemented
15C2×#13110093C2211yescharacteristic, complemented
16C2×#13110092C2211yescharacteristic, complemented
17C2×#13110090C2211yescharacteristic, complemented
18C22×C103⋊C8C2211yescharacteristic
19#15693017C2212yes—
20#15693008C2212yes—
21#15692992—21no—
22#15692992—21no—
23#15692990—22no—
24Q8×Dic103C2212yescomplemented
25D4×Dic103—22no—
26D4×Dic103C2212yescomplemented
27#15692980—21no—
28#15692980C2211yescharacteristic
29C2×C4⋊Dic103—21no—
30C2×C4⋊Dic103C2211yescharacteristic
31Dic103⋊C8C2212yescomplemented
32Dic103⋊C8C2212yescomplemented
33#15692946C2212yescomplemented
34#15692943C2212yescomplemented
35#15692942C2212yes—
36#15692942C2212yes—
37C2×#41×C103C2211yescharacteristic
38C22×D4×C103C2211yescharacteristic
39AGL(1,ℤ/8)×C103—24no—
40C2×SD16×C103C2212yes—
41C2×D8×C103C2212yes—
42C2×M16×C103C2211yescharacteristic
43#13110105—22no—
44#13110105—22no—
45C2×Dic206C2311yescharacteristic
46C2×D412C2311yescharacteristic
47C2×C22⋊D103—21no—
48C2×C22⋊D103—22no—
49C2×C22⋊D103—22no—
50C22×Dic103—21no—
51C22×Dic103—22no—
52C2×C4×D103—21no—
53#13110095—22no—
54#13110093—22no—
55#13110092—22no—
56#13110090—22no—
57C2×C103⋊C8—22no—
58C2×C103⋊C8C2311yescharacteristic
59C2×C103⋊C8C2311yescharacteristic
60C4⋊Dic103—21no—
61C4⋊Dic103—22no—
62C4⋊Dic103D411yescharacteristic
63C4⋊Dic103D411yescharacteristic
64C4⋊Dic103C2312yes—
65C22⋊Dic103—22no—
66C22⋊Dic103—22no—
67C22⋊Dic103—22no—
68C22⋊Dic103D412yes—
69C4×Dic103—22no—
70C4×Dic103C2312yes—
71C24×C103—21no—
72#41×C103—22no—
73#41×C103D414yescomplemented
74C2×Q8×C103C2311yescharacteristic
75C2×D4×C103—21no—
76C2×D4×C103—22no—
77C2×D4×C103—21no—
78C2×D4×C103—22no—
79C2×D4×C103C2312yes—
80C2×D4×C103C2311yescharacteristic
81C22×C4×C103—21no—
82C22×C4×C103C2311yescharacteristic
83SD16×C103—24no—
84D8×C103—24no—
85M16×C103—22no—
86C2×C8×C103C2312yes—
87C23×C103—21no—
88C23×C103—22no—
89C23×C103—42no—
90C23×C103—81no—
91C23×C103—81no—
92C23×C103C2×D411yescharacteristic
93C22×D103—21no—
94Q8×C103—21no—
95Q8×C103C2×D412yes—
96D4×C103—24no—
97D4×C103—22no—
98D4×C103—21no—
99D4×C103—22no—
100D4×C103—42no—
101D4×C103C2×D412yes—
102C2×C4×C103—21no—
103C2×C4×C103—24no—
104C2×C4×C103C2×D411yescharacteristic
105C2×C4×C103C2×D412yes—
106C2×C4×C103#4112yes—
107C2×C4×C103C2411yescharacteristic
108C22⋊D103—42no—
109C22⋊D103—82no—
110C22⋊D103—82no—
111C2×Dic103—22no—
112C2×Dic103—21no—
113C2×Dic103—82no—
114C2×Dic103—81no—
115C2×Dic103C2×D412yes—
116C2×Dic103C2×D412yes—
117D412—21no—
118D412—21no—
119C4×D103—42no—
120Dic206—21no—
121Dic206—21no—
122C8×C103—22no—
123C103⋊C8—21no—
124C103⋊C8—21no—
125C22×C103—21no—
126C22×C103—21no—
127C22×C103—22no—
128C22×C103—41no—
129C22×C103—41no—
130C22×C103—42no—
131C22×C103—42no—
132C22×C103—42no—
133C22×C103—84no—
134C22×C103#12112yes—
135C22×C103C22×D411yescharacteristic
136C2×D103—41no—
137C2×D103—41no—
138C2×D103—41no—
139C4×C103—22no—
140C4×C103#12112yes—
141C4×C103C22×D411yescharacteristic
142C4×C103C2×#4111yescharacteristic
143Dic103—22no—
144Dic103—22no—
145Dic103—41no—
146Dic103—42no—
147C2×C103—22no—
148C2×C103—42no—
149C2×C103—82no—
150C2×C103C2×#12111yescharacteristic
151C2×C103#57611yescharacteristic
152C2×C103#57711yescharacteristic
153D103—81no—
154#3045—1031nomaximal, Sylow
155C103#304511yescharacteristic, complemented, Sylow
156C2×AGL(1,ℤ/8)D10311yescharacteristic, complemented
157C2×#135—1031no—
158#535—1031no—
159#520—1031no—
160#464—1032no—
161#463—1032no—
162#460—1032no—
163#459—1032no—
164#424—1031no—
165#417—1031no—
166C2×#102—1031no—
167C2×#41—1031no—
168C2×#41C2×D10311yescharacteristic
169C22×D4C2×D10311yescharacteristic
170AGL(1,ℤ/8)—24no—
171#135—2064no—
172C2×Q16—1031no—
173C2×SD16—1031no—
174C2×SD16—1031no—
175C2×SD16C2×D10312yes—
176C2×D8—1031no—
177C2×D8C2×D10312yes—
178C2×M16C2×D10311yescharacteristic
179C22×C8—1031no—
180#127—1032no—
181#124—1032no—
182#121—2061no—
183#121—2061no—
184#120—2062no—
185C4×Q8—1032no—
186C4×D4—1032no—
187C4×D4—2062no—
188#117—1031no—
189#117—2061no—
190C2×C4⋊C4—1031no—
191C2×C4⋊C4—2061no—
192C4⋊C8—1032no—
193C4⋊C8—1032no—
194#103—1032no—
195#102—1032no—
196#102—1032no—
197#102—1032no—
198C24—21no—
199#41—22no—
200#41—2062no—
201#41—2062no—
202#41C22⋊D10314yescomplemented
203C2×Q8—1031no—
204C2×Q8C22×D10311yescharacteristic
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—1031no—
210C2×D4—2062no—
211C2×D4—2062no—
212C2×D4—2061no—
213C2×D4C22×D10312yes—
214C2×D4C22×D10311yescharacteristic
215C22×C4—21no—
216C22×C4—2062no—
217C22×C4—2061no—
218C22×C4—2061no—
219C22×C4C22×D10311yescharacteristic
220Q16—2062no—
221SD16—24no—
222SD16—2062no—
223SD16—2062no—
224D8—24no—
225D8—2062no—
226M16—22no—
227C2×C8—1031no—
228C2×C8—1031no—
229C2×C8—2062no—
230C2×C8C22×D10312yes—
231C4⋊C4—1031no—
232C4⋊C4—1031no—
233C4⋊C4—1032no—
234C4⋊C4—2062no—
235C4⋊C4—2061no—
236C22⋊C4—1032no—
237C22⋊C4—2062no—
238C22⋊C4—2062no—
239C22⋊C4—2062no—
240C42—1032no—
241C42—2062no—
242C23—21no—
243C23—22no—
244C23—42no—
245C23—81no—
246C23—81no—
247C23—2061no—
248C23D4×D10311yescharacteristic
249Q8—21no—
250Q8—2061no—
251Q8—2061no—
252Q8C2×C22⋊D10312yes—
253D4—24no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—8242no—
259D4—8242no—
260D4—4122no—
261D4—2061no—
262D4—2061no—
263D4C2×C22⋊D10312yes—
264C2×C4—21no—
265C2×C4—24no—
266C2×C4—8241no—
267C2×C4—8242no—
268C2×C4—1032no—
269C2×C4—1032no—
270C2×C4—4122no—
271C2×C4—2062no—
272C2×C4—2061no—
273C2×C4D4×D10311yescharacteristic
274C2×C4C2×C22⋊D10312yes—
275C2×C4#1311010412yes—
276C2×C4C23×D10311yescharacteristic
277C8—22no—
278C8—2061no—
279C8—2061no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—4121no—
290C22—4121no—
291C22—4121no—
292C22#1569299312yes—
293C22C2×D4×D10311yescharacteristic
294C4—22no—
295C4—4122no—
296C4—4121no—
297C4—2062no—
298C4—2062no—
299C4#1569299312yes—
300C4C22×C22⋊D10311yescharacteristic
301C4C2×#1311010411yescharacteristic
302C2—22no—
303C2—42no—
304C2—82no—
305C2—8241no—
306C2C2×#1569299311yescharacteristic
307C2#2026859511yescharacteristic
308C2#2026860111yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×AGL(1,ℤ/8)×C103C2
socleC22×C103C22×D4
hypercenterC2×AGL(1,ℤ/8)D103
hypocenterC103#3045
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#15693041C2semidirect
2. #20268358C2semidirect
3. #20268274C2semidirect
4. #20268011C2semidirect
5. #20268004C2semidirect
6. #20267989C2semidirect
7. #20267984C2semidirect
8. #20267819C2semidirect
9. #20267793C2semidirect
10. C2×#15692942C2semidirect
11. C2×AGL(1,ℤ/8)×C103C2semidirect
14. C2×#13110095C22semidirect
15. C2×#13110093C22semidirect
16. C2×#13110092C22semidirect
17. C2×#13110090C22semidirect
24. Q8×Dic103C22semidirect
26. D4×Dic103C22semidirect
31. Dic103⋊C8C22semidirect
32. Dic103⋊C8C22semidirect
33. #15692946C22semidirect
34. #15692943C22semidirect
73. #41×C103D4semidirect
155. C103#3045semidirect
156. C2×AGL(1,ℤ/8)D103semidirect
202. #41C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930412
#202683582
#202682742
#202680112
#202680042
#202679892
#202679842
#202678192
#202677932
C2×#156929422
C2×AGL(1,ℤ/8)×C1032
#3045103