Finite Group Databasebeta

← #27204682

Subgroups — #27204682

Order 13184.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15693049C211yesmaximal, characteristic, complemented
2C2×#15693041C211yesmaximal, characteristic, complemented
3#20268355C211yesmaximal, characteristic, complemented
4#20268272C211yesmaximal, characteristic, complemented
5#20268016C212yesmaximal, complemented
6#20268009C212yesmaximal, complemented
7#20267990C212yesmaximal, complemented
8#20267985C212yesmaximal, complemented
9#20267819C211yesmaximal, characteristic, complemented
10C2×#15692941C211yesmaximal, characteristic, complemented
11#417×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C22×D412C2211yescharacteristic
14#15693049—24no—
15#15693041—24no—
16C2×#13110095C2211yescharacteristic, complemented
17C2×#13110094C2212yes—
18C2×#13110093C2211yescharacteristic, complemented
19C2×#13110092C2211yescharacteristic, complemented
20C2×D824C2212yes—
21C2×#13110090C2211yescharacteristic, complemented
22C22×C103⋊C8C2211yescharacteristic
23#15693017C2212yes—
24#15693010C2212yes—
25#15692995—21no—
26#15692995—21no—
27#15692989—22no—
28#15692986C2212yescomplemented
29#15692983C2212yescomplemented
30C4×C22⋊D103—22no—
31#15692980C2211yescharacteristic
32#15692979—21no—
33C4⋊C4×D103—21no—
34Dic103⋊C8C2212yescomplemented
35Dic103⋊C8C2212yescomplemented
36#15692941C2212yes—
37#15692941C2212yes—
38C2×#41×C103C2211yescharacteristic
39C2×M16×C103C2211yescharacteristic
40C2×C4⋊C4×C103C2211yescharacteristic
41#103×C103C2212yescomplemented
42#102×C103C2212yescomplemented
43C23×D103—21no—
44#13110105—22no—
45#13110105D414yescomplemented
46C2×Dic206C2311yescharacteristic
47C2×D412—22no—
48C2×D412—22no—
49C2×D412—21no—
50C2×D412C2312yes—
51C2×D412C2311yescharacteristic
52C2×C22⋊D103—21no—
53C2×C22⋊D103—22no—
54C2×C22⋊D103—22no—
55C2×C4×D103—21no—
56C2×C4×D103—22no—
57#13110095—22no—
58#13110094—24no—
59#13110093—22no—
60#13110092—22no—
61D824—24no—
62#13110090—22no—
63C2×C103⋊C8—22no—
64C2×C103⋊C8C2311yescharacteristic
65C2×C103⋊C8C2311yescharacteristic
66C4⋊Dic103D411yescharacteristic
67C4⋊Dic103D411yescharacteristic
68Dic103⋊C4—22no—
69C22⋊Dic103D412yes—
70(C2×D103)⋊C4—22no—
71(C2×D103)⋊C4—22no—
72(C2×D103)⋊C4—22no—
73C4×Dic103—22no—
74C4×Dic103C2312yes—
75#41×C103—22no—
76#41×C103—22no—
77C2×Q8×C103C2311yescharacteristic
78C2×D4×C103—21no—
79C2×D4×C103C2311yescharacteristic
80C22×C4×C103—21no—
81C22×C4×C103—21no—
82C22×C4×C103C2311yescharacteristic
83M16×C103—22no—
84C2×C8×C103C2312yes—
85C4⋊C4×C103—21no—
86C4⋊C4×C103C2312yes—
87C23×C103—21no—
88C23×C103C2×D411yescharacteristic
89C22×D103—21no—
90C22×D103—22no—
91C22×D103—42no—
92C22×D103—81no—
93C22×D103—81no—
94Q8×C103—21no—
95Q8×C103—21no—
96D4×C103—21no—
97D4×C103—21no—
98D4×C103—42no—
99C2×C4×C103—22no—
100C2×C4×C103—21no—
101C2×C4×C103—42no—
102C2×C4×C103—81no—
103C2×C4×C103C2×D411yescharacteristic
104C2×C4×C103C2×D412yes—
105C2×C4×C103#4112yes—
106C2×C4×C103C2411yescharacteristic
107C22⋊D103—24no—
108C22⋊D103—82no—
109C22⋊D103—82no—
110C2×Dic103—21no—
111C2×Dic103C2×D412yes—
112C2×Dic103C2×D412yes—
113D412—22no—
114D412—21no—
115D412—22no—
116D412—42no—
117D412C2×D412yes—
118C4×D103—24no—
119C4×D103—82no—
120Dic206—21no—
121Dic206C2×D412yes—
122C8×C103—22no—
123C103⋊C8—21no—
124C103⋊C8—21no—
125C22×C103—21no—
126C22×C103—21no—
127C22×C103—41no—
128C22×C103—41no—
129C22×C103—41no—
130C22×C103#12112yes—
131C22×C103C22×D411yescharacteristic
132C2×D103—22no—
133C2×D103—41no—
134C2×D103—41no—
135C2×D103—42no—
136C2×D103—42no—
137C2×D103—42no—
138C2×D103—84no—
139C4×C103—41no—
140C4×C103—42no—
141C4×C103#12112yes—
142C4×C103C22×D411yescharacteristic
143C4×C103C2×#4111yescharacteristic
144Dic103—22no—
145Dic103—22no—
146Dic103—22no—
147C2×C103—22no—
148C2×C103—81no—
149C2×C103C2×#12111yescharacteristic
150C2×C103#57611yescharacteristic
151C2×C103#57711yescharacteristic
152D103—42no—
153D103—82no—
154#3045—1031nomaximal, Sylow
155C103#304511yescharacteristic, complemented, Sylow
156C2×AGL(1,ℤ/8)—1031no—
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#417D10311yescharacteristic, complemented
166C2×#102—1031no—
167C2×#41—1031no—
168C2×#41C2×D10311yescharacteristic
169C22×D4—1031no—
170AGL(1,ℤ/8)—2064no—
171#135—2064no—
172C2×Q16—1031no—
173C2×SD16—1031no—
174C2×SD16—1031no—
175C2×SD16—1032no—
176C2×D8—1031no—
177C2×D8—1032no—
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—2061no—
191C2×C4⋊C4C2×D10311yescharacteristic
192C4⋊C8—1032no—
193C4⋊C8—1032no—
194#103C2×D10312yescomplemented
195#102—1032no—
196#102—1032no—
197#102C2×D10312yescomplemented
198C24—2061no—
199#41—22no—
200#41—22no—
201#41—1034no—
202#41—2062no—
203C2×Q8—1031no—
204C2×Q8C22×D10311yescharacteristic
205C2×D4—21no—
206C2×D4—1031no—
207C2×D4—1032no—
208C2×D4—2062no—
209C2×D4—2062no—
210C2×D4—2061no—
211C2×D4—2061no—
212C2×D4—2062no—
213C2×D4—2062no—
214C2×D4C22×D10311yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—2062no—
218C22×C4—2061no—
219C22×C4C22×D10311yescharacteristic
220Q16—2062no—
221SD16—2064no—
222SD16—2062no—
223SD16—2062no—
224D8—2064no—
225D8—2062no—
226M16—22no—
227C2×C8—1031no—
228C2×C8—1031no—
229C2×C8—2062no—
230C2×C8C22×D10312yes—
231C4⋊C4—21no—
232C4⋊C4—1031no—
233C4⋊C4—1031no—
234C4⋊C4—2062no—
235C4⋊C4C22×D10312yes—
236C22⋊C4—1032no—
237C22⋊C4—2062no—
238C22⋊C4—2062no—
239C22⋊C4—2062no—
240C42—1032no—
241C42—2062no—
242C23—21no—
243C23—8241no—
244C23—8241no—
245C23—4122no—
246C23—2062no—
247C23—2061no—
248C23D4×D10311yescharacteristic
249Q8—21no—
250Q8—21no—
251Q8—1032no—
252Q8—2061no—
253D4—21no—
254D4—21no—
255D4—42no—
256D4—8242no—
257D4—8242no—
258D4—1032no—
259D4—4122no—
260D4—2064no—
261D4—2062no—
262D4—2062no—
263D4—2061no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4—8242no—
269C2×C4—1032no—
270C2×C4—1032no—
271C2×C4—2061no—
272C2×C4—2064no—
273C2×C4D4×D10312yes—
274C2×C4D4×D10311yescharacteristic
275C2×C4#1311010512yes—
276C2×C4C23×D10311yescharacteristic
277C8—22no—
278C8—2061no—
279C8—2061no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—8244no—
286C22—4122no—
287C22—4122no—
288C22—4122no—
289C22—4121no—
290C22—4121no—
291C22—2062no—
292C22#1569299412yes—
293C22C2×D4×D10311yescharacteristic
294C4—42no—
295C4—41no—
296C4—2062no—
297C4—2062no—
298C4—2062no—
299C4#1569299412yes—
300C4C2×D4×D10311yescharacteristic
301C4C2×#1311010511yescharacteristic
302C2—22no—
303C2—81no—
304C2—8242no—
305C2—4122no—
306C2C2×#1569299411yescharacteristic
307C2#2026859511yescharacteristic
308C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#417×C103C2
socleC22×C103C22×D4
hypercenter#417D103
hypocenterC103#3045
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#15693049C2semidirect
2. C2×#15693041C2semidirect
3. #20268355C2semidirect
4. #20268272C2semidirect
5. #20268016C2semidirect
6. #20268009C2semidirect
7. #20267990C2semidirect
8. #20267985C2semidirect
9. #20267819C2semidirect
10. C2×#15692941C2semidirect
11. #417×C103C2semidirect
16. C2×#13110095C22semidirect
18. C2×#13110093C22semidirect
19. C2×#13110092C22semidirect
21. C2×#13110090C22semidirect
28. #15692986C22semidirect
29. #15692983C22semidirect
34. Dic103⋊C8C22semidirect
35. Dic103⋊C8C22semidirect
41. #103×C103C22semidirect
42. #102×C103C22semidirect
45. #13110105D4semidirect
155. C103#3045semidirect
165. #417D103semidirect
194. #103C2×D103semidirect
197. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930492
C2×#156930412
#202683552
#202682722
#202680162
#202680092
#202679902
#202679852
#202678192
C2×#156929412
#417×C1032
#3045103