Finite Group Databasebeta

← #27206635

Subgroups — #27206635

Order 13184.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693047C211yesmaximal, characteristic, complemented
2C22×#13110093C211yesmaximal, characteristic, complemented
3#20268450C211yesmaximal, characteristic, complemented
4#20268178C211yesmaximal, characteristic, complemented
5#20268035C211yesmaximal, characteristic, complemented
6#20268025C211yesmaximal, characteristic, complemented
7#20268006C211yesmaximal, characteristic, complemented
8#20267988C211yesmaximal, characteristic, complemented
9#20267942C211yesmaximal, characteristic, complemented
10#20267934C211yesmaximal, characteristic, complemented
11#20267929C211yesmaximal, characteristic, complemented
12#20267925C211yesmaximal, characteristic, complemented
13#20267891C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15D42×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic, complemented
17C22×Dic206C2211yescharacteristic, complemented
18#15693047—24no—
19C2×#13110093—24no—
20C2×#13110093C2211yescharacteristic
21C2×#13110093C2211yescharacteristic
22C2×#13110093C2211yescharacteristic, complemented
23C2×#13110093C2211yescharacteristic, complemented
24C2×#13110093C2211yescharacteristic, complemented
25C2×#13110093C2211yescharacteristic, complemented
26C2×#13110090C2211yescharacteristic
27C2×#13110090C2211yescharacteristic, complemented
28C2×#13110090C2211yescharacteristic, complemented
29C2×#13110089C2211yescharacteristic, complemented
30C22×C103⋊C8C2211yescharacteristic, complemented
31#15693009C2211yescharacteristic, complemented
32#15693007—21no—
33#15693000C2211yescharacteristic, complemented
34#15692999—21no—
35#15692995C2211yescharacteristic, complemented
36#15692993—21no—
37C4×Dic206C2211yescharacteristic, complemented
38(C22⋊D103)⋊C4—21no—
39#15692954C2211yescharacteristic, complemented
40C4⋊(C103⋊C8)C2211yescharacteristic, complemented
41#15692944C2211yescharacteristic, complemented
42#15692944C2211yescharacteristic, complemented
43#15692942C2211yescharacteristic
44#15692942C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic, complemented
46#15692941C2211yescharacteristic, complemented
47C22⋊(C103⋊C8)C2211yescharacteristic, complemented
48C22⋊(C103⋊C8)C2211yescharacteristic, complemented
49#15692932C2211yescharacteristic, complemented
50C22×D4×C103—21no—
51C22×D4×C103C2211yescharacteristic
52C22×D4×C103C2211yescharacteristic
53#127×C103C2211yescharacteristic
54#121×C103—21no—
55#121×C103C2211yescharacteristic
56#121×C103C2211yescharacteristic
57#120×C103—21no—
58#120×C103—21no—
59C4×D4×C103C2211yescharacteristic
60C4×D4×C103C2211yescharacteristic
61#13110105—22no—
62#13110105—41no—
63C2×Dic206—22no—
64C2×Dic206—21no—
65C2×Dic206—41no—
66C2×Dic206C2311yescharacteristic
67C2×Dic206C2311yescharacteristic
68C2×D412C2311yescharacteristic
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C22×Dic103—21no—
72C2×C4×D103—21no—
73#13110093—22no—
74#13110093—22no—
75#13110093—22no—
76#13110093—22no—
77#13110093—41no—
78#13110093D414yescomplemented
79#13110090—22no—
80#13110090—22no—
81#13110090—41no—
82#13110089—22no—
83C2×C103⋊C8—22no—
84C2×C103⋊C8C2311yescharacteristic
85C2×C103⋊C8C2311yescharacteristic
86C2×C103⋊C8C2311yescharacteristic
87C2×C103⋊C8C2311yescharacteristic
88C4⋊Dic103C2311yescharacteristic
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91C22⋊Dic103—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95C4×Dic103—21no—
96C24×C103—21no—
97C24×C103—21no—
98C2×D4×C103—22no—
99C2×D4×C103—22no—
100C2×D4×C103—21no—
101C2×D4×C103—21no—
102C2×D4×C103—21no—
103C2×D4×C103—21no—
104C2×D4×C103—21no—
105C2×D4×C103—21no—
106C2×D4×C103—41no—
107C2×D4×C103—41no—
108C2×D4×C103—44no—
109C2×D4×C103D411yescharacteristic
110C2×D4×C103C2311yescharacteristic
111C2×D4×C103C2311yescharacteristic
112C2×D4×C103C2311yescharacteristic
113C22×C4×C103—21no—
114C22×C4×C103C2311yescharacteristic
115C22×C4×C103C2311yescharacteristic
116C4⋊C4×C103D411yescharacteristic
117C4⋊C4×C103C2311yescharacteristic
118C22⋊C4×C103—21no—
119C22⋊C4×C103—21no—
120C22⋊C4×C103—21no—
121C22⋊C4×C103D411yescharacteristic
122C22⋊C4×C103D411yescharacteristic
123C42×C103C2311yescharacteristic
124C23×C103—21no—
125C23×C103—21no—
126C23×C103—21no—
127C23×C103—42no—
128C23×C103—42no—
129C23×C103—42no—
130C23×C103—42no—
131C23×C103—81no—
132C23×C103—81no—
133C23×C103C2×D411yescharacteristic
134C23×C103C2×D411yescharacteristic
135C22×D103—21no—
136D4×C103—22no—
137D4×C103—21no—
138D4×C103—21no—
139D4×C103—21no—
140D4×C103—21no—
141D4×C103—21no—
142D4×C103—42no—
143D4×C103—42no—
144D4×C103—42no—
145D4×C103—42no—
146D4×C103—42no—
147D4×C103—81no—
148D4×C103C2×D412yes—
149C2×C4×C103—21no—
150C2×C4×C103—21no—
151C2×C4×C103—21no—
152C2×C4×C103—21no—
153C2×C4×C103—21no—
154C2×C4×C103—42no—
155C2×C4×C103C2×D411yescharacteristic
156C2×C4×C103C2×D411yescharacteristic
157C2×C4×C103C2×D411yescharacteristic
158C2×C4×C103C2×D411yescharacteristic
159C2×C4×C103C2411yescharacteristic
160C22⋊D103—42no—
161C22⋊D103—42no—
162C2×Dic103—21no—
163C2×Dic103—21no—
164C2×Dic103—21no—
165C2×Dic103—42no—
166D412—21no—
167D412—21no—
168C4×D103—42no—
169Dic206—21no—
170Dic206—21no—
171Dic206—21no—
172Dic206—42no—
173Dic206C2×D412yescomplemented
174C103⋊C8—21no—
175C103⋊C8—21no—
176C103⋊C8—21no—
177C103⋊C8C2×D412yescomplemented
178C22×C103—21no—
179C22×C103—21no—
180C22×C103—21no—
181C22×C103—22no—
182C22×C103—21no—
183C22×C103—21no—
184C22×C103—41no—
185C22×C103—41no—
186C22×C103—41no—
187C22×C103—41no—
188C22×C103—41no—
189C22×C103—41no—
190C22×C103—41no—
191C22×C103—41no—
192C22×C103—84no—
193C22×C103—84no—
194C22×C103AGL(1,ℤ/8)12yescomplemented
195C22×C103C22×D411yescharacteristic
196C2×D103—41no—
197C2×D103—41no—
198C2×D103—41no—
199C4×C103—21no—
200C4×C103—21no—
201C4×C103—21no—
202C4×C103—21no—
203C4×C103—41no—
204C4×C103C22×D411yescharacteristic
205C4×C103H(5,𝔽2)11yescharacteristic
206Dic103—22no—
207Dic103—41no—
208Dic103—41no—
209C2×C103—22no—
210C2×C103—41no—
211C2×C103—42no—
212C2×C103—81no—
213C2×C103—81no—
214C2×C103D4211yescharacteristic
215C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C103#57711yescharacteristic
217D103—81no—
218#3265—1031nomaximal, Sylow
219C103#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1031no—
221C22×SD16—1031no—
222#548—1031no—
223D42D10311yescharacteristic, complemented
224#496—1031no—
225#468—1031no—
226#466—1031no—
227#463—1031no—
228#460—1031no—
229#450—1031no—
230#449—1031no—
231#448—1031no—
232#447—1031no—
233#440—1031no—
234#435—1031no—
235C2×#41—1031no—
236C22×Q8—1031no—
237C22×D4—21no—
238C22×D4C2×D10311yescharacteristic
239C22×D4C2×D10311yescharacteristic
240AGL(1,ℤ/8)—2064no—
241C2×SD16—1031no—
242C2×SD16—1031no—
243C2×SD16—1031no—
244C2×SD16—1031no—
245C2×SD16—1031no—
246C2×SD16—1031no—
247C2×SD16—2064no—
248C2×D8—1031no—
249C2×D8—1031no—
250C2×D8—1031no—
251C2×M16—1031no—
252C22×C8—1031no—
253#127C2×D10311yescharacteristic
254#124—1031no—
255#124—2061no—
256C22⋊Q8—1031no—
257C22⋊Q8—2061no—
258#121—21no—
259#121—1031no—
260#121—2061no—
261#121C2×D10311yescharacteristic
262#121C2×D10311yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—1031no—
266C4×D4—2061no—
267C4×D4C2×D10311yescharacteristic
268C4×D4C2×D10311yescharacteristic
269#107—1031no—
270C4⋊C8—1031no—
271#103—1031no—
272#103—1031no—
273#102—1031no—
274#102—1031no—
275#102—1031no—
276#102—1031no—
277C22⋊C8—1031no—
278C22⋊C8—1031no—
279#97—1031no—
280C24—21no—
281C24—21no—
282#41—4121no—
283#41—2062no—
284C2×Q8—1031no—
285C2×Q8—1031no—
286C2×Q8—4121no—
287C2×Q8—2062no—
288C2×Q8—2061no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—1031no—
301C2×D4—2061no—
302C2×D4—2061no—
303C2×D4C22⋊D10311yescharacteristic
304C2×D4C22×D10311yescharacteristic
305C2×D4C22×D10311yescharacteristic
306C2×D4C22×D10311yescharacteristic
307C22×C4—21no—
308C22×C4—2061no—
309C22×C4—2061no—
310C22×C4C22×D10311yescharacteristic
311C22×C4C22×D10311yescharacteristic
312SD16—1034no—
313SD16—4121no—
314SD16—2062no—
315SD16—2062no—
316SD16—2062no—
317SD16—2062no—
318D8—4121no—
319D8—2062no—
320D8—2062no—
321M16—2062no—
322C2×C8—1031no—
323C2×C8—1031no—
324C2×C8—1031no—
325C2×C8—1031no—
326C2×C8—2062no—
327C4⋊C4—1031no—
328C4⋊C4—2061no—
329C4⋊C4—2061no—
330C4⋊C4C22⋊D10311yescharacteristic
331C4⋊C4C22×D10311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—2061no—
336C22⋊C4—2061no—
337C22⋊C4—2061no—
338C22⋊C4—2061no—
339C22⋊C4C22⋊D10311yescharacteristic
340C22⋊C4C22⋊D10311yescharacteristic
341C42—2061no—
342C42C22×D10311yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—2061no—
353C23C2×C22⋊D10311yescharacteristic
354C23C2×C22⋊D10311yescharacteristic
355Q8—1032no—
356Q8—4122no—
357Q8—2061no—
358Q8—2061no—
359Q8—2061no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—4122no—
373D4—4122no—
374D4—2061no—
375D4—2061no—
376D4D4×D10312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—4122no—
384C2×C4—4122no—
385C2×C4—2061no—
386C2×C4—2061no—
387C2×C4—2061no—
388C2×C4C2×C22⋊D10311yescharacteristic
389C2×C4C2×C22⋊D10311yescharacteristic
390C2×C4C2×C22⋊D10311yescharacteristic
391C2×C4C2×C22⋊D10311yescharacteristic
392C2×C4C23×D10311yescharacteristic
393C8—1032no—
394C8—2061no—
395C8—2061no—
396C8—2061no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—4121no—
414C22—4121no—
415C22—4121no—
416C22#1569304712yescomplemented
417C22C22×C22⋊D10311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—4121no—
424C4—4121no—
425C4—2062no—
426C4C2×D4×D10311yescharacteristic
427C4#1569306611yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—8241no—
434C2D4×C22⋊D10311yescharacteristic
435C2C2×#1569304711yescharacteristic
436C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingD42×C103C2
socleC22×C103C22×D4
hypercenterD42D103
hypocenterC103#3265
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#15693047C2semidirect
2. C22×#13110093C2semidirect
3. #20268450C2semidirect
4. #20268178C2semidirect
5. #20268035C2semidirect
6. #20268025C2semidirect
7. #20268006C2semidirect
8. #20267988C2semidirect
9. #20267942C2semidirect
10. #20267934C2semidirect
11. #20267929C2semidirect
12. #20267925C2semidirect
13. #20267891C2semidirect
14. #20267863C2semidirect
15. D42×C103C2semidirect
16. C2×#13110105C22semidirect
17. C22×Dic206C22semidirect
22. C2×#13110093C22semidirect
23. C2×#13110093C22semidirect
24. C2×#13110093C22semidirect
25. C2×#13110093C22semidirect
27. C2×#13110090C22semidirect
28. C2×#13110090C22semidirect
29. C2×#13110089C22semidirect
30. C22×C103⋊C8C22semidirect
31. #15693009C22semidirect
33. #15693000C22semidirect
35. #15692995C22semidirect
37. C4×Dic206C22semidirect
39. #15692954C22semidirect
40. C4⋊(C103⋊C8)C22semidirect
41. #15692944C22semidirect
42. #15692944C22semidirect
44. #15692942C22semidirect
45. #15692942C22semidirect
46. #15692941C22semidirect
47. C22⋊(C103⋊C8)C22semidirect
48. C22⋊(C103⋊C8)C22semidirect
49. #15692932C22semidirect
78. #13110093D4semidirect
173. Dic206C2×D4semidirect
177. C103⋊C8C2×D4semidirect
194. C22×C103AGL(1,ℤ/8)semidirect
219. C103#3265semidirect
223. D42D103semidirect
416. C22#15693047semidirect

Maximal subgroups

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

subgroupindex
C2×#156930472
C22×#131100932
#202684502
#202681782
#202680352
#202680252
#202680062
#202679882
#202679422
#202679342
#202679292
#202679252
#202678912
#202678632
D42×C1032
#3265103