Finite Group Databasebeta

← #27206639

Subgroups — #27206639

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×#15693048C211yesmaximal, characteristic, complemented
2#20268452C211yesmaximal, characteristic, complemented
3D4×C22⋊D103C211yesmaximal, characteristic, complemented
4#20268177C211yesmaximal, characteristic, complemented
5#20268034C211yesmaximal, characteristic, complemented
6#20268027C211yesmaximal, characteristic, complemented
7#20268008C211yesmaximal, characteristic, complemented
8#20267989C211yesmaximal, characteristic, complemented
9#20267940C211yesmaximal, characteristic, complemented
10#20267935C211yesmaximal, characteristic, complemented
11#20267930C211yesmaximal, characteristic, complemented
12#20267925C211yesmaximal, characteristic, complemented
13#20267892C211yesmaximal, characteristic, complemented
14#20267862C211yesmaximal, characteristic, complemented
15C22×SD16×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic, complemented
17C22×C22⋊D103—21no—
18C2×D4×D103C2211yescharacteristic
19#15693048—24no—
20C2×#13110092C2211yescharacteristic, complemented
21C2×#13110092C2211yescharacteristic, complemented
22C2×D824C2211yescharacteristic, complemented
23C2×#13110090C2211yescharacteristic
24C2×#13110090C2211yescharacteristic, complemented
25C2×#13110088C2211yescharacteristic, complemented
26#15693017C2211yescharacteristic
27#15693010—21no—
28#15693010C2211yescharacteristic, complemented
29#15692997—21no—
30#15692997C2211yescharacteristic, complemented
31#15692995—21no—
32#15692995C2211yescharacteristic
33#15692995C2211yescharacteristic, complemented
34#15692993—21no—
35#15692992C2211yescharacteristic
36#15692990—21no—
37#15692989—21no—
38Q8×Dic103C2211yescharacteristic, complemented
39D4×Dic103C2211yescharacteristic
40C4×C22⋊D103—21no—
41C4×C22⋊D103C2211yescharacteristic
42#15692955C2211yescharacteristic, complemented
43Dic103⋊C8C2211yescharacteristic, complemented
44#15692945C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692943C2211yescharacteristic, complemented
47#15692943C2211yescharacteristic, complemented
48#15692942C2211yescharacteristic
49#15692942C2211yescharacteristic, complemented
50C22⋊(C103⋊C8)C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic, complemented
52#15692931C2211yescharacteristic, complemented
53C22×Q8×C103C2211yescharacteristic, complemented
54C22×D4×C103C2211yescharacteristic
55C2×SD16×C103—24no—
56C2×SD16×C103C2211yescharacteristic
57C2×SD16×C103C2211yescharacteristic
58C2×SD16×C103C2211yescharacteristic, complemented
59C2×SD16×C103C2211yescharacteristic, complemented
60C22×C8×C103C2211yescharacteristic, complemented
61C23×D103—21no—
62#13110106—22no—
63#13110106—41no—
64C2×D412—21no—
65C2×D412C2311yescharacteristic
66C2×D412C2311yescharacteristic
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C22⋊D103—21no—
73C2×C22⋊D103—44no—
74C2×C22⋊D103D411yescharacteristic
75D4×D103—22no—
76D4×D103—41no—
77C22×Dic103—21no—
78C2×C4×D103—21no—
79C2×C4×D103C2311yescharacteristic
80#13110092—22no—
81#13110092—41no—
82D824—22no—
83#13110090—22no—
84#13110090—41no—
85#13110088—22no—
86C2×C103⋊C8C2311yescharacteristic
87C2×C103⋊C8C2311yescharacteristic
88C4⋊Dic103—21no—
89C4⋊Dic103C2311yescharacteristic
90C4⋊Dic103C2311yescharacteristic
91Dic103⋊C4—21no—
92Dic103⋊C4D411yescharacteristic
93C22⋊Dic103—21no—
94C22⋊Dic103—21no—
95C22⋊Dic103D411yescharacteristic
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99(C2×D103)⋊C4—21no—
100(C2×D103)⋊C4—21no—
101(C2×D103)⋊C4D411yescharacteristic
102C4×Dic103—21no—
103C4×Dic103C2311yescharacteristic
104C24×C103—21no—
105C2×Q8×C103—21no—
106C2×Q8×C103—22no—
107C2×Q8×C103—41no—
108C2×Q8×C103C2311yescharacteristic
109C2×Q8×C103C2311yescharacteristic
110C2×D4×C103—22no—
111C2×D4×C103—21no—
112C2×D4×C103—41no—
113C2×D4×C103C2311yescharacteristic
114C2×D4×C103C2311yescharacteristic
115C22×C4×C103—21no—
116C22×C4×C103C2311yescharacteristic
117SD16×C103—22no—
118SD16×C103—22no—
119SD16×C103—22no—
120SD16×C103D414yescomplemented
121C2×C8×C103—22no—
122C2×C8×C103C2311yescharacteristic
123C2×C8×C103C2311yescharacteristic
124C23×C103—21no—
125C23×C103—21no—
126C23×C103—42no—
127C23×C103—42no—
128C23×C103—81no—
129C23×C103C2×D411yescharacteristic
130C22×D103—21no—
131C22×D103—21no—
132C22×D103—42no—
133C22×D103—42no—
134C22×D103—81no—
135C22×D103C2×D411yescharacteristic
136Q8×C103—21no—
137Q8×C103—21no—
138Q8×C103—21no—
139Q8×C103—42no—
140Q8×C103C2×D412yescomplemented
141D4×C103—21no—
142D4×C103—21no—
143D4×C103—21no—
144D4×C103—42no—
145D4×C103C2×D412yes—
146C2×C4×C103—21no—
147C2×C4×C103—21no—
148C2×C4×C103—21no—
149C2×C4×C103—21no—
150C2×C4×C103—42no—
151C2×C4×C103C2×D411yescharacteristic
152C2×C4×C103C2411yescharacteristic
153C22⋊D103—22no—
154C22⋊D103—42no—
155C22⋊D103—42no—
156C22⋊D103—42no—
157C22⋊D103—42no—
158C22⋊D103—42no—
159C22⋊D103—81no—
160C2×Dic103—21no—
161C2×Dic103—21no—
162C2×Dic103—42no—
163C2×Dic103C2×D411yescharacteristic
164C2×Dic103C2×D411yescharacteristic
165C2×Dic103C2×D411yescharacteristic
166D412—21no—
167D412—21no—
168D412—21no—
169D412—21no—
170D412—42no—
171C4×D103—21no—
172C4×D103—21no—
173C4×D103—42no—
174C8×C103—21no—
175C8×C103C2×D412yescomplemented
176C103⋊C8—21no—
177C103⋊C8—21no—
178C22×C103—21no—
179C22×C103—21no—
180C22×C103—22no—
181C22×C103—41no—
182C22×C103—41no—
183C22×C103—41no—
184C22×C103—41no—
185C22×C103—41no—
186C22×C103—84no—
187C22×C103AGL(1,ℤ/8)12yescomplemented
188C22×C103C22×D411yescharacteristic
189C2×D103—21no—
190C2×D103—21no—
191C2×D103—21no—
192C2×D103—41no—
193C2×D103—41no—
194C2×D103—41no—
195C2×D103—41no—
196C2×D103—41no—
197C2×D103—41no—
198C2×D103—84no—
199C4×C103—22no—
200C4×C103—21no—
201C4×C103—41no—
202C4×C103C22×D411yescharacteristic
203C4×C103H(5,𝔽2)11yescharacteristic
204Dic103—21no—
205Dic103—21no—
206Dic103—21no—
207Dic103—41no—
208Dic103—41no—
209C2×C103—22no—
210C2×C103—42no—
211C2×C103—81no—
212C2×C103D4211yescharacteristic
213C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C103#57711yescharacteristic
215D103—41no—
216D103—81no—
217D103—81no—
218#3265—1031nomaximal, Sylow
219C103#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1031no—
221C22×SD16D10311yescharacteristic, complemented
222#548—1031no—
223D42—1031no—
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×Q8C2×D10311yescharacteristic, complemented
237C22×D4—1031no—
238C22×D4—2061no—
239C22×D4C2×D10311yescharacteristic
240AGL(1,ℤ/8)—2064no—
241C2×SD16—24no—
242C2×SD16—1031no—
243C2×SD16—1031no—
244C2×SD16C2×D10311yescharacteristic
245C2×SD16C2×D10311yescharacteristic
246C2×SD16C2×D10311yescharacteristic, complemented
247C2×SD16C2×D10311yescharacteristic, complemented
248C2×D8—1031no—
249C2×D8—1031no—
250C2×D8—1031no—
251C2×M16—1031no—
252C22×C8C2×D10311yescharacteristic, complemented
253#127—1031no—
254#124—1031no—
255#124—2061no—
256C22⋊Q8—1031no—
257C22⋊Q8—2061no—
258#121—1031no—
259#121—1031no—
260#121—1031no—
261#121—2061no—
262#121—2061no—
263#120—2061no—
264#120—2061no—
265C4×Q8—1031no—
266C4×D4—1031no—
267C4×D4—1031no—
268C4×D4—2061no—
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—2061no—
282#41—4121no—
283#41—2062no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D10311yescharacteristic
288C2×Q8C22×D10311yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—1031no—
293C2×D4—1031no—
294C2×D4—1031no—
295C2×D4—4124no—
296C2×D4—4121no—
297C2×D4—2061no—
298C2×D4—2061no—
299C2×D4—2061no—
300C2×D4—2061no—
301C2×D4—2061no—
302C2×D4—2061no—
303C2×D4—2061no—
304C2×D4—2062no—
305C2×D4C22×D10311yescharacteristic
306C2×D4C22×D10311yescharacteristic
307C22×C4—21no—
308C22×C4—1031no—
309C22×C4—2061no—
310C22×C4—2061no—
311C22×C4C22×D10311yescharacteristic
312SD16—22no—
313SD16—22no—
314SD16—22no—
315SD16—4121no—
316SD16—2062no—
317SD16C22⋊D10314yescomplemented
318D8—4121no—
319D8—2062no—
320D8—2062no—
321M16—2062no—
322C2×C8—22no—
323C2×C8—1031no—
324C2×C8—1031no—
325C2×C8C22×D10311yescharacteristic
326C2×C8C22×D10311yescharacteristic
327C4⋊C4—1031no—
328C4⋊C4—1031no—
329C4⋊C4—1031no—
330C4⋊C4—2061no—
331C4⋊C4—2061no—
332C22⋊C4—1031no—
333C22⋊C4—1031no—
334C22⋊C4—2061no—
335C22⋊C4—2061no—
336C22⋊C4—2061no—
337C22⋊C4—2061no—
338C22⋊C4—2061no—
339C22⋊C4—2061no—
340C22⋊C4—2061no—
341C42—1031no—
342C42—2061no—
343C23—21no—
344C23—21no—
345C23—42no—
346C23—42no—
347C23—81no—
348C23—8241no—
349C23—1031no—
350C23—4122no—
351C23—4122no—
352C23—2061no—
353C23—2061no—
354C23D4×D10311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8C2×C22⋊D10312yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—8241no—
365D4—4122no—
366D4—4122no—
367D4—4122no—
368D4—4122no—
369D4—4122no—
370D4—4122no—
371D4—2062no—
372D4—2061no—
373D4—2061no—
374D4—2061no—
375D4—2061no—
376D4C2×C22⋊D10312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—1031no—
383C2×C4—1031no—
384C2×C4—1031no—
385C2×C4—4122no—
386C2×C4—4122no—
387C2×C4—2061no—
388C2×C4—2061no—
389C2×C4—2061no—
390C2×C4—2061no—
391C2×C4D4×D10311yescharacteristic
392C2×C4C23×D10311yescharacteristic
393C8—21no—
394C8—2061no—
395C8—2061no—
396C8C2×C22⋊D10312yescomplemented
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—84no—
406C22—8244no—
407C22—4121no—
408C22—4121no—
409C22—4121no—
410C22—4121no—
411C22—4121no—
412C22—4121no—
413C22—2061no—
414C22—2061no—
415C22—2061no—
416C22#1569304812yescomplemented
417C22C2×D4×D10311yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—4121no—
422C4—4121no—
423C4—2061no—
424C4—2061no—
425C4—2061no—
426C4C22×C22⋊D10311yescharacteristic
427C4#1569306611yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—8241no—
432C2—8241no—
433C2—4121no—
434C2D4×C22⋊D10311yescharacteristic
435C2C2×#1569304811yescharacteristic
436C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×SD16×C103C2
socleC22×C103C22×D4
hypercenterC22×SD16D103
hypocenterC103#3265
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15693048C2semidirect
2. #20268452C2semidirect
3. D4×C22⋊D103C2semidirect
4. #20268177C2semidirect
5. #20268034C2semidirect
6. #20268027C2semidirect
7. #20268008C2semidirect
8. #20267989C2semidirect
9. #20267940C2semidirect
10. #20267935C2semidirect
11. #20267930C2semidirect
12. #20267925C2semidirect
13. #20267892C2semidirect
14. #20267862C2semidirect
15. C22×SD16×C103C2semidirect
16. C2×#13110106C22semidirect
20. C2×#13110092C22semidirect
21. C2×#13110092C22semidirect
22. C2×D824C22semidirect
24. C2×#13110090C22semidirect
25. C2×#13110088C22semidirect
28. #15693010C22semidirect
30. #15692997C22semidirect
33. #15692995C22semidirect
38. Q8×Dic103C22semidirect
42. #15692955C22semidirect
43. Dic103⋊C8C22semidirect
44. #15692945C22semidirect
45. #15692945C22semidirect
46. #15692943C22semidirect
47. #15692943C22semidirect
49. #15692942C22semidirect
50. C22⋊(C103⋊C8)C22semidirect
51. (C2×D103)⋊C8C22semidirect
52. #15692931C22semidirect
53. C22×Q8×C103C22semidirect
58. C2×SD16×C103C22semidirect
59. C2×SD16×C103C22semidirect
60. C22×C8×C103C22semidirect
120. SD16×C103D4semidirect
140. Q8×C103C2×D4semidirect
175. C8×C103C2×D4semidirect
187. C22×C103AGL(1,ℤ/8)semidirect
219. C103#3265semidirect
221. C22×SD16D103semidirect
236. C22×Q8C2×D103semidirect
246. C2×SD16C2×D103semidirect
247. C2×SD16C2×D103semidirect
252. C22×C8C2×D103semidirect
317. SD16C22⋊D103semidirect
359. Q8C2×C22⋊D103semidirect
396. C8C2×C22⋊D103semidirect
416. C22#15693048semidirect

Maximal subgroups

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

subgroupindex
C2×#156930482
#202684522
D4×C22⋊D1032
#202681772
#202680342
#202680272
#202680082
#202679892
#202679402
#202679352
#202679302
#202679252
#202678922
#202678622
C22×SD16×C1032
#3265103