Finite Group Databasebeta

← #16830984

Subgroups — #16830984

Order 3712.

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×#11745273C211yesmaximal, characteristic, complemented
2C22×#90773C211yesmaximal, characteristic, complemented
3#14271819C211yesmaximal, characteristic, complemented
4#14271797C211yesmaximal, characteristic, complemented
5#14271551C211yesmaximal, characteristic, complemented
6#14271410C211yesmaximal, characteristic, complemented
7#14271377C211yesmaximal, characteristic, complemented
8#14271362C211yesmaximal, characteristic, complemented
9#14271315C211yesmaximal, characteristic, complemented
10#14271309C211yesmaximal, characteristic, complemented
11#14271301C211yesmaximal, characteristic, complemented
12#14271296C211yesmaximal, characteristic, complemented
13#14271262C211yesmaximal, characteristic, complemented
14#14271234C211yesmaximal, characteristic, complemented
15C29×#466C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic, complemented
17C2×D4×D29—21no—
18C2×D4×D29C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C22×Dic58C2211yescharacteristic, complemented
21C2×D8×C29C2211yescharacteristic, complemented
22C22×C8×C29C2211yescharacteristic, complemented
23C29×#121C2211yescharacteristic
24C29×#121C2211yescharacteristic, complemented
25#11745302C2211yescharacteristic
26#11745301—21no—
27#11745299—21no—
28#11745298C2211yescharacteristic, complemented
29D4×Dic29—21no—
30C2×#90783C2211yescharacteristic, complemented
31C2×#90783C2211yescharacteristic, complemented
32C2×#90782C2211yescharacteristic
33C2×#90782C2211yescharacteristic, complemented
34C4×C22⋊D29C2211yescharacteristic
35#11745273—24no—
36C2×#90773—24no—
37C2×#90773C2211yescharacteristic
38C2×#90773C2211yescharacteristic
39C2×#90773C2211yescharacteristic, complemented
40C2×#90773C2211yescharacteristic, complemented
41C2×#90772C2211yescharacteristic, complemented
42#11745259C2211yescharacteristic, complemented
43#11745257C2211yescharacteristic
44#11745255C2211yescharacteristic
45#11745249C2211yescharacteristic, complemented
46#11745247—21no—
47#11745246—21no—
48#11745244—21no—
49#11745240—21no—
50C29×#107C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic, complemented
54#11745168C2211yescharacteristic, complemented
55#11745163C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745158C2211yescharacteristic, complemented
58#11745158C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic
60#11745157C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29D411yescharacteristic
73C22×Dic29—21no—
74C22×Dic29—21no—
75#90807—22no—
76#90807—41no—
77D4×D29—22no—
78D4×D29—41no—
79D4×D29—44no—
80C2×D116—22no—
81C2×D116—21no—
82C2×D116—21no—
83C2×D116—41no—
84C2×D116C2311yescharacteristic
85C2×D116C2311yescharacteristic
86C2×C4×D29—21no—
87C2×C4×D29C2311yescharacteristic
88C2×Dic58—22no—
89C2×Dic58—21no—
90C2×Dic58—41no—
91C2×Dic58C2311yescharacteristic
92C2×Dic58C2311yescharacteristic
93D8×C29—22no—
94C2×C8×C29—22no—
95C2×C8×C29C2311yescharacteristic
96C2×C8×C29C2311yescharacteristic
97C4⋊C4×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C22⋊C4×C29—21no—
100C22⋊C4×C29—21no—
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29D411yescharacteristic
104#90783—22no—
105#90783—41no—
106#90782—22no—
107#90782—41no—
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781D411yescharacteristic
112C4⋊Dic29—21no—
113#90779—21no—
114#90779D411yescharacteristic
115C4×Dic29—21no—
116C4×Dic29C2311yescharacteristic
117C2×#6597C2311yescharacteristic
118C2×#6597C2311yescharacteristic
119#90773—22no—
120#90773—22no—
121#90773—22no—
122#90773D414yescomplemented
123#90772—22no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29C2×D411yescharacteristic
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—42no—
130C22×D29—42no—
131C22×D29—42no—
132C22×D29—42no—
133C22×D29—81no—
134C22×D29—81no—
135C22×D29C2×D411yescharacteristic
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—42no—
141D4×C29—42no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2411yescharacteristic
148C22⋊D29—22no—
149C22⋊D29—42no—
150C22⋊D29—42no—
151C22⋊D29—42no—
152C22⋊D29—81no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—42no—
156C2×Dic29—42no—
157C2×Dic29C2×D411yescharacteristic
158C2×Dic29C2×D411yescharacteristic
159C2×Dic29C2×D411yescharacteristic
160D116—21no—
161D116—21no—
162D116—21no—
163D116—42no—
164D116—42no—
165D116C2×D412yes—
166C4×D29—21no—
167C4×D29—21no—
168C4×D29—42no—
169Dic58—21no—
170Dic58—21no—
171Dic58—21no—
172Dic58—42no—
173Dic58C2×D412yescomplemented
174C8×C29—21no—
175C8×C29C2×D412yescomplemented
176#6597—21no—
177#6597—21no—
178#3265—291nomaximal, Sylow
179C22×C29—21no—
180C22×C29—21no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29AGL(1,ℤ/8)12yescomplemented
188C22×C29C22×D411yescharacteristic
189C2×D29—21no—
190C2×D29—22no—
191C2×D29—21no—
192C2×D29—21no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—41no—
196C2×D29—41no—
197C2×D29—41no—
198C2×D29—84no—
199C2×D29—84no—
200C4×C29—21no—
201C4×C29—41no—
202C4×C29—41no—
203C4×C29C22×D411yescharacteristic
204C4×C29H(5,𝔽2)11yescharacteristic
205Dic29—22no—
206Dic29—21no—
207Dic29—21no—
208Dic29—21no—
209Dic29—41no—
210C2×AGL(1,ℤ/8)—291no—
211C22×SD16—291no—
212#548—291no—
213D42—291no—
214#496—291no—
215#468—291no—
216#466D2911yescharacteristic, complemented
217#463—291no—
218#460—291no—
219#450—291no—
220#449—291no—
221#448—291no—
222#447—291no—
223#440—291no—
224#435—291no—
225C2×C29—22no—
226C2×C29—81no—
227C2×C29—81no—
228C2×C29D4211yescharacteristic
229C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C29#57711yescharacteristic
231D29—41no—
232D29—42no—
233D29—81no—
234C2×#41—291no—
235C22×Q8—291no—
236C22×D4—291no—
237C22×D4—291no—
238C22×D4—581no—
239AGL(1,ℤ/8)—584no—
240C2×SD16—291no—
241C2×SD16—291no—
242C2×SD16—291no—
243C2×SD16—291no—
244C2×SD16—291no—
245C2×SD16—291no—
246C2×SD16—584no—
247C2×D8—291no—
248C2×D8—291no—
249C2×D8C2×D2911yescharacteristic, complemented
250C2×M16—291no—
251C22×C8C2×D2911yescharacteristic, complemented
252#127—291no—
253#124—291no—
254#124—581no—
255C22⋊Q8—291no—
256C22⋊Q8—581no—
257#121—291no—
258#121—581no—
259#121—581no—
260#121C2×D2911yescharacteristic
261#121C2×D2911yescharacteristic, complemented
262#120—581no—
263#120—581no—
264C4×Q8—291no—
265C4×D4—291no—
266C4×D4—291no—
267C4×D4—581no—
268#107C2×D2911yescharacteristic, complemented
269C4⋊C8—291no—
270#103—291no—
271#103—291no—
272#102—291no—
273#102—291no—
274#102C2×D2911yescharacteristic, complemented
275#102C2×D2911yescharacteristic, complemented
276C22⋊C8—291no—
277C22⋊C8—291no—
278#97—291no—
279C29#326511yescharacteristic, complemented, Sylow
280C24—581no—
281C24—581no—
282#41—582no—
283#41—1161no—
284C2×Q8—291no—
285C2×Q8—291no—
286C2×Q8—582no—
287C2×Q8—581no—
288C2×Q8—1161no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—291no—
292C2×D4—291no—
293C2×D4—291no—
294C2×D4—582no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4—581no—
299C2×D4—582no—
300C2×D4—581no—
301C2×D4—581no—
302C2×D4—1161no—
303C2×D4—1161no—
304C2×D4—1164no—
305C2×D4C22×D2911yescharacteristic
306C2×D4C22×D2911yescharacteristic
307C22×C4—291no—
308C22×C4—581no—
309C22×C4—581no—
310C22×C4—581no—
311C22×C4C22×D2911yescharacteristic
312SD16—294no—
313SD16—582no—
314SD16—582no—
315SD16—582no—
316SD16—582no—
317SD16—1161no—
318D8—22no—
319D8—582no—
320D8—1161no—
321M16—582no—
322C2×C8—22no—
323C2×C8—291no—
324C2×C8—291no—
325C2×C8C22×D2911yescharacteristic
326C2×C8C22×D2911yescharacteristic
327C4⋊C4—291no—
328C4⋊C4—581no—
329C4⋊C4—581no—
330C4⋊C4C22×D2911yescharacteristic
331C4⋊C4C22×D2911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—291no—
335C22⋊C4—291no—
336C22⋊C4—581no—
337C22⋊C4—581no—
338C22⋊C4—581no—
339C22⋊C4—581no—
340C22⋊C4—581no—
341C42—291no—
342C42—581no—
343C23—21no—
344C23—21no—
345C23—291no—
346C23—581no—
347C23—581no—
348C23—1162no—
349C23—1162no—
350C23—1162no—
351C23—1162no—
352C23—2321no—
353C23—2321no—
354C23D4×D2911yescharacteristic
355Q8—292no—
356Q8—581no—
357Q8—581no—
358Q8—581no—
359Q8—1162no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—292no—
367D4—582no—
368D4—581no—
369D4—581no—
370D4—581no—
371D4—1162no—
372D4—1162no—
373D4—1162no—
374D4—1162no—
375D4—1162no—
376D4—2321no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—291no—
382C2×C4—291no—
383C2×C4—291no—
384C2×C4—581no—
385C2×C4—581no—
386C2×C4—581no—
387C2×C4—581no—
388C2×C4—1162no—
389C2×C4—1162no—
390C2×C4—1162no—
391C2×C4D4×D2911yescharacteristic
392C2×C4C23×D2911yescharacteristic
393C8—21no—
394C8—581no—
395C8—581no—
396C8D4×D2912yescomplemented
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—581no—
406C22—582no—
407C22—581no—
408C22—581no—
409C22—1161no—
410C22—1161no—
411C22—1161no—
412C22—1161no—
413C22—1161no—
414C22—2324no—
415C22—2324no—
416C22#1174527312yescomplemented
417C22C2×D4×D2911yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—581no—
422C4—582no—
423C4—581no—
424C4—581no—
425C4—1161no—
426C4C2×D4×D2911yescharacteristic
427C4#1174536411yescharacteristic
428C2—22no—
429C2—81no—
430C2—81no—
431C2—1161no—
432C2—1162no—
433C2—2321no—
434C2#1427179711yescharacteristic
435C2C2×#1174527311yescharacteristic
436C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#466C2
socleC22×C29C22×D4
hypercenter#466D29
hypocenterC29#3265
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. C22×#90773C2semidirect
3. #14271819C2semidirect
4. #14271797C2semidirect
5. #14271551C2semidirect
6. #14271410C2semidirect
7. #14271377C2semidirect
8. #14271362C2semidirect
9. #14271315C2semidirect
10. #14271309C2semidirect
11. #14271301C2semidirect
12. #14271296C2semidirect
13. #14271262C2semidirect
14. #14271234C2semidirect
15. C29×#466C2semidirect
16. C2×#90807C22semidirect
20. C22×Dic58C22semidirect
21. C2×D8×C29C22semidirect
22. C22×C8×C29C22semidirect
24. C29×#121C22semidirect
28. #11745298C22semidirect
30. C2×#90783C22semidirect
31. C2×#90783C22semidirect
33. C2×#90782C22semidirect
39. C2×#90773C22semidirect
40. C2×#90773C22semidirect
41. C2×#90772C22semidirect
42. #11745259C22semidirect
45. #11745249C22semidirect
50. C29×#107C22semidirect
51. C29×#102C22semidirect
52. C29×#102C22semidirect
53. C22⋊#6597C22semidirect
54. #11745168C22semidirect
55. #11745163C22semidirect
56. #11745162C22semidirect
57. #11745158C22semidirect
58. #11745158C22semidirect
60. #11745157C22semidirect
122. #90773D4semidirect
173. Dic58C2×D4semidirect
175. C8×C29C2×D4semidirect
187. C22×C29AGL(1,ℤ/8)semidirect
216. #466D29semidirect
249. C2×D8C2×D29semidirect
251. C22×C8C2×D29semidirect
261. #121C2×D29semidirect
268. #107C2×D29semidirect
274. #102C2×D29semidirect
275. #102C2×D29semidirect
279. C29#3265semidirect
396. C8D4×D29semidirect
416. C22#11745273semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
C22×#907732
#142718192
#142717972
#142715512
#142714102
#142713772
#142713622
#142713152
#142713092
#142713012
#142712962
#142712622
#142712342
C29×#4662
#326529