Finite Group Databasebeta

← #16831105

Subgroups — #16831105

Order 3712.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745276C211yesmaximal, characteristic, complemented
2C2×#11745311C211yesmaximal, characteristic, complemented
3#14271832C211yesmaximal, characteristic, complemented
4#14271797C211yesmaximal, characteristic, complemented
5#14271538C211yesmaximal, characteristic, complemented
6#14271415C211yesmaximal, characteristic, complemented
7#14271414C211yesmaximal, characteristic, complemented
8#14271361C211yesmaximal, characteristic, complemented
9#14271357C211yesmaximal, characteristic, complemented
10#14271311C211yesmaximal, characteristic, complemented
11#14271299C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271248C211yesmaximal, characteristic, complemented
14#14271238C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic, complemented
17C2×#90809C2211yescharacteristic, complemented
18C2×D4×D29—21no—
19C2×D4×D29C2211yescharacteristic
20C22×D116C2211yescharacteristic
21C2×SD16×C29C2211yescharacteristic, complemented
22C2×D8×C29C2211yescharacteristic, complemented
23C29×#121C2211yescharacteristic
24#11745311—24no—
25Q8×Dic29C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic
27C2×#90784C2211yescharacteristic, complemented
28#11745302—21no—
29#11745302C2211yescharacteristic
30#11745302C2211yescharacteristic, complemented
31#11745300—21no—
32#11745300C2211yescharacteristic, complemented
33#11745299—21no—
34C2×#90782C2211yescharacteristic
35C2×#90782C2211yescharacteristic, complemented
36C2×#90782C2211yescharacteristic, complemented
37#11745292—21no—
38#11745292C2211yescharacteristic, complemented
39C4×C22⋊D29—21no—
40C4×C22⋊D29C2211yescharacteristic
41C2×#90777C2211yescharacteristic, complemented
42#11745276—24no—
43C2×D232C2211yescharacteristic
44C2×D232C2211yescharacteristic, complemented
45C2×#90772C2211yescharacteristic, complemented
46#11745257C2211yescharacteristic
47#11745255C2211yescharacteristic
48#11745246—21no—
49#11745244—21no—
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×C22⋊C8C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic
55#11745169C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic, complemented
57#11745162C2211yescharacteristic, complemented
58C8×Dic29C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic, complemented
60#11745156C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63#41×C29—22no—
64#41×C29—41no—
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29C2311yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C22×C4×C29—21no—
71C22×C4×C29C2311yescharacteristic
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C2×C22⋊D29—21no—
78C2×C22⋊D29—21no—
79C2×C22⋊D29D411yescharacteristic
80#90809—22no—
81#90809—41no—
82D4×D29—22no—
83D4×D29—41no—
84D4×D29—44no—
85C2×D116—22no—
86C2×D116—21no—
87C2×D116—21no—
88C2×D116—21no—
89C2×D116—41no—
90C2×D116C2311yescharacteristic
91C2×D116C2311yescharacteristic
92C2×D116C2311yescharacteristic
93C2×C4×D29—21no—
94C2×C4×D29—21no—
95C2×C4×D29C2311yescharacteristic
96SD16×C29—22no—
97D8×C29—41no—
98C2×C8×C29C2311yescharacteristic
99C2×C8×C29C2311yescharacteristic
100C4⋊C4×C29C2311yescharacteristic
101C22⋊C4×C29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29D411yescharacteristic
104#90784—22no—
105#90784D414yescomplemented
106#90782—22no—
107#90782—22no—
108#90782—22no—
109#90781—21no—
110#90781—21no—
111#90781—21no—
112#90781D411yescharacteristic
113C4⋊Dic29—21no—
114C4⋊Dic29C2311yescharacteristic
115#90779D411yescharacteristic
116C4×Dic29—21no—
117C4×Dic29C2311yescharacteristic
118#90777—22no—
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121D232—22no—
122D232—41no—
123#90772—22no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29C2×D411yescharacteristic
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—21no—
130C22×D29—42no—
131C22×D29—42no—
132C22×D29—42no—
133C22×D29—42no—
134C22×D29—81no—
135C22×D29—81no—
136C22×D29C2×D411yescharacteristic
137Q8×C29—21no—
138Q8×C29C2×D412yescomplemented
139D4×C29—21no—
140D4×C29—21no—
141D4×C29—21no—
142D4×C29—21no—
143D4×C29—42no—
144D4×C29—42no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—42no—
150C2×C4×C29C2×D411yescharacteristic
151C2×C4×C29C2411yescharacteristic
152C22⋊D29—22no—
153C22⋊D29—42no—
154C22⋊D29—42no—
155C22⋊D29—42no—
156C22⋊D29—81no—
157C22⋊D29—81no—
158C22⋊D29—81no—
159C22⋊D29—81no—
160C2×Dic29—21no—
161C2×Dic29C2×D411yescharacteristic
162C2×Dic29C2×D411yescharacteristic
163C2×Dic29C2×D411yescharacteristic
164D116—21no—
165D116—21no—
166D116—21no—
167D116—21no—
168D116—21no—
169D116—42no—
170D116—42no—
171D116—42no—
172D116C2×D412yes—
173C4×D29—21no—
174C4×D29—21no—
175C4×D29—42no—
176C4×D29—42no—
177C8×C29—21no—
178C8×C29—21no—
179#6597—21no—
180#6597C2×D412yescomplemented
181#3274—291nomaximal, Sylow
182C22×C29—21no—
183C22×C29—21no—
184C22×C29—21no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—41no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29C22×D411yescharacteristic
192C2×D29—21no—
193C2×D29—22no—
194C2×D29—21no—
195C2×D29—21no—
196C2×D29—41no—
197C2×D29—41no—
198C2×D29—41no—
199C2×D29—41no—
200C2×D29—41no—
201C2×D29—41no—
202C2×D29—41no—
203C2×D29—41no—
204C2×D29—84no—
205C2×D29—84no—
206C4×C29—22no—
207C4×C29—21no—
208C4×C29—41no—
209C4×C29C22×D411yescharacteristic
210C4×C29H(5,𝔽2)11yescharacteristic
211Dic29—21no—
212Dic29—21no—
213Dic29—41no—
214Dic29AGL(1,ℤ/8)12yescomplemented
215C2×AGL(1,ℤ/8)—291no—
216C2×AGL(1,ℤ/8)—291no—
217#550—291no—
218D42—291no—
219#493—291no—
220#469—291no—
221#469—291no—
222#460—291no—
223#459—291no—
224#449—291no—
225#449D2911yescharacteristic, complemented
226#447—291no—
227#447—291no—
228C4×SD16—291no—
229#436—291no—
230C2×C29—41no—
231C2×C29—81no—
232C2×C29—81no—
233C2×C29D4211yescharacteristic
234C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C29#57611yescharacteristic
236D29—41no—
237D29—42no—
238D29—81no—
239D29—81no—
240C2×#41—291no—
241C2×#41C2×D2911yescharacteristic, complemented
242C22×D4—291no—
243C22×D4—291no—
244C22×D4—581no—
245AGL(1,ℤ/8)—584no—
246AGL(1,ℤ/8)—584no—
247C2×SD16—291no—
248C2×SD16—291no—
249C2×SD16C2×D2911yescharacteristic, complemented
250C2×D8—291no—
251C2×D8—291no—
252C2×D8—291no—
253C2×D8—291no—
254C2×D8—291no—
255C2×D8C2×D2911yescharacteristic, complemented
256C2×M16—291no—
257C2×M16—291no—
258#127—291no—
259#127—291no—
260#127—581no—
261#121—291no—
262#121—291no—
263#121—291no—
264#121—581no—
265#121—581no—
266#121—581no—
267#121C2×D2911yescharacteristic
268#120—581no—
269#120—581no—
270C4×Q8—291no—
271C4×D4—291no—
272C4×D4—291no—
273C4×D4—581no—
274#106—291no—
275C4⋊C8—291no—
276#103C2×D2911yescharacteristic, complemented
277#102—291no—
278#102—291no—
279#102—291no—
280#102—291no—
281#102C2×D2911yescharacteristic, complemented
282C22⋊C8—291no—
283C22⋊C8C2×D2911yescharacteristic, complemented
284C4×C8—291no—
285C29#327411yescharacteristic, complemented, Sylow
286C24—581no—
287C24—581no—
288#41—22no—
289#41—41no—
290#41—582no—
291#41—1161no—
292C2×Q8C22×D2911yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—291no—
296C2×D4—291no—
297C2×D4—291no—
298C2×D4—291no—
299C2×D4—582no—
300C2×D4—581no—
301C2×D4—581no—
302C2×D4—581no—
303C2×D4—581no—
304C2×D4—581no—
305C2×D4—581no—
306C2×D4—581no—
307C2×D4—582no—
308C2×D4—581no—
309C2×D4—581no—
310C2×D4—581no—
311C2×D4—1161no—
312C2×D4—1161no—
313C2×D4—1164no—
314C2×D4C22×D2911yescharacteristic
315C2×D4C22×D2911yescharacteristic
316C22×C4—21no—
317C22×C4—291no—
318C22×C4—581no—
319C22×C4—581no—
320C22×C4C22×D2911yescharacteristic
321SD16—22no—
322SD16—294no—
323SD16—582no—
324D8—41no—
325D8—582no—
326D8—582no—
327D8—582no—
328D8—582no—
329D8—1161no—
330M16—582no—
331M16—582no—
332C2×C8—291no—
333C2×C8—291no—
334C2×C8C22×D2911yescharacteristic
335C2×C8C22×D2911yescharacteristic
336C4⋊C4—291no—
337C4⋊C4—291no—
338C4⋊C4—581no—
339C4⋊C4C22×D2911yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—291no—
342C22⋊C4—291no—
343C22⋊C4—581no—
344C22⋊C4—581no—
345C22⋊C4—581no—
346C22⋊C4—581no—
347C42—291no—
348C42—581no—
349C23—21no—
350C23—21no—
351C23—291no—
352C23—581no—
353C23—581no—
354C23—581no—
355C23—1162no—
356C23—1162no—
357C23—1162no—
358C23—1162no—
359C23—2321no—
360C23—2321no—
361C23D4×D2911yescharacteristic
362Q8—21no—
363Q8D4×D2912yescomplemented
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—42no—
369D4—42no—
370D4—292no—
371D4—582no—
372D4—581no—
373D4—581no—
374D4—581no—
375D4—581no—
376D4—581no—
377D4—1162no—
378D4—1162no—
379D4—1162no—
380D4—1162no—
381D4—1162no—
382D4—1162no—
383D4—2321no—
384D4—2321no—
385D4—2321no—
386D4—2321no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—291no—
393C2×C4—291no—
394C2×C4—291no—
395C2×C4—581no—
396C2×C4—581no—
397C2×C4—581no—
398C2×C4—1162no—
399C2×C4—1162no—
400C2×C4D4×D2911yescharacteristic
401C2×C4C23×D2911yescharacteristic
402C8—21no—
403C8—21no—
404C8—292no—
405C8—581no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—581no—
416C22—582no—
417C22—581no—
418C22—581no—
419C22—1161no—
420C22—1161no—
421C22—1161no—
422C22—1161no—
423C22—1161no—
424C22—1161no—
425C22—1161no—
426C22—1161no—
427C22—2324no—
428C22—2324no—
429C22C2×D4×D2911yescharacteristic
430C4—21no—
431C4—22no—
432C4—41no—
433C4—292no—
434C4—581no—
435C4—581no—
436C4—1161no—
437C4C2×D4×D2911yescharacteristic
438C4#1174535911yescharacteristic
439C2—41no—
440C2—81no—
441C2—81no—
442C2—1161no—
443C2—1162no—
444C2—2321no—
445C2—2321no—
446C2#1427179511yescharacteristic
447C2AGL(1,ℤ/8)×D2911yescharacteristic
448C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3274
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. C2×#11745311C2semidirect
3. #14271832C2semidirect
4. #14271797C2semidirect
5. #14271538C2semidirect
6. #14271415C2semidirect
7. #14271414C2semidirect
8. #14271361C2semidirect
9. #14271357C2semidirect
10. #14271311C2semidirect
11. #14271299C2semidirect
12. #14271295C2semidirect
13. #14271248C2semidirect
14. #14271238C2semidirect
15. C29×#449C2semidirect
16. C2×#41×C29C22semidirect
17. C2×#90809C22semidirect
21. C2×SD16×C29C22semidirect
22. C2×D8×C29C22semidirect
25. Q8×Dic29C22semidirect
27. C2×#90784C22semidirect
30. #11745302C22semidirect
32. #11745300C22semidirect
35. C2×#90782C22semidirect
36. C2×#90782C22semidirect
38. #11745292C22semidirect
41. C2×#90777C22semidirect
44. C2×D232C22semidirect
45. C2×#90772C22semidirect
50. C29×#103C22semidirect
51. C29×#102C22semidirect
52. C29×C22⋊C8C22semidirect
53. #11745180C22semidirect
55. #11745169C22semidirect
56. #11745168C22semidirect
57. #11745162C22semidirect
58. C8×Dic29C22semidirect
59. #11745157C22semidirect
60. #11745156C22semidirect
105. #90784D4semidirect
138. Q8×C29C2×D4semidirect
180. #6597C2×D4semidirect
214. Dic29AGL(1,ℤ/8)semidirect
225. #449D29semidirect
241. C2×#41C2×D29semidirect
249. C2×SD16C2×D29semidirect
255. C2×D8C2×D29semidirect
276. #103C2×D29semidirect
281. #102C2×D29semidirect
283. C22⋊C8C2×D29semidirect
285. C29#3274semidirect
363. Q8D4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
C2×#117453112
#142718322
#142717972
#142715382
#142714152
#142714142
#142713612
#142713572
#142713112
#142712992
#142712952
#142712482
#142712382
C29×#4492
#327429