Finite Group Databasebeta

← #16831025

Subgroups — #16831025

Order 3712.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745276C211yesmaximal, characteristic, complemented
2C2×#11745312C211yesmaximal, characteristic, complemented
3#14271832C211yesmaximal, characteristic, complemented
4#14271810C211yesmaximal, characteristic, complemented
5#14271551C211yesmaximal, characteristic, complemented
6#14271408C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271383C211yesmaximal, characteristic, complemented
9#14271357C211yesmaximal, characteristic, complemented
10#14271328C211yesmaximal, characteristic, complemented
11#14271310C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271266C211yesmaximal, characteristic, complemented
14#14271231C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic, complemented
17C2×#90809C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C2×#90805C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic
21C2×D8×C29C2211yescharacteristic
22C29×#121C2211yescharacteristic
23#11745312—24no—
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90785C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic
27#11745302—21no—
28#11745302C2211yescharacteristic, complemented
29#11745300—21no—
30#11745300—21no—
31#11745300C2211yescharacteristic
32#11745299—21no—
33#11745298C2211yescharacteristic
34C2×#90783C2211yescharacteristic, complemented
35C2×#90782C2211yescharacteristic
36C2×#90782C2211yescharacteristic
37#11745292—21no—
38#11745292C2211yescharacteristic, complemented
39C4×C22⋊D29—21no—
40C4×C22⋊D29C2211yescharacteristic
41C22×#6597C2211yescharacteristic, complemented
42#11745276—24no—
43C2×D232C2211yescharacteristic
44C2×#90773C2211yescharacteristic, complemented
45C2×#90772C2211yescharacteristic
46#11745259C2211yescharacteristic
47#11745255C2211yescharacteristic
48#11745245—21no—
49C22⋊C4×D29—21no—
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×C22⋊C8C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745168C2211yescharacteristic
56#11745164C2211yescharacteristic, complemented
57#11745163C2211yescharacteristic, complemented
58#11745162C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic, complemented
60#11745155C2211yescharacteristic, complemented
61C23×D29—21no—
62#41×C29—22no—
63#41×C29—41no—
64C2×Q8×C29C2311yescharacteristic
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29C2311yescharacteristic
68C2×D4×C29C2311yescharacteristic
69C22×C4×C29—21no—
70C22×C4×C29C2311yescharacteristic
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C2×C22⋊D29D411yescharacteristic
78#90809—22no—
79#90809—41no—
80D4×D29—22no—
81D4×D29—41no—
82#90805—22no—
83#90805—41no—
84C2×D116—21no—
85C2×D116C2311yescharacteristic
86C2×D116C2311yescharacteristic
87C2×C4×D29—21no—
88C2×C4×D29—21no—
89C2×C4×D29—21no—
90C2×C4×D29C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92SD16×C29—22no—
93D8×C29—41no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C22⋊C4×C29—21no—
98C22⋊Dic29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29D411yescharacteristic
102#90785—22no—
103#90784D414yescomplemented
104#90783—22no—
105#90782—22no—
106#90782—22no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781D411yescharacteristic
111C4⋊Dic29—21no—
112C4⋊Dic29—21no—
113C4⋊Dic29C2311yescharacteristic
114#90779D411yescharacteristic
115C4×Dic29—21no—
116C4×Dic29C2311yescharacteristic
117C2×#6597—22no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120D232—22no—
121#90773—41no—
122#90772—22no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29C2×D411yescharacteristic
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—81no—
131C22×D29C2×D411yescharacteristic
132Q8×C29—21no—
133Q8×C29C2×D412yes—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—42no—
139D4×C29—81no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—42no—
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2411yescharacteristic
147C22⋊D29—41no—
148C22⋊D29—42no—
149C22⋊D29—42no—
150C22⋊D29—42no—
151C22⋊D29—81no—
152C22⋊D29—81no—
153C22⋊D29—81no—
154C2×Dic29—21no—
155C2×Dic29—21no—
156C2×Dic29C2×D411yescharacteristic
157C2×Dic29C2×D411yescharacteristic
158C2×Dic29C2×D411yescharacteristic
159D116—21no—
160D116—21no—
161D116—21no—
162D116—42no—
163D116C2×D412yes—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—42no—
167C4×D29—42no—
168C4×D29—81no—
169Dic58—21no—
170Dic58—21no—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3268—291nomaximal, Sylow
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29C22×D411yescharacteristic
186C2×D29—21no—
187C2×D29—22no—
188C2×D29—21no—
189C2×D29—21no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C4×C29—21no—
197C4×C29—22no—
198C4×C29—41no—
199C4×C29C22×D411yescharacteristic
200C4×C29H(5,𝔽2)11yescharacteristic
201Dic29—21no—
202Dic29—21no—
203Dic29—21no—
204Dic29—41no—
205Dic29—41no—
206C2×AGL(1,ℤ/8)—291no—
207C2×#135—291no—
208#550—291no—
209#546—291no—
210#496—291no—
211#468—291no—
212#466—291no—
213#464—291no—
214#459—291no—
215#452—291no—
216#449—291no—
217#449D2911yescharacteristic, complemented
218#447—291no—
219#440—291no—
220#435—291no—
221C2×C29—41no—
222C2×C29—81no—
223C2×C29—81no—
224C2×C29D4211yescharacteristic
225C2×C29#57511yescharacteristic
226C2×C29#57611yescharacteristic
227D29—41no—
228D29—42no—
229D29—81no—
230C2×#41—291no—
231C2×#41—291no—
232C2×#41C2×D2911yescharacteristic, complemented
233C22×D4—291no—
234AGL(1,ℤ/8)—584no—
235#135—584no—
236C2×Q16—291no—
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16C2×D2911yescharacteristic
241C2×D8—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8C2×D2911yescharacteristic
245C2×M16—291no—
246C22×C8—291no—
247#127—291no—
248#127—581no—
249#124—291no—
250#123—581no—
251C22⋊Q8—291no—
252#121—291no—
253#121—291no—
254#121—581no—
255#121—581no—
256#121—581no—
257#121C2×D2911yescharacteristic
258#120—581no—
259C4×Q8—291no—
260C4×D4—291no—
261C4×D4—291no—
262C4×D4—581no—
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8—291no—
266#103—291no—
267#103C2×D2911yescharacteristic, complemented
268#102—291no—
269#102—291no—
270#102—291no—
271#102C2×D2911yescharacteristic, complemented
272C22⋊C8—291no—
273C22⋊C8C2×D2911yescharacteristic, complemented
274#97—291no—
275C29#326811yescharacteristic, complemented, Sylow
276C24—581no—
277#41—22no—
278#41—41no—
279#41—582no—
280#41—582no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8C22×D2911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—291no—
290C2×D4—581no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—582no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4—1161no—
299C2×D4C22×D2911yescharacteristic
300C2×D4C22×D2911yescharacteristic
301C22×C4—21no—
302C22×C4—291no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4C22×D2911yescharacteristic
307Q16—582no—
308SD16—22no—
309SD16—294no—
310SD16—582no—
311SD16—1161no—
312D8—41no—
313D8—582no—
314D8—582no—
315D8—582no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—291no—
323C4⋊C4—291no—
324C4⋊C4—581no—
325C4⋊C4—581no—
326C4⋊C4C22×D2911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—291no—
329C22⋊C4—291no—
330C22⋊C4—581no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C42—291no—
337C42—581no—
338C23—21no—
339C23—21no—
340C23—291no—
341C23—581no—
342C23—581no—
343C23—1162no—
344C23—1162no—
345C23—2321no—
346C23D4×D2911yescharacteristic
347Q8—21no—
348Q8—581no—
349Q8—581no—
350Q8D4×D2912yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—42no—
356D4—81no—
357D4—292no—
358D4—581no—
359D4—581no—
360D4—581no—
361D4—1162no—
362D4—1161no—
363D4—1162no—
364D4—1162no—
365D4—1162no—
366D4—2321no—
367D4—2321no—
368D4—2321no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—291no—
375C2×C4—291no—
376C2×C4—291no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4—2321no—
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—21no—
388C8—292no—
389C8—581no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—581no—
400C22—582no—
401C22—581no—
402C22—581no—
403C22—1161no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—2324no—
409C22C2×D4×D2911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—581no—
414C4—581no—
415C4—581no—
416C4—1161no—
417C4—1161no—
418C4C2×D4×D2911yescharacteristic
419C4#1174535911yescharacteristic
420C2—41no—
421C2—81no—
422C2—81no—
423C2—1161no—
424C2—1162no—
425C2—2321no—
426C2#1427179511yescharacteristic
427C2#1427196011yescharacteristic
428C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3268
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×#11745312C2semidirect
3. #14271832C2semidirect
4. #14271810C2semidirect
5. #14271551C2semidirect
6. #14271408C2semidirect
7. #14271397C2semidirect
8. #14271383C2semidirect
9. #14271357C2semidirect
10. #14271328C2semidirect
11. #14271310C2semidirect
12. #14271295C2semidirect
13. #14271266C2semidirect
14. #14271231C2semidirect
15. C29×#449C2semidirect
16. C2×#41×C29C22semidirect
24. Q8×Dic29C22semidirect
25. C2×#90785C22semidirect
28. #11745302C22semidirect
34. C2×#90783C22semidirect
38. #11745292C22semidirect
41. C22×#6597C22semidirect
44. C2×#90773C22semidirect
50. C29×#103C22semidirect
51. C29×#102C22semidirect
52. C29×C22⋊C8C22semidirect
56. #11745164C22semidirect
57. #11745163C22semidirect
58. #11745162C22semidirect
59. #11745157C22semidirect
60. #11745155C22semidirect
103. #90784D4semidirect
217. #449D29semidirect
232. C2×#41C2×D29semidirect
267. #103C2×D29semidirect
271. #102C2×D29semidirect
273. C22⋊C8C2×D29semidirect
275. C29#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
C2×#117453122
#142718322
#142718102
#142715512
#142714082
#142713972
#142713832
#142713572
#142713282
#142713102
#142712952
#142712662
#142712312
C29×#4492
#326829