Finite Group Databasebeta

← #16831100

Subgroups — #16831100

Order 3712.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745270C211yesmaximal, characteristic, complemented
2C2×#11745276C211yesmaximal, characteristic, complemented
3#14271810C211yesmaximal, characteristic, complemented
4#14271804C211yesmaximal, characteristic, complemented
5#14271544C211yesmaximal, characteristic, complemented
6#14271410C211yesmaximal, characteristic, complemented
7#14271381C211yesmaximal, characteristic, complemented
8#14271377C211yesmaximal, characteristic, complemented
9#14271328C211yesmaximal, characteristic, complemented
10#14271323C211yesmaximal, characteristic, complemented
11#14271298C211yesmaximal, characteristic, complemented
12#14271296C211yesmaximal, characteristic, complemented
13#14271245C211yesmaximal, characteristic, complemented
14#14271239C211yesmaximal, characteristic, complemented
15C29×#468C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic, complemented
18C2×#90805C2211yescharacteristic
19C22×D116C2211yescharacteristic, complemented
20C2×SD16×C29C2211yescharacteristic, complemented
21C2×M16×C29C2211yescharacteristic, complemented
22C29×C22⋊Q8C2211yescharacteristic, complemented
23C29×#121C2211yescharacteristic
24#11745309C2211yescharacteristic, complemented
25C2×#90785C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic, complemented
27#11745300—21no—
28#11745299—21no—
29#11745298C2211yescharacteristic, complemented
30C2×#90782C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C4×C22⋊D29C2211yescharacteristic
33#11745276—24no—
34#11745270—24no—
35C2×D232C2211yescharacteristic
36C2×D232C2211yescharacteristic
37C2×#90773C2211yescharacteristic, complemented
38C2×#90773C2211yescharacteristic, complemented
39C2×#90772C2211yescharacteristic, complemented
40#11745259C2211yescharacteristic, complemented
41#11745257—21no—
42#11745257C2211yescharacteristic
43#11745256—21no—
44#11745255C2211yescharacteristic, complemented
45#11745255C2211yescharacteristic, complemented
46#11745245—21no—
47#11745244—21no—
48C22⋊C4×D29—21no—
49C22⋊C4×D29—21no—
50C29×#107C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic, complemented
54#11745168C2211yescharacteristic, complemented
55#11745162C2211yescharacteristic, complemented
56C8×Dic29C2211yescharacteristic, complemented
57#11745158C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic, complemented
60#11745157C2211yescharacteristic, complemented
61C23×D29—21no—
62C23×D29—21no—
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29D411yescharacteristic
70#90809—22no—
71#90809—41no—
72D4×D29—22no—
73D4×D29—41no—
74#90805—22no—
75#90805—41no—
76C2×D116—22no—
77C2×D116—21no—
78C2×D116—21no—
79C2×D116—21no—
80C2×D116—41no—
81C2×D116C2311yescharacteristic
82C2×D116C2311yescharacteristic
83C2×D116C2311yescharacteristic
84C2×C4×D29—21no—
85C2×C4×D29—21no—
86C2×C4×D29—21no—
87C2×C4×D29—21no—
88C2×C4×D29C2311yescharacteristic
89C2×Dic58C2311yescharacteristic
90SD16×C29—22no—
91M16×C29—22no—
92C2×C8×C29C2311yescharacteristic
93C2×C8×C29C2311yescharacteristic
94C4⋊C4×C29—21no—
95C4⋊C4×C29C2311yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C22⋊C4×C29—21no—
98C22⋊C4×C29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29D411yescharacteristic
102#90785—41no—
103#90784—22no—
104#90782—22no—
105#90782—41no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781—21no—
112#90781D411yescharacteristic
113C4⋊Dic29—21no—
114#90779D411yescharacteristic
115C4×Dic29C2311yescharacteristic
116C2×#6597C2311yescharacteristic
117C2×#6597C2311yescharacteristic
118D232—22no—
119D232D414yescomplemented
120#90773—22no—
121#90773—22no—
122#90772—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—42no—
131C22×D29—42no—
132C22×D29—81no—
133C22×D29—81no—
134C22×D29C2×D411yescharacteristic
135Q8×C29—21no—
136Q8×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—81no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2411yescharacteristic
147C22⋊D29—41no—
148C22⋊D29—42no—
149C22⋊D29—42no—
150C2×Dic29—21no—
151C2×Dic29C2×D411yescharacteristic
152C2×Dic29C2×D411yescharacteristic
153C2×Dic29C2×D411yescharacteristic
154D116—21no—
155D116—21no—
156D116—21no—
157D116—21no—
158D116—42no—
159D116—42no—
160D116—81no—
161D116C2×D412yes—
162D116C2×D412yes—
163C4×D29—21no—
164C4×D29—21no—
165C4×D29—42no—
166C4×D29—42no—
167C4×D29—81no—
168C4×D29—81no—
169Dic58—21no—
170Dic58—21no—
171C8×C29—21no—
172C8×C29C2×D412yes—
173#6597—21no—
174#6597—21no—
175#3273—291nomaximal, Sylow
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29C22×D411yescharacteristic
183C2×D29—21no—
184C2×D29—22no—
185C2×D29—22no—
186C2×D29—21no—
187C2×D29—21no—
188C2×D29—41no—
189C2×D29—41no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C2×D29—84no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29—41no—
201C4×C29C22×D411yescharacteristic
202C4×C29H(5,𝔽2)11yescharacteristic
203Dic29—21no—
204Dic29—21no—
205Dic29—21no—
206Dic29—41no—
207C2×AGL(1,ℤ/8)—291no—
208C2×AGL(1,ℤ/8)—291no—
209#546—291no—
210#546—291no—
211#495—291no—
212#468—291no—
213#468D2911yescharacteristic, complemented
214#463—291no—
215#463—291no—
216#452—291no—
217#452—291no—
218#447—291no—
219#447—291no—
220C4×D8—291no—
221#436—291no—
222C2×C29—41no—
223C2×C29—81no—
224C2×C29D4211yescharacteristic
225C2×C29#57511yescharacteristic
226C2×C29#57611yescharacteristic
227D29—41no—
228D29—42no—
229D29—42no—
230D29—81no—
231C2×#41—291no—
232C2×#41—291no—
233C22×D4—291no—
234C22×D4—291no—
235AGL(1,ℤ/8)—584no—
236AGL(1,ℤ/8)—584no—
237C2×Q16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16—291no—
241C2×SD16C2×D2911yescharacteristic, complemented
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×D8—291no—
246C2×M16—291no—
247C2×M16C2×D2911yescharacteristic, complemented
248#124—291no—
249#124—291no—
250#123—581no—
251#123—581no—
252C22⋊Q8—291no—
253C22⋊Q8C2×D2911yescharacteristic, complemented
254#121—291no—
255#121—581no—
256#121—581no—
257#121C2×D2911yescharacteristic
258#120—581no—
259#120—581no—
260C4×D4—291no—
261C4×D4—291no—
262C4×D4—291no—
263C2×C22⋊C4—581no—
264C2×C22⋊C4—581no—
265#107C2×D2911yescharacteristic, complemented
266C4⋊C8—291no—
267#103—291no—
268#103C2×D2911yescharacteristic, complemented
269#102—291no—
270#102—291no—
271#102—291no—
272#102C2×D2911yescharacteristic, complemented
273C22⋊C8—291no—
274C22⋊C8—291no—
275C4×C8—291no—
276C29#327311yescharacteristic, complemented, Sylow
277C24—581no—
278C24—581no—
279#41—582no—
280#41—582no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8C22×D2911yescharacteristic
285C2×D4—21no—
286C2×D4—291no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—291no—
290C2×D4—582no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—582no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—1161no—
298C2×D4—1161no—
299C2×D4C22×D2911yescharacteristic
300C22×C4—291no—
301C22×C4—581no—
302C22×C4—581no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4C22×D2911yescharacteristic
306Q16—1161no—
307SD16—22no—
308SD16—582no—
309SD16—582no—
310SD16—582no—
311D8—294no—
312D8—582no—
313D8—582no—
314D8—1161no—
315M16—22no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8C22×D2911yescharacteristic
320C2×C8C22×D2911yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—291no—
323C4⋊C4—581no—
324C4⋊C4C22×D2911yescharacteristic
325C4⋊C4C22×D2911yescharacteristic
326C22⋊C4—21no—
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—
336C22⋊C4—581no—
337C22⋊C4—581no—
338C42—291no—
339C23—21no—
340C23—291no—
341C23—581no—
342C23—581no—
343C23—581no—
344C23—1162no—
345C23—1162no—
346C23—1162no—
347C23—1162no—
348C23—2321no—
349C23—2321no—
350C23D4×D2911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—581no—
354Q8—581no—
355D4—21no—
356D4—21no—
357D4—81no—
358D4—292no—
359D4—292no—
360D4—581no—
361D4—581no—
362D4—581no—
363D4—581no—
364D4—1162no—
365D4—1162no—
366D4—1161no—
367D4—1162no—
368D4—1162no—
369D4—2321no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—291no—
376C2×C4—291no—
377C2×C4—291no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4—2321no—
384C2×C4—2321no—
385C2×C4D4×D2911yescharacteristic
386C2×C4C23×D2911yescharacteristic
387C8—21no—
388C8—581no—
389C8—581no—
390C8D4×D2912yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—581no—
398C22—582no—
399C22—582no—
400C22—581no—
401C22—581no—
402C22—1161no—
403C22—1161no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—1161no—
409C22—2324no—
410C22—2324no—
411C22C2×D4×D2911yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—581no—
417C4—581no—
418C4—581no—
419C4—1161no—
420C4C2×D4×D2911yescharacteristic
421C4#1174536411yescharacteristic
422C2—41no—
423C2—81no—
424C2—1161no—
425C2—1162no—
426C2—1162no—
427C2—2321no—
428C2#1427179711yescharacteristic
429C2#1427196211yescharacteristic
430C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#468C2
socleC22×C29C22×D4
hypercenter#468D29
hypocenterC29#3273
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. C2×#11745276C2semidirect
3. #14271810C2semidirect
4. #14271804C2semidirect
5. #14271544C2semidirect
6. #14271410C2semidirect
7. #14271381C2semidirect
8. #14271377C2semidirect
9. #14271328C2semidirect
10. #14271323C2semidirect
11. #14271298C2semidirect
12. #14271296C2semidirect
13. #14271245C2semidirect
14. #14271239C2semidirect
15. C29×#468C2semidirect
17. C2×D4×D29C22semidirect
19. C22×D116C22semidirect
20. C2×SD16×C29C22semidirect
21. C2×M16×C29C22semidirect
22. C29×C22⋊Q8C22semidirect
24. #11745309C22semidirect
25. C2×#90785C22semidirect
26. C2×#90784C22semidirect
29. #11745298C22semidirect
37. C2×#90773C22semidirect
38. C2×#90773C22semidirect
39. C2×#90772C22semidirect
40. #11745259C22semidirect
44. #11745255C22semidirect
45. #11745255C22semidirect
50. C29×#107C22semidirect
51. C29×#103C22semidirect
52. C29×#102C22semidirect
53. C22⋊#6597C22semidirect
54. #11745168C22semidirect
55. #11745162C22semidirect
56. C8×Dic29C22semidirect
57. #11745158C22semidirect
58. #11745157C22semidirect
59. #11745157C22semidirect
60. #11745157C22semidirect
119. D232D4semidirect
213. #468D29semidirect
241. C2×SD16C2×D29semidirect
247. C2×M16C2×D29semidirect
253. C22⋊Q8C2×D29semidirect
265. #107C2×D29semidirect
268. #103C2×D29semidirect
272. #102C2×D29semidirect
276. C29#3273semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
C2×#117452762
#142718102
#142718042
#142715442
#142714102
#142713812
#142713772
#142713282
#142713232
#142712982
#142712962
#142712452
#142712392
C29×#4682
#327329