Finite Group Databasebeta

← #16831103

Subgroups — #16831103

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×#11745294C211yesmaximal, characteristic, complemented
2C2×#11745273C211yesmaximal, characteristic, complemented
3#14271810C211yesmaximal, characteristic, complemented
4#14271807C211yesmaximal, characteristic, complemented
5#14271546C211yesmaximal, characteristic, complemented
6#14271408C211yesmaximal, characteristic, complemented
7#14271407C211yesmaximal, characteristic, complemented
8#14271377C211yesmaximal, characteristic, complemented
9#14271376C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271326C211yesmaximal, characteristic, complemented
12#14271295C211yesmaximal, characteristic, complemented
13#14271243C211yesmaximal, characteristic, complemented
14#14271238C211yesmaximal, characteristic, complemented
15C29×#447C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic, complemented
17C2×#90807C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic, complemented
19C2×#90805C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic
21C2×D8×C29C2211yescharacteristic
22C29×#121C2211yescharacteristic
23#11745315—21no—
24C2×C22⋊Dic29—21no—
25#11745301—21no—
26#11745300—21no—
27#11745300C2211yescharacteristic
28#11745299—21no—
29#11745298C2211yescharacteristic, complemented
30#11745298C2211yescharacteristic, complemented
31#11745297—21no—
32D4×Dic29C2211yescharacteristic, complemented
33C2×#90783C2211yescharacteristic, complemented
34C2×#90783C2211yescharacteristic, complemented
35C2×#90783C2211yescharacteristic, complemented
36#11745294—24no—
37C2×#90782C2211yescharacteristic
38C2×#90782C2211yescharacteristic
39C4×C22⋊D29C2211yescharacteristic
40#11745286C2211yescharacteristic, complemented
41C2×#90777C2211yescharacteristic, complemented
42#11745273—24no—
43C2×Dic116C2211yescharacteristic, complemented
44C2×#90773C2211yescharacteristic, complemented
45C2×#90772C2211yescharacteristic, complemented
46#11745259C2211yescharacteristic, complemented
47#11745255C2211yescharacteristic, complemented
48#11745245—21no—
49C22⋊C4×D29—21no—
50C29×#102C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×C22⋊C8C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745168C2211yescharacteristic, complemented
56#11745164C2211yescharacteristic, complemented
57#11745162C2211yescharacteristic, complemented
58C8×Dic29C2211yescharacteristic, complemented
59#11745158C2211yescharacteristic, complemented
60#11745155C2211yescharacteristic, complemented
61C24×C29—21no—
62C23×D29—21no—
63C2×D4×C29—22no—
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—41no—
67C2×D4×C29C2311yescharacteristic
68C2×D4×C29C2311yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C22×C4×C29C2311yescharacteristic
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29—21no—
75C2×C22⋊D29D411yescharacteristic
76C22×Dic29—21no—
77C22×Dic29—21no—
78#90807—22no—
79#90807—41no—
80D4×D29—22no—
81D4×D29—41no—
82#90805—22no—
83#90805—41no—
84C2×D116C2311yescharacteristic
85C2×C4×D29—21no—
86C2×C4×D29—21no—
87C2×C4×D29C2311yescharacteristic
88C2×Dic58C2311yescharacteristic
89C2×Dic58C2311yescharacteristic
90D8×C29—22no—
91D8×C29—41no—
92C2×C8×C29C2311yescharacteristic
93C2×C8×C29C2311yescharacteristic
94C4⋊C4×C29C2311yescharacteristic
95C22⋊C4×C29—21no—
96C22⋊Dic29—21no—
97C22⋊Dic29—21no—
98C22⋊Dic29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29D411yescharacteristic
104#90783—22no—
105#90783—22no—
106#90783—22no—
107#90782—22no—
108#90782D414yescomplemented
109#90781—21no—
110#90781—21no—
111#90781D411yescharacteristic
112C4⋊Dic29—21no—
113C4⋊Dic29C2311yescharacteristic
114#90779—21no—
115#90779D411yescharacteristic
116C4×Dic29C2311yescharacteristic
117#90777—22no—
118C2×#6597C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120Dic116—41no—
121#90773—22no—
122#90772—22no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—42no—
127C23×C29—42no—
128C23×C29—81no—
129C23×C29C2×D411yescharacteristic
130C22×D29—21no—
131C22×D29—42no—
132C22×D29—42no—
133C22×D29—81no—
134C22×D29C2×D411yescharacteristic
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—42no—
141D4×C29—81no—
142D4×C29C2×D412yes—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2411yescharacteristic
148C22⋊D29—41no—
149C22⋊D29—42no—
150C22⋊D29—42no—
151C22⋊D29—42no—
152C22⋊D29—81no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—21no—
156C2×Dic29—42no—
157C2×Dic29—81no—
158C2×Dic29C2×D411yescharacteristic
159C2×Dic29C2×D411yescharacteristic
160C2×Dic29C2×D411yescharacteristic
161D116—21no—
162D116C2×D412yes—
163C4×D29—21no—
164C4×D29—21no—
165C4×D29—42no—
166C4×D29—81no—
167Dic58—21no—
168Dic58—21no—
169Dic58—21no—
170Dic58—21no—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3273—291nomaximal, Sylow
176C22×C29—22no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—21no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—84no—
189C22×C29C22×D411yescharacteristic
190C2×D29—21no—
191C2×D29—22no—
192C2×D29—21no—
193C2×D29—21no—
194C2×D29—41no—
195C2×D29—41no—
196C2×D29—84no—
197C4×C29—21no—
198C4×C29—41no—
199C4×C29C22×D411yescharacteristic
200C4×C29H(5,𝔽2)11yescharacteristic
201Dic29—21no—
202Dic29—21no—
203Dic29—21no—
204Dic29—41no—
205Dic29—41no—
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#468—291no—
214#463—291no—
215#463—291no—
216#452—291no—
217#452—291no—
218#447—291no—
219#447D2911yescharacteristic, complemented
220C4×D8—291no—
221#436—291no—
222C2×C29—41no—
223C2×C29—42no—
224C2×C29—81no—
225C2×C29—81no—
226C2×C29D4211yescharacteristic
227C2×C29#57511yescharacteristic
228C2×C29#57611yescharacteristic
229D29—41no—
230D29—42no—
231C2×#41—291no—
232C2×#41—291no—
233C22×D4—291no—
234C22×D4C2×D2911yescharacteristic, complemented
235AGL(1,ℤ/8)—584no—
236AGL(1,ℤ/8)—584no—
237C2×Q16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16—291no—
241C2×SD16—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8C2×D2911yescharacteristic
245C2×D8C2×D2911yescharacteristic
246C2×M16—291no—
247C2×M16—291no—
248#124—291no—
249#124—291no—
250#123—581no—
251#123—581no—
252C22⋊Q8—291no—
253C22⋊Q8—291no—
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#107—291no—
266C4⋊C8—291no—
267#103—291no—
268#103—291no—
269#102—291no—
270#102—291no—
271#102C2×D2911yescharacteristic, complemented
272#102C2×D2911yescharacteristic, complemented
273C22⋊C8—291no—
274C22⋊C8C2×D2911yescharacteristic, complemented
275C4×C8—291no—
276C29#327311yescharacteristic, complemented, Sylow
277C24—21no—
278C24—581no—
279#41—582no—
280#41—582no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8—291no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—291no—
290C2×D4—291no—
291C2×D4—581no—
292C2×D4—582no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—1161no—
297C2×D4C22×D2911yescharacteristic
298C2×D4C22×D2911yescharacteristic
299C2×D4C22×D2911yescharacteristic
300C22×C4—291no—
301C22×C4—581no—
302C22×C4—581no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4C22×D2911yescharacteristic
306Q16—1161no—
307SD16—582no—
308SD16—582no—
309SD16—582no—
310SD16—582no—
311D8—22no—
312D8—41no—
313D8—294no—
314D8—582no—
315M16—582no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8C22×D2911yescharacteristic
320C2×C8C22×D2911yescharacteristic
321C4⋊C4—291no—
322C4⋊C4—291no—
323C4⋊C4—581no—
324C4⋊C4—581no—
325C4⋊C4C22×D2911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—291no—
328C22⋊C4—291no—
329C22⋊C4—581no—
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—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—291no—
346C23—581no—
347C23—1162no—
348C23—1162no—
349C23—2321no—
350C23D4×D2911yescharacteristic
351Q8—581no—
352Q8—581no—
353Q8—581no—
354Q8—581no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—21no—
360D4—42no—
361D4—81no—
362D4—292no—
363D4—581no—
364D4—1161no—
365D4—1162no—
366D4—1162no—
367D4—1162no—
368D4—2321no—
369D4D4×D2912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—291no—
374C2×C4—291no—
375C2×C4—291no—
376C2×C4—581no—
377C2×C4—581no—
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—21no—
389C8—292no—
390C8—581no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—581no—
405C22—582no—
406C22—581no—
407C22—581no—
408C22—1161no—
409C22—1161no—
410C22—2324no—
411C22C2×D4×D2911yescharacteristic
412C4—21no—
413C4—41no—
414C4—581no—
415C4—581no—
416C4—581no—
417C4—1161no—
418C4—1161no—
419C4—1161no—
420C4C2×D4×D2911yescharacteristic
421C4#1174535911yescharacteristic
422C2—41no—
423C2—42no—
424C2—81no—
425C2—81no—
426C2—1161no—
427C2—1162no—
428C2#1427179511yescharacteristic
429C2#1427195911yescharacteristic
430C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#447C2
socleC22×C29C22×D4
hypercenter#447D29
hypocenterC29#3273
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#11745294C2semidirect
2. C2×#11745273C2semidirect
3. #14271810C2semidirect
4. #14271807C2semidirect
5. #14271546C2semidirect
6. #14271408C2semidirect
7. #14271407C2semidirect
8. #14271377C2semidirect
9. #14271376C2semidirect
10. #14271327C2semidirect
11. #14271326C2semidirect
12. #14271295C2semidirect
13. #14271243C2semidirect
14. #14271238C2semidirect
15. C29×#447C2semidirect
16. C22×D4×C29C22semidirect
18. C2×D4×D29C22semidirect
29. #11745298C22semidirect
30. #11745298C22semidirect
32. D4×Dic29C22semidirect
33. C2×#90783C22semidirect
34. C2×#90783C22semidirect
35. C2×#90783C22semidirect
40. #11745286C22semidirect
41. C2×#90777C22semidirect
43. C2×Dic116C22semidirect
44. C2×#90773C22semidirect
45. C2×#90772C22semidirect
46. #11745259C22semidirect
47. #11745255C22semidirect
50. C29×#102C22semidirect
51. C29×#102C22semidirect
52. C29×C22⋊C8C22semidirect
53. #11745180C22semidirect
54. #11745169C22semidirect
55. #11745168C22semidirect
56. #11745164C22semidirect
57. #11745162C22semidirect
58. C8×Dic29C22semidirect
59. #11745158C22semidirect
60. #11745155C22semidirect
108. #90782D4semidirect
219. #447D29semidirect
234. C22×D4C2×D29semidirect
271. #102C2×D29semidirect
272. #102C2×D29semidirect
274. C22⋊C8C2×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×#117452942
C2×#117452732
#142718102
#142718072
#142715462
#142714082
#142714072
#142713772
#142713762
#142713272
#142713262
#142712952
#142712432
#142712382
C29×#4472
#327329