Finite Group Databasebeta

← #16829589

Subgroups — #16829589

Order 3712.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271717C211yesmaximal, characteristic, complemented
2C4×D4×D29C211yesmaximal, characteristic
3#14271500C211yesmaximal, characteristic, complemented
4#14271497C211yesmaximal, characteristic, complemented
5#14271442C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271367C211yesmaximal, characteristic, complemented
8#14271366C211yesmaximal, characteristic, complemented
9#14271315C211yesmaximal, characteristic
10#14271312C211yesmaximal, characteristic
11#14271265C211yesmaximal, characteristic, complemented
12#14271263C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14#14271218C211yesmaximal, characteristic, complemented
15C29×#440C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C22×C4×D29—21no—
18C2×SD16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745308C2211yescharacteristic
22#11745306C2211yescharacteristic, complemented
23C2×#90784C2211yescharacteristic
24D4×Dic29C2211yescharacteristic
25C2×#90783C2211yescharacteristic
26C4×C22⋊D29—21no—
27C2×#90773C2211yescharacteristic
28#11745259C2211yescharacteristic
29#11745258—21no—
30#11745255C2211yescharacteristic
31C4⋊C4×D29C2211yescharacteristic
32#11745251—21no—
33#11745250C2211yescharacteristic, complemented
34#11745243—21no—
35C22⋊C4×D29—21no—
36C4×D116C2211yescharacteristic
37#11745234—21no—
38C42×D29C2211yescharacteristic
39C4×Dic58—21no—
40C4×Dic58C2211yescharacteristic, complemented
41C29×#107C2211yescharacteristic, complemented
42C29×#103C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic
44C29×#97C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745166C2211yescharacteristic, complemented
51#11745164C2211yescharacteristic, complemented
52#11745162C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54#11745158C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745155C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745151C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C22×Dic29—21no—
65D4×D29—22no—
66D4×D29—22no—
67C2×D116C2311yescharacteristic
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—44no—
72C2×C4×D29D411yescharacteristic
73C2×C4×D29D411yescharacteristic
74C2×C4×D29C2311yescharacteristic
75C2×Dic58—21no—
76C2×Dic58C2311yescharacteristic
77SD16×C29—22no—
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C4⋊C4×C29—21no—
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C42×C29—21no—
85C42×C29C2311yescharacteristic
86C22⋊Dic29—21no—
87#90784—22no—
88#90783—22no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102C4×Dic29—21no—
103C4×Dic29D411yescharacteristic
104C4×Dic29D411yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108#90773—22no—
109C23×C29—21no—
110C22×D29—24no—
111C22×D29—21no—
112C22×D29—42no—
113C22×D29—42no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29#4112yes—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—42no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—24no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—42no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134D116—21no—
135D116#4112yes—
136C4×D29—22no—
137C4×D29—21no—
138C4×D29—21no—
139C4×D29—22no—
140C4×D29—42no—
141C4×D29—42no—
142C4×D29—42no—
143Dic58—21no—
144Dic58—21no—
145Dic58—42no—
146C8×C29—21no—
147C8×C29—21no—
148#6597—21no—
149#6597—21no—
150#3110—291nomaximal, Sylow
151C22×C29—22no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29C22×D411yescharacteristic
155C2×D29—21no—
156C2×D29—21no—
157C2×D29—22no—
158C2×D29—48no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29#13712yes—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29C2×#4111yescharacteristic
168C4×C29C2×#4111yescharacteristic
169Dic29—21no—
170Dic29—21no—
171Dic29—41no—
172Dic29—41no—
173Dic29—41no—
174Dic29AGL(1,ℤ/8)12yes—
175#533—291no—
176C2×C4×D4—291no—
177#484—291no—
178#484—291no—
179#474—291no—
180#474—291no—
181#461—291no—
182#461—291no—
183#450—291no—
184#450—291no—
185#440—291no—
186#440—291no—
187#440—291no—
188#440D2911yescharacteristic, complemented
189#432—291no—
190C2×C29—42no—
191C2×C29#52511yescharacteristic
192C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C29C2×#13711yescharacteristic
194D29—22no—
195D29—42no—
196C22×D4—291no—
197C23×C4—581no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×SD16—291no—
201C2×SD16C2×D2911yescharacteristic
202C4⋊Q8—291no—
203C4⋊Q8—291no—
204#125—581no—
205C22⋊Q8—291no—
206C22⋊Q8—291no—
207C22⋊Q8—581no—
208C4×Q8—291no—
209C4×Q8—581no—
210C4×Q8C2×D2911yescharacteristic, complemented
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—581no—
215C4×D4—581no—
216C4×D4C2×D2911yescharacteristic
217#117—581no—
218C2×C4⋊C4—291no—
219C2×C22⋊C4—581no—
220C2×C42—291no—
221#107—291no—
222#107—291no—
223#107—291no—
224#107C2×D2911yescharacteristic, complemented
225C4⋊C8—291no—
226C4⋊C8—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#103C2×D2911yescharacteristic, complemented
231#102—291no—
232#102—291no—
233#102—291no—
234#102C2×D2911yescharacteristic
235C22⋊C8—291no—
236C22⋊C8—291no—
237#97—291no—
238#97C2×D2911yescharacteristic, complemented
239C29#311011yescharacteristic, complemented, Sylow
240C24—581no—
241C2×Q8—291no—
242C2×Q8—581no—
243C2×Q8C22×D2911yescharacteristic
244C2×D4—291no—
245C2×D4—581no—
246C2×D4—582no—
247C2×D4—582no—
248C2×D4C22×D2911yescharacteristic
249C22×C4—21no—
250C22×C4—291no—
251C22×C4—291no—
252C22×C4—291no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—1164no—
258SD16—22no—
259SD16—582no—
260SD16—582no—
261SD16—582no—
262C2×C8—291no—
263C2×C8—291no—
264C2×C8C22×D2911yescharacteristic
265C2×C8C22×D2911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4C22×D2911yescharacteristic
277C4⋊C4C22×D2911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C42—21no—
285C42—291no—
286C42—291no—
287C42—291no—
288C42—581no—
289C42C22×D2911yescharacteristic
290C23—21no—
291C23—291no—
292C23—584no—
293C23—581no—
294C23—1162no—
295C23—1162no—
296Q8—21no—
297Q8—21no—
298Q8—581no—
299Q8—581no—
300Q8—1162no—
301D4—21no—
302D4—292no—
303D4—584no—
304D4—581no—
305D4#9080512yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—291no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—582no—
314C2×C4—582no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—1162no—
321C2×C4—1162no—
322C2×C4—1162no—
323C2×C4—1162no—
324C2×C4D4×D2911yescharacteristic
325C2×C4D4×D2911yescharacteristic
326C2×C4C23×D2911yescharacteristic
327C8—21no—
328C8—21no—
329C8—581no—
330C8—581no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—292no—
335C22—581no—
336C22—581no—
337C22—582no—
338C22—1168no—
339C22—1161no—
340C22—1161no—
341C22C2×D4×D2911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—292no—
348C4—581no—
349C4—581no—
350C4—1161no—
351C4—1161no—
352C4—1161no—
353C4C2×#9080511yescharacteristic
354C4#41×D2911yescharacteristic
355C2—42no—
356C2—582no—
357C2—1162no—
358C2#1427167211yescharacteristic
359C2AGL(1,ℤ/8)×D2911yescharacteristic
360C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#440C2
socleC22×C29C22×D4
prime radicalC2×D4×D29C22
hypercenter#440D29
hypocenterC29#3110
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14271717C2semidirect
3. #14271500C2semidirect
4. #14271497C2semidirect
5. #14271442C2semidirect
6. #14271441C2semidirect
7. #14271367C2semidirect
8. #14271366C2semidirect
11. #14271265C2semidirect
12. #14271263C2semidirect
13. #14271261C2semidirect
14. #14271218C2semidirect
15. C29×#440C2semidirect
19. C4×Q8×C29C22semidirect
22. #11745306C22semidirect
33. #11745250C22semidirect
40. C4×Dic58C22semidirect
41. C29×#107C22semidirect
42. C29×#103C22semidirect
44. C29×#97C22semidirect
45. #11745183C22semidirect
50. #11745166C22semidirect
51. #11745164C22semidirect
52. #11745162C22semidirect
53. #11745162C22semidirect
54. #11745158C22semidirect
56. #11745155C22semidirect
57. #11745155C22semidirect
58. #11745151C22semidirect
188. #440D29semidirect
210. C4×Q8C2×D29semidirect
224. #107C2×D29semidirect
230. #103C2×D29semidirect
238. #97C2×D29semidirect
239. C29#3110semidirect

Maximal subgroups

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

subgroupindex
#142717172
C4×D4×D292
#142715002
#142714972
#142714422
#142714412
#142713672
#142713662
#142713152
#142713122
#142712652
#142712632
#142712612
#142712182
C29×#4402
#311029