Finite Group Databasebeta

← D29×#485 #16829380

Subgroups — D29×#485 #16829380

Order 3712.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D29C211yesmaximal, characteristic
2#117×D29C211yesmaximal, characteristic
3#14271507C211yesmaximal, characteristic, complemented
4#14271506C211yesmaximal, characteristic, complemented
5#14271505C211yesmaximal, characteristic, complemented
6#14271504C211yesmaximal, characteristic, complemented
7#14271503C211yesmaximal, characteristic, complemented
8#14271502C211yesmaximal, characteristic, complemented
9#14271501C211yesmaximal, characteristic, complemented
10#107×D29C211yesmaximal, characteristic, complemented
11#106×D29C211yesmaximal, characteristic, complemented
12#103×D29C211yesmaximal, characteristic, complemented
13#103×D29C211yesmaximal, characteristic, complemented
14C22⋊C8×D29C211yesmaximal, characteristic
15C29×#485C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C22×C4×D29C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C29×#117C2211yescharacteristic
20#11745308C2211yescharacteristic
21#11745288C2211yescharacteristic
22#11745286C2211yescharacteristic
23C2×C8×D29C2211yescharacteristic
24C2×C8×D29C2211yescharacteristic
25#11745259C2211yescharacteristic
26#11745258—21no—
27#11745254C2211yescharacteristic
28#11745254C2211yescharacteristic
29C4⋊C4×D29—21no—
30C4⋊C4×D29C2211yescharacteristic
31C4⋊C4×D29C2211yescharacteristic
32C4⋊C4×D29C2211yescharacteristic
33C22⋊C4×D29—21no—
34C22⋊C4×D29—21no—
35#11745240—21no—
36#11745239—21no—
37#11745234—21no—
38C42×D29—21no—
39C29×#107C2211yescharacteristic, complemented
40C29×#106C2211yescharacteristic, complemented
41C29×#103C2211yescharacteristic, complemented
42C29×#103C2211yescharacteristic, complemented
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46C22⋊#6597C2211yescharacteristic
47#11745168C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745166C2211yescharacteristic, complemented
50#11745165C2211yescharacteristic, complemented
51#11745164C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745158C2211yescharacteristic, complemented
54#11745158C2211yescharacteristic, complemented
55#11745156C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29D411yescharacteristic
60C2×Q8×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C22×Dic29D411yescharacteristic
63Q8×D29—22no—
64Q8×D29—22no—
65C2×C4×D29—22no—
66C2×C4×D29—22no—
67C2×C4×D29—21no—
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29D411yescharacteristic
72C2×C4×D29D411yescharacteristic
73C2×C4×D29C2311yescharacteristic
74C2×C4×D29C2311yescharacteristic
75C2×Dic58—21no—
76C2×Dic58C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29—21no—
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C42×C29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C8×D29—22no—
107C8×D29—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29—22no—
110C22×D29—22no—
111C22×D29—22no—
112C22×D29C2×D411yescharacteristic
113C22×D29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C2×Dic29—22no—
125C2×Dic29—21no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C4×D29—22no—
132C4×D29—21no—
133C4×D29—21no—
134C4×D29—22no—
135C4×D29—42no—
136C4×D29—42no—
137C4×D29—42no—
138C4×D29—42no—
139C4×D29#4112yes—
140C4×D29#4112yes—
141Dic58—21no—
142Dic58—21no—
143Dic58—42no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597—21no—
148C2×#485—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29C22×D411yescharacteristic
153C2×D29—21no—
154C2×D29—21no—
155C2×D29—21no—
156C2×D29—44no—
157C2×D29#12312yes—
158C2×D29#13512yes—
159C2×D29#13712yes—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29—41no—
165C4×C29C2×#4111yescharacteristic
166C4×C29C2×#4111yescharacteristic
167Dic29—21no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29#12312yes—
173C2×C22⋊Q8—291no—
174C2×#117—291no—
175#485—291no—
176#485—291no—
177#485—291no—
178#485—291no—
179#485—291no—
180#485—291no—
181#485—291no—
182#485D2911yescharacteristic, direct product factor
183C2×#107—291no—
184C2×#106—291no—
185C2×#103—291no—
186C2×#103—291no—
187C2×C22⋊C8—291no—
188C2×C29—41no—
189C2×C29C2×#12311yescharacteristic
190C2×C29C2×#13511yescharacteristic
191C2×C29C2×#13711yescharacteristic
192D29—41no—
193D29#48514yesdirect product factor
194C22×Q8—291no—
195C23×C4—291no—
196C22×C8—291no—
197C22×C8—291no—
198C22⋊Q8—291no—
199C22⋊Q8—291no—
200C22⋊Q8—291no—
201C22⋊Q8—581no—
202C22⋊Q8—581no—
203C22⋊Q8C2×D2911yescharacteristic
204#117—291no—
205#117—291no—
206#117—291no—
207#117—581no—
208#117—581no—
209#117C2×D2911yescharacteristic
210C2×C4⋊C4—291no—
211C2×C4⋊C4—291no—
212C2×C4⋊C4—291no—
213C2×C4⋊C4—581no—
214C2×C22⋊C4—581no—
215C2×C22⋊C4—581no—
216C2×C42—581no—
217#107—291no—
218#107—291no—
219#107—291no—
220#107C2×D2911yescharacteristic, complemented
221#106—291no—
222#106—291no—
223#106—291no—
224#106C2×D2911yescharacteristic, complemented
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#103—291no—
231#103C2×D2911yescharacteristic, complemented
232#103C2×D2911yescharacteristic, complemented
233C22⋊C8—291no—
234C22⋊C8—291no—
235C22⋊C8—291no—
236C22⋊C8C2×D2911yescharacteristic
237C29C2×#48511yescharacteristic, complemented, Sylow
238C24—291no—
239C2×Q8—291no—
240C2×Q8—581no—
241C2×Q8—582no—
242C2×Q8—582no—
243C2×Q8C22×D2911yescharacteristic
244C22×C4—291no—
245C22×C4—291no—
246C22×C4—291no—
247C22×C4—291no—
248C22×C4—291no—
249C22×C4—582no—
250C22×C4—582no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4C22×D2911yescharacteristic
256C2×C8—291no—
257C2×C8—291no—
258C2×C8—582no—
259C2×C8—582no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—291no—
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4C22×D2911yescharacteristic
273C4⋊C4C22×D2911yescharacteristic
274C4⋊C4C22×D2911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—21no—
284C42—581no—
285C42—581no—
286C42—581no—
287C23—291no—
288C23—291no—
289C23—582no—
290C23—582no—
291C23—582no—
292C23D4×D2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—581no—
296Q8—581no—
297Q8—1162no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—291no—
305C2×C4—292no—
306C2×C4—292no—
307C2×C4—291no—
308C2×C4—582no—
309C2×C4—582no—
310C2×C4—582no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—1162no—
318C2×C4—1162no—
319C2×C4—1162no—
320C2×C4—1162no—
321C2×C4D4×D2911yescharacteristic
322C2×C4C23×D2911yescharacteristic
323C8—21no—
324C8—21no—
325C8—581no—
326C8—581no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—292no—
331C22—292no—
332C22—292no—
333C22—581no—
334C22—581no—
335C22—581no—
336C22—1164no—
337C22C2×D4×D2911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—292no—
344C4—581no—
345C4—1161no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4#41×D2911yescharacteristic
350C4#41×D2911yescharacteristic
351C2—41no—
352C2—294no—
353C2—1161no—
354C2#123×D2911yescharacteristic
355C2#135×D2911yescharacteristic
356C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#485C2
socleC22×C29C22×D4
prime radicalC23×D29D4
hypercenter#485D29
hypocenterC29C2×#485
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #14271507C2semidirect
4. #14271506C2semidirect
5. #14271505C2semidirect
6. #14271504C2semidirect
7. #14271503C2semidirect
8. #14271502C2semidirect
9. #14271501C2semidirect
10. #107×D29C2semidirect
11. #106×D29C2semidirect
12. #103×D29C2semidirect
13. #103×D29C2semidirect
15. C29×#485C2semidirect
39. C29×#107C22semidirect
40. C29×#106C22semidirect
41. C29×#103C22semidirect
42. C29×#103C22semidirect
44. #11745183C22semidirect
45. #11745183C22semidirect
49. #11745166C22semidirect
50. #11745165C22semidirect
51. #11745164C22semidirect
52. #11745164C22semidirect
53. #11745158C22semidirect
54. #11745158C22semidirect
55. #11745156C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. #11745155C22semidirect
182. #485D29direct (N × H)
193. D29#485direct (N × H)
220. #107C2×D29semidirect
224. #106C2×D29semidirect
231. #103C2×D29semidirect
232. #103C2×D29semidirect
237. C29C2×#485semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D292
#117×D292
#142715072
#142715062
#142715052
#142715042
#142715032
#142715022
#142715012
#107×D292
#106×D292
#103×D292
C22⋊C8×D292
C29×#4852
C2×#48529