Finite Group Databasebeta

← #16831301

Subgroups — #16831301

Order 3712.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271814C211yesmaximal, characteristic, complemented
2D4×C22⋊D29C211yesmaximal, characteristic, complemented
3#14271508C211yesmaximal, characteristic, complemented
4#14271476C211yesmaximal, characteristic, complemented
5#14271475C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271399C211yesmaximal, characteristic, complemented
8#14271398C211yesmaximal, characteristic, complemented
9#14271357C211yesmaximal, characteristic, complemented
10#14271298C211yesmaximal, characteristic, complemented
11#14271297C211yesmaximal, characteristic, complemented
12#14271243C211yesmaximal, characteristic, complemented
13C8×C22⋊D29C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C2×C29×#102C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C22×C22⋊D29—21no—
18C2×D4×D29C2211yescharacteristic
19C2×#90805—21no—
20C22×C8×C29C2211yescharacteristic, complemented
21C2×C4⋊C4×C29C2211yescharacteristic, complemented
22#11745315—21no—
23#11745302C2211yescharacteristic
24#11745301—21no—
25#11745300C2211yescharacteristic
26#11745299—21no—
27D4×Dic29C2211yescharacteristic
28C2×#90782C2211yescharacteristic
29C2×#90782C2211yescharacteristic, complemented
30#11745292C2211yescharacteristic
31#11745292C2211yescharacteristic, complemented
32#11745291—21no—
33C4×C22⋊D29C2211yescharacteristic
34C2×D232C2211yescharacteristic, complemented
35C2×C8×D29C2211yescharacteristic, complemented
36#11745258—21no—
37#11745257C2211yescharacteristic, complemented
38#11745256—21no—
39#11745255C2211yescharacteristic, complemented
40C4⋊C4×D29C2211yescharacteristic, complemented
41#11745250C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic
43C29×#102C2211yescharacteristic
44C29×#102C2211yescharacteristic, complemented
45C29×#102C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic, complemented
48C22⋊#6597C2211yescharacteristic, complemented
49#11745169C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic, complemented
51#11745168C2211yescharacteristic, complemented
52#11745166C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54C8×Dic29C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C24×C29—21no—
60C23×D29—21no—
61C2×D4×C29—22no—
62C2×D4×C29—21no—
63C2×D4×C29—41no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29—21no—
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—21no—
74C2×C22⋊D29—44no—
75C2×C22⋊D29D411yescharacteristic
76C22×Dic29—21no—
77D4×D29—22no—
78D4×D29—41no—
79#90805—44no—
80C2×D116—21no—
81C2×D116C2311yescharacteristic
82C2×D116C2311yescharacteristic
83C2×C4×D29—21no—
84C2×C4×D29—21no—
85C2×C4×D29C2311yescharacteristic
86C2×Dic58—21no—
87C2×C8×C29—41no—
88C2×C8×C29C2311yescharacteristic
89C2×C8×C29C2311yescharacteristic
90C4⋊C4×C29—21no—
91C4⋊C4×C29C2311yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C22⋊Dic29—21no—
94C22⋊Dic29—21no—
95C22⋊Dic29D411yescharacteristic
96#90782—22no—
97#90782—41no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781D411yescharacteristic
103C4⋊Dic29C2311yescharacteristic
104C4⋊Dic29C2311yescharacteristic
105#90779—21no—
106#90779—21no—
107#90779D411yescharacteristic
108C4×Dic29C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111D232—41no—
112C8×D29—41no—
113C23×C29—21no—
114C23×C29—21no—
115C23×C29—42no—
116C23×C29—42no—
117C23×C29—81no—
118C23×C29C2×D411yescharacteristic
119C22×D29—21no—
120C22×D29—21no—
121C22×D29—42no—
122C22×D29—42no—
123C22×D29—81no—
124C22×D29C2×D411yescharacteristic
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—21no—
128D4×C29—42no—
129D4×C29#4112yescomplemented
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—42no—
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2411yescharacteristic
137C22⋊D29—42no—
138C22⋊D29—42no—
139C22⋊D29—42no—
140C22⋊D29—42no—
141C22⋊D29—42no—
142C22⋊D29—81no—
143C22⋊D29D814yescomplemented
144C2×Dic29—21no—
145C2×Dic29—21no—
146C2×Dic29—42no—
147C2×Dic29C2×D411yescharacteristic
148C2×Dic29C2×D411yescharacteristic
149C2×Dic29C2×D411yescharacteristic
150D116—21no—
151D116—21no—
152D116—21no—
153D116—21no—
154D116—42no—
155C4×D29—21no—
156C4×D29—21no—
157C4×D29—42no—
158C4×D29—42no—
159Dic58—42no—
160C8×C29—21no—
161C8×C29—21no—
162#6597—21no—
163#6597—21no—
164#3294—291nomaximal, Sylow
165C22×C29—21no—
166C22×C29—21no—
167C22×C29—22no—
168C22×C29—41no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—84no—
174C22×C29C2×D812yes—
175C22×C29C22×D411yescharacteristic
176C2×D29—21no—
177C2×D29—21no—
178C2×D29—41no—
179C2×D29—41no—
180C2×D29—41no—
181C2×D29—41no—
182C2×D29—41no—
183C2×D29—41no—
184C2×D29—84no—
185C2×D29C2×D812yes—
186C4×C29—21no—
187C4×C29—41no—
188C4×C29—41no—
189C4×C29C2×#4111yescharacteristic
190C4×C29H(5,𝔽2)11yescharacteristic
191Dic29—21no—
192Dic29—21no—
193Dic29—41no—
194Dic29—41no—
195Dic29C2×D812yes—
196#547—291no—
197D42—291no—
198#486—291no—
199#480—291no—
200#480—291no—
201#474—291no—
202#466—291no—
203#466—291no—
204#459—291no—
205#447—291no—
206#447—291no—
207C4×D8—291no—
208C8×D4—291no—
209C2×#102—291no—
210C2×#102D2911yescharacteristic, complemented
211C2×C29—22no—
212C2×C29—42no—
213C2×C29—81no—
214C2×C29#54611yescharacteristic
215C2×C29C22×D811yescharacteristic
216C2×C29#57711yescharacteristic
217D29—22no—
218D29—81no—
219D29—81no—
220C2×#41—581no—
221C22×D4—291no—
222C22×D4—581no—
223C22×D4C2×D2911yescharacteristic
224C2×D8—291no—
225C2×D8—291no—
226C2×D8—291no—
227C22×C8—291no—
228C22×C8C2×D2911yescharacteristic, complemented
229C4⋊Q8—291no—
230#127—291no—
231#123—581no—
232#123—581no—
233C22⋊Q8—581no—
234#121—291no—
235#121—291no—
236#121—291no—
237#121—291no—
238#121—581no—
239#120—581no—
240#120—581no—
241C4×D4—291no—
242C4×D4—291no—
243C4×D4—291no—
244C2×C4⋊C4—291no—
245C2×C4⋊C4C2×D2911yescharacteristic, complemented
246#107—291no—
247#107—291no—
248#107—291no—
249C4⋊C8—291no—
250#102—291no—
251#102—291no—
252#102—291no—
253#102—291no—
254#102—291no—
255#102—291no—
256#102C2×D2911yescharacteristic
257#102C2×D2911yescharacteristic
258#102C2×D2911yescharacteristic, complemented
259#102C2×D2911yescharacteristic, complemented
260C22⋊C8—291no—
261C22⋊C8—291no—
262C4×C8—291no—
263C29#329411yescharacteristic, complemented, Sylow
264C24—21no—
265C24—581no—
266#41—1164no—
267C2×Q8—581no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—291no—
272C2×D4—291no—
273C2×D4—291no—
274C2×D4—581no—
275C2×D4—581no—
276C2×D4—581no—
277C2×D4—581no—
278C2×D4—582no—
279C2×D4—581no—
280C2×D4—581no—
281C2×D4—581no—
282C2×D4—1161no—
283C2×D4—1164no—
284C2×D4C22×D2911yescharacteristic
285C2×D4C22×D2911yescharacteristic
286C22×C4—21no—
287C22×C4—291no—
288C22×C4—581no—
289C22×C4—581no—
290C22×C4—581no—
291C22×C4C22×D2911yescharacteristic
292D8—582no—
293D8—1161no—
294D8—1161no—
295C2×C8—41no—
296C2×C8—291no—
297C2×C8—291no—
298C2×C8—1161no—
299C2×C8C22×D2911yescharacteristic
300C2×C8C22×D2911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—291no—
303C4⋊C4—291no—
304C4⋊C4—291no—
305C4⋊C4—581no—
306C4⋊C4—581no—
307C4⋊C4C22×D2911yescharacteristic
308C4⋊C4C22×D2911yescharacteristic
309C22⋊C4—291no—
310C22⋊C4—291no—
311C22⋊C4—581no—
312C22⋊C4—581no—
313C22⋊C4—581no—
314C22⋊C4—581no—
315C22⋊C4—581no—
316C22⋊C4—581no—
317C42—291no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—291no—
324C23—581no—
325C23—581no—
326C23—1162no—
327C23—1162no—
328C23—2321no—
329C23D4×D2911yescharacteristic
330Q8—1162no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—294no—
336D4—581no—
337D4—581no—
338D4—581no—
339D4—581no—
340D4—1162no—
341D4—1162no—
342D4—1162no—
343D4—1162no—
344D4—1162no—
345D4—1162no—
346D4—2321no—
347D4#9080512yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—291no—
354C2×C4—291no—
355C2×C4—291no—
356C2×C4—581no—
357C2×C4—581no—
358C2×C4—581no—
359C2×C4—581no—
360C2×C4—1162no—
361C2×C4—1162no—
362C2×C4—1162no—
363C2×C4D4×D2911yescharacteristic
364C2×C4C23×D2911yescharacteristic
365C8—21no—
366C8—21no—
367C8—581no—
368C8—581no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—292no—
379C22—581no—
380C22—581no—
381C22—1161no—
382C22—1161no—
383C22—1161no—
384C22—1161no—
385C22—1161no—
386C22—1161no—
387C22—2324no—
388C22D8×D2912yes—
389C22C2×D4×D2911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—292no—
394C4—581no—
395C4—581no—
396C4—1161no—
397C4—1161no—
398C4C2×#9080511yescharacteristic
399C4#1174535911yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—582no—
404C2—2321no—
405C2—2321no—
406C2#1427180311yescharacteristic
407C2C2×D8×D2911yescharacteristic
408C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC22×C29C22×D4
hypercenterC2×#102D29
hypocenterC29#3294
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14271814C2semidirect
2. D4×C22⋊D29C2semidirect
3. #14271508C2semidirect
4. #14271476C2semidirect
5. #14271475C2semidirect
6. #14271441C2semidirect
7. #14271399C2semidirect
8. #14271398C2semidirect
9. #14271357C2semidirect
10. #14271298C2semidirect
11. #14271297C2semidirect
12. #14271243C2semidirect
13. C8×C22⋊D29C2semidirect
14. #102×D29C2semidirect
15. C2×C29×#102C2semidirect
20. C22×C8×C29C22semidirect
21. C2×C4⋊C4×C29C22semidirect
29. C2×#90782C22semidirect
31. #11745292C22semidirect
34. C2×D232C22semidirect
35. C2×C8×D29C22semidirect
37. #11745257C22semidirect
39. #11745255C22semidirect
40. C4⋊C4×D29C22semidirect
41. #11745250C22semidirect
44. C29×#102C22semidirect
45. C29×#102C22semidirect
47. #11745180C22semidirect
48. C22⋊#6597C22semidirect
49. #11745169C22semidirect
50. #11745169C22semidirect
51. #11745168C22semidirect
52. #11745166C22semidirect
53. #11745162C22semidirect
54. C8×Dic29C22semidirect
55. #11745157C22semidirect
56. #11745157C22semidirect
57. #11745155C22semidirect
58. #11745155C22semidirect
129. D4×C29#41semidirect
143. C22⋊D29D8semidirect
210. C2×#102D29semidirect
228. C22×C8C2×D29semidirect
245. C2×C4⋊C4C2×D29semidirect
258. #102C2×D29semidirect
259. #102C2×D29semidirect
263. C29#3294semidirect
347. D4#90805semidirect

Maximal subgroups

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

subgroupindex
#142718142
D4×C22⋊D292
#142715082
#142714762
#142714752
#142714412
#142713992
#142713982
#142713572
#142712982
#142712972
#142712432
C8×C22⋊D292
#102×D292
C2×C29×#1022
#329429