Finite Group Databasebeta

← #16831332

Subgroups — #16831332

Order 3712.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271854C211yesmaximal, characteristic, complemented
2#14271808C211yesmaximal, characteristic
3#14271518C211yesmaximal, characteristic, complemented
4#14271495C211yesmaximal, characteristic, complemented
5#14271489C211yesmaximal, characteristic, complemented
6#14271463C211yesmaximal, characteristic, complemented
7#14271403C211yesmaximal, characteristic, complemented
8#14271395C211yesmaximal, characteristic, complemented
9#14271385C211yesmaximal, characteristic, complemented
10#14271322C211yesmaximal, characteristic, complemented
11#14271312C211yesmaximal, characteristic, complemented
12C8×D116C211yesmaximal, characteristic, complemented
13#14271156C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C4×SD16×C29C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745308C2211yescharacteristic
22#11745308C2211yescharacteristic, complemented
23C2×#90785C2211yescharacteristic, complemented
24C2×#90784C2211yescharacteristic
25#11745292—21no—
26C2×#90781—21no—
27C2×C8×D29C2211yescharacteristic
28C2×C8×D29C2211yescharacteristic, complemented
29#11745259C2211yescharacteristic
30#11745257C2211yescharacteristic
31#11745256—21no—
32#11745254C2211yescharacteristic, complemented
33C4⋊C4×D29C2211yescharacteristic
34#11745251—21no—
35#11745248—21no—
36#11745244—21no—
37#11745238—21no—
38#11745237C2211yescharacteristic
39C4×D116C2211yescharacteristic
40#11745234—21no—
41#11745232C2211yescharacteristic, complemented
42C29×#106C2211yescharacteristic, complemented
43C29×#103C2211yescharacteristic, complemented
44C29×#102C2211yescharacteristic
45C4×C8×C29C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745164C2211yescharacteristic, complemented
54#11745158C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58C4⋊#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C22×Dic29—21no—
66#90807—22no—
67#90807—41no—
68D4×D29—22no—
69D4×D29—41no—
70C2×D116—21no—
71C2×D116D411yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29C2311yescharacteristic
75C2×C4×D29C2311yescharacteristic
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
86#90785—41no—
87#90784—41no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29D411yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C8×D29—41no—
110C8×D29—41no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29—42no—
114C22×D29—42no—
115C22×D29—81no—
116C22×D29C2×D411yescharacteristic
117C22×D29C2×D411yescharacteristic
118Q8×C29—21no—
119Q8×C29—21no—
120D4×C29—21no—
121D4×C29#4112yes—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—81no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2411yescharacteristic
129C22⋊D29—42no—
130C22⋊D29—42no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—42no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—22no—
138D116—21no—
139D116—21no—
140D116—81no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—21no—
144C4×D29—21no—
145C4×D29—42no—
146Dic58—21no—
147Dic58—21no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3296—291nomaximal, Sylow
153C22×C29—22no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—84no—
166C2×D29#13512yes—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29C2×#4111yescharacteristic
173C4×C29H(5,𝔽2)11yescharacteristic
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178Dic29—41no—
179#552—291no—
180#546—291no—
181#488—291no—
182#483—291no—
183#482—291no—
184#478—291no—
185#467—291no—
186#465—291no—
187#464—291no—
188#452—291no—
189#450—291no—
190C4×SD16D2911yescharacteristic, complemented
191C8×D4—291no—
192#416—291no—
193C2×#102—291no—
194C2×C29—42no—
195C2×C29#54611yescharacteristic
196C2×C29C2×#13511yescharacteristic
197C2×C29#57711yescharacteristic
198D29—22no—
199D29—41no—
200D29—81no—
201C2×#41—291no—
202C22×D4—291no—
203C2×Q16—291no—
204C2×SD16—291no—
205C2×SD16C2×D2911yescharacteristic
206C22×C8—291no—
207C22×C8—291no—
208#126—581no—
209#125—291no—
210#125—581no—
211#124—291no—
212#123—581no—
213#123—581no—
214C22⋊Q8—291no—
215C22⋊Q8—291no—
216C22⋊Q8—291no—
217#121—291no—
218#121—581no—
219#120—581no—
220C4×Q8C2×D2911yescharacteristic, complemented
221C4×D4—291no—
222C4×D4C2×D2911yescharacteristic
223#117—291no—
224#117—581no—
225C2×C4⋊C4—291no—
226C2×C22⋊C4—581no—
227#107—291no—
228#106—291no—
229#106C2×D2911yescharacteristic, complemented
230C4⋊C8—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103C2×D2911yescharacteristic, complemented
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102C2×D2911yescharacteristic
241C22⋊C8—291no—
242C22⋊C8—291no—
243C4×C8C2×D2911yescharacteristic, complemented
244C29#329611yescharacteristic, complemented, Sylow
245C24—581no—
246#41—582no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—581no—
253C2×D4—581no—
254C2×D4—582no—
255C2×D4—581no—
256C2×D4—1161no—
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—291no—
260C22×C4—291no—
261C22×C4—581no—
262C22×C4—581no—
263Q16—1161no—
264SD16—22no—
265SD16—1161no—
266C2×C8—291no—
267C2×C8—291no—
268C2×C8—1161no—
269C2×C8—1161no—
270C2×C8C22×D2911yescharacteristic
271C2×C8C22×D2911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—291no—
286C22⋊C4—291no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—21no—
295C42—581no—
296C42C22×D2911yescharacteristic
297C23—21no—
298C23—291no—
299C23—291no—
300C23—581no—
301C23—1162no—
302C23—1162no—
303C23—2321no—
304Q8—21no—
305Q8—21no—
306Q8—581no—
307Q8—581no—
308D4—21no—
309D4—582no—
310D4—581no—
311D4—581no—
312D4—1162no—
313D4—1162no—
314D4—2321no—
315D4#9080512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—581no—
329C2×C4—1162no—
330C2×C4—1162no—
331C2×C4D4×D2911yescharacteristic
332C2×C4D4×D2911yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—21no—
335C8—21no—
336C8—581no—
337C8—581no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—292no—
342C22—581no—
343C22—581no—
344C22—581no—
345C22—581no—
346C22—581no—
347C22—1161no—
348C22—1161no—
349C22—1161no—
350C22—2324no—
351C22C2×D4×D2911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—581no—
358C4—581no—
359C4—1161no—
360C4—1161no—
361C4—1161no—
362C4C2×#9080511yescharacteristic
363C4#1174536411yescharacteristic
364C2—42no—
365C2—582no—
366C2—1161no—
367C2—2321no—
368C2#1427180911yescharacteristic
369C2#135×D2911yescharacteristic
370C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC4×SD16×C29C2
socleC22×C29C22×D4
prime radical#14271808C2
hypercenterC4×SD16D29
hypocenterC29#3296
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14271854C2semidirect
3. #14271518C2semidirect
4. #14271495C2semidirect
5. #14271489C2semidirect
6. #14271463C2semidirect
7. #14271403C2semidirect
8. #14271395C2semidirect
9. #14271385C2semidirect
10. #14271322C2semidirect
11. #14271312C2semidirect
12. C8×D116C2semidirect
13. #14271156C2semidirect
14. #102×D29C2semidirect
15. C4×SD16×C29C2semidirect
19. C4×Q8×C29C22semidirect
22. #11745308C22semidirect
23. C2×#90785C22semidirect
28. C2×C8×D29C22semidirect
32. #11745254C22semidirect
41. #11745232C22semidirect
42. C29×#106C22semidirect
43. C29×#103C22semidirect
45. C4×C8×C29C22semidirect
51. #11745168C22semidirect
52. #11745164C22semidirect
53. #11745164C22semidirect
54. #11745158C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. C4⋊#6597C22semidirect
190. C4×SD16D29semidirect
220. C4×Q8C2×D29semidirect
229. #106C2×D29semidirect
234. #103C2×D29semidirect
243. C4×C8C2×D29semidirect
244. C29#3296semidirect

Maximal subgroups

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

subgroupindex
#142718542
#142718082
#142715182
#142714952
#142714892
#142714632
#142714032
#142713952
#142713852
#142713222
#142713122
C8×D1162
#142711562
#102×D292
C4×SD16×C292
#329629