Finite Group Databasebeta

← #16831449

Subgroups — #16831449

Order 3712.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271814C211yesmaximal, characteristic, complemented
2#14271807C211yesmaximal, characteristic, complemented
3#14271521C211yesmaximal, characteristic, complemented
4#14271493C211yesmaximal, characteristic, complemented
5#14271480C211yesmaximal, characteristic, complemented
6#14271451C211yesmaximal, characteristic, complemented
7#14271415C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271377C211yesmaximal, characteristic, complemented
10#14271309C211yesmaximal, characteristic, complemented
11#14271297C211yesmaximal, characteristic, complemented
12#14271272C211yesmaximal, characteristic, complemented
13#14271234C211yesmaximal, characteristic, complemented
14#14271161C211yesmaximal, characteristic, complemented
15C2×C29×#102C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×#90805—21no—
19C22×C8×C29C2211yescharacteristic
20C2×C4⋊C4×C29C2211yescharacteristic
21#11745315—21no—
22C2×C22⋊Dic29—21no—
23#11745301—21no—
24#11745300C2211yescharacteristic
25#11745298C2211yescharacteristic
26#11745297—21no—
27D4×Dic29C2211yescharacteristic
28C2×#90782C2211yescharacteristic
29C2×#90782C2211yescharacteristic
30#11745292C2211yescharacteristic
31#11745291—21no—
32C4×C22⋊D29C2211yescharacteristic
33#11745286C2211yescharacteristic
34C2×#90773C2211yescharacteristic, complemented
35C2×#90772C2211yescharacteristic, 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
45C29×#102C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48C22⋊#6597C2211yescharacteristic
49#11745169C2211yescharacteristic, complemented
50#11745168C2211yescharacteristic, complemented
51#11745165C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54#11745162C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745158C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745156C2211yescharacteristic, complemented
59C24×C29—21no—
60C2×D4×C29—22no—
61C2×D4×C29—21no—
62C2×D4×C29—41no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29C2311yescharacteristic
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29D411yescharacteristic
71C22×Dic29—21no—
72C22×Dic29—21no—
73#90807—22no—
74#90807—41no—
75#90805—44no—
76C2×D116—21no—
77C2×D116C2311yescharacteristic
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29C2311yescharacteristic
81C2×Dic58—21no—
82C2×Dic58C2311yescharacteristic
83C2×C8×C29—41no—
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C4⋊C4×C29—21no—
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29—21no—
92C22⋊Dic29—21no—
93C22⋊Dic29—21no—
94C22⋊Dic29D411yescharacteristic
95#90782—22no—
96#90782—41no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100#90781D411yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104#90779—21no—
105#90779—21no—
106#90779D411yescharacteristic
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110#90773—41no—
111#90772—41no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—42no—
115C23×C29—42no—
116C23×C29—81no—
117C23×C29C2×D411yescharacteristic
118C22×D29—21no—
119C22×D29C2×D411yescharacteristic
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—21no—
123D4×C29—42no—
124D4×C29#4112yescomplemented
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—42no—
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2411yescharacteristic
132C22⋊D29—22no—
133C22⋊D29—42no—
134C22⋊D29—42no—
135C22⋊D29—81no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—42no—
140C2×Dic29—81no—
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143C2×Dic29C2×D411yescharacteristic
144D116—21no—
145D116—21no—
146D116—42no—
147C4×D29—21no—
148C4×D29—21no—
149C4×D29—42no—
150C4×D29—42no—
151Dic58—21no—
152Dic58—21no—
153Dic58—42no—
154C8×C29—21no—
155C8×C29—21no—
156#6597—21no—
157#6597—21no—
158#3306—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—22no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—84no—
168C22×C29AGL(1,ℤ/8)12yes—
169C22×C29C22×D411yescharacteristic
170C2×D29—21no—
171C2×D29—21no—
172C2×D29—21no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—41no—
176C4×C29—21no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29C2×#4111yescharacteristic
180C4×C29H(5,𝔽2)11yescharacteristic
181Dic29—21no—
182Dic29—21no—
183Dic29—21no—
184Dic29—41no—
185Dic29—41no—
186Dic29—41no—
187#547—291no—
188#546—291no—
189#489—291no—
190#483—291no—
191#481—291no—
192#476—291no—
193#469—291no—
194#465—291no—
195#463—291no—
196#449—291no—
197#447—291no—
198#442—291no—
199#435—291no—
200#417—291no—
201C2×#102D2911yescharacteristic, complemented
202C2×C29—22no—
203C2×C29—42no—
204C2×C29—81no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—41no—
209D29—81no—
210C2×#41—291no—
211C2×#41—581no—
212C22×D4C2×D2911yescharacteristic
213C2×SD16—291no—
214C2×D8—291no—
215C2×D8—291no—
216C2×M16—291no—
217C22×C8C2×D2911yescharacteristic
218C4⋊Q8—291no—
219#124—291no—
220#123—581no—
221#123—581no—
222#123—581no—
223C22⋊Q8—291no—
224C22⋊Q8—581no—
225#121—291no—
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230C4×D4—291no—
231C4×D4—291no—
232C4×D4—291no—
233C2×C4⋊C4—291no—
234C2×C4⋊C4C2×D2911yescharacteristic
235C2×C22⋊C4—581no—
236#106—291no—
237#106—291no—
238#106—291no—
239C4⋊C8—291no—
240#103—291no—
241#103—291no—
242#103—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102C2×D2911yescharacteristic
247#102C2×D2911yescharacteristic
248#102C2×D2911yescharacteristic
249#102C2×D2911yescharacteristic
250C22⋊C8—291no—
251C22⋊C8—291no—
252#97—291no—
253C29#330611yescharacteristic, complemented, Sylow
254C24—21no—
255#41—582no—
256#41—1164no—
257#41—1161no—
258C2×Q8—291no—
259C2×Q8—581no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—291no—
264C2×D4—291no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4C22×D2911yescharacteristic
270C2×D4C22×D2911yescharacteristic
271C22×C4—21no—
272C22×C4—291no—
273C22×C4—581no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4—581no—
277C22×C4C22×D2911yescharacteristic
278SD16—1161no—
279D8—582no—
280D8—1161no—
281M16—1161no—
282C2×C8—41no—
283C2×C8—291no—
284C2×C8—291no—
285C2×C8C22×D2911yescharacteristic
286C2×C8C22×D2911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4C22×D2911yescharacteristic
295C4⋊C4C22×D2911yescharacteristic
296C22⋊C4—291no—
297C22⋊C4—291no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C22⋊C4—581no—
306C42—291no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—291no—
313C23—581no—
314C23D4×D2911yescharacteristic
315Q8—581no—
316Q8—581no—
317Q8—1162no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—582no—
323D4—581no—
324D4—581no—
325D4—1162no—
326D4—1162no—
327D4—1162no—
328D4—2321no—
329D4#9080512yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—291no—
336C2×C4—291no—
337C2×C4—291no—
338C2×C4—581no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—1162no—
344C2×C4—1162no—
345C2×C4—1162no—
346C2×C4—2321no—
347C2×C4D4×D2911yescharacteristic
348C2×C4C23×D2911yescharacteristic
349C8—21no—
350C8—21no—
351C8—581no—
352C8—581no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—581no—
363C22—581no—
364C22—581no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22#1174527312yes—
369C22C2×D4×D2911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—581no—
374C4—581no—
375C4—581no—
376C4—1161no—
377C4—1161no—
378C4—1161no—
379C4C2×#9080511yescharacteristic
380C4#1174535911yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—1161no—
385C2—2321no—
386C2#1427180311yescharacteristic
387C2C2×#1174527311yescharacteristic
388C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#102C2
socleC22×C29C22×D4
hypercenterC2×#102D29
hypocenterC29#3306
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. #14271807C2semidirect
3. #14271521C2semidirect
4. #14271493C2semidirect
5. #14271480C2semidirect
6. #14271451C2semidirect
7. #14271415C2semidirect
8. #14271392C2semidirect
9. #14271377C2semidirect
10. #14271309C2semidirect
11. #14271297C2semidirect
12. #14271272C2semidirect
13. #14271234C2semidirect
14. #14271161C2semidirect
15. C2×C29×#102C2semidirect
34. C2×#90773C22semidirect
35. C2×#90772C22semidirect
37. #11745257C22semidirect
39. #11745255C22semidirect
40. C4⋊C4×D29C22semidirect
41. #11745250C22semidirect
49. #11745169C22semidirect
50. #11745168C22semidirect
51. #11745165C22semidirect
52. #11745164C22semidirect
53. #11745163C22semidirect
54. #11745162C22semidirect
55. #11745158C22semidirect
56. #11745158C22semidirect
57. #11745156C22semidirect
58. #11745156C22semidirect
124. D4×C29#41semidirect
201. C2×#102D29semidirect
253. C29#3306semidirect
329. D4#90805semidirect

Maximal subgroups

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

subgroupindex
#142718142
#142718072
#142715212
#142714932
#142714802
#142714512
#142714152
#142713922
#142713772
#142713092
#142712972
#142712722
#142712342
#142711612
C2×C29×#1022
#330629