Finite Group Databasebeta

← #16829673

Subgroups — #16829673

Order 3712.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271782C211yesmaximal, characteristic, complemented
2#14271635C211yesmaximal, characteristic, complemented
3#14271503C211yesmaximal, characteristic, complemented
4#14271485C211yesmaximal, characteristic, complemented
5#14271453C211yesmaximal, characteristic, complemented
6#14271444C211yesmaximal, characteristic, complemented
7#14271375C211yesmaximal, characteristic, complemented
8#14271312C211yesmaximal, characteristic, complemented
9#14271295C211yesmaximal, characteristic
10#14271272C211yesmaximal, characteristic, complemented
11#14271264C211yesmaximal, characteristic, complemented
12#14271248C211yesmaximal, characteristic, complemented
13D8×Dic29C211yesmaximal, characteristic, complemented
14#14271223C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#124C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745308C2211yescharacteristic
22Q8×Dic29C2211yescharacteristic, complemented
23C2×#90784C2211yescharacteristic
24#11745300C2211yescharacteristic
25D4×Dic29C2211yescharacteristic
26D4×Dic29C2211yescharacteristic, complemented
27C2×#90782C2211yescharacteristic
28C4×C22⋊D29—21no—
29C2×#90781—21no—
30#11745255C2211yescharacteristic
31#11745254C2211yescharacteristic
32#11745248—21no—
33#11745247—21no—
34#11745243—21no—
35C22⋊C4×D29—21no—
36#11745241—21no—
37#11745240—21no—
38C4×D116C2211yescharacteristic
39#11745234C2211yescharacteristic
40#11745231C2211yescharacteristic, complemented
41C29×C4⋊C8C2211yescharacteristic, complemented
42C29×#103C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic, complemented
44#11745183C2211yescharacteristic, complemented
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745166C2211yescharacteristic, complemented
53#11745166C2211yescharacteristic, complemented
54#11745163C2211yescharacteristic, complemented
55C8×Dic29C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58C4⋊#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C22×Dic29—21no—
67C22×Dic29—21no—
68D4×D29—22no—
69D4×D29—22no—
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29C2311yescharacteristic
74C2×Dic58—21no—
75SD16×C29—22no—
76D8×C29—22no—
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C42×C29C2311yescharacteristic
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87#90784—22no—
88#90782—22no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781D411yescharacteristic
94#90781D411yescharacteristic
95C4⋊Dic29—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779D411yescharacteristic
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29—21no—
110C22×D29—21no—
111C22×D29—24no—
112C22×D29—81no—
113C22×D29—81no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29#4112yes—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—81no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—24no—
128C22⋊D29—81no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—81no—
133C2×Dic29—81no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—21no—
138D116#4112yes—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—81no—
142C4×D29—81no—
143Dic58—81no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597—21no—
148#3118—291nomaximal, Sylow
149C22×C29—22no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29C22×D411yescharacteristic
156C2×D29—21no—
157C2×D29—22no—
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—84no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29C2×#4111yescharacteristic
168C4×C29C2×#4111yescharacteristic
169Dic29—21no—
170Dic29—21no—
171Dic29—21no—
172Dic29—41no—
173Dic29—41no—
174Dic29—41no—
175#542—291no—
176#518—291no—
177#485—291no—
178#482—291no—
179#476—291no—
180#474—291no—
181#463—291no—
182#463D2911yescharacteristic, complemented
183#450—291no—
184#447—291no—
185#442—291no—
186#440—291no—
187C4×SD16—291no—
188C4×D8—291no—
189#433—291no—
190C2×C29—42no—
191C2×C29—81no—
192C2×C29#52511yescharacteristic
193C2×C29#57611yescharacteristic
194C2×C29#57711yescharacteristic
195D29—41no—
196D29—42no—
197C22×D4—291no—
198C2×SD16—291no—
199C2×SD16C2×D2911yescharacteristic
200C2×D8—291no—
201C2×D8C2×D2911yescharacteristic
202C4⋊Q8—291no—
203#126—581no—
204#124—581no—
205#124C2×D2911yescharacteristic, complemented
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—581no—
209#121—291no—
210C4×Q8—291no—
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—581no—
216C4×D4—581no—
217C4×D4C2×D2911yescharacteristic
218#117—291no—
219#117—291no—
220C2×C22⋊C4—581no—
221C2×C22⋊C4—581no—
222#107—291no—
223#107—291no—
224#106—291no—
225#106—291no—
226C4⋊C8—291no—
227C4⋊C8C2×D2911yescharacteristic, complemented
228#103—291no—
229#103C2×D2911yescharacteristic, complemented
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235#102C2×D2911yescharacteristic, complemented
236C22⋊C8—291no—
237C22⋊C8—291no—
238#97—291no—
239C4×C8—291no—
240C29#311811yescharacteristic, complemented, Sylow
241C24—581no—
242C2×Q8—581no—
243C2×Q8C22×D2911yescharacteristic
244C2×D4—291no—
245C2×D4—581no—
246C2×D4—582no—
247C2×D4—582no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C2×D4C22×D2911yescharacteristic
251C22×C4—21no—
252C22×C4—291no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4—581no—
257SD16—22no—
258SD16—582no—
259D8—22no—
260D8—582no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4C22×D2911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—291no—
278C22⋊C4—291no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—291no—
287C42—581no—
288C42—581no—
289C42C22×D2911yescharacteristic
290C23—21no—
291C23—21no—
292C23—291no—
293C23—584no—
294C23—581no—
295C23—2321no—
296C23—2321no—
297Q8—21no—
298Q8—21no—
299Q8—2321no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—292no—
304D4—584no—
305D4—581no—
306D4—2321no—
307D4#9080712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—2321no—
320C2×C4—2321no—
321C2×C4—2321no—
322C2×C4—2321no—
323C2×C4D4×D2911yescharacteristic
324C2×C4D4×D2911yescharacteristic
325C2×C4C23×D2911yescharacteristic
326C8—21no—
327C8—21no—
328C8—581no—
329C8—581no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—581no—
337C22—582no—
338C22—581no—
339C22—581no—
340C22—1161no—
341C22—1161no—
342C22—2324no—
343C22C2×D4×D2911yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—581no—
349C4—581no—
350C4—581no—
351C4—1161no—
352C4—1161no—
353C4—1161no—
354C4C2×#9080711yescharacteristic
355C4#41×D2911yescharacteristic
356C2—42no—
357C2—81no—
358C2—1161no—
359C2—1162no—
360C2#1427167311yescharacteristic
361C2#1427196511yescharacteristic
362C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
prime radical#14271295C2
hypercenter#463D29
hypocenterC29#3118
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #14271782C2semidirect
2. #14271635C2semidirect
3. #14271503C2semidirect
4. #14271485C2semidirect
5. #14271453C2semidirect
6. #14271444C2semidirect
7. #14271375C2semidirect
8. #14271312C2semidirect
10. #14271272C2semidirect
11. #14271264C2semidirect
12. #14271248C2semidirect
13. D8×Dic29C2semidirect
14. #14271223C2semidirect
15. C29×#463C2semidirect
19. C29×#124C22semidirect
22. Q8×Dic29C22semidirect
26. D4×Dic29C22semidirect
40. #11745231C22semidirect
41. C29×C4⋊C8C22semidirect
42. C29×#103C22semidirect
43. C29×#102C22semidirect
44. #11745183C22semidirect
47. #11745180C22semidirect
52. #11745166C22semidirect
53. #11745166C22semidirect
54. #11745163C22semidirect
55. C8×Dic29C22semidirect
56. #11745156C22semidirect
57. #11745156C22semidirect
58. C4⋊#6597C22semidirect
182. #463D29semidirect
205. #124C2×D29semidirect
227. C4⋊C8C2×D29semidirect
229. #103C2×D29semidirect
235. #102C2×D29semidirect
240. C29#3118semidirect

Maximal subgroups

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

subgroupindex
#142717822
#142716352
#142715032
#142714852
#142714532
#142714442
#142713752
#142713122
#142712952
#142712722
#142712642
#142712482
D8×Dic292
#142712232
C29×#4632
#311829