Finite Group Databasebeta

← #16829443

Subgroups — #16829443

Order 3712.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271729C211yesmaximal, characteristic
2#14271644C211yesmaximal, characteristic, complemented
3#14271490C211yesmaximal, characteristic, complemented
4#14271488C211yesmaximal, characteristic, complemented
5#14271485C211yesmaximal, characteristic, complemented
6#14271484C211yesmaximal, characteristic, complemented
7#14271481C211yesmaximal, characteristic, complemented
8#14271480C211yesmaximal, characteristic, complemented
9#14271478C211yesmaximal, characteristic, complemented
10#14271204C211yesmaximal, characteristic, complemented
11#14271200C211yesmaximal, characteristic, complemented
12#14271166C211yesmaximal, characteristic, complemented
13#102×D29C211yesmaximal, characteristic, complemented
14#14271128C211yesmaximal, characteristic, complemented
15C29×#480C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×#121C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic, complemented
20#11745302—21no—
21#11745300C2211yescharacteristic
22#11745299—21no—
23#11745292C2211yescharacteristic
24C4×C22⋊D29—21no—
25C4×C22⋊D29—21no—
26#11745288C2211yescharacteristic, complemented
27C2×#90772C2211yescharacteristic
28C2×C8×D29C2211yescharacteristic
29#11745257C2211yescharacteristic
30#11745255—21no—
31#11745254C2211yescharacteristic
32#11745254C2211yescharacteristic
33#11745254C2211yescharacteristic, complemented
34C4⋊C4×D29C2211yescharacteristic
35C4⋊C4×D29C2211yescharacteristic, complemented
36#11745249—21no—
37#11745247—21no—
38#11745244—21no—
39C29×#107C2211yescharacteristic, complemented
40C29×#107C2211yescharacteristic, complemented
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic, complemented
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic, complemented
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic, complemented
50#11745168C2211yescharacteristic, complemented
51#11745166C2211yescharacteristic, complemented
52#11745165C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745156C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C22×C4×C29C2311yescharacteristic
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29D411yescharacteristic
68C2×C22⋊D29D411yescharacteristic
69D4×D29—22no—
70D4×D29—22no—
71#90805—22no—
72#90805—22no—
73C2×D116—21no—
74C2×D116D411yescharacteristic
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×C4×D29C2311yescharacteristic
80C2×Dic58D411yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106#90772—22no—
107C8×D29—22no—
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111C22×D29—42no—
112C22×D29—81no—
113C22×D29—81no—
114C22×D29C2×D411yescharacteristic
115C22×D29C2×D411yescharacteristic
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—81no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—81no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—22no—
128C22⋊D29—22no—
129C22⋊D29—42no—
130C22⋊D29—81no—
131C22⋊D29—81no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—22no—
138D116—21no—
139D116—21no—
140D116—81no—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—81no—
144C4×D29—81no—
145C4×D29#4112yes—
146C4×D29#4112yes—
147Dic58—22no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3096—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—21no—
164C2×D29—21no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—84no—
169C2×D29#12312yes—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29C2×#4111yescharacteristic
175C4×C29C2×#4111yescharacteristic
176Dic29—21no—
177Dic29—41no—
178Dic29—41no—
179Dic29—41no—
180Dic29#12312yes—
181#535—291no—
182#520—291no—
183#482—291no—
184#482—291no—
185#482—291no—
186#482—291no—
187#481—291no—
188#481—291no—
189#480—291no—
190#480D2911yescharacteristic, complemented
191#428—291no—
192#427—291no—
193#418—291no—
194C2×#102—291no—
195#408—291no—
196C2×C29—41no—
197C2×C29—81no—
198C2×C29C2×#12311yescharacteristic
199C2×C29#57611yescharacteristic
200C2×C29#57711yescharacteristic
201D29—22no—
202D29—41no—
203D29—81no—
204C2×#41—291no—
205C22×D4—291no—
206C2×M16—291no—
207C22×C8—291no—
208#127—581no—
209#124—581no—
210#121—291no—
211#121—291no—
212#121—291no—
213#121C2×D2911yescharacteristic
214#120—581no—
215#120—581no—
216C4×Q8—581no—
217C4×D4—581no—
218C4×D4—581no—
219C4×D4—581no—
220#117—291no—
221#117—291no—
222#117—291no—
223#117—291no—
224C2×C4⋊C4—291no—
225C2×C4⋊C4—291no—
226C2×C4⋊C4C2×D2911yescharacteristic, complemented
227#107—291no—
228#107—291no—
229#107C2×D2911yescharacteristic, complemented
230#107C2×D2911yescharacteristic, complemented
231#106—291no—
232#106—291no—
233#106—291no—
234#106—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102—291no—
241#102C2×D2911yescharacteristic
242#102C2×D2911yescharacteristic
243C22⋊C8—291no—
244C22⋊C8—291no—
245C22⋊C8—291no—
246C22⋊C8C2×D2911yescharacteristic, complemented
247C29#309611yescharacteristic, complemented, Sylow
248C24—581no—
249#41—582no—
250#41—582no—
251C2×Q8—291no—
252C2×D4—21no—
253C2×D4—291no—
254C2×D4—291no—
255C2×D4—291no—
256C2×D4—291no—
257C2×D4—581no—
258C2×D4—582no—
259C2×D4—582no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4C22×D2911yescharacteristic
264C22×C4—21no—
265C22×C4—291no—
266C22×C4—291no—
267C22×C4—581no—
268C22×C4—581no—
269C22×C4C22×D2911yescharacteristic
270M16—582no—
271C2×C8—291no—
272C2×C8—291no—
273C2×C8—582no—
274C2×C8C22×D2911yescharacteristic
275C2×C8C22×D2911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—291no—
278C4⋊C4—291no—
279C4⋊C4—291no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C4⋊C4C22×D2911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—581no—
294C42—581no—
295C42—581no—
296C42—581no—
297C23—21no—
298C23—291no—
299C23—291no—
300C23—581no—
301C23—1162no—
302C23—2321no—
303C23—2321no—
304C23D4×D2911yescharacteristic
305Q8—582no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—582no—
310D4—582no—
311D4—582no—
312D4—581no—
313D4—581no—
314D4—1162no—
315D4—2321no—
316D4—2321no—
317D4—2321no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—291no—
325C2×C4—292no—
326C2×C4—292no—
327C2×C4—291no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—581no—
332C2×C4—581no—
333C2×C4—2321no—
334C2×C4—2321no—
335C2×C4D4×D2911yescharacteristic
336C2×C4C23×D2911yescharacteristic
337C8—21no—
338C8—21no—
339C8—581no—
340C8—581no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—292no—
348C22—581no—
349C22—581no—
350C22—581no—
351C22—581no—
352C22—581no—
353C22—1161no—
354C22—1161no—
355C22—1161no—
356C22—2324no—
357C22C2×D4×D2911yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—292no—
363C4—581no—
364C4—1161no—
365C4—1161no—
366C4—1161no—
367C4#41×D2911yescharacteristic
368C4#41×D2911yescharacteristic
369C2—41no—
370C2—81no—
371C2—582no—
372C2—1161no—
373C2—2321no—
374C2#123×D2911yescharacteristic
375C2#1427196411yescharacteristic
376C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#480C2
socleC22×C29C22×D4
prime radical#14271729C2
hypercenter#480D29
hypocenterC29#3096
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #14271644C2semidirect
3. #14271490C2semidirect
4. #14271488C2semidirect
5. #14271485C2semidirect
6. #14271484C2semidirect
7. #14271481C2semidirect
8. #14271480C2semidirect
9. #14271478C2semidirect
10. #14271204C2semidirect
11. #14271200C2semidirect
12. #14271166C2semidirect
13. #102×D29C2semidirect
14. #14271128C2semidirect
15. C29×#480C2semidirect
19. C2×C4⋊C4×C29C22semidirect
26. #11745288C22semidirect
33. #11745254C22semidirect
35. C4⋊C4×D29C22semidirect
39. C29×#107C22semidirect
40. C29×#107C22semidirect
43. C29×C22⋊C8C22semidirect
46. C22⋊#6597C22semidirect
49. #11745168C22semidirect
50. #11745168C22semidirect
51. #11745166C22semidirect
52. #11745165C22semidirect
55. #11745156C22semidirect
56. #11745156C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
190. #480D29semidirect
226. C2×C4⋊C4C2×D29semidirect
229. #107C2×D29semidirect
230. #107C2×D29semidirect
246. C22⋊C8C2×D29semidirect
247. C29#3096semidirect

Maximal subgroups

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

subgroupindex
#142717292
#142716442
#142714902
#142714882
#142714852
#142714842
#142714812
#142714802
#142714782
#142712042
#142712002
#142711662
#102×D292
#142711282
C29×#4802
#309629