Finite Group Databasebeta

← #16829731

Subgroups — #16829731

Order 3712.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271766C211yesmaximal, characteristic, complemented
2#14271637C211yesmaximal, characteristic, complemented
3#14271487C211yesmaximal, characteristic, complemented
4#14271466C211yesmaximal, characteristic, complemented
5#14271462C211yesmaximal, characteristic, complemented
6#14271357C211yesmaximal, characteristic, complemented
7#14271357C211yesmaximal, characteristic, complemented
8#14271299C211yesmaximal, characteristic, complemented
9#14271296C211yesmaximal, characteristic, complemented
10#14271274C211yesmaximal, characteristic, complemented
11#14271272C211yesmaximal, characteristic, complemented
12#14271245C211yesmaximal, characteristic, complemented
13#14271243C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#482C211yesmaximal, characteristic, complemented
16C22×D116C2211yescharacteristic
17C29×#121C2211yescharacteristic
18C29×#117C2211yescharacteristic
19#11745302C2211yescharacteristic, complemented
20#11745301—21no—
21#11745300—21no—
22D4×Dic29C2211yescharacteristic, complemented
23C2×#90782C2211yescharacteristic
24C2×#90782C2211yescharacteristic
25#11745292C2211yescharacteristic
26#11745288C2211yescharacteristic
27C2×D232C2211yescharacteristic
28C2×D232C2211yescharacteristic
29#11745255C2211yescharacteristic
30#11745255C2211yescharacteristic
31#11745255C2211yescharacteristic
32#11745255C2211yescharacteristic
33#11745255C2211yescharacteristic, complemented
34#11745252C2211yescharacteristic, complemented
35#11745248—21no—
36#11745245—21no—
37C22⋊C4×D29—21no—
38C22⋊C4×D29—21no—
39C4×D116—21no—
40C4×D116—21no—
41C29×#107C2211yescharacteristic, complemented
42C29×#106C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic, complemented
44C29×#102C2211yescharacteristic, complemented
45C29×C22⋊C8C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745163C2211yescharacteristic, complemented
50#11745162C2211yescharacteristic, complemented
51#11745162C2211yescharacteristic, complemented
52C8×Dic29C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C22×Dic29—21no—
67C2×D116—21no—
68C2×D116—22no—
69C2×D116—22no—
70C2×D116C2311yescharacteristic
71C2×D116C2311yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C42×C29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29D411yescharacteristic
88C22⋊Dic29D411yescharacteristic
89#90782—22no—
90#90782—22no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29D411yescharacteristic
99C4⋊Dic29D411yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102C4×Dic29C2311yescharacteristic
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106D232—22no—
107D232—22no—
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111C22×D29—21no—
112C22×D29—24no—
113C22×D29—21no—
114C22×D29—81no—
115C22×D29—81no—
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×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—81no—
127C22⋊D29—81no—
128C22⋊D29—81no—
129C2×Dic29—21no—
130C2×Dic29—81no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135D116—24no—
136D116—21no—
137D116—21no—
138D116—21no—
139D116—21no—
140D116#4112yes—
141D116#4112yes—
142C4×D29—81no—
143C4×D29—81no—
144C4×D29—81no—
145C4×D29—81no—
146C4×D29—81no—
147C8×C29—21no—
148C8×C29—21no—
149#6597—21no—
150#6597—21no—
151#3122—291nomaximal, Sylow
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29C22×D411yescharacteristic
159C2×D29—22no—
160C2×D29—22no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—84no—
169C4×C29—21no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29C2×#4111yescharacteristic
174C4×C29C2×#4111yescharacteristic
175Dic29—21no—
176Dic29—21no—
177Dic29—21no—
178Dic29—21no—
179Dic29—41no—
180#540—291no—
181#518—291no—
182#482—291no—
183#482D2911yescharacteristic, complemented
184#478—291no—
185#478—291no—
186#459—291no—
187#459—291no—
188#447—291no—
189#447—291no—
190#442—291no—
191#442—291no—
192C4×D8—291no—
193C4×D8—291no—
194#433—291no—
195C2×C29—41no—
196C2×C29—81no—
197C2×C29#52511yescharacteristic
198C2×C29#57611yescharacteristic
199C2×C29#57611yescharacteristic
200D29—42no—
201D29—42no—
202D29—81no—
203C22×D4—291no—
204C2×D8—291no—
205C2×D8—291no—
206C2×D8—291no—
207C2×D8—291no—
208#127—291no—
209#125—291no—
210#123—581no—
211#123—581no—
212#121—291no—
213#121—581no—
214#121—581no—
215#121C2×D2911yescharacteristic
216C4×D4—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—291no—
221C4×D4—291no—
222C4×D4—581no—
223C4×D4—581no—
224#117—291no—
225#117C2×D2911yescharacteristic
226C2×C22⋊C4—581no—
227C2×C22⋊C4—581no—
228#107—291no—
229#107C2×D2911yescharacteristic, complemented
230#106—291no—
231#106C2×D2911yescharacteristic, complemented
232C4⋊C8—291no—
233C4⋊C8—291no—
234#102—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102C2×D2911yescharacteristic, complemented
241#102C2×D2911yescharacteristic, complemented
242C22⋊C8—291no—
243C22⋊C8C2×D2911yescharacteristic
244#97—291no—
245C4×C8—291no—
246C29#312211yescharacteristic, complemented, Sylow
247C24—581no—
248C2×D4—21no—
249C2×D4—291no—
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—582no—
253C2×D4—582no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—581no—
258C2×D4C22×D2911yescharacteristic
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4—581no—
264C22×C4—581no—
265C22×C4C22×D2911yescharacteristic
266D8—582no—
267D8—582no—
268D8—582no—
269D8—582no—
270C2×C8—291no—
271C2×C8—291no—
272C2×C8C22×D2911yescharacteristic
273C2×C8C22×D2911yescharacteristic
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4C22×D2911yescharacteristic
280C4⋊C4C22×D2911yescharacteristic
281C4⋊C4C22×D2911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—291no—
285C22⋊C4—291no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C42—21no—
294C42—291no—
295C42—291no—
296C23—21no—
297C23—584no—
298C23—581no—
299C23—581no—
300C23—581no—
301C23—2321no—
302C23—2321no—
303C23D4×D2911yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—292no—
308D4—292no—
309D4—584no—
310D4—581no—
311D4—581no—
312D4—581no—
313D4—581no—
314D4—2321no—
315D4—2321no—
316D4—2321no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—291no—
323C2×C4—291no—
324C2×C4—291no—
325C2×C4—291no—
326C2×C4—581no—
327C2×C4—2321no—
328C2×C4—2321no—
329C2×C4—2321no—
330C2×C4—2321no—
331C2×C4—2321no—
332C2×C4—2321no—
333C2×C4D4×D2911yescharacteristic
334C2×C4C23×D2911yescharacteristic
335C8—21no—
336C8—21no—
337C8—581no—
338C8—581no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—582no—
346C22—582no—
347C22—1161no—
348C22—1161no—
349C22—1161no—
350C22—1161no—
351C22—1161no—
352C22—1161no—
353C22—1161no—
354C22—2324no—
355C22C2×D4×D2911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—581no—
361C4—581no—
362C4—581no—
363C4—581no—
364C4—1161no—
365C4#41×D2911yescharacteristic
366C4#41×D2911yescharacteristic
367C2—41no—
368C2—81no—
369C2—1162no—
370C2—1162no—
371C2—2321no—
372C2#1427167111yescharacteristic
373C2#1427196511yescharacteristic
374C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#482C2
socleC22×C29C22×D4
hypercenter#482D29
hypocenterC29#3122
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14271766C2semidirect
2. #14271637C2semidirect
3. #14271487C2semidirect
4. #14271466C2semidirect
5. #14271462C2semidirect
6. #14271357C2semidirect
7. #14271357C2semidirect
8. #14271299C2semidirect
9. #14271296C2semidirect
10. #14271274C2semidirect
11. #14271272C2semidirect
12. #14271245C2semidirect
13. #14271243C2semidirect
14. #14271221C2semidirect
15. C29×#482C2semidirect
19. #11745302C22semidirect
22. D4×Dic29C22semidirect
33. #11745255C22semidirect
34. #11745252C22semidirect
41. C29×#107C22semidirect
42. C29×#106C22semidirect
43. C29×#102C22semidirect
44. C29×#102C22semidirect
49. #11745163C22semidirect
50. #11745162C22semidirect
51. #11745162C22semidirect
52. C8×Dic29C22semidirect
55. #11745157C22semidirect
56. #11745157C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
183. #482D29semidirect
229. #107C2×D29semidirect
231. #106C2×D29semidirect
240. #102C2×D29semidirect
241. #102C2×D29semidirect
246. C29#3122semidirect

Maximal subgroups

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

subgroupindex
#142717662
#142716372
#142714872
#142714662
#142714622
#142713572
#142712992
#142712962
#142712742
#142712722
#142712452
#142712432
#142712212
C29×#4822
#312229