Finite Group Databasebeta

← #16832581

Subgroups — #16832581

Order 3712.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271898C211yesmaximal, characteristic, complemented
2#14271896C211yesmaximal, characteristic, complemented
3#14271552C211yesmaximal, characteristic, complemented
4#14271549C211yesmaximal, characteristic, complemented
5#14271544C211yesmaximal, characteristic, complemented
6#14271388C211yesmaximal, characteristic, complemented
7#14271385C211yesmaximal, characteristic, complemented
8#14271381C211yesmaximal, characteristic, complemented
9#14271377C211yesmaximal, characteristic, complemented
10#14271358C211yesmaximal, characteristic, complemented
11#14271357C211yesmaximal, characteristic, complemented
12#14271291C211yesmaximal, characteristic, complemented
13#14271262C211yesmaximal, characteristic, complemented
14#14271245C211yesmaximal, characteristic, complemented
15C29×#440C211yesmaximal, characteristic, complemented
16C2×SD16×C29C2211yescharacteristic
17C4×Q8×C29C2211yescharacteristic
18C4×D4×C29C2211yescharacteristic
19#11745309C2211yescharacteristic
20#11745309C2211yescharacteristic
21C2×#90785C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23#11745302C2211yescharacteristic
24#11745298C2211yescharacteristic
25C2×#90782C2211yescharacteristic
26C2×#90782C2211yescharacteristic
27#11745291—21no—
28C4×C22⋊D29—21no—
29C2×D232C2211yescharacteristic
30C2×D232C2211yescharacteristic
31C2×#90773C2211yescharacteristic
32C2×#90773C2211yescharacteristic
33#11745256—21no—
34#11745256—21no—
35#11745255C2211yescharacteristic
36#11745255C2211yescharacteristic
37#11745255C2211yescharacteristic
38#11745249C2211yescharacteristic
39#11745247—21no—
40#11745245—21no—
41#11745237—21no—
42#11745237C2211yescharacteristic
43#11745236C2211yescharacteristic
44C4×D116—21no—
45C4×Dic58C2211yescharacteristic
46C29×#107C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#102C2211yescharacteristic
49C29×#97C2211yescharacteristic
50#11745163C2211yescharacteristic
51#11745162C2211yescharacteristic
52#11745162C2211yescharacteristic
53C8×Dic29C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C2×D116—21no—
65C2×D116—21no—
66C2×D116C2311yescharacteristic
67C2×D116C2311yescharacteristic
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×Dic58D411yescharacteristic
73C2×Dic58C2311yescharacteristic
74SD16×C29—22no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C42×C29—21no—
82C42×C29C2311yescharacteristic
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85#90785—41no—
86#90784—41no—
87#90782—41no—
88#90782—41no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98C4⋊Dic29D411yescharacteristic
99#90779—21no—
100#90779D411yescharacteristic
101#90779D411yescharacteristic
102C4×Dic29—21no—
103C4×Dic29C2311yescharacteristic
104C4×Dic29C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107D232—22no—
108D232—41no—
109#90773—22no—
110#90773—41no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29—21no—
114C22×D29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—81no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—42no—
127C22⋊D29—81no—
128C2×Dic29—21no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133D116—21no—
134D116—21no—
135D116—21no—
136D116—21no—
137D116—21no—
138D116—21no—
139D116—42no—
140D116—81no—
141C4×D29—81no—
142C4×D29—81no—
143C4×D29—81no—
144Dic58—21no—
145Dic58—21no—
146Dic58—41no—
147C8×C29—21no—
148C8×C29#4112yes—
149#6597—21no—
150#6597—21no—
151#3403—291nomaximal, Sylow
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29C22×D411yescharacteristic
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29H(5,𝔽2)11yescharacteristic
172Dic29—21no—
173Dic29—21no—
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177#559—291no—
178#559—291no—
179#496—291no—
180#496—291no—
181#495—291no—
182#464—291no—
183#464—291no—
184#463—291no—
185#463—291no—
186#459—291no—
187#459—291no—
188#446—291no—
189#440—291no—
190#440D2911yescharacteristic, complemented
191C4×D8—291no—
192C2×C29—81no—
193C2×C29#55011yescharacteristic
194C2×C29#57511yescharacteristic
195C2×C29#57611yescharacteristic
196D29—81no—
197D29—81no—
198D29—81no—
199C2×Q16—291no—
200C2×SD16—291no—
201C2×SD16—291no—
202C2×SD16—291no—
203C2×SD16C2×D2911yescharacteristic
204C2×D8—291no—
205C2×D8—291no—
206C2×D8—291no—
207C2×D8—291no—
208#127—291no—
209#127—291no—
210#124—291no—
211#124—291no—
212#124—291no—
213#124—291no—
214#124—581no—
215#124—581no—
216#123—581no—
217#123—581no—
218#123—581no—
219#123—581no—
220C4×Q8—291no—
221C4×Q8—291no—
222C4×Q8C2×D2911yescharacteristic
223C4×D4—291no—
224C4×D4—291no—
225C4×D4—291no—
226C4×D4—581no—
227C4×D4—581no—
228C4×D4C2×D2911yescharacteristic
229#107C2×D2911yescharacteristic
230C4⋊C8—291no—
231C4⋊C8—291no—
232C4⋊C8—291no—
233#103—291no—
234#103C2×D2911yescharacteristic
235#102—291no—
236#102—291no—
237#102—291no—
238#102C2×D2911yescharacteristic
239#97—291no—
240#97C2×D2911yescharacteristic
241C4×C8—291no—
242C29#340311yescharacteristic, complemented, Sylow
243C2×Q8—291no—
244C2×Q8—291no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—291no—
248C2×D4—291no—
249C2×D4—581no—
250C2×D4—581no—
251C2×D4—581no—
252C2×D4—581no—
253C2×D4C22×D2911yescharacteristic
254C22×C4—21no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—581no—
258Q16—1161no—
259SD16—22no—
260SD16—582no—
261SD16—1161no—
262SD16—1161no—
263D8—582no—
264D8—1161no—
265D8—1161no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8C22×D2911yescharacteristic
270C2×C8C22×D2911yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—291no—
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—581no—
276C4⋊C4C22×D2911yescharacteristic
277C4⋊C4C22×D2911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C42—21no—
291C42—291no—
292C42—291no—
293C42—581no—
294C42C22×D2911yescharacteristic
295C23—21no—
296C23—581no—
297C23—581no—
298C23—581no—
299Q8—21no—
300Q8—21no—
301Q8—581no—
302Q8—581no—
303Q8—1161no—
304D4—21no—
305D4—21no—
306D4—581no—
307D4—581no—
308D4—581no—
309D4—581no—
310D4—581no—
311D4—581no—
312D4—1162no—
313D4—1162no—
314D4—2321no—
315D4—2321no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—291no—
323C2×C4—291no—
324C2×C4—581no—
325C2×C4—2321no—
326C2×C4—2321no—
327C2×C4—2321no—
328C2×C4D4×D2911yescharacteristic
329C2×C4D4×D2911yescharacteristic
330C2×C4C23×D2911yescharacteristic
331C8—21no—
332C8—581no—
333C8—581no—
334C8#9080512yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22—1161no—
342C22—1161no—
343C22—1161no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22C2×D4×D2911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—581no—
354C4—581no—
355C4—581no—
356C4—581no—
357C4—1161no—
358C4C2×#9080511yescharacteristic
359C4#1174536411yescharacteristic
360C2—81no—
361C2—2321no—
362C2—2321no—
363C2—2321no—
364C2#1427183411yescharacteristic
365C2#1427196211yescharacteristic
366C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#440C2
socleC22×C29C22×D4
hypercenter#440D29
hypocenterC29#3403
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14271898C2semidirect
2. #14271896C2semidirect
3. #14271552C2semidirect
4. #14271549C2semidirect
5. #14271544C2semidirect
6. #14271388C2semidirect
7. #14271385C2semidirect
8. #14271381C2semidirect
9. #14271377C2semidirect
10. #14271358C2semidirect
11. #14271357C2semidirect
12. #14271291C2semidirect
13. #14271262C2semidirect
14. #14271245C2semidirect
15. C29×#440C2semidirect
190. #440D29semidirect
242. C29#3403semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142718962
#142715522
#142715492
#142715442
#142713882
#142713852
#142713812
#142713772
#142713582
#142713572
#142712912
#142712622
#142712452
C29×#4402
#340329