Finite Group Databasebeta

← #16832575

Subgroups — #16832575

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#14271899C211yesmaximal, characteristic, complemented
2#14271896C211yesmaximal, characteristic, complemented
3#14271551C211yesmaximal, characteristic, complemented
4#14271550C211yesmaximal, characteristic, complemented
5#14271546C211yesmaximal, characteristic, complemented
6#14271386C211yesmaximal, characteristic, complemented
7#14271384C211yesmaximal, characteristic, complemented
8#14271377C211yesmaximal, characteristic, complemented
9#14271376C211yesmaximal, characteristic, complemented
10#14271356C211yesmaximal, characteristic, complemented
11#14271292C211yesmaximal, characteristic, complemented
12#14271263C211yesmaximal, characteristic, complemented
13#14271260C211yesmaximal, characteristic, complemented
14#14271243C211yesmaximal, characteristic, complemented
15C29×#459C211yesmaximal, characteristic, complemented
16C2×D8×C29C2211yescharacteristic
17C2×D8×C29C2211yescharacteristic
18C29×#127C2211yescharacteristic
19C4×D4×C29C2211yescharacteristic
20#11745302C2211yescharacteristic
21#11745298—21no—
22#11745298C2211yescharacteristic
23#11745298C2211yescharacteristic
24#11745298C2211yescharacteristic
25#11745297—21no—
26#11745297—21no—
27D4×Dic29—21no—
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31C2×#90783C2211yescharacteristic
32C2×#90783C2211yescharacteristic
33C2×#90782C2211yescharacteristic
34C2×#90782C2211yescharacteristic
35#11745291—21no—
36C4×C22⋊D29—21no—
37C2×Dic116C2211yescharacteristic
38C2×#90773C2211yescharacteristic
39#11745255C2211yescharacteristic
40#11745249C2211yescharacteristic
41#11745247—21no—
42#11745245—21no—
43#11745237C2211yescharacteristic
44C4×Dic58C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46C29×C4⋊C8C2211yescharacteristic
47C29×#102C2211yescharacteristic
48C29×#102C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745163C2211yescharacteristic
53#11745162C2211yescharacteristic
54#11745162C2211yescharacteristic
55C8×Dic29C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745155C2211yescharacteristic
58#11745151C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C22×Dic29—21no—
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×Dic58D411yescharacteristic
72C2×Dic58C2311yescharacteristic
73C2×Dic58C2311yescharacteristic
74D8×C29—41no—
75D8×C29—41no—
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C42×C29C2311yescharacteristic
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89#90783—22no—
90#90783—22no—
91#90783—41no—
92#90782—22no—
93#90782—41no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97C4⋊Dic29D411yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779D411yescharacteristic
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29C2311yescharacteristic
106C4×Dic29C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109Dic116—41no—
110#90773—41no—
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—21no—
114C22×D29—21no—
115D4×C29—21no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—42no—
122D4×C29—81no—
123C2×C4×C29—21no—
124C2×C4×C29—81no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—42no—
129C22⋊D29—81no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—81no—
134C2×Dic29—81no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139D116—21no—
140D116—21no—
141C4×D29—81no—
142Dic58—21no—
143Dic58—21no—
144Dic58—21no—
145Dic58—21no—
146Dic58—41no—
147C8×C29—21no—
148C8×C29—21no—
149#6597—21no—
150#6597#4112yes—
151#3403—291nomaximal, Sylow
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29C22×D411yescharacteristic
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29C2×#4111yescharacteristic
169C4×C29H(5,𝔽2)11yescharacteristic
170Dic29—21no—
171Dic29—21no—
172Dic29—21no—
173Dic29—21no—
174Dic29—41no—
175Dic29—41no—
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#459D2911yescharacteristic, complemented
188#446—291no—
189#440—291no—
190#440—291no—
191C4×D8—291no—
192C2×C29—81no—
193C2×C29—81no—
194C2×C29—81no—
195C2×C29#55011yescharacteristic
196C2×C29#57511yescharacteristic
197C2×C29#57611yescharacteristic
198D29—81no—
199C2×Q16—291no—
200C2×SD16—291no—
201C2×SD16—291no—
202C2×SD16—291no—
203C2×SD16—291no—
204C2×D8—291no—
205C2×D8—291no—
206C2×D8C2×D2911yescharacteristic
207C2×D8C2×D2911yescharacteristic
208#127—291no—
209#127C2×D2911yescharacteristic
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×Q8—291no—
223C4×D4—291no—
224C4×D4—291no—
225C4×D4—291no—
226C4×D4—581no—
227C4×D4—581no—
228C4×D4C2×D2911yescharacteristic
229#107—291no—
230C4⋊C8—291no—
231C4⋊C8—291no—
232C4⋊C8C2×D2911yescharacteristic
233#103—291no—
234#103—291no—
235#102—291no—
236#102—291no—
237#102C2×D2911yescharacteristic
238#102C2×D2911yescharacteristic
239#97—291no—
240#97—291no—
241C4×C8—291no—
242C29#340311yescharacteristic, complemented, Sylow
243C2×Q8—291no—
244C2×Q8—291no—
245C2×Q8—291no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—291no—
249C2×D4—581no—
250C2×D4—581no—
251C2×D4C22×D2911yescharacteristic
252C2×D4C22×D2911yescharacteristic
253C2×D4C22×D2911yescharacteristic
254C22×C4—21no—
255C22×C4—581no—
256C22×C4—581no—
257C22×C4—581no—
258Q16—1161no—
259SD16—582no—
260SD16—582no—
261SD16—1161no—
262SD16—1161no—
263D8—41no—
264D8—41no—
265D8—582no—
266D8—1161no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8C22×D2911yescharacteristic
270C2×C8C22×D2911yescharacteristic
271C4⋊C4—291no—
272C4⋊C4—291no—
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—581no—
276C4⋊C4—581no—
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—291no—
291C42—291no—
292C42—581no—
293C42—581no—
294C42C22×D2911yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—581no—
299Q8—581no—
300Q8—581no—
301Q8—581no—
302Q8—581no—
303Q8—1161no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—581no—
313D4—581no—
314D4—1162no—
315D4—2321no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—291no—
319C2×C4—291no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—2321no—
326C2×C4—2321no—
327C2×C4—2321no—
328C2×C4D4×D2911yescharacteristic
329C2×C4D4×D2911yescharacteristic
330C2×C4C23×D2911yescharacteristic
331C8—21no—
332C8—21no—
333C8—292no—
334C8—581no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22C2×D4×D2911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—581no—
352C4—581no—
353C4—581no—
354C4—581no—
355C4—1161no—
356C4—1161no—
357C4—1161no—
358C4#1174535911yescharacteristic
359C4#41×D2911yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—2321no—
364C2#1427183111yescharacteristic
365C2#1427195911yescharacteristic
366C2#1427196411yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#459C2
socleC22×C29C22×D4
hypercenter#459D29
hypocenterC29#3403
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14271899C2semidirect
2. #14271896C2semidirect
3. #14271551C2semidirect
4. #14271550C2semidirect
5. #14271546C2semidirect
6. #14271386C2semidirect
7. #14271384C2semidirect
8. #14271377C2semidirect
9. #14271376C2semidirect
10. #14271356C2semidirect
11. #14271292C2semidirect
12. #14271263C2semidirect
13. #14271260C2semidirect
14. #14271243C2semidirect
15. C29×#459C2semidirect
187. #459D29semidirect
242. C29#3403semidirect

Maximal subgroups

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

subgroupindex
#142718992
#142718962
#142715512
#142715502
#142715462
#142713862
#142713842
#142713772
#142713762
#142713562
#142712922
#142712632
#142712602
#142712432
C29×#4592
#340329