Finite Group Databasebeta

← #16832563

Subgroups — #16832563

Order 3712.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271896C211yesmaximal, characteristic, complemented
2#14271883C211yesmaximal, characteristic, complemented
3#14271557C211yesmaximal, characteristic, complemented
4#14271551C211yesmaximal, characteristic
5#14271546C211yesmaximal, characteristic, complemented
6#14271384C211yesmaximal, characteristic, complemented
7#14271384C211yesmaximal, characteristic, complemented
8#14271378C211yesmaximal, characteristic, complemented
9#14271377C211yesmaximal, characteristic, complemented
10#14271368C211yesmaximal, characteristic, complemented
11#14271362C211yesmaximal, characteristic, complemented
12#14271291C211yesmaximal, characteristic, complemented
13#14271269C211yesmaximal, characteristic, complemented
14#14271250C211yesmaximal, characteristic, complemented
15C29×#442C211yesmaximal, characteristic, complemented
16C2×D8×C29C2211yescharacteristic
17C4×D4×C29C2211yescharacteristic
18C4×D4×C29C2211yescharacteristic
19#11745302C2211yescharacteristic
20#11745298C2211yescharacteristic
21#11745298C2211yescharacteristic
22#11745298C2211yescharacteristic
23C2×#90783C2211yescharacteristic
24C2×#90783C2211yescharacteristic
25C2×#90783C2211yescharacteristic
26C2×#90782C2211yescharacteristic
27#11745291—21no—
28C4×C22⋊D29—21no—
29#11745288—21no—
30#11745286—21no—
31C2×Dic116C2211yescharacteristic
32C2×Dic116C2211yescharacteristic
33C2×#90773C2211yescharacteristic
34C2×#90773C2211yescharacteristic
35#11745255C2211yescharacteristic
36#11745249C2211yescharacteristic
37#11745249C2211yescharacteristic
38#11745249C2211yescharacteristic
39#11745247—21no—
40#11745245—21no—
41#11745241—21no—
42#11745241—21no—
43#11745237C2211yescharacteristic
44#11745231C2211yescharacteristic
45C4×Dic58C2211yescharacteristic
46C29×#106C2211yescharacteristic
47C29×#102C2211yescharacteristic
48C29×#102C2211yescharacteristic
49C29×#97C2211yescharacteristic
50#11745163C2211yescharacteristic
51#11745162C2211yescharacteristic
52#11745162C2211yescharacteristic
53C8×Dic29C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745157C2211yescharacteristic
58C4⋊#6597C2211yescharacteristic
59C2×D4×C29C2311yescharacteristic
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×D116C2311yescharacteristic
66C2×C4×D29—21no—
67C2×Dic58D411yescharacteristic
68C2×Dic58C2311yescharacteristic
69C2×Dic58C2311yescharacteristic
70C2×Dic58C2311yescharacteristic
71D8×C29—22no—
72C2×C8×C29C2311yescharacteristic
73C2×C8×C29C2311yescharacteristic
74C4⋊C4×C29C2311yescharacteristic
75C4⋊C4×C29C2311yescharacteristic
76C22⋊C4×C29—21no—
77C22⋊C4×C29—21no—
78C42×C29C2311yescharacteristic
79C22⋊Dic29—21no—
80C22⋊Dic29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85#90783—41no—
86#90783—41no—
87#90783—41no—
88#90782—41no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29D411yescharacteristic
95#90779—21no—
96#90779—21no—
97#90779—21no—
98#90779D411yescharacteristic
99#90779D411yescharacteristic
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29C2311yescharacteristic
104C4×Dic29C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107Dic116—22no—
108Dic116—41no—
109#90773—22no—
110#90773—41no—
111C23×C29—21no—
112C23×C29—21no—
113C22×D29—21no—
114D4×C29—21no—
115D4×C29—21no—
116D4×C29—21no—
117D4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—42no—
121C2×C4×C29—81no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2411yescharacteristic
125C22⋊D29—42no—
126C22⋊D29—81no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134D116—21no—
135D116—21no—
136C4×D29—81no—
137Dic58—21no—
138Dic58—21no—
139Dic58—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—41no—
144C8×C29—21no—
145C8×C29#4112yes—
146#6597—21no—
147#6597—21no—
148#3401—291nomaximal, Sylow
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29C22×D411yescharacteristic
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29C2×#4111yescharacteristic
164C4×C29H(5,𝔽2)11yescharacteristic
165Dic29—21no—
166Dic29—21no—
167Dic29—21no—
168Dic29—21no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172#559—291no—
173#556—291no—
174#497—291no—
175#496—291no—
176#495—291no—
177#464—291no—
178#464—291no—
179#463—291no—
180#463—291no—
181#461—291no—
182#460—291no—
183#446—291no—
184#442D2911yescharacteristic, complemented
185#441—291no—
186C4×SD16—291no—
187C2×C29—81no—
188C2×C29—81no—
189C2×C29#55011yescharacteristic
190C2×C29#57511yescharacteristic
191C2×C29#57711yescharacteristic
192D29—81no—
193C2×Q16—291no—
194C2×Q16—291no—
195C2×SD16—291no—
196C2×SD16—291no—
197C2×SD16—291no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8C2×D2911yescharacteristic
202C4⋊Q8—291no—
203#127—291no—
204#126—581no—
205#126—581no—
206#124—291no—
207#124—291no—
208#124—291no—
209#124—291no—
210#124—581no—
211#123—581no—
212#123—581no—
213C22⋊Q8—581no—
214C4×Q8—291no—
215C4×Q8—291no—
216C4×Q8—291no—
217C4×Q8—291no—
218C4×D4—291no—
219C4×D4—581no—
220C4×D4C2×D2911yescharacteristic
221C4×D4C2×D2911yescharacteristic
222#117—581no—
223#106C2×D2911yescharacteristic
224C4⋊C8—291no—
225C4⋊C8—291no—
226C4⋊C8—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#102—291no—
231#102C2×D2911yescharacteristic
232#102C2×D2911yescharacteristic
233#97—291no—
234#97C2×D2911yescharacteristic
235C4×C8—291no—
236C29#340111yescharacteristic, complemented, Sylow
237C2×Q8—291no—
238C2×Q8—291no—
239C2×Q8—291no—
240C2×Q8—291no—
241C2×D4—291no—
242C2×D4—581no—
243C2×D4—581no—
244C2×D4C22×D2911yescharacteristic
245C2×D4C22×D2911yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—581no—
249Q16—582no—
250Q16—1161no—
251SD16—582no—
252SD16—1161no—
253SD16—1161no—
254SD16—1161no—
255SD16—1161no—
256D8—22no—
257D8—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C4⋊C4—291no—
263C4⋊C4—291no—
264C4⋊C4—291no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4C22×D2911yescharacteristic
271C4⋊C4C22×D2911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C42—291no—
284C42—291no—
285C42—581no—
286C42—581no—
287C42—581no—
288C42C22×D2911yescharacteristic
289C23—21no—
290C23—21no—
291C23—581no—
292Q8—581no—
293Q8—581no—
294Q8—581no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—1161no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—581no—
304D4—581no—
305D4—1162no—
306D4—2321no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—291no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—2321no—
319C2×C4D4×D2911yescharacteristic
320C2×C4D4×D2911yescharacteristic
321C2×C4C23×D2911yescharacteristic
322C8—21no—
323C8—581no—
324C8—581no—
325C8#9080512yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—1161no—
333C22—1161no—
334C22—1161no—
335C22C2×D4×D2911yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—581no—
341C4—581no—
342C4—581no—
343C4—581no—
344C4—1161no—
345C4—1161no—
346C4—1161no—
347C4C2×#9080511yescharacteristic
348C4#1174536411yescharacteristic
349C2—81no—
350C2—81no—
351C2—2321no—
352C2#1427183411yescharacteristic
353C2#1427195911yescharacteristic
354C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#442C2
socleC22×C29C22×D4
prime radical#14271551C2
hypercenter#442D29
hypocenterC29#3401
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14271896C2semidirect
2. #14271883C2semidirect
3. #14271557C2semidirect
5. #14271546C2semidirect
6. #14271384C2semidirect
7. #14271384C2semidirect
8. #14271378C2semidirect
9. #14271377C2semidirect
10. #14271368C2semidirect
11. #14271362C2semidirect
12. #14271291C2semidirect
13. #14271269C2semidirect
14. #14271250C2semidirect
15. C29×#442C2semidirect
184. #442D29semidirect
236. C29#3401semidirect

Maximal subgroups

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

subgroupindex
#142718962
#142718832
#142715572
#142715512
#142715462
#142713842
#142713782
#142713772
#142713682
#142713622
#142712912
#142712692
#142712502
C29×#4422
#340129