Finite Group Databasebeta

← #16831377

Subgroups — #16831377

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271848C211yesmaximal, characteristic, complemented
2#14271819C211yesmaximal, characteristic
3#14271516C211yesmaximal, characteristic, complemented
4#14271506C211yesmaximal, characteristic, complemented
5#14271469C211yesmaximal, characteristic, complemented
6#14271405C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271384C211yesmaximal, characteristic, complemented
9#14271326C211yesmaximal, characteristic, complemented
10#14271321C211yesmaximal, characteristic, complemented
11#14271257C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271156C211yesmaximal, characteristic, complemented
14C2×#11745158C211yesmaximal, characteristic, complemented
15C29×#480C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C29×#121C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745301—21no—
21#11745298C2211yescharacteristic
22D4×Dic29—21no—
23C2×#90783C2211yescharacteristic
24#11745291—21no—
25C4×C22⋊D29C2211yescharacteristic
26#11745288—21no—
27#11745286C2211yescharacteristic
28C22×#6597C2211yescharacteristic
29C2×Dic116C2211yescharacteristic
30C2×Dic116C2211yescharacteristic
31C2×C8×D29C2211yescharacteristic
32#11745260—21no—
33#11745259C2211yescharacteristic
34#11745259C2211yescharacteristic
35#11745254C2211yescharacteristic
36#11745252C2211yescharacteristic
37#11745251—21no—
38#11745249C2211yescharacteristic
39#11745249C2211yescharacteristic
40#11745247—21no—
41#11745240—21no—
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C29×#102C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745168C2211yescharacteristic
49#11745164C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745162C2211yescharacteristic
52C8×Dic29C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745158C2211yescharacteristic
58#11745156C2211yescharacteristic
59C2×D4×C29—21no—
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29D411yescharacteristic
65C22×Dic29—21no—
66C22×Dic29—21no—
67#90807—22no—
68#90807—41no—
69C2×C4×D29C2311yescharacteristic
70C2×Dic58—22no—
71C2×Dic58—21no—
72C2×Dic58—41no—
73C2×Dic58C2311yescharacteristic
74C2×Dic58C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29—21no—
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29D411yescharacteristic
87#90783—41no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781D411yescharacteristic
92C4⋊Dic29—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779D411yescharacteristic
101C4×Dic29—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C2×#6597—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108Dic116—22no—
109Dic116—41no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C22×D29C2×D411yescharacteristic
114D4×C29—21no—
115D4×C29—21no—
116D4×C29—42no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—42no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2411yescharacteristic
125C22⋊D29—22no—
126C22⋊D29—42no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—42no—
132C2×Dic29—42no—
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C4×D29—21no—
137C4×D29—21no—
138Dic58—21no—
139Dic58—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—42no—
144Dic58#4112yes—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3300—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29#13512yes—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C29H(5,𝔽2)11yescharacteristic
166Dic29—22no—
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173#552—291no—
174#548—291no—
175#488—291no—
176#485—291no—
177#480D2911yescharacteristic, complemented
178#479—291no—
179#467—291no—
180#465—291no—
181#464—291no—
182#452—291no—
183#451—291no—
184C4×Q16—291no—
185C8×D4—291no—
186#416—291no—
187C2×#103—291no—
188C2×C29—22no—
189C2×C29—81no—
190C2×C29#54611yescharacteristic
191C2×C29C2×#13511yescharacteristic
192C2×C29#57811yescharacteristic
193D29—41no—
194C2×#41—291no—
195C22×Q8—291no—
196C2×Q16—291no—
197C2×Q16—291no—
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8—291no—
201#126—581no—
202#125—291no—
203#125—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—291no—
209C22⋊Q8—291no—
210C22⋊Q8—581no—
211#121—581no—
212#121C2×D2911yescharacteristic
213C4×Q8—291no—
214C4×Q8—291no—
215C4×D4—291no—
216C4×D4—581no—
217#117—291no—
218#117—581no—
219C2×C4⋊C4C2×D2911yescharacteristic
220#107C2×D2911yescharacteristic
221#107C2×D2911yescharacteristic
222#106—291no—
223C4⋊C8—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#103—291no—
231#102—291no—
232#102C2×D2911yescharacteristic
233#102C2×D2911yescharacteristic
234C22⋊C8—291no—
235C22⋊C8C2×D2911yescharacteristic
236C4×C8—291no—
237C29#330011yescharacteristic, complemented, Sylow
238#41—582no—
239#41—1161no—
240C2×Q8—291no—
241C2×Q8—291no—
242C2×Q8—291no—
243C2×Q8—582no—
244C2×Q8—581no—
245C2×Q8—1161no—
246C2×D4—21no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C22×C4—21no—
251C22×C4—291no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4C22×D2911yescharacteristic
255Q16—582no—
256Q16—1161no—
257SD16—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—1161no—
261C2×C8—1161no—
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4C22×D2911yescharacteristic
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—291no—
279C22⋊C4—291no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—291no—
287C42—581no—
288C42—581no—
289C42—581no—
290C23—21no—
291C23—291no—
292C23D4×D2911yescharacteristic
293Q8—292no—
294Q8—581no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—581no—
299Q8—1162no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—582no—
304D4—1162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—1162no—
321C2×C4—1162no—
322C2×C4D4×D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—581no—
327C8—581no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—581no—
334C22—581no—
335C22—581no—
336C22#1174527412yes—
337C22C2×D4×D2911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—581no—
343C4—582no—
344C4—581no—
345C4—581no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4#41×D2911yescharacteristic
350C4#1174536411yescharacteristic
351C2—22no—
352C2—81no—
353C2—1161no—
354C2#1427180511yescharacteristic
355C2C2×#1174527411yescharacteristic
356C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#480C2
socleC22×C29C22×D4
prime radical#14271819C2
hypercenter#480D29
hypocenterC29#3300
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
1. #14271848C2semidirect
3. #14271516C2semidirect
4. #14271506C2semidirect
5. #14271469C2semidirect
6. #14271405C2semidirect
7. #14271390C2semidirect
8. #14271384C2semidirect
9. #14271326C2semidirect
10. #14271321C2semidirect
11. #14271257C2semidirect
12. #14271226C2semidirect
13. #14271156C2semidirect
14. C2×#11745158C2semidirect
15. C29×#480C2semidirect
177. #480D29semidirect
237. C29#3300semidirect

Maximal subgroups

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

subgroupindex
#142718482
#142718192
#142715162
#142715062
#142714692
#142714052
#142713902
#142713842
#142713262
#142713212
#142712572
#142712262
#142711562
C2×#117451582
C29×#4802
#330029