Finite Group Databasebeta

← #16829011

Subgroups — #16829011

Order 3712.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745280C211yesmaximal, characteristic, complemented
2C2×SD16×D29C211yesmaximal, characteristic, complemented
3#14271731C211yesmaximal, characteristic
4#14271639C211yesmaximal, characteristic, complemented
5#14271388C211yesmaximal, characteristic, complemented
6#14271387C211yesmaximal, characteristic, complemented
7#14271382C211yesmaximal, characteristic, complemented
8#14271364C211yesmaximal, characteristic, complemented
9#14271363C211yesmaximal, characteristic, complemented
10#14271362C211yesmaximal, characteristic, complemented
11#14271361C211yesmaximal, characteristic, complemented
12#14271188C211yesmaximal, characteristic, complemented
13#14271166C211yesmaximal, characteristic, complemented
14#14271158C211yesmaximal, characteristic, complemented
15C29×#464C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C2×Q16×C29C2211yescharacteristic, complemented
20C2×SD16×C29C2211yescharacteristic
21C29×#124C2211yescharacteristic
22C4×Q8×C29C2211yescharacteristic, complemented
23#11745309C2211yescharacteristic
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90785C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic
27C2×#90784C2211yescharacteristic, complemented
28#11745302C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30#11745280—24no—
31SD16×D29—24no—
32C2×#90773C2211yescharacteristic
33C2×#90773C2211yescharacteristic, complemented
34C2×#90772C2211yescharacteristic
35C2×C8×D29C2211yescharacteristic
36#11745254—21no—
37#11745254C2211yescharacteristic
38#11745249—21no—
39#11745249C2211yescharacteristic, complemented
40#11745246—21no—
41#11745246—21no—
42#11745244—21no—
43#11745244—21no—
44#11745236C2211yescharacteristic
45#11745234—21no—
46#11745234C2211yescharacteristic
47C4×Dic58—21no—
48C4×Dic58C2211yescharacteristic, complemented
49C29×C4⋊C8C2211yescharacteristic, complemented
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic
52#11745183C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745169C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745162C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic
59#11745157C2211yescharacteristic, complemented
60C4⋊#6597C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68#90809—22no—
69#90809—22no—
70Q8×D29—22no—
71Q8×D29D414yescomplemented
72D4×D29—22no—
73D4×D29—22no—
74C2×D116—21no—
75C2×D116—21no—
76C2×D116—21no—
77C2×D116C2311yescharacteristic
78C2×D116C2311yescharacteristic
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×C4×D29C2311yescharacteristic
82C2×Dic58—21no—
83C2×Dic58C2311yescharacteristic
84Q16×C29—22no—
85SD16×C29—22no—
86C2×C8×C29C2311yescharacteristic
87C2×C8×C29C2311yescharacteristic
88C4⋊C4×C29—21no—
89C4⋊C4×C29C2311yescharacteristic
90C22⋊C4×C29—21no—
91C22⋊C4×C29—21no—
92C42×C29—21no—
93C42×C29C2311yescharacteristic
94#90785—22no—
95#90784—22no—
96#90784—22no—
97#90783—22no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101#90781D411yescharacteristic
102#90781D411yescharacteristic
103C4⋊Dic29—21no—
104C4⋊Dic29C2311yescharacteristic
105#90779—21no—
106#90779—21no—
107#90779D411yescharacteristic
108#90779D411yescharacteristic
109C4×Dic29—21no—
110C4×Dic29—21no—
111C4×Dic29—21no—
112C4×Dic29—21no—
113C4×Dic29C2311yescharacteristic
114C2×#6597C2311yescharacteristic
115C2×#6597C2311yescharacteristic
116#90773—22no—
117#90773—22no—
118#90772—22no—
119C8×D29—22no—
120C23×C29—21no—
121C22×D29—21no—
122C22×D29—21no—
123C22×D29—42no—
124C22×D29—81no—
125C22×D29—81no—
126C22×D29C2×D411yescharacteristic
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29C2×D412yes—
131D4×C29—21no—
132D4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2411yescharacteristic
139C22⋊D29—42no—
140C22⋊D29—81no—
141C22⋊D29—81no—
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29C2×D411yescharacteristic
145C2×Dic29C2×D411yescharacteristic
146C2×Dic29C2×D411yescharacteristic
147D116—21no—
148D116—21no—
149D116—21no—
150D116—21no—
151D116—42no—
152D116—81no—
153D116—81no—
154C4×D29—24no—
155C4×D29—42no—
156C4×D29C2×D412yes—
157C4×D29#4112yes—
158Dic58—21no—
159Dic58—24no—
160Dic58C2×D412yes—
161C8×C29—21no—
162C8×C29—21no—
163#6597—21no—
164#6597—21no—
165#3043—291nomaximal, Sylow
166C22×C29—41no—
167C22×C29—41no—
168C22×C29—41no—
169C22×C29C22×D411yescharacteristic
170C2×D29—21no—
171C2×D29—21no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—41no—
176C2×D29—41no—
177C2×D29—41no—
178C2×D29—84no—
179C2×D29#12112yes—
180C4×C29—22no—
181C4×C29—21no—
182C4×C29—21no—
183C4×C29—41no—
184C4×C29—41no—
185C4×C29C22×D411yescharacteristic
186C4×C29C2×#4111yescharacteristic
187Dic29—22no—
188Dic29—21no—
189Dic29—21no—
190Dic29—41no—
191Dic29#12112yes—
192C2×#137—291no—
193C22×SD16—291no—
194#535—291no—
195#519—291no—
196#464—291no—
197#464—291no—
198#464—291no—
199#464D2911yescharacteristic, complemented
200#460—291no—
201#460—291no—
202#460—291no—
203#460—291no—
204#424—291no—
205#418—291no—
206#416—291no—
207C2×C29—81no—
208C2×C29C2×#12111yescharacteristic
209C2×C29#57711yescharacteristic
210C2×C29#57711yescharacteristic
211D29—22no—
212D29—81no—
213D29—81no—
214C2×#41—291no—
215C22×Q8—291no—
216C22×D4—291no—
217#137—584no—
218C2×Q16—291no—
219C2×Q16C2×D2911yescharacteristic, complemented
220C2×SD16—291no—
221C2×SD16—291no—
222C2×SD16—291no—
223C2×SD16—291no—
224C2×SD16—291no—
225C2×SD16—584no—
226C2×SD16C2×D2911yescharacteristic
227C2×M16—291no—
228C22×C8—291no—
229#127—291no—
230#127—291no—
231#124—291no—
232#124C2×D2911yescharacteristic
233#121—581no—
234#121—581no—
235#120—581no—
236#120—581no—
237C4×Q8—291no—
238C4×Q8—291no—
239C4×Q8—291no—
240C4×Q8—581no—
241C4×Q8—581no—
242C4×Q8C2×D2911yescharacteristic, complemented
243#117—291no—
244#117—291no—
245#117—581no—
246#117—581no—
247C4⋊C8—291no—
248C4⋊C8—291no—
249C4⋊C8—291no—
250C4⋊C8C2×D2911yescharacteristic, complemented
251#103—291no—
252#103C2×D2911yescharacteristic, complemented
253#102—291no—
254#102—291no—
255#102—291no—
256#102—291no—
257#102—291no—
258#102C2×D2911yescharacteristic
259C29#304311yescharacteristic, complemented, Sylow
260C24—581no—
261#41—582no—
262#41—582no—
263C2×Q8—294no—
264C2×Q8—291no—
265C2×Q8—581no—
266C2×Q8—582no—
267C2×Q8C22×D2911yescharacteristic
268C2×Q8C22×D2911yescharacteristic
269C2×D4—291no—
270C2×D4—291no—
271C2×D4—581no—
272C2×D4—582no—
273C2×D4—582no—
274C2×D4—581no—
275C2×D4—581no—
276C2×D4—581no—
277C2×D4—581no—
278C2×D4—581no—
279C2×D4C22×D2911yescharacteristic
280C22×C4—291no—
281C22×C4—581no—
282C22×C4—581no—
283Q16—22no—
284Q16—582no—
285SD16—22no—
286SD16—582no—
287SD16—582no—
288SD16—582no—
289SD16—582no—
290SD16—582no—
291M16—582no—
292C2×C8—291no—
293C2×C8—291no—
294C2×C8—582no—
295C2×C8C22×D2911yescharacteristic
296C2×C8C22×D2911yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—291no—
299C4⋊C4—291no—
300C4⋊C4—291no—
301C4⋊C4—581no—
302C4⋊C4—581no—
303C4⋊C4—581no—
304C4⋊C4C22×D2911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—291no—
308C22⋊C4—291no—
309C22⋊C4—581no—
310C22⋊C4—581no—
311C22⋊C4—581no—
312C42—21no—
313C42—291no—
314C42—581no—
315C42—581no—
316C42—581no—
317C42—581no—
318C42C22×D2911yescharacteristic
319C23—21no—
320C23—291no—
321C23—581no—
322C23—581no—
323C23—1162no—
324C23—2321no—
325C23—2321no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—292no—
330Q8—584no—
331Q8—581no—
332Q8D4×D2912yes—
333D4—21no—
334D4—21no—
335D4—581no—
336D4—581no—
337D4—581no—
338D4—581no—
339D4—1162no—
340D4—1162no—
341D4—2321no—
342D4—2321no—
343D4—2321no—
344D4—2321no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—291no—
349C2×C4—292no—
350C2×C4—292no—
351C2×C4—291no—
352C2×C4—291no—
353C2×C4—584no—
354C2×C4—581no—
355C2×C4—581no—
356C2×C4—1162no—
357C2×C4D4×D2911yescharacteristic
358C2×C4D4×D2911yescharacteristic
359C2×C4C23×D2911yescharacteristic
360C8—21no—
361C8—21no—
362C8—581no—
363C8—581no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—292no—
368C22—581no—
369C22—581no—
370C22—1161no—
371C22—1161no—
372C22—1161no—
373C22—1161no—
374C22—1161no—
375C22—1161no—
376C22—2324no—
377C22C2×D4×D2911yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—292no—
384C4—582no—
385C4—581no—
386C4—581no—
387C4—1161no—
388C4C2×D4×D2911yescharacteristic
389C4#41×D2911yescharacteristic
390C2—81no—
391C2—582no—
392C2—2321no—
393C2—2321no—
394C2#121×D2911yescharacteristic
395C2#1427197011yescharacteristic
396C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#464C2
socleC22×C29C22×D4
prime radical#14271731C2
hypercenter#464D29
hypocenterC29#3043
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#11745280C2semidirect
2. C2×SD16×D29C2semidirect
4. #14271639C2semidirect
5. #14271388C2semidirect
6. #14271387C2semidirect
7. #14271382C2semidirect
8. #14271364C2semidirect
9. #14271363C2semidirect
10. #14271362C2semidirect
11. #14271361C2semidirect
12. #14271188C2semidirect
13. #14271166C2semidirect
14. #14271158C2semidirect
15. C29×#464C2semidirect
19. C2×Q16×C29C22semidirect
22. C4×Q8×C29C22semidirect
24. Q8×Dic29C22semidirect
25. C2×#90785C22semidirect
27. C2×#90784C22semidirect
33. C2×#90773C22semidirect
39. #11745249C22semidirect
48. C4×Dic58C22semidirect
49. C29×C4⋊C8C22semidirect
50. C29×#103C22semidirect
52. #11745183C22semidirect
55. #11745169C22semidirect
56. #11745162C22semidirect
57. #11745162C22semidirect
59. #11745157C22semidirect
60. C4⋊#6597C22semidirect
71. Q8×D29D4semidirect
199. #464D29semidirect
219. C2×Q16C2×D29semidirect
242. C4×Q8C2×D29semidirect
250. C4⋊C8C2×D29semidirect
252. #103C2×D29semidirect
259. C29#3043semidirect

Maximal subgroups

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

subgroupindex
C2×#117452802
C2×SD16×D292
#142717312
#142716392
#142713882
#142713872
#142713822
#142713642
#142713632
#142713622
#142713612
#142711882
#142711662
#142711582
C29×#4642
#304329