Finite Group Databasebeta

← #16829032

Subgroups — #16829032

Order 3712.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745273C211yesmaximal, characteristic, complemented
2C2×#11745278C211yesmaximal, characteristic, complemented
3#14271731C211yesmaximal, characteristic, complemented
4#14271642C211yesmaximal, characteristic, complemented
5#14271388C211yesmaximal, characteristic, complemented
6#14271382C211yesmaximal, characteristic, complemented
7#14271380C211yesmaximal, characteristic, complemented
8#14271364C211yesmaximal, characteristic, complemented
9#14271362C211yesmaximal, characteristic, complemented
10#14271358C211yesmaximal, characteristic, complemented
11#14271356C211yesmaximal, characteristic, complemented
12#14271188C211yesmaximal, characteristic, complemented
13#14271163C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic, complemented
20C2×D8×C29C2211yescharacteristic
21C29×#124C2211yescharacteristic
22C4×D4×C29C2211yescharacteristic, complemented
23#11745309C2211yescharacteristic
24C2×#90785C2211yescharacteristic, complemented
25#11745302C2211yescharacteristic
26D4×Dic29C2211yescharacteristic, complemented
27C2×#90783C2211yescharacteristic
28C2×#90782C2211yescharacteristic
29C2×#90782C2211yescharacteristic, complemented
30C4×C22⋊D29—21no—
31C2×#90779—21no—
32#11745278—24no—
33#11745273—24no—
34C2×#90773C2211yescharacteristic
35C2×#90773C2211yescharacteristic, complemented
36C2×#90772C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic
38C4⋊C4×D29C2211yescharacteristic
39#11745249C2211yescharacteristic, complemented
40#11745246—21no—
41#11745246—21no—
42#11745244—21no—
43#11745244—21no—
44#11745243—21no—
45#11745239—21no—
46#11745236C2211yescharacteristic
47#11745234C2211yescharacteristic
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×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C22×Dic29—21no—
71C22×Dic29—21no—
72#90809—22no—
73#90809—22no—
74#90807—22no—
75#90807D414yescomplemented
76D4×D29—22no—
77D4×D29—22no—
78C2×D116—21no—
79C2×D116—21no—
80C2×D116—21no—
81C2×D116C2311yescharacteristic
82C2×D116C2311yescharacteristic
83C2×C4×D29—21no—
84C2×C4×D29—21no—
85C2×C4×D29C2311yescharacteristic
86C2×Dic58C2311yescharacteristic
87SD16×C29—22no—
88D8×C29—22no—
89C2×C8×C29C2311yescharacteristic
90C2×C8×C29C2311yescharacteristic
91C4⋊C4×C29C2311yescharacteristic
92C22⋊C4×C29—21no—
93C22⋊C4×C29—21no—
94C22⋊C4×C29—21no—
95C42×C29C2311yescharacteristic
96C22⋊Dic29—21no—
97#90785—22no—
98#90783—22no—
99#90782—22no—
100#90782—22no—
101#90781—21no—
102#90781—21no—
103#90781D411yescharacteristic
104#90781D411yescharacteristic
105C4⋊Dic29C2311yescharacteristic
106#90779—21no—
107#90779—21no—
108#90779—21no—
109#90779D411yescharacteristic
110#90779D411yescharacteristic
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—
121C23×C29—21no—
122C22×D29—21no—
123C22×D29—21no—
124C22×D29—42no—
125C22×D29—81no—
126C22×D29—81no—
127C22×D29C2×D411yescharacteristic
128Q8×C29—21no—
129Q8×C29—21no—
130D4×C29—21no—
131D4×C29—21no—
132D4×C29—21no—
133D4×C29C2×D412yes—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—81no—
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2411yescharacteristic
140C22⋊D29—24no—
141C22⋊D29—42no—
142C22⋊D29—81no—
143C22⋊D29—81no—
144C2×Dic29—21no—
145C2×Dic29—24no—
146C2×Dic29—21no—
147C2×Dic29—81no—
148C2×Dic29C2×D411yescharacteristic
149C2×Dic29C2×D411yescharacteristic
150C2×Dic29C2×D411yescharacteristic
151D116—21no—
152D116—21no—
153D116—21no—
154D116—21no—
155D116—42no—
156D116—81no—
157D116—81no—
158C4×D29—42no—
159C4×D29—81no—
160C4×D29C2×D412yes—
161C4×D29#4112yes—
162Dic58—21no—
163Dic58C2×D412yes—
164C8×C29—21no—
165C8×C29—21no—
166#6597—21no—
167#6597—21no—
168#3045—291nomaximal, Sylow
169C22×C29—22no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29C22×D411yescharacteristic
176C2×D29—21no—
177C2×D29—21no—
178C2×D29—41no—
179C2×D29—41no—
180C2×D29—41no—
181C2×D29—41no—
182C2×D29—41no—
183C2×D29—41no—
184C2×D29—84no—
185C2×D29#12112yes—
186C4×C29—21no—
187C4×C29—21no—
188C4×C29—41no—
189C4×C29—41no—
190C4×C29C22×D411yescharacteristic
191C4×C29C2×#4111yescharacteristic
192Dic29—22no—
193Dic29—21no—
194Dic29—21no—
195Dic29—41no—
196Dic29#12112yes—
197C2×AGL(1,ℤ/8)—291no—
198C2×#135—291no—
199#535—291no—
200#520—291no—
201#464—291no—
202#464—291no—
203#463—291no—
204#463D2911yescharacteristic, complemented
205#460—291no—
206#460—291no—
207#459—291no—
208#459—291no—
209#424—291no—
210#417—291no—
211C2×#102—291no—
212C2×C29—42no—
213C2×C29—81no—
214C2×C29C2×#12111yescharacteristic
215C2×C29#57611yescharacteristic
216C2×C29#57711yescharacteristic
217D29—22no—
218D29—81no—
219D29—81no—
220C2×#41—291no—
221C2×#41—291no—
222C22×D4—291no—
223AGL(1,ℤ/8)—584no—
224#135—584no—
225C2×Q16—291no—
226C2×SD16—291no—
227C2×SD16—291no—
228C2×SD16—291no—
229C2×SD16C2×D2911yescharacteristic, complemented
230C2×D8—291no—
231C2×D8—291no—
232C2×D8C2×D2911yescharacteristic
233C2×M16—291no—
234C22×C8—291no—
235#127—291no—
236#127—291no—
237#124—291no—
238#124C2×D2911yescharacteristic
239#121—581no—
240#121—581no—
241#120—581no—
242#120—581no—
243C4×Q8—291no—
244C4×Q8—291no—
245C4×D4—291no—
246C4×D4—581no—
247C4×D4—581no—
248C4×D4C2×D2911yescharacteristic, complemented
249#117—291no—
250#117—581no—
251C2×C4⋊C4—291no—
252C2×C4⋊C4—581no—
253C4⋊C8—291no—
254C4⋊C8—291no—
255C4⋊C8—291no—
256C4⋊C8C2×D2911yescharacteristic, complemented
257#103—291no—
258#103C2×D2911yescharacteristic, complemented
259#102—291no—
260#102—291no—
261#102—291no—
262#102—291no—
263#102—291no—
264#102C2×D2911yescharacteristic
265C29#304511yescharacteristic, complemented, Sylow
266C24—581no—
267#41—294no—
268#41—582no—
269#41—582no—
270#41—582no—
271C2×Q8—291no—
272C2×Q8C22×D2911yescharacteristic
273C2×D4—291no—
274C2×D4—291no—
275C2×D4—581no—
276C2×D4—582no—
277C2×D4—582no—
278C2×D4—581no—
279C2×D4—581no—
280C2×D4—581no—
281C2×D4—581no—
282C2×D4—581no—
283C2×D4—581no—
284C2×D4C22×D2911yescharacteristic
285C2×D4C22×D2911yescharacteristic
286C22×C4—21no—
287C22×C4—291no—
288C22×C4—581no—
289C22×C4—581no—
290C22×C4—581no—
291C22×C4—581no—
292Q16—582no—
293SD16—22no—
294SD16—582no—
295SD16—582no—
296SD16—582no—
297D8—22no—
298D8—582no—
299D8—582no—
300M16—582no—
301C2×C8—291no—
302C2×C8—291no—
303C2×C8—582no—
304C2×C8C22×D2911yescharacteristic
305C2×C8C22×D2911yescharacteristic
306C4⋊C4—291no—
307C4⋊C4—291no—
308C4⋊C4—291no—
309C4⋊C4—581no—
310C4⋊C4—581no—
311C4⋊C4—581no—
312C4⋊C4C22×D2911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—291no—
317C22⋊C4—291no—
318C22⋊C4—581no—
319C22⋊C4—581no—
320C22⋊C4—581no—
321C42—291no—
322C42—581no—
323C42—581no—
324C42C22×D2911yescharacteristic
325C23—21no—
326C23—21no—
327C23—291no—
328C23—581no—
329C23—581no—
330C23—1162no—
331C23—2321no—
332C23—2321no—
333Q8—21no—
334Q8—21no—
335Q8—292no—
336Q8—581no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—584no—
341D4—581no—
342D4—581no—
343D4—581no—
344D4—581no—
345D4—1162no—
346D4—1162no—
347D4—2321no—
348D4—2321no—
349D4—2321no—
350D4—2321no—
351D4D4×D2912yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—81no—
355C2×C4—291no—
356C2×C4—292no—
357C2×C4—292no—
358C2×C4—291no—
359C2×C4—291no—
360C2×C4—584no—
361C2×C4—581no—
362C2×C4—581no—
363C2×C4—1162no—
364C2×C4—2321no—
365C2×C4—2321no—
366C2×C4D4×D2911yescharacteristic
367C2×C4D4×D2911yescharacteristic
368C2×C4C23×D2911yescharacteristic
369C8—21no—
370C8—21no—
371C8—581no—
372C8—581no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—292no—
380C22—581no—
381C22—581no—
382C22—1161no—
383C22—1161no—
384C22—1161no—
385C22—1161no—
386C22—1161no—
387C22—1161no—
388C22—2324no—
389C22C2×D4×D2911yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—292no—
395C4—582no—
396C4—581no—
397C4—581no—
398C4—1161no—
399C4C2×D4×D2911yescharacteristic
400C4#41×D2911yescharacteristic
401C2—42no—
402C2—81no—
403C2—582no—
404C2—2321no—
405C2—2321no—
406C2#121×D2911yescharacteristic
407C2#1427196711yescharacteristic
408C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
hypercenter#463D29
hypocenterC29#3045
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11745273C2semidirect
2. C2×#11745278C2semidirect
3. #14271731C2semidirect
4. #14271642C2semidirect
5. #14271388C2semidirect
6. #14271382C2semidirect
7. #14271380C2semidirect
8. #14271364C2semidirect
9. #14271362C2semidirect
10. #14271358C2semidirect
11. #14271356C2semidirect
12. #14271188C2semidirect
13. #14271163C2semidirect
14. #102×D29C2semidirect
15. C29×#463C2semidirect
19. C2×SD16×C29C22semidirect
22. C4×D4×C29C22semidirect
24. C2×#90785C22semidirect
26. D4×Dic29C22semidirect
29. C2×#90782C22semidirect
35. 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
75. #90807D4semidirect
204. #463D29semidirect
229. C2×SD16C2×D29semidirect
248. C4×D4C2×D29semidirect
256. C4⋊C8C2×D29semidirect
258. #103C2×D29semidirect
265. C29#3045semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
C2×#117452782
#142717312
#142716422
#142713882
#142713822
#142713802
#142713642
#142713622
#142713582
#142713562
#142711882
#142711632
#102×D292
C29×#4632
#304529