Finite Group Databasebeta

← #16829126

Subgroups — #16829126

Order 3712.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D29C211yesmaximal, characteristic, complemented
2C2×#11745263C211yesmaximal, characteristic, complemented
3#14271736C211yesmaximal, characteristic, complemented
4#14271729C211yesmaximal, characteristic
5#14271412C211yesmaximal, characteristic, complemented
6#14271411C211yesmaximal, characteristic, complemented
7#14271408C211yesmaximal, characteristic, complemented
8#14271407C211yesmaximal, characteristic, complemented
9#14271393C211yesmaximal, characteristic, complemented
10#14271392C211yesmaximal, characteristic, complemented
11#14271389C211yesmaximal, characteristic, complemented
12#14271198C211yesmaximal, characteristic, complemented
13#14271170C211yesmaximal, characteristic, complemented
14#14271166C211yesmaximal, characteristic, complemented
15C29×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×#90805C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C22×C8×C29C2211yescharacteristic, complemented
21C29×C22⋊Q8C2211yescharacteristic, complemented
22C29×#121C2211yescharacteristic
23#11745308C2211yescharacteristic, complemented
24C2×#90784C2211yescharacteristic
25#11745302—21no—
26#11745300C2211yescharacteristic
27#11745299—21no—
28C2×#90783C2211yescharacteristic
29#11745292C2211yescharacteristic
30#11745286C2211yescharacteristic, complemented
31C2×#90777C2211yescharacteristic, complemented
32SD16×D29—24no—
33C2×#90773C2211yescharacteristic
34#11745263—24no—
35C2×#90772C2211yescharacteristic
36C2×#90772C2211yescharacteristic, complemented
37C2×C8×D29C2211yescharacteristic
38C2×C8×D29C2211yescharacteristic, complemented
39#11745259C2211yescharacteristic, complemented
40#11745257C2211yescharacteristic
41#11745256—21no—
42#11745254C2211yescharacteristic
43#11745254C2211yescharacteristic
44#11745250—21no—
45#11745247—21no—
46#11745247—21no—
47#11745245—21no—
48#11745244—21no—
49C29×#106C2211yescharacteristic, complemented
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic
52#11745183C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745165C2211yescharacteristic, complemented
56#11745164C2211yescharacteristic, complemented
57#11745158C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic
59#11745155C2211yescharacteristic, complemented
60#11745155C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29D411yescharacteristic
70C2×C22⋊D29D411yescharacteristic
71Q8×D29—22no—
72Q8×D29—22no—
73D4×D29—22no—
74D4×D29—22no—
75#90805—22no—
76#90805—22no—
77C2×D116—21no—
78C2×D116D411yescharacteristic
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×C4×D29C2311yescharacteristic
82C2×C4×D29C2311yescharacteristic
83C2×Dic58—21no—
84C2×Dic58D411yescharacteristic
85C2×Dic58C2311yescharacteristic
86SD16×C29—22no—
87C2×C8×C29—22no—
88C2×C8×C29C2311yescharacteristic
89C2×C8×C29C2311yescharacteristic
90C4⋊C4×C29—21no—
91C4⋊C4×C29C2311yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C22⋊C4×C29—21no—
94C22⋊C4×C29—21no—
95C22⋊Dic29—21no—
96C22⋊Dic29—21no—
97#90784—22no—
98#90783—22no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105C4⋊Dic29—21no—
106C4⋊Dic29C2311yescharacteristic
107C4⋊Dic29C2311yescharacteristic
108#90779—21no—
109#90779—21no—
110C4×Dic29—21no—
111C4×Dic29—21no—
112#90777—22no—
113C2×#6597C2311yescharacteristic
114C2×#6597C2311yescharacteristic
115#90773—22no—
116#90772—22no—
117#90772—22no—
118C8×D29—22no—
119C8×D29D414yescomplemented
120C23×C29—21no—
121C23×C29C2×D411yescharacteristic
122C22×D29—21no—
123C22×D29—42no—
124C22×D29—81no—
125C22×D29—81no—
126C22×D29C2×D411yescharacteristic
127C22×D29C2×D411yescharacteristic
128Q8×C29—21no—
129Q8×C29—21no—
130D4×C29—21no—
131D4×C29—21no—
132D4×C29—81no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2411yescharacteristic
140C22⋊D29—22no—
141C22⋊D29—22no—
142C22⋊D29—42no—
143C22⋊D29—81no—
144C22⋊D29—81no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29C2×D411yescharacteristic
149C2×Dic29C2×D411yescharacteristic
150D116—22no—
151D116—21no—
152D116—21no—
153D116—81no—
154C4×D29—21no—
155C4×D29—21no—
156C4×D29—42no—
157C4×D29C2×D412yes—
158C4×D29#4112yes—
159Dic58—22no—
160Dic58—21no—
161Dic58—21no—
162Dic58—42no—
163C8×C29—21no—
164C8×C29C2×D412yes—
165#6597—21no—
166#6597C2×D412yes—
167#3057—291nomaximal, Sylow
168C22×C29—21no—
169C22×C29—21no—
170C22×C29—21no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29C22×D411yescharacteristic
175C2×D29—21no—
176C2×D29—21no—
177C2×D29—21no—
178C2×D29—21no—
179C2×D29—21no—
180C2×D29—41no—
181C2×D29—41no—
182C2×D29—41no—
183C2×D29—84no—
184C2×D29#12112yes—
185C4×C29—21no—
186C4×C29—41no—
187C4×C29—41no—
188C4×C29—41no—
189C4×C29C22×D411yescharacteristic
190C4×C29C2×#4111yescharacteristic
191Dic29—21no—
192Dic29—41no—
193Dic29—41no—
194Dic29—41no—
195Dic29#12112yes—
196C22×SD16—291no—
197C2×#131—291no—
198#536—291no—
199#535—291no—
200#468—291no—
201#468—291no—
202#468—291no—
203#468—291no—
204#465—291no—
205#465—291no—
206#465—291no—
207#465D2911yescharacteristic, complemented
208#427—291no—
209#419—291no—
210#418—291no—
211C2×C29—41no—
212C2×C29—81no—
213C2×C29C2×#12111yescharacteristic
214C2×C29#57711yescharacteristic
215C2×C29#57711yescharacteristic
216D29—22no—
217D29—41no—
218D29—81no—
219C2×#41—291no—
220C22×Q8—291no—
221C22×D4—291no—
222C2×SD16—291no—
223C2×SD16—291no—
224C2×SD16—291no—
225C2×SD16—584no—
226C2×SD16C2×D2911yescharacteristic
227#131—584no—
228C2×M16—291no—
229C2×M16—291no—
230C2×M16—291no—
231C22×C8—291no—
232C22×C8—291no—
233C22×C8C2×D2911yescharacteristic, complemented
234C4⋊Q8—581no—
235#127—581no—
236#124—581no—
237#124—581no—
238#123—581no—
239#123—581no—
240C22⋊Q8—291no—
241C22⋊Q8—291no—
242C22⋊Q8—291no—
243C22⋊Q8C2×D2911yescharacteristic, complemented
244#121—291no—
245#121—291no—
246#121—291no—
247#121C2×D2911yescharacteristic
248#120—581no—
249#120—581no—
250#117—291no—
251#117—291no—
252#107—291no—
253#107—291no—
254#106—291no—
255#106C2×D2911yescharacteristic, complemented
256#103—291no—
257#103—291no—
258#103—291no—
259#103C2×D2911yescharacteristic, complemented
260#102—291no—
261#102—291no—
262#102—291no—
263#102C2×D2911yescharacteristic
264C29#305711yescharacteristic, complemented, Sylow
265C24—581no—
266#41—582no—
267#41—582no—
268C2×Q8—291no—
269C2×Q8—291no—
270C2×Q8—581no—
271C2×Q8—582no—
272C2×Q8—582no—
273C2×Q8C22×D2911yescharacteristic
274C2×D4—21no—
275C2×D4—291no—
276C2×D4—291no—
277C2×D4—291no—
278C2×D4—291no—
279C2×D4—581no—
280C2×D4—582no—
281C2×D4—582no—
282C2×D4—581no—
283C2×D4—581no—
284C2×D4—581no—
285C2×D4C22×D2911yescharacteristic
286C22×C4—291no—
287C22×C4—291no—
288C22×C4—581no—
289C22×C4C22×D2911yescharacteristic
290SD16—22no—
291SD16—582no—
292SD16—582no—
293SD16—582no—
294M16—582no—
295M16—582no—
296M16—582no—
297C2×C8—22no—
298C2×C8—291no—
299C2×C8—294no—
300C2×C8—291no—
301C2×C8—582no—
302C2×C8C22×D2911yescharacteristic
303C2×C8C22×D2911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—291no—
306C4⋊C4—291no—
307C4⋊C4—581no—
308C4⋊C4—581no—
309C4⋊C4—581no—
310C4⋊C4C22×D2911yescharacteristic
311C4⋊C4C22×D2911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—581no—
315C22⋊C4—581no—
316C22⋊C4—581no—
317C22⋊C4—581no—
318C22⋊C4—581no—
319C22⋊C4—581no—
320C22⋊C4—581no—
321C22⋊C4—581no—
322C42—581no—
323C42—581no—
324C23—21no—
325C23—291no—
326C23—291no—
327C23—581no—
328C23—1162no—
329C23—2321no—
330C23—2321no—
331C23D4×D2911yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—582no—
335Q8—581no—
336Q8—581no—
337Q8—1162no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—582no—
342D4—582no—
343D4—582no—
344D4—581no—
345D4—581no—
346D4—1162no—
347D4—2321no—
348D4—2321no—
349D4—2321no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—291no—
356C2×C4—292no—
357C2×C4—292no—
358C2×C4—291no—
359C2×C4—581no—
360C2×C4—581no—
361C2×C4—581no—
362C2×C4—581no—
363C2×C4—581no—
364C2×C4—1162no—
365C2×C4D4×D2911yescharacteristic
366C2×C4C23×D2911yescharacteristic
367C8—21no—
368C8—292no—
369C8—581no—
370C8D4×D2912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—292no—
378C22—581no—
379C22—581no—
380C22—581no—
381C22—581no—
382C22—581no—
383C22—1161no—
384C22—1161no—
385C22—1161no—
386C22—2324no—
387C22C2×D4×D2911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—292no—
393C4—581no—
394C4—1161no—
395C4—1161no—
396C4—1161no—
397C4C2×D4×D2911yescharacteristic
398C4#41×D2911yescharacteristic
399C2—41no—
400C2—81no—
401C2—582no—
402C2—1161no—
403C2—2321no—
404C2#121×D2911yescharacteristic
405C2#1427196911yescharacteristic
406C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#465C2
socleC22×C29C22×D4
prime radical#14271729C2
hypercenter#465D29
hypocenterC29#3057
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D29C2semidirect
2. C2×#11745263C2semidirect
3. #14271736C2semidirect
5. #14271412C2semidirect
6. #14271411C2semidirect
7. #14271408C2semidirect
8. #14271407C2semidirect
9. #14271393C2semidirect
10. #14271392C2semidirect
11. #14271389C2semidirect
12. #14271198C2semidirect
13. #14271170C2semidirect
14. #14271166C2semidirect
15. C29×#465C2semidirect
20. C22×C8×C29C22semidirect
21. C29×C22⋊Q8C22semidirect
23. #11745308C22semidirect
30. #11745286C22semidirect
31. C2×#90777C22semidirect
36. C2×#90772C22semidirect
38. C2×C8×D29C22semidirect
39. #11745259C22semidirect
49. C29×#106C22semidirect
50. C29×#103C22semidirect
52. #11745183C22semidirect
55. #11745165C22semidirect
56. #11745164C22semidirect
57. #11745158C22semidirect
59. #11745155C22semidirect
60. #11745155C22semidirect
119. C8×D29D4semidirect
207. #465D29semidirect
233. C22×C8C2×D29semidirect
243. C22⋊Q8C2×D29semidirect
255. #106C2×D29semidirect
259. #103C2×D29semidirect
264. C29#3057semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D292
C2×#117452632
#142717362
#142717292
#142714122
#142714112
#142714082
#142714072
#142713932
#142713922
#142713892
#142711982
#142711702
#142711662
C29×#4652
#305729