Finite Group Databasebeta

← #16831014

Subgroups — #16831014

Order 3712.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745276C211yesmaximal, characteristic, complemented
2C2×#11745266C211yesmaximal, characteristic, complemented
3#14271815C211yesmaximal, characteristic, complemented
4#14271810C211yesmaximal, characteristic, complemented
5#14271554C211yesmaximal, characteristic, complemented
6#14271422C211yesmaximal, characteristic, complemented
7#14271377C211yesmaximal, characteristic, complemented
8#14271367C211yesmaximal, characteristic, complemented
9#14271328C211yesmaximal, characteristic, complemented
10#14271323C211yesmaximal, characteristic, complemented
11#14271315C211yesmaximal, characteristic, complemented
12#14271306C211yesmaximal, characteristic, complemented
13#14271274C211yesmaximal, characteristic, complemented
14#14271234C211yesmaximal, characteristic, complemented
15C29×#465C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×#90805C2211yescharacteristic
19C2×#90805C2211yescharacteristic, complemented
20C2×SD16×C29C2211yescharacteristic
21C22×C8×C29C2211yescharacteristic, complemented
22C29×C22⋊Q8C2211yescharacteristic, complemented
23C29×#121C2211yescharacteristic
24#11745306C2211yescharacteristic, complemented
25C2×#90785C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic
27#11745300—21no—
28#11745299—21no—
29#11745298C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C4×C22⋊D29C2211yescharacteristic
33#11745276—24no—
34C2×Dic116C2211yescharacteristic, complemented
35#11745266—24no—
36C2×D232C2211yescharacteristic
37C2×#90773C2211yescharacteristic
38C2×#90773C2211yescharacteristic, complemented
39C2×#90772C2211yescharacteristic
40#11745259C2211yescharacteristic
41#11745259C2211yescharacteristic
42#11745256—21no—
43#11745255C2211yescharacteristic
44#11745255C2211yescharacteristic, complemented
45C4⋊C4×D29—21no—
46#11745246—21no—
47#11745245—21no—
48#11745245—21no—
49C22⋊C4×D29—21no—
50C29×#106C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic
53C22⋊#6597C2211yescharacteristic, complemented
54#11745168C2211yescharacteristic
55#11745163C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745158C2211yescharacteristic, complemented
58#11745158C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic
60#11745157C2211yescharacteristic, 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
70#90809—22no—
71#90809—41no—
72D4×D29—22no—
73D4×D29—41no—
74#90805—22no—
75#90805—22no—
76#90805—41no—
77#90805—41no—
78C2×D116—21no—
79C2×D116C2311yescharacteristic
80C2×D116C2311yescharacteristic
81C2×C4×D29—21no—
82C2×C4×D29—21no—
83C2×C4×D29—21no—
84C2×C4×D29—21no—
85C2×C4×D29—21no—
86C2×C4×D29C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88C2×Dic58C2311yescharacteristic
89SD16×C29—22no—
90C2×C8×C29—22no—
91C2×C8×C29C2311yescharacteristic
92C2×C8×C29C2311yescharacteristic
93C4⋊C4×C29—21no—
94C4⋊C4×C29C2311yescharacteristic
95C4⋊C4×C29C2311yescharacteristic
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊Dic29—21no—
99C22⋊Dic29—21no—
100C22⋊Dic29D411yescharacteristic
101#90785—41no—
102#90784—22no—
103#90783—41no—
104#90782—22no—
105#90781—21no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781D411yescharacteristic
110C4⋊Dic29—21no—
111C4⋊Dic29—21no—
112#90779—21no—
113#90779—21no—
114#90779D411yescharacteristic
115C4×Dic29C2311yescharacteristic
116C2×#6597C2311yescharacteristic
117C2×#6597C2311yescharacteristic
118Dic116—22no—
119D232D414yescomplemented
120#90773—22no—
121#90773—22no—
122#90772—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—42no—
128C22×D29—42no—
129C22×D29—81no—
130C22×D29C2×D411yescharacteristic
131Q8×C29—21no—
132Q8×C29—21no—
133D4×C29—21no—
134D4×C29—21no—
135D4×C29—81no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29C2×D411yescharacteristic
142C2×C4×C29C2411yescharacteristic
143C22⋊D29—41no—
144C22⋊D29—42no—
145C22⋊D29—42no—
146C22⋊D29—42no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29C2×D411yescharacteristic
150C2×Dic29C2×D411yescharacteristic
151C2×Dic29C2×D411yescharacteristic
152D116—21no—
153D116—21no—
154D116—42no—
155D116C2×D412yes—
156D116C2×D412yes—
157C4×D29—21no—
158C4×D29—21no—
159C4×D29—42no—
160C4×D29—42no—
161C4×D29—42no—
162C4×D29—42no—
163C4×D29—81no—
164Dic58—21no—
165Dic58—21no—
166Dic58—21no—
167Dic58—21no—
168C8×C29—21no—
169C8×C29C2×D412yes—
170#6597—21no—
171#6597—21no—
172#3267—291nomaximal, Sylow
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—21no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29C22×D411yescharacteristic
180C2×D29—21no—
181C2×D29—22no—
182C2×D29—22no—
183C2×D29—21no—
184C2×D29—21no—
185C2×D29—41no—
186C2×D29—41no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—84no—
190C4×C29—21no—
191C4×C29—41no—
192C4×C29—41no—
193C4×C29—41no—
194C4×C29C22×D411yescharacteristic
195C4×C29H(5,𝔽2)11yescharacteristic
196Dic29—21no—
197Dic29—21no—
198Dic29—21no—
199Dic29—41no—
200Dic29—41no—
201C2×AGL(1,ℤ/8)—291no—
202C2×#135—291no—
203#547—291no—
204#546—291no—
205#497—291no—
206#470—291no—
207#465D2911yescharacteristic, complemented
208#463—291no—
209#461—291no—
210#452—291no—
211#452—291no—
212#450—291no—
213#449—291no—
214#442—291no—
215#435—291no—
216C2×C29—41no—
217C2×C29—81no—
218C2×C29D4211yescharacteristic
219C2×C29#57511yescharacteristic
220C2×C29#57711yescharacteristic
221D29—41no—
222D29—42no—
223D29—42no—
224C2×#41—291no—
225C2×#41—291no—
226C2×#41—291no—
227C22×D4—291no—
228AGL(1,ℤ/8)—584no—
229#135—584no—
230C2×Q16—291no—
231C2×Q16—291no—
232C2×SD16—291no—
233C2×SD16—291no—
234C2×SD16—291no—
235C2×SD16—291no—
236C2×SD16C2×D2911yescharacteristic
237C2×D8—291no—
238C2×D8—291no—
239C2×M16—291no—
240C22×C8C2×D2911yescharacteristic, complemented
241C4⋊Q8—291no—
242#124—291no—
243#123—581no—
244#123—581no—
245#123—581no—
246C22⋊Q8—291no—
247C22⋊Q8—291no—
248C22⋊Q8C2×D2911yescharacteristic, complemented
249#121—581no—
250#121—581no—
251#121C2×D2911yescharacteristic
252#120—581no—
253C4×D4—291no—
254C4×D4—291no—
255C4×D4—291no—
256C2×C4⋊C4—581no—
257C2×C22⋊C4—581no—
258#106C2×D2911yescharacteristic, complemented
259C4⋊C8—291no—
260#103—291no—
261#103—291no—
262#103C2×D2911yescharacteristic, complemented
263#102—291no—
264#102—291no—
265#102C2×D2911yescharacteristic
266C22⋊C8—291no—
267C22⋊C8—291no—
268#97—291no—
269C29#326711yescharacteristic, complemented, Sylow
270C24—581no—
271#41—582no—
272#41—582no—
273#41—582no—
274#41—1161no—
275#41—1161no—
276#41—1161no—
277C2×Q8—291no—
278C2×Q8—291no—
279C2×Q8C22×D2911yescharacteristic
280C2×D4—21no—
281C2×D4—291no—
282C2×D4—291no—
283C2×D4—291no—
284C2×D4—581no—
285C2×D4—581no—
286C2×D4—582no—
287C2×D4—581no—
288C2×D4—581no—
289C2×D4—1161no—
290C2×D4C22×D2911yescharacteristic
291C22×C4—291no—
292C22×C4—581no—
293C22×C4—581no—
294C22×C4—581no—
295C22×C4—581no—
296C22×C4—581no—
297C22×C4C22×D2911yescharacteristic
298Q16—582no—
299Q16—1161no—
300SD16—22no—
301SD16—582no—
302SD16—582no—
303SD16—582no—
304SD16—1161no—
305D8—294no—
306D8—582no—
307M16—582no—
308C2×C8—22no—
309C2×C8—291no—
310C2×C8—291no—
311C2×C8C22×D2911yescharacteristic
312C2×C8C22×D2911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—291no—
315C4⋊C4—581no—
316C4⋊C4—581no—
317C4⋊C4—581no—
318C4⋊C4—581no—
319C4⋊C4C22×D2911yescharacteristic
320C4⋊C4C22×D2911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—291no—
324C22⋊C4—291no—
325C22⋊C4—581no—
326C22⋊C4—581no—
327C22⋊C4—581no—
328C22⋊C4—581no—
329C22⋊C4—581no—
330C22⋊C4—581no—
331C42—291no—
332C23—21no—
333C23—291no—
334C23—581no—
335C23—581no—
336C23—1162no—
337C23—1162no—
338C23—2321no—
339C23D4×D2911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—581no—
343Q8—581no—
344Q8—581no—
345Q8—581no—
346D4—21no—
347D4—21no—
348D4—81no—
349D4—292no—
350D4—292no—
351D4—581no—
352D4—581no—
353D4—1162no—
354D4—1161no—
355D4—1162no—
356D4—1162no—
357D4—1162no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—291no—
364C2×C4—291no—
365C2×C4—291no—
366C2×C4—581no—
367C2×C4—581no—
368C2×C4—581no—
369C2×C4—581no—
370C2×C4—1162no—
371C2×C4—1162no—
372C2×C4—1162no—
373C2×C4—1162no—
374C2×C4—2321no—
375C2×C4D4×D2911yescharacteristic
376C2×C4C23×D2911yescharacteristic
377C8—21no—
378C8—581no—
379C8—581no—
380C8D4×D2912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—581no—
388C22—582no—
389C22—582no—
390C22—581no—
391C22—581no—
392C22—1161no—
393C22—1161no—
394C22—1161no—
395C22—1161no—
396C22—2324no—
397C22C2×D4×D2911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—581no—
403C4—581no—
404C4—581no—
405C4—1161no—
406C4—1161no—
407C4C2×D4×D2911yescharacteristic
408C4#1174536411yescharacteristic
409C2—41no—
410C2—81no—
411C2—1161no—
412C2—1162no—
413C2—1162no—
414C2#1427179711yescharacteristic
415C2#1427196011yescharacteristic
416C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#465C2
socleC22×C29C22×D4
hypercenter#465D29
hypocenterC29#3267
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×#11745276C2semidirect
2. C2×#11745266C2semidirect
3. #14271815C2semidirect
4. #14271810C2semidirect
5. #14271554C2semidirect
6. #14271422C2semidirect
7. #14271377C2semidirect
8. #14271367C2semidirect
9. #14271328C2semidirect
10. #14271323C2semidirect
11. #14271315C2semidirect
12. #14271306C2semidirect
13. #14271274C2semidirect
14. #14271234C2semidirect
15. C29×#465C2semidirect
19. C2×#90805C22semidirect
21. C22×C8×C29C22semidirect
22. C29×C22⋊Q8C22semidirect
24. #11745306C22semidirect
25. C2×#90785C22semidirect
34. C2×Dic116C22semidirect
38. C2×#90773C22semidirect
44. #11745255C22semidirect
50. C29×#106C22semidirect
51. C29×#103C22semidirect
53. C22⋊#6597C22semidirect
55. #11745163C22semidirect
56. #11745162C22semidirect
57. #11745158C22semidirect
58. #11745158C22semidirect
60. #11745157C22semidirect
119. D232D4semidirect
207. #465D29semidirect
240. C22×C8C2×D29semidirect
248. C22⋊Q8C2×D29semidirect
258. #106C2×D29semidirect
262. #103C2×D29semidirect
269. C29#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
C2×#117452662
#142718152
#142718102
#142715542
#142714222
#142713772
#142713672
#142713282
#142713232
#142713152
#142713062
#142712742
#142712342
C29×#4652
#326729