Finite Group Databasebeta

← #16831024

Subgroups — #16831024

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×#11745270C211yesmaximal, characteristic, complemented
2C2×#11745281C211yesmaximal, characteristic, complemented
3#14271815C211yesmaximal, characteristic, complemented
4#14271804C211yesmaximal, characteristic, complemented
5#14271556C211yesmaximal, characteristic, complemented
6#14271393C211yesmaximal, characteristic, complemented
7#14271381C211yesmaximal, characteristic, complemented
8#14271367C211yesmaximal, characteristic, complemented
9#14271328C211yesmaximal, characteristic, complemented
10#14271323C211yesmaximal, characteristic, complemented
11#14271313C211yesmaximal, characteristic, complemented
12#14271311C211yesmaximal, characteristic, complemented
13#14271274C211yesmaximal, characteristic, complemented
14#14271232C211yesmaximal, characteristic, complemented
15C29×#470C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90809C2211yescharacteristic, complemented
18C2×#90805C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C2×Q16×C29C2211yescharacteristic, complemented
21C2×M16×C29C2211yescharacteristic
22C29×C22⋊Q8C2211yescharacteristic
23C29×C22⋊Q8C2211yescharacteristic
24#11745309C2211yescharacteristic
25#11745306C2211yescharacteristic, complemented
26C2×#90785C2211yescharacteristic, complemented
27C2×#90784C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29C2×#90784C2211yescharacteristic, complemented
30C4×C22⋊D29C2211yescharacteristic
31#11745281—24no—
32#11745270—24no—
33C2×D232C2211yescharacteristic
34C2×D232C2211yescharacteristic
35C2×#90773C2211yescharacteristic
36C2×#90773C2211yescharacteristic
37C2×C8×D29C2211yescharacteristic, complemented
38#11745259C2211yescharacteristic, complemented
39#11745257—21no—
40#11745257C2211yescharacteristic
41#11745256—21no—
42#11745256—21no—
43#11745255C2211yescharacteristic
44#11745255C2211yescharacteristic, complemented
45C4⋊C4×D29—21no—
46#11745246—21no—
47#11745245—21no—
48#11745244—21no—
49C22⋊C4×D29—21no—
50C29×#106C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#103C2211yescharacteristic, complemented
53C22⋊#6597C2211yescharacteristic
54#11745168C2211yescharacteristic, complemented
55#11745163C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745158C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic
59#11745157C2211yescharacteristic
60#11745157C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29D411yescharacteristic
67#90809—22no—
68#90809—22no—
69#90809—41no—
70#90809—41no—
71#90805—22no—
72#90805—41no—
73C2×D116—22no—
74C2×D116—21no—
75C2×D116—21no—
76C2×D116—21no—
77C2×D116—21no—
78C2×D116—41no—
79C2×D116C2311yescharacteristic
80C2×D116C2311yescharacteristic
81C2×D116C2311yescharacteristic
82C2×C4×D29—21no—
83C2×C4×D29—21no—
84C2×C4×D29—21no—
85C2×C4×D29—21no—
86C2×C4×D29—21no—
87C2×C4×D29C2311yescharacteristic
88C2×Dic58C2311yescharacteristic
89Q16×C29—22no—
90M16×C29—22no—
91C2×C8×C29C2311yescharacteristic
92C2×C8×C29C2311yescharacteristic
93C4⋊C4×C29—21no—
94C4⋊C4×C29—21no—
95C4⋊C4×C29C2311yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C22⋊C4×C29—21no—
98C22⋊C4×C29—21no—
99C22⋊Dic29D411yescharacteristic
100#90785—41no—
101#90784—22no—
102#90784—22no—
103#90784—41no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781D411yescharacteristic
111C4⋊Dic29—21no—
112#90779—21no—
113#90779—21no—
114#90779D411yescharacteristic
115C4×Dic29C2311yescharacteristic
116C2×#6597C2311yescharacteristic
117C2×#6597C2311yescharacteristic
118D232—22no—
119D232D414yescomplemented
120#90773—22no—
121#90773—22no—
122C8×D29—22no—
123C23×C29C2×D411yescharacteristic
124C22×D29—21no—
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—42no—
128C22×D29—42no—
129C22×D29—81no—
130C22×D29C2×D411yescharacteristic
131Q8×C29—21no—
132Q8×C29—21no—
133Q8×C29—21no—
134Q8×C29—21no—
135C2×C4×C29—21no—
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—
145C2×Dic29—21no—
146C2×Dic29C2×D411yescharacteristic
147C2×Dic29C2×D411yescharacteristic
148C2×Dic29C2×D411yescharacteristic
149D116—21no—
150D116—21no—
151D116—21no—
152D116—21no—
153D116—42no—
154D116—42no—
155D116—42no—
156D116—81no—
157D116C2×D412yes—
158D116C2×D412yes—
159C4×D29—21no—
160C4×D29—21no—
161C4×D29—42no—
162C4×D29—42no—
163C4×D29—42no—
164C4×D29—42no—
165C4×D29—81no—
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×C29C22×D411yescharacteristic
177C2×D29—21no—
178C2×D29—22no—
179C2×D29—22no—
180C2×D29—21no—
181C2×D29—21no—
182C2×D29—41no—
183C2×D29—41no—
184C2×D29—41no—
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×C29—41no—
195C4×C29C22×D411yescharacteristic
196C4×C29H(5,𝔽2)11yescharacteristic
197Dic29—21no—
198Dic29—21no—
199Dic29—21no—
200Dic29—41no—
201C2×AGL(1,ℤ/8)—291no—
202C2×#135—291no—
203#547—291no—
204#546—291no—
205#497—291no—
206#470D2911yescharacteristic, complemented
207#465—291no—
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×C29D4211yescharacteristic
218C2×C29#57511yescharacteristic
219C2×C29#57711yescharacteristic
220D29—41no—
221D29—42no—
222D29—42no—
223D29—81no—
224C2×#41—291no—
225C2×#41—291no—
226C2×#41—291no—
227C22×D4—291no—
228AGL(1,ℤ/8)—584no—
229#135—584no—
230C2×Q16—291no—
231C2×Q16C2×D2911yescharacteristic, complemented
232C2×SD16—291no—
233C2×SD16—291no—
234C2×SD16—291no—
235C2×SD16—291no—
236C2×SD16—291no—
237C2×D8—291no—
238C2×D8—291no—
239C2×M16C2×D2911yescharacteristic
240C22×C8—291no—
241C4⋊Q8—291no—
242#124—291no—
243#123—581no—
244#123—581no—
245#123—581no—
246C22⋊Q8—291no—
247C22⋊Q8C2×D2911yescharacteristic
248C22⋊Q8C2×D2911yescharacteristic
249#121—291no—
250#121—581no—
251#121—581no—
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#103C2×D2911yescharacteristic, complemented
262#103C2×D2911yescharacteristic, complemented
263#102—291no—
264#102—291no—
265#102—291no—
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×Q8C22×D2911yescharacteristic
279C2×Q8C22×D2911yescharacteristic
280C2×D4—291no—
281C2×D4—291no—
282C2×D4—291no—
283C2×D4—291no—
284C2×D4—582no—
285C2×D4—581no—
286C2×D4—581no—
287C2×D4—581no—
288C2×D4—581no—
289C2×D4—581no—
290C2×D4—1161no—
291C22×C4—291no—
292C22×C4—581no—
293C22×C4—581no—
294C22×C4—581no—
295C22×C4—581no—
296C22×C4—581no—
297C22×C4C22×D2911yescharacteristic
298Q16—22no—
299Q16—1161no—
300SD16—582no—
301SD16—582no—
302SD16—582no—
303SD16—582no—
304SD16—1161no—
305D8—294no—
306D8—582no—
307M16—22no—
308C2×C8—291no—
309C2×C8—291no—
310C2×C8—582no—
311C2×C8C22×D2911yescharacteristic
312C2×C8C22×D2911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—291no—
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—291no—
333C23—581no—
334C23—581no—
335C23—581no—
336C23—1162no—
337C23—1162no—
338C23—2321no—
339C23D4×D2911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—581no—
345Q8—581no—
346D4—292no—
347D4—292no—
348D4—581no—
349D4—581no—
350D4—581no—
351D4—581no—
352D4—1162no—
353D4—1162no—
354D4—1162no—
355D4—1161no—
356D4—1162no—
357D4—2321no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—291no—
365C2×C4—291no—
366C2×C4—291no—
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—581no—
385C22—582no—
386C22—582no—
387C22—581no—
388C22—581no—
389C22—1161no—
390C22—1161no—
391C22—1161no—
392C22—1161no—
393C22—1161no—
394C22—1161no—
395C22—1161no—
396C22—2324no—
397C22C2×D4×D2911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—581no—
404C4—581no—
405C4—581no—
406C4—1161no—
407C4C2×D4×D2911yescharacteristic
408C4#1174536411yescharacteristic
409C2—41no—
410C2—1161no—
411C2—1162no—
412C2—1162no—
413C2—2321no—
414C2#1427179711yescharacteristic
415C2#1427196211yescharacteristic
416C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#470C2
socleC22×C29C22×D4
hypercenter#470D29
hypocenterC29#3267
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. C2×#11745281C2semidirect
3. #14271815C2semidirect
4. #14271804C2semidirect
5. #14271556C2semidirect
6. #14271393C2semidirect
7. #14271381C2semidirect
8. #14271367C2semidirect
9. #14271328C2semidirect
10. #14271323C2semidirect
11. #14271313C2semidirect
12. #14271311C2semidirect
13. #14271274C2semidirect
14. #14271232C2semidirect
15. C29×#470C2semidirect
17. C2×#90809C22semidirect
20. C2×Q16×C29C22semidirect
25. #11745306C22semidirect
26. C2×#90785C22semidirect
29. C2×#90784C22semidirect
37. C2×C8×D29C22semidirect
38. #11745259C22semidirect
44. #11745255C22semidirect
50. C29×#106C22semidirect
51. C29×#103C22semidirect
52. C29×#103C22semidirect
54. #11745168C22semidirect
55. #11745163C22semidirect
56. #11745162C22semidirect
57. #11745158C22semidirect
60. #11745157C22semidirect
119. D232D4semidirect
206. #470D29semidirect
231. C2×Q16C2×D29semidirect
258. #106C2×D29semidirect
261. #103C2×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×#117452702
C2×#117452812
#142718152
#142718042
#142715562
#142713932
#142713812
#142713672
#142713282
#142713232
#142713132
#142713112
#142712742
#142712322
C29×#4702
#326729