Finite Group Databasebeta

← #16831012

Subgroups — #16831012

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×#11745273C211yesmaximal, characteristic, complemented
2C2×#11745278C211yesmaximal, characteristic, complemented
3#14271817C211yesmaximal, characteristic, complemented
4#14271806C211yesmaximal, characteristic, complemented
5#14271558C211yesmaximal, characteristic, complemented
6#14271420C211yesmaximal, characteristic, complemented
7#14271391C211yesmaximal, characteristic, complemented
8#14271369C211yesmaximal, characteristic, complemented
9#14271328C211yesmaximal, characteristic, complemented
10#14271322C211yesmaximal, characteristic, complemented
11#14271315C211yesmaximal, characteristic, complemented
12#14271305C211yesmaximal, characteristic, complemented
13#14271273C211yesmaximal, characteristic, complemented
14#14271233C211yesmaximal, characteristic, complemented
15C29×#463C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C2×#90807C2211yescharacteristic, complemented
19C2×D4×D29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic, complemented
21C2×D8×C29C2211yescharacteristic
22C29×#124C2211yescharacteristic
23C4×D4×C29C2211yescharacteristic, complemented
24#11745308C2211yescharacteristic
25C2×#90785C2211yescharacteristic, complemented
26C2×#90785C2211yescharacteristic, complemented
27#11745300C2211yescharacteristic
28C2×#90783C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292—21no—
32C2×C4⋊Dic29—21no—
33#11745278—24no—
34#11745273—24no—
35C2×#90773C2211yescharacteristic
36C2×#90773C2211yescharacteristic
37C2×#90772C2211yescharacteristic
38C2×C8×D29C2211yescharacteristic, complemented
39#11745259C2211yescharacteristic
40#11745259C2211yescharacteristic, complemented
41#11745248—21no—
42#11745248—21no—
43#11745246—21no—
44#11745245—21no—
45#11745244—21no—
46C22⋊C4×D29—21no—
47C4×D116C2211yescharacteristic
48C4×D116C2211yescharacteristic
49#11745231C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic
53#11745180C2211yescharacteristic, complemented
54#11745168C2211yescharacteristic
55#11745168C2211yescharacteristic, complemented
56#11745164C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic
59#11745156C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, 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—41no—
74#90807—22no—
75#90807—22no—
76#90807—41no—
77#90807—41no—
78D4×D29—22no—
79D4×D29—41no—
80C2×D116—21no—
81C2×D116D411yescharacteristic
82C2×D116C2311yescharacteristic
83C2×C4×D29—21no—
84C2×C4×D29—21no—
85C2×C4×D29C2311yescharacteristic
86C2×C4×D29C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88C2×Dic58C2311yescharacteristic
89SD16×C29—22no—
90D8×C29—22no—
91C2×C8×C29C2311yescharacteristic
92C2×C8×C29C2311yescharacteristic
93C4⋊C4×C29C2311yescharacteristic
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C42×C29C2311yescharacteristic
98C22⋊Dic29—21no—
99#90785—22no—
100#90785—41no—
101#90783—22no—
102#90783—41no—
103#90782D414yescomplemented
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781—21no—
108#90781D411yescharacteristic
109#90781D411yescharacteristic
110C4⋊Dic29—21no—
111C4⋊Dic29—21no—
112C4⋊Dic29—21no—
113C4⋊Dic29—21no—
114C4⋊Dic29D411yescharacteristic
115C4⋊Dic29C2311yescharacteristic
116#90779—21no—
117C2×#6597C2311yescharacteristic
118C2×#6597C2311yescharacteristic
119#90773—22no—
120#90773—22no—
121#90772—22no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29—21no—
125C22×D29—21no—
126C22×D29—42no—
127C22×D29—42no—
128C22×D29—81no—
129C22×D29C2×D411yescharacteristic
130C22×D29C2×D411yescharacteristic
131Q8×C29—21no—
132Q8×C29—21no—
133D4×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29C2×D412yes—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—42no—
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2×D411yescharacteristic
142C2×C4×C29C2411yescharacteristic
143C22⋊D29—42no—
144C22⋊D29—42no—
145C22⋊D29—42no—
146C22⋊D29—81no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150C2×Dic29—42no—
151C2×Dic29—42no—
152C2×Dic29C2×D411yescharacteristic
153C2×Dic29C2×D411yescharacteristic
154D116—21no—
155D116—41no—
156D116—42no—
157D116C2×D412yes—
158C4×D29—21no—
159C4×D29—21no—
160C4×D29—21no—
161C4×D29—21no—
162C4×D29—42no—
163C4×D29—81no—
164Dic58—21no—
165Dic58—21no—
166Dic58—21no—
167Dic58—21no—
168C8×C29—21no—
169C8×C29—21no—
170#6597—21no—
171#6597C2×D412yes—
172#3267—291nomaximal, Sylow
173C22×C29—22no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29—41no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29C22×D411yescharacteristic
180C2×D29—21no—
181C2×D29—21no—
182C2×D29—22no—
183C2×D29—21no—
184C2×D29—21no—
185C2×D29—21no—
186C2×D29—21no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—84no—
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—41no—
193C4×C29—41no—
194C4×C29C22×D411yescharacteristic
195C4×C29H(5,𝔽2)11yescharacteristic
196Dic29—21no—
197Dic29—21no—
198Dic29—41no—
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#465—291no—
208#463D2911yescharacteristic, complemented
209#461—291no—
210#452—291no—
211#452—291no—
212#450—291no—
213#449—291no—
214#442—291no—
215#435—291no—
216C2×C29—42no—
217C2×C29—81no—
218C2×C29D4211yescharacteristic
219C2×C29#57511yescharacteristic
220C2×C29#57711yescharacteristic
221D29—41no—
222D29—41no—
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, complemented
237C2×D8—291no—
238C2×D8C2×D2911yescharacteristic
239C2×M16—291no—
240C22×C8—291no—
241C4⋊Q8—291no—
242#124C2×D2911yescharacteristic
243#123—581no—
244#123—581no—
245#123—581no—
246C22⋊Q8—291no—
247C22⋊Q8—291no—
248C22⋊Q8—291no—
249#121—291no—
250#121—581no—
251#121—581no—
252#120—581no—
253C4×D4—291no—
254C4×D4—291no—
255C4×D4C2×D2911yescharacteristic, complemented
256C2×C4⋊C4—581no—
257C2×C22⋊C4—581no—
258#106—291no—
259C4⋊C8C2×D2911yescharacteristic, complemented
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—291no—
281C2×D4—291no—
282C2×D4—581no—
283C2×D4—581no—
284C2×D4—582no—
285C2×D4—581no—
286C2×D4—581no—
287C2×D4—581no—
288C2×D4—1161no—
289C2×D4C22×D2911yescharacteristic
290C2×D4C22×D2911yescharacteristic
291C22×C4—21no—
292C22×C4—291no—
293C22×C4—291no—
294C22×C4—581no—
295C22×C4—581no—
296C22×C4—581no—
297C22×C4—581no—
298Q16—582no—
299Q16—1161no—
300SD16—22no—
301SD16—582no—
302SD16—582no—
303SD16—582no—
304SD16—1161no—
305D8—22no—
306D8—294no—
307M16—582no—
308C2×C8—291no—
309C2×C8—291no—
310C2×C8—582no—
311C2×C8C22×D2911yescharacteristic
312C2×C8C22×D2911yescharacteristic
313C4⋊C4—291no—
314C4⋊C4—291no—
315C4⋊C4—581no—
316C4⋊C4—581no—
317C4⋊C4—581no—
318C4⋊C4—581no—
319C4⋊C4—581no—
320C4⋊C4C22×D2911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—291no—
325C22⋊C4—291no—
326C22⋊C4—581no—
327C22⋊C4—581no—
328C22⋊C4—581no—
329C22⋊C4—581no—
330C22⋊C4—581no—
331C42C22×D2911yescharacteristic
332C23—21no—
333C23—21no—
334C23—291no—
335C23—291no—
336C23—581no—
337C23—1162no—
338C23—1162no—
339C23—2321no—
340Q8—21no—
341Q8—21no—
342Q8—581no—
343Q8—581no—
344Q8—581no—
345Q8—581no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—292no—
350D4—581no—
351D4—1161no—
352D4—1162no—
353D4—1162no—
354D4—1162no—
355D4—1162no—
356D4—2321no—
357D4D4×D2912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—291no—
362C2×C4—291no—
363C2×C4—581no—
364C2×C4—581no—
365C2×C4—581no—
366C2×C4—581no—
367C2×C4—581no—
368C2×C4—581no—
369C2×C4—581no—
370C2×C4—1162no—
371C2×C4—1162no—
372C2×C4—1162no—
373C2×C4—2321no—
374C2×C4D4×D2911yescharacteristic
375C2×C4D4×D2911yescharacteristic
376C2×C4C23×D2911yescharacteristic
377C8—21no—
378C8—21no—
379C8—292no—
380C8—581no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—581no—
388C22—581no—
389C22—582no—
390C22—581no—
391C22—581no—
392C22—581no—
393C22—581no—
394C22—1161no—
395C22—1161no—
396C22—2324no—
397C22C2×D4×D2911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—581no—
403C4—581no—
404C4—1161no—
405C4—1161no—
406C4—1161no—
407C4C2×D4×D2911yescharacteristic
408C4#1174536411yescharacteristic
409C2—42no—
410C2—81no—
411C2—1161no—
412C2—1161no—
413C2—1162no—
414C2#1427179711yescharacteristic
415C2#1427195911yescharacteristic
416C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#463C2
socleC22×C29C22×D4
hypercenter#463D29
hypocenterC29#3267
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. #14271817C2semidirect
4. #14271806C2semidirect
5. #14271558C2semidirect
6. #14271420C2semidirect
7. #14271391C2semidirect
8. #14271369C2semidirect
9. #14271328C2semidirect
10. #14271322C2semidirect
11. #14271315C2semidirect
12. #14271305C2semidirect
13. #14271273C2semidirect
14. #14271233C2semidirect
15. C29×#463C2semidirect
18. C2×#90807C22semidirect
20. C2×SD16×C29C22semidirect
23. C4×D4×C29C22semidirect
25. C2×#90785C22semidirect
26. C2×#90785C22semidirect
38. C2×C8×D29C22semidirect
40. #11745259C22semidirect
49. #11745231C22semidirect
50. C29×C4⋊C8C22semidirect
51. C29×#103C22semidirect
53. #11745180C22semidirect
55. #11745168C22semidirect
56. #11745164C22semidirect
57. #11745164C22semidirect
59. #11745156C22semidirect
60. #11745151C22semidirect
103. #90782D4semidirect
208. #463D29semidirect
236. C2×SD16C2×D29semidirect
255. C4×D4C2×D29semidirect
259. C4⋊C8C2×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×#117452732
C2×#117452782
#142718172
#142718062
#142715582
#142714202
#142713912
#142713692
#142713282
#142713222
#142713152
#142713052
#142712732
#142712332
C29×#4632
#326729