Finite Group Databasebeta

← #16831026

Subgroups — #16831026

Order 3712.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745278C211yesmaximal, characteristic, complemented
2#14271832C211yesmaximal, characteristic, complemented
3#14271807C211yesmaximal, characteristic, complemented
4#14271551C211yesmaximal, characteristic, complemented
5#14271409C211yesmaximal, characteristic, complemented
6#14271396C211yesmaximal, characteristic, complemented
7#14271383C211yesmaximal, characteristic, complemented
8#14271356C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271307C211yesmaximal, characteristic, complemented
11#14271305C211yesmaximal, characteristic, complemented
12#14271297C211yesmaximal, characteristic, complemented
13#14271264C211yesmaximal, characteristic, complemented
14#14271232C211yesmaximal, characteristic, complemented
15C2×C29×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C2×#90809C2211yescharacteristic, complemented
19C2×#90807C2211yescharacteristic
20C29×AGL(1,ℤ/8)—24no—
21C2×SD16×C29C2211yescharacteristic
22C2×SD16×C29C2211yescharacteristic
23C2×D8×C29C2211yescharacteristic
24C2×D8×C29C2211yescharacteristic
25C2×M16×C29C2211yescharacteristic
26#11745315—21no—
27C2×C22⋊Dic29—21no—
28Q8×Dic29C2211yescharacteristic, complemented
29C2×#90785C2211yescharacteristic, complemented
30#11745302—21no—
31#11745302C2211yescharacteristic, complemented
32#11745301—21no—
33#11745300—21no—
34#11745300C2211yescharacteristic
35#11745300C2211yescharacteristic, complemented
36#11745298C2211yescharacteristic
37#11745297—21no—
38D4×Dic29C2211yescharacteristic
39C2×#90783C2211yescharacteristic, complemented
40C2×#90782C2211yescharacteristic
41C2×#90782C2211yescharacteristic
42#11745292—21no—
43#11745292C2211yescharacteristic
44C4×C22⋊D29—21no—
45C4×C22⋊D29C2211yescharacteristic
46#11745286C2211yescharacteristic
47#11745278—24no—
48C2×#90773C2211yescharacteristic, complemented
49C2×C8×D29C2211yescharacteristic, complemented
50#11745183C2211yescharacteristic, complemented
51#11745180C2211yescharacteristic
52#11745180C2211yescharacteristic
53#11745180C2211yescharacteristic, complemented
54C22⋊#6597C2211yescharacteristic
55#11745169C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic, complemented
57#11745166C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59#11745163C2211yescharacteristic, complemented
60#11745162C2211yescharacteristic, complemented
61C24×C29—21no—
62#41×C29—22no—
63#41×C29—41no—
64C2×Q8×C29C2311yescharacteristic
65C2×D4×C29—22no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—41no—
69C2×D4×C29C2311yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C2×D4×C29C2311yescharacteristic
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C2×C22⋊D29—21no—
78C2×C22⋊D29—21no—
79C2×C22⋊D29—21no—
80C2×C22⋊D29D411yescharacteristic
81C22×Dic29—21no—
82C22×Dic29—21no—
83#90809—22no—
84#90809—41no—
85#90807—22no—
86#90807—41no—
87C2×D116—21no—
88C2×D116C2311yescharacteristic
89C2×C4×D29—21no—
90C2×C4×D29C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92SD16×C29—22no—
93SD16×C29D414yescomplemented
94D8×C29—22no—
95D8×C29—22no—
96M16×C29—22no—
97C2×C8×C29C2311yescharacteristic
98C2×C8×C29C2311yescharacteristic
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29—21no—
102C22⋊Dic29—21no—
103C22⋊Dic29—21no—
104C22⋊Dic29—21no—
105C22⋊Dic29D411yescharacteristic
106#90785—22no—
107#90783—41no—
108#90782—22no—
109#90782—41no—
110#90781—21no—
111#90781D411yescharacteristic
112C4⋊Dic29—21no—
113C4⋊Dic29C2311yescharacteristic
114C4⋊Dic29C2311yescharacteristic
115#90779—21no—
116#90779D411yescharacteristic
117C4×Dic29—21no—
118C4×Dic29C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121#90773—22no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—42no—
127C23×C29—42no—
128C23×C29—81no—
129C23×C29C2×D411yescharacteristic
130C22×D29—21no—
131C22×D29C2×D411yescharacteristic
132Q8×C29—21no—
133Q8×C29C2×D412yes—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—42no—
140D4×C29—42no—
141D4×C29C2×D412yes—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—42no—
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2411yescharacteristic
148C22⋊D29—41no—
149C22⋊D29—42no—
150C22⋊D29—42no—
151C22⋊D29—81no—
152C22⋊D29—81no—
153C22⋊D29—81no—
154C22⋊D29—81no—
155C2×Dic29—21no—
156C2×Dic29—21no—
157C2×Dic29—21no—
158C2×Dic29—42no—
159C2×Dic29—81no—
160C2×Dic29C2×D411yescharacteristic
161C2×Dic29C2×D411yescharacteristic
162C2×Dic29C2×D411yescharacteristic
163D116—21no—
164D116—21no—
165D116—42no—
166C4×D29—21no—
167C4×D29—21no—
168C4×D29—42no—
169Dic58—21no—
170Dic58—21no—
171C8×C29—21no—
172C8×C29C2×D412yes—
173#6597—21no—
174#6597—21no—
175#3268—291nomaximal, Sylow
176C22×C29—22no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—21no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29—84no—
189C22×C29C22×D411yescharacteristic
190C2×D29—21no—
191C2×D29—21no—
192C2×D29—21no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—41no—
196C4×C29—22no—
197C4×C29—21no—
198C4×C29C22×D411yescharacteristic
199C4×C29H(5,𝔽2)11yescharacteristic
200Dic29—21no—
201Dic29—21no—
202Dic29—21no—
203Dic29—41no—
204Dic29—41no—
205Dic29—41no—
206C2×AGL(1,ℤ/8)D2911yescharacteristic, complemented
207C2×#135—291no—
208#550—291no—
209#546—291no—
210#496—291no—
211#468—291no—
212#466—291no—
213#464—291no—
214#459—291no—
215#452—291no—
216#449—291no—
217#449—291no—
218#447—291no—
219#440—291no—
220#435—291no—
221C2×C29—41no—
222C2×C29—42no—
223C2×C29—81no—
224C2×C29—81no—
225C2×C29D4211yescharacteristic
226C2×C29#57511yescharacteristic
227C2×C29#57611yescharacteristic
228D29—41no—
229D29—81no—
230C2×#41—291no—
231C2×#41—291no—
232C2×#41C2×D2911yescharacteristic
233C22×D4C2×D2911yescharacteristic
234AGL(1,ℤ/8)—24no—
235#135—584no—
236C2×Q16—291no—
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16C2×D2911yescharacteristic
240C2×SD16C2×D2911yescharacteristic
241C2×D8—291no—
242C2×D8—291no—
243C2×D8C2×D2911yescharacteristic
244C2×D8C2×D2911yescharacteristic
245C2×M16C2×D2911yescharacteristic
246C22×C8—291no—
247#127—291no—
248#127—581no—
249#124—291no—
250#123—581no—
251C22⋊Q8—291no—
252#121—291no—
253#121—291no—
254#121—291no—
255#121—581no—
256#121—581no—
257#121—581no—
258#120—581no—
259C4×Q8—291no—
260C4×D4—291no—
261C4×D4—291no—
262C4×D4—581no—
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8—291no—
266#103—291no—
267#103—291no—
268#102—291no—
269#102—291no—
270#102—291no—
271#102—291no—
272C22⋊C8—291no—
273C22⋊C8—291no—
274#97—291no—
275C29#326811yescharacteristic, complemented, Sylow
276C24—21no—
277#41—22no—
278#41—41no—
279#41—582no—
280#41—582no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8C22×D2911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—291no—
290C2×D4—291no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4C22×D2911yescharacteristic
299C2×D4C22×D2911yescharacteristic
300C2×D4C22×D2911yescharacteristic
301C22×C4—21no—
302C22×C4—291no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4C22×D2911yescharacteristic
307Q16—582no—
308SD16—22no—
309SD16—582no—
310SD16—1161no—
311SD16C22⋊D2914yescomplemented
312D8—22no—
313D8—22no—
314D8—582no—
315D8—1161no—
316M16—22no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—291no—
323C4⋊C4—291no—
324C4⋊C4—291no—
325C4⋊C4—581no—
326C4⋊C4—581no—
327C22⋊C4—291no—
328C22⋊C4—291no—
329C22⋊C4—581no—
330C22⋊C4—581no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C42—291no—
337C42—581no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—291no—
345C23—581no—
346C23D4×D2911yescharacteristic
347Q8—21no—
348Q8—581no—
349Q8—581no—
350Q8C2×C22⋊D2912yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—42no—
358D4—581no—
359D4—581no—
360D4—1162no—
361D4—1161no—
362D4—1162no—
363D4—1162no—
364D4—2321no—
365D4—2321no—
366D4—2321no—
367D4—2321no—
368D4C2×C22⋊D2912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—291no—
374C2×C4—291no—
375C2×C4—291no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4—2321no—
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—581no—
388C8—581no—
389C8C2×C22⋊D2912yes—
390C22—21no—
391C22—22no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—581no—
404C22—581no—
405C22—581no—
406C22—1161no—
407C22—1161no—
408C22—1161no—
409C22C2×D4×D2911yescharacteristic
410C4—21no—
411C4—22no—
412C4—581no—
413C4—581no—
414C4—581no—
415C4—1161no—
416C4—1161no—
417C4—1161no—
418C4#1174535911yescharacteristic
419C4C22×C22⋊D2911yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—1161no—
425C2—2321no—
426C2D4×C22⋊D2911yescharacteristic
427C2#1427195911yescharacteristic
428C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×AGL(1,ℤ/8)C2
socleC22×C29C22×D4
hypercenterC2×AGL(1,ℤ/8)D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#11745278C2semidirect
2. #14271832C2semidirect
3. #14271807C2semidirect
4. #14271551C2semidirect
5. #14271409C2semidirect
6. #14271396C2semidirect
7. #14271383C2semidirect
8. #14271356C2semidirect
9. #14271325C2semidirect
10. #14271307C2semidirect
11. #14271305C2semidirect
12. #14271297C2semidirect
13. #14271264C2semidirect
14. #14271232C2semidirect
15. C2×C29×AGL(1,ℤ/8)C2semidirect
18. C2×#90809C22semidirect
28. Q8×Dic29C22semidirect
29. C2×#90785C22semidirect
31. #11745302C22semidirect
35. #11745300C22semidirect
39. C2×#90783C22semidirect
48. C2×#90773C22semidirect
49. C2×C8×D29C22semidirect
50. #11745183C22semidirect
53. #11745180C22semidirect
55. #11745169C22semidirect
56. #11745168C22semidirect
57. #11745166C22semidirect
58. #11745164C22semidirect
59. #11745163C22semidirect
60. #11745162C22semidirect
93. SD16×C29D4semidirect
206. C2×AGL(1,ℤ/8)D29semidirect
275. C29#3268semidirect
311. SD16C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452782
#142718322
#142718072
#142715512
#142714092
#142713962
#142713832
#142713562
#142713252
#142713072
#142713052
#142712972
#142712642
#142712322
C2×C29×AGL(1,ℤ/8)2
#326829