Finite Group Databasebeta

← #16831039

Subgroups — #16831039

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×#11745270C211yesmaximal, characteristic, complemented
2C2×#11745278C211yesmaximal, characteristic, complemented
3#14271831C211yesmaximal, characteristic, complemented
4#14271804C211yesmaximal, characteristic, complemented
5#14271549C211yesmaximal, characteristic, complemented
6#14271400C211yesmaximal, characteristic, complemented
7#14271388C211yesmaximal, characteristic, complemented
8#14271357C211yesmaximal, characteristic, complemented
9#14271323C211yesmaximal, characteristic, complemented
10#14271311C211yesmaximal, characteristic, complemented
11#14271309C211yesmaximal, characteristic, complemented
12#14271296C211yesmaximal, characteristic, complemented
13#14271262C211yesmaximal, characteristic, complemented
14#14271232C211yesmaximal, characteristic, complemented
15C29×#468C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90807C2211yescharacteristic, complemented
18C2×#90805C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic, complemented
21C2×M16×C29C2211yescharacteristic
22C29×C22⋊Q8C2211yescharacteristic
23C29×#121C2211yescharacteristic
24#11745309C2211yescharacteristic
25C2×#90785C2211yescharacteristic, complemented
26C2×#90784C2211yescharacteristic, complemented
27#11745302—21no—
28#11745302C2211yescharacteristic, complemented
29#11745301—21no—
30C2×#90782C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32C4×C22⋊D29C2211yescharacteristic
33#11745278—24no—
34#11745270—24no—
35C2×D232C2211yescharacteristic
36C2×D232C2211yescharacteristic
37C2×#90773C2211yescharacteristic
38C2×#90773C2211yescharacteristic
39C2×C8×D29C2211yescharacteristic, complemented
40#11745257—21no—
41#11745257C2211yescharacteristic
42#11745257C2211yescharacteristic, complemented
43#11745256—21no—
44#11745255C2211yescharacteristic
45#11745249C2211yescharacteristic, complemented
46#11745246—21no—
47#11745244—21no—
48#11745243—21no—
49C22⋊C4×D29—21no—
50C29×#107C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, 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×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29D411yescharacteristic
71C22×Dic29—21no—
72#90809—22no—
73#90809—41no—
74#90807—22no—
75#90807—41no—
76#90805—22no—
77#90805—41no—
78C2×D116—22no—
79C2×D116—21no—
80C2×D116—21no—
81C2×D116—21no—
82C2×D116—21no—
83C2×D116—41no—
84C2×D116C2311yescharacteristic
85C2×D116C2311yescharacteristic
86C2×D116C2311yescharacteristic
87C2×C4×D29—21no—
88C2×C4×D29—21no—
89C2×C4×D29—21no—
90C2×C4×D29C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92SD16×C29—22no—
93M16×C29—22no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C4⋊C4×C29—21no—
97C4⋊C4×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C22⋊C4×C29—21no—
100C22⋊C4×C29—21no—
101C22⋊Dic29D411yescharacteristic
102#90785—22no—
103#90784—41no—
104#90782—22no—
105#90782—41no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781D411yescharacteristic
112#90779—21no—
113#90779D411yescharacteristic
114C4×Dic29—21no—
115C4×Dic29C2311yescharacteristic
116C2×#6597C2311yescharacteristic
117C2×#6597C2311yescharacteristic
118D232—22no—
119D232—22no—
120#90773—22no—
121#90773D414yescomplemented
122C8×D29—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—81no—
131C22×D29C2×D411yescharacteristic
132Q8×C29—21no—
133Q8×C29—21no—
134D4×C29—21no—
135D4×C29—21no—
136D4×C29—81no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2411yescharacteristic
144C22⋊D29—41no—
145C22⋊D29—42no—
146C22⋊D29—42no—
147C22⋊D29—42no—
148C22⋊D29—81no—
149C2×Dic29—21no—
150C2×Dic29—42no—
151C2×Dic29C2×D411yescharacteristic
152C2×Dic29C2×D411yescharacteristic
153C2×Dic29C2×D411yescharacteristic
154D116—21no—
155D116—21no—
156D116—21no—
157D116—21no—
158D116—21no—
159D116—42no—
160D116—42no—
161D116—81no—
162D116—81no—
163D116C2×D412yes—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—42no—
167C4×D29—42no—
168C4×D29—81no—
169Dic58—21no—
170Dic58C2×D412yes—
171C8×C29—21no—
172C8×C29C2×D412yes—
173#6597—21no—
174#6597—21no—
175#3268—291nomaximal, Sylow
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29C22×D411yescharacteristic
183C2×D29—21no—
184C2×D29—22no—
185C2×D29—21no—
186C2×D29—21no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—41no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C4×C29—21no—
197C4×C29—41no—
198C4×C29—41no—
199C4×C29—41no—
200C4×C29C22×D411yescharacteristic
201C4×C29H(5,𝔽2)11yescharacteristic
202Dic29—22no—
203Dic29—21no—
204Dic29—21no—
205Dic29—21no—
206C2×AGL(1,ℤ/8)—291no—
207C2×#135—291no—
208#550—291no—
209#546—291no—
210#496—291no—
211#468D2911yescharacteristic, complemented
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—81no—
223C2×C29D4211yescharacteristic
224C2×C29#57511yescharacteristic
225C2×C29#57611yescharacteristic
226D29—41no—
227D29—42no—
228D29—81no—
229D29—81no—
230C2×#41—291no—
231C2×#41—291no—
232C2×#41—291no—
233C22×D4—291no—
234AGL(1,ℤ/8)—584no—
235#135—584no—
236C2×Q16—291no—
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16C2×D2911yescharacteristic, complemented
241C2×D8—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×M16C2×D2911yescharacteristic
246C22×C8—291no—
247#127—291no—
248#127—581no—
249#124—291no—
250#123—581no—
251C22⋊Q8C2×D2911yescharacteristic
252#121—291no—
253#121—291no—
254#121—581no—
255#121—581no—
256#121—581no—
257#121C2×D2911yescharacteristic
258#120—581no—
259C4×Q8—291no—
260C4×D4—291no—
261C4×D4—291no—
262C4×D4—581no—
263C2×C22⋊C4—581no—
264#107C2×D2911yescharacteristic, complemented
265C4⋊C8—291no—
266#103—291no—
267#103C2×D2911yescharacteristic, complemented
268#102—291no—
269#102—291no—
270#102—291no—
271#102C2×D2911yescharacteristic, complemented
272C22⋊C8—291no—
273C22⋊C8—291no—
274#97—291no—
275C29#326811yescharacteristic, complemented, Sylow
276C24—581no—
277#41—582no—
278#41—582no—
279#41—582no—
280#41—1161no—
281#41—1161no—
282#41—1161no—
283C2×Q8—291no—
284C2×Q8C22×D2911yescharacteristic
285C2×D4—21no—
286C2×D4—291no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—291no—
290C2×D4—582no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—581no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4—581no—
299C2×D4—1161no—
300C2×D4C22×D2911yescharacteristic
301C22×C4—291no—
302C22×C4—581no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4C22×D2911yescharacteristic
307Q16—582no—
308SD16—22no—
309SD16—294no—
310SD16—582no—
311SD16—1161no—
312D8—582no—
313D8—582no—
314D8—582no—
315D8—1161no—
316M16—22no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—291no—
324C4⋊C4—581no—
325C4⋊C4C22×D2911yescharacteristic
326C4⋊C4C22×D2911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—291no—
330C22⋊C4—291no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4—581no—
335C22⋊C4—581no—
336C42—291no—
337C42—581no—
338C23—21no—
339C23—291no—
340C23—581no—
341C23—581no—
342C23—581no—
343C23—1162no—
344C23—1162no—
345C23—2321no—
346C23D4×D2911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—292no—
350Q8—581no—
351D4—21no—
352D4—21no—
353D4—81no—
354D4—292no—
355D4—581no—
356D4—581no—
357D4—581no—
358D4—581no—
359D4—581no—
360D4—1162no—
361D4—1162no—
362D4—1161no—
363D4—1162no—
364D4—1162no—
365D4—1162no—
366D4—2321no—
367D4—2321no—
368D4—2321no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—291no—
375C2×C4—291no—
376C2×C4—291no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—1162no—
381C2×C4—1162no—
382C2×C4—1162no—
383C2×C4—2321no—
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—581no—
388C8—581no—
389C8D4×D2912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—581no—
397C22—582no—
398C22—581no—
399C22—581no—
400C22—1161no—
401C22—1161no—
402C22—1161no—
403C22—1161no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—2324no—
409C22C2×D4×D2911yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—581no—
415C4—582no—
416C4—581no—
417C4—581no—
418C4C2×D4×D2911yescharacteristic
419C4#1174536411yescharacteristic
420C2—41no—
421C2—81no—
422C2—1161no—
423C2—1162no—
424C2—2321no—
425C2—2321no—
426C2#1427179711yescharacteristic
427C2#1427196211yescharacteristic
428C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#468C2
socleC22×C29C22×D4
hypercenter#468D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. C2×#11745278C2semidirect
3. #14271831C2semidirect
4. #14271804C2semidirect
5. #14271549C2semidirect
6. #14271400C2semidirect
7. #14271388C2semidirect
8. #14271357C2semidirect
9. #14271323C2semidirect
10. #14271311C2semidirect
11. #14271309C2semidirect
12. #14271296C2semidirect
13. #14271262C2semidirect
14. #14271232C2semidirect
15. C29×#468C2semidirect
17. C2×#90807C22semidirect
20. C2×SD16×C29C22semidirect
25. C2×#90785C22semidirect
26. C2×#90784C22semidirect
28. #11745302C22semidirect
39. C2×C8×D29C22semidirect
42. #11745257C22semidirect
45. #11745249C22semidirect
50. C29×#107C22semidirect
51. C29×#103C22semidirect
52. C29×#102C22semidirect
54. #11745168C22semidirect
55. #11745163C22semidirect
56. #11745162C22semidirect
57. #11745158C22semidirect
60. #11745157C22semidirect
121. #90773D4semidirect
211. #468D29semidirect
240. C2×SD16C2×D29semidirect
264. #107C2×D29semidirect
267. #103C2×D29semidirect
271. #102C2×D29semidirect
275. C29#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
C2×#117452782
#142718312
#142718042
#142715492
#142714002
#142713882
#142713572
#142713232
#142713112
#142713092
#142712962
#142712622
#142712322
C29×#4682
#326829