Finite Group Databasebeta

← #16831027

Subgroups — #16831027

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×#11745276C211yesmaximal, characteristic, complemented
2C2×#11745281C211yesmaximal, characteristic, complemented
3#14271835C211yesmaximal, characteristic, complemented
4#14271806C211yesmaximal, characteristic, complemented
5#14271553C211yesmaximal, characteristic, complemented
6#14271412C211yesmaximal, characteristic, complemented
7#14271398C211yesmaximal, characteristic, complemented
8#14271359C211yesmaximal, characteristic, complemented
9#14271324C211yesmaximal, characteristic, complemented
10#14271311C211yesmaximal, characteristic, complemented
11#14271307C211yesmaximal, characteristic, complemented
12#14271298C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14#14271233C211yesmaximal, characteristic, complemented
15C29×#464C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C2×#90809C2211yescharacteristic, complemented
19C2×D4×D29C2211yescharacteristic
20C2×Q16×C29C2211yescharacteristic, complemented
21C2×SD16×C29C2211yescharacteristic
22C29×#124C2211yescharacteristic
23C4×Q8×C29C2211yescharacteristic, complemented
24#11745308C2211yescharacteristic
25C2×#90784C2211yescharacteristic
26C2×#90784C2211yescharacteristic, complemented
27C2×#90784C2211yescharacteristic, complemented
28#11745300C2211yescharacteristic
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745281—24no—
32#11745276—24no—
33C2×D232C2211yescharacteristic
34C2×D232C2211yescharacteristic
35C2×#90772C2211yescharacteristic
36C2×C8×D29C2211yescharacteristic, complemented
37#11745257—21no—
38#11745257—21no—
39#11745257C2211yescharacteristic
40#11745257C2211yescharacteristic, complemented
41#11745246—21no—
42#11745245—21no—
43#11745244—21no—
44C22⋊C4×D29—21no—
45#11745236—21no—
46#11745236C2211yescharacteristic, complemented
47C4×D116—21no—
48C4×D116C2211yescharacteristic
49C4×D116C2211yescharacteristic
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×#103C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic
53#11745183C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745169C2211yescharacteristic, complemented
56#11745168C2211yescharacteristic
57#11745168C2211yescharacteristic, complemented
58#11745157C2211yescharacteristic
59#11745155C2211yescharacteristic, complemented
60#11745151C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67#90809—22no—
68#90809—22no—
69#90809—22no—
70#90809—41no—
71#90809—41no—
72#90809—41no—
73D4×D29—22no—
74D4×D29—41no—
75C2×D116—21no—
76C2×D116—21no—
77C2×D116—21no—
78C2×D116—21no—
79C2×D116—21no—
80C2×D116—21no—
81C2×D116—21no—
82C2×D116D411yescharacteristic
83C2×D116C2311yescharacteristic
84C2×D116C2311yescharacteristic
85C2×D116C2311yescharacteristic
86C2×C4×D29—21no—
87C2×C4×D29—21no—
88C2×C4×D29—21no—
89C2×C4×D29—21no—
90C2×C4×D29C2311yescharacteristic
91C2×C4×D29C2311yescharacteristic
92Q16×C29—22no—
93SD16×C29—22no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C4⋊C4×C29—21no—
97C4⋊C4×C29C2311yescharacteristic
98C22⋊C4×C29—21no—
99C22⋊C4×C29—21no—
100C42×C29—21no—
101C42×C29C2311yescharacteristic
102C22⋊Dic29—21no—
103#90784—22no—
104#90784—41no—
105#90784D414yescomplemented
106#90782—22no—
107#90782—41no—
108#90781—21no—
109#90781—21no—
110#90781—21no—
111#90781—21no—
112#90781D411yescharacteristic
113#90781D411yescharacteristic
114C4⋊Dic29D411yescharacteristic
115C4⋊Dic29C2311yescharacteristic
116#90779—21no—
117C2×#6597C2311yescharacteristic
118C2×#6597C2311yescharacteristic
119D232—22no—
120D232—22no—
121#90772—22no—
122C8×D29—22no—
123C23×C29—21no—
124C22×D29—21no—
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—42no—
128C22×D29—42no—
129C22×D29—81no—
130C22×D29C2×D411yescharacteristic
131C22×D29C2×D411yescharacteristic
132Q8×C29—21no—
133Q8×C29—21no—
134Q8×C29—21no—
135Q8×C29C2×D412yes—
136D4×C29—21no—
137D4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29C2×D411yescharacteristic
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2411yescharacteristic
144C22⋊D29—42no—
145C22⋊D29—81no—
146C2×Dic29—21no—
147C2×Dic29C2×D411yescharacteristic
148C2×Dic29C2×D411yescharacteristic
149D116—21no—
150D116—21no—
151D116—21no—
152D116—21no—
153D116—21no—
154D116—41no—
155D116—42no—
156D116—42no—
157D116—42no—
158D116—42no—
159D116—81no—
160D116—81no—
161D116—81no—
162D116C2×D412yes—
163C4×D29—21no—
164C4×D29—21no—
165C4×D29—21no—
166C4×D29—21no—
167C4×D29—42no—
168C4×D29—42no—
169C4×D29—42no—
170C4×D29—81no—
171C8×C29—21no—
172C8×C29—21no—
173#6597—21no—
174#6597C2×D412yes—
175#3268—291nomaximal, Sylow
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—41no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—84no—
196C4×C29—22no—
197C4×C29—21no—
198C4×C29—21no—
199C4×C29—41no—
200C4×C29—41no—
201C4×C29C22×D411yescharacteristic
202C4×C29H(5,𝔽2)11yescharacteristic
203Dic29—21no—
204Dic29—21no—
205Dic29—41no—
206C2×AGL(1,ℤ/8)—291no—
207C2×#135—291no—
208#550—291no—
209#546—291no—
210#496—291no—
211#468—291no—
212#466—291no—
213#464D2911yescharacteristic, complemented
214#459—291no—
215#452—291no—
216#449—291no—
217#449—291no—
218#447—291no—
219#440—291no—
220#435—291no—
221C2×C29—81no—
222C2×C29D4211yescharacteristic
223C2×C29#57511yescharacteristic
224C2×C29#57611yescharacteristic
225D29—41no—
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×Q16C2×D2911yescharacteristic, complemented
237C2×SD16—291no—
238C2×SD16—291no—
239C2×SD16—291no—
240C2×SD16C2×D2911yescharacteristic
241C2×D8—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×M16—291no—
246C22×C8—291no—
247#127—291no—
248#127—581no—
249#124C2×D2911yescharacteristic
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×Q8C2×D2911yescharacteristic, complemented
260C4×D4—291no—
261C4×D4—291no—
262C4×D4—581no—
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8C2×D2911yescharacteristic, complemented
266#103—291no—
267#103C2×D2911yescharacteristic, complemented
268#102—291no—
269#102—291no—
270#102—291no—
271#102C2×D2911yescharacteristic
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×Q8C22×D2911yescharacteristic
284C2×Q8C22×D2911yescharacteristic
285C2×D4—291no—
286C2×D4—291no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—581no—
290C2×D4—581no—
291C2×D4—581no—
292C2×D4—581no—
293C2×D4—581no—
294C2×D4—581no—
295C2×D4—582no—
296C2×D4—581no—
297C2×D4—581no—
298C2×D4—581no—
299C2×D4—1161no—
300C2×D4C22×D2911yescharacteristic
301C22×C4—291no—
302C22×C4—291no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4—581no—
306C22×C4—581no—
307Q16—22no—
308SD16—22no—
309SD16—294no—
310SD16—582no—
311SD16—1161no—
312D8—582no—
313D8—582no—
314D8—582no—
315D8—1161no—
316M16—582no—
317C2×C8—291no—
318C2×C8—291no—
319C2×C8—582no—
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—291no—
324C4⋊C4—291no—
325C4⋊C4—581no—
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—21no—
337C42C22×D2911yescharacteristic
338C23—21no—
339C23—291no—
340C23—291no—
341C23—581no—
342C23—581no—
343C23—581no—
344C23—1162no—
345C23—1162no—
346C23—2321no—
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D2912yes—
351D4—21no—
352D4—21no—
353D4—292no—
354D4—581no—
355D4—581no—
356D4—581no—
357D4—581no—
358D4—581no—
359D4—1161no—
360D4—1162no—
361D4—1162no—
362D4—1162no—
363D4—1162no—
364D4—1162no—
365D4—2321no—
366D4—2321no—
367D4—2321no—
368D4—2321no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—291no—
373C2×C4—291no—
374C2×C4—581no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—1162no—
380C2×C4—1162no—
381C2×C4—1162no—
382C2×C4—2321no—
383C2×C4D4×D2911yescharacteristic
384C2×C4D4×D2911yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—21no—
388C8—292no—
389C8—581no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—581no—
394C22—581no—
395C22—582no—
396C22—581no—
397C22—581no—
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—22no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—581no—
416C4—581no—
417C4—1161no—
418C4C2×D4×D2911yescharacteristic
419C4#1174536411yescharacteristic
420C2—81no—
421C2—1161no—
422C2—1161no—
423C2—1162no—
424C2—2321no—
425C2—2321no—
426C2#1427179711yescharacteristic
427C2#1427196211yescharacteristic
428C2#1427196511yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#464C2
socleC22×C29C22×D4
hypercenter#464D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. C2×#11745281C2semidirect
3. #14271835C2semidirect
4. #14271806C2semidirect
5. #14271553C2semidirect
6. #14271412C2semidirect
7. #14271398C2semidirect
8. #14271359C2semidirect
9. #14271324C2semidirect
10. #14271311C2semidirect
11. #14271307C2semidirect
12. #14271298C2semidirect
13. #14271261C2semidirect
14. #14271233C2semidirect
15. C29×#464C2semidirect
18. C2×#90809C22semidirect
20. C2×Q16×C29C22semidirect
23. C4×Q8×C29C22semidirect
26. C2×#90784C22semidirect
27. C2×#90784C22semidirect
36. C2×C8×D29C22semidirect
40. #11745257C22semidirect
46. #11745236C22semidirect
50. C29×C4⋊C8C22semidirect
51. C29×#103C22semidirect
53. #11745183C22semidirect
54. #11745169C22semidirect
55. #11745169C22semidirect
57. #11745168C22semidirect
59. #11745155C22semidirect
60. #11745151C22semidirect
105. #90784D4semidirect
213. #464D29semidirect
236. C2×Q16C2×D29semidirect
259. C4×Q8C2×D29semidirect
265. C4⋊C8C2×D29semidirect
267. #103C2×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×#117452762
C2×#117452812
#142718352
#142718062
#142715532
#142714122
#142713982
#142713592
#142713242
#142713112
#142713072
#142712982
#142712612
#142712332
C29×#4642
#326829