Finite Group Databasebeta

← #16831037

Subgroups — #16831037

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×#11745266C211yesmaximal, characteristic, complemented
3#14271834C211yesmaximal, characteristic, complemented
4#14271809C211yesmaximal, characteristic, complemented
5#14271552C211yesmaximal, characteristic, complemented
6#14271409C211yesmaximal, characteristic, complemented
7#14271399C211yesmaximal, characteristic, complemented
8#14271386C211yesmaximal, characteristic, complemented
9#14271359C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271310C211yesmaximal, characteristic, complemented
12#14271310C211yesmaximal, characteristic, complemented
13#14271299C211yesmaximal, characteristic, complemented
14#14271265C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C2×#90805C2211yescharacteristic, complemented
19C22×D116C2211yescharacteristic
20C2×M16×C29C2211yescharacteristic
21C22×C8×C29C2211yescharacteristic, complemented
22C4×D4×C29C2211yescharacteristic
23#11745302—21no—
24#11745299—21no—
25#11745292C2211yescharacteristic
26#11745292C2211yescharacteristic
27#11745292C2211yescharacteristic, complemented
28#11745286C2211yescharacteristic
29#11745270—24no—
30C2×Dic116C2211yescharacteristic, complemented
31#11745266—24no—
32C2×D232C2211yescharacteristic
33C2×D232C2211yescharacteristic
34C2×D232C2211yescharacteristic
35C2×D232C2211yescharacteristic
36C2×#90773C2211yescharacteristic
37C2×#90773C2211yescharacteristic
38C2×#90773C2211yescharacteristic, complemented
39C2×#90773C2211yescharacteristic, complemented
40#11745256—21no—
41#11745255—21no—
42#11745246—21no—
43#11745246—21no—
44#11745246—21no—
45C22⋊C4×D29—21no—
46#11745237C2211yescharacteristic
47#11745236C2211yescharacteristic, complemented
48C4×D116C2211yescharacteristic
49C4×Dic58C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×C22⋊C8C2211yescharacteristic
52C29×C22⋊C8C2211yescharacteristic, complemented
53C29×#97C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic
55#11745169C2211yescharacteristic
56#11745169C2211yescharacteristic, complemented
57#11745169C2211yescharacteristic, complemented
58#11745166C2211yescharacteristic, complemented
59#11745164C2211yescharacteristic, complemented
60#11745164C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×D4×C29D411yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71#90805—22no—
72#90805—22no—
73#90805—22no—
74#90805—41no—
75#90805—41no—
76#90805—41no—
77C2×D116—22no—
78C2×D116—21no—
79C2×D116—21no—
80C2×D116—21no—
81C2×D116—41no—
82C2×D116C2311yescharacteristic
83C2×D116C2311yescharacteristic
84C2×D116C2311yescharacteristic
85C2×D116C2311yescharacteristic
86C2×C4×D29—21no—
87C2×C4×D29—21no—
88C2×C4×D29—21no—
89C2×C4×D29—21no—
90C2×Dic58C2311yescharacteristic
91C2×Dic58C2311yescharacteristic
92M16×C29—22no—
93C2×C8×C29—22no—
94C2×C8×C29C2311yescharacteristic
95C2×C8×C29C2311yescharacteristic
96C2×C8×C29C2311yescharacteristic
97C2×C8×C29C2311yescharacteristic
98C4⋊C4×C29D411yescharacteristic
99C22⋊C4×C29D411yescharacteristic
100C22⋊C4×C29D411yescharacteristic
101C42×C29C2311yescharacteristic
102C22⋊Dic29—21no—
103#90781—21no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781—21no—
108#90781—21no—
109C4⋊Dic29C2311yescharacteristic
110C4⋊Dic29C2311yescharacteristic
111#90779—21no—
112#90779—21no—
113C4×Dic29—21no—
114Dic116—22no—
115D232—22no—
116D232—22no—
117D232—22no—
118D232—41no—
119#90773—22no—
120#90773—22no—
121#90773—41no—
122#90773D414yescomplemented
123C23×C29C2×D411yescharacteristic
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—42no—
130C22×D29—42no—
131C22×D29—81no—
132D4×C29—41no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2411yescharacteristic
142C22⋊D29—42no—
143C22⋊D29—42no—
144C22⋊D29—42no—
145C22⋊D29—81no—
146C22⋊D29—81no—
147C22⋊D29—81no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150C2×Dic29—21no—
151C2×Dic29—21no—
152D116—21no—
153D116—21no—
154D116—21no—
155D116—21no—
156D116—21no—
157D116—21no—
158D116—21no—
159D116—42no—
160D116—42no—
161D116—81no—
162D116C2×D412yes—
163C4×D29—42no—
164C4×D29—42no—
165C4×D29—42no—
166C4×D29—81no—
167Dic58—21no—
168Dic58—21no—
169Dic58—21no—
170Dic58C2×D412yes—
171C8×C29—21no—
172C8×C29—21no—
173C8×C29—21no—
174C8×C29C2×D412yes—
175#3268—291nomaximal, Sylow
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—21no—
180C22×C29—21no—
181C22×C29—21no—
182C22×C29C22×D411yescharacteristic
183C2×D29—22no—
184C2×D29—41no—
185C2×D29—41no—
186C2×D29—41no—
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—21no—
198C4×C29—21no—
199C4×C29—21no—
200C4×C29C22×D411yescharacteristic
201C4×C29H(5,𝔽2)11yescharacteristic
202Dic29—22no—
203Dic29—41no—
204Dic29—41no—
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#464—291no—
214#459—291no—
215#452—291no—
216#449—291no—
217#449—291no—
218#447—291no—
219#440—291no—
220#435D2911yescharacteristic, complemented
221C2×C29—41no—
222C2×C29—41no—
223C2×C29D4211yescharacteristic
224C2×C29#57511yescharacteristic
225C2×C29#57611yescharacteristic
226D29—42no—
227D29—81no—
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×SD16—291no—
241C2×D8—291no—
242C2×D8—291no—
243C2×D8—291no—
244C2×D8—291no—
245C2×M16C2×D2911yescharacteristic
246C22×C8C2×D2911yescharacteristic, complemented
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—581no—
262C4×D4C2×D2911yescharacteristic
263C2×C22⋊C4—581no—
264#107—291no—
265C4⋊C8C2×D2911yescharacteristic, complemented
266#103—291no—
267#103—291no—
268#102—291no—
269#102—291no—
270#102—291no—
271#102—291no—
272C22⋊C8C2×D2911yescharacteristic
273C22⋊C8C2×D2911yescharacteristic, complemented
274#97C2×D2911yescharacteristic, complemented
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×Q8—291no—
285C2×D4—291no—
286C2×D4—291no—
287C2×D4—291no—
288C2×D4—291no—
289C2×D4—582no—
290C2×D4—581no—
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×D4D11611yescharacteristic
301C22×C4—581no—
302C22×C4—581no—
303C22×C4—581no—
304C22×C4—581no—
305C22×C4C22×D2911yescharacteristic
306C22×C4C22×D2911yescharacteristic
307Q16—582no—
308SD16—294no—
309SD16—582no—
310SD16—582no—
311SD16—1161no—
312D8—582no—
313D8—582no—
314D8—582no—
315D8—1161no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D2911yescharacteristic
319C2×C8C22×D2911yescharacteristic
320C2×C8C22×D2911yescharacteristic
321C2×C8C22×D2911yescharacteristic
322C4⋊C4—291no—
323C4⋊C4—291no—
324C4⋊C4—581no—
325C4⋊C4—581no—
326C4⋊C4D11611yescharacteristic
327C22⋊C4—581no—
328C22⋊C4—581no—
329C22⋊C4—581no—
330C22⋊C4—581no—
331C22⋊C4—581no—
332C22⋊C4—581no—
333C22⋊C4—581no—
334C22⋊C4D11611yescharacteristic
335C22⋊C4D11611yescharacteristic
336C42—581no—
337C42C22×D2911yescharacteristic
338C23—581no—
339C23—581no—
340C23—581no—
341C23—581no—
342C23—1162no—
343C23—1162no—
344C23—2321no—
345C23C2×D11611yescharacteristic
346C23C2×D11611yescharacteristic
347Q8—292no—
348Q8—581no—
349Q8—581no—
350Q8—581no—
351D4—41no—
352D4—292no—
353D4—581no—
354D4—581no—
355D4—581no—
356D4—581no—
357D4—581no—
358D4—581no—
359D4—581no—
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—21no—
373C2×C4—581no—
374C2×C4—581no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—1162no—
378C2×C4—1162no—
379C2×C4—1162no—
380C2×C4—2321no—
381C2×C4C2×D11611yescharacteristic
382C2×C4C2×D11611yescharacteristic
383C2×C4C2×D11611yescharacteristic
384C2×C4C2×D11611yescharacteristic
385C2×C4C23×D2911yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D2912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—582no—
397C22—1161no—
398C22—1161no—
399C22—1161no—
400C22—1161no—
401C22—1161no—
402C22—1161no—
403C22—1161no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22—2324no—
409C22C22×D11611yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—582no—
415C4—1161no—
416C4—1161no—
417C4—1161no—
418C4C2×D4×D2911yescharacteristic
419C4#1174536411yescharacteristic
420C2—41no—
421C2—41no—
422C2—1162no—
423C2—2321no—
424C2—2321no—
425C2—2321no—
426C2D4×D11611yescharacteristic
427C2#1427196311yescharacteristic
428C2#1427196811yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#435C2
socleC22×C29C22×D4
hypercenter#435D29
hypocenterC29#3268
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. C2×#11745266C2semidirect
3. #14271834C2semidirect
4. #14271809C2semidirect
5. #14271552C2semidirect
6. #14271409C2semidirect
7. #14271399C2semidirect
8. #14271386C2semidirect
9. #14271359C2semidirect
10. #14271327C2semidirect
11. #14271310C2semidirect
12. #14271310C2semidirect
13. #14271299C2semidirect
14. #14271265C2semidirect
15. C29×#435C2semidirect
18. C2×#90805C22semidirect
21. C22×C8×C29C22semidirect
27. #11745292C22semidirect
30. C2×Dic116C22semidirect
38. C2×#90773C22semidirect
39. C2×#90773C22semidirect
47. #11745236C22semidirect
49. C4×Dic58C22semidirect
50. C29×C4⋊C8C22semidirect
52. C29×C22⋊C8C22semidirect
53. C29×#97C22semidirect
56. #11745169C22semidirect
57. #11745169C22semidirect
58. #11745166C22semidirect
59. #11745164C22semidirect
60. #11745164C22semidirect
122. #90773D4semidirect
220. #435D29semidirect
246. C22×C8C2×D29semidirect
265. C4⋊C8C2×D29semidirect
273. C22⋊C8C2×D29semidirect
274. #97C2×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×#117452662
#142718342
#142718092
#142715522
#142714092
#142713992
#142713862
#142713592
#142713272
#142713102
#142712992
#142712652
C29×#4352
#326829