Finite Group Databasebeta

← #16831340

Subgroups — #16831340

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271861C211yesmaximal, characteristic, complemented
2#14271804C211yesmaximal, characteristic, complemented
3#14271519C211yesmaximal, characteristic, complemented
4#14271490C211yesmaximal, characteristic, complemented
5#14271466C211yesmaximal, characteristic, complemented
6#14271400C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271381C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271299C211yesmaximal, characteristic, complemented
11#14271245C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14C2×#11745157C211yesmaximal, characteristic, complemented
15C29×#484C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C22×D116C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C29C2211yescharacteristic
20#11745309C2211yescharacteristic
21C2×#90784C2211yescharacteristic, complemented
22#11745292—21no—
23#11745292C2211yescharacteristic
24C4×C22⋊D29—21no—
25C4×C22⋊D29C2211yescharacteristic
26C22×#6597C2211yescharacteristic
27C2×D232C2211yescharacteristic
28C2×D232C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic, complemented
30#11745260—21no—
31#11745257—21no—
32#11745257C2211yescharacteristic
33#11745257C2211yescharacteristic, complemented
34#11745256—21no—
35#11745256—21no—
36#11745255C2211yescharacteristic
37#11745255C2211yescharacteristic, complemented
38#11745254C2211yescharacteristic, complemented
39#11745252C2211yescharacteristic, complemented
40#11745244—21no—
41C22⋊C4×D29—21no—
42C29×#107C2211yescharacteristic, complemented
43C29×#107C2211yescharacteristic, complemented
44C29×#103C2211yescharacteristic, complemented
45C29×#103C2211yescharacteristic, complemented
46C29×C22⋊C8C2211yescharacteristic
47#11745183C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic, complemented
51#11745162C2211yescharacteristic, complemented
52C8×Dic29C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic, complemented
58#11745156C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29D411yescharacteristic
65#90809—22no—
66#90809—41no—
67C2×D116—22no—
68C2×D116—21no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116—21no—
72C2×D116—41no—
73C2×D116C2311yescharacteristic
74C2×D116C2311yescharacteristic
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊Dic29D411yescharacteristic
89#90784—41no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781D411yescharacteristic
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C2×#6597—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—22no—
109D232—41no—
110C8×D29—41no—
111C23×C29C2×D411yescharacteristic
112C22×D29—21no—
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29—81no—
118C22×D29C2×D411yescharacteristic
119Q8×C29—21no—
120Q8×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—81no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—22no—
131C22⋊D29—42no—
132C2×Dic29—21no—
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136D116—21no—
137D116—21no—
138D116—21no—
139D116—21no—
140D116—21no—
141D116—42no—
142D116—42no—
143D116—81no—
144D116—81no—
145D116#4112yes—
146C4×D29—21no—
147C4×D29—21no—
148C4×D29—42no—
149C4×D29—81no—
150C4×D29—81no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3297—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29#13512yes—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—22no—
162C2×D29—21no—
163C2×D29—21no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—84no—
173C4×C29—21no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29—41no—
177C4×C29—41no—
178C4×C29C2×#4111yescharacteristic
179C4×C29H(5,𝔽2)11yescharacteristic
180Dic29—21no—
181Dic29—21no—
182Dic29—21no—
183Dic29—41no—
184#553—291no—
185#546—291no—
186#488—291no—
187#484D2911yescharacteristic, complemented
188#482—291no—
189#478—291no—
190#466—291no—
191#465—291no—
192#463—291no—
193#449—291no—
194#447—291no—
195C4×D8—291no—
196C8×D4—291no—
197#416—291no—
198C2×#102—291no—
199C2×C29—22no—
200C2×C29#54611yescharacteristic
201C2×C29C2×#13511yescharacteristic
202C2×C29#57611yescharacteristic
203D29—41no—
204D29—42no—
205D29—81no—
206D29—81no—
207C2×#41—291no—
208C22×D4—291no—
209C2×SD16—291no—
210C2×D8—291no—
211C2×D8—291no—
212C22×C8—291no—
213C22×C8—291no—
214#126—581no—
215#125—291no—
216#124—291no—
217#123—581no—
218#123—581no—
219C22⋊Q8C2×D2911yescharacteristic
220#121—291no—
221#121—291no—
222#121—291no—
223#121—581no—
224#121—581no—
225#120—581no—
226C4×D4—291no—
227C4×D4—291no—
228C4×D4—291no—
229C4×D4—581no—
230#117—291no—
231C2×C4⋊C4C2×D2911yescharacteristic
232C2×C22⋊C4—581no—
233#107C2×D2911yescharacteristic, complemented
234#107C2×D2911yescharacteristic, complemented
235#106—291no—
236C4⋊C8—291no—
237#103—291no—
238#103C2×D2911yescharacteristic, complemented
239#103C2×D2911yescharacteristic, complemented
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247C22⋊C8—291no—
248C22⋊C8C2×D2911yescharacteristic
249C4×C8—291no—
250C29#329711yescharacteristic, complemented, Sylow
251C24—581no—
252#41—582no—
253#41—1161no—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—291no—
256C2×D4—291no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—582no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4—1161no—
266C22×C4—21no—
267C22×C4—291no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4C22×D2911yescharacteristic
272SD16—1161no—
273D8—582no—
274D8—1161no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—1161no—
278C2×C8—1161no—
279C2×C8C22×D2911yescharacteristic
280C2×C8C22×D2911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4C22×D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
289C4⋊C4C22×D2911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—291no—
292C22⋊C4—291no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C42—291no—
302C42—581no—
303C23—291no—
304C23—581no—
305C23—581no—
306C23—581no—
307C23—1162no—
308C23—1162no—
309C23—2321no—
310C23D4×D2911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—292no—
314D4—582no—
315D4—581no—
316D4—581no—
317D4—581no—
318D4—581no—
319D4—581no—
320D4—1162no—
321D4—1162no—
322D4—1162no—
323D4—2321no—
324D4—2321no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—291no—
333C2×C4—291no—
334C2×C4—291no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—581no—
338C2×C4—1162no—
339C2×C4—2321no—
340C2×C4—2321no—
341C2×C4D4×D2911yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—21no—
344C8—21no—
345C8—581no—
346C8—581no—
347C22—21no—
348C22—21no—
349C22—581no—
350C22—582no—
351C22—581no—
352C22—581no—
353C22—1161no—
354C22—1161no—
355C22—1161no—
356C22—1161no—
357C22—1161no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22—2324no—
362C22#1174528112yes—
363C22C2×D4×D2911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—581no—
370C4—581no—
371C4—581no—
372C4—1161no—
373C4#41×D2911yescharacteristic
374C4#1174536411yescharacteristic
375C2—22no—
376C2—1161no—
377C2—1162no—
378C2—2321no—
379C2—2321no—
380C2#1427180511yescharacteristic
381C2C2×#1174528111yescharacteristic
382C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#484C2
socleC22×C29C22×D4
hypercenter#484D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14271861C2semidirect
2. #14271804C2semidirect
3. #14271519C2semidirect
4. #14271490C2semidirect
5. #14271466C2semidirect
6. #14271400C2semidirect
7. #14271394C2semidirect
8. #14271381C2semidirect
9. #14271311C2semidirect
10. #14271299C2semidirect
11. #14271245C2semidirect
12. #14271226C2semidirect
13. #14271158C2semidirect
14. C2×#11745157C2semidirect
15. C29×#484C2semidirect
21. C2×#90784C22semidirect
29. C2×C8×D29C22semidirect
33. #11745257C22semidirect
37. #11745255C22semidirect
38. #11745254C22semidirect
39. #11745252C22semidirect
42. C29×#107C22semidirect
43. C29×#107C22semidirect
44. C29×#103C22semidirect
45. C29×#103C22semidirect
47. #11745183C22semidirect
50. #11745168C22semidirect
51. #11745162C22semidirect
52. C8×Dic29C22semidirect
57. #11745157C22semidirect
58. #11745156C22semidirect
187. #484D29semidirect
233. #107C2×D29semidirect
234. #107C2×D29semidirect
238. #103C2×D29semidirect
239. #103C2×D29semidirect
250. C29#3297semidirect

Maximal subgroups

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

subgroupindex
#142718612
#142718042
#142715192
#142714902
#142714662
#142714002
#142713942
#142713812
#142713112
#142712992
#142712452
#142712262
#142711582
C2×#117451572
C29×#4842
#329729