Finite Group Databasebeta

← #16831342

Subgroups — #16831342

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#14271859C211yesmaximal, characteristic, complemented
2#14271517C211yesmaximal, characteristic, complemented
3#14271496C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271463C211yesmaximal, characteristic, complemented
6#14271397C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271308C211yesmaximal, characteristic, complemented
10#14271297C211yesmaximal, characteristic, complemented
11C4×#90782C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271159C211yesmaximal, characteristic, complemented
14C2×#11745180C211yesmaximal, characteristic, complemented
15C29×#546C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C29×#124C2211yescharacteristic
19C29×#123—21no—
20C29×C22⋊Q8C2211yescharacteristic
21C29×#121—21no—
22C29×#121C2211yescharacteristic
23C29×#120—21no—
24C4×D4×C29C2211yescharacteristic
25C4×D4×C29C2211yescharacteristic
26C2×C22⋊C4×C29—21no—
27C2×#90784C2211yescharacteristic, complemented
28#11745301—21no—
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745292C2211yescharacteristic, complemented
33#11745288C2211yescharacteristic, complemented
34C2×C4⋊Dic29C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic, complemented
37#11745260—21no—
38#11745245—21no—
39#11745243—21no—
40C4×D116C2211yescharacteristic, complemented
41#11745232C2211yescharacteristic, complemented
42#11745183C2211yescharacteristic, complemented
43#11745183C2211yescharacteristic, complemented
44#11745183C2211yescharacteristic, complemented
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745180C2211yescharacteristic
51C22⋊#6597C2211yescharacteristic
52C22⋊#6597C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic, complemented
54#11745156C2211yescharacteristic, complemented
55#11745155C2211yescharacteristic, complemented
56#11745155C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C24×C29—21no—
60#41×C29—22no—
61#41×C29—41no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—22no—
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—41no—
68C2×D4×C29D411yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C22×C4×C29C2311yescharacteristic
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C22×Dic29—21no—
78C2×D116C2311yescharacteristic
79C2×C4×D29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29D411yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C22⋊C4×C29—21no—
88C22⋊C4×C29D411yescharacteristic
89C22⋊C4×C29D411yescharacteristic
90C42×C29C2311yescharacteristic
91C22⋊Dic29—21no—
92#90784—41no—
93#90782—22no—
94#90782—41no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104C4×Dic29—21no—
105C2×#6597—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—42no—
114C23×C29—42no—
115C23×C29—81no—
116C23×C29C2×D411yescharacteristic
117C23×C29C2×D411yescharacteristic
118C22×D29—21no—
119Q8×C29—21no—
120Q8×C29—21no—
121D4×C29—22no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—42no—
126D4×C29—42no—
127D4×C29—81no—
128D4×C29#4112yes—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—42no—
136C2×C4×C29—81no—
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2411yescharacteristic
142C22⋊D29—42no—
143C22⋊D29—81no—
144C2×Dic29—21no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—81no—
148D116—21no—
149D116—21no—
150C4×D29—81no—
151#6597—21no—
152#6597—21no—
153#6597—21no—
154#6597—21no—
155#3297—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—22no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—84no—
168C22×C29#13512yes—
169C22×C29C22×D411yescharacteristic
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29C2×#4111yescharacteristic
180C4×C29H(5,𝔽2)11yescharacteristic
181Dic29—41no—
182Dic29—41no—
183Dic29—41no—
184#553—291no—
185#546D2911yescharacteristic, complemented
186#488—291no—
187#484—291no—
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—41no—
201C2×C29—42no—
202C2×C29—81no—
203C2×C29#54611yescharacteristic
204C2×C29C2×#13511yescharacteristic
205C2×C29#57611yescharacteristic
206D29—81no—
207C2×#41C2×D2911yescharacteristic
208C22×D4C2×D2911yescharacteristic
209C2×SD16—291no—
210C2×D8—291no—
211C2×D8—291no—
212C22×C8—291no—
213C22×C8—291no—
214#126—581no—
215#125—291no—
216#124C2×D2911yescharacteristic
217#123—21no—
218#123—581no—
219C22⋊Q8C2×D2911yescharacteristic
220#121—21no—
221#121—291no—
222#121—291no—
223#121—581no—
224#121C2×D2911yescharacteristic
225#120—21no—
226C4×D4—291no—
227C4×D4—581no—
228C4×D4C2×D2911yescharacteristic
229C4×D4C2×D2911yescharacteristic
230#117—291no—
231C2×C4⋊C4—291no—
232C2×C22⋊C4—21no—
233#107—291no—
234#107—291no—
235#106—291no—
236C4⋊C8—291no—
237#103—291no—
238#103—291no—
239#103—291no—
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⋊C8—291no—
249C4×C8—291no—
250C29#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—291no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4C22⋊D2911yescharacteristic
264C2×D4C22×D2911yescharacteristic
265C2×D4C22×D2911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4C22×D2911yescharacteristic
271C22×C4C22×D2911yescharacteristic
272SD16—1161no—
273D8—582no—
274D8—1161no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—291no—
278C2×C8—291no—
279C2×C8—1161no—
280C2×C8—1161no—
281C4⋊C4—21no—
282C4⋊C4—291no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4—581no—
288C4⋊C4C22⋊D2911yescharacteristic
289C4⋊C4C22×D2911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4C22⋊D2911yescharacteristic
300C22⋊C4C22⋊D2911yescharacteristic
301C42—581no—
302C42C22×D2911yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—581no—
309C23C2×C22⋊D2911yescharacteristic
310C23C2×C22⋊D2911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—581no—
321D4—581no—
322D4—1162no—
323D4—2321no—
324D4#9080712yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—2321no—
337C2×C4—2321no—
338C2×C4C2×C22⋊D2911yescharacteristic
339C2×C4C2×C22⋊D2911yescharacteristic
340C2×C4C2×C22⋊D2911yescharacteristic
341C2×C4C2×C22⋊D2911yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—581no—
344C8—581no—
345C8—581no—
346C8—581no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—1161no—
360C22—1161no—
361C22—1161no—
362C22#1174531212yes—
363C22C22×C22⋊D2911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—1161no—
371C4—1161no—
372C4—1161no—
373C4C2×#9080711yescharacteristic
374C4#1174535911yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—2321no—
380C2#1427180711yescharacteristic
381C2C2×#1174531211yescharacteristic
382C2#1427196611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#546C2
socleC22×C29C22×D4
hypercenter#546D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14271859C2semidirect
2. #14271517C2semidirect
3. #14271496C2semidirect
4. #14271484C2semidirect
5. #14271463C2semidirect
6. #14271397C2semidirect
7. #14271394C2semidirect
8. #14271375C2semidirect
9. #14271308C2semidirect
10. #14271297C2semidirect
11. C4×#90782C2semidirect
12. D4×#6597C2semidirect
13. #14271159C2semidirect
14. C2×#11745180C2semidirect
15. C29×#546C2semidirect
27. C2×#90784C22semidirect
32. #11745292C22semidirect
33. #11745288C22semidirect
36. C22×#6597C22semidirect
40. C4×D116C22semidirect
41. #11745232C22semidirect
42. #11745183C22semidirect
43. #11745183C22semidirect
44. #11745183C22semidirect
52. C22⋊#6597C22semidirect
53. #11745157C22semidirect
54. #11745156C22semidirect
55. #11745155C22semidirect
56. #11745155C22semidirect
57. C4⋊#6597C22semidirect
58. C4×#6597C22semidirect
185. #546D29semidirect
250. C29#3297semidirect

Maximal subgroups

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

subgroupindex
#142718592
#142715172
#142714962
#142714842
#142714632
#142713972
#142713942
#142713752
#142713082
#142712972
C4×#907822
D4×#65972
#142711592
C2×#117451802
C29×#5462
#329729