Finite Group Databasebeta

← #16831327

Subgroups — #16831327

Order 3712.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271853C211yesmaximal, characteristic, complemented
2#14271517C211yesmaximal, characteristic, complemented
3#14271491C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271463C211yesmaximal, characteristic, complemented
6#14271402C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271382C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271314C211yesmaximal, characteristic, complemented
11C4×#90783C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271159C211yesmaximal, characteristic, complemented
14C2×#11745180C211yesmaximal, characteristic, complemented
15C29×#546C211yesmaximal, characteristic
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×#90785C2211yescharacteristic, complemented
28#11745297—21no—
29C2×#90783C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31#11745288C2211yescharacteristic, complemented
32C2×C4⋊Dic29C2211yescharacteristic
33#11745286C2211yescharacteristic
34#11745286C2211yescharacteristic, complemented
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic, complemented
37#11745251—21no—
38#11745241—21no—
39#11745239—21no—
40#11745232C2211yescharacteristic, complemented
41C4×Dic58C2211yescharacteristic, 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#11745158C2211yescharacteristic, complemented
54#11745156C2211yescharacteristic, complemented
55#11745156C2211yescharacteristic, 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
75C22×Dic29—21no—
76C2×Dic58C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29D411yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C22⋊C4×C29D411yescharacteristic
86C22⋊C4×C29D411yescharacteristic
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91#90785—41no—
92#90783—22no—
93#90783—41no—
94C4⋊Dic29—21no—
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779—21no—
103C4×Dic29—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
118Q8×C29—21no—
119Q8×C29—21no—
120D4×C29—22no—
121D4×C29—21no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—42no—
125D4×C29—42no—
126D4×C29—81no—
127D4×C29#4112yes—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—42no—
135C2×C4×C29—81no—
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2411yescharacteristic
141C2×Dic29—21no—
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29—21no—
145C2×Dic29—42no—
146Dic58—21no—
147Dic58—21no—
148#6597—21no—
149#6597—21no—
150#6597—21no—
151#6597—21no—
152#3296—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—22no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—84no—
165C22×C29#13512yes—
166C22×C29C22×D411yescharacteristic
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29C2×#4111yescharacteristic
174C4×C29H(5,𝔽2)11yescharacteristic
175Dic29—41no—
176Dic29—41no—
177Dic29—41no—
178Dic29—41no—
179#552—291no—
180#546D2911yescharacteristic
181#488—291no—
182#483—291no—
183#482—291no—
184#478—291no—
185#467—291no—
186#465—291no—
187#464—291no—
188#452—291no—
189#450—291no—
190C4×SD16—291no—
191C8×D4—291no—
192#416—291no—
193C2×#102—291no—
194C2×C29—22no—
195C2×C29—41no—
196C2×C29—42no—
197C2×C29—81no—
198C2×C29#54611yescharacteristic
199C2×C29C2×#13511yescharacteristic
200C2×C29#57711yescharacteristic
201C2×#41C2×D2911yescharacteristic
202C22×D4C2×D2911yescharacteristic
203C2×Q16—291no—
204C2×SD16—291no—
205C2×SD16—291no—
206C22×C8—291no—
207C22×C8—291no—
208#126—581no—
209#125—291no—
210#125—581no—
211#124C2×D2911yescharacteristic
212#123—21no—
213#123—581no—
214C22⋊Q8—291no—
215C22⋊Q8—291no—
216C22⋊Q8C2×D2911yescharacteristic
217#121—21no—
218#121C2×D2911yescharacteristic
219#120—21no—
220C4×Q8—291no—
221C4×D4C2×D2911yescharacteristic
222C4×D4C2×D2911yescharacteristic
223#117—291no—
224#117—581no—
225C2×C4⋊C4—291no—
226C2×C22⋊C4—21no—
227#107—291no—
228#106—291no—
229#106—291no—
230C4⋊C8—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102—291no—
241C22⋊C8—291no—
242C22⋊C8—291no—
243C4×C8—291no—
244C29#329611yescharacteristic, complemented, Sylow
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—291no—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D2911yescharacteristic
256C2×D4C22×D2911yescharacteristic
257C2×D4C22×D2911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—581no—
261C22×C4C22×D2911yescharacteristic
262C22×C4C22×D2911yescharacteristic
263Q16—1161no—
264SD16—582no—
265SD16—1161no—
266C2×C8—291no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—1161no—
271C2×C8—1161no—
272C4⋊C4—21no—
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22⋊D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4C22⋊D2911yescharacteristic
293C22⋊C4C22⋊D2911yescharacteristic
294C42—581no—
295C42—581no—
296C42C22×D2911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D2911yescharacteristic
303C23C2×C22⋊D2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—581no—
307Q8—581no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#9080712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—1162no—
329C2×C4C2×C22⋊D2911yescharacteristic
330C2×C4C2×C22⋊D2911yescharacteristic
331C2×C4C2×C22⋊D2911yescharacteristic
332C2×C4C2×C22⋊D2911yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—581no—
335C8—581no—
336C8—581no—
337C8—581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1174531212yes—
351C22C22×C22⋊D2911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—1161no—
359C4—1161no—
360C4—1161no—
361C4—1161no—
362C4C2×#9080711yescharacteristic
363C4#1174535911yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1427180711yescharacteristic
369C2C2×#1174531211yescharacteristic
370C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#546C2
socleC22×C29C22×D4
hypercenter#546D29
hypocenterC29#3296
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. #14271853C2semidirect
2. #14271517C2semidirect
3. #14271491C2semidirect
4. #14271484C2semidirect
5. #14271463C2semidirect
6. #14271402C2semidirect
7. #14271390C2semidirect
8. #14271382C2semidirect
9. #14271325C2semidirect
10. #14271314C2semidirect
11. C4×#90783C2semidirect
12. D4×#6597C2semidirect
13. #14271159C2semidirect
14. C2×#11745180C2semidirect
27. C2×#90785C22semidirect
31. #11745288C22semidirect
34. #11745286C22semidirect
36. C22×#6597C22semidirect
40. #11745232C22semidirect
41. C4×Dic58C22semidirect
42. #11745183C22semidirect
43. #11745183C22semidirect
44. #11745183C22semidirect
52. C22⋊#6597C22semidirect
53. #11745158C22semidirect
54. #11745156C22semidirect
55. #11745156C22semidirect
56. #11745155C22semidirect
57. C4⋊#6597C22semidirect
58. C4×#6597C22semidirect
244. C29#3296semidirect

Maximal subgroups

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

subgroupindex
#142718532
#142715172
#142714912
#142714842
#142714632
#142714022
#142713902
#142713822
#142713252
#142713142
C4×#907832
D4×#65972
#142711592
C2×#117451802
C29×#5462
#329629