Finite Group Databasebeta

← #16829669

Subgroups — #16829669

Order 3712.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271780C211yesmaximal, characteristic, complemented
2#14271638C211yesmaximal, characteristic, complemented
3#14271505C211yesmaximal, characteristic, complemented
4#14271484C211yesmaximal, characteristic, complemented
5#14271451C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271376C211yesmaximal, characteristic, complemented
8#14271376C211yesmaximal, characteristic, complemented
9#14271314C211yesmaximal, characteristic, complemented
10#14271275C211yesmaximal, characteristic, complemented
11#14271260C211yesmaximal, characteristic, complemented
12#14271254C211yesmaximal, characteristic, complemented
13D8×Dic29C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#447C211yesmaximal, characteristic
16C22×D4×C29C2211yescharacteristic
17C2×D8×C29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C29×#121C2211yescharacteristic
20C2×C22⋊Dic29—21no—
21C2×C22⋊Dic29—21no—
22#11745298—21no—
23#11745298C2211yescharacteristic, complemented
24#11745297—21no—
25D4×Dic29—21no—
26D4×Dic29—21no—
27D4×Dic29C2211yescharacteristic
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30D4×Dic29C2211yescharacteristic
31D4×Dic29C2211yescharacteristic, complemented
32C2×#90783C2211yescharacteristic
33C2×#90783C2211yescharacteristic
34#11745288C2211yescharacteristic
35#11745288C2211yescharacteristic
36#11745286C2211yescharacteristic
37#11745250C2211yescharacteristic, complemented
38#11745249C2211yescharacteristic, complemented
39#11745241—21no—
40#11745240—21no—
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic, complemented
48C22⋊#6597C2211yescharacteristic
49#11745166C2211yescharacteristic, complemented
50#11745165C2211yescharacteristic, complemented
51#11745164C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54#11745162C2211yescharacteristic, complemented
55#11745162C2211yescharacteristic, complemented
56C8×Dic29C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C24×C29—21no—
60C2×D4×C29—22no—
61C2×D4×C29—22no—
62C2×D4×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C22×Dic29—21no—
69C22×Dic29—21no—
70C22×Dic29—21no—
71C22×Dic29—21no—
72C22×Dic29—21no—
73C2×Dic58—21no—
74C2×Dic58C2311yescharacteristic
75D8×C29—22no—
76D8×C29—22no—
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29D411yescharacteristic
91C22⋊Dic29D411yescharacteristic
92#90783—22no—
93#90783—22no—
94C4⋊Dic29D411yescharacteristic
95C4⋊Dic29D411yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—24no—
109C23×C29—21no—
110C23×C29—21no—
111C23×C29—21no—
112C23×C29—81no—
113C23×C29—81no—
114C23×C29C2×D411yescharacteristic
115D4×C29—24no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—81no—
121D4×C29#4112yes—
122D4×C29#4112yes—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—81no—
133C2×Dic29—81no—
134C2×Dic29—81no—
135C2×Dic29—81no—
136C2×Dic29—81no—
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139C2×Dic29C2×D411yescharacteristic
140C2×Dic29C2×D411yescharacteristic
141Dic58—21no—
142Dic58—21no—
143Dic58—81no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597—21no—
148#3118—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—22no—
151C22×C29—22no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—84no—
162C22×C29C22×D411yescharacteristic
163C4×C29—21no—
164C4×C29—41no—
165C4×C29C2×#4111yescharacteristic
166C4×C29C2×#4111yescharacteristic
167Dic29—21no—
168Dic29—21no—
169Dic29—21no—
170Dic29—21no—
171Dic29—41no—
172Dic29—41no—
173Dic29—41no—
174Dic29—41no—
175#542—291no—
176#518—291no—
177#485—291no—
178#482—291no—
179#476—291no—
180#474—291no—
181#463—291no—
182#463—291no—
183#450—291no—
184#447D2911yescharacteristic
185#442—291no—
186#440—291no—
187C4×SD16—291no—
188C4×D8—291no—
189#433—291no—
190C2×C29—41no—
191C2×C29—42no—
192C2×C29—42no—
193C2×C29—81no—
194C2×C29#52511yescharacteristic
195C2×C29#57611yescharacteristic
196C2×C29#57711yescharacteristic
197C22×D4C2×D2911yescharacteristic
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8C2×D2911yescharacteristic
201C2×D8C2×D2911yescharacteristic
202C4⋊Q8—291no—
203#126—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—581no—
209#121C2×D2911yescharacteristic
210C4×Q8—291no—
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—291no—
216C4×D4—581no—
217C4×D4—581no—
218#117—291no—
219#117—291no—
220C2×C22⋊C4—581no—
221C2×C22⋊C4—581no—
222#107—291no—
223#107—291no—
224#106—291no—
225#106—291no—
226C4⋊C8—291no—
227C4⋊C8—291no—
228#103—291no—
229#103—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102C2×D2911yescharacteristic
235#102C2×D2911yescharacteristic
236C22⋊C8—291no—
237C22⋊C8C2×D2911yescharacteristic
238#97—291no—
239C4×C8—291no—
240C29#311811yescharacteristic, complemented, Sylow
241C24—21no—
242C2×Q8—291no—
243C2×Q8—581no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D2911yescharacteristic
249C2×D4C22×D2911yescharacteristic
250C2×D4C22×D2911yescharacteristic
251C22×C4—581no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4C22×D2911yescharacteristic
257SD16—582no—
258SD16—582no—
259D8—22no—
260D8—22no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4C22×D2911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—291no—
276C22⋊C4—291no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—291no—
287C42—291no—
288C42—581no—
289C42—581no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D2911yescharacteristic
297Q8—581no—
298Q8—581no—
299Q8—2321no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#9080712yes—
307D4#9080712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—291no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—2321no—
320C2×C4—2321no—
321C2×C4—2321no—
322C2×C4—2321no—
323C2×C4—2321no—
324C2×C4D4×D2911yescharacteristic
325C2×C4C23×D2911yescharacteristic
326C8—21no—
327C8—21no—
328C8—581no—
329C8—581no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D2911yescharacteristic
344C4—21no—
345C4—41no—
346C4—581no—
347C4—581no—
348C4—581no—
349C4—581no—
350C4—1161no—
351C4—1161no—
352C4—1161no—
353C4—1161no—
354C4C2×#9080711yescharacteristic
355C4C2×#9080711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#1427166911yescharacteristic
361C2#1427196411yescharacteristic
362C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#447C2
socleC22×C29C22×D4
hypercenter#447D29
hypocenterC29#3118
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14271780C2semidirect
2. #14271638C2semidirect
3. #14271505C2semidirect
4. #14271484C2semidirect
5. #14271451C2semidirect
6. #14271441C2semidirect
7. #14271376C2semidirect
8. #14271376C2semidirect
9. #14271314C2semidirect
10. #14271275C2semidirect
11. #14271260C2semidirect
12. #14271254C2semidirect
13. D8×Dic29C2semidirect
14. #14271221C2semidirect
23. #11745298C22semidirect
31. D4×Dic29C22semidirect
37. #11745250C22semidirect
38. #11745249C22semidirect
46. #11745180C22semidirect
47. #11745180C22semidirect
49. #11745166C22semidirect
50. #11745165C22semidirect
51. #11745164C22semidirect
52. #11745164C22semidirect
53. #11745163C22semidirect
54. #11745162C22semidirect
55. #11745162C22semidirect
56. C8×Dic29C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
240. C29#3118semidirect

Maximal subgroups

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

subgroupindex
#142717802
#142716382
#142715052
#142714842
#142714512
#142714412
#142713762
#142713142
#142712752
#142712602
#142712542
D8×Dic292
#142712212
C29×#4472
#311829