Finite Group Databasebeta

← #16829738

Subgroups — #16829738

Order 3712.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271773C211yesmaximal, characteristic, complemented
2#14271638C211yesmaximal, characteristic
3#14271505C211yesmaximal, characteristic, complemented
4#14271501C211yesmaximal, characteristic, complemented
5#14271465C211yesmaximal, characteristic, complemented
6#14271461C211yesmaximal, characteristic, complemented
7#14271366C211yesmaximal, characteristic, complemented
8#14271366C211yesmaximal, characteristic, complemented
9#14271314C211yesmaximal, characteristic
10#14271264C211yesmaximal, characteristic, complemented
11#14271260C211yesmaximal, characteristic, complemented
12#14271254C211yesmaximal, characteristic, complemented
13SD16×Dic29C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#450C211yesmaximal, characteristic
16C22×D4×C29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C29×C22⋊Q8C2211yescharacteristic
20C2×C22⋊Dic29—21no—
21C2×C22⋊Dic29—21no—
22Q8×Dic29C2211yescharacteristic, complemented
23#11745306C2211yescharacteristic, complemented
24D4×Dic29—21no—
25D4×Dic29—21no—
26D4×Dic29C2211yescharacteristic
27D4×Dic29C2211yescharacteristic
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic
30C2×#90783C2211yescharacteristic
31C2×#90783C2211yescharacteristic
32#11745288C2211yescharacteristic
33#11745288C2211yescharacteristic
34#11745286C2211yescharacteristic
35#11745252—21no—
36#11745252C2211yescharacteristic, complemented
37#11745251—21no—
38#11745249C2211yescharacteristic, complemented
39#11745241—21no—
40#11745241—21no—
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44#11745183C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
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×Q8×C29C2311yescharacteristic
61C2×D4×C29—22no—
62C2×D4×C29—22no—
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C2×D4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C22×Dic29—21no—
68C22×Dic29—21no—
69C22×Dic29—21no—
70C22×Dic29—21no—
71C2×Dic58C2311yescharacteristic
72SD16×C29—22no—
73SD16×C29—22no—
74C2×C8×C29C2311yescharacteristic
75C2×C8×C29C2311yescharacteristic
76C4⋊C4×C29—21no—
77C4⋊C4×C29C2311yescharacteristic
78C22⋊C4×C29—21no—
79C22⋊Dic29—21no—
80C22⋊Dic29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29D411yescharacteristic
86C22⋊Dic29D411yescharacteristic
87#90783—22no—
88#90783—22no—
89C4⋊Dic29—21no—
90C4⋊Dic29—21no—
91C4⋊Dic29D411yescharacteristic
92C4⋊Dic29D411yescharacteristic
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—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—81no—
112C23×C29—81no—
113C23×C29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116D4×C29—24no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29#4112yes—
120D4×C29#4112yes—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—81no—
132C2×Dic29—81no—
133C2×Dic29—81no—
134C2×Dic29—81no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139Dic58—21no—
140Dic58—21no—
141C8×C29—21no—
142C8×C29—21no—
143#6597—21no—
144#6597—21no—
145#3123—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—22no—
148C22×C29—22no—
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—84no—
156C22×C29C22×D411yescharacteristic
157C4×C29—21no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29C2×#4111yescharacteristic
161C4×C29C2×#4111yescharacteristic
162Dic29—21no—
163Dic29—21no—
164Dic29—21no—
165Dic29—21no—
166Dic29—41no—
167Dic29—41no—
168Dic29—41no—
169Dic29—41no—
170#541—291no—
171#518—291no—
172#485—291no—
173#485—291no—
174#478—291no—
175#478—291no—
176#461—291no—
177#461—291no—
178#450—291no—
179#450D2911yescharacteristic
180#440—291no—
181#440—291no—
182C4×SD16—291no—
183C4×SD16—291no—
184#433—291no—
185C2×C29—41no—
186C2×C29—42no—
187C2×C29—42no—
188C2×C29#52511yescharacteristic
189C2×C29#57711yescharacteristic
190C2×C29#57711yescharacteristic
191C22×D4C2×D2911yescharacteristic
192C2×SD16—291no—
193C2×SD16—291no—
194C2×SD16C2×D2911yescharacteristic
195C2×SD16C2×D2911yescharacteristic
196C4⋊Q8—291no—
197#126—581no—
198#126—581no—
199#125—291no—
200#125—581no—
201#125—581no—
202C22⋊Q8—291no—
203C22⋊Q8C2×D2911yescharacteristic
204C4×Q8—291no—
205C4×Q8—291no—
206C4×D4—291no—
207C4×D4—291no—
208C4×D4—291no—
209C4×D4—291no—
210C4×D4—581no—
211C4×D4—581no—
212#117—291no—
213#117—291no—
214C2×C22⋊C4—581no—
215C2×C22⋊C4—581no—
216#107—291no—
217#107—291no—
218#106—291no—
219#106—291no—
220C4⋊C8—291no—
221C4⋊C8—291no—
222#103—291no—
223#103—291no—
224#103—291no—
225#103—291no—
226#102—291no—
227#102—291no—
228#102C2×D2911yescharacteristic
229#102C2×D2911yescharacteristic
230C22⋊C8—291no—
231C22⋊C8C2×D2911yescharacteristic
232#97—291no—
233C4×C8—291no—
234C29#312311yescharacteristic, complemented, Sylow
235C24—21no—
236C2×Q8—291no—
237C2×Q8C22×D2911yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D2911yescharacteristic
242C2×D4C22×D2911yescharacteristic
243C22×C4—581no—
244C22×C4—581no—
245C22×C4—581no—
246C22×C4—581no—
247C22×C4C22×D2911yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—582no—
251SD16—582no—
252C2×C8—291no—
253C2×C8—291no—
254C2×C8C22×D2911yescharacteristic
255C2×C8C22×D2911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—291no—
258C4⋊C4—291no—
259C4⋊C4—291no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4C22×D2911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—291no—
272C22⋊C4—291no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C42—291no—
280C42—291no—
281C42—581no—
282C42—581no—
283C42—581no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D2911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—581no—
293Q8—581no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#9080712yes—
298D4#9080712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—291no—
304C2×C4—291no—
305C2×C4—291no—
306C2×C4—291no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—2321no—
312C2×C4—2321no—
313C2×C4—2321no—
314C2×C4—2321no—
315C2×C4D4×D2911yescharacteristic
316C2×C4C23×D2911yescharacteristic
317C8—21no—
318C8—21no—
319C8—581no—
320C8—581no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D2911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—581no—
336C4—581no—
337C4—581no—
338C4—581no—
339C4—1161no—
340C4—1161no—
341C4—1161no—
342C4—1161no—
343C4C2×#9080711yescharacteristic
344C4C2×#9080711yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1427166911yescharacteristic
349C2#1427196911yescharacteristic
350C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#450C2
socleC22×C29C22×D4
prime radicalC22×D4×C29C22
hypercenter#450D29
hypocenterC29#3123
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14271773C2semidirect
3. #14271505C2semidirect
4. #14271501C2semidirect
5. #14271465C2semidirect
6. #14271461C2semidirect
7. #14271366C2semidirect
8. #14271366C2semidirect
10. #14271264C2semidirect
11. #14271260C2semidirect
12. #14271254C2semidirect
13. SD16×Dic29C2semidirect
14. #14271221C2semidirect
22. Q8×Dic29C22semidirect
23. #11745306C22semidirect
36. #11745252C22semidirect
38. #11745249C22semidirect
44. #11745183C22semidirect
45. #11745183C22semidirect
49. #11745166C22semidirect
50. #11745165C22semidirect
51. #11745164C22semidirect
52. #11745164C22semidirect
53. #11745163C22semidirect
54. #11745162C22semidirect
55. #11745162C22semidirect
56. C8×Dic29C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
234. C29#3123semidirect

Maximal subgroups

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

subgroupindex
#142717732
#142716382
#142715052
#142715012
#142714652
#142714612
#142713662
#142713142
#142712642
#142712602
#142712542
SD16×Dic292
#142712212
C29×#4502
#312329