Finite Group Databasebeta

← #16829670

Subgroups — #16829670

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#14271637C211yesmaximal, characteristic, complemented
2#14271501C211yesmaximal, characteristic, complemented
3#14271484C211yesmaximal, characteristic, complemented
4#14271450C211yesmaximal, characteristic, complemented
5#14271440C211yesmaximal, characteristic, complemented
6#14271375C211yesmaximal, characteristic, complemented
7#14271375C211yesmaximal, characteristic, complemented
8#14271313C211yesmaximal, characteristic, complemented
9#14271296C211yesmaximal, characteristic
10#14271273C211yesmaximal, characteristic, complemented
11#14271261C211yesmaximal, characteristic, complemented
12C4×#90784C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271224C211yesmaximal, characteristic, complemented
15C29×#542C211yesmaximal, characteristic, complemented
16C22×D116C2211yescharacteristic
17C29×C4⋊Q8C2211yescharacteristic, complemented
18C29×#126—21no—
19C29×#124—21no—
20C29×#124C2211yescharacteristic, complemented
21C29×#123—21no—
22C29×C22⋊Q8—21no—
23C29×C22⋊Q8C2211yescharacteristic
24C29×#121C2211yescharacteristic
25C4×Q8×C29C2211yescharacteristic, complemented
26C4×D4×C29C2211yescharacteristic, complemented
27C29×#117C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29C2×#90784C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31C2×#90782C2211yescharacteristic
32#11745288C2211yescharacteristic
33#11745255—21no—
34#11745255—21no—
35C22⋊C4×D29—21no—
36C22⋊C4×D29—21no—
37C4×D116C2211yescharacteristic
38C4×D116C2211yescharacteristic
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic
41#11745183C2211yescharacteristic, complemented
42#11745183C2211yescharacteristic, complemented
43#11745180C2211yescharacteristic, complemented
44#11745180C2211yescharacteristic, complemented
45C22⋊#6597C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745157C2211yescharacteristic
48#11745157C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745156C2211yescharacteristic, complemented
52#11745156C2211yescharacteristic, complemented
53#11745155C2211yescharacteristic, complemented
54#11745155C2211yescharacteristic, complemented
55C4⋊#6597C2211yescharacteristic, complemented
56C4⋊#6597C2211yescharacteristic, complemented
57#11745151C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C22×C4×C29C2311yescharacteristic
66C2×D116—21no—
67C2×D116—22no—
68C2×D116—22no—
69C2×D116C2311yescharacteristic
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C4⋊C4×C29—21no—
76C4⋊C4×C29—21no—
77C4⋊C4×C29—21no—
78C4⋊C4×C29D411yescharacteristic
79C4⋊C4×C29D411yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C22⋊C4×C29D411yescharacteristic
88C22⋊C4×C29D411yescharacteristic
89C42×C29—21no—
90C42×C29C2311yescharacteristic
91C42×C29C2311yescharacteristic
92C22⋊Dic29—21no—
93#90784—22no—
94#90784—22no—
95#90782—22no—
96#90782—22no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111C22×D29—21no—
112C22×D29—24no—
113C22×D29—81no—
114C22×D29—81no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—81no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—81no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—81no—
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2411yescharacteristic
133C2×Dic29—21no—
134C2×Dic29—21no—
135D116—24no—
136D116—21no—
137D116—21no—
138D116#4112yes—
139D116#4112yes—
140C4×D29—81no—
141C4×D29—81no—
142C4×D29—81no—
143C4×D29—81no—
144#6597—21no—
145#6597—21no—
146#6597—21no—
147#6597—21no—
148#3118—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29C22×D411yescharacteristic
156C2×D29—22no—
157C2×D29—22no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—84no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29C2×#4111yescharacteristic
173Dic29—41no—
174Dic29—41no—
175#542D2911yescharacteristic, complemented
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#447—291no—
185#442—291no—
186#440—291no—
187C4×SD16—291no—
188C4×D8—291no—
189#433—291no—
190C2×C29—41no—
191C2×C29—81no—
192C2×C29#52511yescharacteristic
193C2×C29#57611yescharacteristic
194C2×C29#57711yescharacteristic
195D29—42no—
196D29—42no—
197C22×D4—291no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8C2×D2911yescharacteristic, complemented
203#126—21no—
204#124—21no—
205#124C2×D2911yescharacteristic, complemented
206#123—21no—
207C22⋊Q8—21no—
208C22⋊Q8C2×D2911yescharacteristic
209#121C2×D2911yescharacteristic
210C4×Q8C2×D2911yescharacteristic, complemented
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—581no—
216C4×D4—581no—
217C4×D4C2×D2911yescharacteristic, complemented
218#117—291no—
219#117C2×D2911yescharacteristic
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#102—291no—
235#102—291no—
236C22⋊C8—291no—
237C22⋊C8—291no—
238#97—291no—
239C4×C8—291no—
240C29#311811yescharacteristic, complemented, Sylow
241C24—581no—
242C2×Q8—21no—
243C2×Q8C22×D2911yescharacteristic
244C2×D4—21no—
245C2×D4—291no—
246C2×D4—291no—
247C2×D4—582no—
248C2×D4—582no—
249C2×D4—581no—
250C2×D4C22×D2911yescharacteristic
251C22×C4—21no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4C22×D2911yescharacteristic
257SD16—582no—
258SD16—582no—
259D8—582no—
260D8—582no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8—291no—
264C2×C8—291no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—291no—
269C4⋊C4—291no—
270C4⋊C4C22⋊D2911yescharacteristic
271C4⋊C4C22⋊D2911yescharacteristic
272C4⋊C4C22×D2911yescharacteristic
273C4⋊C4C22×D2911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4C22⋊D2911yescharacteristic
285C22⋊C4C22⋊D2911yescharacteristic
286C42—21no—
287C42—581no—
288C42C22×D2911yescharacteristic
289C42C22×D2911yescharacteristic
290C23—21no—
291C23—584no—
292C23—581no—
293C23—581no—
294C23—2321no—
295C23—2321no—
296C23C2×C22⋊D2911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—292no—
304D4—292no—
305D4—584no—
306D4—581no—
307D4—581no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—2321no—
317C2×C4—2321no—
318C2×C4—2321no—
319C2×C4—2321no—
320C2×C4C2×C22⋊D2911yescharacteristic
321C2×C4C2×C22⋊D2911yescharacteristic
322C2×C4C2×C22⋊D2911yescharacteristic
323C2×C4C2×C22⋊D2911yescharacteristic
324C2×C4C2×C22⋊D2911yescharacteristic
325C2×C4C23×D2911yescharacteristic
326C8—581no—
327C8—581no—
328C8—581no—
329C8—581no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—582no—
337C22—582no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22—1161no—
342C22—2324no—
343C22C22×C22⋊D2911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—1161no—
353C4—1161no—
354C4#41×D2911yescharacteristic
355C4#41×D2911yescharacteristic
356C2—41no—
357C2—81no—
358C2—1162no—
359C2—1162no—
360C2#1427167011yescharacteristic
361C2#1427196611yescharacteristic
362C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#542C2
socleC22×C29C22×D4
prime radical#14271296C2
hypercenter#542D29
hypocenterC29#3118
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #14271637C2semidirect
2. #14271501C2semidirect
3. #14271484C2semidirect
4. #14271450C2semidirect
5. #14271440C2semidirect
6. #14271375C2semidirect
7. #14271375C2semidirect
8. #14271313C2semidirect
10. #14271273C2semidirect
11. #14271261C2semidirect
12. C4×#90784C2semidirect
13. C4×#90782C2semidirect
14. #14271224C2semidirect
15. C29×#542C2semidirect
17. C29×C4⋊Q8C22semidirect
20. C29×#124C22semidirect
25. C4×Q8×C29C22semidirect
26. C4×D4×C29C22semidirect
41. #11745183C22semidirect
42. #11745183C22semidirect
43. #11745180C22semidirect
44. #11745180C22semidirect
51. #11745156C22semidirect
52. #11745156C22semidirect
53. #11745155C22semidirect
54. #11745155C22semidirect
55. C4⋊#6597C22semidirect
56. C4⋊#6597C22semidirect
57. #11745151C22semidirect
58. C4×#6597C22semidirect
175. #542D29semidirect
202. C4⋊Q8C2×D29semidirect
205. #124C2×D29semidirect
210. C4×Q8C2×D29semidirect
217. C4×D4C2×D29semidirect
240. C29#3118semidirect

Maximal subgroups

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

subgroupindex
#142716372
#142715012
#142714842
#142714502
#142714402
#142713752
#142713132
#142712962
#142712732
#142712612
C4×#907842
C4×#907822
#142712242
C29×#5422
#311829