Finite Group Databasebeta

← #16829676

Subgroups — #16829676

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#14271784C211yesmaximal, characteristic, complemented
2#14271504C211yesmaximal, characteristic, complemented
3#14271487C211yesmaximal, characteristic, complemented
4#14271453C211yesmaximal, characteristic, complemented
5#14271443C211yesmaximal, characteristic, complemented
6#14271378C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271314C211yesmaximal, characteristic, complemented
9#14271297C211yesmaximal, characteristic
10#14271273C211yesmaximal, characteristic, complemented
11#14271263C211yesmaximal, characteristic, complemented
12C4×#90783C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14#14271224C211yesmaximal, characteristic, complemented
15C29×#518C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C4×D4×C29—21no—
18C4×D4×C29—21no—
19C4×D4×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21C4×D4×C29C2211yescharacteristic
22C4×D4×C29C2211yescharacteristic
23C29×#117C2211yescharacteristic
24C29×#117C2211yescharacteristic
25C2×C22⋊C4×C29—21no—
26C2×C22⋊C4×C29—21no—
27C2×#90783C2211yescharacteristic
28C2×#90783C2211yescharacteristic
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745286C2211yescharacteristic
33#11745260—21no—
34#11745258—21no—
35#11745247—21no—
36#11745245—21no—
37#11745237C2211yescharacteristic, complemented
38C4×D116C2211yescharacteristic, complemented
39#11745231C2211yescharacteristic, complemented
40C4×Dic58C2211yescharacteristic, complemented
41#11745180C2211yescharacteristic
42#11745180C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45C22⋊#6597C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745158C2211yescharacteristic, complemented
48#11745158C2211yescharacteristic, complemented
49#11745157C2211yescharacteristic, complemented
50#11745157C2211yescharacteristic, complemented
51#11745156C2211yescharacteristic, complemented
52#11745156C2211yescharacteristic, complemented
53#11745155C2211yescharacteristic, complemented
54#11745155C2211yescharacteristic, complemented
55C4⋊#6597C2211yescharacteristic, complemented
56C4⋊#6597C2211yescharacteristic, complemented
57#11745151C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C24×C29—21no—
60C2×D4×C29—22no—
61C2×D4×C29—22no—
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29—21no—
69C22×C4×C29C2311yescharacteristic
70C2×C22⋊D29—21no—
71C2×D116C2311yescharacteristic
72C2×C4×D29—21no—
73C2×Dic58—21no—
74C2×Dic58C2311yescharacteristic
75C4⋊C4×C29D411yescharacteristic
76C4⋊C4×C29D411yescharacteristic
77C4⋊C4×C29C2311yescharacteristic
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C22⋊C4×C29D411yescharacteristic
85C22⋊C4×C29D411yescharacteristic
86C42×C29—21no—
87C42×C29C2311yescharacteristic
88C42×C29C2311yescharacteristic
89C22⋊Dic29—21no—
90#90783—22no—
91#90783—22no—
92#90782—22no—
93#90782—22no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103C4×Dic29—21no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—24no—
109C23×C29—21no—
110C23×C29—21no—
111C23×C29—81no—
112C23×C29—81no—
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115D4×C29—24no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29#4112yes—
119D4×C29#4112yes—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—81no—
125C2×C4×C29—81no—
126C2×C4×C29—81no—
127C2×C4×C29—81no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2411yescharacteristic
134C22⋊D29—81no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138D116—21no—
139D116—21no—
140C4×D29—81no—
141Dic58—21no—
142Dic58—21no—
143Dic58—81no—
144#6597—21no—
145#6597—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—84no—
159C22×C29C22×D411yescharacteristic
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29C2×#4111yescharacteristic
172Dic29—41no—
173Dic29—41no—
174Dic29—41no—
175#542—291no—
176#518D2911yescharacteristic, complemented
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—42no—
192C2×C29—42no—
193C2×C29#52511yescharacteristic
194C2×C29#57611yescharacteristic
195C2×C29#57711yescharacteristic
196D29—81no—
197C22×D4C2×D2911yescharacteristic
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8—291no—
203#126—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—581no—
209#121—291no—
210C4×Q8—291no—
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—291no—
214C4×D4C2×D2911yescharacteristic
215C4×D4C2×D2911yescharacteristic
216C4×D4C2×D2911yescharacteristic
217C4×D4C2×D2911yescharacteristic
218#117C2×D2911yescharacteristic
219#117C2×D2911yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
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—21no—
242C2×Q8—291no—
243C2×Q8—581no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C2×D4C22×D2911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
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—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
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—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—581no—
296C23C2×C22⋊D2911yescharacteristic
297Q8—581no—
298Q8—581no—
299Q8—2321no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—581no—
304D4—581no—
305D4—2321no—
306D4#9080512yes—
307D4#9080512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
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—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1161no—
341C22—1161no—
342C22—1161no—
343C22C22×C22⋊D2911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1161no—
352C4—1161no—
353C4—1161no—
354C4C2×#9080511yescharacteristic
355C4C2×#9080511yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—2321no—
360C2#1427167411yescharacteristic
361C2#1427196611yescharacteristic
362C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#518C2
socleC22×C29C22×D4
prime radical#14271297C2
hypercenter#518D29
hypocenterC29#3118
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14271784C2semidirect
2. #14271504C2semidirect
3. #14271487C2semidirect
4. #14271453C2semidirect
5. #14271443C2semidirect
6. #14271378C2semidirect
7. #14271378C2semidirect
8. #14271314C2semidirect
10. #14271273C2semidirect
11. #14271263C2semidirect
12. C4×#90783C2semidirect
13. C4×#90782C2semidirect
14. #14271224C2semidirect
15. C29×#518C2semidirect
37. #11745237C22semidirect
38. C4×D116C22semidirect
39. #11745231C22semidirect
40. C4×Dic58C22semidirect
47. #11745158C22semidirect
48. #11745158C22semidirect
49. #11745157C22semidirect
50. #11745157C22semidirect
51. #11745156C22semidirect
52. #11745156C22semidirect
53. #11745155C22semidirect
54. #11745155C22semidirect
55. C4⋊#6597C22semidirect
56. C4⋊#6597C22semidirect
57. #11745151C22semidirect
58. C4×#6597C22semidirect
176. #518D29semidirect
240. C29#3118semidirect

Maximal subgroups

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

subgroupindex
#142717842
#142715042
#142714872
#142714532
#142714432
#142713782
#142713142
#142712972
#142712732
#142712632
C4×#907832
C4×#907822
#142712242
C29×#5182
#311829