Finite Group Databasebeta

← #16828317

Subgroups — #16828317

Order 3712.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745273C211yesmaximal, characteristic
2#14271642C211yesmaximal, characteristic, complemented
3#14271635C211yesmaximal, characteristic, complemented
4#14271275C211yesmaximal, characteristic, complemented
5#14271273C211yesmaximal, characteristic, complemented
6#14271263C211yesmaximal, characteristic, complemented
7#14271262C211yesmaximal, characteristic, complemented
8#14271254C211yesmaximal, characteristic, complemented
9C4×#90773C211yesmaximal, characteristic, complemented
10#14271243C211yesmaximal, characteristic, complemented
11#14271204C211yesmaximal, characteristic, complemented
12#14271156C211yesmaximal, characteristic, complemented
13#102×D29C211yesmaximal, characteristic, complemented
14#14271117C211yesmaximal, characteristic, complemented
15C4×D8×C29C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×D8×C29C2211yescharacteristic
19C4×D4×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic, complemented
21D4×Dic29C2211yescharacteristic
22D4×Dic29C2211yescharacteristic, complemented
23C2×#90783C2211yescharacteristic
24C2×#90782C2211yescharacteristic
25C4×C22⋊D29—21no—
26C4×C22⋊D29—21no—
27C2×#90781—21no—
28C2×#90779—21no—
29#11745273C418yescomplemented
30C2×#90773C2211yescharacteristic
31C2×#90772C2211yescharacteristic
32C2×C8×D29C2211yescharacteristic
33#11745255C2211yescharacteristic
34#11745254C2211yescharacteristic
35C4⋊C4×D29C2211yescharacteristic
36#11745249C2211yescharacteristic, complemented
37#11745243—21no—
38#11745243—21no—
39C22⋊C4×D29—21no—
40#11745239—21no—
41C4×D116C2211yescharacteristic
42#11745234C2211yescharacteristic
43C4×Dic58C2211yescharacteristic, complemented
44C29×#107C2211yescharacteristic, complemented
45C29×#102C2211yescharacteristic
46C29×#102C2211yescharacteristic, complemented
47C4×C8×C29C2211yescharacteristic, complemented
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic
51#11745165C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54C8×Dic29C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59#11745151C2211yescharacteristic, complemented
60C23×D29—21no—
61C2×D4×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C22×C4×C29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68C22×Dic29—21no—
69C22×Dic29—21no—
70#90807—22no—
71#90807C2×C414yescomplemented
72D4×D29—22no—
73D4×D29C2×C414yescomplemented
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×Dic58C2311yescharacteristic
80D8×C29C2×C414yescomplemented
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90#90783C2×C414yescomplemented
91#90782C2×C414yescomplemented
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96#90781D411yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103#90779D411yescharacteristic
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110#90773C2×C414yescomplemented
111#90772C2×C414yescomplemented
112C8×D29—22no—
113C23×C29—21no—
114C23×C29—21no—
115C22×D29—21no—
116C22×D29—24no—
117C22×D29—81no—
118C22×D29—81no—
119C22×D29C2×D411yescharacteristic
120D4×C29—21no—
121D4×C29—21no—
122D4×C29C22×C412yes—
123D4×C29C22×C412yes—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—81no—
127C2×C4×C29—81no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—24no—
132C22⋊D29—24no—
133C2×Dic29—21no—
134C2×Dic29—24no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—81no—
138C2×Dic29—81no—
139C2×Dic29C2×D411yescharacteristic
140C2×Dic29C2×D411yescharacteristic
141C2×Dic29C2×D411yescharacteristic
142D116—21no—
143D116C22×C412yes—
144C4×D29—81no—
145C4×D29—81no—
146C4×D29—81no—
147C4×D29C22×C412yes—
148C4×D29#4112yes—
149Dic58—21no—
150Dic58C22×C412yes—
151C8×C29—21no—
152C8×C29C22×C412yes—
153#6597—21no—
154#6597C22×C412yes—
155#2946—291nomaximal, Sylow
156C22×C29—22no—
157C22×C29—22no—
158C22×C29—41no—
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29C22×D411yescharacteristic
163C2×D29—21no—
164C2×D29—21no—
165C2×D29—22no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—84no—
169C2×D29C4×D412yes—
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29C23×C411yescharacteristic
175C4×C29C2×#4111yescharacteristic
176Dic29—22no—
177Dic29—21no—
178Dic29—21no—
179Dic29—41no—
180Dic29—41no—
181Dic29C4×D412yes—
182C2×AGL(1,ℤ/8)—291no—
183#520—291no—
184#518—291no—
185#442—291no—
186#442—291no—
187#440—291no—
188#440—291no—
189C4×SD16—291no—
190C4×SD16—291no—
191C4×D8—291no—
192C4×D8D2911yescharacteristic, complemented
193#428—291no—
194#416—291no—
195C2×#102—291no—
196#405—291no—
197C2×C29—42no—
198C2×C29—42no—
199C2×C29C2×C4×D411yescharacteristic
200C2×C29#57611yescharacteristic
201C2×C29#57711yescharacteristic
202D29—22no—
203D29—42no—
204C2×#41—291no—
205C22×D4—291no—
206AGL(1,ℤ/8)—298no—
207C2×SD16—291no—
208C2×SD16—291no—
209C2×D8—291no—
210C2×D8C2×D2911yescharacteristic
211C2×M16—291no—
212C22×C8—291no—
213C4×Q8—291no—
214C4×Q8—291no—
215C4×D4—291no—
216C4×D4—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—581no—
220C4×D4—581no—
221C4×D4—581no—
222C4×D4—581no—
223C4×D4C2×D2911yescharacteristic
224C4×D4C2×D2911yescharacteristic, complemented
225#117—291no—
226#117—291no—
227#117—581no—
228C2×C4⋊C4—291no—
229C2×C4⋊C4—581no—
230C2×C22⋊C4—581no—
231C2×C22⋊C4—581no—
232#107—291no—
233#107C2×D2911yescharacteristic, complemented
234#106—291no—
235#106—291no—
236#103—291no—
237#103—291no—
238#102—291no—
239#102—291no—
240#102—291no—
241#102—291no—
242#102C2×D2911yescharacteristic
243#102C2×D2911yescharacteristic, complemented
244#97—291no—
245#97—291no—
246C4×C8—291no—
247C4×C8C2×D2911yescharacteristic, complemented
248C29#294611yescharacteristic, complemented, Sylow
249C24—581no—
250#41—294no—
251#41—582no—
252C2×Q8—291no—
253C2×D4—294no—
254C2×D4—291no—
255C2×D4—582no—
256C2×D4—581no—
257C2×D4—581no—
258C2×D4C22×D2911yescharacteristic
259C2×D4C22×D2911yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—291no—
263C22×C4—581no—
264C22×C4—581no—
265C22×C4—581no—
266C22×C4—581no—
267C22×C4—581no—
268C22×C4—581no—
269SD16—294no—
270SD16—294no—
271D8—294no—
272D8C4×D2914yescomplemented
273M16—294no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—582no—
277C2×C8C22×D2911yescharacteristic
278C2×C8C22×D2911yescharacteristic
279C4⋊C4—291no—
280C4⋊C4—291no—
281C4⋊C4—291no—
282C4⋊C4—291no—
283C4⋊C4—581no—
284C4⋊C4—581no—
285C4⋊C4—581no—
286C4⋊C4C22×D2911yescharacteristic
287C4⋊C4C22×D2911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—291no—
291C22⋊C4—291no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C42—291no—
298C42—581no—
299C42—581no—
300C42—581no—
301C42C22×D2911yescharacteristic
302C23—21no—
303C23—21no—
304C23—291no—
305C23—584no—
306C23—581no—
307C23—2321no—
308C23—2321no—
309Q8—292no—
310Q8—581no—
311D4—21no—
312D4—21no—
313D4—292no—
314D4—584no—
315D4—584no—
316D4—581no—
317D4C2×C4×D2912yes—
318D4C2×C4×D2912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—291no—
324C2×C4—292no—
325C2×C4—292no—
326C2×C4—291no—
327C2×C4—291no—
328C2×C4—584no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—581no—
332C2×C4—2321no—
333C2×C4—2321no—
334C2×C4—2321no—
335C2×C4—2321no—
336C2×C4—2321no—
337C2×C4D4×D2911yescharacteristic
338C2×C4D4×D2911yescharacteristic
339C2×C4C23×D2911yescharacteristic
340C8—21no—
341C8—292no—
342C8—581no—
343C8C2×C4×D2912yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—292no—
351C22—581no—
352C22—581no—
353C22—582no—
354C22—1161no—
355C22—1161no—
356C22—2324no—
357C22C2×D4×D2911yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—292no—
363C4—582no—
364C4—581no—
365C4—581no—
366C4—1161no—
367C4—1161no—
368C4C22×C4×D2911yescharacteristic
369C4#41×D2911yescharacteristic
370C2—42no—
371C2—42no—
372C2—582no—
373C2—1162no—
374C2C4×D4×D2911yescharacteristic
375C2#1427196411yescharacteristic
376C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC4×D8×C29C2
socleC22×C29C22×D4
prime radicalC2×#11745273C2
cosocleC2×C4×C29C24
hypercenterC4×D8D29
hypocenterC29#2946
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #14271642C2semidirect
3. #14271635C2semidirect
4. #14271275C2semidirect
5. #14271273C2semidirect
6. #14271263C2semidirect
7. #14271262C2semidirect
8. #14271254C2semidirect
9. C4×#90773C2semidirect
10. #14271243C2semidirect
11. #14271204C2semidirect
12. #14271156C2semidirect
13. #102×D29C2semidirect
14. #14271117C2semidirect
15. C4×D8×C29C2semidirect
20. C4×D4×C29C22semidirect
22. D4×Dic29C22semidirect
29. #11745273C4semidirect
36. #11745249C22semidirect
43. C4×Dic58C22semidirect
44. C29×#107C22semidirect
46. C29×#102C22semidirect
47. C4×C8×C29C22semidirect
49. #11745180C22semidirect
51. #11745165C22semidirect
52. #11745164C22semidirect
53. #11745163C22semidirect
54. C8×Dic29C22semidirect
55. #11745158C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
59. #11745151C22semidirect
71. #90807C2×C4semidirect
73. D4×D29C2×C4semidirect
80. D8×C29C2×C4semidirect
90. #90783C2×C4semidirect
91. #90782C2×C4semidirect
110. #90773C2×C4semidirect
111. #90772C2×C4semidirect
192. C4×D8D29semidirect
224. C4×D4C2×D29semidirect
233. #107C2×D29semidirect
243. #102C2×D29semidirect
247. C4×C8C2×D29semidirect
248. C29#2946semidirect
272. D8C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452732
#142716422
#142716352
#142712752
#142712732
#142712632
#142712622
#142712542
C4×#907732
#142712432
#142712042
#142711562
#102×D292
#142711172
C4×D8×C292
#294629