Finite Group Databasebeta

← #34079207

Subgroups — #34079207

Order 19328.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752766C211yesmaximal, characteristic, complemented
2C4×D4×D151C211yesmaximal, characteristic
3#23752549C211yesmaximal, characteristic, complemented
4#23752546C211yesmaximal, characteristic, complemented
5#23752491C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752416C211yesmaximal, characteristic, complemented
8#23752415C211yesmaximal, characteristic, complemented
9#23752364C211yesmaximal, characteristic
10#23752361C211yesmaximal, characteristic
11#23752314C211yesmaximal, characteristic, complemented
12#23752312C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C22×C4×D151—21no—
18C2×#14558993C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21#18012738C2211yescharacteristic, complemented
22#18012737C2211yescharacteristic, complemented
23#18012729—21no—
24#18012719C2211yescharacteristic
25#18012717—21no—
26#18012715C2211yescharacteristic
27C4×Dic302—21no—
28C4×Dic302C2211yescharacteristic, complemented
29C4×D604C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012696—21no—
35C4⋊C4×D151C2211yescharacteristic
36C22⋊C4×D151—21no—
37C42×D151C2211yescharacteristic
38#18012673C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012662C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic, complemented
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64D4×D151—22no—
65D4×D151—22no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—44no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558993—22no—
75#14558992—22no—
76#14558991—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151D411yescharacteristic
95C4×Dic151D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100SD16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C42×C151C2311yescharacteristic
109C22×D151—24no—
110C22×D151—21no—
111C22×D151—42no—
112C22×D151—42no—
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—21no—
116Dic302—42no—
117D604—21no—
118D604#4112yes—
119C22⋊D151—24no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—42no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—22no—
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—22no—
131C4×D151—42no—
132C4×D151—42no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137Q8×C151—21no—
138Q8×C151—21no—
139D4×C151—21no—
140D4×C151#4112yes—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—42no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C8×C151—21no—
149C8×C151—21no—
150C22×C151—22no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151C22×D411yescharacteristic
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—22no—
157C2×D151—48no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151#13712yes—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151C2×#4111yescharacteristic
167C4×C151C2×#4111yescharacteristic
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173Dic151AGL(1,ℤ/8)12yes—
174C2×C151—42no—
175C2×C151#52511yescharacteristic
176C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C151C2×#13711yescharacteristic
178D151—22no—
179D151—42no—
180C151#311011yescharacteristic, complemented, Sylow
181#3110—1511nomaximal, Sylow
182#533—1511no—
183C2×C4×D4—1511no—
184#484—1511no—
185#484—1511no—
186#474—1511no—
187#474—1511no—
188#461—1511no—
189#461—1511no—
190#450—1511no—
191#450—1511no—
192#440—1511no—
193#440—1511no—
194#440—1511no—
195#440D15111yescharacteristic, complemented
196#432—1511no—
197C22×D4—1511no—
198C23×C4—3021no—
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×SD16—1511no—
202C2×SD16C2×D15111yescharacteristic
203C4⋊Q8—1511no—
204C4⋊Q8—1511no—
205#125—3021no—
206C22⋊Q8—3021no—
207C22⋊Q8—1511no—
208C22⋊Q8—1511no—
209C4×Q8—3021no—
210C4×Q8—1511no—
211C4×Q8C2×D15111yescharacteristic, complemented
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4C2×D15111yescharacteristic
218#117—3021no—
219C2×C4⋊C4—1511no—
220C2×C22⋊C4—3021no—
221C2×C42—1511no—
222#107—1511no—
223#107—1511no—
224#107—1511no—
225#107C2×D15111yescharacteristic, complemented
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228#103—1511no—
229#103—1511no—
230#103—1511no—
231#103C2×D15111yescharacteristic, complemented
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236C22⋊C8—1511no—
237C22⋊C8—1511no—
238#97—1511no—
239#97C2×D15111yescharacteristic, complemented
240C24—3021no—
241C2×Q8—3021no—
242C2×Q8—1511no—
243C2×Q8C22×D15111yescharacteristic
244C2×D4—3022no—
245C2×D4—3022no—
246C2×D4—3021no—
247C2×D4—1511no—
248C2×D4C22×D15111yescharacteristic
249C22×C4—21no—
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—6044no—
255C22×C4—1511no—
256C22×C4—1511no—
257C22×C4—1511no—
258SD16—22no—
259SD16—3022no—
260SD16—3022no—
261SD16—3022no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4C22×D15111yescharacteristic
277C4⋊C4C22×D15111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C42—21no—
285C42—3021no—
286C42—1511no—
287C42—1511no—
288C42—1511no—
289C42C22×D15111yescharacteristic
290C23—21no—
291C23—3024no—
292C23—3021no—
293C23—6042no—
294C23—6042no—
295C23—1511no—
296Q8—21no—
297Q8—21no—
298Q8—3021no—
299Q8—3021no—
300Q8—6042no—
301D4—21no—
302D4—3024no—
303D4—3021no—
304D4—1512no—
305D4#1455900412yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3022no—
311C2×C4—3022no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4—6042no—
320C2×C4—6042no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4D4×D15111yescharacteristic
325C2×C4D4×D15111yescharacteristic
326C2×C4C23×D15111yescharacteristic
327C8—21no—
328C8—21no—
329C8—3021no—
330C8—3021no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—3021no—
335C22—3021no—
336C22—3022no—
337C22—6048no—
338C22—6041no—
339C22—6041no—
340C22—1512no—
341C22C2×D4×D15111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3021no—
348C4—3021no—
349C4—6041no—
350C4—6041no—
351C4—6041no—
352C4—1512no—
353C4#41×D15111yescharacteristic
354C4C2×#1455900411yescharacteristic
355C2—42no—
356C2—3022no—
357C2—6042no—
358C2#2375272111yescharacteristic
359C2AGL(1,ℤ/8)×D15111yescharacteristic
360C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#440D151
hypocenterC151#3110
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752766C2semidirect
3. #23752549C2semidirect
4. #23752546C2semidirect
5. #23752491C2semidirect
6. #23752490C2semidirect
7. #23752416C2semidirect
8. #23752415C2semidirect
11. #23752314C2semidirect
12. #23752312C2semidirect
13. #23752310C2semidirect
14. #23752267C2semidirect
15. #440×C151C2semidirect
21. #18012738C22semidirect
22. #18012737C22semidirect
28. C4×Dic302C22semidirect
38. #18012673C22semidirect
39. #18012672C22semidirect
40. #18012672C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012664C22semidirect
44. #18012663C22semidirect
45. #18012662C22semidirect
51. #18012650C22semidirect
53. C4×Q8×C151C22semidirect
55. #107×C151C22semidirect
56. #103×C151C22semidirect
58. #97×C151C22semidirect
180. C151#3110semidirect
195. #440D151semidirect
211. C4×Q8C2×D151semidirect
225. #107C2×D151semidirect
231. #103C2×D151semidirect
239. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527662
C4×D4×D1512
#237525492
#237525462
#237524912
#237524902
#237524162
#237524152
#237523642
#237523612
#237523142
#237523122
#237523102
#237522672
#440×C1512
#3110151