Finite Group Databasebeta

← #34078416

Subgroups — #34078416

Order 19328.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012785C211yesmaximal, characteristic, complemented
2C2×#18012767C211yesmaximal, characteristic, complemented
3C2×#18012759C211yesmaximal, characteristic, complemented
4#23752793C211yesmaximal, characteristic, complemented
5#23752377C212yesmaximal, complemented
6#23752364C212yesmaximal, complemented
7#23752360C212yesmaximal, complemented
8#23752347C212yesmaximal, complemented
9C2×#18012659C211yesmaximal, characteristic, complemented
10#23752180C211yesmaximal, characteristic, complemented
11#417×C151C211yesmaximal, characteristic, complemented
12#18012785—24no—
13#18012785—24no—
14C2×#14559005C2212yes—
15C2×#14559004—21no—
16C2×#14559004C2211yescharacteristic
17C2×#14559004C2211yescharacteristic, complemented
18C22×D604—21no—
19C22×D604C2211yescharacteristic
20C2×D4×D151—22no—
21C2×D4×D151C2212yes—
22#18012767—24no—
23#18012759—24no—
24C2×#14558994C2211yescharacteristic, complemented
25C2×#14558993C2212yescomplemented
26C2×#14558992C2211yescharacteristic, complemented
27C2×#14558991C2211yescharacteristic, complemented
28C2×D1208C2212yescomplemented
29C2×#14558989C2211yescharacteristic, complemented
30C22×C151⋊C8C2211yescharacteristic, complemented
31#18012719—21no—
32#18012719C2212yescomplemented
33#18012714—21no—
34#18012714C2212yescomplemented
35#18012713—22no—
36#18012659C2212yescomplemented
37#18012659C2212yescomplemented
38(C2×D151)⋊C8C2212yescomplemented
39(C2×D151)⋊C8C2212yescomplemented
40C2×#41×C151C2211yescharacteristic
41C2×M16×C151C2211yescharacteristic, complemented
42C2×C4⋊C4×C151C2211yescharacteristic, complemented
43#103×C151C2212yescomplemented
44#102×C151C2212yescomplemented
45C23×D151—22no—
46C23×D151—21no—
47#14559005—24no—
48#14559005—24no—
49#14559004—28no—
50#14559004—22no—
51#14559004—22no—
52#14559004—22no—
53#14559004—22no—
54C2×Dic302D411yescharacteristic
55C2×Dic302C2311yescharacteristic
56C2×D604—28no—
57C2×D604—22no—
58C2×D604—22no—
59C2×D604—21no—
60C2×D604—22no—
61C2×D604D411yescharacteristic
62C2×D604D414yescomplemented
63C2×D604C2311yescharacteristic
64C2×D604C2312yes—
65C2×C22⋊D151—22no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151D412yes—
68D4×D151—216no—
69D4×D151—24no—
70D4×D151—24no—
71C2×C4×D151—22no—
72C2×C4×D151—21no—
73C2×C4×D151C2312yes—
74#14558994—22no—
75#14558993—24no—
76#14558992—22no—
77#14558991—22no—
78D1208—24no—
79#14558989—22no—
80C2×C151⋊C8—22no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—22no—
84(C2×D151)⋊C4—22no—
85(C2×D151)⋊C4—22no—
86#41×C151—22no—
87#41×C151D414yescomplemented
88C2×Q8×C151C2311yescharacteristic
89C2×D4×C151—21no—
90C2×D4×C151C2311yescharacteristic
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151C2311yescharacteristic
94M16×C151—22no—
95C2×C8×C151C2312yes—
96C4⋊C4×C151—21no—
97C4⋊C4×C151C2312yes—
98C22×D151—22no—
99C22×D151—28no—
100C22×D151—24no—
101C22×D151—21no—
102C22×D151—82no—
103C22×D151—82no—
104C22×D151—81no—
105C22×D151—81no—
106C22×D151C2×D412yes—
107Dic302—22no—
108Dic302—21no—
109Dic302—21no—
110D604—28no—
111D604—22no—
112D604—24no—
113D604—22no—
114D604—21no—
115D604—21no—
116D604—82no—
117D604C2×D414yes—
118C22⋊D151—28no—
119C22⋊D151—24no—
120C22⋊D151—42no—
121C2×Dic151—21no—
122C2×Dic151C2×D412yes—
123C4×D151—28no—
124C4×D151—22no—
125C4×D151—22no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130C23×C151C2×D411yescharacteristic
131Q8×C151—21no—
132Q8×C151C2×D412yes—
133D4×C151—24no—
134D4×C151—21no—
135D4×C151C2×D412yes—
136C2×C4×C151—21no—
137C2×C4×C151—24no—
138C2×C4×C151—22no—
139C2×C4×C151—81no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D412yes—
142C2×C4×C151C2×D412yes—
143C2×C4×C151C2411yescharacteristic
144C8×C151—22no—
145C22×C151—21no—
146C22×C151—21no—
147C22×C151—22no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151#12012yes—
151C22×C151C22×D411yescharacteristic
152C2×D151—22no—
153C2×D151—24no—
154C2×D151—22no—
155C2×D151—22no—
156C2×D151—42no—
157C2×D151—42no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—84no—
162C2×D151—88no—
163C4×C151—22no—
164C4×C151—42no—
165C4×C151#12012yes—
166C4×C151C22×D411yescharacteristic
167C4×C151C22×D411yescharacteristic
168Dic151—22no—
169Dic151—41no—
170C2×C151—22no—
171C2×C151—42no—
172C2×C151C2×#12011yescharacteristic
173C2×C151#57611yescharacteristic
174C2×C151#57711yescharacteristic
175D151—42no—
176D151—44no—
177D151—81no—
178C151#301211yescharacteristic, complemented, Sylow
179#3012—1511nomaximal, Sylow
180C2×H(5,𝔽2)—1511no—
181C2×AGL(1,ℤ/8)—1511no—
182C2×#135—1511no—
183#537—1511no—
184#452—1512no—
185#450—1512no—
186#449—1512no—
187#447—1512no—
188#417D15111yescharacteristic, complemented
189C2×#102—1511no—
190#408—1511no—
191H(5,𝔽2)—3024no—
192H(5,𝔽2)—3024no—
193C2×#41—3021no—
194C2×#41—1512no—
195C2×#41—1511no—
196C2×#41—1511no—
197C2×#41C2×D15111yescharacteristic
198C22×D4—3021no—
199C22×D4—3022no—
200C22×D4—1512no—
201C22×D4—1511no—
202AGL(1,ℤ/8)—3024no—
203#135—3024no—
204C2×Q16—1511no—
205C2×SD16—1511no—
206C2×SD16—1511no—
207C2×SD16—1512no—
208C2×D8—1511no—
209C2×D8—1512no—
210C2×M16C2×D15111yescharacteristic, complemented
211C22×C8—1511no—
212C22⋊Q8—3021no—
213C22⋊Q8—1512no—
214#121—3021no—
215#121—3022no—
216#121—1512no—
217C2×C4⋊C4C2×D15111yescharacteristic, complemented
218#103C2×D15112yescomplemented
219#102—1512no—
220#102—1512no—
221#102C2×D15112yescomplemented
222C22⋊C8—1512no—
223C22⋊C8—1512no—
224C24—3022no—
225C24—3021no—
226#41—22no—
227#41—3028no—
228#41—3024no—
229#41—3024no—
230#41—3022no—
231#41—3022no—
232#41—3022no—
233#41—3022no—
234#41D60414yescomplemented
235C2×Q8—1511no—
236C2×Q8—1511no—
237C2×Q8C22×D15111yescharacteristic
238C2×D4—21no—
239C2×D4—3028no—
240C2×D4—3022no—
241C2×D4—3022no—
242C2×D4—30216no—
243C2×D4—3024no—
244C2×D4—3024no—
245C2×D4—3021no—
246C2×D4—3022no—
247C2×D4—3021no—
248C2×D4—3022no—
249C2×D4—1512no—
250C2×D4—1511no—
251C2×D4—1514no—
252C2×D4—1511no—
253C2×D4—1512no—
254C2×D4C22×D15111yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—3022no—
258C22×C4—3021no—
259C22×C4—1512no—
260C22×C4C22×D15111yescharacteristic
261Q16—3022no—
262SD16—3024no—
263SD16—3022no—
264SD16—3022no—
265D8—3024no—
266D8—3022no—
267M16—22no—
268C2×C8—3022no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8C22×D15112yes—
272C4⋊C4—21no—
273C4⋊C4—3022no—
274C4⋊C4C22×D15112yes—
275C22⋊C4—3022no—
276C22⋊C4—3022no—
277C23—21no—
278C23—3028no—
279C23—3022no—
280C23—3024no—
281C23—3021no—
282C23—1512no—
283C23—12081no—
284C23—12081no—
285C23—12082no—
286C23—12082no—
287C23D4×D15111yescharacteristic
288Q8—21no—
289Q8—3022no—
290Q8—3021no—
291Q8—3021no—
292Q8C2×D60412yes—
293D4—24no—
294D4—21no—
295D4—3028no—
296D4—3028no—
297D4—3024no—
298D4—3022no—
299D4—3024no—
300D4—3021no—
301D4—3022no—
302D4—3021no—
303D4—6042no—
304D4—1514no—
305D4—12082no—
306D4C2×D60412yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—81no—
311C2×C4—3028no—
312C2×C4—3022no—
313C2×C4—3022no—
314C2×C4—3021no—
315C2×C4—6042no—
316C2×C4—1512no—
317C2×C4D4×D15111yescharacteristic
318C2×C4D4×D15112yes—
319C2×C4C2×D60412yes—
320C2×C4C23×D15111yescharacteristic
321C8—22no—
322C8—3021no—
323C8—3021no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—3022no—
330C22—3022no—
331C22—3022no—
332C22—3024no—
333C22—6042no—
334C22—6042no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—12084no—
339C22—12088no—
340C22#1801270912yes—
341C22C2×D4×D15111yescharacteristic
342C4—22no—
343C4—42no—
344C4—3022no—
345C4—6041no—
346C4#1801270912yes—
347C4C2×D4×D15111yescharacteristic
348C4C22×D60411yescharacteristic
349C2—22no—
350C2—42no—
351C2—6042no—
352C2—6044no—
353C2—12081no—
354C2C2×#1801270911yescharacteristic
355C2#2375301611yescharacteristic
356C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#417×C151C2
socleC22×C151C22×D4
hypercenter#417D151
hypocenterC151#3012
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#18012785C2semidirect
2. C2×#18012767C2semidirect
3. C2×#18012759C2semidirect
4. #23752793C2semidirect
5. #23752377C2semidirect
6. #23752364C2semidirect
7. #23752360C2semidirect
8. #23752347C2semidirect
9. C2×#18012659C2semidirect
10. #23752180C2semidirect
11. #417×C151C2semidirect
17. C2×#14559004C22semidirect
24. C2×#14558994C22semidirect
25. C2×#14558993C22semidirect
26. C2×#14558992C22semidirect
27. C2×#14558991C22semidirect
28. C2×D1208C22semidirect
29. C2×#14558989C22semidirect
30. C22×C151⋊C8C22semidirect
32. #18012719C22semidirect
34. #18012714C22semidirect
36. #18012659C22semidirect
37. #18012659C22semidirect
38. (C2×D151)⋊C8C22semidirect
39. (C2×D151)⋊C8C22semidirect
41. C2×M16×C151C22semidirect
42. C2×C4⋊C4×C151C22semidirect
43. #103×C151C22semidirect
44. #102×C151C22semidirect
62. C2×D604D4semidirect
87. #41×C151D4semidirect
178. C151#3012semidirect
188. #417D151semidirect
210. C2×M16C2×D151semidirect
217. C2×C4⋊C4C2×D151semidirect
218. #103C2×D151semidirect
221. #102C2×D151semidirect
234. #41D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127852
C2×#180127672
C2×#180127592
#237527932
#237523772
#237523642
#237523602
#237523472
C2×#180126592
#237521802
#417×C1512
#3012151