Finite Group Databasebeta

← #34078357

Subgroups — #34078357

Order 19328.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#14559003C211yesmaximal, characteristic, complemented
2C2×#18012763C212yesmaximal, complemented
3#121×D151C211yesmaximal, characteristic, complemented
4#23752358C212yesmaximal, complemented
5#23752354C212yesmaximal, complemented
6#23752353C211yesmaximal, characteristic, complemented
7#23752350C211yesmaximal, characteristic, complemented
8#23752346C211yesmaximal, characteristic, complemented
9#23752210C212yesmaximal, complemented
10#23752174C211yesmaximal, characteristic, complemented
11#447×C151C211yesmaximal, characteristic, complemented
12C2×#14559003—28no—
13C2×#14559003—21no—
14C2×#14559003—21no—
15C2×#14559003C2212yes—
16C2×#14559003C2212yescomplemented
17C22×Dic302C2211yescharacteristic, complemented
18C22×C22⋊D151—21no—
19C2×D4×D151—21no—
20C2×D4×D151C2211yescharacteristic, complemented
21C23×Dic151—21no—
22C22×C4×D151C2211yescharacteristic
23#18012763—28no—
24C2×#14558993C2212yescomplemented
25C2×#14558992C2212yescomplemented
26C2×#14558989C2212yescomplemented
27C2×#14558987C2212yescomplemented
28#18012714C2211yescharacteristic, complemented
29#18012713C2211yescharacteristic
30#18012712—21no—
31#18012711—21no—
32#18012710C2211yescharacteristic, complemented
33C4⋊C4×D151C2211yescharacteristic, complemented
34C22⋊C4×D151—21no—
35#18012664C2212yescomplemented
36#18012662C2212yescomplemented
37#18012660C2212yescomplemented
38C22⋊(C151⋊C8)C2211yescharacteristic, complemented
39(C2×D151)⋊C8C2212yescomplemented
40C22×D4×C151C2211yescharacteristic, complemented
41C2×D8×C151C2212yescomplemented
42#121×C151C2211yescharacteristic
43#102×C151C2212yescomplemented
44C22⋊C8×C151C2211yescharacteristic, complemented
45C23×D151—21no—
46C23×D151D411yescharacteristic
47#14559003—28no—
48#14559003—28no—
49#14559003—24no—
50#14559003—24no—
51#14559003—24no—
52#14559003D418yescomplemented
53C2×Dic302—24no—
54C2×Dic302—21no—
55C2×Dic302C2312yes—
56C2×D604—21no—
57C2×D604C2311yescharacteristic
58C2×C22⋊D151—28no—
59C2×C22⋊D151—22no—
60C2×C22⋊D151—22no—
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64D4×D151—24no—
65D4×D151—44no—
66C22×Dic151—28no—
67C22×Dic151—22no—
68C22×Dic151—22no—
69C22×Dic151—21no—
70C22×Dic151D411yescharacteristic
71C2×C4×D151—24no—
72C2×C4×D151—21no—
73C2×C4×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76C2×C4×D151C2311yescharacteristic
77#14558993—24no—
78#14558992—24no—
79#14558989—24no—
80#14558987—24no—
81C2×C151⋊C8C2312yes—
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87C24×C151—21no—
88C2×D4×C151—24no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151C2311yescharacteristic
92C2×D4×C151C2312yes—
93C22×C4×C151C2311yescharacteristic
94D8×C151—24no—
95C2×C8×C151C2312yes—
96C4⋊C4×C151C2311yescharacteristic
97C22⋊C4×C151—21no—
98C22×D151—22no—
99C22×D151—22no—
100C22×D151—21no—
101C22×D151—41no—
102C22×D151—42no—
103C22×D151—42no—
104C22×D151—42no—
105C22×D151C2×D411yescharacteristic
106C22×D151C2×D411yescharacteristic
107Dic302—24no—
108Dic302—22no—
109Dic302C2×D414yescomplemented
110D604—22no—
111D604—42no—
112C22⋊D151—28no—
113C22⋊D151—28no—
114C22⋊D151—42no—
115C22⋊D151—42no—
116C22⋊D151—42no—
117C2×Dic151—24no—
118C2×Dic151—28no—
119C2×Dic151—22no—
120C2×Dic151—22no—
121C2×Dic151—28no—
122C2×Dic151—21no—
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C4×D151—22no—
126C4×D151—22no—
127C4×D151—22no—
128C4×D151—42no—
129C4×D151C2×D414yes—
130C151⋊C8—22no—
131C23×C151—24no—
132C23×C151—22no—
133C23×C151—21no—
134C23×C151—42no—
135C23×C151—42no—
136C23×C151C2×D411yescharacteristic
137D4×C151—24no—
138D4×C151—22no—
139D4×C151—22no—
140D4×C151—42no—
141D4×C151C2×D414yescomplemented
142C2×C4×C151—22no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—22no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—24no—
150C22×C151—48no—
151C22×C151—42no—
152C22×C151—42no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151AGL(1,ℤ/8)12yescomplemented
157C22×C151C22×D411yescharacteristic
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—21no—
163C2×D151—44no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—84no—
168C2×D151#12012yes—
169C4×C151—21no—
170C4×C151—41no—
171C4×C151C22×D412yes—
172Dic151—21no—
173Dic151—24no—
174Dic151—41no—
175Dic151#12012yes—
176C2×C151—22no—
177C2×C151—44no—
178C2×C151—81no—
179C2×C151C2×#12011yescharacteristic
180C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C151#57511yescharacteristic
182D151—22no—
183D151—41no—
184D151—81no—
185C151#300611yescharacteristic, complemented, Sylow
186#3006—1511nomaximal, Sylow
187C22×#41—1511no—
188C2×AGL(1,ℤ/8)—1512no—
189C2×#121—1511no—
190#449—1512no—
191#449—1512no—
192#448—1511no—
193#448—1511no—
194#447—1511no—
195#447D15111yescharacteristic, complemented
196#417—1512no—
197#407—1511no—
198C2×#41—3028no—
199C2×#41—3021no—
200C2×#41—3021no—
201C2×#41—1512no—
202C2×#41—1512no—
203C22×Q8—1511no—
204C22×D4—3021no—
205C22×D4—3021no—
206C22×D4—1511no—
207C22×D4C2×D15111yescharacteristic, complemented
208C23×C4—3021no—
209C23×C4—1511no—
210AGL(1,ℤ/8)—3028no—
211C2×SD16—1512no—
212C2×SD16—1512no—
213C2×D8—1512no—
214C2×D8C2×D15112yescomplemented
215C2×M16—1512no—
216#121—3021no—
217#121—3021no—
218#121—1511no—
219#121—1511no—
220#121—1511no—
221#121C2×D15111yescharacteristic
222C2×C4⋊C4—1511no—
223C2×C22⋊C4—3021no—
224#103—1512no—
225#103—1512no—
226#102—1512no—
227#102C2×D15112yescomplemented
228C22⋊C8—1511no—
229C22⋊C8—1512no—
230C22⋊C8C2×D15111yescharacteristic, complemented
231C24—21no—
232C24—3021no—
233C24—1511no—
234#41—3028no—
235#41—3028no—
236#41—3024no—
237#41—3024no—
238#41—3024no—
239#41—1518no—
240C2×Q8—3024no—
241C2×Q8—3021no—
242C2×Q8—1512no—
243C2×D4—24no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—3021no—
247C2×D4—3028no—
248C2×D4—3022no—
249C2×D4—3022no—
250C2×D4—3021no—
251C2×D4—3021no—
252C2×D4—3024no—
253C2×D4—3021no—
254C2×D4—6044no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C2×D4C22×D15112yes—
258C22×C4—3024no—
259C22×C4—3021no—
260C22×C4—3028no—
261C22×C4—3021no—
262C22×C4—3022no—
263C22×C4—3022no—
264C22×C4—1511no—
265C22×C4—1511no—
266C22×C4—1511no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4C22×D15111yescharacteristic
270SD16—3024no—
271SD16—3024no—
272D8—24no—
273D8—3024no—
274M16—3024no—
275C2×C8—1512no—
276C2×C8C22×D15112yes—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4C22×D15111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C23—24no—
285C23—22no—
286C23—21no—
287C23—42no—
288C23—42no—
289C23—3022no—
290C23—3022no—
291C23—3021no—
292C23—6041no—
293C23—6042no—
294C23—6042no—
295C23—6042no—
296C23—1511no—
297C23—1511no—
298C23D4×D15111yescharacteristic
299Q8—3024no—
300Q8—3022no—
301Q8—1514no—
302D4—24no—
303D4—22no—
304D4—22no—
305D4—42no—
306D4—3028no—
307D4—3028no—
308D4—3022no—
309D4—6042no—
310D4—6042no—
311D4—6042no—
312D4—6042no—
313D4D4×D15114yescomplemented
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—3022no—
317C2×C4—3022no—
318C2×C4—3024no—
319C2×C4—3028no—
320C2×C4—3022no—
321C2×C4—3022no—
322C2×C4—3028no—
323C2×C4—3022no—
324C2×C4—3021no—
325C2×C4—6042no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4—1514no—
329C2×C4D4×D15111yescharacteristic
330C2×C4C23×D15111yescharacteristic
331C8—22no—
332C8—3022no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—3021no—
343C22—3021no—
344C22—3021no—
345C22—3021no—
346C22—3021no—
347C22—6044no—
348C22—6041no—
349C22—6041no—
350C22—6041no—
351C22—1512no—
352C22—12084no—
353C22#1801276312yescomplemented
354C22C2×D4×D15111yescharacteristic
355C4—21no—
356C4—41no—
357C4—3021no—
358C4—3024no—
359C4—6041no—
360C4—1512no—
361C4C2×D4×D15112yes—
362C2—22no—
363C2—44no—
364C2—81no—
365C2—3022no—
366C2—6041no—
367C2—12081no—
368C2#120×D15111yescharacteristic
369C2C2×#1801276311yescharacteristic
370C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3006
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#14559003C2semidirect
2. C2×#18012763C2semidirect
3. #121×D151C2semidirect
4. #23752358C2semidirect
5. #23752354C2semidirect
6. #23752353C2semidirect
7. #23752350C2semidirect
8. #23752346C2semidirect
9. #23752210C2semidirect
10. #23752174C2semidirect
11. #447×C151C2semidirect
16. C2×#14559003C22semidirect
17. C22×Dic302C22semidirect
20. C2×D4×D151C22semidirect
24. C2×#14558993C22semidirect
25. C2×#14558992C22semidirect
26. C2×#14558989C22semidirect
27. C2×#14558987C22semidirect
28. #18012714C22semidirect
32. #18012710C22semidirect
33. C4⋊C4×D151C22semidirect
35. #18012664C22semidirect
36. #18012662C22semidirect
37. #18012660C22semidirect
38. C22⋊(C151⋊C8)C22semidirect
39. (C2×D151)⋊C8C22semidirect
40. C22×D4×C151C22semidirect
41. C2×D8×C151C22semidirect
43. #102×C151C22semidirect
44. C22⋊C8×C151C22semidirect
52. #14559003D4semidirect
109. Dic302C2×D4semidirect
141. D4×C151C2×D4semidirect
156. C22×C151AGL(1,ℤ/8)semidirect
185. C151#3006semidirect
195. #447D151semidirect
207. C22×D4C2×D151semidirect
214. C2×D8C2×D151semidirect
227. #102C2×D151semidirect
230. C22⋊C8C2×D151semidirect
313. D4D4×D151semidirect
353. C22#18012763semidirect

Maximal subgroups

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

subgroupindex
C22×#145590032
C2×#180127632
#121×D1512
#237523582
#237523542
#237523532
#237523502
#237523462
#237522102
#237521742
#447×C1512
#3006151