Finite Group Databasebeta

← #34079287

Subgroups — #34079287

Order 19328.

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#23752829C211yesmaximal, characteristic, complemented
2#23752687C211yesmaximal, characteristic, complemented
3#23752554C211yesmaximal, characteristic, complemented
4#23752533C211yesmaximal, characteristic, complemented
5#23752500C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752425C211yesmaximal, characteristic, complemented
8#23752425C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic, complemented
10#23752324C211yesmaximal, characteristic, complemented
11#23752309C211yesmaximal, characteristic, complemented
12#23752303C211yesmaximal, characteristic, complemented
13D8×Dic151C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic
16C2×#14558992C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18#18012738C2211yescharacteristic, complemented
19#18012732—21no—
20#18012726—21no—
21#18012726C2211yescharacteristic, complemented
22#18012720—21no—
23#18012718C2211yescharacteristic
24#18012716—21no—
25#18012704C2211yescharacteristic, complemented
26D4×Dic151—21no—
27D4×Dic151—21no—
28D4×Dic151C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic, complemented
33#18012698C2211yescharacteristic
34#18012698C2211yescharacteristic
35C2×C22⋊Dic151—21no—
36C2×C22⋊Dic151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C22×Dic151—21no—
62C22×Dic151—21no—
63C22×Dic151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66#14558992—22no—
67#14558992—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C4⋊Dic151D411yescharacteristic
71C4⋊Dic151D411yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78C22⋊Dic151—21no—
79C22⋊Dic151—21no—
80C22⋊Dic151—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151D411yescharacteristic
88C22⋊Dic151D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151C2311yescharacteristic
92C4×Dic151C2311yescharacteristic
93C24×C151—21no—
94C2×D4×C151—22no—
95C2×D4×C151—22no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102D8×C151—22no—
103D8×C151—22no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108Dic302—21no—
109Dic302—21no—
110Dic302—81no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—81no—
116C2×Dic151—81no—
117C2×Dic151—81no—
118C2×Dic151—81no—
119C2×Dic151—81no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C151⋊C8—21no—
125C151⋊C8—21no—
126C23×C151—24no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—81no—
131C23×C151—81no—
132C23×C151C2×D411yescharacteristic
133D4×C151—24no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—81no—
139D4×C151#4112yes—
140D4×C151#4112yes—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—21no—
149C22×C151—22no—
150C22×C151—22no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—84no—
161C22×C151C22×D411yescharacteristic
162C4×C151—21no—
163C4×C151—41no—
164C4×C151C2×#4111yescharacteristic
165C4×C151C2×#4111yescharacteristic
166Dic151—21no—
167Dic151—21no—
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173Dic151—41no—
174C2×C151—41no—
175C2×C151—42no—
176C2×C151—42no—
177C2×C151—81no—
178C2×C151#52511yescharacteristic
179C2×C151#57611yescharacteristic
180C2×C151#57711yescharacteristic
181C151#311811yescharacteristic, complemented, Sylow
182#3118—1511nomaximal, Sylow
183#542—1511no—
184#518—1511no—
185#485—1511no—
186#482—1511no—
187#476—1511no—
188#474—1511no—
189#463—1511no—
190#463—1511no—
191#450—1511no—
192#447D15111yescharacteristic
193#442—1511no—
194#440—1511no—
195C4×SD16—1511no—
196C4×D8—1511no—
197#433—1511no—
198C22×D4C2×D15111yescharacteristic
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×D8C2×D15111yescharacteristic
202C2×D8C2×D15111yescharacteristic
203C4⋊Q8—1511no—
204#126—3021no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210#121C2×D15111yescharacteristic
211C4×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4—1511no—
219#117—1511no—
220#117—1511no—
221C2×C22⋊C4—3021no—
222C2×C22⋊C4—3021no—
223#107—1511no—
224#107—1511no—
225#106—1511no—
226#106—1511no—
227C4⋊C8—1511no—
228C4⋊C8—1511no—
229#103—1511no—
230#103—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236#102C2×D15111yescharacteristic
237C22⋊C8—1511no—
238C22⋊C8C2×D15111yescharacteristic
239#97—1511no—
240C4×C8—1511no—
241C24—21no—
242C2×Q8—3021no—
243C2×Q8—1511no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D15111yescharacteristic
249C2×D4C22×D15111yescharacteristic
250C2×D4C22×D15111yescharacteristic
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4C22×D15111yescharacteristic
257SD16—3022no—
258SD16—3022no—
259D8—22no—
260D8—22no—
261C2×C8—1511no—
262C2×C8—1511no—
263C2×C8C22×D15111yescharacteristic
264C2×C8C22×D15111yescharacteristic
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22×D15111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—1511no—
285C22⋊C4—1511no—
286C42—3021no—
287C42—3021no—
288C42—1511no—
289C42—1511no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D15111yescharacteristic
297Q8—3021no—
298Q8—3021no—
299Q8—12081no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#1455900312yes—
307D4#1455900312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—12081no—
320C2×C4—12081no—
321C2×C4—12081no—
322C2×C4—12081no—
323C2×C4—12081no—
324C2×C4D4×D15111yescharacteristic
325C2×C4C23×D15111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3021no—
329C8—3021no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—41no—
346C4—3021no—
347C4—3021no—
348C4—3021no—
349C4—3021no—
350C4—6041no—
351C4—6041no—
352C4—6041no—
353C4—6041no—
354C4C2×#1455900311yescharacteristic
355C4C2×#1455900311yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#2375271811yescharacteristic
361C2#2375301311yescharacteristic
362C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3118
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. #23752829C2semidirect
2. #23752687C2semidirect
3. #23752554C2semidirect
4. #23752533C2semidirect
5. #23752500C2semidirect
6. #23752490C2semidirect
7. #23752425C2semidirect
8. #23752425C2semidirect
9. #23752363C2semidirect
10. #23752324C2semidirect
11. #23752309C2semidirect
12. #23752303C2semidirect
13. D8×Dic151C2semidirect
14. #23752270C2semidirect
18. #18012738C22semidirect
21. #18012726C22semidirect
25. #18012704C22semidirect
32. D4×Dic151C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
181. C151#3118semidirect

Maximal subgroups

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

subgroupindex
#237528292
#237526872
#237525542
#237525332
#237525002
#237524902
#237524252
#237523632
#237523242
#237523092
#237523032
D8×Dic1512
#237522702
#447×C1512
#3118151