Finite Group Databasebeta

← #34080156

Subgroups — #34080156

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752815C211yesmaximal, characteristic, complemented
2#23752779C211yesmaximal, characteristic, complemented
3#23752600C211yesmaximal, characteristic, complemented
4#23752587C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752426C211yesmaximal, characteristic, complemented
8#23752425C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752405C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic, complemented
13#23752346C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558993C2211yescharacteristic, complemented
18C2×#14558992C2211yescharacteristic, complemented
19C2×D1208C2211yescharacteristic, complemented
20C2×#14558989C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic, complemented
23#18012735C2211yescharacteristic
24#18012735C2211yescharacteristic
25#18012735C2211yescharacteristic, complemented
26#18012730C2211yescharacteristic, complemented
27#18012726C2211yescharacteristic
28#18012726C2211yescharacteristic
29#18012723—21no—
30#18012721—21no—
31#18012713C2211yescharacteristic
32#18012711—21no—
33#18012710—21no—
34#18012710—21no—
35#18012710—21no—
36#18012708—21no—
37#18012708—21no—
38D4×Dic151C2211yescharacteristic, complemented
39#18012701C2211yescharacteristic, complemented
40#18012698C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic, 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
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C22×Dic151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75#14558993—41no—
76#14558992—41no—
77D1208—41no—
78#14558989—41no—
79#14558989—41no—
80#14558989—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—21no—
84C4⋊Dic151D411yescharacteristic
85C4⋊Dic151D411yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151D411yescharacteristic
94C22⋊Dic151D411yescharacteristic
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99C24×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—41no—
103C2×D4×C151—41no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C2×D4×C151C2311yescharacteristic
107C22×C4×C151C2311yescharacteristic
108D8×C151—41no—
109D8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—21no—
116Dic302—21no—
117Dic302—21no—
118D604—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122C22⋊D151—42no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C22⋊D151—81no—
126C22⋊D151—81no—
127C22⋊D151—81no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—81no—
133C2×Dic151C2×D411yescharacteristic
134C2×Dic151C2×D411yescharacteristic
135C2×Dic151C2×D411yescharacteristic
136C2×Dic151C2×D411yescharacteristic
137C4×D151—42no—
138C4×D151—81no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—42no—
145C23×C151—81no—
146C23×C151—81no—
147C23×C151C2×D411yescharacteristic
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—42no—
155D4×C151—81no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2411yescharacteristic
161C8×C151—21no—
162C8×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—84no—
176C22×C151C22×D411yescharacteristic
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C4×C151—21no—
184C4×C151—41no—
185C4×C151H(5,𝔽2)11yescharacteristic
186C4×C151H(5,𝔽2)11yescharacteristic
187Dic151—21no—
188Dic151—21no—
189Dic151—21no—
190Dic151—21no—
191Dic151—41no—
192Dic151—41no—
193C2×C151—41no—
194C2×C151—81no—
195C2×C151—81no—
196C2×C151—81no—
197C2×C151#53511yescharacteristic
198C2×C151#57611yescharacteristic
199C2×C151#57611yescharacteristic
200D151—81no—
201D151—81no—
202C151#322011yescharacteristic, complemented, Sylow
203#3220—1511nomaximal, Sylow
204#540—1511no—
205#535—1511no—
206#496—1511no—
207#493—1511no—
208#490—1511no—
209#488—1511no—
210#463—1511no—
211#463—1511no—
212#459—1511no—
213#459—1511no—
214#449—1511no—
215#449—1511no—
216#447—1511no—
217#447D15111yescharacteristic, complemented
218#433—1511no—
219C2×#41—1511no—
220C22×D4C2×D15111yescharacteristic
221C2×SD16—1511no—
222C2×SD16—1511no—
223C2×D8—1511no—
224C2×D8—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C2×D8C2×D15111yescharacteristic
228C2×D8C2×D15111yescharacteristic
229#127—1511no—
230#127—1511no—
231#127—1511no—
232#125—1511no—
233#124—1511no—
234#124—1511no—
235#123—3021no—
236#123—3021no—
237#121—3021no—
238#121—3021no—
239#121—3021no—
240#121—3021no—
241#121—1511no—
242#121C2×D15111yescharacteristic
243#120—3021no—
244#120—3021no—
245C4×D4—1511no—
246C4×D4—1511no—
247#117—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250#103—1511no—
251#103—1511no—
252#102—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102C2×D15111yescharacteristic
257#102C2×D15111yescharacteristic
258C22⋊C8—1511no—
259C22⋊C8C2×D15111yescharacteristic
260#97—1511no—
261C4×C8—1511no—
262C24—21no—
263#41—6041no—
264#41—6041no—
265C2×Q8—1511no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—1511no—
279C2×D4—1511no—
280C2×D4C22×D15111yescharacteristic
281C2×D4C22×D15111yescharacteristic
282C2×D4C22×D15111yescharacteristic
283C22×C4—3021no—
284C22×C4—3021no—
285C22×C4—3021no—
286C22×C4C22×D15111yescharacteristic
287SD16—6041no—
288SD16—6041no—
289D8—41no—
290D8—41no—
291D8—6041no—
292D8—6041no—
293D8—6041no—
294D8—6041no—
295C2×C8—1511no—
296C2×C8—1511no—
297C2×C8C22×D15111yescharacteristic
298C2×C8C22×D15111yescharacteristic
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—1511no—
302C4⋊C4—1511no—
303C4⋊C4—1511no—
304C4⋊C4C22×D15111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—1511no—
314C22⋊C4—1511no—
315C42—1511no—
316C42—1511no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—3021no—
324C23—3021no—
325C23D4×D15111yescharacteristic
326Q8—3021no—
327Q8—3021no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—3021no—
337D4—3021no—
338D4—3021no—
339D4—3021no—
340D4—6042no—
341D4—12081no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346D4—12081no—
347D4—12081no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—6042no—
354C2×C4—1511no—
355C2×C4—1511no—
356C2×C4—1511no—
357C2×C4—1511no—
358C2×C4—12081no—
359C2×C4—12081no—
360C2×C4D4×D15111yescharacteristic
361C2×C4C23×D15111yescharacteristic
362C8—21no—
363C8—21no—
364C8—3021no—
365C8—3021no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22C2×D4×D15111yescharacteristic
386C4—21no—
387C4—41no—
388C4—3021no—
389C4—3021no—
390C4—3021no—
391C4—3021no—
392C4—6041no—
393C4—6041no—
394C4#1801278411yescharacteristic
395C4#1801278411yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—12081no—
401C2—12081no—
402C2#2375277711yescharacteristic
403C2#2375301311yescharacteristic
404C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3220
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. #23752815C2semidirect
2. #23752779C2semidirect
3. #23752600C2semidirect
4. #23752587C2semidirect
5. #23752575C2semidirect
6. #23752565C2semidirect
7. #23752426C2semidirect
8. #23752425C2semidirect
9. #23752406C2semidirect
10. #23752405C2semidirect
11. #23752359C2semidirect
12. #23752355C2semidirect
13. #23752346C2semidirect
14. #23752270C2semidirect
15. #447×C151C2semidirect
17. C2×#14558993C22semidirect
18. C2×#14558992C22semidirect
19. C2×D1208C22semidirect
22. C2×#14558989C22semidirect
25. #18012735C22semidirect
26. #18012730C22semidirect
38. D4×Dic151C22semidirect
39. #18012701C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
45. #18012661C22semidirect
48. #18012659C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
202. C151#3220semidirect
217. #447D151semidirect

Maximal subgroups

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

subgroupindex
#237528152
#237527792
#237526002
#237525872
#237525752
#237525652
#237524262
#237524252
#237524062
#237524052
#237523592
#237523552
#237523462
#237522702
#447×C1512
#3220151