Finite Group Databasebeta

← #34080157

Subgroups — #34080157

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#23752813C211yesmaximal, characteristic, complemented
2#23752780C211yesmaximal, characteristic, complemented
3#23752598C211yesmaximal, characteristic, complemented
4#23752587C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752568C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752408C211yesmaximal, characteristic, complemented
9#23752407C211yesmaximal, characteristic, complemented
10#23752360C211yesmaximal, characteristic, complemented
11#23752356C211yesmaximal, characteristic, complemented
12#23752347C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558991C2211yescharacteristic, complemented
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic, complemented
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic, complemented
24#18012736C2211yescharacteristic
25#18012735C2211yescharacteristic
26#18012735C2211yescharacteristic, complemented
27#18012730C2211yescharacteristic, complemented
28#18012728C2211yescharacteristic
29#18012722—21no—
30#18012721—21no—
31#18012714C2211yescharacteristic
32#18012713—21no—
33#18012712—21no—
34#18012712—21no—
35#18012712—21no—
36#18012710C2211yescharacteristic
37#18012709—21no—
38#18012709—21no—
39C4×D604C2211yescharacteristic, complemented
40#18012696C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic, complemented
53C2×D8×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59C23×D151—21no—
60#14559005—41no—
61#14559005—41no—
62C2×D604—21no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75D4×D151—41no—
76D4×D151—41no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151C2311yescharacteristic
80#14558991—41no—
81D1208—41no—
82D1208—41no—
83#14558989—41no—
84#14558989—41no—
85#14558989—41no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C4⋊Dic151—21no—
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91Dic151⋊C4D411yescharacteristic
92Dic151⋊C4D411yescharacteristic
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4D411yescharacteristic
99(C2×D151)⋊C4D411yescharacteristic
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151—21no—
105SD16×C151—41no—
106D8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—81no—
119C22×D151—81no—
120C22×D151C2×D411yescharacteristic
121D604—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—42no—
128D604—81no—
129D604—81no—
130D604—81no—
131C22⋊D151—42no—
132C22⋊D151—81no—
133C22⋊D151—81no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C22⋊D151—81no—
137C2×Dic151—21no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C4×D151—21no—
142C4×D151—21no—
143C4×D151—42no—
144C4×D151—81no—
145C151⋊C8—21no—
146C151⋊C8—21no—
147C23×C151—21no—
148C23×C151—21no—
149Q8×C151—21no—
150Q8×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—81no—
158C2×C4×C151C2×D411yescharacteristic
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2411yescharacteristic
161C8×C151—21no—
162C8×C151—21no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151C22×D411yescharacteristic
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—84no—
183C4×C151—21no—
184C4×C151—21no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151H(5,𝔽2)11yescharacteristic
188C4×C151H(5,𝔽2)11yescharacteristic
189Dic151—21no—
190Dic151—21no—
191Dic151—21no—
192Dic151—41no—
193C2×C151—81no—
194C2×C151—81no—
195C2×C151#53511yescharacteristic
196C2×C151#57611yescharacteristic
197C2×C151#57611yescharacteristic
198D151—41no—
199D151—81no—
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#463D15111yescharacteristic, complemented
212#459—1511no—
213#459—1511no—
214#449—1511no—
215#449—1511no—
216#447—1511no—
217#447—1511no—
218#433—1511no—
219C2×#41—1511no—
220C22×D4—1511no—
221C2×SD16—1511no—
222C2×SD16C2×D15111yescharacteristic, complemented
223C2×D8—1511no—
224C2×D8—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C2×D8—1511no—
228C2×D8C2×D15111yescharacteristic
229#127—1511no—
230#127—1511no—
231#127—1511no—
232#125—1511no—
233#124—1511no—
234#124C2×D15111yescharacteristic
235#123—3021no—
236#123—3021no—
237#121—3021no—
238#121—3021no—
239#121—3021no—
240#121—3021no—
241#121—1511no—
242#121—1511no—
243#120—3021no—
244#120—3021no—
245C4×D4—1511no—
246C4×D4C2×D15111yescharacteristic, complemented
247#117—1511no—
248C4⋊C8—1511no—
249C4⋊C8C2×D15111yescharacteristic, complemented
250#103—1511no—
251#103C2×D15111yescharacteristic, complemented
252#102—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102C2×D15111yescharacteristic
258C22⋊C8—1511no—
259C22⋊C8—1511no—
260#97—1511no—
261C4×C8—1511no—
262C24—3021no—
263#41—6041no—
264#41—6041no—
265C2×Q8C22×D15111yescharacteristic
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—6041no—
277C2×D4—6041no—
278C2×D4—1511no—
279C2×D4—1511no—
280C2×D4—1511no—
281C2×D4C22×D15111yescharacteristic
282C2×D4C22×D15111yescharacteristic
283C22×C4—21no—
284C22×C4—3021no—
285C22×C4—3021no—
286C22×C4—1511no—
287SD16—41no—
288SD16—6041no—
289D8—41no—
290D8—6041no—
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—21no—
307C22⋊C4—21no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—1511no—
314C22⋊C4—1511no—
315C42—1511no—
316C42C22×D15111yescharacteristic
317C23—21no—
318C23—21no—
319C23—3021no—
320C23—3021no—
321C23—3021no—
322C23—6042no—
323C23—1511no—
324C23—12081no—
325C23—12081no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—3021no—
333D4—3021no—
334D4—3021no—
335D4—3021no—
336D4—3021no—
337D4—3021no—
338D4—6042no—
339D4—6042no—
340D4—12081no—
341D4—12081no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346D4—12081no—
347D4—12081no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—6042no—
355C2×C4—1511no—
356C2×C4—1511no—
357C2×C4—1511no—
358C2×C4—12081no—
359C2×C4D4×D15111yescharacteristic
360C2×C4D4×D15111yescharacteristic
361C2×C4C23×D15111yescharacteristic
362C8—21no—
363C8—21no—
364C8—3021no—
365C8—3021no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3021no—
373C22—3021no—
374C22—3021no—
375C22—6041no—
376C22—6041no—
377C22—6041no—
378C22—6041no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—12084no—
385C22C2×D4×D15111yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—3021no—
391C4—3021no—
392C4—3021no—
393C4—6041no—
394C4#1801278411yescharacteristic
395C4#1801278511yescharacteristic
396C2—81no—
397C2—81no—
398C2—6041no—
399C2—12081no—
400C2—12081no—
401C2—12081no—
402C2#2375277811yescharacteristic
403C2#2375301411yescharacteristic
404C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
hypercenter#463D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23752813C2semidirect
2. #23752780C2semidirect
3. #23752598C2semidirect
4. #23752587C2semidirect
5. #23752575C2semidirect
6. #23752568C2semidirect
7. #23752424C2semidirect
8. #23752408C2semidirect
9. #23752407C2semidirect
10. #23752360C2semidirect
11. #23752356C2semidirect
12. #23752347C2semidirect
13. #23752344C2semidirect
14. #23752272C2semidirect
15. #463×C151C2semidirect
18. C2×#14558991C22semidirect
20. C2×D1208C22semidirect
23. C2×#14558989C22semidirect
26. #18012735C22semidirect
27. #18012730C22semidirect
39. C4×D604C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012663C22semidirect
44. #18012661C22semidirect
47. #18012659C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
52. C2×SD16×C151C22semidirect
55. C4×D4×C151C22semidirect
56. C4⋊C8×C151C22semidirect
57. #103×C151C22semidirect
202. C151#3220semidirect
211. #463D151semidirect
222. C2×SD16C2×D151semidirect
246. C4×D4C2×D151semidirect
249. C4⋊C8C2×D151semidirect
251. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528132
#237527802
#237525982
#237525872
#237525752
#237525682
#237524242
#237524082
#237524072
#237523602
#237523562
#237523472
#237523442
#237522722
#463×C1512
#3220151