Finite Group Databasebeta

← #34080159

Subgroups — #34080159

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#23752775C211yesmaximal, characteristic, complemented
3#23752600C211yesmaximal, characteristic, complemented
4#23752587C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752428C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752404C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic, complemented
11#23752354C211yesmaximal, characteristic, complemented
12#23752347C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558993C2211yescharacteristic, complemented
19C2×#14558992C2211yescharacteristic, complemented
20C2×D1208C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic, complemented
24#18012735C2211yescharacteristic
25#18012735C2211yescharacteristic, complemented
26#18012730C2211yescharacteristic, complemented
27#18012727C2211yescharacteristic
28#18012726C2211yescharacteristic
29#18012722—21no—
30#18012721—21no—
31#18012714C2211yescharacteristic
32#18012713—21no—
33#18012712—21no—
34#18012711—21no—
35#18012711—21no—
36#18012710C2211yescharacteristic
37#18012707—21no—
38#18012707—21no—
39C4×D604C2211yescharacteristic, complemented
40#18012696C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic, complemented
54#127×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic, complemented
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—41no—
61#14559003—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73D4×D151—41no—
74D4×D151—41no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78#14558993—41no—
79#14558992—41no—
80D1208—41no—
81#14558989—41no—
82#14558989—41no—
83#14558989—41no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90Dic151⋊C4D411yescharacteristic
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
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×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151C2311yescharacteristic
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151—21no—
107D8×C151—41no—
108D8×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—42no—
117C22×D151—81no—
118C22×D151—81no—
119C22×D151C2×D411yescharacteristic
120Dic302—21no—
121Dic302—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—81no—
127C22⋊D151—42no—
128C22⋊D151—42no—
129C22⋊D151—81no—
130C22⋊D151—81no—
131C22⋊D151—81no—
132C22⋊D151—81no—
133C22⋊D151—81no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—42no—
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—81no—
143C151⋊C8—21no—
144C151⋊C8—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—21no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—81no—
155D4×C151—81no—
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×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151C22×D411yescharacteristic
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
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×C151H(5,𝔽2)11yescharacteristic
187C4×C151H(5,𝔽2)11yescharacteristic
188Dic151—21no—
189Dic151—21no—
190Dic151—21no—
191Dic151—41no—
192Dic151—41no—
193C2×C151—81no—
194C2×C151—81no—
195C2×C151—81no—
196C2×C151#53511yescharacteristic
197C2×C151#57611yescharacteristic
198C2×C151#57611yescharacteristic
199D151—41no—
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#459D15111yescharacteristic, complemented
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×SD16—1511no—
223C2×D8—1511no—
224C2×D8—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C2×D8C2×D15111yescharacteristic
228C2×D8C2×D15111yescharacteristic, complemented
229#127—1511no—
230#127—1511no—
231#127C2×D15111yescharacteristic
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#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#103—1511no—
252#102—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102C2×D15111yescharacteristic
257#102C2×D15111yescharacteristic, complemented
258C22⋊C8—1511no—
259C22⋊C8—1511no—
260#97—1511no—
261C4×C8—1511no—
262C24—3021no—
263#41—6041no—
264#41—6041no—
265C2×Q8—1511no—
266C2×D4—21no—
267C2×D4—21no—
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×D4C22×D15111yescharacteristic
281C2×D4C22×D15111yescharacteristic
282C2×D4C22×D15111yescharacteristic
283C22×C4—21no—
284C22×C4—3021no—
285C22×C4—3021no—
286C22×C4—1511no—
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—
316C42C22×D15111yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—3021no—
321C23—3021no—
322C23—6042no—
323C23—1511no—
324C23—12081no—
325C23—12081no—
326Q8—3021no—
327Q8—3021no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—3021no—
337D4—3021no—
338D4—3021no—
339D4—3021no—
340D4—6042no—
341D4—6042no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346D4—12081no—
347D4—12081no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—3021no—
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—41no—
373C22—41no—
374C22—41no—
375C22—3021no—
376C22—3021no—
377C22—3021no—
378C22—6041no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—12084no—
385C22C2×D4×D15111yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—3021no—
390C4—3021no—
391C4—3021no—
392C4—6041no—
393C4—6041no—
394C4#1801278411yescharacteristic
395C4#1801278511yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—6041no—
400C2—12081no—
401C2—12081no—
402C2#2375277811yescharacteristic
403C2#2375301311yescharacteristic
404C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752813C2semidirect
2. #23752775C2semidirect
3. #23752600C2semidirect
4. #23752587C2semidirect
5. #23752575C2semidirect
6. #23752565C2semidirect
7. #23752428C2semidirect
8. #23752427C2semidirect
9. #23752404C2semidirect
10. #23752358C2semidirect
11. #23752354C2semidirect
12. #23752347C2semidirect
13. #23752344C2semidirect
14. #23752272C2semidirect
15. #459×C151C2semidirect
18. C2×#14558993C22semidirect
19. C2×#14558992C22semidirect
23. C2×#14558989C22semidirect
25. #18012735C22semidirect
26. #18012730C22semidirect
39. C4×D604C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
46. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
53. C2×D8×C151C22semidirect
55. C4×D4×C151C22semidirect
56. C4⋊C8×C151C22semidirect
58. #102×C151C22semidirect
202. C151#3220semidirect
213. #459D151semidirect
228. C2×D8C2×D151semidirect
246. C4×D4C2×D151semidirect
249. C4⋊C8C2×D151semidirect
257. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528132
#237527752
#237526002
#237525872
#237525752
#237525652
#237524282
#237524272
#237524042
#237523582
#237523542
#237523472
#237523442
#237522722
#459×C1512
#3220151