Finite Group Databasebeta

← #34080095

Subgroups — #34080095

Order 19328.

444 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752759C211yesmaximal, characteristic, complemented
2#124×D151C211yesmaximal, characteristic, complemented
3#23752600C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic, complemented
5#23752573C211yesmaximal, characteristic, complemented
6#23752570C211yesmaximal, characteristic, complemented
7#23752428C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752424C211yesmaximal, characteristic, complemented
10#23752352C211yesmaximal, characteristic, complemented
11#23752349C211yesmaximal, characteristic, complemented
12#23752347C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752268C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×Q8×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19C2×#14558993C2211yescharacteristic, complemented
20C2×#14558992C2211yescharacteristic, complemented
21C2×#14558991C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×#14558989C2211yescharacteristic
25#18012738C2211yescharacteristic, complemented
26#18012735C2211yescharacteristic, complemented
27#18012728C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012725—21no—
31#18012725—21no—
32#18012725—21no—
33#18012714C2211yescharacteristic
34#18012712—21no—
35#18012710C2211yescharacteristic
36C4×D604C2211yescharacteristic, complemented
37C4×C22⋊D151—21no—
38C22⋊C4×D151—21no—
39C22⋊C4×D151—21no—
40C42×D151C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51#18012649C2211yescharacteristic, 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#14559004—44no—
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64Q8×D151—41no—
65Q8×D151—41no—
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73D4×D151—41no—
74D4×D151—41no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151D411yescharacteristic
78C2×C4×D151D411yescharacteristic
79C2×C4×D151C2311yescharacteristic
80#14558993—41no—
81#14558992—41no—
82#14558991—41no—
83D1208—41no—
84#14558989—41no—
85#14558989—41no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99C4×Dic151D411yescharacteristic
100C4×Dic151D411yescharacteristic
101C4×Dic151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151—21no—
106SD16×C151—41no—
107D8×C151—41no—
108C2×C8×C151C2311yescharacteristic
109C2×C8×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C42×C151C2311yescharacteristic
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—42no—
119C22×D151—42no—
120C22×D151C2×D411yescharacteristic
121Dic302—21no—
122Dic302—21no—
123Dic302—42no—
124Dic302—42no—
125D604—21no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130C22⋊D151—42no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C2×Dic151C2×D411yescharacteristic
139C4×D151—22no—
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—41no—
143C4×D151—42no—
144C4×D151—42no—
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—42no—
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—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C2×D151—84no—
179C2×D151AGL(1,ℤ/8)12yes—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151H(5,𝔽2)11yescharacteristic
185C4×C151H(5,𝔽2)11yescharacteristic
186Dic151—21no—
187Dic151—21no—
188Dic151—21no—
189Dic151—41no—
190Dic151—41no—
191C2×C151—81no—
192C2×C151—81no—
193C2×C151#53511yescharacteristic
194C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C151#57511yescharacteristic
196D151—22no—
197D151—81no—
198D151—81no—
199C151#321311yescharacteristic, complemented, Sylow
200#3213—1511nomaximal, Sylow
201#532—1511no—
202C2×#124—1511no—
203#496—1511no—
204#496—1511no—
205#489—1511no—
206#489—1511no—
207#463—1511no—
208#463—1511no—
209#463—1511no—
210#463D15111yescharacteristic, complemented
211#448—1511no—
212#448—1511no—
213#447—1511no—
214#447—1511no—
215#432—1511no—
216C2×#41—3021no—
217C22×Q8—1511no—
218C22×D4—1511no—
219C2×SD16—1511no—
220C2×SD16—1511no—
221C2×SD16—1511no—
222C2×SD16C2×D15111yescharacteristic, complemented
223C2×D8—1511no—
224C2×D8—1511no—
225C2×D8—1511no—
226C2×D8C2×D15111yescharacteristic
227C4⋊Q8—1511no—
228#127—1511no—
229#124—3021no—
230#124—3021no—
231#124—3021no—
232#124—1511no—
233#124—1511no—
234#124—1511no—
235#124C2×D15111yescharacteristic
236#121—3021no—
237#121—1511no—
238#121—1511no—
239C4×D4—3021no—
240C4×D4—1511no—
241C4×D4C2×D15111yescharacteristic, complemented
242C2×C22⋊C4—3021no—
243C2×C22⋊C4—3021no—
244C2×C42—1511no—
245C4⋊C8—1511no—
246C4⋊C8C2×D15111yescharacteristic, complemented
247#103—1511no—
248#103—1511no—
249#103—1511no—
250#103C2×D15111yescharacteristic, complemented
251#102—1511no—
252#102—1511no—
253#102—1511no—
254#102C2×D15111yescharacteristic
255C22⋊C8—1511no—
256C22⋊C8—1511no—
257#97—1511no—
258#97—1511no—
259C24—3021no—
260#41—6044no—
261C2×Q8—3021no—
262C2×Q8—3021no—
263C2×Q8—6041no—
264C2×Q8—6041no—
265C2×Q8—1511no—
266C2×Q8C22×D15111yescharacteristic
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—6041no—
273C2×D4—6041no—
274C2×D4—1511no—
275C2×D4—1511no—
276C2×D4C22×D15111yescharacteristic
277C2×D4C22×D15111yescharacteristic
278C22×C4—21no—
279C22×C4—3021no—
280C22×C4—3021no—
281C22×C4—1511no—
282C22×C4—1511no—
283C22×C4—1511no—
284SD16—41no—
285SD16—6041no—
286SD16—6041no—
287SD16—6041no—
288D8—41no—
289D8—6041no—
290D8—6041no—
291D8—6041no—
292C2×C8—1511no—
293C2×C8—1511no—
294C2×C8C22×D15111yescharacteristic
295C2×C8C22×D15111yescharacteristic
296C4⋊C4—3021no—
297C4⋊C4—1511no—
298C4⋊C4C22×D15111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C42—1511no—
312C42—1511no—
313C42—1511no—
314C42C22×D15111yescharacteristic
315C23—21no—
316C23—21no—
317C23—3021no—
318C23—3021no—
319C23—6042no—
320C23—6042no—
321C23—6042no—
322C23—1511no—
323Q8—21no—
324Q8—21no—
325Q8—3021no—
326Q8—3021no—
327Q8—6042no—
328Q8—6042no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—3021no—
334D4—3021no—
335D4—3021no—
336D4—3021no—
337D4—6042no—
338D4—6042no—
339D4—6042no—
340D4—6042no—
341D4—6042no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—3022no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—6041no—
351C2×C4—6042no—
352C2×C4—6042no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4—1511no—
356C2×C4D4×D15111yescharacteristic
357C2×C4D4×D15111yescharacteristic
358C2×C4C23×D15111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3021no—
362C8—3021no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—3021no—
370C22—3021no—
371C22—6041no—
372C22—6041no—
373C22—6041no—
374C22—6041no—
375C22—6041no—
376C22—6041no—
377C22—1512no—
378C22—12084no—
379C22C2×D4×D15111yescharacteristic
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—3021no—
385C4—3021no—
386C4—3021no—
387C4—6041no—
388C4—6041no—
389C4#1801278411yescharacteristic
390C4#1801278511yescharacteristic
391C2—81no—
392C2—81no—
393C2—3022no—
394C2—12081no—
395C2—12081no—
396C2#2375277811yescharacteristic
397C2AGL(1,ℤ/8)×D15111yescharacteristic
398C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
hypercenter#463D151
hypocenterC151#3213
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. #23752759C2semidirect
2. #124×D151C2semidirect
3. #23752600C2semidirect
4. #23752598C2semidirect
5. #23752573C2semidirect
6. #23752570C2semidirect
7. #23752428C2semidirect
8. #23752427C2semidirect
9. #23752424C2semidirect
10. #23752352C2semidirect
11. #23752349C2semidirect
12. #23752347C2semidirect
13. #23752344C2semidirect
14. #23752268C2semidirect
15. #463×C151C2semidirect
19. C2×#14558993C22semidirect
20. C2×#14558992C22semidirect
21. C2×#14558991C22semidirect
25. #18012738C22semidirect
26. #18012735C22semidirect
36. C4×D604C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012663C22semidirect
44. #18012662C22semidirect
50. #18012649C22semidirect
51. #18012649C22semidirect
52. C2×SD16×C151C22semidirect
55. C4×D4×C151C22semidirect
56. C4⋊C8×C151C22semidirect
57. #103×C151C22semidirect
199. C151#3213semidirect
210. #463D151semidirect
222. C2×SD16C2×D151semidirect
241. C4×D4C2×D151semidirect
246. C4⋊C8C2×D151semidirect
250. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527592
#124×D1512
#237526002
#237525982
#237525732
#237525702
#237524282
#237524272
#237524242
#237523522
#237523492
#237523472
#237523442
#237522682
#463×C1512
#3213151