Finite Group Databasebeta

← #34079919

Subgroups — #34079919

Order 19328.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752722C211yesmaximal, characteristic, complemented
2#121×D151C211yesmaximal, characteristic, complemented
3#23752544C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752524C211yesmaximal, characteristic, complemented
7#23752463C211yesmaximal, characteristic, complemented
8#23752458C211yesmaximal, characteristic, complemented
9#23752456C211yesmaximal, characteristic, complemented
10#23752364C211yesmaximal, characteristic, complemented
11#23752358C211yesmaximal, characteristic, complemented
12#23752354C211yesmaximal, characteristic, complemented
13#23752344C211yesmaximal, characteristic, complemented
14#23752175C211yesmaximal, characteristic, complemented
15#469×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic, complemented
17C2×D4×D151—21no—
18C2×D4×D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20C2×#14558993C2211yescharacteristic, complemented
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558989C2211yescharacteristic, complemented
23C2×#14558988C2211yescharacteristic, complemented
24#18012721—21no—
25#18012719C2211yescharacteristic
26#18012718C2211yescharacteristic, complemented
27#18012714C2211yescharacteristic
28#18012713C2211yescharacteristic
29#18012712—21no—
30#18012711—21no—
31#18012710C2211yescharacteristic
32#18012710C2211yescharacteristic
33#18012707—21no—
34D4×Dic151—21no—
35(C22⋊D151)⋊C4—21no—
36#18012697C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic
38C22⋊C4×D151—21no—
39#18012673C2211yescharacteristic, complemented
40#18012672C2211yescharacteristic, complemented
41#18012670C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012662C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic, complemented
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic, complemented
53C2×M16×C151C2211yescharacteristic, complemented
54#121×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic, complemented
56#106×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C23×D151D411yescharacteristic
61#14559003—41no—
62#14559003—41no—
63C2×Dic302C2311yescharacteristic
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71D4×D151—41no—
72D4×D151—41no—
73D4×D151—44no—
74C22×Dic151—21no—
75C22×Dic151D411yescharacteristic
76C2×C4×D151—21no—
77C2×C4×D151—41no—
78C2×C4×D151—41no—
79C2×C4×D151D411yescharacteristic
80C2×C4×D151D411yescharacteristic
81C2×C4×D151C2311yescharacteristic
82C2×C4×D151C2311yescharacteristic
83#14558993—41no—
84#14558992—41no—
85#14558989—41no—
86#14558988—41no—
87C2×C151⋊C8C2311yescharacteristic
88C2×C151⋊C8C2311yescharacteristic
89C4⋊Dic151—21no—
90C4⋊Dic151C2311yescharacteristic
91C4⋊Dic151C2311yescharacteristic
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96C22⋊Dic151—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101C4×Dic151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107D8×C151—41no—
108M16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22⋊C4×C151—21no—
115C22×D151—22no—
116C22×D151—21no—
117C22×D151—41no—
118C22×D151—41no—
119C22×D151—42no—
120C22×D151—42no—
121C22×D151—42no—
122C22×D151C2×D411yescharacteristic
123C22×D151C2×D411yescharacteristic
124Dic302—21no—
125Dic302—21no—
126D604—21no—
127D604—21no—
128D604—42no—
129C22⋊D151—42no—
130C22⋊D151—42no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—41no—
138C2×Dic151—42no—
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C4×D151—21no—
142C4×D151—21no—
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—41no—
146C4×D151—41no—
147C4×D151—42no—
148C151⋊C8—21no—
149C151⋊C8—21no—
150C23×C151—21no—
151C23×C151—21no—
152C23×C151C2×D411yescharacteristic
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—42no—
158D4×C151—42no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2411yescharacteristic
165C8×C151—21no—
166C8×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151C22×D411yescharacteristic
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—21no—
182C2×D151—44no—
183C2×D151—41no—
184C2×D151—41no—
185C2×D151—41no—
186C2×D151—84no—
187C2×D151AGL(1,ℤ/8)12yes—
188C4×C151—21no—
189C4×C151—41no—
190C4×C151—41no—
191C4×C151H(5,𝔽2)11yescharacteristic
192C4×C151H(5,𝔽2)11yescharacteristic
193Dic151—21no—
194Dic151—21no—
195Dic151—41no—
196Dic151—41no—
197Dic151—41no—
198C2×C151—41no—
199C2×C151—81no—
200C2×C151—81no—
201C2×C151#53411yescharacteristic
202C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C151#57511yescharacteristic
204D151—22no—
205D151—41no—
206D151—81no—
207C151#319411yescharacteristic, complemented, Sylow
208#3194—1511nomaximal, Sylow
209#525—1511no—
210C2×#121—1511no—
211#483—1511no—
212#482—1511no—
213#482—1511no—
214#480—1511no—
215#469—1511no—
216#469D15111yescharacteristic, complemented
217#468—1511no—
218#468—1511no—
219#450—1511no—
220#449—1511no—
221#449—1511no—
222#447—1511no—
223#407—1511no—
224C2×#41—1511no—
225C22×D4—3021no—
226C22×D4—1511no—
227C23×C4—1511no—
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×D8—1511no—
231C2×D8C2×D15111yescharacteristic, complemented
232C2×M16—1511no—
233C2×M16C2×D15111yescharacteristic, complemented
234#123—3021no—
235C22⋊Q8—1511no—
236C22⋊Q8—1511no—
237#121—3021no—
238#121—3021no—
239#121—1511no—
240#121—1511no—
241#121—1511no—
242#121—1511no—
243#121C2×D15111yescharacteristic
244#121C2×D15111yescharacteristic, complemented
245#120—3021no—
246C4×D4—3021no—
247C4×D4—3021no—
248#117—1511no—
249C2×C4⋊C4—1511no—
250C2×C22⋊C4—3021no—
251#107—1511no—
252#107—1511no—
253#106—1511no—
254#106C2×D15111yescharacteristic, complemented
255#103—1511no—
256#103—1511no—
257#102—1511no—
258#102—1511no—
259#102—1511no—
260#102—1511no—
261#102C2×D15111yescharacteristic, complemented
262#102C2×D15111yescharacteristic, complemented
263C22⋊C8—1511no—
264C22⋊C8—1511no—
265C22⋊C8—1511no—
266C22⋊C8—1511no—
267C24—3021no—
268C24—1511no—
269#41—6041no—
270#41—6041no—
271C2×Q8—1511no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—6041no—
281C2×D4—6041no—
282C2×D4—6044no—
283C2×D4—1511no—
284C2×D4C22×D15111yescharacteristic
285C2×D4C22×D15111yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—6041no—
289C22×C4—6041no—
290C22×C4—1511no—
291C22×C4—1511no—
292C22×C4—1511no—
293C22×C4—1511no—
294C22×C4—1511no—
295C22×C4C22×D15111yescharacteristic
296SD16—6041no—
297SD16—6041no—
298D8—41no—
299D8—6041no—
300M16—41no—
301M16—6041no—
302C2×C8—1511no—
303C2×C8—1511no—
304C2×C8C22×D15111yescharacteristic
305C2×C8C22×D15111yescharacteristic
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4—1511no—
311C4⋊C4C22×D15111yescharacteristic
312C4⋊C4C22×D15111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C42—3021no—
323C23—21no—
324C23—21no—
325C23—3022no—
326C23—3021no—
327C23—6041no—
328C23—6041no—
329C23—6042no—
330C23—6042no—
331C23—6042no—
332C23—1511no—
333C23—1511no—
334C23D4×D15111yescharacteristic
335Q8—3021no—
336Q8—3021no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—3021no—
344D4—3021no—
345D4—6042no—
346D4—6042no—
347D4—6042no—
348D4—6042no—
349D4—6042no—
350D4—6042no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—6041no—
363C2×C4—6041no—
364C2×C4—6042no—
365C2×C4—6041no—
366C2×C4—6042no—
367C2×C4—1511no—
368C2×C4—1511no—
369C2×C4D4×D15111yescharacteristic
370C2×C4C23×D15111yescharacteristic
371C8—21no—
372C8—21no—
373C8—3021no—
374C8—3021no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3021no—
385C22—3021no—
386C22—3021no—
387C22—3021no—
388C22—3021no—
389C22—6044no—
390C22—6041no—
391C22—6041no—
392C22—6041no—
393C22—1512no—
394C22—12084no—
395C22C2×D4×D15111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—3021no—
400C4—3021no—
401C4—6041no—
402C4—6041no—
403C4—6041no—
404C4#1801278411yescharacteristic
405C4#1801278511yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—3022no—
410C2—6041no—
411C2—12081no—
412C2#2375277011yescharacteristic
413C2AGL(1,ℤ/8)×D15111yescharacteristic
414C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151#3194
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23752722C2semidirect
2. #121×D151C2semidirect
3. #23752544C2semidirect
4. #23752538C2semidirect
5. #23752534C2semidirect
6. #23752524C2semidirect
7. #23752463C2semidirect
8. #23752458C2semidirect
9. #23752456C2semidirect
10. #23752364C2semidirect
11. #23752358C2semidirect
12. #23752354C2semidirect
13. #23752344C2semidirect
14. #23752175C2semidirect
15. #469×C151C2semidirect
16. C2×#14559003C22semidirect
20. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558989C22semidirect
23. C2×#14558988C22semidirect
26. #18012718C22semidirect
36. #18012697C22semidirect
39. #18012673C22semidirect
40. #18012672C22semidirect
41. #18012670C22semidirect
42. #18012664C22semidirect
43. #18012662C22semidirect
44. #18012661C22semidirect
45. #18012660C22semidirect
46. #18012660C22semidirect
47. #18012659C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. C2×D8×C151C22semidirect
53. C2×M16×C151C22semidirect
55. #121×C151C22semidirect
56. #106×C151C22semidirect
57. #102×C151C22semidirect
58. #102×C151C22semidirect
207. C151#3194semidirect
216. #469D151semidirect
231. C2×D8C2×D151semidirect
233. C2×M16C2×D151semidirect
244. #121C2×D151semidirect
254. #106C2×D151semidirect
261. #102C2×D151semidirect
262. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
#121×D1512
#237525442
#237525382
#237525342
#237525242
#237524632
#237524582
#237524562
#237523642
#237523582
#237523542
#237523442
#237521752
#469×C1512
#3194151