Finite Group Databasebeta

← #34080953

Subgroups — #34080953

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752909C211yesmaximal, characteristic, complemented
2#23752850C211yesmaximal, characteristic, complemented
3#23752568C211yesmaximal, characteristic, complemented
4#23752546C211yesmaximal, characteristic, complemented
5#23752537C211yesmaximal, characteristic, complemented
6#23752514C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752438C211yesmaximal, characteristic, complemented
9#23752429C211yesmaximal, characteristic, complemented
10#23752344C211yesmaximal, characteristic, complemented
11D8×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13#23752208C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18C22×C151⋊C8C2211yescharacteristic, complemented
19C2×C8×D151C2211yescharacteristic
20#18012732—21no—
21#18012730C2211yescharacteristic, complemented
22#18012728C2211yescharacteristic
23#18012722—21no—
24#18012720—21no—
25#18012715C2211yescharacteristic
26#18012713C2211yescharacteristic
27#18012711—21no—
28#18012710—21no—
29#18012710C2211yescharacteristic
30#18012707—21no—
31D4×Dic151C2211yescharacteristic
32D4×Dic151C2211yescharacteristic, complemented
33C4×C22⋊D151C2211yescharacteristic
34(C22⋊D151)⋊C4—21no—
35#18012698C2211yescharacteristic, complemented
36C4⋊C4×D151C2211yescharacteristic
37C2×(C2×D151)⋊C4—21no—
38#18012673C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic, complemented
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic, complemented
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic, complemented
56#103×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151D411yescharacteristic
65D4×D151—22no—
66D4×D151—41no—
67C22×Dic151—21no—
68C22×Dic151—21no—
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71#14558989—41no—
72C2×C151⋊C8—41no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C8×D151—41no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151D411yescharacteristic
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96#41×C151—22no—
97#41×C151—41no—
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151C2311yescharacteristic
105SD16×C151—41no—
106D8×C151—22no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22×D151—21no—
112C22×D151—42no—
113C22×D151—42no—
114C22×D151—81no—
115C22×D151C2×D411yescharacteristic
116D604—21no—
117D604—21no—
118C22⋊D151—22no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—81no—
126C2×Dic151—81no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151—21no—
136C23×C151—21no—
137C23×C151C2×D411yescharacteristic
138Q8×C151—21no—
139Q8×C151—21no—
140D4×C151—21no—
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—42no—
144D4×C151—81no—
145D4×C151#4112yes—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—42no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—22no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—84no—
171C2×D151#13512yes—
172C4×C151—21no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151C2×#4111yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—21no—
178Dic151—21no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—42no—
184C2×C151—41no—
185C2×C151—81no—
186C2×C151#54611yescharacteristic
187C2×C151C2×#13511yescharacteristic
188C2×C151#57611yescharacteristic
189D151—22no—
190D151—81no—
191C151#329711yescharacteristic, complemented, Sylow
192#3297—1511nomaximal, Sylow
193#553—1511no—
194#546—1511no—
195#488—1511no—
196#484—1511no—
197#482—1511no—
198#478—1511no—
199#466—1511no—
200#465—1511no—
201#463—1511no—
202#449D15111yescharacteristic, complemented
203#447—1511no—
204C4×D8—1511no—
205C8×D4—1511no—
206#416—1511no—
207C2×#102—1511no—
208C2×#41C2×D15111yescharacteristic
209C22×D4—1511no—
210C2×SD16C2×D15111yescharacteristic, complemented
211C2×D8—1511no—
212C2×D8C2×D15111yescharacteristic
213C22×C8—1511no—
214C22×C8—1511no—
215#126—3021no—
216#125—1511no—
217#124—1511no—
218#123—3021no—
219#123—3021no—
220C22⋊Q8—1511no—
221#121—3021no—
222#121—3021no—
223#121—1511no—
224#121—1511no—
225#121C2×D15111yescharacteristic, complemented
226#120—3021no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4—1511no—
230C4×D4—1511no—
231#117—1511no—
232C2×C4⋊C4—1511no—
233C2×C22⋊C4—3021no—
234#107—1511no—
235#107—1511no—
236#106—1511no—
237C4⋊C8—1511no—
238#103—1511no—
239#103—1511no—
240#103C2×D15111yescharacteristic, complemented
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102C2×D15111yescharacteristic
248C22⋊C8—1511no—
249C22⋊C8C2×D15111yescharacteristic, complemented
250C4×C8—1511no—
251C24—3021no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D15111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—3022no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—6041no—
262C2×D4—1511no—
263C2×D4—1511no—
264C2×D4C22×D15111yescharacteristic
265C2×D4C22×D15111yescharacteristic
266C22×C4—21no—
267C22×C4—3021no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—1511no—
271C22×C4C22×D15111yescharacteristic
272SD16—41no—
273D8—22no—
274D8—6041no—
275C2×C8—6041no—
276C2×C8—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4—1511no—
289C4⋊C4C22×D15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—1511no—
300C22⋊C4—1511no—
301C42—3021no—
302C42—1511no—
303C23—21no—
304C23—21no—
305C23—3021no—
306C23—6042no—
307C23—6042no—
308C23—1511no—
309C23—12081no—
310C23D4×D15111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—3022no—
319D4—3021no—
320D4—3021no—
321D4—6042no—
322D4—6042no—
323D4—12081no—
324D4#1455900312yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—1511no—
336C2×C4—1511no—
337C2×C4—1511no—
338C2×C4—12081no—
339C2×C4—12081no—
340C2×C4—12081no—
341C2×C4D4×D15111yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3021no—
346C8—3021no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3021no—
357C22—3021no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22—1512no—
362C22—12084no—
363C22C2×D4×D15111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—3021no—
368C4—3021no—
369C4—3021no—
370C4—6041no—
371C4—6041no—
372C4—6041no—
373C4C2×#1455900311yescharacteristic
374C4#1801278411yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—3022no—
379C2—12081no—
380C2#2375284911yescharacteristic
381C2#135×D15111yescharacteristic
382C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3297
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752909C2semidirect
2. #23752850C2semidirect
3. #23752568C2semidirect
4. #23752546C2semidirect
5. #23752537C2semidirect
6. #23752514C2semidirect
7. #23752446C2semidirect
8. #23752438C2semidirect
9. #23752429C2semidirect
10. #23752344C2semidirect
11. D8×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. #23752208C2semidirect
14. #102×D151C2semidirect
15. #449×C151C2semidirect
18. C22×C151⋊C8C22semidirect
21. #18012730C22semidirect
32. D4×Dic151C22semidirect
35. #18012698C22semidirect
38. #18012673C22semidirect
39. #18012672C22semidirect
40. #18012671C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012663C22semidirect
43. #18012663C22semidirect
48. #18012660C22semidirect
51. C8×Dic151C22semidirect
53. C2×SD16×C151C22semidirect
55. #121×C151C22semidirect
56. #103×C151C22semidirect
58. C22⋊C8×C151C22semidirect
191. C151#3297semidirect
202. #449D151semidirect
210. C2×SD16C2×D151semidirect
225. #121C2×D151semidirect
240. #103C2×D151semidirect
249. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529092
#237528502
#237525682
#237525462
#237525372
#237525142
#237524462
#237524382
#237524292
#237523442
D8×Dic1512
(C22⋊D151)⋊C82
#237522082
#102×D1512
#449×C1512
#3297151