Finite Group Databasebeta

← #34079352

Subgroups — #34079352

Order 19328.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752813C211yesmaximal, characteristic, complemented
2#23752684C211yesmaximal, characteristic, complemented
3#23752538C211yesmaximal, characteristic, complemented
4#23752535C211yesmaximal, characteristic, complemented
5#23752514C211yesmaximal, characteristic, complemented
6#23752511C211yesmaximal, characteristic, complemented
7#23752406C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752347C211yesmaximal, characteristic, complemented
10#23752344C211yesmaximal, characteristic, complemented
11#23752325C211yesmaximal, characteristic, complemented
12C4×#14558989C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752274C211yesmaximal, characteristic, complemented
15#442×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C2×D1208C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012735C2211yescharacteristic, complemented
21#18012730C2211yescharacteristic, complemented
22#18012722—21no—
23#18012721—21no—
24#18012714C2211yescharacteristic
25#18012713—21no—
26#18012712—21no—
27#18012710C2211yescharacteristic
28C4×D604C2211yescharacteristic
29C4×D604C2211yescharacteristic, complemented
30D4×Dic151C2211yescharacteristic
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012697C2211yescharacteristic
35#18012696C2211yescharacteristic
36C2×(C2×D151)⋊C4—21no—
37C22⋊C4×D151—21no—
38#18012672C2211yescharacteristic, complemented
39#18012672C2211yescharacteristic, complemented
40#18012671C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic, complemented
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic, complemented
55#106×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic, complemented
58#97×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×D604—21no—
61C2×D604C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67D4×D151—22no—
68D4×D151—22no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74D1208—22no—
75#14558989—22no—
76#14558989—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96C2×D4×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100D8×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—24no—
110C22×D151—21no—
111C22×D151—81no—
112C22×D151—81no—
113C22×D151C2×D411yescharacteristic
114D604—21no—
115D604—21no—
116D604—21no—
117D604—81no—
118D604#4112yes—
119C22⋊D151—24no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C22⋊D151—81no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—81no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—81no—
132C4×D151—81no—
133C4×D151—81no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137C23×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151#4112yes—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—81no—
145C2×C4×C151—81no—
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151—21no—
151C22×C151—22no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151C22×D411yescharacteristic
158C2×D151—21no—
159C2×D151—22no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—84no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151C2×#4111yescharacteristic
173C4×C151C2×#4111yescharacteristic
174Dic151—21no—
175Dic151—21no—
176Dic151—21no—
177Dic151—41no—
178Dic151—41no—
179C2×C151—42no—
180C2×C151—81no—
181C2×C151#52511yescharacteristic
182C2×C151#57611yescharacteristic
183C2×C151#57611yescharacteristic
184D151—41no—
185D151—42no—
186D151—81no—
187C151#312211yescharacteristic, complemented, Sylow
188#3122—1511nomaximal, Sylow
189#540—1511no—
190#518—1511no—
191#482—1511no—
192#482—1511no—
193#478—1511no—
194#478—1511no—
195#459—1511no—
196#459—1511no—
197#447—1511no—
198#447—1511no—
199#442—1511no—
200#442D15111yescharacteristic, complemented
201C4×D8—1511no—
202C4×D8—1511no—
203#433—1511no—
204C22×D4—1511no—
205C2×D8—1511no—
206C2×D8—1511no—
207C2×D8—1511no—
208C2×D8C2×D15111yescharacteristic
209#127—1511no—
210#125—1511no—
211#123—3021no—
212#123—3021no—
213#121—3021no—
214#121—3021no—
215#121—1511no—
216#121—1511no—
217C4×D4—3021no—
218C4×D4—3021no—
219C4×D4—1511no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4—1511no—
223C4×D4C2×D15111yescharacteristic
224C4×D4C2×D15111yescharacteristic, complemented
225#117—1511no—
226#117—1511no—
227C2×C22⋊C4—3021no—
228C2×C22⋊C4—3021no—
229#107—1511no—
230#107—1511no—
231#106—1511no—
232#106C2×D15111yescharacteristic, complemented
233C4⋊C8—1511no—
234C4⋊C8—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102C2×D15111yescharacteristic
242#102C2×D15111yescharacteristic, complemented
243C22⋊C8—1511no—
244C22⋊C8—1511no—
245#97C2×D15111yescharacteristic, complemented
246C4×C8—1511no—
247C24—3021no—
248C2×D4—3021no—
249C2×D4—3022no—
250C2×D4—3022no—
251C2×D4—3021no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4C22×D15111yescharacteristic
258C2×D4C22×D15111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—3021no—
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—1511no—
266D8—22no—
267D8—3022no—
268D8—3022no—
269D8—3022no—
270C2×C8—1511no—
271C2×C8—1511no—
272C2×C8C22×D15111yescharacteristic
273C2×C8C22×D15111yescharacteristic
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4C22×D15111yescharacteristic
281C4⋊C4C22×D15111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—1511no—
292C22⋊C4—1511no—
293C42—3021no—
294C42—1511no—
295C42C22×D15111yescharacteristic
296C23—21no—
297C23—21no—
298C23—3024no—
299C23—3021no—
300C23—3021no—
301C23—1511no—
302C23—12081no—
303C23—12081no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—3024no—
308D4—3021no—
309D4—3021no—
310D4—3021no—
311D4—1512no—
312D4—12081no—
313D4—12081no—
314D4—12081no—
315D4—12081no—
316D4#1455900412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—1511no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4—12081no—
329C2×C4—12081no—
330C2×C4—12081no—
331C2×C4—12081no—
332C2×C4D4×D15111yescharacteristic
333C2×C4D4×D15111yescharacteristic
334C2×C4C23×D15111yescharacteristic
335C8—21no—
336C8—21no—
337C8—3021no—
338C8—3021no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3021no—
346C22—3022no—
347C22—3021no—
348C22—3021no—
349C22—6041no—
350C22—6041no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22—12084no—
355C22C2×D4×D15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—3021no—
361C4—3021no—
362C4—3021no—
363C4—6041no—
364C4—6041no—
365C4#41×D15111yescharacteristic
366C4C2×#1455900411yescharacteristic
367C2—42no—
368C2—81no—
369C2—6041no—
370C2—6042no—
371C2—12081no—
372C2#2375272111yescharacteristic
373C2#2375301611yescharacteristic
374C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#442×C151C2
socleC22×C151C22×D4
hypercenter#442D151
hypocenterC151#3122
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #23752813C2semidirect
2. #23752684C2semidirect
3. #23752538C2semidirect
4. #23752535C2semidirect
5. #23752514C2semidirect
6. #23752511C2semidirect
7. #23752406C2semidirect
8. #23752405C2semidirect
9. #23752347C2semidirect
10. #23752344C2semidirect
11. #23752325C2semidirect
12. C4×#14558989C2semidirect
13. C4×#14558989C2semidirect
14. #23752274C2semidirect
15. #442×C151C2semidirect
20. #18012735C22semidirect
21. #18012730C22semidirect
29. C4×D604C22semidirect
38. #18012672C22semidirect
39. #18012672C22semidirect
40. #18012671C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
44. #18012661C22semidirect
46. #18012660C22semidirect
48. #18012659C22semidirect
51. C4×C151⋊C8C22semidirect
54. C4×D4×C151C22semidirect
55. #106×C151C22semidirect
57. #102×C151C22semidirect
58. #97×C151C22semidirect
187. C151#3122semidirect
200. #442D151semidirect
224. C4×D4C2×D151semidirect
232. #106C2×D151semidirect
242. #102C2×D151semidirect
245. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528132
#237526842
#237525382
#237525352
#237525142
#237525112
#237524062
#237524052
#237523472
#237523442
#237523252
C4×#145589892
#237522742
#442×C1512
#3122151