Finite Group Databasebeta

← #34079351

Subgroups — #34079351

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#23752816C211yesmaximal, characteristic, complemented
2#23752684C211yesmaximal, characteristic, complemented
3#23752535C211yesmaximal, characteristic, complemented
4#23752534C211yesmaximal, characteristic, complemented
5#23752513C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752404C211yesmaximal, characteristic, complemented
8#23752344C211yesmaximal, characteristic, complemented
9#23752344C211yesmaximal, characteristic, complemented
10#23752324C211yesmaximal, characteristic, complemented
11#23752321C211yesmaximal, characteristic, complemented
12D8×Dic151C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19#18012731C2211yescharacteristic, complemented
20#18012720—21no—
21#18012720—21no—
22#18012711—21no—
23#18012711—21no—
24#18012710C2211yescharacteristic
25#18012710C2211yescharacteristic
26C4×D604C2211yescharacteristic
27D4×Dic151C2211yescharacteristic
28D4×Dic151C2211yescharacteristic, complemented
29D4×Dic151C2211yescharacteristic, complemented
30#18012701C2211yescharacteristic
31C4×C22⋊D151—21no—
32(C22⋊D151)⋊C4—21no—
33#18012697C2211yescharacteristic
34#18012696C2211yescharacteristic
35C2×(C2×D151)⋊C4—21no—
36C22⋊C4×D151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012661C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012660C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic, complemented
47#18012660C2211yescharacteristic, complemented
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#127×C151C2211yescharacteristic, complemented
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic, complemented
57#102×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64D4×D151—22no—
65D4×D151—22no—
66C22×Dic151—21no—
67C22×Dic151—21no—
68C22×Dic151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558989—22no—
73#14558989—22no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4D411yescharacteristic
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151—21no—
101D8×C151—22no—
102D8×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—24no—
110C22×D151—81no—
111C22×D151—81no—
112C22×D151C2×D411yescharacteristic
113D604—21no—
114D604#4112yes—
115C22⋊D151—24no—
116C22⋊D151—81no—
117C22⋊D151—81no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—81no—
122C2×Dic151—81no—
123C2×Dic151—81no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—21no—
128C4×D151—21no—
129C4×D151—81no—
130C4×D151—81no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C23×C151—21no—
134C23×C151—21no—
135C23×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—81no—
142D4×C151—81no—
143D4×C151#4112yes—
144C2×C4×C151—21no—
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×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151C22×D411yescharacteristic
161C2×D151—21no—
162C2×D151—22no—
163C2×D151—21no—
164C2×D151—21no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—84no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—41no—
171C4×C151C2×#4111yescharacteristic
172C4×C151C2×#4111yescharacteristic
173Dic151—21no—
174Dic151—21no—
175Dic151—21no—
176Dic151—41no—
177Dic151—41no—
178Dic151—41no—
179C2×C151—42no—
180C2×C151—81no—
181C2×C151—81no—
182C2×C151#52511yescharacteristic
183C2×C151#57611yescharacteristic
184C2×C151#57611yescharacteristic
185D151—41no—
186D151—42no—
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#459D15111yescharacteristic, complemented
197#447—1511no—
198#447—1511no—
199#442—1511no—
200#442—1511no—
201C4×D8—1511no—
202C4×D8—1511no—
203#433—1511no—
204C22×D4—1511no—
205C2×D8—1511no—
206C2×D8—1511no—
207C2×D8C2×D15111yescharacteristic
208C2×D8C2×D15111yescharacteristic
209#127C2×D15111yescharacteristic, complemented
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×D4—1511no—
224C4×D4C2×D15111yescharacteristic
225#117—1511no—
226#117—1511no—
227C2×C22⋊C4—3021no—
228C2×C22⋊C4—3021no—
229#107—1511no—
230#107—1511no—
231#106—1511no—
232#106—1511no—
233C4⋊C8—1511no—
234C4⋊C8C2×D15111yescharacteristic, complemented
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102C2×D15111yescharacteristic, complemented
242#102C2×D15111yescharacteristic, complemented
243C22⋊C8—1511no—
244C22⋊C8—1511no—
245#97—1511no—
246C4×C8—1511no—
247C24—3021no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—3022no—
251C2×D4—3022no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C2×D4C22×D15111yescharacteristic
258C2×D4C22×D15111yescharacteristic
259C22×C4—21no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—1511no—
266D8—22no—
267D8—22no—
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⋊C4—1511no—
281C4⋊C4C22×D15111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—3021no—
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—21no—
299C23—3024no—
300C23—3021no—
301C23—1511no—
302C23—12081no—
303C23—12081no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—3024no—
312D4—3021no—
313D4—1512no—
314D4—12081no—
315D4—12081no—
316D4#1455900312yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—1511no—
325C2×C4—1511no—
326C2×C4—1511no—
327C2×C4—12081no—
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—41no—
346C22—41no—
347C22—41no—
348C22—3021no—
349C22—3022no—
350C22—3021no—
351C22—3021no—
352C22—6041no—
353C22—6041no—
354C22—12084no—
355C22C2×D4×D15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—3021no—
360C4—3021no—
361C4—3021no—
362C4—6041no—
363C4—6041no—
364C4—6041no—
365C4#41×D15111yescharacteristic
366C4C2×#1455900311yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—6041no—
371C2—6042no—
372C2#2375272211yescharacteristic
373C2#2375301311yescharacteristic
374C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3122
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. #23752816C2semidirect
2. #23752684C2semidirect
3. #23752535C2semidirect
4. #23752534C2semidirect
5. #23752513C2semidirect
6. #23752512C2semidirect
7. #23752404C2semidirect
8. #23752344C2semidirect
9. #23752344C2semidirect
10. #23752324C2semidirect
11. #23752321C2semidirect
12. D8×Dic151C2semidirect
13. #23752292C2semidirect
14. #23752272C2semidirect
15. #459×C151C2semidirect
19. #18012731C22semidirect
28. D4×Dic151C22semidirect
29. D4×Dic151C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
46. #18012660C22semidirect
47. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
54. #127×C151C22semidirect
56. C4⋊C8×C151C22semidirect
57. #102×C151C22semidirect
58. #102×C151C22semidirect
187. C151#3122semidirect
196. #459D151semidirect
209. #127C2×D151semidirect
234. C4⋊C8C2×D151semidirect
241. #102C2×D151semidirect
242. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237526842
#237525352
#237525342
#237525132
#237525122
#237524042
#237523442
#237523242
#237523212
D8×Dic1512
#237522922
#237522722
#459×C1512
#3122151