Finite Group Databasebeta

← #34079347

Subgroups — #34079347

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#23752815C211yesmaximal, characteristic, complemented
2#23752687C211yesmaximal, characteristic, complemented
3#23752537C211yesmaximal, characteristic, complemented
4#23752533C211yesmaximal, characteristic, complemented
5#23752514C211yesmaximal, characteristic, complemented
6#23752510C211yesmaximal, characteristic, complemented
7#23752405C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752346C211yesmaximal, characteristic, complemented
10#23752324C211yesmaximal, characteristic, complemented
11#23752321C211yesmaximal, characteristic, complemented
12D8×Dic151C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14558989C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18#18012735C2211yescharacteristic, complemented
19#18012730C2211yescharacteristic, complemented
20#18012723—21no—
21#18012721—21no—
22#18012713C2211yescharacteristic
23#18012711—21no—
24#18012710—21no—
25D4×Dic151—21no—
26D4×Dic151—21no—
27D4×Dic151C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31D4×Dic151C2211yescharacteristic, complemented
32#18012701C2211yescharacteristic, complemented
33#18012698C2211yescharacteristic
34#18012698C2211yescharacteristic
35C2×C22⋊Dic151—21no—
36C2×C22⋊Dic151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42Dic151⋊C8C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×D604C2311yescharacteristic
60C2×C22⋊D151—21no—
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C22×Dic151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C22×Dic151—21no—
68C2×C4×D151—21no—
69#14558989—22no—
70#14558989—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151—21no—
74C4⋊Dic151D411yescharacteristic
75C4⋊Dic151D411yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80C22⋊Dic151—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151D411yescharacteristic
87C22⋊Dic151D411yescharacteristic
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90C4×Dic151—21no—
91C4×Dic151C2311yescharacteristic
92C4×Dic151C2311yescharacteristic
93C24×C151—21no—
94C2×D4×C151—22no—
95C2×D4×C151—22no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102D8×C151—22no—
103D8×C151—22no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22×D151—21no—
109D604—21no—
110D604—21no—
111C22⋊D151—81no—
112C22⋊D151—81no—
113C22⋊D151—81no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—81no—
118C2×Dic151—81no—
119C2×Dic151—81no—
120C2×Dic151—81no—
121C2×Dic151—81no—
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C4×D151—81no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—24no—
130C23×C151—21no—
131C23×C151—21no—
132C23×C151—21no—
133C23×C151—81no—
134C23×C151—81no—
135C23×C151C2×D411yescharacteristic
136D4×C151—24no—
137D4×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—81no—
142D4×C151#4112yes—
143D4×C151#4112yes—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151—21no—
151C22×C151—21no—
152C22×C151—22no—
153C22×C151—22no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—84no—
164C22×C151C22×D411yescharacteristic
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151C2×#4111yescharacteristic
171C4×C151C2×#4111yescharacteristic
172Dic151—21no—
173Dic151—21no—
174Dic151—21no—
175Dic151—21no—
176Dic151—41no—
177Dic151—41no—
178Dic151—41no—
179C2×C151—41no—
180C2×C151—42no—
181C2×C151—42no—
182C2×C151—81no—
183C2×C151#52511yescharacteristic
184C2×C151#57611yescharacteristic
185C2×C151#57611yescharacteristic
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#447D15111yescharacteristic, complemented
199#442—1511no—
200#442—1511no—
201C4×D8—1511no—
202C4×D8—1511no—
203#433—1511no—
204C22×D4C2×D15111yescharacteristic
205C2×D8—1511no—
206C2×D8—1511no—
207C2×D8C2×D15111yescharacteristic
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#121C2×D15111yescharacteristic
217C4×D4—3021no—
218C4×D4—3021no—
219C4×D4—1511no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4—1511no—
223C4×D4—1511no—
224C4×D4—1511no—
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⋊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
243C22⋊C8—1511no—
244C22⋊C8C2×D15111yescharacteristic
245#97—1511no—
246C4×C8—1511no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C2×D4C22×D15111yescharacteristic
258C2×D4C22×D15111yescharacteristic
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—3021no—
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4C22×D15111yescharacteristic
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—
295C42—1511no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—3021no—
303C23D4×D15111yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—3021no—
311D4—3021no—
312D4—12081no—
313D4—12081no—
314D4—12081no—
315D4#1455900312yes—
316D4#1455900312yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—1511no—
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×C4—12081no—
333C2×C4D4×D15111yescharacteristic
334C2×C4C23×D15111yescharacteristic
335C8—21no—
336C8—21no—
337C8—3021no—
338C8—3021no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—6041no—
353C22—6041no—
354C22—6041no—
355C22C2×D4×D15111yescharacteristic
356C4—21no—
357C4—41no—
358C4—3021no—
359C4—3021no—
360C4—3021no—
361C4—3021no—
362C4—6041no—
363C4—6041no—
364C4—6041no—
365C4C2×#1455900311yescharacteristic
366C4C2×#1455900311yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—12081no—
372C2#2375271811yescharacteristic
373C2#2375301311yescharacteristic
374C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3122
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23752815C2semidirect
2. #23752687C2semidirect
3. #23752537C2semidirect
4. #23752533C2semidirect
5. #23752514C2semidirect
6. #23752510C2semidirect
7. #23752405C2semidirect
8. #23752405C2semidirect
9. #23752346C2semidirect
10. #23752324C2semidirect
11. #23752321C2semidirect
12. D8×Dic151C2semidirect
13. #23752292C2semidirect
14. #23752270C2semidirect
15. #447×C151C2semidirect
18. #18012735C22semidirect
19. #18012730C22semidirect
31. D4×Dic151C22semidirect
32. #18012701C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. Dic151⋊C8C22semidirect
43. #18012661C22semidirect
44. #18012661C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
187. C151#3122semidirect
198. #447D151semidirect

Maximal subgroups

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

subgroupindex
#237528152
#237526872
#237525372
#237525332
#237525142
#237525102
#237524052
#237523462
#237523242
#237523212
D8×Dic1512
#237522922
#237522702
#447×C1512
#3122151