Finite Group Databasebeta

← C151×#18318 #50323243

Subgroups — C151×#18318 #50323243

Order 38656.

1172 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#543×C151C211yesmaximal, characteristic, complemented
2#3193×C151C212yesmaximal, complemented
3#2539×C151C211yesmaximal, characteristic
4#1614×C151C214yesmaximal, complemented
5#1596×C151C214yesmaximal, complemented
6#1508×C151C212yesmaximal, complemented
7#1462×C151C211yesmaximal, characteristic, complemented
8#543×C151—24no—
9#543×C151—22no—
10#543×C151C2214yes—
11C2×#123×C151—21no—
12C2×C22⋊Q8×C151—22no—
13C2×C22⋊Q8×C151—21no—
14C2×C22⋊Q8×C151—22no—
15C2×C22⋊Q8×C151C2212yes—
16C2×#121×C151C2211yescharacteristic
17C2×#120×C151—21no—
18C22×C22⋊C4×C151—21no—
19C22×C22⋊C4×C151C2211yescharacteristic
20#484×C151C2214yescomplemented
21#480×C151—22no—
22#468×C151—24no—
23#450×C151C2214yescomplemented
24#448×C151—22no—
25#407×C151C2212yes—
26#399×C151C2212yes—
27#392×C151C2212yes—
28#390×C151—22no—
29C4×C22⋊C4×C151C2211yescharacteristic
30#328×C151C2218yescomplemented
31#323×C151C2214yes—
32C25×C151D411yescharacteristic
33C22×Q8×C151—21no—
34C22×Q8×C151D412yescomplemented
35C22×D4×C151—21no—
36C22×D4×C151—22no—
37C22×D4×C151C2311yescharacteristic
38C23×C4×C151—21no—
39C23×C4×C151—21no—
40C23×C4×C151D411yescharacteristic
41C23×C4×C151C2311yescharacteristic
42C2×SD16×C151—24no—
43C2×M16×C151—22no—
44#123×C151—44no—
45C22⋊Q8×C151—28no—
46C22⋊Q8×C151—24no—
47C22⋊Q8×C151—28no—
48C22⋊Q8×C151—24no—
49C22⋊Q8×C151—22no—
50C22⋊Q8×C151—22no—
51C22⋊Q8×C151—28no—
52C22⋊Q8×C151—28no—
53C22⋊Q8×C151D414yescomplemented
54C22⋊Q8×C151C2314yes—
55#121×C151—22no—
56#121×C151—22no—
57#120×C151—44no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151D412yescomplemented
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C22⋊C4×C151—22no—
65C2×C22⋊C4×C151—24no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151D412yes—
75C2×C22⋊C4×C151C2312yes—
76C2×C42×C151—21no—
77#107×C151—24no—
78#103×C151—24no—
79#102×C151—24no—
80C22⋊C8×C151—22no—
81C22⋊C8×C151C2314yes—
82#95×C151C2312yes—
83C24×C151—21no—
84C24×C151—21no—
85C24×C151—24no—
86C24×C151—21no—
87C24×C151—42no—
88C24×C151—81no—
89C24×C151C2×D411yescharacteristic
90C24×C151C2×D412yes—
91C2×Q8×C151—24no—
92C2×Q8×C151—22no—
93C2×Q8×C151—82no—
94C2×Q8×C151—82no—
95C2×Q8×C151C2×D414yes—
96C2×D4×C151—22no—
97C2×D4×C151—44no—
98C2×D4×C151—42no—
99C2×D4×C151—42no—
100C2×D4×C151—41no—
101C2×D4×C151—41no—
102C2×D4×C151—44no—
103C2×D4×C151—81no—
104C2×D4×C151—82no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—24no—
110C22×C4×C151—24no—
111C22×C4×C151—21no—
112C22×C4×C151—21no—
113C22×C4×C151—42no—
114C22×C4×C151—81no—
115C22×C4×C151—82no—
116C22×C4×C151—82no—
117C22×C4×C151C2×D412yes—
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2×D412yes—
121C22×C4×C151C2411yescharacteristic
122SD16×C151—84no—
123M16×C151—82no—
124C2×C8×C151—24no—
125C4⋊C4×C151—28no—
126C4⋊C4×C151—24no—
127C4⋊C4×C151—24no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—24no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—44no—
132C4⋊C4×C151C2×D414yes—
133C22⋊C4×C151—28no—
134C22⋊C4×C151—24no—
135C22⋊C4×C151—24no—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—24no—
138C22⋊C4×C151—24no—
139C22⋊C4×C151—44no—
140C22⋊C4×C151—44no—
141C22⋊C4×C151—42no—
142C42×C151—81no—
143C23×C151—24no—
144C23×C151—24no—
145C23×C151—22no—
146C23×C151—22no—
147C23×C151—22no—
148C23×C151—22no—
149C23×C151—41no—
150C23×C151—42no—
151C23×C151—42no—
152C23×C151—42no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—42no—
156C23×C151—42no—
157C23×C151—41no—
158C23×C151—42no—
159C23×C151—81no—
160C23×C151—81no—
161C23×C151—88no—
162C23×C151#12011yescharacteristic
163C23×C151#12011yescharacteristic
164C23×C151#13714yes—
165C23×C151C22×D411yescharacteristic
166Q8×C151—44no—
167Q8×C151—82no—
168Q8×C151—84no—
169D4×C151—44no—
170D4×C151—88no—
171D4×C151—82no—
172D4×C151—82no—
173C2×C4×C151—24no—
174C2×C4×C151—22no—
175C2×C4×C151—24no—
176C2×C4×C151—24no—
177C2×C4×C151—42no—
178C2×C4×C151—41no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—44no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—44no—
186C2×C4×C151—42no—
187C2×C4×C151—41no—
188C2×C4×C151—41no—
189C2×C4×C151—41no—
190C2×C4×C151—81no—
191C2×C4×C151—84no—
192C2×C4×C151—84no—
193C2×C4×C151#12012yes—
194C2×C4×C151C22×D412yes—
195C8×C151—44no—
196C22×C151—21no—
197C22×C151—21no—
198C22×C151—21no—
199C22×C151—21no—
200C22×C151—21no—
201C22×C151—24no—
202C22×C151—21no—
203C22×C151—21no—
204C22×C151—44no—
205C22×C151—44no—
206C22×C151—48no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151—82no—
210C22×C151—82no—
211C22×C151—82no—
212C22×C151—84no—
213C22×C151—81no—
214C22×C151—81no—
215C22×C151—81no—
216C22×C151#45312yes—
217C22×C151C2×#12011yescharacteristic
218C22×C151C2×#13712yes—
219C4×C151—22no—
220C4×C151—22no—
221C4×C151—44no—
222C4×C151—42no—
223C4×C151—44no—
224C4×C151—44no—
225C4×C151—81no—
226C2×C151—22no—
227C2×C151—22no—
228C2×C151—41no—
229C2×C151—44no—
230C2×C151—161no—
231C2×C151#300411yescharacteristic
232C2×C151C2×#45311yescharacteristic
233C2×C151#302611yescharacteristic
234#18318C15111yesmaximal, characteristic, direct product factor, Sylow
235C151#1831811yescharacteristic, direct product factor, Sylow
236C2×#543C2×C15111yescharacteristic, complemented
237#3193C2×C15112yescomplemented
238#2539C2×C15111yescharacteristic
239#1614C2×C15114yescomplemented
240#1596C2×C15114yescomplemented
241#1508C2×C15112yescomplemented
242#1462C2×C15111yescharacteristic, complemented
243#543—24no—
244#543—22no—
245#543C22×C15114yes—
246C2×#123—21no—
247C2×C22⋊Q8—22no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—22no—
250C2×C22⋊Q8C22×C15112yes—
251C2×#121C22×C15111yescharacteristic
252C2×#120—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4C22×C15111yescharacteristic
255#484C22×C15114yescomplemented
256#480—22no—
257#468—24no—
258#450C22×C15114yescomplemented
259#448—22no—
260#407C22×C15112yes—
261#399C22×C15112yes—
262#392C22×C15112yes—
263#390—22no—
264C4×C22⋊C4C22×C15111yescharacteristic
265#328C22×C15118yescomplemented
266#323C22×C15114yes—
267C25D4×C15111yescharacteristic
268C22×Q8—21no—
269C22×Q8D4×C15112yescomplemented
270C22×D4—21no—
271C22×D4—22no—
272C22×D4C23×C15111yescharacteristic
273C23×C4—21no—
274C23×C4—21no—
275C23×C4D4×C15111yescharacteristic
276C23×C4C23×C15111yescharacteristic
277C2×SD16—24no—
278C2×M16—22no—
279#123—44no—
280C22⋊Q8—28no—
281C22⋊Q8—28no—
282C22⋊Q8—24no—
283C22⋊Q8—28no—
284C22⋊Q8—24no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—28no—
288C22⋊Q8D4×C15114yescomplemented
289C22⋊Q8C23×C15114yes—
290#121—22no—
291#121—22no—
292#120—44no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4D4×C15112yescomplemented
298C2×C4⋊C4C23×C15111yescharacteristic
299C2×C22⋊C4—22no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4D4×C15112yes—
310C2×C22⋊C4C23×C15112yes—
311C2×C42—21no—
312#107—24no—
313#103—24no—
314#102—24no—
315C22⋊C8—22no—
316C22⋊C8C23×C15114yes—
317#95C23×C15112yes—
318C24—21no—
319C24—21no—
320C24—24no—
321C24—21no—
322C24—42no—
323C24—81no—
324C24C2×D4×C15111yescharacteristic
325C24C2×D4×C15112yes—
326C2×Q8—24no—
327C2×Q8—22no—
328C2×Q8—82no—
329C2×Q8—82no—
330C2×Q8C2×D4×C15114yes—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—44no—
338C2×D4—81no—
339C2×D4—82no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—81no—
350C22×C4—82no—
351C22×C4—82no—
352C22×C4C2×D4×C15112yes—
353C22×C4C2×D4×C15111yescharacteristic
354C22×C4C2×D4×C15112yes—
355C22×C4C2×D4×C15112yes—
356C22×C4C24×C15111yescharacteristic
357SD16—84no—
358M16—82no—
359C2×C8—24no—
360C4⋊C4—24no—
361C4⋊C4—28no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—44no—
367C4⋊C4C2×D4×C15114yes—
368C22⋊C4—28no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—42no—
377C42—81no—
378C23—24no—
379C23—24no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—42no—
394C23—81no—
395C23—81no—
396C23—88no—
397C23#120×C15111yescharacteristic
398C23#120×C15111yescharacteristic
399C23#137×C15114yes—
400C23C22×D4×C15111yescharacteristic
401Q8—44no—
402Q8—82no—
403Q8—84no—
404D4—44no—
405D4—88no—
406D4—82no—
407D4—82no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—81no—
426C2×C4—84no—
427C2×C4—84no—
428C2×C4#120×C15112yes—
429C2×C4C22×D4×C15112yes—
430C8—44no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—24no—
437C22—21no—
438C22—21no—
439C22—44no—
440C22—44no—
441C22—48no—
442C22—42no—
443C22—42no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22—84no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22#453×C15112yes—
452C22C2×#120×C15111yescharacteristic
453C22C2×#137×C15112yes—
454C4—22no—
455C4—22no—
456C4—44no—
457C4—42no—
458C4—44no—
459C4—44no—
460C4—81no—
461C2—22no—
462C2—22no—
463C2—41no—
464C2—44no—
465C2—161no—
466C2#3004×C15111yescharacteristic
467C2C2×#453×C15111yescharacteristic
468C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2539×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#543×C151C2semidirect
2. #3193×C151C2semidirect
4. #1614×C151C2semidirect
5. #1596×C151C2semidirect
6. #1508×C151C2semidirect
7. #1462×C151C2semidirect
20. #484×C151C22semidirect
23. #450×C151C22semidirect
30. #328×C151C22semidirect
34. C22×Q8×C151D4semidirect
53. C22⋊Q8×C151D4semidirect
62. C2×C4⋊C4×C151D4semidirect
234. #18318C151direct (N × H)
235. C151#18318direct (N × H)
236. C2×#543C2×C151semidirect
237. #3193C2×C151semidirect
239. #1614C2×C151semidirect
240. #1596C2×C151semidirect
241. #1508C2×C151semidirect
242. #1462C2×C151semidirect
255. #484C22×C151semidirect
258. #450C22×C151semidirect
265. #328C22×C151semidirect
269. C22×Q8D4×C151semidirect
288. C22⋊Q8D4×C151semidirect
297. C2×C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#543×C1512
#3193×C1512
#2539×C1512
#1614×C1512
#1596×C1512
#1508×C1512
#1462×C1512
#18318151