Finite Group Databasebeta

← C151×#23949 #50328874

Subgroups — C151×#23949 #50328874

Order 38656.

1258 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3492×C151C211yesmaximal, characteristic
2#3004×C151C212yesmaximal, complemented
3C2×#391×C151C211yesmaximal, characteristic, complemented
4#2028×C151C212yesmaximal, complemented
5#2007×C151C212yesmaximal, complemented
6#1896×C151C212yesmaximal, complemented
7#1882×C151C214yesmaximal, complemented
8#1821×C151C211yesmaximal, characteristic, complemented
9C23×Q8×C151C2211yescharacteristic
10C2×#137×C151C2214yes—
11#554×C151—22no—
12#553×C151—22no—
13#552×C151—22no—
14#547×C151—22no—
15#544×C151C2211yescharacteristic
16#539×C151—22no—
17#537×C151C2211yescharacteristic
18#525×C151—22no—
19#525×C151C2212yes—
20#520×C151C2212yes—
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C42×C151C2211yescharacteristic
23#451×C151—22no—
24#451×C151—22no—
25#448×C151—22no—
26#448×C151—22no—
27C2×#104×C151C2214yes—
28#419×C151C2214yes—
29#407×C151C2212yes—
30#391×C151—22no—
31#391×C151C2212yes—
32#391×C151C2212yes—
33C2×#95×C151—22no—
34#343×C151C2212yes—
35#343×C151C2212yes—
36#339×C151C2214yes—
37C2×#41×C151—22no—
38C2×#41×C151C2312yes—
39C22×Q8×C151—21no—
40C22×Q8×C151—24no—
41C22×Q8×C151—22no—
42C22×Q8×C151—22no—
43C22×Q8×C151—42no—
44C22×Q8×C151C2312yes—
45C23×C4×C151—21no—
46C23×C4×C151—21no—
47C23×C4×C151D412yes—
48C23×C4×C151C2311yescharacteristic
49#137×C151—28no—
50#137×C151—44no—
51C2×Q16×C151—24no—
52C2×SD16×C151—24no—
53C2×M16×C151C2314yes—
54C4⋊Q8×C151—22no—
55#126×C151—24no—
56#125×C151—24no—
57#125×C151—22no—
58#123×C151—24no—
59#123×C151—24no—
60#123×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—24no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151D412yes—
66C22⋊Q8×C151D412yes—
67#121×C151—22no—
68#121×C151—22no—
69#121×C151—22no—
70#121×C151D412yes—
71#121×C151D412yes—
72#120×C151—22no—
73C4×Q8×C151—22no—
74C4×D4×C151—24no—
75C4×D4×C151—22no—
76C4×D4×C151—24no—
77C4×D4×C151—22no—
78C4×D4×C151—22no—
79#117×C151—22no—
80#117×C151—22no—
81#117×C151C2312yes—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151D412yes—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C42×C151—21no—
89C2×C42×C151—42no—
90C2×C42×C151C2312yes—
91#104×C151—44no—
92#103×C151—24no—
93#103×C151—24no—
94C22⋊C8×C151—22no—
95C22⋊C8×C151—22no—
96#95×C151—24no—
97#95×C151—24no—
98C24×C151C2×D411yescharacteristic
99#41×C151—24no—
100#41×C151—24no—
101#41×C151—84no—
102C2×Q8×C151—24no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—24no—
106C2×Q8×C151—24no—
107C2×Q8×C151—48no—
108C2×Q8×C151—48no—
109C2×Q8×C151—42no—
110C2×Q8×C151—42no—
111C2×Q8×C151C2×D412yes—
112C2×Q8×C151#4114yescomplemented
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151C2×D412yes—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—24no—
121C22×C4×C151—24no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—24no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—42no—
129C22×C4×C151—42no—
130C22×C4×C151—42no—
131C22×C4×C151—41no—
132C22×C4×C151—41no—
133C22×C4×C151—44no—
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2×D412yes—
137C22×C4×C151C2×D412yes—
138C22×C4×C151C2×D412yes—
139C22×C4×C151C2411yescharacteristic
140Q16×C151—48no—
141SD16×C151—48no—
142M16×C151—24no—
143M16×C151—24no—
144C2×C8×C151—24no—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151C2×D412yes—
155C4⋊C4×C151C2×D412yes—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—22no—
160C22⋊C4×C151—22no—
161C22⋊C4×C151—22no—
162C22⋊C4×C151—22no—
163C42×C151—24no—
164C42×C151—22no—
165C42×C151—24no—
166C42×C151—42no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—22no—
170C23×C151—22no—
171C23×C151—22no—
172C23×C151#12011yescharacteristic
173C23×C151#12011yescharacteristic
174C23×C151C22×D411yescharacteristic
175Q8×C151—28no—
176Q8×C151—24no—
177Q8×C151—48no—
178Q8×C151—44no—
179Q8×C151—82no—
180D4×C151—24no—
181D4×C151—42no—
182D4×C151—42no—
183D4×C151—44no—
184D4×C151—44no—
185D4×C151—82no—
186C2×C4×C151—21no—
187C2×C4×C151—21no—
188C2×C4×C151—24no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—24no—
197C2×C4×C151—44no—
198C2×C4×C151—44no—
199C2×C4×C151—48no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—44no—
205C2×C4×C151—44no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—82no—
209C2×C4×C151—84no—
210C2×C4×C151#12012yes—
211C2×C4×C151C22×D412yes—
212C2×C4×C151C2×#4112yes—
213C2×C4×C151H(5,𝔽2)12yes—
214C8×C151—44no—
215C22×C151—24no—
216C22×C151—24no—
217C22×C151—21no—
218C22×C151—21no—
219C22×C151—21no—
220C22×C151—21no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151#45512yes—
227C22×C151#45612yes—
228C22×C151C2×#12011yescharacteristic
229C22×C151#52511yescharacteristic
230C22×C151#53511yescharacteristic
231C4×C151—22no—
232C4×C151—44no—
233C4×C151—44no—
234C4×C151—42no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—42no—
238C4×C151—42no—
239C4×C151#54614yes—
240C2×C151—21no—
241C2×C151—21no—
242C2×C151—22no—
243C2×C151—22no—
244C2×C151—82no—
245C2×C151#240411yescharacteristic
246C2×C151C2×#45511yescharacteristic
247C2×C151C2×#45611yescharacteristic
248#23949C15111yesmaximal, characteristic, direct product factor, Sylow
249C151#2394911yescharacteristic, direct product factor, Sylow
250#3492C2×C15111yescharacteristic
251#3004C2×C15112yescomplemented
252C2×#391C2×C15111yescharacteristic, complemented
253#2028C2×C15112yescomplemented
254#2007C2×C15112yescomplemented
255#1896C2×C15112yescomplemented
256#1882C2×C15114yescomplemented
257#1821C2×C15111yescharacteristic, complemented
258C23×Q8C22×C15111yescharacteristic
259C2×#137C22×C15114yes—
260#554—22no—
261#553—22no—
262#552—22no—
263#547—22no—
264#544C22×C15111yescharacteristic
265#539—22no—
266#537C22×C15111yescharacteristic
267#525—22no—
268#525C22×C15112yes—
269#520C22×C15112yes—
270C22×C4⋊C4C22×C15111yescharacteristic
271C22×C42C22×C15111yescharacteristic
272#451—22no—
273#451—22no—
274#448—22no—
275#448—22no—
276C2×#104C22×C15114yes—
277#419C22×C15114yes—
278#407C22×C15112yes—
279#391—22no—
280#391C22×C15112yes—
281#391C22×C15112yes—
282C2×#95—22no—
283#343C22×C15112yes—
284#343C22×C15112yes—
285#339C22×C15114yes—
286C2×#41—22no—
287C2×#41C23×C15112yes—
288C22×Q8—24no—
289C22×Q8—21no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—42no—
293C22×Q8C23×C15112yes—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4D4×C15112yes—
297C23×C4C23×C15111yescharacteristic
298#137—28no—
299#137—44no—
300C2×Q16—24no—
301C2×SD16—24no—
302C2×M16C23×C15114yes—
303C4⋊Q8—22no—
304#126—24no—
305#125—24no—
306#125—22no—
307#123—24no—
308#123—24no—
309#123—22no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8D4×C15112yes—
315C22⋊Q8D4×C15112yes—
316#121—22no—
317#121—22no—
318#121—22no—
319#121D4×C15112yes—
320#121D4×C15112yes—
321#120—22no—
322C4×Q8—22no—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—22no—
328#117—22no—
329#117—22no—
330#117C23×C15112yes—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4D4×C15112yes—
335C2×C4⋊C4C23×C15111yescharacteristic
336C2×C4⋊C4C23×C15111yescharacteristic
337C2×C42—21no—
338C2×C42—42no—
339C2×C42C23×C15112yes—
340#104—44no—
341#103—24no—
342#103—24no—
343C22⋊C8—22no—
344C22⋊C8—22no—
345#95—24no—
346#95—24no—
347C24C2×D4×C15111yescharacteristic
348#41—24no—
349#41—24no—
350#41—84no—
351C2×Q8—24no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—24no—
355C2×Q8—24no—
356C2×Q8—48no—
357C2×Q8—48no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8C2×D4×C15112yes—
361C2×Q8#41×C15114yescomplemented
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4C2×D4×C15112yes—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—44no—
383C22×C4C2×D4×C15111yescharacteristic
384C22×C4C2×D4×C15112yes—
385C22×C4C2×D4×C15112yes—
386C22×C4C2×D4×C15112yes—
387C22×C4C2×D4×C15112yes—
388C22×C4C24×C15111yescharacteristic
389Q16—48no—
390SD16—48no—
391M16—24no—
392M16—24no—
393C2×C8—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4C2×D4×C15112yes—
404C4⋊C4C2×D4×C15112yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C42—24no—
413C42—22no—
414C42—24no—
415C42—42no—
416C23—22no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—22no—
421C23#120×C15111yescharacteristic
422C23#120×C15111yescharacteristic
423C23C22×D4×C15111yescharacteristic
424Q8—28no—
425Q8—24no—
426Q8—48no—
427Q8—44no—
428Q8—82no—
429D4—24no—
430D4—44no—
431D4—44no—
432D4—42no—
433D4—42no—
434D4—82no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—48no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—82no—
458C2×C4—84no—
459C2×C4#120×C15112yes—
460C2×C4C22×D4×C15112yes—
461C2×C4C2×#41×C15112yes—
462C2×C4H(5,𝔽2)×C15112yes—
463C8—44no—
464C22—24no—
465C22—24no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22#455×C15112yes—
476C22#456×C15112yes—
477C22C2×#120×C15111yescharacteristic
478C22#525×C15111yescharacteristic
479C22#535×C15111yescharacteristic
480C4—22no—
481C4—44no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4#546×C15114yes—
489C2—21no—
490C2—22no—
491C2—22no—
492C2—21no—
493C2—82no—
494C2#2404×C15111yescharacteristic
495C2C2×#455×C15111yescharacteristic
496C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3492×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3004×C151C2semidirect
3. C2×#391×C151C2semidirect
4. #2028×C151C2semidirect
5. #2007×C151C2semidirect
6. #1896×C151C2semidirect
7. #1882×C151C2semidirect
8. #1821×C151C2semidirect
112. C2×Q8×C151#41semidirect
248. #23949C151direct (N × H)
249. C151#23949direct (N × H)
251. #3004C2×C151semidirect
252. C2×#391C2×C151semidirect
253. #2028C2×C151semidirect
254. #2007C2×C151semidirect
255. #1896C2×C151semidirect
256. #1882C2×C151semidirect
257. #1821C2×C151semidirect
361. C2×Q8#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3492×C1512
#3004×C1512
C2×#391×C1512
#2028×C1512
#2007×C1512
#1896×C1512
#1882×C1512
#1821×C1512
#23949151