Finite Group Databasebeta

← C151×#24547 #50329472

Subgroups — C151×#24547 #50329472

Order 38656.

1022 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C151C211yesmaximal, characteristic
2C2×#417×C151C211yesmaximal, characteristic, complemented
3#2504×C151C211yesmaximal, characteristic, complemented
4#2341×C151C211yesmaximal, characteristic, complemented
5#2073×C151C212yesmaximal, complemented
6#2054×C151C212yesmaximal, complemented
7#1895×C151C211yesmaximal, characteristic, complemented
8#1880×C151C212yesmaximal, complemented
9#1851×C151C211yesmaximal, characteristic, complemented
10#1823×C151C211yesmaximal, characteristic, complemented
11#1805×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C22×SD16×C151C2211yescharacteristic
14C22×D8×C151C2211yescharacteristic
15C22×M16×C151C2211yescharacteristic
16C2×#121×C151C2211yescharacteristic
17C2×C4×Q8×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19#449×C151—24no—
20C2×C4⋊C8×C151C2212yes—
21#417×C151—24no—
22C2×#103×C151C2212yes—
23C2×#103×C151C2211yescharacteristic
24C2×#102×C151C2212yes—
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2212yes—
27C2×C22⋊C8×C151C2211yescharacteristic
28#397×C151—21no—
29#397×C151—21no—
30#390×C151—22no—
31#390×C151C2212yes—
32#390×C151C2212yes—
33#386×C151—22no—
34#382×C151C2212yes—
35#380×C151—21no—
36#380×C151C2211yescharacteristic
37C4×C22⋊C4×C151—21no—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C2×#41×C151—22no—
44C2×#41×C151—24no—
45C2×#41×C151—42no—
46C2×#41×C151D414yes—
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C23×C4×C151—21no—
53C23×C4×C151—21no—
54C23×C4×C151C2311yescharacteristic
55C2×SD16×C151—22no—
56C2×SD16×C151—24no—
57C2×D8×C151—22no—
58C2×D8×C151—42no—
59C2×M16×C151—22no—
60C2×M16×C151—42no—
61C22×C8×C151C2311yescharacteristic
62C22×C8×C151C2312yes—
63C22×C8×C151C2311yescharacteristic
64#121×C151—22no—
65#121×C151—22no—
66C4×Q8×C151—24no—
67C4×Q8×C151—42no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2312yes—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—21no—
81C2×C22⋊C4×C151D412yes—
82C2×C42×C151—22no—
83C2×C42×C151C2312yes—
84C4⋊C8×C151—42no—
85#103×C151—24no—
86#103×C151—22no—
87#102×C151—24no—
88#102×C151—22no—
89#102×C151—42no—
90C22⋊C8×C151—22no—
91#95×C151—21no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151D411yescharacteristic
95#95×C151D411yescharacteristic
96C24×C151—21no—
97C24×C151—21no—
98C24×C151C2×D411yescharacteristic
99#41×C151—28no—
100#41×C151—44no—
101#41×C151—48no—
102C2×Q8×C151—21no—
103C2×Q8×C151—22no—
104C2×Q8×C151C2×D412yes—
105C2×Q8×C151#4114yes—
106C2×D4×C151—24no—
107C2×D4×C151—21no—
108C2×D4×C151—22no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—44no—
115C2×D4×C151—44no—
116C2×D4×C151—42no—
117C2×D4×C151C2×D412yes—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—24no—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—44no—
126C22×C4×C151—42no—
127C22×C4×C151—81no—
128C22×C4×C151—81no—
129C22×C4×C151C2×D412yes—
130C22×C4×C151C2×D412yes—
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D412yes—
133C22×C4×C151#4112yes—
134C22×C4×C151C2411yescharacteristic
135SD16×C151—44no—
136D8×C151—44no—
137M16×C151—44no—
138C2×C8×C151—21no—
139C2×C8×C151—21no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—44no—
152C4⋊C4×C151—42no—
153C22⋊C4×C151—42no—
154C22⋊C4×C151—44no—
155C22⋊C4×C151—42no—
156C22⋊C4×C151—82no—
157C22⋊C4×C151—82no—
158C22⋊C4×C151—82no—
159C22⋊C4×C151—81no—
160C42×C151—22no—
161C42×C151—22no—
162C42×C151—44no—
163C23×C151—22no—
164C23×C151—22no—
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—22no—
168C23×C151—42no—
169C23×C151—42no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151—41no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151#12112yes—
178C23×C151C22×D411yescharacteristic
179Q8×C151—22no—
180Q8×C151—24no—
181Q8×C151#12314yes—
182D4×C151—22no—
183D4×C151—22no—
184D4×C151—48no—
185D4×C151—41no—
186D4×C151—41no—
187D4×C151—42no—
188D4×C151—42no—
189D4×C151—84no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—24no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—48no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—84no—
212C2×C4×C151#12112yes—
213C2×C4×C151C22×D411yescharacteristic
214C2×C4×C151C2×#4112yes—
215C2×C4×C151C2×#4111yescharacteristic
216C2×C4×C151H(5,𝔽2)12yes—
217C8×C151—41no—
218C8×C151—42no—
219C8×C151—41no—
220C22×C151—22no—
221C22×C151—22no—
222C22×C151—22no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—82no—
229C22×C151—82no—
230C22×C151—81no—
231C22×C151—81no—
232C22×C151—81no—
233C22×C151—82no—
234C22×C151—82no—
235C22×C151C2×#12111yescharacteristic
236C22×C151#54612yes—
237C22×C151#57512yes—
238C22×C151#57611yescharacteristic
239C22×C151#57711yescharacteristic
240C4×C151—22no—
241C4×C151—24no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151—81no—
245C4×C151—82no—
246C4×C151—82no—
247C4×C151C2×#12311yescharacteristic
248C4×C151#53411yescharacteristic
249C4×C151#55112yes—
250C2×C151—42no—
251C2×C151—82no—
252C2×C151—161no—
253C2×C151#241211yescharacteristic
254C2×C151#304011yescharacteristic
255C2×C151#304511yescharacteristic
256C2×C151#330912yes—
257C2×C151#332612yes—
258#24547C15111yesmaximal, characteristic, direct product factor, Sylow
259C151#2454711yescharacteristic, direct product factor, Sylow
260C2×#449C2×C15111yescharacteristic
261C2×#417C2×C15111yescharacteristic, complemented
262#2504C2×C15111yescharacteristic, complemented
263#2341C2×C15111yescharacteristic, complemented
264#2073C2×C15112yescomplemented
265#2054C2×C15112yescomplemented
266#1895C2×C15111yescharacteristic, complemented
267#1880C2×C15112yescomplemented
268#1851C2×C15111yescharacteristic, complemented
269#1823C2×C15111yescharacteristic, complemented
270#1805C2×C15112yescomplemented
271C22×#41C22×C15111yescharacteristic
272C22×SD16C22×C15111yescharacteristic
273C22×D8C22×C15111yescharacteristic
274C22×M16C22×C15111yescharacteristic
275C2×#121C22×C15111yescharacteristic
276C2×C4×Q8C22×C15112yes—
277C22×C4⋊C4C22×C15111yescharacteristic
278#449—24no—
279C2×C4⋊C8C22×C15112yes—
280#417—24no—
281C2×#103C22×C15111yescharacteristic
282C2×#103C22×C15112yes—
283C2×#102C22×C15112yes—
284C2×#102C22×C15111yescharacteristic
285C2×#102C22×C15112yes—
286C2×C22⋊C8C22×C15111yescharacteristic
287#397—21no—
288#397—21no—
289#390—22no—
290#390C22×C15112yes—
291#390C22×C15112yes—
292#386—22no—
293#382C22×C15112yes—
294#380—21no—
295#380C22×C15111yescharacteristic
296C4×C22⋊C4—21no—
297C4×C22⋊C4C22×C15111yescharacteristic
298#340C22×C15112yes—
299#340C22×C15112yes—
300#340C22×C15112yes—
301#336C22×C15112yes—
302C2×#41—22no—
303C2×#41—24no—
304C2×#41—42no—
305C2×#41D4×C15114yes—
306C22×Q8C23×C15111yescharacteristic
307C22×D4—21no—
308C22×D4—21no—
309C22×D4C23×C15111yescharacteristic
310C22×D4C23×C15111yescharacteristic
311C23×C4—21no—
312C23×C4—21no—
313C23×C4C23×C15111yescharacteristic
314C2×SD16—24no—
315C2×SD16—22no—
316C2×D8—22no—
317C2×D8—42no—
318C2×M16—22no—
319C2×M16—42no—
320C22×C8C23×C15112yes—
321C22×C8C23×C15111yescharacteristic
322C22×C8C23×C15111yescharacteristic
323#121—22no—
324#121—22no—
325C4×Q8—24no—
326C4×Q8—42no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4C23×C15112yes—
332C2×C4⋊C4C23×C15112yes—
333C2×C4⋊C4C23×C15111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4D4×C15112yes—
341C2×C42—22no—
342C2×C42C23×C15112yes—
343C4⋊C8—42no—
344#103—24no—
345#103—22no—
346#102—24no—
347#102—22no—
348#102—42no—
349C22⋊C8—22no—
350#95—21no—
351#95—22no—
352#95—22no—
353#95D4×C15111yescharacteristic
354#95D4×C15111yescharacteristic
355C24—21no—
356C24—21no—
357C24C2×D4×C15111yescharacteristic
358#41—28no—
359#41—44no—
360#41—48no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8C2×D4×C15112yes—
364C2×Q8#41×C15114yes—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—44no—
374C2×D4—44no—
375C2×D4—42no—
376C2×D4C2×D4×C15112yes—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—81no—
387C22×C4—81no—
388C22×C4C2×D4×C15112yes—
389C22×C4C2×D4×C15112yes—
390C22×C4C2×D4×C15111yescharacteristic
391C22×C4C2×D4×C15112yes—
392C22×C4#41×C15112yes—
393C22×C4C24×C15111yescharacteristic
394SD16—44no—
395D8—44no—
396M16—44no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—44no—
411C4⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—44no—
414C22⋊C4—42no—
415C22⋊C4—82no—
416C22⋊C4—82no—
417C22⋊C4—82no—
418C22⋊C4—81no—
419C42—22no—
420C42—22no—
421C42—44no—
422C23—22no—
423C23—22no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—42no—
428C23—42no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23#121×C15112yes—
437C23C22×D4×C15111yescharacteristic
438Q8—22no—
439Q8—24no—
440Q8#123×C15114yes—
441D4—22no—
442D4—22no—
443D4—48no—
444D4—41no—
445D4—41no—
446D4—42no—
447D4—42no—
448D4—84no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—48no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4#121×C15112yes—
472C2×C4C22×D4×C15111yescharacteristic
473C2×C4C2×#41×C15112yes—
474C2×C4C2×#41×C15111yescharacteristic
475C2×C4H(5,𝔽2)×C15112yes—
476C8—41no—
477C8—42no—
478C8—41no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—82no—
488C22—82no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—82no—
493C22—82no—
494C22C2×#121×C15111yescharacteristic
495C22#546×C15112yes—
496C22#575×C15112yes—
497C22#576×C15111yescharacteristic
498C22#577×C15111yescharacteristic
499C4—22no—
500C4—24no—
501C4—42no—
502C4—42no—
503C4—81no—
504C4—82no—
505C4—82no—
506C4C2×#123×C15111yescharacteristic
507C4#534×C15111yescharacteristic
508C4#551×C15112yes—
509C2—42no—
510C2—82no—
511C2—161no—
512C2#2412×C15111yescharacteristic
513C2#3040×C15111yescharacteristic
514C2#3045×C15111yescharacteristic
515C2#3309×C15112yes—
516C2#3326×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#417×C151C2semidirect
3. #2504×C151C2semidirect
4. #2341×C151C2semidirect
5. #2073×C151C2semidirect
6. #2054×C151C2semidirect
7. #1895×C151C2semidirect
8. #1880×C151C2semidirect
9. #1851×C151C2semidirect
10. #1823×C151C2semidirect
11. #1805×C151C2semidirect
258. #24547C151direct (N × H)
259. C151#24547direct (N × H)
261. C2×#417C2×C151semidirect
262. #2504C2×C151semidirect
263. #2341C2×C151semidirect
264. #2073C2×C151semidirect
265. #2054C2×C151semidirect
266. #1895C2×C151semidirect
267. #1880C2×C151semidirect
268. #1851C2×C151semidirect
269. #1823C2×C151semidirect
270. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1512
C2×#417×C1512
#2504×C1512
#2341×C1512
#2073×C1512
#2054×C1512
#1895×C1512
#1880×C1512
#1851×C1512
#1823×C1512
#1805×C1512
#24547151