Finite Group Databasebeta

← C151×#24197 #50329122

Subgroups — C151×#24197 #50329122

Order 38656.

1116 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C151C211yesmaximal, characteristic, complemented
2C2×#461×C151C211yesmaximal, characteristic, complemented
3C2×#442×C151C211yesmaximal, characteristic
4#2580×C151C211yesmaximal, characteristic, complemented
5#2042×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal
7#1985×C151C211yesmaximal, characteristic, complemented
8#1960×C151C211yesmaximal, characteristic, complemented
9#1880×C151C212yesmaximal, complemented
10#1865×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13C22×D8×C151C2211yescharacteristic
14#556×C151—24no—
15#556×C151—24no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#126×C151—22no—
18C2×#124×C151C2212yes—
19C2×C22⋊Q8×C151—21no—
20C2×C4×Q8×C151C2212yes—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151—21no—
25#461×C151—24no—
26#442×C151—24no—
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2212yes—
30C2×#103×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2212yes—
35C2×#97×C151C2211yescharacteristic
36#399×C151—21no—
37#393×C151—21no—
38#390×C151C2212yes—
39#389×C151C2212yes—
40#385×C151—22no—
41#382×C151C2211yescharacteristic
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151D411yescharacteristic
46C22×Q8×C151C2312yes—
47C22×D4×C151C2311yescharacteristic
48C22×D4×C151C2311yescharacteristic
49C23×C4×C151—21no—
50C23×C4×C151—21no—
51C2×SD16×C151—24no—
52C2×SD16×C151—24no—
53C2×SD16×C151—42no—
54C2×D8×C151—22no—
55C2×D8×C151—22no—
56C2×D8×C151—22no—
57C22×C8×C151C2312yes—
58C22×C8×C151C2311yescharacteristic
59C22×C8×C151C2311yescharacteristic
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151D414yes—
62#126×C151—216no—
63#124×C151—24no—
64#124×C151—24no—
65C22⋊Q8×C151—28no—
66C4×Q8×C151—24no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—24no—
70C4×D4×C151—22no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151D414yes—
74#117×C151—28no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151D412yes—
80C2×C4⋊C4×C151D411yescharacteristic
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—22no—
90C2×C42×C151—22no—
91C2×C42×C151C2312yes—
92C2×C42×C151C2311yescharacteristic
93#106×C151—22no—
94C4⋊C8×C151—22no—
95#103×C151—24no—
96#103×C151—24no—
97#103×C151—42no—
98#102×C151—22no—
99#102×C151—22no—
100#102×C151—42no—
101#97×C151—22no—
102#95×C151—21no—
103#95×C151—21no—
104#95×C151—22no—
105C24×C151—21no—
106C24×C151—21no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—42no—
114C2×Q8×C151C2×D414yes—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151C2×D412yes—
126C2×D4×C151#4112yes—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—21no—
132C22×C4×C151—44no—
133C22×C4×C151—42no—
134C22×C4×C151—82no—
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2×D412yes—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2411yescharacteristic
140SD16×C151—48no—
141D8×C151—28no—
142C2×C8×C151—21no—
143C2×C8×C151—21no—
144C2×C8×C151—21no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151#4112yes—
151C4⋊C4×C151—28no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—82no—
162C4⋊C4×C151C2×D412yes—
163C22⋊C4×C151—28no—
164C22⋊C4×C151—28no—
165C22⋊C4×C151—24no—
166C22⋊C4×C151—44no—
167C22⋊C4×C151—42no—
168C22⋊C4×C151—82no—
169C42×C151—28no—
170C42×C151—22no—
171C42×C151—22no—
172C42×C151C2×D412yes—
173C42×C151C2×D412yes—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151C22×D411yescharacteristic
185Q8×C151—24no—
186Q8×C151—24no—
187Q8×C151—44no—
188Q8×C151—42no—
189Q8×C151—42no—
190D4×C151—22no—
191D4×C151—22no—
192D4×C151—22no—
193D4×C151—22no—
194D4×C151—41no—
195D4×C151—41no—
196D4×C151—41no—
197D4×C151—41no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—24no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—48no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—84no—
218C2×C4×C151#12012yes—
219C2×C4×C151#12012yes—
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×D411yescharacteristic
222C2×C4×C151C2×#4111yescharacteristic
223C2×C4×C151C2×#4111yescharacteristic
224C2×C4×C151H(5,𝔽2)11yescharacteristic
225C2×C4×C1512−1+411yescharacteristic
226C8×C151—22no—
227C8×C151—41no—
228C8×C151—42no—
229C22×C151—44no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—42no—
233C22×C151—42no—
234C22×C151—82no—
235C22×C151—82no—
236C22×C151—82no—
237C22×C151—81no—
238C22×C151—81no—
239C22×C151C2×#12011yescharacteristic
240C22×C151#54811yescharacteristic
241C22×C151#55011yescharacteristic
242C22×C151#57512yes—
243C22×C151#57712yes—
244C4×C151—22no—
245C4×C151—22no—
246C4×C151—44no—
247C4×C151—42no—
248C4×C151—42no—
249C4×C151—42no—
250C4×C151—82no—
251C4×C151—81no—
252C4×C151#52511yescharacteristic
253C4×C151#53711yescharacteristic
254C4×C151#54611yescharacteristic
255C4×C151#54711yescharacteristic
256C2×C151—82no—
257C2×C151—82no—
258C2×C151#240711yescharacteristic
259C2×C151#300511yescharacteristic
260C2×C151#301011yescharacteristic
261C2×C151#337612yes—
262C2×C151#340112yes—
263#24197C15111yesmaximal, characteristic, direct product factor, Sylow
264C151#2419711yescharacteristic, direct product factor, Sylow
265C2×#556C2×C15111yescharacteristic, complemented
266C2×#461C2×C15111yescharacteristic, complemented
267C2×#442C2×C15111yescharacteristic
268#2580C2×C15111yescharacteristic, complemented
269#2042C2×C15112yescomplemented
270#2012C2×C15112yes—
271#1985C2×C15111yescharacteristic, complemented
272#1960C2×C15111yescharacteristic, complemented
273#1880C2×C15112yescomplemented
274#1865C2×C15112yescomplemented
275#1804C2×C15111yescharacteristic, complemented
276C22×SD16C22×C15112yes—
277C22×D8C22×C15111yescharacteristic
278#556—24no—
279#556—24no—
280C2×C4⋊Q8C22×C15111yescharacteristic
281C2×#126—22no—
282C2×#124C22×C15112yes—
283C2×C22⋊Q8—21no—
284C2×C4×Q8C22×C15112yes—
285C2×C4×Q8C22×C15111yescharacteristic
286C2×C4×D4C22×C15111yescharacteristic
287C2×C4×D4C22×C15111yescharacteristic
288C2×#117—21no—
289#461—24no—
290#442—24no—
291C2×#106C22×C15111yescharacteristic
292C2×C4⋊C8C22×C15111yescharacteristic
293C2×#103C22×C15112yes—
294C2×#103C22×C15112yes—
295C2×#103C22×C15112yes—
296C2×#102C22×C15111yescharacteristic
297C2×#102C22×C15111yescharacteristic
298C2×#102C22×C15112yes—
299C2×#97C22×C15111yescharacteristic
300#399—21no—
301#393—21no—
302#390C22×C15112yes—
303#389C22×C15112yes—
304#385—22no—
305#382C22×C15111yescharacteristic
306#340C22×C15112yes—
307#336C22×C15112yes—
308#336C22×C15112yes—
309C22×Q8D4×C15111yescharacteristic
310C22×Q8C23×C15112yes—
311C22×D4C23×C15111yescharacteristic
312C22×D4C23×C15111yescharacteristic
313C23×C4—21no—
314C23×C4—21no—
315C2×SD16—24no—
316C2×SD16—24no—
317C2×SD16—42no—
318C2×D8—22no—
319C2×D8—22no—
320C2×D8—22no—
321C22×C8C23×C15112yes—
322C22×C8C23×C15111yescharacteristic
323C22×C8C23×C15111yescharacteristic
324C4⋊Q8—22no—
325C4⋊Q8D4×C15114yes—
326#126—216no—
327#124—24no—
328#124—24no—
329C22⋊Q8—28no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4D4×C15114yes—
338#117—28no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4D4×C15111yescharacteristic
344C2×C4⋊C4D4×C15112yes—
345C2×C4⋊C4C23×C15111yescharacteristic
346C2×C4⋊C4C23×C15112yes—
347C2×C4⋊C4C23×C15111yescharacteristic
348C2×C22⋊C4—22no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C42—22no—
355C2×C42C23×C15112yes—
356C2×C42C23×C15111yescharacteristic
357#106—22no—
358C4⋊C8—22no—
359#103—24no—
360#103—24no—
361#103—42no—
362#102—22no—
363#102—22no—
364#102—42no—
365#97—22no—
366#95—21no—
367#95—21no—
368#95—22no—
369C24—21no—
370C24—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—42no—
378C2×Q8C2×D4×C15114yes—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4C2×D4×C15112yes—
390C2×D4#41×C15112yes—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—44no—
397C22×C4—42no—
398C22×C4—82no—
399C22×C4C2×D4×C15112yes—
400C22×C4C2×D4×C15112yes—
401C22×C4C2×D4×C15111yescharacteristic
402C22×C4C2×D4×C15111yescharacteristic
403C22×C4C24×C15111yescharacteristic
404SD16—48no—
405D8—28no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8#41×C15112yes—
415C4⋊C4—28no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—82no—
426C4⋊C4C2×D4×C15112yes—
427C22⋊C4—28no—
428C22⋊C4—28no—
429C22⋊C4—24no—
430C22⋊C4—44no—
431C22⋊C4—42no—
432C22⋊C4—82no—
433C42—28no—
434C42—22no—
435C42—22no—
436C42C2×D4×C15112yes—
437C42C2×D4×C15112yes—
438C23—22no—
439C23—22no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23C22×D4×C15111yescharacteristic
449Q8—24no—
450Q8—24no—
451Q8—44no—
452Q8—42no—
453Q8—42no—
454D4—22no—
455D4—22no—
456D4—22no—
457D4—22no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—48no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—84no—
482C2×C4#120×C15112yes—
483C2×C4#120×C15112yes—
484C2×C4C22×D4×C15111yescharacteristic
485C2×C4C22×D4×C15111yescharacteristic
486C2×C4C2×#41×C15111yescharacteristic
487C2×C4C2×#41×C15111yescharacteristic
488C2×C4H(5,𝔽2)×C15111yescharacteristic
489C2×C42−1+4×C15111yescharacteristic
490C8—22no—
491C8—41no—
492C8—42no—
493C22—44no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22—81no—
502C22—81no—
503C22C2×#120×C15111yescharacteristic
504C22#548×C15111yescharacteristic
505C22#550×C15111yescharacteristic
506C22#575×C15112yes—
507C22#577×C15112yes—
508C4—22no—
509C4—22no—
510C4—44no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—82no—
515C4—81no—
516C4#525×C15111yescharacteristic
517C4#537×C15111yescharacteristic
518C4#546×C15111yescharacteristic
519C4#547×C15111yescharacteristic
520C2—82no—
521C2—82no—
522C2#2407×C15111yescharacteristic
523C2#3005×C15111yescharacteristic
524C2#3010×C15111yescharacteristic
525C2#3376×C15112yes—
526C2#3401×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#556×C151C2semidirect
2. C2×#461×C151C2semidirect
4. #2580×C151C2semidirect
5. #2042×C151C2semidirect
7. #1985×C151C2semidirect
8. #1960×C151C2semidirect
9. #1880×C151C2semidirect
10. #1865×C151C2semidirect
11. #1804×C151C2semidirect
263. #24197C151direct (N × H)
264. C151#24197direct (N × H)
265. C2×#556C2×C151semidirect
266. C2×#461C2×C151semidirect
268. #2580C2×C151semidirect
269. #2042C2×C151semidirect
271. #1985C2×C151semidirect
272. #1960C2×C151semidirect
273. #1880C2×C151semidirect
274. #1865C2×C151semidirect
275. #1804C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#461×C1512
C2×#442×C1512
#2580×C1512
#2042×C1512
#2012×C1512
#1985×C1512
#1960×C1512
#1880×C1512
#1865×C1512
#1804×C1512
#24197151