Finite Group Databasebeta

← C151×#18758 #50323683

Subgroups — C151×#18758 #50323683

Order 38656.

1192 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic, complemented
2#3227×C151C211yesmaximal, characteristic, complemented
3#3103×C151C211yesmaximal, characteristic, complemented
4#3036×C151C211yesmaximal, characteristic
5#1651×C151C214yesmaximal, complemented
6#1627×C151C214yesmaximal, complemented
7#1549×C151C211yesmaximal, characteristic, complemented
8#1487×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10C23×Q8×C151—21no—
11C2×AGL(1,ℤ/8)×C151—21no—
12D4×Q8×C151—22no—
13D4×Q8×C151—22no—
14D4×Q8×C151—22no—
15D4×Q8×C151C2214yes—
16#532×C151C2211yescharacteristic
17C2×C4⋊Q8×C151—21no—
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151—22no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24#498×C151C2212yescomplemented
25#486×C151C2212yescomplemented
26#481×C151—21no—
27#481×C151—22no—
28#476×C151—22no—
29#475×C151C2212yescomplemented
30#463×C151—22no—
31#461×C151C2212yes—
32#460×C151C2212yescomplemented
33#459×C151C2212yes—
34#448×C151—21no—
35C4×SD16×C151—22no—
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38#423×C151C2211yescharacteristic
39#417×C151—21no—
40#332×C151C2214yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151—22no—
45C22×Q8×C151—24no—
46C22×Q8×C151—21no—
47C22×Q8×C151—24no—
48C22×Q8×C151—48no—
49C22×Q8×C151D411yescharacteristic
50C22×D4×C151D411yescharacteristic
51C23×C4×C151—22no—
52C23×C4×C151—21no—
53AGL(1,ℤ/8)×C151—44no—
54C2×SD16×C151—22no—
55C2×SD16×C151—22no—
56C2×D8×C151—22no—
57C2×M16×C151—21no—
58C4⋊Q8×C151—24no—
59C4⋊Q8×C151—24no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151D412yes—
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2312yes—
65#127×C151C2311yescharacteristic
66#124×C151—21no—
67C22⋊Q8×C151—28no—
68C22⋊Q8×C151—24no—
69C22⋊Q8×C151—28no—
70C22⋊Q8×C151—24no—
71#121×C151—21no—
72#121×C151—21no—
73C4×Q8×C151—21no—
74C4×Q8×C151—21no—
75C4×Q8×C151D412yes—
76C4×Q8×C151C2312yes—
77C4×D4×C151—24no—
78C4×D4×C151—24no—
79C4×D4×C151—21no—
80C4×D4×C151—21no—
81C4×D4×C151—21no—
82C4×D4×C151—21no—
83C4×D4×C151D412yes—
84C4×D4×C151C2312yes—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151D411yescharacteristic
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151D412yes—
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151C2311yescharacteristic
95#106×C151—22no—
96#106×C151—24no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151—21no—
99C4⋊C8×C151C2312yes—
100C4⋊C8×C151C2312yes—
101#103×C151—22no—
102#103×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—24no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110C24×C151—21no—
111#41×C151—42no—
112#41×C151—42no—
113C2×Q8×C151—24no—
114C2×Q8×C151—28no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—21no—
119C2×Q8×C151—48no—
120C2×Q8×C151—44no—
121C2×Q8×C151—416no—
122C2×Q8×C151—48no—
123C2×Q8×C151—48no—
124C2×Q8×C151C2×D412yes—
125C2×D4×C151—21no—
126C2×D4×C151—22no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151—21no—
130C2×D4×C151—41no—
131C2×D4×C151SD1614yescomplemented
132C2×D4×C151C2×D412yes—
133C22×C4×C151—21no—
134C22×C4×C151—28no—
135C22×C4×C151—21no—
136C22×C4×C151—22no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—48no—
141C22×C4×C151—44no—
142C22×C4×C151—41no—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146SD16×C151—44no—
147SD16×C151—44no—
148D8×C151—44no—
149M16×C151—42no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C4⋊C4×C151—28no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151C2×D412yes—
164C4⋊C4×C151C2×D412yes—
165C4⋊C4×C151C2×D414yes—
166C22⋊C4×C151—28no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—41no—
170C22⋊C4×C151—41no—
171C42×C151—22no—
172C42×C151—22no—
173C42×C151C2×D411yescharacteristic
174C42×C151C2×D411yescharacteristic
175C42×C151C2×D411yescharacteristic
176C42×C151C2411yescharacteristic
177C23×C151—22no—
178C23×C151—24no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—41no—
182C23×C151#12011yescharacteristic
183Q8×C151—24no—
184Q8×C151—22no—
185Q8×C151—416no—
186Q8×C151—44no—
187Q8×C151—44no—
188Q8×C151—41no—
189Q8×C151—41no—
190Q8×C151AGL(1,ℤ/8)14yescomplemented
191D4×C151—22no—
192D4×C151—24no—
193D4×C151—42no—
194D4×C151—41no—
195D4×C151—42no—
196D4×C151—41no—
197D4×C151—82no—
198D4×C151C2×SD1614yes—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—22no—
205C2×C4×C151—41no—
206C2×C4×C151—416no—
207C2×C4×C151—44no—
208C2×C4×C151—44no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—44no—
212C2×C4×C151—41no—
213C2×C4×C151—82no—
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12011yescharacteristic
217C2×C4×C151C2×SD1612yes—
218C2×C4×C151#13712yes—
219C2×C4×C151C22×D411yescharacteristic
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×D411yescharacteristic
222C8×C151—42no—
223C8×C151—42no—
224C8×C151—42no—
225C22×C151—21no—
226C22×C151—21no—
227C22×C151—24no—
228C22×C151—48no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—81no—
232C22×C151—81no—
233C22×C151—81no—
234C22×C151#44812yes—
235C22×C151C2×#12011yescharacteristic
236C4×C151—24no—
237C4×C151—21no—
238C4×C151—21no—
239C4×C151—21no—
240C4×C151—44no—
241C4×C151—42no—
242C4×C151—42no—
243C4×C151—81no—
244C4×C151#44812yes—
245C4×C151C22×SD1611yescharacteristic
246C4×C151C2×AGL(1,ℤ/8)12yes—
247C4×C151C2×#13711yescharacteristic
248C2×C151—22no—
249C2×C151—44no—
250C2×C151—161no—
251C2×C151C2×#44811yescharacteristic
252C2×C151#300311yescharacteristic
253C2×C151#302011yescharacteristic
254#18758C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#1875811yescharacteristic, direct product factor, Sylow
256C2×D4×Q8C2×C15111yescharacteristic, complemented
257#3227C2×C15111yescharacteristic, complemented
258#3103C2×C15111yescharacteristic, complemented
259#3036C2×C15111yescharacteristic
260#1651C2×C15114yescomplemented
261#1627C2×C15114yescomplemented
262#1549C2×C15111yescharacteristic, complemented
263#1487C2×C15111yescharacteristic, complemented
264#1478C2×C15111yescharacteristic, complemented
265C23×Q8—21no—
266C2×AGL(1,ℤ/8)—21no—
267D4×Q8—22no—
268D4×Q8—22no—
269D4×Q8—22no—
270D4×Q8C22×C15114yes—
271#532C22×C15111yescharacteristic
272C2×C4⋊Q8—21no—
273C2×C4⋊Q8C22×C15111yescharacteristic
274C2×C22⋊Q8—21no—
275C2×C22⋊Q8—22no—
276C2×C4×Q8C22×C15111yescharacteristic
277C2×C4×D4—21no—
278C2×C4×D4C22×C15111yescharacteristic
279#498C22×C15112yescomplemented
280#486C22×C15112yescomplemented
281#481—21no—
282#481—22no—
283#476—22no—
284#475C22×C15112yescomplemented
285#463—22no—
286#461C22×C15112yes—
287#460C22×C15112yescomplemented
288#459C22×C15112yes—
289#448—21no—
290C4×SD16—22no—
291#431C22×C15111yescharacteristic
292#431C22×C15111yescharacteristic
293#423C22×C15111yescharacteristic
294#417—21no—
295#332C22×C15114yescomplemented
296Q8⋊C8C22×C15114yescomplemented
297D4⋊C8C22×C15114yes—
298C2×#41—21no—
299C22×Q8—22no—
300C22×Q8—24no—
301C22×Q8—24no—
302C22×Q8—21no—
303C22×Q8—48no—
304C22×Q8D4×C15111yescharacteristic
305C22×D4D4×C15111yescharacteristic
306C23×C4—22no—
307C23×C4—21no—
308AGL(1,ℤ/8)—44no—
309C2×SD16—22no—
310C2×SD16—22no—
311C2×D8—22no—
312C2×M16—21no—
313C4⋊Q8—24no—
314C4⋊Q8—24no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8D4×C15112yes—
318C4⋊Q8C23×C15111yescharacteristic
319C4⋊Q8C23×C15112yes—
320#127C23×C15111yescharacteristic
321#124—21no—
322C22⋊Q8—24no—
323C22⋊Q8—28no—
324C22⋊Q8—24no—
325C22⋊Q8—28no—
326#121—21no—
327#121—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8D4×C15112yes—
331C4×Q8C23×C15112yes—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4D4×C15112yes—
339C4×D4C23×C15112yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4D4×C15111yescharacteristic
344C2×C4⋊C4D4×C15111yescharacteristic
345C2×C4⋊C4D4×C15112yes—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C42—21no—
349C2×C42C23×C15111yescharacteristic
350#106—22no—
351#106—24no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8C23×C15112yes—
355C4⋊C8C23×C15112yes—
356#103—22no—
357#103—22no—
358#102—22no—
359#102—22no—
360#102—24no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C4×C8—21no—
364C4×C8C23×C15112yes—
365C24—21no—
366#41—42no—
367#41—42no—
368C2×Q8—24no—
369C2×Q8—28no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—48no—
375C2×Q8—44no—
376C2×Q8—416no—
377C2×Q8—48no—
378C2×Q8—48no—
379C2×Q8C2×D4×C15112yes—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4SD16×C15114yescomplemented
387C2×D4C2×D4×C15112yes—
388C22×C4—21no—
389C22×C4—28no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—48no—
396C22×C4—44no—
397C22×C4—41no—
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15111yescharacteristic
400C22×C4C2×D4×C15111yescharacteristic
401SD16—44no—
402SD16—44no—
403D8—44no—
404M16—42no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C4⋊C4—28no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4C2×D4×C15112yes—
419C4⋊C4C2×D4×C15112yes—
420C4⋊C4C2×D4×C15114yes—
421C22⋊C4—28no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C42—22no—
427C42—22no—
428C42C2×D4×C15111yescharacteristic
429C42C2×D4×C15111yescharacteristic
430C42C2×D4×C15111yescharacteristic
431C42C24×C15111yescharacteristic
432C23—24no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23—41no—
437C23#120×C15111yescharacteristic
438Q8—24no—
439Q8—22no—
440Q8—416no—
441Q8—44no—
442Q8—44no—
443Q8—41no—
444Q8—41no—
445Q8AGL(1,ℤ/8)×C15114yescomplemented
446D4—24no—
447D4—22no—
448D4—42no—
449D4—41no—
450D4—42no—
451D4—41no—
452D4—82no—
453D4C2×SD16×C15114yes—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—416no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4#120×C15111yescharacteristic
470C2×C4#120×C15111yescharacteristic
471C2×C4#120×C15111yescharacteristic
472C2×C4C2×SD16×C15112yes—
473C2×C4#137×C15112yes—
474C2×C4C22×D4×C15111yescharacteristic
475C2×C4C22×D4×C15111yescharacteristic
476C2×C4C22×D4×C15111yescharacteristic
477C8—42no—
478C8—42no—
479C8—42no—
480C22—21no—
481C22—21no—
482C22—24no—
483C22—48no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22#448×C15112yes—
490C22C2×#120×C15111yescharacteristic
491C4—24no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—42no—
497C4—42no—
498C4—81no—
499C4#448×C15112yes—
500C4C22×SD16×C15111yescharacteristic
501C4C2×AGL(1,ℤ/8)×C15112yes—
502C4C2×#137×C15111yescharacteristic
503C2—22no—
504C2—44no—
505C2—161no—
506C2C2×#448×C15111yescharacteristic
507C2#3003×C15111yescharacteristic
508C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3036×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D4×Q8×C151C2semidirect
2. #3227×C151C2semidirect
3. #3103×C151C2semidirect
5. #1651×C151C2semidirect
6. #1627×C151C2semidirect
7. #1549×C151C2semidirect
8. #1487×C151C2semidirect
9. #1478×C151C2semidirect
24. #498×C151C22semidirect
25. #486×C151C22semidirect
29. #475×C151C22semidirect
32. #460×C151C22semidirect
40. #332×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
131. C2×D4×C151SD16semidirect
190. Q8×C151AGL(1,ℤ/8)semidirect
254. #18758C151direct (N × H)
255. C151#18758direct (N × H)
256. C2×D4×Q8C2×C151semidirect
257. #3227C2×C151semidirect
258. #3103C2×C151semidirect
260. #1651C2×C151semidirect
261. #1627C2×C151semidirect
262. #1549C2×C151semidirect
263. #1487C2×C151semidirect
264. #1478C2×C151semidirect
279. #498C22×C151semidirect
280. #486C22×C151semidirect
284. #475C22×C151semidirect
287. #460C22×C151semidirect
295. #332C22×C151semidirect
296. Q8⋊C8C22×C151semidirect
386. C2×D4SD16×C151semidirect
445. Q8AGL(1,ℤ/8)×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1512
#3227×C1512
#3103×C1512
#3036×C1512
#1651×C1512
#1627×C1512
#1549×C1512
#1487×C1512
#1478×C1512
#18758151