Finite Group Databasebeta

← C151×#22759 #50327684

Subgroups — C151×#22759 #50327684

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C151C211yesmaximal, characteristic
2#2354×C151C211yesmaximal, characteristic
3Q8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
4#1936×C151C212yesmaximal
5#1919×C151C212yesmaximal, complemented
6#1880×C151C212yesmaximal
7#1834×C151C211yesmaximal, characteristic, complemented
8#1803×C151C211yesmaximal, characteristic, complemented
9#1802×C151C211yesmaximal, characteristic
10#1770×C151C211yesmaximal, characteristic, complemented
11#1763×C151C212yesmaximal, complemented
12C22×SD16×C151C2211yescharacteristic
13C2×C4×Q8×C151C2212yes—
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16C2×#117×C151—21no—
17C4×SD16×C151C418yescomplemented
18C2×#106×C151C2211yescharacteristic
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×#103×C151C2212yes—
21C2×#103×C151C2211yescharacteristic
22C2×#102×C151C2212yes—
23C2×#102×C151C2211yescharacteristic
24C2×#97×C151C2212yes—
25C2×C4×C8×C151C2211yescharacteristic
26#390×C151C2212yes—
27#389×C151—22no—
28#389×C151C2212yes—
29#388×C151—22no—
30#384×C151—21no—
31#384×C151C2211yescharacteristic
32#384×C151C2211yescharacteristic
33#380×C151—21no—
34C4×C4⋊C4×C151—21no—
35C4×C4⋊C4×C151C2212yes—
36C4×C4⋊C4×C151C2211yescharacteristic
37#340×C151C2212yes—
38#340×C151C2212yes—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#336×C151C2212yes—
42C22×Q8×C151C2311yescharacteristic
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C2×SD16×C151—22no—
46C2×SD16×C151—22no—
47C2×SD16×C151C2×C414yes—
48C22×C8×C151C2312yes—
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2311yescharacteristic
51C4×Q8×C151—22no—
52C4×Q8×C151—24no—
53C4×Q8×C151—42no—
54C4×Q8×C151C2×C414yes—
55C4×D4×C151—22no—
56C4×D4×C151C2×C414yes—
57#117×C151—44no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151D411yescharacteristic
66C2×C4⋊C4×C151D411yescharacteristic
67C2×C4⋊C4×C151C2312yes—
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C42×C151—21no—
75C2×C42×C151—22no—
76C2×C42×C151—22no—
77C2×C42×C151C2312yes—
78C2×C42×C151C2311yescharacteristic
79#106×C151C2×C414yes—
80C4⋊C8×C151—22no—
81#103×C151—24no—
82#103×C151C2×C414yes—
83#102×C151—42no—
84#102×C151C2×C414yes—
85#97×C151—42no—
86C4×C8×C151C2×C414yes—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151D412yes—
90C24×C151—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151—21no—
93C2×Q8×C151—21no—
94C2×Q8×C151C22×C412yes—
95C2×Q8×C151#4112yes—
96C2×Q8×C151#4112yes—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151C22×C412yes—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—21no—
106C22×C4×C151—24no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—42no—
110C22×C4×C151—42no—
111C22×C4×C151C2×D412yes—
112C22×C4×C151C2×D412yes—
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2411yescharacteristic
116SD16×C151—28no—
117C2×C8×C151—21no—
118C2×C8×C151—21no—
119C2×C8×C151—21no—
120C2×C8×C151—21no—
121C2×C8×C151—22no—
122C2×C8×C151—22no—
123C2×C8×C151—22no—
124C2×C8×C151C22×C412yes—
125C2×C8×C151C22×C412yes—
126C4⋊C4×C151—24no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—44no—
136C4⋊C4×C151—42no—
137C4⋊C4×C151—42no—
138C4⋊C4×C151—81no—
139C4⋊C4×C151—81no—
140C4⋊C4×C151—82no—
141C4⋊C4×C151C22×C412yes—
142C4⋊C4×C151C22×C412yes—
143C22⋊C4×C151—24no—
144C22⋊C4×C151—44no—
145C22⋊C4×C151—82no—
146C42×C151—24no—
147C42×C151—22no—
148C42×C151—22no—
149C42×C151—44no—
150C42×C151—44no—
151C42×C151C22×C412yes—
152C42×C151#4112yes—
153C23×C151—22no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151—41no—
160C23×C151C22×D411yescharacteristic
161Q8×C151—22no—
162Q8×C151—22no—
163Q8×C151—22no—
164Q8×C151#11714yescomplemented
165D4×C151—22no—
166D4×C151—22no—
167D4×C151—41no—
168D4×C151—41no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—41no—
185C2×C4×C151—41no—
186C2×C4×C151—48no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151C4×D412yes—
194C2×C4×C151C4×D412yes—
195C2×C4×C151AGL(1,ℤ/8)12yes—
196C2×C4×C151#13712yes—
197C2×C4×C151C23×C411yescharacteristic
198C2×C4×C151C2×#4111yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C2×C4×C151C2×#4111yescharacteristic
201C2×C4×C151H(5,𝔽2)11yescharacteristic
202C2×C4×C1512−1+411yescharacteristic
203C8×C151—22no—
204C8×C151—22no—
205C8×C151—42no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151—81no—
210C22×C151—81no—
211C22×C151—81no—
212C22×C151—81no—
213C22×C151C2×C4×D411yescharacteristic
214C22×C151#54611yescharacteristic
215C22×C151#54811yescharacteristic
216C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C151C2×#13711yescharacteristic
218C22×C151#57711yescharacteristic
219C22×C151#57711yescharacteristic
220C4×C151—24no—
221C4×C151—22no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—82no—
227C4×C151—82no—
228C4×C151#44014yes—
229C4×C151C2×#11711yescharacteristic
230C4×C151#52011yescharacteristic
231C4×C151#55211yescharacteristic
232C4×C151#55311yescharacteristic
233C2×C151—82no—
234C2×C151#235211yescharacteristic
235C2×C151C2×#44011yescharacteristic
236C2×C151#295211yescharacteristic
237C2×C151#332911yescharacteristic
238C2×C151#333211yescharacteristic
239C2×C151#336811yescharacteristic
240C2×C151#336911yescharacteristic
241#22759C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#2275911yescharacteristic, direct product factor, Sylow
243C2×C4×SD16C2×C15111yescharacteristic
244#2354C2×C15111yescharacteristic
245Q8×C4⋊C4C2×C15111yescharacteristic, complemented
246#1936C2×C15112yes—
247#1919C2×C15112yescomplemented
248#1880C2×C15112yes—
249#1834C2×C15111yescharacteristic, complemented
250#1803C2×C15111yescharacteristic, complemented
251#1802C2×C15111yescharacteristic
252#1770C2×C15111yescharacteristic, complemented
253#1763C2×C15112yescomplemented
254C22×SD16C22×C15111yescharacteristic
255C2×C4×Q8C22×C15112yes—
256C2×C4×Q8C22×C15111yescharacteristic
257C2×C4×D4C22×C15111yescharacteristic
258C2×#117—21no—
259C4×SD16C4×C15118yescomplemented
260C2×#106C22×C15111yescharacteristic
261C2×C4⋊C8C22×C15111yescharacteristic
262C2×#103C22×C15112yes—
263C2×#103C22×C15111yescharacteristic
264C2×#102C22×C15112yes—
265C2×#102C22×C15111yescharacteristic
266C2×#97C22×C15112yes—
267C2×C4×C8C22×C15111yescharacteristic
268#390C22×C15112yes—
269#389—22no—
270#389C22×C15112yes—
271#388—22no—
272#384—21no—
273#384C22×C15111yescharacteristic
274#384C22×C15111yescharacteristic
275#380—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4C22×C15112yes—
278C4×C4⋊C4C22×C15111yescharacteristic
279#340C22×C15112yes—
280#340C22×C15112yes—
281#340C22×C15112yes—
282#340C22×C15112yes—
283#336C22×C15112yes—
284C22×Q8C23×C15111yescharacteristic
285C22×D4C23×C15111yescharacteristic
286C23×C4—21no—
287C2×SD16—22no—
288C2×SD16—22no—
289C2×SD16C2×C4×C15114yes—
290C22×C8C23×C15112yes—
291C22×C8C23×C15111yescharacteristic
292C22×C8C23×C15111yescharacteristic
293C4×Q8—22no—
294C4×Q8—24no—
295C4×Q8—42no—
296C4×Q8C2×C4×C15114yes—
297C4×D4—22no—
298C4×D4C2×C4×C15114yes—
299#117—44no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4D4×C15111yescharacteristic
308C2×C4⋊C4D4×C15111yescharacteristic
309C2×C4⋊C4C23×C15112yes—
310C2×C4⋊C4C23×C15112yes—
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C4⋊C4C23×C15111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42C23×C15112yes—
320C2×C42C23×C15111yescharacteristic
321#106C2×C4×C15114yes—
322C4⋊C8—22no—
323#103—24no—
324#103C2×C4×C15114yes—
325#102—42no—
326#102C2×C4×C15114yes—
327#97—42no—
328C4×C8C2×C4×C15114yes—
329#95—22no—
330#95—22no—
331#95D4×C15112yes—
332C24—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8C22×C4×C15112yes—
337C2×Q8#41×C15112yes—
338C2×Q8#41×C15112yes—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4C22×C4×C15112yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4C2×D4×C15112yes—
354C22×C4C2×D4×C15112yes—
355C22×C4C2×D4×C15111yescharacteristic
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C24×C15111yescharacteristic
358SD16—28no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8C22×C4×C15112yes—
367C2×C8C22×C4×C15112yes—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—44no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—81no—
381C4⋊C4—81no—
382C4⋊C4—82no—
383C4⋊C4C22×C4×C15112yes—
384C4⋊C4C22×C4×C15112yes—
385C22⋊C4—24no—
386C22⋊C4—44no—
387C22⋊C4—82no—
388C42—24no—
389C42—22no—
390C42—22no—
391C42—44no—
392C42—44no—
393C42C22×C4×C15112yes—
394C42#41×C15112yes—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C22×D4×C15111yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—22no—
406Q8#117×C15114yescomplemented
407D4—22no—
408D4—22no—
409D4—41no—
410D4—41no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—48no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4C4×D4×C15112yes—
436C2×C4C4×D4×C15112yes—
437C2×C4AGL(1,ℤ/8)×C15112yes—
438C2×C4#137×C15112yes—
439C2×C4C23×C4×C15111yescharacteristic
440C2×C4C2×#41×C15111yescharacteristic
441C2×C4C2×#41×C15111yescharacteristic
442C2×C4C2×#41×C15111yescharacteristic
443C2×C4H(5,𝔽2)×C15111yescharacteristic
444C2×C42−1+4×C15111yescharacteristic
445C8—22no—
446C8—22no—
447C8—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C2×C4×D4×C15111yescharacteristic
456C22#546×C15111yescharacteristic
457C22#548×C15111yescharacteristic
458C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
459C22C2×#137×C15111yescharacteristic
460C22#577×C15111yescharacteristic
461C22#577×C15111yescharacteristic
462C4—24no—
463C4—22no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—82no—
469C4—82no—
470C4#440×C15114yes—
471C4C2×#117×C15111yescharacteristic
472C4#520×C15111yescharacteristic
473C4#552×C15111yescharacteristic
474C4#553×C15111yescharacteristic
475C2—82no—
476C2#2352×C15111yescharacteristic
477C2C2×#440×C15111yescharacteristic
478C2#2952×C15111yescharacteristic
479C2#3329×C15111yescharacteristic
480C2#3332×C15111yescharacteristic
481C2#3368×C15111yescharacteristic
482C2#3369×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. Q8×C4⋊C4×C151C2semidirect
5. #1919×C151C2semidirect
7. #1834×C151C2semidirect
8. #1803×C151C2semidirect
10. #1770×C151C2semidirect
11. #1763×C151C2semidirect
17. C4×SD16×C151C4semidirect
164. Q8×C151#117semidirect
241. #22759C151direct (N × H)
242. C151#22759direct (N × H)
245. Q8×C4⋊C4C2×C151semidirect
247. #1919C2×C151semidirect
249. #1834C2×C151semidirect
250. #1803C2×C151semidirect
252. #1770C2×C151semidirect
253. #1763C2×C151semidirect
259. C4×SD16C4×C151semidirect
406. Q8#117×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C1512
#2354×C1512
Q8×C4⋊C4×C1512
#1936×C1512
#1919×C1512
#1880×C1512
#1834×C1512
#1803×C1512
#1802×C1512
#1770×C1512
#1763×C1512
#22759151