Finite Group Databasebeta

← C151×#24969 #50329894

Subgroups — C151×#24969 #50329894

Order 38656.

842 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
1#2538×C151C211yesmaximal, characteristic
2D4×C4⋊C4×C151C211yesmaximal, characteristic
3#2077×C151C212yesmaximal, complemented
4#2035×C151C212yesmaximal, complemented
5#1954×C151C211yesmaximal, characteristic
6#1948×C151C211yesmaximal, characteristic, complemented
7#1872×C151C212yesmaximal, complemented
8#1834×C151C211yesmaximal, characteristic, complemented
9#1823×C151C212yesmaximal, complemented
10#1803×C151C211yesmaximal, characteristic, complemented
11C4×#103×C151C211yesmaximal, characteristic, complemented
12C2×C22⋊Q8×C151C2212yes—
13C2×C4×Q8×C151C2211yescharacteristic
14C2×C4×D4×C151—21no—
15C2×C4×D4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17C2×#106×C151C2212yes—
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#103×C151C2211yescharacteristic
20C2×#103×C151C2211yescharacteristic
21C2×#103×C151C2212yes—
22C2×C22⋊C8×C151C2212yes—
23C2×C22⋊C8×C151C2212yes—
24C2×C4×C8×C151C2211yescharacteristic
25#396×C151—22no—
26#390×C151—21no—
27#389×C151—21no—
28#389×C151—21no—
29#385×C151—22no—
30#384×C151C2211yescharacteristic
31#384×C151C2211yescharacteristic
32#380×C151C2212yes—
33#380×C151C2212yes—
34C4×C4⋊C4×C151C2211yescharacteristic
35#340×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#340×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41C22×Q8×C151C2311yescharacteristic
42C22×D4×C151D411yescharacteristic
43C23×C4×C151—22no—
44C23×C4×C151C2312yes—
45C22×C8×C151C2311yescharacteristic
46C22×C8×C151C2311yescharacteristic
47C22×C8×C151C2312yes—
48C22⋊Q8×C151—24no—
49C22⋊Q8×C151—42no—
50C4×Q8×C151—22no—
51C4×Q8×C151—22no—
52C4×D4×C151—22no—
53C4×D4×C151—22no—
54C4×D4×C151—44no—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—42no—
64C2×C4⋊C4×C151D411yescharacteristic
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2312yes—
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151D412yes—
74C2×C42×C151—21no—
75C2×C42×C151—21no—
76C2×C42×C151C2311yescharacteristic
77#106×C151—42no—
78C4⋊C8×C151—22no—
79#103×C151—22no—
80#103×C151—22no—
81#103×C151—42no—
82C22⋊C8×C151—42no—
83C22⋊C8×C151—42no—
84C4×C8×C151—22no—
85#95×C151—21no—
86#95×C151—22no—
87#95×C151—22no—
88C24×C151C2×D412yes—
89C2×Q8×C151—21no—
90C2×Q8×C151—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151—21no—
93C2×Q8×C151—21no—
94C2×Q8×C151#4112yes—
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C2×D4×C151SD1614yes—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—21no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—44no—
111C22×C4×C151—44no—
112C22×C4×C151—82no—
113C22×C4×C151C2×D412yes—
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2411yescharacteristic
117C2×C8×C151—21no—
118C2×C8×C151—21no—
119C2×C8×C151—21no—
120C2×C8×C151—21no—
121C2×C8×C151—22no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—22no—
125C2×C8×C151—22no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—44no—
137C4⋊C4×C151—44no—
138C4⋊C4×C151—42no—
139C4⋊C4×C151—42no—
140C4⋊C4×C151—42no—
141C4⋊C4×C151—81no—
142C4⋊C4×C151—81no—
143C4⋊C4×C151#4112yes—
144C22⋊C4×C151—24no—
145C22⋊C4×C151—44no—
146C22⋊C4×C151—44no—
147C22⋊C4×C151—82no—
148C42×C151—42no—
149C42×C151—42no—
150C42×C151#4112yes—
151C42×C151#4112yes—
152C23×C151—22no—
153C23×C151—22no—
154C23×C151—22no—
155C23×C151—22no—
156C23×C151—22no—
157C23×C151—22no—
158C23×C151C2×SD1614yes—
159C23×C151C22×D411yescharacteristic
160Q8×C151—22no—
161Q8×C151—22no—
162Q8×C151—41no—
163Q8×C151—41no—
164D4×C151—28no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—41no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—41no—
184C2×C4×C151—41no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—41no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—88no—
193C2×C4×C151#12312yes—
194C2×C4×C151#12312yes—
195C2×C4×C151C2×SD1612yes—
196C2×C4×C151#13712yes—
197C2×C4×C151C2×#4111yescharacteristic
198C2×C4×C151C2×#4111yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C2×C4×C151C2×#4111yescharacteristic
201C2×C4×C151H(5,𝔽2)11yescharacteristic
202C2×C4×C151H(5,𝔽2)11yescharacteristic
203C8×C151—42no—
204C8×C151—41no—
205C8×C151—41no—
206C22×C151—24no—
207C22×C151—24no—
208C22×C151—24no—
209C22×C151—42no—
210C22×C151—42no—
211C22×C151—42no—
212C22×C151—42no—
213C22×C151C2×#12311yescharacteristic
214C22×C151#54611yescharacteristic
215C22×C151#54611yescharacteristic
216C22×C151C22×SD1611yescharacteristic
217C22×C151C2×#13711yescharacteristic
218C22×C151#57611yescharacteristic
219C22×C151#57811yescharacteristic
220C4×C151—22no—
221C4×C151—42no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—82no—
225C4×C151—81no—
226C4×C151—82no—
227C4×C151—81no—
228C4×C151#48314yes—
229C4×C151#52911yescharacteristic
230C4×C151#54011yescharacteristic
231C4×C151#55311yescharacteristic
232C4×C151#55511yescharacteristic
233C2×C151—44no—
234C2×C151#242011yescharacteristic
235C2×C151C2×#48311yescharacteristic
236C2×C151#309811yescharacteristic
237C2×C151#329511yescharacteristic
238C2×C151#329811yescharacteristic
239C2×C151#332811yescharacteristic
240C2×C151#333311yescharacteristic
241#24969C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#2496911yescharacteristic, direct product factor, Sylow
243#2538C2×C15111yescharacteristic
244D4×C4⋊C4C2×C15111yescharacteristic
245#2077C2×C15112yescomplemented
246#2035C2×C15112yescomplemented
247#1954C2×C15111yescharacteristic
248#1948C2×C15111yescharacteristic, complemented
249#1872C2×C15112yescomplemented
250#1834C2×C15111yescharacteristic, complemented
251#1823C2×C15112yescomplemented
252#1803C2×C15111yescharacteristic, complemented
253C4×#103C2×C15111yescharacteristic, complemented
254C2×C22⋊Q8C22×C15112yes—
255C2×C4×Q8C22×C15111yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C22×C15111yescharacteristic
258C22×C4⋊C4C22×C15112yes—
259C2×#106C22×C15112yes—
260C2×C4⋊C8C22×C15111yescharacteristic
261C2×#103C22×C15111yescharacteristic
262C2×#103C22×C15111yescharacteristic
263C2×#103C22×C15112yes—
264C2×C22⋊C8C22×C15112yes—
265C2×C22⋊C8C22×C15112yes—
266C2×C4×C8C22×C15111yescharacteristic
267#396—22no—
268#390—21no—
269#389—21no—
270#389—21no—
271#385—22no—
272#384C22×C15111yescharacteristic
273#384C22×C15111yescharacteristic
274#380C22×C15112yes—
275#380C22×C15112yes—
276C4×C4⋊C4C22×C15111yescharacteristic
277#340C22×C15112yes—
278#340C22×C15111yescharacteristic
279#340C22×C15112yes—
280#340C22×C15111yescharacteristic
281#340C22×C15112yes—
282#340C22×C15112yes—
283C22×Q8C23×C15111yescharacteristic
284C22×D4D4×C15111yescharacteristic
285C23×C4—22no—
286C23×C4C23×C15112yes—
287C22×C8C23×C15111yescharacteristic
288C22×C8C23×C15111yescharacteristic
289C22×C8C23×C15112yes—
290C22⋊Q8—24no—
291C22⋊Q8—42no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—44no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4D4×C15111yescharacteristic
307C2×C4⋊C4C23×C15112yes—
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C4⋊C4C23×C15112yes—
310C2×C4⋊C4C23×C15111yescharacteristic
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4D4×C15112yes—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42C23×C15111yescharacteristic
319#106—42no—
320C4⋊C8—22no—
321#103—22no—
322#103—22no—
323#103—42no—
324C22⋊C8—42no—
325C22⋊C8—42no—
326C4×C8—22no—
327#95—21no—
328#95—22no—
329#95—22no—
330C24C2×D4×C15112yes—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8#41×C15112yes—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4SD16×C15114yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—82no—
355C22×C4C2×D4×C15112yes—
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C2×D4×C15111yescharacteristic
358C22×C4C24×C15111yescharacteristic
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8—22no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—44no—
379C4⋊C4—44no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—81no—
384C4⋊C4—81no—
385C4⋊C4#41×C15112yes—
386C22⋊C4—24no—
387C22⋊C4—44no—
388C22⋊C4—44no—
389C22⋊C4—82no—
390C42—42no—
391C42—42no—
392C42#41×C15112yes—
393C42#41×C15112yes—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23C2×SD16×C15114yes—
401C23C22×D4×C15111yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—41no—
405Q8—41no—
406D4—28no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—88no—
435C2×C4#123×C15112yes—
436C2×C4#123×C15112yes—
437C2×C4C2×SD16×C15112yes—
438C2×C4#137×C15112yes—
439C2×C4C2×#41×C15111yescharacteristic
440C2×C4C2×#41×C15111yescharacteristic
441C2×C4C2×#41×C15111yescharacteristic
442C2×C4C2×#41×C15111yescharacteristic
443C2×C4H(5,𝔽2)×C15111yescharacteristic
444C2×C4H(5,𝔽2)×C15111yescharacteristic
445C8—42no—
446C8—41no—
447C8—41no—
448C22—24no—
449C22—24no—
450C22—24no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22C2×#123×C15111yescharacteristic
456C22#546×C15111yescharacteristic
457C22#546×C15111yescharacteristic
458C22C22×SD16×C15111yescharacteristic
459C22C2×#137×C15111yescharacteristic
460C22#576×C15111yescharacteristic
461C22#578×C15111yescharacteristic
462C4—22no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—82no—
467C4—81no—
468C4—82no—
469C4—81no—
470C4#483×C15114yes—
471C4#529×C15111yescharacteristic
472C4#540×C15111yescharacteristic
473C4#553×C15111yescharacteristic
474C4#555×C15111yescharacteristic
475C2—44no—
476C2#2420×C15111yescharacteristic
477C2C2×#483×C15111yescharacteristic
478C2#3098×C15111yescharacteristic
479C2#3295×C15111yescharacteristic
480C2#3298×C15111yescharacteristic
481C2#3328×C15111yescharacteristic
482C2#3333×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2077×C151C2semidirect
4. #2035×C151C2semidirect
6. #1948×C151C2semidirect
7. #1872×C151C2semidirect
8. #1834×C151C2semidirect
9. #1823×C151C2semidirect
10. #1803×C151C2semidirect
11. C4×#103×C151C2semidirect
241. #24969C151direct (N × H)
242. C151#24969direct (N × H)
245. #2077C2×C151semidirect
246. #2035C2×C151semidirect
248. #1948C2×C151semidirect
249. #1872C2×C151semidirect
250. #1834C2×C151semidirect
251. #1823C2×C151semidirect
252. #1803C2×C151semidirect
253. C4×#103C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2538×C1512
D4×C4⋊C4×C1512
#2077×C1512
#2035×C1512
#1954×C1512
#1948×C1512
#1872×C1512
#1834×C1512
#1823×C1512
#1803×C1512
C4×#103×C1512
#24969151