Finite Group Databasebeta

← C151×#24828 #50329753

Subgroups — C151×#24828 #50329753

Order 38656.

824 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#475×C151C211yesmaximal, characteristic, complemented
2C2×#440×C151C211yesmaximal, characteristic
3#2563×C151C211yesmaximal, characteristic
4#2351×C151C211yesmaximal, characteristic, complemented
5#2085×C151C212yesmaximal, complemented
6#2065×C151C212yesmaximal
7#1993×C151C211yesmaximal, characteristic, complemented
8#1940×C151C211yesmaximal, characteristic, complemented
9#1880×C151C212yesmaximal
10#1805×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic
12C22×SD16×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×Q8×C151C2212yes—
15C2×C4×Q8×C151C2211yescharacteristic
16C2×C4×D4×C151C2211yescharacteristic
17#475×C151—24no—
18#440×C151—24no—
19C2×#107×C151C2211yescharacteristic
20C2×#106×C151C2212yes—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2212yes—
27C2×#97×C151C2211yescharacteristic
28#393×C151—21no—
29#393×C151—21no—
30#390×C151C2212yes—
31#389×C151—22no—
32#389×C151C2212yes—
33#382×C151—21no—
34#382×C151C2212yes—
35#382×C151C2211yescharacteristic
36#380×C151—22no—
37C4×C4⋊C4×C151—21no—
38C4×C4⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151Q814yescomplemented
50C22×C8×C151C2312yes—
51C22×C8×C151C2311yescharacteristic
52C22×C8×C151C2311yescharacteristic
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55C4×Q8×C151—22no—
56C4×Q8×C151—24no—
57C4×Q8×C151—42no—
58C4×Q8×C151D414yes—
59C4×D4×C151—22no—
60C4×D4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151D412yes—
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C42×C151—21no—
74C2×C42×C151—22no—
75C2×C42×C151C2312yes—
76C2×C42×C151C2311yescharacteristic
77#107×C151—22no—
78#106×C151—24no—
79C4⋊C8×C151—22no—
80C4⋊C8×C151—42no—
81#103×C151—22no—
82#103×C151—24no—
83#102×C151—22no—
84#102×C151—42no—
85#97×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151—21no—
91#95×C151D411yescharacteristic
92#95×C151D411yescharacteristic
93C24×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151—42no—
98C2×Q8×C151—82no—
99C2×Q8×C151C2×D412yes—
100C2×Q8×C151C2×Q812yes—
101C2×Q8×C151#4112yes—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151C2×Q812yes—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—44no—
114C22×C4×C151—42no—
115C22×C4×C151C2×D412yes—
116C22×C4×C151C2×D412yes—
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2411yescharacteristic
120SD16×C151—28no—
121C2×C8×C151—21no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—22no—
125C2×C8×C151—22no—
126C2×C8×C151—21no—
127C2×C8×C151—22no—
128C2×C8×C151—21no—
129C2×C8×C151C2×Q812yes—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—42no—
139C4⋊C4×C151—44no—
140C4⋊C4×C151—44no—
141C4⋊C4×C151—42no—
142C4⋊C4×C151C2×D412yes—
143C22⋊C4×C151—42no—
144C22⋊C4×C151—82no—
145C22⋊C4×C151—82no—
146C42×C151—24no—
147C42×C151—22no—
148C42×C151—22no—
149C42×C151—44no—
150C42×C151C2×D412yes—
151C42×C151#4112yes—
152C23×C151—22no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—42no—
156C23×C151—42no—
157C23×C151C22×D411yescharacteristic
158Q8×C151—22no—
159Q8×C151—22no—
160Q8×C151—22no—
161Q8×C151—84no—
162Q8×C151C22⋊Q814yes—
163D4×C151—22no—
164D4×C151—22no—
165D4×C151—41no—
166D4×C151—41no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—41no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—84no—
189C2×C4×C151#12112yes—
190C2×C4×C151#12112yes—
191C2×C4×C151C22×D411yescharacteristic
192C2×C4×C151C22×Q811yescharacteristic
193C2×C4×C151C2×#4111yescharacteristic
194C2×C4×C151C2×#4111yescharacteristic
195C2×C4×C151H(5,𝔽2)11yescharacteristic
196C2×C4×C1512−1+411yescharacteristic
197C8×C151—22no—
198C8×C151—41no—
199C8×C151—42no—
200C22×C151—44no—
201C22×C151—42no—
202C22×C151—81no—
203C22×C151—81no—
204C22×C151—82no—
205C22×C151C2×#12111yescharacteristic
206C22×C151#54611yescharacteristic
207C22×C151D4×Q811yescharacteristic
208C22×C151#57512yes—
209C22×C151#57712yes—
210C4×C151—24no—
211C4×C151—22no—
212C4×C151—22no—
213C4×C151—42no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—81no—
217C4×C151—82no—
218C4×C151—82no—
219C4×C151C2×C22⋊Q811yescharacteristic
220C4×C151#53711yescharacteristic
221C4×C151#55211yescharacteristic
222C4×C151#55411yescharacteristic
223C2×C151—82no—
224C2×C151#241711yescharacteristic
225C2×C151#304011yescharacteristic
226C2×C151#304311yescharacteristic
227C2×C151#332112yes—
228C2×C151#338812yes—
229#24828C15111yesmaximal, characteristic, direct product factor, Sylow
230C151#2482811yescharacteristic, direct product factor, Sylow
231C2×#475C2×C15111yescharacteristic, complemented
232C2×#440C2×C15111yescharacteristic
233#2563C2×C15111yescharacteristic
234#2351C2×C15111yescharacteristic, complemented
235#2085C2×C15112yescomplemented
236#2065C2×C15112yes—
237#1993C2×C15111yescharacteristic, complemented
238#1940C2×C15111yescharacteristic, complemented
239#1880C2×C15112yes—
240#1805C2×C15112yescomplemented
241#1804C2×C15111yescharacteristic
242C22×SD16C22×C15111yescharacteristic
243C2×C4⋊Q8C22×C15111yescharacteristic
244C2×C4×Q8C22×C15112yes—
245C2×C4×Q8C22×C15111yescharacteristic
246C2×C4×D4C22×C15111yescharacteristic
247#475—24no—
248#440—24no—
249C2×#107C22×C15111yescharacteristic
250C2×#106C22×C15112yes—
251C2×C4⋊C8C22×C15111yescharacteristic
252C2×C4⋊C8C22×C15112yes—
253C2×#103C22×C15112yes—
254C2×#103C22×C15111yescharacteristic
255C2×#102C22×C15111yescharacteristic
256C2×#102C22×C15112yes—
257C2×#97C22×C15111yescharacteristic
258#393—21no—
259#393—21no—
260#390C22×C15112yes—
261#389—22no—
262#389C22×C15112yes—
263#382—21no—
264#382C22×C15112yes—
265#382C22×C15111yescharacteristic
266#380—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4C22×C15111yescharacteristic
269#340C22×C15112yes—
270#340C22×C15112yes—
271#340C22×C15112yes—
272#336C22×C15112yes—
273C22×Q8—21no—
274C22×Q8C23×C15111yescharacteristic
275C22×D4C23×C15111yescharacteristic
276C23×C4—21no—
277C2×SD16—22no—
278C2×SD16—22no—
279C2×SD16Q8×C15114yescomplemented
280C22×C8C23×C15112yes—
281C22×C8C23×C15111yescharacteristic
282C22×C8C23×C15111yescharacteristic
283C4⋊Q8—22no—
284C4⋊Q8—22no—
285C4×Q8—22no—
286C4×Q8—24no—
287C4×Q8—42no—
288C4×Q8D4×C15114yes—
289C4×D4—22no—
290C4×D4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4D4×C15112yes—
296C2×C4⋊C4C23×C15111yescharacteristic
297C2×C4⋊C4C23×C15112yes—
298C2×C4⋊C4C23×C15112yes—
299C2×C4⋊C4C23×C15111yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C42—21no—
304C2×C42—22no—
305C2×C42C23×C15112yes—
306C2×C42C23×C15111yescharacteristic
307#107—22no—
308#106—24no—
309C4⋊C8—22no—
310C4⋊C8—42no—
311#103—22no—
312#103—24no—
313#102—22no—
314#102—42no—
315#97—22no—
316#95—21no—
317#95—22no—
318#95—22no—
319#95—22no—
320#95—21no—
321#95D4×C15111yescharacteristic
322#95D4×C15111yescharacteristic
323C24—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—42no—
328C2×Q8—82no—
329C2×Q8C2×D4×C15112yes—
330C2×Q8C2×Q8×C15112yes—
331C2×Q8#41×C15112yes—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4C2×Q8×C15112yes—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—44no—
344C22×C4—42no—
345C22×C4C2×D4×C15112yes—
346C22×C4C2×D4×C15112yes—
347C22×C4C2×D4×C15111yescharacteristic
348C22×C4C2×D4×C15111yescharacteristic
349C22×C4C24×C15111yescharacteristic
350SD16—28no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—21no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8C2×Q8×C15112yes—
360C4⋊C4—24no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—42no—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4—42no—
372C4⋊C4C2×D4×C15112yes—
373C22⋊C4—42no—
374C22⋊C4—82no—
375C22⋊C4—82no—
376C42—24no—
377C42—22no—
378C42—22no—
379C42—44no—
380C42C2×D4×C15112yes—
381C42#41×C15112yes—
382C23—22no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23C22×D4×C15111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—22no—
391Q8—84no—
392Q8C22⋊Q8×C15114yes—
393D4—22no—
394D4—22no—
395D4—41no—
396D4—41no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—84no—
419C2×C4#121×C15112yes—
420C2×C4#121×C15112yes—
421C2×C4C22×D4×C15111yescharacteristic
422C2×C4C22×Q8×C15111yescharacteristic
423C2×C4C2×#41×C15111yescharacteristic
424C2×C4C2×#41×C15111yescharacteristic
425C2×C4H(5,𝔽2)×C15111yescharacteristic
426C2×C42−1+4×C15111yescharacteristic
427C8—22no—
428C8—41no—
429C8—42no—
430C22—44no—
431C22—42no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22C2×#121×C15111yescharacteristic
436C22#546×C15111yescharacteristic
437C22D4×Q8×C15111yescharacteristic
438C22#575×C15112yes—
439C22#577×C15112yes—
440C4—24no—
441C4—22no—
442C4—22no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—81no—
447C4—82no—
448C4—82no—
449C4C2×C22⋊Q8×C15111yescharacteristic
450C4#537×C15111yescharacteristic
451C4#552×C15111yescharacteristic
452C4#554×C15111yescharacteristic
453C2—82no—
454C2#2417×C15111yescharacteristic
455C2#3040×C15111yescharacteristic
456C2#3043×C15111yescharacteristic
457C2#3321×C15112yes—
458C2#3388×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×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
1. C2×#475×C151C2semidirect
4. #2351×C151C2semidirect
5. #2085×C151C2semidirect
7. #1993×C151C2semidirect
8. #1940×C151C2semidirect
10. #1805×C151C2semidirect
49. C2×SD16×C151Q8semidirect
229. #24828C151direct (N × H)
230. C151#24828direct (N × H)
231. C2×#475C2×C151semidirect
234. #2351C2×C151semidirect
235. #2085C2×C151semidirect
237. #1993C2×C151semidirect
238. #1940C2×C151semidirect
240. #1805C2×C151semidirect
279. C2×SD16Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#475×C1512
C2×#440×C1512
#2563×C1512
#2351×C1512
#2085×C1512
#2065×C1512
#1993×C1512
#1940×C1512
#1880×C1512
#1805×C1512
#1804×C1512
#24828151