Finite Group Databasebeta

← C151×#24833 #50329758

Subgroups — C151×#24833 #50329758

Order 38656.

868 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic
3#2567×C151C211yesmaximal, characteristic, complemented
4#2349×C151C211yesmaximal, characteristic
5#2083×C151C212yesmaximal, complemented
6#2068×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1940×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal
10#1805×C151C211yesmaximal, characteristic, complemented
11#1802×C151C212yesmaximal
12C22×SD16×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2212yes—
16C2×C4×D4×C151C2211yescharacteristic
17#474×C151—24no—
18#440×C151—24no—
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2212yes—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2212yes—
25C2×#102×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#97×C151C2211yescharacteristic
28#395×C151—21no—
29#395×C151—21no—
30#391×C151C2212yes—
31#389×C151—22no—
32#389×C151C2212yes—
33#385×C151—22no—
34#384×C151C2212yes—
35#382×C151C2211yescharacteristic
36#380×C151—21no—
37C4×C4⋊C4×C151C2211yescharacteristic
38C2×#95×C151—21no—
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—
47C23×C4×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C2×SD16×C151Q814yescomplemented
51C22×C8×C151C2312yes—
52C22×C8×C151C2311yescharacteristic
53C22×C8×C151C2311yescharacteristic
54C4⋊Q8×C151—22no—
55C4⋊Q8×C151—22no—
56C4×Q8×C151—22no—
57C4×Q8×C151—22no—
58C4×D4×C151—24no—
59C4×D4×C151—22no—
60C4×D4×C151—42no—
61C4×D4×C151D414yes—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151D412yes—
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2312yes—
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151—22no—
74C2×C42×C151—21no—
75C2×C42×C151C2312yes—
76C2×C42×C151C2311yescharacteristic
77#107×C151—22no—
78#107×C151—24no—
79C4⋊C8×C151—22no—
80C4⋊C8×C151—42no—
81#103×C151—22no—
82#103×C151—42no—
83#102×C151—22no—
84#102×C151—24no—
85#97×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—21no—
89#95×C151—22no—
90#95×C151—22no—
91#95×C151D411yescharacteristic
92#95×C151D411yescharacteristic
93C24×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151—21no—
98C2×Q8×C151—21no—
99C2×Q8×C151—42no—
100C2×Q8×C151—82no—
101C2×Q8×C151C2×Q812yes—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151C2×D412yes—
106C2×D4×C151C2×Q812yes—
107C2×D4×C151#4112yes—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—24no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—21no—
114C22×C4×C151—44no—
115C22×C4×C151—44no—
116C22×C4×C151—82no—
117C22×C4×C151—82no—
118C22×C4×C151C2×D412yes—
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2×D412yes—
122C22×C4×C151C2411yescharacteristic
123SD16×C151—28no—
124C2×C8×C151—21no—
125C2×C8×C151—21no—
126C2×C8×C151—21no—
127C2×C8×C151—22no—
128C2×C8×C151—22no—
129C2×C8×C151—21no—
130C2×C8×C151—22no—
131C2×C8×C151—21no—
132C2×C8×C151C2×Q812yes—
133C4⋊C4×C151—24no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—42no—
142C4⋊C4×C151—42no—
143C4⋊C4×C151—82no—
144C4⋊C4×C151—82no—
145C4⋊C4×C151—82no—
146C4⋊C4×C151C2×D412yes—
147C22⋊C4×C151—24no—
148C22⋊C4×C151—44no—
149C42×C151—22no—
150C42×C151—22no—
151C42×C151—42no—
152C42×C151C2×D412yes—
153C42×C151#4112yes—
154C23×C151—22no—
155C23×C151—22no—
156C23×C151—22no—
157C23×C151—42no—
158C23×C151—42no—
159C23×C151C22×D411yescharacteristic
160Q8×C151—22no—
161Q8×C151—22no—
162Q8×C151—41no—
163Q8×C151—41no—
164Q8×C151—84no—
165D4×C151—22no—
166D4×C151—22no—
167D4×C151—22no—
168D4×C151C22⋊Q814yes—
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—41no—
179C2×C4×C151—41no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—41no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—84no—
190C2×C4×C151—88no—
191C2×C4×C151#12112yes—
192C2×C4×C151#12112yes—
193C2×C4×C151#13714yes—
194C2×C4×C151C22×D411yescharacteristic
195C2×C4×C151C22×Q811yescharacteristic
196C2×C4×C151C2×#4111yescharacteristic
197C2×C4×C151C2×#4111yescharacteristic
198C2×C4×C151H(5,𝔽2)11yescharacteristic
199C2×C4×C1512−1+411yescharacteristic
200C8×C151—22no—
201C8×C151—41no—
202C8×C151—42no—
203C22×C151—24no—
204C22×C151—44no—
205C22×C151—42no—
206C22×C151—42no—
207C22×C151—44no—
208C22×C151C2×#12111yescharacteristic
209C22×C151#54611yescharacteristic
210C22×C151D4×Q811yescharacteristic
211C22×C151C2×#13712yes—
212C22×C151#57612yes—
213C4×C151—22no—
214C4×C151—22no—
215C4×C151—24no—
216C4×C151—42no—
217C4×C151—42no—
218C4×C151—42no—
219C4×C151—81no—
220C4×C151—82no—
221C4×C151—82no—
222C4×C151C2×C22⋊Q811yescharacteristic
223C4×C151#53711yescharacteristic
224C4×C151#55211yescharacteristic
225C4×C151#55411yescharacteristic
226C2×C151—44no—
227C2×C151#241711yescharacteristic
228C2×C151#303911yescharacteristic
229C2×C151#304111yescharacteristic
230C2×C151#331412yes—
231C2×C151#338512yes—
232#24833C15111yesmaximal, characteristic, direct product factor, Sylow
233C151#2483311yescharacteristic, direct product factor, Sylow
234C2×#474C2×C15111yescharacteristic
235C2×#440C2×C15111yescharacteristic
236#2567C2×C15111yescharacteristic, complemented
237#2349C2×C15111yescharacteristic
238#2083C2×C15112yescomplemented
239#2068C2×C15112yescomplemented
240#1993C2×C15111yescharacteristic, complemented
241#1940C2×C15111yescharacteristic, complemented
242#1877C2×C15112yes—
243#1805C2×C15111yescharacteristic, complemented
244#1802C2×C15112yes—
245C22×SD16C22×C15111yescharacteristic
246C2×C4⋊Q8C22×C15111yescharacteristic
247C2×C4×Q8C22×C15111yescharacteristic
248C2×C4×D4C22×C15112yes—
249C2×C4×D4C22×C15111yescharacteristic
250#474—24no—
251#440—24no—
252C2×#107C22×C15112yes—
253C2×#107C22×C15111yescharacteristic
254C2×C4⋊C8C22×C15111yescharacteristic
255C2×C4⋊C8C22×C15112yes—
256C2×#103C22×C15111yescharacteristic
257C2×#103C22×C15112yes—
258C2×#102C22×C15111yescharacteristic
259C2×#102C22×C15112yes—
260C2×#97C22×C15111yescharacteristic
261#395—21no—
262#395—21no—
263#391C22×C15112yes—
264#389—22no—
265#389C22×C15112yes—
266#385—22no—
267#384C22×C15112yes—
268#382C22×C15111yescharacteristic
269#380—21no—
270C4×C4⋊C4C22×C15111yescharacteristic
271C2×#95—21no—
272#340C22×C15112yes—
273#340C22×C15112yes—
274#340C22×C15112yes—
275#336C22×C15112yes—
276C22×Q8—21no—
277C22×Q8C23×C15111yescharacteristic
278C22×D4C23×C15111yescharacteristic
279C23×C4—21no—
280C23×C4—22no—
281C2×SD16—22no—
282C2×SD16—22no—
283C2×SD16Q8×C15114yescomplemented
284C22×C8C23×C15112yes—
285C22×C8C23×C15111yescharacteristic
286C22×C8C23×C15111yescharacteristic
287C4⋊Q8—22no—
288C4⋊Q8—22no—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×D4—24no—
292C4×D4—22no—
293C4×D4—42no—
294C4×D4D4×C15114yes—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4D4×C15112yes—
301C2×C4⋊C4C23×C15112yes—
302C2×C4⋊C4C23×C15111yescharacteristic
303C2×C4⋊C4C23×C15112yes—
304C2×C4⋊C4C23×C15111yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C42—21no—
308C2×C42C23×C15112yes—
309C2×C42C23×C15111yescharacteristic
310#107—22no—
311#107—24no—
312C4⋊C8—22no—
313C4⋊C8—42no—
314#103—22no—
315#103—42no—
316#102—22no—
317#102—24no—
318#97—22no—
319#95—21no—
320#95—22no—
321#95—21no—
322#95—22no—
323#95—22no—
324#95D4×C15111yescharacteristic
325#95D4×C15111yescharacteristic
326C24—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—42no—
333C2×Q8—82no—
334C2×Q8C2×Q8×C15112yes—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4C2×D4×C15112yes—
339C2×D4C2×Q8×C15112yes—
340C2×D4#41×C15112yes—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—82no—
350C22×C4—82no—
351C22×C4C2×D4×C15112yes—
352C22×C4C2×D4×C15111yescharacteristic
353C22×C4C2×D4×C15111yescharacteristic
354C22×C4C2×D4×C15112yes—
355C22×C4C24×C15111yescharacteristic
356SD16—28no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—21no—
365C2×C8C2×Q8×C15112yes—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—82no—
377C4⋊C4—82no—
378C4⋊C4—82no—
379C4⋊C4C2×D4×C15112yes—
380C22⋊C4—24no—
381C22⋊C4—44no—
382C42—22no—
383C42—22no—
384C42—42no—
385C42C2×D4×C15112yes—
386C42#41×C15112yes—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—42no—
391C23—42no—
392C23C22×D4×C15111yescharacteristic
393Q8—22no—
394Q8—22no—
395Q8—41no—
396Q8—41no—
397Q8—84no—
398D4—22no—
399D4—22no—
400D4—22no—
401D4C22⋊Q8×C15114yes—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—84no—
423C2×C4—88no—
424C2×C4#121×C15112yes—
425C2×C4#121×C15112yes—
426C2×C4#137×C15114yes—
427C2×C4C22×D4×C15111yescharacteristic
428C2×C4C22×Q8×C15111yescharacteristic
429C2×C4C2×#41×C15111yescharacteristic
430C2×C4C2×#41×C15111yescharacteristic
431C2×C4H(5,𝔽2)×C15111yescharacteristic
432C2×C42−1+4×C15111yescharacteristic
433C8—22no—
434C8—41no—
435C8—42no—
436C22—24no—
437C22—44no—
438C22—42no—
439C22—42no—
440C22—44no—
441C22C2×#121×C15111yescharacteristic
442C22#546×C15111yescharacteristic
443C22D4×Q8×C15111yescharacteristic
444C22C2×#137×C15112yes—
445C22#576×C15112yes—
446C4—22no—
447C4—22no—
448C4—24no—
449C4—42no—
450C4—42no—
451C4—42no—
452C4—82no—
453C4—81no—
454C4—82no—
455C4C2×C22⋊Q8×C15111yescharacteristic
456C4#537×C15111yescharacteristic
457C4#552×C15111yescharacteristic
458C4#554×C15111yescharacteristic
459C2—44no—
460C2#2417×C15111yescharacteristic
461C2#3039×C15111yescharacteristic
462C2#3041×C15111yescharacteristic
463C2#3314×C15112yes—
464C2#3385×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
3. #2567×C151C2semidirect
5. #2083×C151C2semidirect
6. #2068×C151C2semidirect
7. #1993×C151C2semidirect
8. #1940×C151C2semidirect
10. #1805×C151C2semidirect
50. C2×SD16×C151Q8semidirect
232. #24833C151direct (N × H)
233. C151#24833direct (N × H)
236. #2567C2×C151semidirect
238. #2083C2×C151semidirect
239. #2068C2×C151semidirect
240. #1993C2×C151semidirect
241. #1940C2×C151semidirect
243. #1805C2×C151semidirect
283. C2×SD16Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1512
C2×#440×C1512
#2567×C1512
#2349×C1512
#2083×C1512
#2068×C1512
#1993×C1512
#1940×C1512
#1877×C1512
#1805×C1512
#1802×C1512
#24833151