Finite Group Databasebeta

← C151×#24692 #50329617

Subgroups — C151×#24692 #50329617

Order 38656.

884 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C151C211yesmaximal, characteristic, complemented
2C2×#442×C151C211yesmaximal, characteristic
3#2542×C151C211yesmaximal, characteristic, complemented
4#2357×C151C211yesmaximal, characteristic, complemented
5#2071×C151C212yesmaximal, complemented
6#2054×C151C212yesmaximal
7#1993×C151C211yesmaximal, characteristic, complemented
8#1948×C151C212yesmaximal, complemented
9#1940×C151C211yesmaximal, characteristic, complemented
10#1926×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C22×D8×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C22⋊Q8×C151—22no—
15C2×C4×D4×C151C2211yescharacteristic
16C2×C4×D4×C151C2211yescharacteristic
17#476×C151—24no—
18#442×C151—24no—
19C2×#106×C151C2211yescharacteristic
20C2×#106×C151C2212yes—
21C2×C4⋊C8×C151C2212yes—
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#102×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#97×C151C2211yescharacteristic
28#399×C151—21no—
29#399×C151—21no—
30#390×C151C2212yes—
31#390×C151C2212yes—
32#388×C151—22no—
33#384×C151C2212yes—
34#382×C151C2211yescharacteristic
35#381×C151—21no—
36C4×C4⋊C4×C151C2212yes—
37C4×C4⋊C4×C151C2211yescharacteristic
38C4×C22⋊C4×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×D4×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C2×D8×C151—22no—
49C2×D8×C151—22no—
50C2×D8×C151—22no—
51C22×C8×C151C2311yescharacteristic
52C22×C8×C151C2312yes—
53C22×C8×C151C2311yescharacteristic
54C4⋊Q8×C151—22no—
55C4⋊Q8×C151—22no—
56C22⋊Q8×C151—48no—
57C4×D4×C151—22no—
58C4×D4×C151—22no—
59C4×D4×C151—22no—
60C4×D4×C151D414yes—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151D412yes—
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2312yes—
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—22no—
75C2×C42×C151—22no—
76C2×C42×C151C2312yes—
77C2×C42×C151C2311yescharacteristic
78#106×C151—22no—
79#106×C151—24no—
80C4⋊C8×C151—24no—
81C4⋊C8×C151—22no—
82#102×C151—22no—
83#102×C151—24no—
84#102×C151—24no—
85#102×C151—22no—
86#97×C151—22no—
87#95×C151—21no—
88#95×C151—22no—
89#95×C151—21no—
90#95×C151D411yescharacteristic
91#95×C151D411yescharacteristic
92C24×C151—21no—
93C24×C151—21no—
94C2×Q8×C151—44no—
95C2×Q8×C151—42no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151C2×D412yes—
107C2×D4×C151#4112yes—
108C22×C4×C151—21no—
109C22×C4×C151—24no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—21no—
113C22×C4×C151—44no—
114C22×C4×C151—42no—
115C22×C4×C151—82no—
116C22×C4×C151C2×D412yes—
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2411yescharacteristic
121D8×C151—28no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—21no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C2×C8×C151—21no—
129C2×C8×C151—21no—
130C2×C8×C151#4112yes—
131C4⋊C4×C151—24no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—21no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—44no—
140C4⋊C4×C151—42no—
141C4⋊C4×C151—44no—
142C4⋊C4×C151C2×D412yes—
143C22⋊C4×C151—24no—
144C22⋊C4×C151—44no—
145C22⋊C4×C151—42no—
146C22⋊C4×C151—44no—
147C22⋊C4×C151—44no—
148C22⋊C4×C151—82no—
149C42×C151—22no—
150C42×C151—22no—
151C42×C151—82no—
152C42×C151C2×D412yes—
153C42×C151#4112yes—
154C23×C151—22no—
155C23×C151—22no—
156C23×C151—41no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151—41no—
160C23×C151—42no—
161C23×C151—42no—
162C23×C151—42no—
163C23×C151—42no—
164C23×C151C22×D411yescharacteristic
165Q8×C151—84no—
166D4×C151—22no—
167D4×C151—22no—
168D4×C151—22no—
169D4×C151—22no—
170D4×C151—41no—
171D4×C151—41no—
172D4×C151—41no—
173D4×C151—41no—
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—42no—
183C2×C4×C151—42no—
184C2×C4×C151—41no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—84no—
192C2×C4×C151—84no—
193C2×C4×C151#12112yes—
194C2×C4×C151#12112yes—
195C2×C4×C151AGL(1,ℤ/8)14yes—
196C2×C4×C151C22×D411yescharacteristic
197C2×C4×C151C2×#4111yescharacteristic
198C2×C4×C151C2×#4111yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C2×C4×C1512−1+411yescharacteristic
201C2×C4×C1512−1+411yescharacteristic
202C8×C151—22no—
203C8×C151—42no—
204C8×C151—41no—
205C22×C151—44no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151—42no—
210C22×C151—82no—
211C22×C151—82no—
212C22×C151—82no—
213C22×C151—81no—
214C22×C151—81no—
215C22×C151C2×#12111yescharacteristic
216C22×C151#54711yescharacteristic
217C22×C151#54811yescharacteristic
218C22×C151C2×AGL(1,ℤ/8)12yes—
219C22×C151#57712yes—
220C4×C151—24no—
221C4×C151—22no—
222C4×C151—22no—
223C4×C151—42no—
224C4×C151—42no—
225C4×C151—82no—
226C4×C151—81no—
227C4×C151—82no—
228C4×C151#52511yescharacteristic
229C4×C151#53611yescharacteristic
230C4×C151#55211yescharacteristic
231C4×C151#55611yescharacteristic
232C2×C151—82no—
233C2×C151—82no—
234C2×C151#241511yescharacteristic
235C2×C151#303811yescharacteristic
236C2×C151#304211yescharacteristic
237C2×C151#334512yes—
238C2×C151#337312yes—
239#24692C15111yesmaximal, characteristic, direct product factor, Sylow
240C151#2469211yescharacteristic, direct product factor, Sylow
241C2×#476C2×C15111yescharacteristic, complemented
242C2×#442C2×C15111yescharacteristic
243#2542C2×C15111yescharacteristic, complemented
244#2357C2×C15111yescharacteristic, complemented
245#2071C2×C15112yescomplemented
246#2054C2×C15112yes—
247#1993C2×C15111yescharacteristic, complemented
248#1948C2×C15112yescomplemented
249#1940C2×C15111yescharacteristic, complemented
250#1926C2×C15112yescomplemented
251#1804C2×C15111yescharacteristic, complemented
252C22×D8C22×C15111yescharacteristic
253C2×C4⋊Q8C22×C15111yescharacteristic
254C2×C22⋊Q8—22no—
255C2×C4×D4C22×C15111yescharacteristic
256C2×C4×D4C22×C15111yescharacteristic
257#476—24no—
258#442—24no—
259C2×#106C22×C15111yescharacteristic
260C2×#106C22×C15112yes—
261C2×C4⋊C8C22×C15112yes—
262C2×C4⋊C8C22×C15111yescharacteristic
263C2×#102C22×C15112yes—
264C2×#102C22×C15112yes—
265C2×#102C22×C15111yescharacteristic
266C2×#102C22×C15111yescharacteristic
267C2×#97C22×C15111yescharacteristic
268#399—21no—
269#399—21no—
270#390C22×C15112yes—
271#390C22×C15112yes—
272#388—22no—
273#384C22×C15112yes—
274#382C22×C15111yescharacteristic
275#381—21no—
276C4×C4⋊C4C22×C15112yes—
277C4×C4⋊C4C22×C15111yescharacteristic
278C4×C22⋊C4—21no—
279#340C22×C15112yes—
280#340C22×C15112yes—
281#340C22×C15112yes—
282#336C22×C15112yes—
283C22×Q8—21no—
284C22×D4C23×C15111yescharacteristic
285C22×D4C23×C15111yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C2×D8—22no—
289C2×D8—22no—
290C2×D8—22no—
291C22×C8C23×C15111yescharacteristic
292C22×C8C23×C15112yes—
293C22×C8C23×C15111yescharacteristic
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C22⋊Q8—48no—
297C4×D4—22no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4D4×C15114yes—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C15112yes—
305C2×C4⋊C4C23×C15111yescharacteristic
306C2×C4⋊C4C23×C15112yes—
307C2×C4⋊C4C23×C15112yes—
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C42—22no—
316C2×C42C23×C15112yes—
317C2×C42C23×C15111yescharacteristic
318#106—22no—
319#106—24no—
320C4⋊C8—24no—
321C4⋊C8—22no—
322#102—24no—
323#102—22no—
324#102—24no—
325#102—22no—
326#97—22no—
327#95—21no—
328#95—22no—
329#95—21no—
330#95D4×C15111yescharacteristic
331#95D4×C15111yescharacteristic
332C24—21no—
333C24—21no—
334C2×Q8—44no—
335C2×Q8—42no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4C2×D4×C15112yes—
347C2×D4#41×C15112yes—
348C22×C4—21no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—44no—
354C22×C4—42no—
355C22×C4—82no—
356C22×C4C2×D4×C15112yes—
357C22×C4C2×D4×C15111yescharacteristic
358C22×C4C2×D4×C15111yescharacteristic
359C22×C4C2×D4×C15112yes—
360C22×C4C24×C15111yescharacteristic
361D8—28no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8#41×C15112yes—
371C4⋊C4—24no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—44no—
380C4⋊C4—42no—
381C4⋊C4—44no—
382C4⋊C4C2×D4×C15112yes—
383C22⋊C4—24no—
384C22⋊C4—44no—
385C22⋊C4—42no—
386C22⋊C4—44no—
387C22⋊C4—44no—
388C22⋊C4—82no—
389C42—22no—
390C42—22no—
391C42—82no—
392C42C2×D4×C15112yes—
393C42#41×C15112yes—
394C23—22no—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23C22×D4×C15111yescharacteristic
405Q8—84no—
406D4—22no—
407D4—22no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—84no—
432C2×C4—84no—
433C2×C4#121×C15112yes—
434C2×C4#121×C15112yes—
435C2×C4AGL(1,ℤ/8)×C15114yes—
436C2×C4C22×D4×C15111yescharacteristic
437C2×C4C2×#41×C15111yescharacteristic
438C2×C4C2×#41×C15111yescharacteristic
439C2×C4C2×#41×C15111yescharacteristic
440C2×C42−1+4×C15111yescharacteristic
441C2×C42−1+4×C15111yescharacteristic
442C8—22no—
443C8—42no—
444C8—41no—
445C22—44no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—82no—
451C22—81no—
452C22—81no—
453C22—82no—
454C22—82no—
455C22C2×#121×C15111yescharacteristic
456C22#547×C15111yescharacteristic
457C22#548×C15111yescharacteristic
458C22C2×AGL(1,ℤ/8)×C15112yes—
459C22#577×C15112yes—
460C4—22no—
461C4—22no—
462C4—24no—
463C4—42no—
464C4—42no—
465C4—82no—
466C4—81no—
467C4—82no—
468C4#525×C15111yescharacteristic
469C4#536×C15111yescharacteristic
470C4#552×C15111yescharacteristic
471C4#556×C15111yescharacteristic
472C2—82no—
473C2—82no—
474C2#2415×C15111yescharacteristic
475C2#3038×C15111yescharacteristic
476C2#3042×C15111yescharacteristic
477C2#3345×C15112yes—
478C2#3373×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
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×#476×C151C2semidirect
3. #2542×C151C2semidirect
4. #2357×C151C2semidirect
5. #2071×C151C2semidirect
7. #1993×C151C2semidirect
8. #1948×C151C2semidirect
9. #1940×C151C2semidirect
10. #1926×C151C2semidirect
11. #1804×C151C2semidirect
239. #24692C151direct (N × H)
240. C151#24692direct (N × H)
241. C2×#476C2×C151semidirect
243. #2542C2×C151semidirect
244. #2357C2×C151semidirect
245. #2071C2×C151semidirect
247. #1993C2×C151semidirect
248. #1948C2×C151semidirect
249. #1940C2×C151semidirect
250. #1926C2×C151semidirect
251. #1804C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
C2×#442×C1512
#2542×C1512
#2357×C1512
#2071×C1512
#2054×C1512
#1993×C1512
#1948×C1512
#1940×C1512
#1926×C1512
#1804×C1512
#24692151