Finite Group Databasebeta

← C151×#22223 #50327148

Subgroups — C151×#22223 #50327148

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
1C2×#489×C151C211yesmaximal, characteristic
2C4×C4⋊Q8×C151C211yesmaximal, characteristic, complemented
3C4×#124×C151C211yesmaximal, characteristic
4#1993×C151C211yesmaximal, characteristic, complemented
5#1959×C151C211yesmaximal, characteristic
6#1928×C151C212yesmaximal, complemented
7#1926×C151C212yesmaximal
8#1865×C151C212yesmaximal, complemented
9#1862×C151C212yesmaximal
10#1847×C151C211yesmaximal, characteristic, complemented
11#1745×C151C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×#124×C151C2211yescharacteristic
14C2×C4×Q8×C151—21no—
15C2×C4×Q8×C151C2211yescharacteristic
16C2×C4×D4×C151C2211yescharacteristic
17#489×C151C418yescomplemented
18C2×#107×C151C2212yes—
19C2×#106×C151C2212yes—
20C2×#103×C151C2212yes—
21C2×#103×C151C2212yes—
22C2×#102×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#97×C151C2211yescharacteristic
25C2×#97×C151C2211yescharacteristic
26#391×C151—21no—
27#391×C151C2211yescharacteristic
28#390×C151C2211yescharacteristic
29#389×C151—21no—
30#389×C151C2212yes—
31#388×C151—21no—
32#388×C151—21no—
33#384×C151C2211yescharacteristic
34#382×C151C2211yescharacteristic
35C4×C4⋊C4×C151—21no—
36C4×C4⋊C4×C151C2212yes—
37C4×C22⋊C4×C151—21no—
38C4×C22⋊C4×C151—21no—
39C43×C151C2211yescharacteristic
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43#336×C151C2212yes—
44C22×Q8×C151—21no—
45C22×Q8×C151C2311yescharacteristic
46C22×D4×C151C2311yescharacteristic
47C23×C4×C151—21no—
48C22×C8×C151C2312yes—
49C22×C8×C151C2312yes—
50C4⋊Q8×C151—22no—
51C4⋊Q8×C151C2×C414yescomplemented
52#124×C151—22no—
53#124×C151C2×C414yes—
54C4×Q8×C151—42no—
55C4×Q8×C151—44no—
56C4×D4×C151—42no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151C2311yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2312yes—
65C2×C4⋊C4×C151C2312yes—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—21no—
71C2×C42×C151—21no—
72C2×C42×C151—22no—
73C2×C42×C151D411yescharacteristic
74C2×C42×C151D411yescharacteristic
75C2×C42×C151D411yescharacteristic
76C2×C42×C151D411yescharacteristic
77C2×C42×C151C2311yescharacteristic
78C2×C42×C151C2311yescharacteristic
79C2×C42×C151C2311yescharacteristic
80#107×C151—42no—
81#106×C151—42no—
82#103×C151—42no—
83#103×C151C2×C418yescomplemented
84#102×C151—42no—
85#102×C151C2×C418yes—
86#97×C151—22no—
87#97×C151C2×C414yescomplemented
88#95×C151—21no—
89#95×C151—21no—
90#95×C151—21no—
91#95×C151—21no—
92#95×C151—22no—
93#95×C151—22no—
94C24×C151—21no—
95C2×Q8×C151—24no—
96C2×Q8×C151—21no—
97C2×Q8×C151—22no—
98C2×Q8×C151—22no—
99C2×Q8×C151—42no—
100C2×Q8×C151—42no—
101C2×Q8×C151C22×C412yes—
102C2×D4×C151—21no—
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151C22×C412yes—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—22no—
111C22×C4×C151—42no—
112C22×C4×C151—42no—
113C22×C4×C151—42no—
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2411yescharacteristic
121C2×C8×C151—22no—
122C2×C8×C151—22no—
123C2×C8×C151—22no—
124C2×C8×C151—22no—
125C2×C8×C151—22no—
126C2×C8×C151C22×C414yes—
127C4⋊C4×C151—24no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—42no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151—42no—
136C4⋊C4×C151—44no—
137C4⋊C4×C151C22×C414yes—
138C22⋊C4×C151—24no—
139C22⋊C4×C151—24no—
140C22⋊C4×C151—42no—
141C22⋊C4×C151—42no—
142C22⋊C4×C151—42no—
143C42×C151—22no—
144C42×C151—22no—
145C42×C151—22no—
146C42×C151—22no—
147C42×C151—41no—
148C42×C151—41no—
149C42×C151—42no—
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—24no—
162Q8×C151—48no—
163Q8×C151—42no—
164D4×C151—24no—
165D4×C151—42no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—24no—
175C2×C4×C151—22no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—41no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—42no—
194C2×C4×C151—41no—
195C2×C4×C151—84no—
196C2×C4×C151C4×D412yes—
197C2×C4×C151C4×D412yes—
198C2×C4×C151AGL(1,ℤ/8)12yes—
199C2×C4×C151#13712yes—
200C2×C4×C151C23×C411yescharacteristic
201C2×C4×C151C2×#4111yescharacteristic
202C2×C4×C151H(5,𝔽2)12yes—
203C2×C4×C1512−1+412yes—
204C8×C151—24no—
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#53511yescharacteristic
215C22×C151#53611yescharacteristic
216C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C151C2×#13711yescharacteristic
218C22×C151#57511yescharacteristic
219C22×C151#57511yescharacteristic
220C4×C151—22no—
221C4×C151—22no—
222C4×C151—22no—
223C4×C151—22no—
224C4×C151—42no—
225C4×C151—44no—
226C4×C151—41no—
227C4×C151—41no—
228C4×C151—82no—
229C4×C151—81no—
230C4×C151—81no—
231C4×C151#52012yes—
232C4×C151#54212yes—
233C2×C151—82no—
234C2×C151#232611yescharacteristic
235C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
236C2×C151C4×#13711yescharacteristic
237C2×C151#321311yescharacteristic
238C2×C151#321611yescharacteristic
239C2×C151#323911yescharacteristic
240C2×C151#324011yescharacteristic
241#22223C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#2222311yescharacteristic, direct product factor, Sylow
243C2×#489C2×C15111yescharacteristic
244C4×C4⋊Q8C2×C15111yescharacteristic, complemented
245C4×#124C2×C15111yescharacteristic
246#1993C2×C15111yescharacteristic, complemented
247#1959C2×C15111yescharacteristic
248#1928C2×C15112yescomplemented
249#1926C2×C15112yes—
250#1865C2×C15112yescomplemented
251#1862C2×C15112yes—
252#1847C2×C15111yescharacteristic, complemented
253#1745C2×C15111yescharacteristic, complemented
254C2×C4⋊Q8C22×C15111yescharacteristic
255C2×#124C22×C15111yescharacteristic
256C2×C4×Q8—21no—
257C2×C4×Q8C22×C15111yescharacteristic
258C2×C4×D4C22×C15111yescharacteristic
259#489C4×C15118yescomplemented
260C2×#107C22×C15112yes—
261C2×#106C22×C15112yes—
262C2×#103C22×C15112yes—
263C2×#103C22×C15112yes—
264C2×#102C22×C15112yes—
265C2×#102C22×C15112yes—
266C2×#97C22×C15111yescharacteristic
267C2×#97C22×C15111yescharacteristic
268#391—21no—
269#391C22×C15111yescharacteristic
270#390C22×C15111yescharacteristic
271#389—21no—
272#389C22×C15112yes—
273#388—21no—
274#388—21no—
275#384C22×C15111yescharacteristic
276#382C22×C15111yescharacteristic
277C4×C4⋊C4—21no—
278C4×C4⋊C4C22×C15112yes—
279C4×C22⋊C4—21no—
280C4×C22⋊C4—21no—
281C43C22×C15111yescharacteristic
282#340C22×C15112yes—
283#340C22×C15112yes—
284#336C22×C15112yes—
285#336C22×C15112yes—
286C22×Q8—21no—
287C22×Q8C23×C15111yescharacteristic
288C22×D4C23×C15111yescharacteristic
289C23×C4—21no—
290C22×C8C23×C15112yes—
291C22×C8C23×C15112yes—
292C4⋊Q8—22no—
293C4⋊Q8C2×C4×C15114yescomplemented
294#124—22no—
295#124C2×C4×C15114yes—
296C4×Q8—42no—
297C4×Q8—44no—
298C4×D4—42no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C23×C15111yescharacteristic
305C2×C4⋊C4C23×C15111yescharacteristic
306C2×C4⋊C4C23×C15112yes—
307C2×C4⋊C4C23×C15112yes—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C42—22no—
314C2×C42—21no—
315C2×C42D4×C15111yescharacteristic
316C2×C42D4×C15111yescharacteristic
317C2×C42D4×C15111yescharacteristic
318C2×C42D4×C15111yescharacteristic
319C2×C42C23×C15111yescharacteristic
320C2×C42C23×C15111yescharacteristic
321C2×C42C23×C15111yescharacteristic
322#107—42no—
323#106—42no—
324#103—42no—
325#103C2×C4×C15118yescomplemented
326#102—42no—
327#102C2×C4×C15118yes—
328#97—22no—
329#97C2×C4×C15114yescomplemented
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—22no—
335#95—22no—
336C24—21no—
337C2×Q8—24no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8C22×C4×C15112yes—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4C22×C4×C15112yes—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C2×D4×C15111yescharacteristic
358C22×C4C2×D4×C15111yescharacteristic
359C22×C4C2×D4×C15111yescharacteristic
360C22×C4C2×D4×C15111yescharacteristic
361C22×C4C2×D4×C15111yescharacteristic
362C22×C4C24×C15111yescharacteristic
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8C22×C4×C15114yes—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—44no—
379C4⋊C4C22×C4×C15114yes—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42—22no—
389C42—41no—
390C42—41no—
391C42—42no—
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—24no—
404Q8—48no—
405Q8—42no—
406D4—24no—
407D4—42no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—84no—
438C2×C4C4×D4×C15112yes—
439C2×C4C4×D4×C15112yes—
440C2×C4AGL(1,ℤ/8)×C15112yes—
441C2×C4#137×C15112yes—
442C2×C4C23×C4×C15111yescharacteristic
443C2×C4C2×#41×C15111yescharacteristic
444C2×C4H(5,𝔽2)×C15112yes—
445C2×C42−1+4×C15112yes—
446C8—24no—
447C8—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C2×C4×D4×C15111yescharacteristic
456C22#535×C15111yescharacteristic
457C22#536×C15111yescharacteristic
458C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
459C22C2×#137×C15111yescharacteristic
460C22#575×C15111yescharacteristic
461C22#575×C15111yescharacteristic
462C4—22no—
463C4—22no—
464C4—22no—
465C4—22no—
466C4—44no—
467C4—41no—
468C4—41no—
469C4—42no—
470C4—81no—
471C4—82no—
472C4—81no—
473C4#520×C15112yes—
474C4#542×C15112yes—
475C2—82no—
476C2#2326×C15111yescharacteristic
477C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
478C2C4×#137×C15111yescharacteristic
479C2#3213×C15111yescharacteristic
480C2#3216×C15111yescharacteristic
481C2#3239×C15111yescharacteristic
482C2#3240×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 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Q8×C151C2semidirect
4. #1993×C151C2semidirect
6. #1928×C151C2semidirect
8. #1865×C151C2semidirect
10. #1847×C151C2semidirect
11. #1745×C151C2semidirect
17. #489×C151C4semidirect
51. C4⋊Q8×C151C2×C4semidirect
83. #103×C151C2×C4semidirect
87. #97×C151C2×C4semidirect
241. #22223C151direct (N × H)
242. C151#22223direct (N × H)
244. C4×C4⋊Q8C2×C151semidirect
246. #1993C2×C151semidirect
248. #1928C2×C151semidirect
250. #1865C2×C151semidirect
252. #1847C2×C151semidirect
253. #1745C2×C151semidirect
259. #489C4×C151semidirect
293. C4⋊Q8C2×C4×C151semidirect
325. #103C2×C4×C151semidirect
329. #97C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#489×C1512
C4×C4⋊Q8×C1512
C4×#124×C1512
#1993×C1512
#1959×C1512
#1928×C1512
#1926×C1512
#1865×C1512
#1862×C1512
#1847×C1512
#1745×C1512
#22223151