Finite Group Databasebeta

← C151×#24135 #50329060

Subgroups — C151×#24135 #50329060

Order 38656.

1076 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C151C211yesmaximal, characteristic
2C2×#477×C151C211yesmaximal, characteristic, complemented
3C2×#441×C151C211yesmaximal, characteristic, complemented
4#2536×C151C211yesmaximal, characteristic
5#2036×C151C212yesmaximal, complemented
6#2001×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1955×C151C211yesmaximal, characteristic
9#1873×C151C212yesmaximal, complemented
10#1854×C151C212yesmaximal, complemented
11#1805×C151C211yesmaximal, characteristic, complemented
12C22×Q16×C151C2211yescharacteristic
13#556×C151—24no—
14#556×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#126×C151—22no—
17C2×#124×C151—21no—
18C2×C22⋊Q8×C151C2212yes—
19C2×C22⋊Q8×C151C2212yes—
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151C2212yes—
25#477×C151—24no—
26#441×C151—24no—
27C2×#107×C151C2212yes—
28C2×#106×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2212yes—
34C2×C22⋊C8×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36C2×#97×C151C2211yescharacteristic
37#398×C151—21no—
38#394×C151—21no—
39#388×C151—22no—
40#382×C151C2211yescharacteristic
41#380×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151C2311yescharacteristic
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151D411yescharacteristic
49C23×C4×C151C2312yes—
50C2×Q16×C151—22no—
51C2×Q16×C151—22no—
52C2×Q16×C151—22no—
53C22×C8×C151C2311yescharacteristic
54C22×C8×C151C2312yes—
55C22×C8×C151C2311yescharacteristic
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151D414yes—
58#126×C151—216no—
59#124×C151—28no—
60C22⋊Q8×C151—24no—
61C22⋊Q8×C151—24no—
62C22⋊Q8×C151—24no—
63C22⋊Q8×C151—42no—
64C4×Q8×C151—28no—
65C4×Q8×C151—22no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×Q8×C151D414yes—
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71#117×C151—24no—
72#117×C151—24no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151D411yescharacteristic
79C2×C4⋊C4×C151C2312yes—
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2312yes—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151D412yes—
88C2×C42×C151—22no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—24no—
93#106×C151—22no—
94C4⋊C8×C151—22no—
95#103×C151—22no—
96#103×C151—24no—
97#103×C151—22no—
98#103×C151—42no—
99C22⋊C8×C151—24no—
100C22⋊C8×C151—42no—
101#97×C151—22no—
102#95×C151—22no—
103#95×C151—21no—
104#95×C151—21no—
105C24×C151C2×D412yes—
106C2×Q8×C151—24no—
107C2×Q8×C151—21no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—44no—
118C2×Q8×C151C2×D412yes—
119C2×Q8×C151#4112yes—
120C2×D4×C151—22no—
121C2×D4×C151—42no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151C2×D412yes—
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2411yescharacteristic
138Q16×C151—28no—
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151—21no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—21no—
145C2×C8×C151—22no—
146C2×C8×C151—21no—
147C2×C8×C151#4112yes—
148C4⋊C4×C151—28no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—44no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151C2×D412yes—
161C4⋊C4×C151C2×D414yes—
162C22⋊C4×C151—28no—
163C22⋊C4×C151—28no—
164C22⋊C4×C151—24no—
165C22⋊C4×C151—44no—
166C22⋊C4×C151—44no—
167C42×C151—28no—
168C42×C151—24no—
169C42×C151—42no—
170C42×C151C2×D412yes—
171C42×C151C2×D412yes—
172C23×C151—22no—
173C23×C151—22no—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151C22×D411yescharacteristic
180Q8×C151—22no—
181Q8×C151—22no—
182Q8×C151—22no—
183Q8×C151—22no—
184Q8×C151—48no—
185Q8×C151—41no—
186Q8×C151—41no—
187Q8×C151—41no—
188Q8×C151—41no—
189D4×C151—44no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—24no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—44no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151#12012yes—
215C2×C4×C151#12012yes—
216C2×C4×C151C22×D411yescharacteristic
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C2×#4111yescharacteristic
219C2×C4×C151C2×#4111yescharacteristic
220C2×C4×C151H(5,𝔽2)11yescharacteristic
221C2×C4×C1512−1+411yescharacteristic
222C8×C151—22no—
223C8×C151—41no—
224C8×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151C2×#12011yescharacteristic
233C22×C151#54611yescharacteristic
234C22×C151#54711yescharacteristic
235C22×C151#57512yes—
236C22×C151#57812yes—
237C4×C151—22no—
238C4×C151—22no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—44no—
243C4×C151—42no—
244C4×C151—81no—
245C4×C151—82no—
246C4×C151#52511yescharacteristic
247C4×C151#53711yescharacteristic
248C4×C151#54811yescharacteristic
249C4×C151#55011yescharacteristic
250C2×C151—82no—
251C2×C151#240711yescharacteristic
252C2×C151#300511yescharacteristic
253C2×C151#301111yescharacteristic
254C2×C151#331312yes—
255C2×C151#334912yes—
256#24135C15111yesmaximal, characteristic, direct product factor, Sylow
257C151#2413511yescharacteristic, direct product factor, Sylow
258C2×#556C2×C15111yescharacteristic
259C2×#477C2×C15111yescharacteristic, complemented
260C2×#441C2×C15111yescharacteristic, complemented
261#2536C2×C15111yescharacteristic
262#2036C2×C15112yescomplemented
263#2001C2×C15112yescomplemented
264#1993C2×C15111yescharacteristic, complemented
265#1955C2×C15111yescharacteristic
266#1873C2×C15112yescomplemented
267#1854C2×C15112yescomplemented
268#1805C2×C15111yescharacteristic, complemented
269C22×Q16C22×C15111yescharacteristic
270#556—24no—
271#556—24no—
272C2×C4⋊Q8C22×C15111yescharacteristic
273C2×#126—22no—
274C2×#124—21no—
275C2×C22⋊Q8C22×C15112yes—
276C2×C22⋊Q8C22×C15112yes—
277C2×C4×Q8—21no—
278C2×C4×Q8C22×C15111yescharacteristic
279C2×C4×Q8C22×C15111yescharacteristic
280C2×C4×D4C22×C15111yescharacteristic
281C2×#117C22×C15112yes—
282#477—24no—
283#441—24no—
284C2×#107C22×C15112yes—
285C2×#106C22×C15111yescharacteristic
286C2×C4⋊C8C22×C15111yescharacteristic
287C2×#103C22×C15112yes—
288C2×#103C22×C15111yescharacteristic
289C2×#103C22×C15111yescharacteristic
290C2×#103C22×C15112yes—
291C2×C22⋊C8C22×C15112yes—
292C2×C22⋊C8C22×C15112yes—
293C2×#97C22×C15111yescharacteristic
294#398—21no—
295#394—21no—
296#388—22no—
297#382C22×C15111yescharacteristic
298#380C22×C15112yes—
299#340C22×C15112yes—
300#340C22×C15112yes—
301#340C22×C15112yes—
302C22×Q8—21no—
303C22×Q8C23×C15111yescharacteristic
304C22×Q8C23×C15111yescharacteristic
305C22×D4D4×C15111yescharacteristic
306C23×C4C23×C15112yes—
307C2×Q16—22no—
308C2×Q16—22no—
309C2×Q16—22no—
310C22×C8C23×C15111yescharacteristic
311C22×C8C23×C15112yes—
312C22×C8C23×C15111yescharacteristic
313C4⋊Q8—22no—
314C4⋊Q8D4×C15114yes—
315#126—216no—
316#124—28no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—42no—
321C4×Q8—28no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8D4×C15114yes—
326C4×D4—22no—
327C4×D4—22no—
328#117—24no—
329#117—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4D4×C15111yescharacteristic
336C2×C4⋊C4C23×C15111yescharacteristic
337C2×C4⋊C4C23×C15112yes—
338C2×C4⋊C4C23×C15111yescharacteristic
339C2×C4⋊C4C23×C15112yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4D4×C15112yes—
345C2×C42—22no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42C23×C15111yescharacteristic
349#107—24no—
350#106—22no—
351C4⋊C8—22no—
352#103—22no—
353#103—22no—
354#103—24no—
355#103—42no—
356C22⋊C8—24no—
357C22⋊C8—42no—
358#97—22no—
359#95—22no—
360#95—21no—
361#95—21no—
362C24C2×D4×C15112yes—
363C2×Q8—24no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—44no—
375C2×Q8C2×D4×C15112yes—
376C2×Q8#41×C15112yes—
377C2×D4—22no—
378C2×D4—42no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4C2×D4×C15112yes—
392C22×C4C2×D4×C15111yescharacteristic
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C24×C15111yescharacteristic
395Q16—28no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—21no—
404C2×C8#41×C15112yes—
405C4⋊C4—28no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—44no—
416C4⋊C4—42no—
417C4⋊C4C2×D4×C15112yes—
418C4⋊C4C2×D4×C15114yes—
419C22⋊C4—28no—
420C22⋊C4—28no—
421C22⋊C4—24no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C42—28no—
425C42—24no—
426C42—42no—
427C42C2×D4×C15112yes—
428C42C2×D4×C15112yes—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23C22×D4×C15111yescharacteristic
437Q8—22no—
438Q8—22no—
439Q8—22no—
440Q8—22no—
441Q8—48no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446D4—44no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4#120×C15112yes—
472C2×C4#120×C15112yes—
473C2×C4C22×D4×C15111yescharacteristic
474C2×C4C22×D4×C15111yescharacteristic
475C2×C4C2×#41×C15111yescharacteristic
476C2×C4C2×#41×C15111yescharacteristic
477C2×C4H(5,𝔽2)×C15111yescharacteristic
478C2×C42−1+4×C15111yescharacteristic
479C8—22no—
480C8—41no—
481C8—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22C2×#120×C15111yescharacteristic
490C22#546×C15111yescharacteristic
491C22#547×C15111yescharacteristic
492C22#575×C15112yes—
493C22#578×C15112yes—
494C4—22no—
495C4—22no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—44no—
500C4—42no—
501C4—81no—
502C4—82no—
503C4#525×C15111yescharacteristic
504C4#537×C15111yescharacteristic
505C4#548×C15111yescharacteristic
506C4#550×C15111yescharacteristic
507C2—82no—
508C2#2407×C15111yescharacteristic
509C2#3005×C15111yescharacteristic
510C2#3011×C15111yescharacteristic
511C2#3313×C15112yes—
512C2#3349×C15112yes—
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
2. C2×#477×C151C2semidirect
3. C2×#441×C151C2semidirect
5. #2036×C151C2semidirect
6. #2001×C151C2semidirect
7. #1993×C151C2semidirect
9. #1873×C151C2semidirect
10. #1854×C151C2semidirect
11. #1805×C151C2semidirect
256. #24135C151direct (N × H)
257. C151#24135direct (N × H)
259. C2×#477C2×C151semidirect
260. C2×#441C2×C151semidirect
262. #2036C2×C151semidirect
263. #2001C2×C151semidirect
264. #1993C2×C151semidirect
266. #1873C2×C151semidirect
267. #1854C2×C151semidirect
268. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#477×C1512
C2×#441×C1512
#2536×C1512
#2036×C1512
#2001×C1512
#1993×C1512
#1955×C1512
#1873×C1512
#1854×C1512
#1805×C1512
#24135151