Finite Group Databasebeta

← C151×#24623 #50329548

Subgroups — C151×#24623 #50329548

Order 38656.

718 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3094×C151C211yesmaximal, characteristic
2C2×#481×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic, complemented
4C2×#428×C151C211yesmaximal, characteristic, complemented
5#2090×C151C212yesmaximal, complemented
6#2063×C151C212yesmaximal, complemented
7#1951×C151C212yesmaximal, complemented
8#1931×C151C212yesmaximal, complemented
9#1900×C151C211yesmaximal, characteristic
10#1855×C151C211yesmaximal, characteristic, complemented
11#1821×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151C2211yescharacteristic
13C2×#121×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16#482×C151—21no—
17#482×C151—21no—
18#481×C151—21no—
19#481×C151—21no—
20#481×C151—21no—
21#481×C151—22no—
22#480×C151—21no—
23#433×C151—22no—
24#432×C151—21no—
25#431×C151—21no—
26C2×#108×C151C2212yes—
27#428×C151—21no—
28#428×C151—21no—
29#428×C151C2211yescharacteristic
30#428×C151C2212yes—
31#428×C151C2212yes—
32#428×C151C2211yescharacteristic
33C2×#107×C151—21no—
34C2×#106×C151—21no—
35C2×#106×C151C2212yes—
36#424×C151C2212yes—
37#418×C151C2211yescharacteristic
38#418×C151C2211yescharacteristic
39C2×#102×C151C2212yes—
40C2×#100×C151C2212yes—
41#407×C151C2211yescharacteristic
42#407×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44#405×C151C2212yes—
45#343×C151C2212yes—
46#343×C151C2212yes—
47#343×C151C2212yes—
48#341×C151C2212yes—
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151C2311yescharacteristic
53C2×M16×C151—21no—
54C2×M16×C151—24no—
55C2×M16×C151C2311yescharacteristic
56C2×M16×C151C2312yes—
57C2×M16×C151C2311yescharacteristic
58C2×M16×C151C2312yes—
59C22×C8×C151—21no—
60C22×C8×C151C2312yes—
61#121×C151—21no—
62#121×C151—21no—
63#121×C151—21no—
64#121×C151—21no—
65#117×C151—21no—
66#117×C151—21no—
67#117×C151D411yescharacteristic
68#117×C151D411yescharacteristic
69#117×C151C2311yescharacteristic
70#117×C151C2311yescharacteristic
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151D411yescharacteristic
77C2×C4⋊C4×C151D411yescharacteristic
78C2×C4⋊C4×C151C2312yes—
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C22⋊C4×C151—21no—
81C2×C22⋊C4×C151—21no—
82C2×C42×C151—21no—
83#108×C151—24no—
84#107×C151—22no—
85#107×C151—22no—
86#107×C151—21no—
87#107×C151—21no—
88#106×C151—22no—
89#106×C151—22no—
90#106×C151—22no—
91#106×C151—22no—
92#106×C151—21no—
93#106×C151—21no—
94C4⋊C8×C151—22no—
95C4⋊C8×C151—22no—
96#102×C151—22no—
97#102×C151—22no—
98#102×C151—21no—
99#102×C151—21no—
100#102×C151—21no—
101#102×C151—21no—
102#100×C151—24no—
103C22⋊C8×C151—21no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151D411yescharacteristic
108C22⋊C8×C151D411yescharacteristic
109C22⋊C8×C151D412yes—
110#97×C151—22no—
111C4×C8×C151—22no—
112C24×C151—21no—
113C24×C151#4111yescharacteristic
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—41no—
119C2×D4×C151—41no—
120C2×D4×C151—82no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—41no—
128C22×C4×C151—41no—
129C22×C4×C151—82no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151#4111yescharacteristic
135C22×C4×C151C2411yescharacteristic
136M16×C151—24no—
137M16×C151—22no—
138M16×C151—22no—
139M16×C151—22no—
140M16×C151—22no—
141M16×C151—22no—
142M16×C151#4114yes—
143C2×C8×C151—24no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151C2×D412yes—
151C2×C8×C151C2×D412yes—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—41no—
159C4⋊C4×C151—41no—
160C4⋊C4×C151C2×D411yescharacteristic
161C4⋊C4×C151C2×D411yescharacteristic
162C4⋊C4×C151C2×D411yescharacteristic
163C4⋊C4×C151C2×D411yescharacteristic
164C22⋊C4×C151—21no—
165C22⋊C4×C151—21no—
166C22⋊C4×C151—21no—
167C22⋊C4×C151—21no—
168C22⋊C4×C151—41no—
169C22⋊C4×C151—41no—
170C42×C151—21no—
171C42×C151—21no—
172C42×C151—21no—
173C42×C151—21no—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—42no—
179C23×C151—81no—
180C23×C151—81no—
181C23×C151#12111yescharacteristic
182C23×C151#12111yescharacteristic
183C23×C151C2×#4111yescharacteristic
184D4×C151—41no—
185D4×C151—41no—
186D4×C151—42no—
187D4×C151—82no—
188D4×C151—82no—
189C2×C4×C151—22no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—42no—
203C2×C4×C151—81no—
204C2×C4×C151—82no—
205C2×C4×C151—82no—
206C2×C4×C151—82no—
207C2×C4×C151—81no—
208C2×C4×C151#12111yescharacteristic
209C2×C4×C151#12111yescharacteristic
210C2×C4×C151C22×D411yescharacteristic
211C2×C4×C151C22×D411yescharacteristic
212C2×C4×C151C2×#4112yes—
213C2×C4×C1512−1+412yes—
214C8×C151—24no—
215C8×C151—22no—
216C8×C151—22no—
217C8×C151—41no—
218C8×C151—41no—
219C8×C151—42no—
220C22×C151—21no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—21no—
224C22×C151—21no—
225C22×C151—21no—
226C22×C151—21no—
227C22×C151—44no—
228C22×C151—81no—
229C22×C151—81no—
230C22×C151—81no—
231C22×C151—162no—
232C22×C151#47112yes—
233C22×C151C2×#12111yescharacteristic
234C22×C151#55212yes—
235C4×C151—21no—
236C4×C151—21no—
237C4×C151—41no—
238C4×C151—41no—
239C4×C151—41no—
240C4×C151—41no—
241C4×C151—81no—
242C4×C151—82no—
243C4×C151#52511yescharacteristic
244C4×C151#53611yescharacteristic
245C4×C151#54712yes—
246C2×C151—22no—
247C2×C151—22no—
248C2×C151—41no—
249C2×C151—161no—
250C2×C151#241311yescharacteristic
251C2×C151C2×#47111yescharacteristic
252C2×C151#306811yescharacteristic
253#24623C15111yesmaximal, characteristic, direct product factor, Sylow
254C151#2462311yescharacteristic, direct product factor, Sylow
255#3094C2×C15111yescharacteristic
256C2×#481C2×C15111yescharacteristic
257#2924C2×C15111yescharacteristic, complemented
258C2×#428C2×C15111yescharacteristic, complemented
259#2090C2×C15112yescomplemented
260#2063C2×C15112yescomplemented
261#1951C2×C15112yescomplemented
262#1931C2×C15112yescomplemented
263#1900C2×C15111yescharacteristic
264#1855C2×C15111yescharacteristic, complemented
265#1821C2×C15111yescharacteristic, complemented
266C22×M16C22×C15111yescharacteristic
267C2×#121C22×C15111yescharacteristic
268C2×#117C22×C15111yescharacteristic
269C22×C4⋊C4C22×C15111yescharacteristic
270#482—21no—
271#482—21no—
272#481—21no—
273#481—21no—
274#481—21no—
275#481—22no—
276#480—21no—
277#433—22no—
278#432—21no—
279#431—21no—
280C2×#108C22×C15112yes—
281#428—21no—
282#428—21no—
283#428C22×C15112yes—
284#428C22×C15111yescharacteristic
285#428C22×C15111yescharacteristic
286#428C22×C15112yes—
287C2×#107—21no—
288C2×#106—21no—
289C2×#106C22×C15112yes—
290#424C22×C15112yes—
291#418C22×C15111yescharacteristic
292#418C22×C15111yescharacteristic
293C2×#102C22×C15112yes—
294C2×#100C22×C15112yes—
295#407C22×C15111yescharacteristic
296#407C22×C15111yescharacteristic
297C2×C22⋊C8C22×C15111yescharacteristic
298#405C22×C15112yes—
299#343C22×C15112yes—
300#343C22×C15112yes—
301#343C22×C15112yes—
302#341C22×C15112yes—
303C22×D4—21no—
304C22×D4C23×C15111yescharacteristic
305C23×C4—21no—
306C23×C4C23×C15111yescharacteristic
307C2×M16—21no—
308C2×M16—24no—
309C2×M16C23×C15111yescharacteristic
310C2×M16C23×C15112yes—
311C2×M16C23×C15111yescharacteristic
312C2×M16C23×C15112yes—
313C22×C8—21no—
314C22×C8C23×C15112yes—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#117—21no—
320#117—21no—
321#117D4×C15111yescharacteristic
322#117D4×C15111yescharacteristic
323#117C23×C15111yescharacteristic
324#117C23×C15111yescharacteristic
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C15111yescharacteristic
331C2×C4⋊C4D4×C15111yescharacteristic
332C2×C4⋊C4C23×C15112yes—
333C2×C4⋊C4C23×C15111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42—21no—
337#108—24no—
338#107—22no—
339#107—22no—
340#107—21no—
341#107—21no—
342#106—22no—
343#106—22no—
344#106—22no—
345#106—22no—
346#106—21no—
347#106—21no—
348C4⋊C8—22no—
349C4⋊C8—22no—
350#102—22no—
351#102—22no—
352#102—21no—
353#102—21no—
354#102—21no—
355#102—21no—
356#100—24no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8D4×C15111yescharacteristic
362C22⋊C8D4×C15111yescharacteristic
363C22⋊C8D4×C15112yes—
364#97—22no—
365C4×C8—22no—
366C24—21no—
367C24#41×C15111yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—82no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—82no—
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4#41×C15111yescharacteristic
389C22×C4C24×C15111yescharacteristic
390M16—24no—
391M16—22no—
392M16—22no—
393M16—22no—
394M16—22no—
395M16—22no—
396M16#41×C15114yes—
397C2×C8—24no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8C2×D4×C15112yes—
405C2×C8C2×D4×C15112yes—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4C2×D4×C15111yescharacteristic
415C4⋊C4C2×D4×C15111yescharacteristic
416C4⋊C4C2×D4×C15111yescharacteristic
417C4⋊C4C2×D4×C15111yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—81no—
434C23—81no—
435C23#121×C15111yescharacteristic
436C23#121×C15111yescharacteristic
437C23C2×#41×C15111yescharacteristic
438D4—41no—
439D4—41no—
440D4—42no—
441D4—82no—
442D4—82no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4#121×C15111yescharacteristic
463C2×C4#121×C15111yescharacteristic
464C2×C4C22×D4×C15111yescharacteristic
465C2×C4C22×D4×C15111yescharacteristic
466C2×C4C2×#41×C15112yes—
467C2×C42−1+4×C15112yes—
468C8—24no—
469C8—22no—
470C8—22no—
471C8—41no—
472C8—41no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—162no—
486C22#471×C15112yes—
487C22C2×#121×C15111yescharacteristic
488C22#552×C15112yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—81no—
496C4—82no—
497C4#525×C15111yescharacteristic
498C4#536×C15111yescharacteristic
499C4#547×C15112yes—
500C2—22no—
501C2—22no—
502C2—41no—
503C2—161no—
504C2#2413×C15111yescharacteristic
505C2C2×#471×C15111yescharacteristic
506C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2924×C151C2semidirect
4. C2×#428×C151C2semidirect
5. #2090×C151C2semidirect
6. #2063×C151C2semidirect
7. #1951×C151C2semidirect
8. #1931×C151C2semidirect
10. #1855×C151C2semidirect
11. #1821×C151C2semidirect
253. #24623C151direct (N × H)
254. C151#24623direct (N × H)
257. #2924C2×C151semidirect
258. C2×#428C2×C151semidirect
259. #2090C2×C151semidirect
260. #2063C2×C151semidirect
261. #1951C2×C151semidirect
262. #1931C2×C151semidirect
264. #1855C2×C151semidirect
265. #1821C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3094×C1512
C2×#481×C1512
#2924×C1512
C2×#428×C1512
#2090×C1512
#2063×C1512
#1951×C1512
#1931×C1512
#1900×C1512
#1855×C1512
#1821×C1512
#24623151