Finite Group Databasebeta

← C2×#2077×C151 #50328561

Subgroups — C2×#2077×C151 #50328561

Order 38656.

1270 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
1C22×#106×C151C211yesmaximal, characteristic, complemented
2C22×C22⋊C8×C151C211yesmaximal, characteristic
3C2×#380×C151C211yesmaximal, characteristic
4C2×#380×C151C211yesmaximal, characteristic
5#2077×C151C218yesmaximal, direct product factor
6C2×#340×C151C211yesmaximal, characteristic, complemented
7C2×#340×C151C211yesmaximal, characteristic, complemented
8C2×#340×C151C211yesmaximal, characteristic, complemented
9C24×C4×C151C2211yescharacteristic
10C23×C8×C151C2211yescharacteristic
11C23×C8×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C22⋊C4×C151—21no—
17C22×C22⋊C4×C151—21no—
18C2×#106×C151—24no—
19C2×#106×C151C2214yescomplemented
20C2×C22⋊C8×C151—24no—
21C2×C22⋊C8×C151C2214yes—
22#380×C151—22no—
23#380×C151—22no—
24#380×C151C2214yes—
25#380×C151C2214yes—
26C2×#95×C151—21no—
27C2×#95×C151—21no—
28#340×C151C2214yescomplemented
29#340×C151C2214yescomplemented
30#340×C151C2214yescomplemented
31C25×C151D411yescharacteristic
32C23×C4×C151—22no—
33C23×C4×C151—22no—
34C23×C4×C151—22no—
35C23×C4×C151—22no—
36C23×C4×C151—22no—
37C23×C4×C151—22no—
38C23×C4×C151—21no—
39C23×C4×C151—21no—
40C23×C4×C151—21no—
41C23×C4×C151—21no—
42C23×C4×C151D412yes—
43C23×C4×C151D411yescharacteristic
44C23×C4×C151C2312yes—
45C23×C4×C151C2311yescharacteristic
46C22×C8×C151—22no—
47C22×C8×C151—22no—
48C22×C8×C151—22no—
49C22×C8×C151—22no—
50C22×C8×C151—22no—
51C22×C8×C151D414yes—
52C22×C8×C151C2312yes—
53C22×C8×C151C2312yes—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2312yes—
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2312yes—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—44no—
73C2×C22⋊C4×C151—44no—
74#106×C151—28no—
75C22⋊C8×C151—28no—
76#95×C151—24no—
77#95×C151—24no—
78C24×C151—22no—
79C24×C151—22no—
80C24×C151—22no—
81C24×C151—22no—
82C24×C151—22no—
83C24×C151—22no—
84C24×C151SD1614yes—
85C24×C151C2×D412yes—
86C24×C151C2×D411yescharacteristic
87C22×C4×C151—22no—
88C22×C4×C151—22no—
89C22×C4×C151—22no—
90C22×C4×C151—24no—
91C22×C4×C151—24no—
92C22×C4×C151—24no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—44no—
104C22×C4×C151—44no—
105C22×C4×C151—44no—
106C22×C4×C151—44no—
107C22×C4×C151—42no—
108C22×C4×C151—42no—
109C22×C4×C151—42no—
110C22×C4×C151—42no—
111C22×C4×C151—42no—
112C22×C4×C151—42no—
113C22×C4×C151—42no—
114C22×C4×C151—42no—
115C22×C4×C151—42no—
116C22×C4×C151—42no—
117C22×C4×C151—42no—
118C22×C4×C151—42no—
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2×D412yes—
122C22×C4×C151#4112yes—
123C22×C4×C151#4112yes—
124C22×C4×C151#4112yes—
125C22×C4×C151#4112yes—
126C22×C4×C151#4112yes—
127C22×C4×C151C2411yescharacteristic
128C2×C8×C151—28no—
129C2×C8×C151—22no—
130C2×C8×C151—22no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C2×C8×C151—44no—
135C2×C8×C151C2×D414yes—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—42no—
145C4⋊C4×C151—42no—
146C4⋊C4×C151—42no—
147C4⋊C4×C151—42no—
148C22⋊C4×C151—48no—
149C22⋊C4×C151—48no—
150C23×C151—22no—
151C23×C151—22no—
152C23×C151—22no—
153C23×C151—22no—
154C23×C151—22no—
155C23×C151—22no—
156C23×C151—28no—
157C23×C151—28no—
158C23×C151—28no—
159C23×C151—44no—
160C23×C151—44no—
161C23×C151—44no—
162C23×C151—44no—
163C23×C151#12112yes—
164C23×C151#12312yes—
165C23×C151#12312yes—
166C23×C151C2×SD1614yes—
167C23×C151C2×SD1612yes—
168C23×C151#13512yes—
169C23×C151AGL(1,ℤ/8)12yes—
170C23×C151#13712yes—
171C23×C151C22×D411yescharacteristic
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—44no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—48no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
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—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—84no—
194C2×C4×C151—84no—
195C2×C4×C151—84no—
196C2×C4×C151—84no—
197C2×C4×C151#12112yes—
198C2×C4×C151#12314yes—
199C2×C4×C151#12312yes—
200C2×C4×C151#12312yes—
201C2×C4×C151#12414yes—
202C2×C4×C151#12614yes—
203C2×C4×C151#12614yes—
204C2×C4×C151C22×D411yescharacteristic
205C2×C4×C151C2×#4111yescharacteristic
206C2×C4×C151C2×#4111yescharacteristic
207C2×C4×C151C2×#4111yescharacteristic
208C2×C4×C151C2×#4111yescharacteristic
209C2×C4×C151C2×#4111yescharacteristic
210C8×C151—24no—
211C8×C151—42no—
212C22×C151—24no—
213C22×C151—24no—
214C22×C151—24no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151—416no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151#39714yes—
221C22×C151#46514yes—
222C22×C151#46814yes—
223C22×C151#48114yes—
224C22×C151#48214yes—
225C22×C151#48314yes—
226C22×C151#48514yes—
227C22×C151C2×#12111yescharacteristic
228C22×C151C2×#12311yescharacteristic
229C22×C151C2×#12311yescharacteristic
230C22×C151C22×SD1611yescharacteristic
231C22×C151C2×#13511yescharacteristic
232C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
233C22×C151C2×#13711yescharacteristic
234C4×C151—42no—
235C4×C151—82no—
236C4×C151—82no—
237C4×C151—82no—
238C4×C151—82no—
239C4×C151#39714yes—
240C4×C151C2×#12311yescharacteristic
241C4×C151C2×#12411yescharacteristic
242C4×C151C2×#12611yescharacteristic
243C4×C151C2×#12611yescharacteristic
244C2×C151—44no—
245C2×C151#207718yesdirect product factor
246C2×C151C2×#39711yescharacteristic
247C2×C151C2×#46511yescharacteristic
248C2×C151C2×#46811yescharacteristic
249C2×C151C2×#48311yescharacteristic
250C2×C151C2×#48211yescharacteristic
251C2×C151C2×#48511yescharacteristic
252C2×C151C2×#48111yescharacteristic
253C2×#2077C15111yesmaximal, characteristic, direct product factor, Sylow
254C151C2×#207711yescharacteristic, direct product factor, Sylow
255C22×#106C2×C15111yescharacteristic, complemented
256C22×C22⋊C8C2×C15111yescharacteristic
257C2×#380C2×C15111yescharacteristic
258C2×#380C2×C15111yescharacteristic
259#2077C2×C15118yesdirect product factor
260C2×#340C2×C15111yescharacteristic, complemented
261C2×#340C2×C15111yescharacteristic, complemented
262C2×#340C2×C15111yescharacteristic, complemented
263C24×C4C22×C15111yescharacteristic
264C23×C8C22×C15111yescharacteristic
265C23×C8C22×C15111yescharacteristic
266C22×C4⋊C4C22×C15111yescharacteristic
267C22×C4⋊C4C22×C15111yescharacteristic
268C22×C4⋊C4C22×C15111yescharacteristic
269C22×C4⋊C4C22×C15111yescharacteristic
270C22×C22⋊C4—21no—
271C22×C22⋊C4—21no—
272C2×#106—24no—
273C2×#106C22×C15114yescomplemented
274C2×C22⋊C8—24no—
275C2×C22⋊C8C22×C15114yes—
276#380—22no—
277#380—22no—
278#380C22×C15114yes—
279#380C22×C15114yes—
280C2×#95—21no—
281C2×#95—21no—
282#340C22×C15114yescomplemented
283#340C22×C15114yescomplemented
284#340C22×C15114yescomplemented
285C25D4×C15111yescharacteristic
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4D4×C15111yescharacteristic
297C23×C4D4×C15112yes—
298C23×C4C23×C15112yes—
299C23×C4C23×C15111yescharacteristic
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8D4×C15114yes—
306C22×C8C23×C15112yes—
307C22×C8C23×C15112yes—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C23×C15112yes—
321C2×C4⋊C4C23×C15112yes—
322C2×C4⋊C4C23×C15112yes—
323C2×C4⋊C4C23×C15112yes—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328#106—28no—
329C22⋊C8—28no—
330#95—24no—
331#95—24no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24SD16×C15114yes—
339C24C2×D4×C15112yes—
340C24C2×D4×C15111yescharacteristic
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4C2×D4×C15112yes—
374C22×C4C2×D4×C15111yescharacteristic
375C22×C4C2×D4×C15112yes—
376C22×C4#41×C15112yes—
377C22×C4#41×C15112yes—
378C22×C4#41×C15112yes—
379C22×C4#41×C15112yes—
380C22×C4#41×C15112yes—
381C22×C4C24×C15111yescharacteristic
382C2×C8—28no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—44no—
389C2×C8C2×D4×C15114yes—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—42no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C22⋊C4—48no—
403C22⋊C4—48no—
404C23—28no—
405C23—28no—
406C23—28no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—44no—
414C23—44no—
415C23—44no—
416C23—44no—
417C23#121×C15112yes—
418C23#123×C15112yes—
419C23#123×C15112yes—
420C23C2×SD16×C15114yes—
421C23C2×SD16×C15112yes—
422C23#135×C15112yes—
423C23AGL(1,ℤ/8)×C15112yes—
424C23#137×C15112yes—
425C23C22×D4×C15111yescharacteristic
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—44no—
430C2×C4—48no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—84no—
448C2×C4—84no—
449C2×C4—84no—
450C2×C4—84no—
451C2×C4#121×C15112yes—
452C2×C4#123×C15112yes—
453C2×C4#123×C15112yes—
454C2×C4#123×C15114yes—
455C2×C4#124×C15114yes—
456C2×C4#126×C15114yes—
457C2×C4#126×C15114yes—
458C2×C4C22×D4×C15111yescharacteristic
459C2×C4C2×#41×C15111yescharacteristic
460C2×C4C2×#41×C15111yescharacteristic
461C2×C4C2×#41×C15111yescharacteristic
462C2×C4C2×#41×C15111yescharacteristic
463C2×C4C2×#41×C15111yescharacteristic
464C8—24no—
465C8—42no—
466C22—24no—
467C22—24no—
468C22—24no—
469C22—416no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22#397×C15114yes—
475C22#465×C15114yes—
476C22#468×C15114yes—
477C22#481×C15114yes—
478C22#482×C15114yes—
479C22#483×C15114yes—
480C22#485×C15114yes—
481C22C2×#121×C15111yescharacteristic
482C22C2×#123×C15111yescharacteristic
483C22C2×#123×C15111yescharacteristic
484C22C22×SD16×C15111yescharacteristic
485C22C2×#135×C15111yescharacteristic
486C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
487C22C2×#137×C15111yescharacteristic
488C4—42no—
489C4—82no—
490C4—82no—
491C4—82no—
492C4—82no—
493C4#397×C15114yes—
494C4C2×#123×C15111yescharacteristic
495C4C2×#124×C15111yescharacteristic
496C4C2×#126×C15111yescharacteristic
497C4C2×#126×C15111yescharacteristic
498C2—44no—
499C2#2077×C15118yesdirect product factor
500C2C2×#397×C15111yescharacteristic
501C2C2×#465×C15111yescharacteristic
502C2C2×#468×C15111yescharacteristic
503C2C2×#483×C15111yescharacteristic
504C2C2×#482×C15111yescharacteristic
505C2C2×#485×C15111yescharacteristic
506C2C2×#481×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC25×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#106×C151C2semidirect
5. #2077×C151C2direct (N × H)
6. C2×#340×C151C2semidirect
7. C2×#340×C151C2semidirect
8. C2×#340×C151C2semidirect
19. C2×#106×C151C22semidirect
28. #340×C151C22semidirect
29. #340×C151C22semidirect
30. #340×C151C22semidirect
245. C2×C151#2077direct (N × H)
253. C2×#2077C151direct (N × H)
254. C151C2×#2077direct (N × H)
255. C22×#106C2×C151semidirect
259. #2077C2×C151direct (N × H)
260. C2×#340C2×C151semidirect
261. C2×#340C2×C151semidirect
262. C2×#340C2×C151semidirect
273. C2×#106C22×C151semidirect
282. #340C22×C151semidirect
283. #340C22×C151semidirect
284. #340C22×C151semidirect
499. C2#2077×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#106×C1512
C22×C22⋊C8×C1512
C2×#380×C1512
#2077×C1512
C2×#340×C1512
C2×#2077151