Finite Group Databasebeta

← C151×#24865 #50329790

Subgroups — C151×#24865 #50329790

Order 38656.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C151C211yesmaximal, characteristic, complemented
2C22×#102×C151C211yesmaximal, characteristic, complemented
3#2408×C151C211yesmaximal, characteristic
4D4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
5#2094×C151C211yesmaximal, characteristic, complemented
6#2071×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#1926×C151C211yesmaximal, characteristic, complemented
10#1926×C151C211yesmaximal, characteristic, complemented
11#1874×C151C211yesmaximal, characteristic, complemented
12#1869×C151C211yesmaximal, characteristic, complemented
13#1853×C151C211yesmaximal, characteristic, complemented
14#1807×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×#121×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×#120×C151—21no—
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic, complemented
25#481×C151—24no—
26C2×#106×C151C2211yescharacteristic, complemented
27C2×#106×C151C2211yescharacteristic, complemented
28C2×#106×C151C2211yescharacteristic, complemented
29C2×#106×C151C2211yescharacteristic, complemented
30C2×#102×C151—24no—
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×C22⋊C8×C151C2211yescharacteristic, complemented
41C2×C22⋊C8×C151C2211yescharacteristic, complemented
42#394×C151—21no—
43#392×C151—21no—
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#389×C151—21no—
47#385×C151—21no—
48#385×C151—21no—
49#384×C151C2211yescharacteristic, complemented
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic, complemented
53#379×C151—21no—
54C4×C4⋊C4×C151C2211yescharacteristic, complemented
55#340×C151C2211yescharacteristic, complemented
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—41no—
70C22×D4×C151—41no—
71C22×D4×C151D411yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C22×D4×C151C2311yescharacteristic
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C22×C8×C151—22no—
79C22×C8×C151—22no—
80C22×C8×C151—41no—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85#121×C151—22no—
86#121×C151—22no—
87#121×C151—41no—
88#121×C151—41no—
89#120×C151—44no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—44no—
93C2×C4⋊C4×C151—22no—
94C2×C4⋊C4×C151—22no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—41no—
100C2×C4⋊C4×C151—41no—
101C2×C4⋊C4×C151D411yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151D411yescharacteristic
118C2×C22⋊C4×C151D411yescharacteristic
119C2×C42×C151—21no—
120C2×C42×C151C2311yescharacteristic
121#106×C151—22no—
122#106×C151—22no—
123#106×C151—41no—
124#106×C151—41no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—41no—
131#102×C151—41no—
132#102×C151D414yescomplemented
133C22⋊C8×C151—22no—
134C22⋊C8×C151—22no—
135C22⋊C8×C151—41no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140C24×C151—21no—
141C24×C151—21no—
142C24×C151—42no—
143C24×C151—42no—
144C24×C151—42no—
145C24×C151—42no—
146C24×C151—42no—
147C24×C151—81no—
148C24×C151—81no—
149C24×C151C2×D411yescharacteristic
150C24×C151C2×D411yescharacteristic
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—28no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—44no—
165C2×D4×C151—44no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—44no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—42no—
174C2×D4×C151—81no—
175C2×D4×C151—81no—
176C2×D4×C151SD1614yes—
177C2×D4×C151C2×D412yes—
178C2×D4×C151#4112yes—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—42no—
196C22×C4×C151—42no—
197C22×C4×C151—42no—
198C22×C4×C151—42no—
199C22×C4×C151—81no—
200C22×C4×C151—81no—
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151#4112yes—
206C22×C4×C151#4112yes—
207C22×C4×C151C2411yescharacteristic
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—44no—
220C2×C8×C151C2×D412yes—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—42no—
234C4⋊C4×C151—42no—
235C4⋊C4×C151—42no—
236C4⋊C4×C151—81no—
237C4⋊C4×C151C2×D412yes—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—42no—
243C22⋊C4×C151—42no—
244C22⋊C4×C151—42no—
245C22⋊C4×C151—42no—
246C22⋊C4×C151—42no—
247C22⋊C4×C151—81no—
248C22⋊C4×C151—81no—
249C42×C151—21no—
250C42×C151—21no—
251C42×C151—42no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—22no—
263C23×C151—22no—
264C23×C151—48no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—41no—
277C23×C151—84no—
278C23×C151—84no—
279C23×C151—84no—
280C23×C151—84no—
281C23×C151—84no—
282C23×C151—84no—
283C23×C151#12312yes—
284C23×C151C2×SD1612yes—
285C23×C151C2×SD1612yes—
286C23×C151AGL(1,ℤ/8)12yes—
287C23×C151C22×D411yescharacteristic
288D4×C151—28no—
289D4×C151—22no—
290D4×C151—22no—
291D4×C151—22no—
292D4×C151—22no—
293D4×C151—48no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—41no—
298D4×C151—84no—
299D4×C151—84no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—22no—
307C2×C4×C151—22no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—22no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—84no—
337C2×C4×C151—84no—
338C2×C4×C151#12312yes—
339C2×C4×C151C2×SD1612yes—
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C2×#4111yescharacteristic
342C2×C4×C151C2×#4111yescharacteristic
343C2×C4×C151C2×#4111yescharacteristic
344C2×C4×C151H(5,𝔽2)11yescharacteristic
345C2×C4×C151H(5,𝔽2)11yescharacteristic
346C8×C151—22no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C22×C151—22no—
351C22×C151—22no—
352C22×C151—22no—
353C22×C151—22no—
354C22×C151—22no—
355C22×C151—22no—
356C22×C151—22no—
357C22×C151—22no—
358C22×C151—22no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—42no—
364C22×C151—42no—
365C22×C151—42no—
366C22×C151—42no—
367C22×C151—42no—
368C22×C151—42no—
369C22×C151—816no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—81no—
377C22×C151—81no—
378C22×C151#48114yescomplemented
379C22×C151C2×#12311yescharacteristic
380C22×C151D4211yescharacteristic
381C22×C151#54611yescharacteristic
382C22×C151C22×SD1611yescharacteristic
383C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C151#57611yescharacteristic
385C22×C151#57711yescharacteristic
386C4×C151—22no—
387C4×C151—22no—
388C4×C151—41no—
389C4×C151—41no—
390C4×C151—42no—
391C4×C151—81no—
392C4×C151—81no—
393C4×C151—81no—
394C4×C151—81no—
395C4×C151—81no—
396C4×C151#52511yescharacteristic
397C4×C151#53811yescharacteristic
398C4×C151#54611yescharacteristic
399C4×C151#55111yescharacteristic
400C2×C151—24no—
401C2×C151—42no—
402C2×C151—82no—
403C2×C151—82no—
404C2×C151#241811yescharacteristic
405C2×C151C2×#48111yescharacteristic
406C2×C151#309611yescharacteristic
407C2×C151#326411yescharacteristic
408C2×C151D4×SD1611yescharacteristic
409C2×C151#329511yescharacteristic
410C2×C151#330611yescharacteristic
411#24865C15111yesmaximal, characteristic, direct product factor, Sylow
412C151#2486511yescharacteristic, direct product factor, Sylow
413C2×#481C2×C15111yescharacteristic, complemented
414C22×#102C2×C15111yescharacteristic, complemented
415#2408C2×C15111yescharacteristic
416D4×C4⋊C4C2×C15111yescharacteristic, complemented
417#2094C2×C15111yescharacteristic, complemented
418#2071C2×C15111yescharacteristic, complemented
419#2034C2×C15111yescharacteristic, complemented
420#2034C2×C15111yescharacteristic, complemented
421#1926C2×C15111yescharacteristic, complemented
422#1926C2×C15111yescharacteristic, complemented
423#1874C2×C15111yescharacteristic, complemented
424#1869C2×C15111yescharacteristic, complemented
425#1853C2×C15111yescharacteristic, complemented
426#1807C2×C15111yescharacteristic, complemented
427#1786C2×C15111yescharacteristic, complemented
428C23×D4C22×C15111yescharacteristic
429C23×C8C22×C15111yescharacteristic
430C2×#121C22×C15111yescharacteristic
431C2×#121C22×C15111yescharacteristic
432C2×#120—21no—
433C2×C4×D4—21no—
434C2×C4×D4C22×C15111yescharacteristic
435C22×C4⋊C4C22×C15111yescharacteristic
436C22×C4⋊C4C22×C15111yescharacteristic, complemented
437#481—24no—
438C2×#106C22×C15111yescharacteristic, complemented
439C2×#106C22×C15111yescharacteristic, complemented
440C2×#106C22×C15111yescharacteristic, complemented
441C2×#106C22×C15111yescharacteristic, complemented
442C2×#102—24no—
443C2×#102C22×C15111yescharacteristic
444C2×#102C22×C15111yescharacteristic
445C2×#102C22×C15111yescharacteristic
446C2×#102C22×C15111yescharacteristic
447C2×#102C22×C15111yescharacteristic
448C2×#102C22×C15111yescharacteristic
449C2×#102C22×C15111yescharacteristic
450C2×#102C22×C15111yescharacteristic
451C2×C22⋊C8C22×C15111yescharacteristic
452C2×C22⋊C8C22×C15111yescharacteristic, complemented
453C2×C22⋊C8C22×C15111yescharacteristic, complemented
454#394—21no—
455#392—21no—
456#390C22×C15111yescharacteristic
457#390C22×C15111yescharacteristic
458#389—21no—
459#385—21no—
460#385—21no—
461#384C22×C15111yescharacteristic, complemented
462#380C22×C15111yescharacteristic
463#380C22×C15111yescharacteristic
464#380C22×C15111yescharacteristic, complemented
465#379—21no—
466C4×C4⋊C4C22×C15111yescharacteristic, complemented
467#340C22×C15111yescharacteristic, complemented
468#340C22×C15111yescharacteristic, complemented
469#340C22×C15111yescharacteristic, complemented
470#340C22×C15111yescharacteristic, complemented
471#336C22×C15111yescharacteristic, complemented
472#336C22×C15111yescharacteristic, complemented
473C25—21no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—21no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4D4×C15111yescharacteristic
484C22×D4C23×C15111yescharacteristic
485C22×D4C23×C15111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C15111yescharacteristic
489C23×C4C23×C15111yescharacteristic
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—41no—
493C22×C8C23×C15111yescharacteristic
494C22×C8C23×C15111yescharacteristic
495C22×C8C23×C15111yescharacteristic
496C22×C8C23×C15111yescharacteristic
497#121—22no—
498#121—22no—
499#121—41no—
500#121—41no—
501#120—44no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—44no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4D4×C15111yescharacteristic
514C2×C4⋊C4C23×C15111yescharacteristic
515C2×C4⋊C4C23×C15111yescharacteristic
516C2×C4⋊C4C23×C15111yescharacteristic
517C2×C4⋊C4C23×C15111yescharacteristic
518C2×C4⋊C4C23×C15111yescharacteristic
519C2×C4⋊C4C23×C15111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4D4×C15111yescharacteristic
530C2×C22⋊C4D4×C15111yescharacteristic
531C2×C42—21no—
532C2×C42C23×C15111yescharacteristic
533#106—22no—
534#106—22no—
535#106—41no—
536#106—41no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—41no—
543#102—41no—
544#102D4×C15114yescomplemented
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×D4×C15111yescharacteristic
562C24C2×D4×C15111yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—28no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4SD16×C15114yes—
589C2×D4C2×D4×C15112yes—
590C2×D4#41×C15112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C15111yescharacteristic
614C22×C4C2×D4×C15111yescharacteristic
615C22×C4C2×D4×C15111yescharacteristic
616C22×C4C2×D4×C15111yescharacteristic
617C22×C4#41×C15112yes—
618C22×C4#41×C15112yes—
619C22×C4C24×C15111yescharacteristic
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8C2×D4×C15112yes—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4C2×D4×C15112yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#123×C15112yes—
696C23C2×SD16×C15112yes—
697C23C2×SD16×C15112yes—
698C23AGL(1,ℤ/8)×C15112yes—
699C23C22×D4×C15111yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4#123×C15112yes—
751C2×C4C2×SD16×C15112yes—
752C2×C4C22×D4×C15111yescharacteristic
753C2×C4C2×#41×C15111yescharacteristic
754C2×C4C2×#41×C15111yescharacteristic
755C2×C4C2×#41×C15111yescharacteristic
756C2×C4H(5,𝔽2)×C15111yescharacteristic
757C2×C4H(5,𝔽2)×C15111yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22#481×C15114yescomplemented
791C22C2×#123×C15111yescharacteristic
792C22D42×C15111yescharacteristic
793C22#546×C15111yescharacteristic
794C22C22×SD16×C15111yescharacteristic
795C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
796C22#576×C15111yescharacteristic
797C22#577×C15111yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4#525×C15111yescharacteristic
809C4#538×C15111yescharacteristic
810C4#546×C15111yescharacteristic
811C4#551×C15111yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2#2418×C15111yescharacteristic
817C2C2×#481×C15111yescharacteristic
818C2#3096×C15111yescharacteristic
819C2#3264×C15111yescharacteristic
820C2D4×SD16×C15111yescharacteristic
821C2#3295×C15111yescharacteristic
822C2#3306×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2408×C151C2
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
1. C2×#481×C151C2semidirect
2. C22×#102×C151C2semidirect
4. D4×C4⋊C4×C151C2semidirect
5. #2094×C151C2semidirect
6. #2071×C151C2semidirect
7. #2034×C151C2semidirect
8. #2034×C151C2semidirect
9. #1926×C151C2semidirect
10. #1926×C151C2semidirect
11. #1874×C151C2semidirect
12. #1869×C151C2semidirect
13. #1853×C151C2semidirect
14. #1807×C151C2semidirect
15. #1786×C151C2semidirect
24. C22×C4⋊C4×C151C22semidirect
26. C2×#106×C151C22semidirect
27. C2×#106×C151C22semidirect
28. C2×#106×C151C22semidirect
29. C2×#106×C151C22semidirect
40. C2×C22⋊C8×C151C22semidirect
41. C2×C22⋊C8×C151C22semidirect
49. #384×C151C22semidirect
52. #380×C151C22semidirect
54. C4×C4⋊C4×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
132. #102×C151D4semidirect
378. C22×C151#481semidirect
411. #24865C151direct (N × H)
412. C151#24865direct (N × H)
413. C2×#481C2×C151semidirect
414. C22×#102C2×C151semidirect
416. D4×C4⋊C4C2×C151semidirect
417. #2094C2×C151semidirect
418. #2071C2×C151semidirect
419. #2034C2×C151semidirect
420. #2034C2×C151semidirect
421. #1926C2×C151semidirect
422. #1926C2×C151semidirect
423. #1874C2×C151semidirect
424. #1869C2×C151semidirect
425. #1853C2×C151semidirect
426. #1807C2×C151semidirect
427. #1786C2×C151semidirect
436. C22×C4⋊C4C22×C151semidirect
438. C2×#106C22×C151semidirect
439. C2×#106C22×C151semidirect
440. C2×#106C22×C151semidirect
441. C2×#106C22×C151semidirect
452. C2×C22⋊C8C22×C151semidirect
453. C2×C22⋊C8C22×C151semidirect
461. #384C22×C151semidirect
464. #380C22×C151semidirect
466. C4×C4⋊C4C22×C151semidirect
467. #340C22×C151semidirect
468. #340C22×C151semidirect
469. #340C22×C151semidirect
470. #340C22×C151semidirect
471. #336C22×C151semidirect
472. #336C22×C151semidirect
544. #102D4×C151semidirect
790. C22#481×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1512
C22×#102×C1512
#2408×C1512
D4×C4⋊C4×C1512
#2094×C1512
#2071×C1512
#2034×C1512
#1926×C1512
#1874×C1512
#1869×C1512
#1853×C1512
#1807×C1512
#1786×C1512
#24865151