Finite Group Databasebeta

← C151×#22874 #50327799

Subgroups — C151×#22874 #50327799

Order 38656.

1314 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
3C22×#102×C151C211yesmaximal, characteristic
4#2360×C151C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C151C211yesmaximal, characteristic
6#1968×C151C211yesmaximal, characteristic, complemented
7#1934×C151C211yesmaximal, characteristic, complemented
8#1926×C151C211yesmaximal, characteristic, complemented
9#1892×C151C211yesmaximal, characteristic, complemented
10#1880×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1864×C151C211yesmaximal, characteristic, complemented
13#1853×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic, complemented
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25C22×C22⋊C4×C151—21no—
26#450×C151C418yescomplemented
27C4×SD16×C151—24no—
28C2×#106×C151C2211yescharacteristic, complemented
29C2×#106×C151C2211yescharacteristic, complemented
30C2×#103×C151C2211yescharacteristic, complemented
31C2×#103×C151C2211yescharacteristic, complemented
32C2×#102×C151—24no—
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic, complemented
41C2×C4×C8×C151C2211yescharacteristic, complemented
42#391×C151C2211yescharacteristic, complemented
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#389×C151—21no—
46#389×C151C2211yescharacteristic, complemented
47#387×C151—21no—
48#386×C151—21no—
49#386×C151—21no—
50#385×C151—21no—
51#380×C151C2211yescharacteristic
52#379×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic, complemented
54C4×C22⋊C4×C151—21no—
55C4×C22⋊C4×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61#336×C151C2211yescharacteristic, complemented
62C25×C151—21no—
63C22×Q8×C151C2311yescharacteristic
64C22×D4×C151—21no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151C2×C414yes—
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77C2×SD16×C151—22no—
78C2×SD16×C151—22no—
79C2×SD16×C151—41no—
80C2×SD16×C151—41no—
81C2×SD16×C151C2×C414yescomplemented
82C2×SD16×C151C2×C414yescomplemented
83C22×C8×C151—22no—
84C22×C8×C151—22no—
85C22×C8×C151—41no—
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151C2×C414yescomplemented
92C4×Q8×C151—22no—
93C4×Q8×C151—41no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—41no—
97C4×D4×C151—41no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—22no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—41no—
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
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×C151—44no—
118C2×C22⋊C4×C151D411yescharacteristic
119C2×C22⋊C4×C151D411yescharacteristic
120C2×C42×C151—21no—
121C2×C42×C151—21no—
122C2×C42×C151C2311yescharacteristic
123C2×C42×C151C2311yescharacteristic
124#106×C151—22no—
125#106×C151—41no—
126#103×C151—22no—
127#103×C151—41no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—22no—
131#102×C151C2×C414yescomplemented
132#102×C151C2×C414yescomplemented
133#102×C151D414yes—
134C22⋊C8×C151C2×C414yescomplemented
135C4×C8×C151—22no—
136C4×C8×C151—41no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142#95×C151D411yescharacteristic
143#95×C151D411yescharacteristic
144C24×C151—21no—
145C24×C151—21no—
146C24×C151—24no—
147C24×C151—42no—
148C24×C151—42no—
149C24×C151—42no—
150C24×C151—42no—
151C24×C151—81no—
152C24×C151—81no—
153C24×C151C2×D411yescharacteristic
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151C22×C412yes—
160C2×D4×C151—28no—
161C2×D4×C151—24no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—44no—
171C2×D4×C151—44no—
172C2×D4×C151—44no—
173C2×D4×C151—42no—
174C2×D4×C151—42no—
175C2×D4×C151C22×C412yes—
176C2×D4×C151C22×C412yes—
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—42no—
190C22×C4×C151—42no—
191C22×C4×C151—42no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—81no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151C22×C412yes—
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151#4112yes—
205C22×C4×C151C2411yescharacteristic
206SD16×C151—28no—
207SD16×C151—44no—
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—44no—
218C2×C8×C151C22×C412yes—
219C2×C8×C151C22×C412yes—
220C2×C8×C151C2×D412yes—
221C4⋊C4×C151—24no—
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—42no—
231C4⋊C4×C151—42no—
232C4⋊C4×C151—81no—
233C4⋊C4×C151C22×C412yes—
234C4⋊C4×C151C2×D412yes—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—42no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—81no—
243C22⋊C4×C151—81no—
244C22⋊C4×C151SD1614yescomplemented
245C42×C151—21no—
246C42×C151—21no—
247C42×C151—21no—
248C42×C151—21no—
249C42×C151—42no—
250C42×C151—81no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—22no—
256C23×C151—22no—
257C23×C151—22no—
258C23×C151—22no—
259C23×C151—48no—
260C23×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—48no—
271C23×C151—84no—
272C23×C151—84no—
273C23×C151—84no—
274C23×C151—84no—
275C23×C151—84no—
276C23×C151C4×D412yes—
277C23×C151C2×SD1612yes—
278C23×C151#13512yes—
279C23×C151C22×D411yescharacteristic
280Q8×C151—22no—
281Q8×C151—22no—
282Q8×C151—41no—
283Q8×C151—41no—
284D4×C151—22no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—48no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151C4×D414yes—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—22no—
303C2×C4×C151—22no—
304C2×C4×C151—22no—
305C2×C4×C151—21no—
306C2×C4×C151—22no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
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—84no—
328C2×C4×C151—84no—
329C2×C4×C151—84no—
330C2×C4×C151C4×D412yes—
331C2×C4×C151C2×SD1612yes—
332C2×C4×C151C2×SD1612yes—
333C2×C4×C151C23×C411yescharacteristic
334C2×C4×C151C22×D411yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151C2×#4111yescharacteristic
337C2×C4×C151H(5,𝔽2)11yescharacteristic
338C2×C4×C151H(5,𝔽2)11yescharacteristic
339C8×C151—22no—
340C8×C151—22no—
341C8×C151—22no—
342C8×C151—41no—
343C22×C151—22no—
344C22×C151—22no—
345C22×C151—22no—
346C22×C151—22no—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—24no—
350C22×C151—42no—
351C22×C151—42no—
352C22×C151—42no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—42no—
358C22×C151—42no—
359C22×C151—816no—
360C22×C151—81no—
361C22×C151—81no—
362C22×C151—81no—
363C22×C151—81no—
364C22×C151C4×SD1614yescomplemented
365C22×C151C2×C4×D411yescharacteristic
366C22×C151D4211yescharacteristic
367C22×C151#54611yescharacteristic
368C22×C151C22×SD1611yescharacteristic
369C22×C151C2×#13511yescharacteristic
370C22×C151#57611yescharacteristic
371C22×C151#57711yescharacteristic
372C4×C151—22no—
373C4×C151—22no—
374C4×C151—22no—
375C4×C151—42no—
376C4×C151—42no—
377C4×C151—41no—
378C4×C151—42no—
379C4×C151—41no—
380C4×C151—81no—
381C4×C151—81no—
382C4×C151—81no—
383C4×C151C2×C4×D411yescharacteristic
384C4×C151#51811yescharacteristic
385C4×C151#54611yescharacteristic
386C4×C151#55111yescharacteristic
387C2×C151—24no—
388C2×C151—44no—
389C2×C151—82no—
390C2×C151#235811yescharacteristic
391C2×C151C2×C4×SD1611yescharacteristic
392C2×C151#294611yescharacteristic
393C2×C151#328011yescharacteristic
394C2×C151D4×SD1611yescharacteristic
395C2×C151#329511yescharacteristic
396C2×C151#329611yescharacteristic
397#22874C15111yesmaximal, characteristic, direct product factor, Sylow
398C151#2287411yescharacteristic, direct product factor, Sylow
399C2×#450C2×C15111yescharacteristic
400C2×C4×SD16C2×C15111yescharacteristic, complemented
401C22×#102C2×C15111yescharacteristic
402#2360C2×C15111yescharacteristic, complemented
403D4×C22⋊C4C2×C15111yescharacteristic
404#1968C2×C15111yescharacteristic, complemented
405#1934C2×C15111yescharacteristic, complemented
406#1926C2×C15111yescharacteristic, complemented
407#1892C2×C15111yescharacteristic, complemented
408#1880C2×C15111yescharacteristic, complemented
409#1877C2×C15111yescharacteristic, complemented
410#1864C2×C15111yescharacteristic, complemented
411#1853C2×C15111yescharacteristic, complemented
412C4×#102C2×C15111yescharacteristic, complemented
413C8×C22⋊C4C2×C15111yescharacteristic, complemented
414C23×D4C22×C15111yescharacteristic
415C22×SD16C22×C15111yescharacteristic
416C22×SD16C22×C15111yescharacteristic
417C23×C8C22×C15111yescharacteristic
418C2×C22⋊Q8C22×C15111yescharacteristic
419C2×C4×Q8C22×C15111yescharacteristic, complemented
420C2×C4×D4C22×C15111yescharacteristic
421C2×C4×D4C22×C15111yescharacteristic
422C22×C4⋊C4C22×C15111yescharacteristic
423C22×C22⋊C4—21no—
424#450C4×C15118yescomplemented
425C4×SD16—24no—
426C2×#106C22×C15111yescharacteristic, complemented
427C2×#106C22×C15111yescharacteristic, complemented
428C2×#103C22×C15111yescharacteristic, complemented
429C2×#103C22×C15111yescharacteristic, complemented
430C2×#102—24no—
431C2×#102C22×C15111yescharacteristic
432C2×#102C22×C15111yescharacteristic
433C2×#102C22×C15111yescharacteristic
434C2×#102C22×C15111yescharacteristic
435C2×#102C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×C22⋊C8C22×C15111yescharacteristic
438C2×C4×C8C22×C15111yescharacteristic, complemented
439C2×C4×C8C22×C15111yescharacteristic, complemented
440#391C22×C15111yescharacteristic, complemented
441#390C22×C15111yescharacteristic
442#390C22×C15111yescharacteristic
443#389—21no—
444#389C22×C15111yescharacteristic, complemented
445#387—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#380C22×C15111yescharacteristic
450#379—21no—
451C4×C4⋊C4C22×C15111yescharacteristic, complemented
452C4×C22⋊C4—21no—
453C4×C22⋊C4C22×C15111yescharacteristic
454#340C22×C15111yescharacteristic, complemented
455#340C22×C15111yescharacteristic, complemented
456#340C22×C15111yescharacteristic, complemented
457#340C22×C15111yescharacteristic, complemented
458#336C22×C15111yescharacteristic, complemented
459#336C22×C15111yescharacteristic, complemented
460C25—21no—
461C22×Q8C23×C15111yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C2×C4×C15114yes—
469C22×D4C23×C15111yescharacteristic
470C22×D4C23×C15111yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4C23×C15111yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16C2×C4×C15114yescomplemented
480C2×SD16C2×C4×C15114yescomplemented
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8C23×C15111yescharacteristic
485C22×C8C23×C15111yescharacteristic
486C22×C8C23×C15111yescharacteristic
487C22×C8C23×C15111yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C2×C4×C15114yescomplemented
490C4×Q8—22no—
491C4×Q8—41no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C15111yescharacteristic
503C2×C4⋊C4C23×C15111yescharacteristic
504C2×C4⋊C4C23×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4D4×C15111yescharacteristic
517C2×C22⋊C4D4×C15111yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C15111yescharacteristic
521C2×C42C23×C15111yescharacteristic
522#106—22no—
523#106—41no—
524#103—22no—
525#103—41no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102C2×C4×C15114yescomplemented
530#102C2×C4×C15114yescomplemented
531#102D4×C15114yes—
532C22⋊C8C2×C4×C15114yescomplemented
533C4×C8—22no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95D4×C15111yescharacteristic
541#95D4×C15111yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×D4×C15111yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×C4×C15112yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C22×C4×C15112yes—
574C2×D4C22×C4×C15112yes—
575C2×D4C2×D4×C15112yes—
576C2×D4#41×C15112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4C22×C4×C15112yes—
597C22×C4C2×D4×C15111yescharacteristic
598C22×C4C2×D4×C15111yescharacteristic
599C22×C4C2×D4×C15111yescharacteristic
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4C2×D4×C15111yescharacteristic
602C22×C4#41×C15112yes—
603C22×C4C24×C15111yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C22×C4×C15112yes—
617C2×C8C22×C4×C15112yes—
618C2×C8C2×D4×C15112yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C22×C4×C15112yes—
632C4⋊C4C2×D4×C15112yes—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4SD16×C15114yescomplemented
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—42no—
648C42—81no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×D4×C15112yes—
675C23C2×SD16×C15112yes—
676C23#135×C15112yes—
677C23C22×D4×C15111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×D4×C15114yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4C4×D4×C15112yes—
729C2×C4C2×SD16×C15112yes—
730C2×C4C2×SD16×C15112yes—
731C2×C4C23×C4×C15111yescharacteristic
732C2×C4C22×D4×C15111yescharacteristic
733C2×C4C2×#41×C15111yescharacteristic
734C2×C4C2×#41×C15111yescharacteristic
735C2×C4H(5,𝔽2)×C15111yescharacteristic
736C2×C4H(5,𝔽2)×C15111yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C4×SD16×C15114yescomplemented
763C22C2×C4×D4×C15111yescharacteristic
764C22D42×C15111yescharacteristic
765C22#546×C15111yescharacteristic
766C22C22×SD16×C15111yescharacteristic
767C22C2×#135×C15111yescharacteristic
768C22#576×C15111yescharacteristic
769C22#577×C15111yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—42no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—41no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4C2×C4×D4×C15111yescharacteristic
782C4#518×C15111yescharacteristic
783C4#546×C15111yescharacteristic
784C4#551×C15111yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2358×C15111yescharacteristic
789C2C2×C4×SD16×C15111yescharacteristic
790C2#2946×C15111yescharacteristic
791C2#3280×C15111yescharacteristic
792C2D4×SD16×C15111yescharacteristic
793C2#3295×C15111yescharacteristic
794C2#3296×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C151C2semidirect
4. #2360×C151C2semidirect
6. #1968×C151C2semidirect
7. #1934×C151C2semidirect
8. #1926×C151C2semidirect
9. #1892×C151C2semidirect
10. #1880×C151C2semidirect
11. #1877×C151C2semidirect
12. #1864×C151C2semidirect
13. #1853×C151C2semidirect
14. C4×#102×C151C2semidirect
15. C8×C22⋊C4×C151C2semidirect
21. C2×C4×Q8×C151C22semidirect
26. #450×C151C4semidirect
28. C2×#106×C151C22semidirect
29. C2×#106×C151C22semidirect
30. C2×#103×C151C22semidirect
31. C2×#103×C151C22semidirect
40. C2×C4×C8×C151C22semidirect
41. C2×C4×C8×C151C22semidirect
42. #391×C151C22semidirect
46. #389×C151C22semidirect
53. C4×C4⋊C4×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #336×C151C22semidirect
61. #336×C151C22semidirect
81. C2×SD16×C151C2×C4semidirect
82. C2×SD16×C151C2×C4semidirect
91. C22⋊Q8×C151C2×C4semidirect
131. #102×C151C2×C4semidirect
132. #102×C151C2×C4semidirect
134. C22⋊C8×C151C2×C4semidirect
244. C22⋊C4×C151SD16semidirect
364. C22×C151C4×SD16semidirect
397. #22874C151direct (N × H)
398. C151#22874direct (N × H)
400. C2×C4×SD16C2×C151semidirect
402. #2360C2×C151semidirect
404. #1968C2×C151semidirect
405. #1934C2×C151semidirect
406. #1926C2×C151semidirect
407. #1892C2×C151semidirect
408. #1880C2×C151semidirect
409. #1877C2×C151semidirect
410. #1864C2×C151semidirect
411. #1853C2×C151semidirect
412. C4×#102C2×C151semidirect
413. C8×C22⋊C4C2×C151semidirect
419. C2×C4×Q8C22×C151semidirect
424. #450C4×C151semidirect
426. C2×#106C22×C151semidirect
427. C2×#106C22×C151semidirect
428. C2×#103C22×C151semidirect
429. C2×#103C22×C151semidirect
438. C2×C4×C8C22×C151semidirect
439. C2×C4×C8C22×C151semidirect
440. #391C22×C151semidirect
444. #389C22×C151semidirect
451. C4×C4⋊C4C22×C151semidirect
454. #340C22×C151semidirect
455. #340C22×C151semidirect
456. #340C22×C151semidirect
457. #340C22×C151semidirect
458. #336C22×C151semidirect
459. #336C22×C151semidirect
479. C2×SD16C2×C4×C151semidirect
480. C2×SD16C2×C4×C151semidirect
489. C22⋊Q8C2×C4×C151semidirect
529. #102C2×C4×C151semidirect
530. #102C2×C4×C151semidirect
532. C22⋊C8C2×C4×C151semidirect
642. C22⋊C4SD16×C151semidirect
762. C22C4×SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1512
C2×C4×SD16×C1512
C22×#102×C1512
#2360×C1512
D4×C22⋊C4×C1512
#1968×C1512
#1934×C1512
#1926×C1512
#1892×C1512
#1880×C1512
#1877×C1512
#1864×C1512
#1853×C1512
C4×#102×C1512
C8×C22⋊C4×C1512
#22874151