Finite Group Databasebeta

← C151×#23482 #50328407

Subgroups — C151×#23482 #50328407

Order 38656.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic, complemented
4C2×#417×C151C211yesmaximal, characteristic, complemented
5C2×#407×C151C211yesmaximal, characteristic, complemented
6C2×#380×C151C211yesmaximal, characteristic, complemented
7#2036×C151C212yesmaximal, complemented
8#2035×C151C212yesmaximal, complemented
9#2034×C151C212yesmaximal, complemented
10#2033×C151C212yesmaximal, complemented
11#1736×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C24×C4×C151C2211yescharacteristic
14C22×M16×C151C2211yescharacteristic
15C22×M16×C151C2211yescharacteristic
16#525×C151—24no—
17#525×C151—24no—
18C2×#123×C151—21no—
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×#121×C151C2211yescharacteristic
23C2×#120×C151—21no—
24C2×C4×D4×C151—21no—
25C2×C4×D4×C151—21no—
26C2×#117×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C4⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151—21no—
30#428×C151—24no—
31C2×#107×C151C2212yescomplemented
32C2×#106×C151C2212yescomplemented
33#417×C151—24no—
34#417×C151—24no—
35C2×#103×C151C2212yescomplemented
36C2×#103×C151C2212yescomplemented
37C2×#102×C151C2212yescomplemented
38C2×#102×C151C2212yescomplemented
39#407×C151—24no—
40C2×C22⋊C8×C151C2212yes—
41C2×C22⋊C8×C151C2212yes—
42#380×C151—21no—
43#380×C151—21no—
44#380×C151C2212yes—
45#380×C151C2212yes—
46C2×#95×C151—21no—
47#340×C151C2212yescomplemented
48#340×C151C2212yescomplemented
49C25×C151D411yescharacteristic
50C2×#41×C151—22no—
51C2×#41×C151—22no—
52C2×#41×C151—22no—
53C2×#41×C151—22no—
54C2×#41×C151—22no—
55C2×#41×C151D414yes—
56C22×Q8×C151C2311yescharacteristic
57C22×D4×C151—21no—
58C22×D4×C151—21no—
59C22×D4×C151—21no—
60C22×D4×C151C2311yescharacteristic
61C23×C4×C151—22no—
62C23×C4×C151—21no—
63C23×C4×C151—22no—
64C23×C4×C151—22no—
65C23×C4×C151—22no—
66C23×C4×C151—22no—
67C23×C4×C151—22no—
68C23×C4×C151—21no—
69C23×C4×C151—21no—
70C23×C4×C151D411yescharacteristic
71C23×C4×C151D411yescharacteristic
72C23×C4×C151D411yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—22no—
79C2×M16×C151—22no—
80C2×M16×C151—22no—
81C2×M16×C151D414yescomplemented
82C22×C8×C151C2312yes—
83C22×C8×C151C2312yes—
84#123×C151—28no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89#121×C151—22no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#120×C151—28no—
94C4×D4×C151—28no—
95C4×D4×C151—28no—
96#117×C151—22no—
97#117×C151D414yes—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151C2312yes—
107C2×C4⋊C4×C151C2312yes—
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
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—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—44no—
118C2×C42×C151—21no—
119#107×C151—24no—
120#106×C151—24no—
121#103×C151—24no—
122#103×C151—24no—
123#102×C151—24no—
124#102×C151—24no—
125C22⋊C8×C151—24no—
126C22⋊C8×C151—24no—
127#95×C151—22no—
128#95×C151—22no—
129C24×C151—22no—
130C24×C151—22no—
131C24×C151—22no—
132C24×C151—22no—
133C24×C151—22no—
134C24×C151—21no—
135C24×C151—41no—
136C24×C151—41no—
137C24×C151C2×D411yescharacteristic
138C24×C151C2×D411yescharacteristic
139C24×C151C2×D411yescharacteristic
140#41×C151—28no—
141#41×C151—28no—
142#41×C151—44no—
143#41×C151—44no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151C2×D412yes—
150C2×D4×C151—24no—
151C2×D4×C151—24no—
152C2×D4×C151—24no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—42no—
159C2×D4×C151—42no—
160C2×D4×C151—42no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151C2×D412yes—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—24no—
174C22×C4×C151—22no—
175C22×C4×C151—22no—
176C22×C4×C151—22no—
177C22×C4×C151—22no—
178C22×C4×C151—21no—
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—22no—
191C22×C4×C151—22no—
192C22×C4×C151—44no—
193C22×C4×C151—44no—
194C22×C4×C151—42no—
195C22×C4×C151—44no—
196C22×C4×C151—42no—
197C22×C4×C151—44no—
198C22×C4×C151—42no—
199C22×C4×C151—42no—
200C22×C4×C151—42no—
201C22×C4×C151—42no—
202C22×C4×C151—42no—
203C22×C4×C151—42no—
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D412yes—
208C22×C4×C151C2×D412yes—
209C22×C4×C151C2×D412yes—
210C22×C4×C151#4112yes—
211C22×C4×C151#4112yes—
212C22×C4×C151#4112yes—
213C22×C4×C151C2411yescharacteristic
214M16×C151—28no—
215M16×C151—44no—
216C2×C8×C151—22no—
217C2×C8×C151—22no—
218C2×C8×C151—22no—
219C2×C8×C151—22no—
220C2×C8×C151—22no—
221C2×C8×C151C2×D414yes—
222C4⋊C4×C151—24no—
223C4⋊C4×C151—24no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—22no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—42no—
231C4⋊C4×C151—42no—
232C4⋊C4×C151C2×D412yes—
233C4⋊C4×C151C2×D412yes—
234C22⋊C4×C151—24no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—24no—
238C22⋊C4×C151—24no—
239C22⋊C4×C151—44no—
240C22⋊C4×C151—44no—
241C42×C151—24no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—28no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—22no—
260C23×C151—44no—
261C23×C151—44no—
262C23×C151—44no—
263C23×C151—44no—
264C23×C151—44no—
265C23×C151—44no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151#12012yes—
273C23×C151#12112yes—
274C23×C151#12312yes—
275C23×C151AGL(1,ℤ/8)12yes—
276C23×C151#13712yes—
277C23×C151C22×D411yescharacteristic
278Q8×C151—22no—
279Q8×C151—22no—
280Q8×C151—41no—
281Q8×C151—41no—
282D4×C151—22no—
283D4×C151—22no—
284D4×C151—48no—
285D4×C151—48no—
286D4×C151—48no—
287D4×C151—41no—
288D4×C151—41no—
289C2×C4×C151—22no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—44no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—48no—
314C2×C4×C151—44no—
315C2×C4×C151—44no—
316C2×C4×C151—42no—
317C2×C4×C151—42no—
318C2×C4×C151—42no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—84no—
323C2×C4×C151—84no—
324C2×C4×C151#12012yes—
325C2×C4×C151#12114yes—
326C2×C4×C151#12114yes—
327C2×C4×C151#12112yes—
328C2×C4×C151#12314yes—
329C2×C4×C151#12312yes—
330C2×C4×C151#12414yes—
331C2×C4×C151C22×D411yescharacteristic
332C2×C4×C151C22×D411yescharacteristic
333C2×C4×C151C22×D411yescharacteristic
334C2×C4×C151C2×#4111yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151C2×#4111yescharacteristic
337C8×C151—24no—
338C8×C151—42no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—22no—
342C22×C151—22no—
343C22×C151—22no—
344C22×C151—22no—
345C22×C151—22no—
346C22×C151—22no—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—22no—
350C22×C151—22no—
351C22×C151—416no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—41no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—42no—
361C22×C151—42no—
362C22×C151—42no—
363C22×C151—81no—
364C22×C151—81no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151#39414yes—
368C22×C151C2×#12011yescharacteristic
369C22×C151C2×#12111yescharacteristic
370C22×C151C2×#12311yescharacteristic
371C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C151C2×#13711yescharacteristic
373C22×C151#57511yescharacteristic
374C22×C151#57511yescharacteristic
375C4×C151—41no—
376C4×C151—41no—
377C4×C151—42no—
378C4×C151—42no—
379C4×C151—42no—
380C4×C151—82no—
381C4×C151—82no—
382C4×C151#39414yes—
383C4×C151C2×#12111yescharacteristic
384C4×C151C2×#12111yescharacteristic
385C4×C151C2×#12311yescharacteristic
386C4×C151C2×#12411yescharacteristic
387C2×C151—24no—
388C2×C151—42no—
389C2×C151—42no—
390C2×C151—82no—
391C2×C151C2×#39411yescharacteristic
392C2×C151#300611yescharacteristic
393C2×C151#300711yescharacteristic
394C2×C151#305511yescharacteristic
395C2×C151#305611yescharacteristic
396C2×C151#309211yescharacteristic
397C2×C151#309311yescharacteristic
398#23482C15111yesmaximal, characteristic, direct product factor, Sylow
399C151#2348211yescharacteristic, direct product factor, Sylow
400C2×#525C2×C15111yescharacteristic
401C2×#428C2×C15111yescharacteristic, complemented
402C2×#417C2×C15111yescharacteristic, complemented
403C2×#417C2×C15111yescharacteristic, complemented
404C2×#407C2×C15111yescharacteristic, complemented
405C2×#380C2×C15111yescharacteristic, complemented
406#2036C2×C15112yescomplemented
407#2035C2×C15112yescomplemented
408#2034C2×C15112yescomplemented
409#2033C2×C15112yescomplemented
410#1736C2×C15111yescharacteristic, complemented
411C22×#41C22×C15111yescharacteristic
412C24×C4C22×C15111yescharacteristic
413C22×M16C22×C15111yescharacteristic
414C22×M16C22×C15111yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C15111yescharacteristic
419C2×C22⋊Q8C22×C15111yescharacteristic
420C2×#121C22×C15111yescharacteristic
421C2×#121C22×C15111yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C15111yescharacteristic
426C22×C4⋊C4C22×C15111yescharacteristic
427C22×C4⋊C4C22×C15111yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C15112yescomplemented
431C2×#106C22×C15112yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C15112yescomplemented
435C2×#103C22×C15112yescomplemented
436C2×#102C22×C15112yescomplemented
437C2×#102C22×C15112yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C15112yes—
440C2×C22⋊C8C22×C15112yes—
441#380—21no—
442#380—21no—
443#380C22×C15112yes—
444#380C22×C15112yes—
445C2×#95—21no—
446#340C22×C15112yescomplemented
447#340C22×C15112yescomplemented
448C25D4×C15111yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C15114yes—
455C22×Q8C23×C15111yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C15111yescharacteristic
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—21no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C15111yescharacteristic
470C23×C4D4×C15111yescharacteristic
471C23×C4D4×C15111yescharacteristic
472C23×C4C23×C15111yescharacteristic
473C23×C4C23×C15111yescharacteristic
474C23×C4C23×C15111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C15114yescomplemented
481C22×C8C23×C15112yes—
482C22×C8C23×C15112yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C15114yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C15112yes—
506C2×C4⋊C4C23×C15112yes—
507C2×C4⋊C4C23×C15111yescharacteristic
508C2×C4⋊C4C23×C15111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C15111yescharacteristic
537C24C2×D4×C15111yescharacteristic
538C24C2×D4×C15111yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C15112yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C15112yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
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—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C15111yescharacteristic
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606C22×C4C2×D4×C15112yes—
607C22×C4C2×D4×C15112yes—
608C22×C4C2×D4×C15112yes—
609C22×C4#41×C15112yes—
610C22×C4#41×C15112yes—
611C22×C4#41×C15112yes—
612C22×C4C24×C15111yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C15114yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C15112yes—
632C4⋊C4C2×D4×C15112yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C15112yes—
672C23#121×C15112yes—
673C23#123×C15112yes—
674C23AGL(1,ℤ/8)×C15112yes—
675C23#137×C15112yes—
676C23C22×D4×C15111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C15112yes—
724C2×C4#121×C15112yes—
725C2×C4#121×C15114yes—
726C2×C4#121×C15114yes—
727C2×C4#123×C15112yes—
728C2×C4#123×C15114yes—
729C2×C4#124×C15114yes—
730C2×C4C22×D4×C15111yescharacteristic
731C2×C4C22×D4×C15111yescharacteristic
732C2×C4C22×D4×C15111yescharacteristic
733C2×C4C2×#41×C15111yescharacteristic
734C2×C4C2×#41×C15111yescharacteristic
735C2×C4C2×#41×C15111yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C15114yes—
767C22C2×#120×C15111yescharacteristic
768C22C2×#121×C15111yescharacteristic
769C22C2×#123×C15111yescharacteristic
770C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
771C22C2×#137×C15111yescharacteristic
772C22#575×C15111yescharacteristic
773C22#575×C15111yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C15114yes—
782C4C2×#121×C15111yescharacteristic
783C4C2×#121×C15111yescharacteristic
784C4C2×#123×C15111yescharacteristic
785C4C2×#124×C15111yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C15111yescharacteristic
791C2#3006×C15111yescharacteristic
792C2#3007×C15111yescharacteristic
793C2#3055×C15111yescharacteristic
794C2#3056×C15111yescharacteristic
795C2#3092×C15111yescharacteristic
796C2#3093×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#525×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C151C2semidirect
3. C2×#417×C151C2semidirect
4. C2×#417×C151C2semidirect
5. C2×#407×C151C2semidirect
6. C2×#380×C151C2semidirect
7. #2036×C151C2semidirect
8. #2035×C151C2semidirect
9. #2034×C151C2semidirect
10. #2033×C151C2semidirect
11. #1736×C151C2semidirect
31. C2×#107×C151C22semidirect
32. C2×#106×C151C22semidirect
35. C2×#103×C151C22semidirect
36. C2×#103×C151C22semidirect
37. C2×#102×C151C22semidirect
38. C2×#102×C151C22semidirect
47. #340×C151C22semidirect
48. #340×C151C22semidirect
81. C2×M16×C151D4semidirect
398. #23482C151direct (N × H)
399. C151#23482direct (N × H)
401. C2×#428C2×C151semidirect
402. C2×#417C2×C151semidirect
403. C2×#417C2×C151semidirect
404. C2×#407C2×C151semidirect
405. C2×#380C2×C151semidirect
406. #2036C2×C151semidirect
407. #2035C2×C151semidirect
408. #2034C2×C151semidirect
409. #2033C2×C151semidirect
410. #1736C2×C151semidirect
430. C2×#107C22×C151semidirect
431. C2×#106C22×C151semidirect
434. C2×#103C22×C151semidirect
435. C2×#103C22×C151semidirect
436. C2×#102C22×C151semidirect
437. C2×#102C22×C151semidirect
446. #340C22×C151semidirect
447. #340C22×C151semidirect
480. C2×M16D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1512
C2×#428×C1512
C2×#417×C1512
C2×#407×C1512
C2×#380×C1512
#2036×C1512
#2035×C1512
#2034×C1512
#2033×C1512
#1736×C1512
#23482151