Finite Group Databasebeta

← C151×#23876 #50328801

Subgroups — C151×#23876 #50328801

Order 38656.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
2#3488×C151C211yesmaximal, characteristic, complemented
3C2×#453×C151C212yesmaximal, complemented
4#3003×C151C211yesmaximal, characteristic, complemented
5#2433×C151C211yesmaximal, characteristic, complemented
6#2006×C151C212yesmaximal, complemented
7#2002×C151C212yesmaximal, complemented
8#1900×C151C211yesmaximal, characteristic, complemented
9#1883×C151C212yesmaximal, complemented
10#1871×C151C211yesmaximal, characteristic, complemented
11#1789×C151C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C151C2211yescharacteristic, complemented
13C22×#41×C151C2211yescharacteristic
14C23×D4×C151C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C151—21no—
16C2×AGL(1,ℤ/8)×C151—21no—
17C2×AGL(1,ℤ/8)×C151—28no—
18C2×AGL(1,ℤ/8)×C151C2212yes—
19C2×AGL(1,ℤ/8)×C151C2212yescomplemented
20C2×AGL(1,ℤ/8)×C151C2212yescomplemented
21C22×SD16×C151—21no—
22C22×D8×C151—21no—
23C22×M16×C151C2211yescharacteristic, complemented
24#550×C151—21no—
25#548×C151—21no—
26#546×C151—21no—
27#546×C151—22no—
28D42×C151—22no—
29D42×C151—21no—
30#537×C151—21no—
31#537×C151C2211yescharacteristic, complemented
32#535×C151—21no—
33#535×C151C2211yescharacteristic, complemented
34C2×#127×C151C2212yescomplemented
35#525×C151—21no—
36#525×C151C2211yescharacteristic
37C2×#121×C151—21no—
38C2×#121×C151C2211yescharacteristic
39C2×#120×C151—22no—
40#520×C151C2211yescharacteristic, complemented
41#453×C151—28no—
42#450×C151—21no—
43#450×C151—21no—
44#447×C151—21no—
45#447×C151—21no—
46C2×#104×C151C2212yescomplemented
47C2×#104×C151C2212yescomplemented
48C2×#104×C151C2212yescomplemented
49#418×C151C2212yescomplemented
50C2×#100×C151C2212yescomplemented
51#407×C151C2211yescharacteristic, complemented
52#392×C151—22no—
53#390×C151C2212yescomplemented
54C4×C22⋊C4×C151C2211yescharacteristic, complemented
55#343×C151C2212yescomplemented
56#339×C151C2212yescomplemented
57C25×C151—21no—
58H(5,𝔽2)×C151—24no—
59H(5,𝔽2)×C151—42no—
60C2×#41×C151—24no—
61C2×#41×C151—21no—
62C2×#41×C151—21no—
63C2×#41×C151—21no—
64C2×#41×C151—21no—
65C2×#41×C151—42no—
66C2×#41×C151D411yescharacteristic, complemented
67C2×#41×C151D411yescharacteristic, complemented
68C2×#41×C151C2311yescharacteristic
69C2×#41×C151C2311yescharacteristic
70C2×#41×C151C2311yescharacteristic
71C22×Q8×C151D411yescharacteristic, complemented
72C22×D4×C151—22no—
73C22×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—22no—
78C22×D4×C151—24no—
79C22×D4×C151—24no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151—42no—
85C22×D4×C151D412yes—
86C22×D4×C151D411yescharacteristic, complemented
87C22×D4×C151C2312yes—
88C22×D4×C151C2311yescharacteristic
89C23×C4×C151—21no—
90C23×C4×C151C2311yescharacteristic
91AGL(1,ℤ/8)×C151—28no—
92AGL(1,ℤ/8)×C151—28no—
93AGL(1,ℤ/8)×C151—24no—
94AGL(1,ℤ/8)×C151—24no—
95AGL(1,ℤ/8)×C151—24no—
96AGL(1,ℤ/8)×C151—24no—
97AGL(1,ℤ/8)×C151—42no—
98AGL(1,ℤ/8)×C151D418yescomplemented
99C2×SD16×C151—28no—
100C2×SD16×C151—22no—
101C2×SD16×C151—22no—
102C2×SD16×C151—22no—
103C2×D8×C151—28no—
104C2×D8×C151—22no—
105C2×D8×C151—22no—
106C2×D8×C151—22no—
107C2×M16×C151—21no—
108C2×M16×C151—24no—
109C2×M16×C151C2312yes—
110C2×M16×C151C2312yes—
111C22×C8×C151—21no—
112#127×C151—22no—
113#127×C151—21no—
114#127×C151—24no—
115#127×C151—42no—
116#124×C151—22no—
117#124×C151—21no—
118#123×C151—22no—
119#123×C151—21no—
120C22⋊Q8×C151—22no—
121C22⋊Q8×C151—21no—
122C22⋊Q8×C151—21no—
123C22⋊Q8×C151D411yescharacteristic, complemented
124C22⋊Q8×C151D411yescharacteristic, complemented
125#121×C151—22no—
126#121×C151—22no—
127#121×C151—22no—
128#121×C151—22no—
129#121×C151—22no—
130#121×C151—21no—
131#121×C151—21no—
132#121×C151—21no—
133#121×C151—21no—
134#121×C151—21no—
135#121×C151—21no—
136#121×C151—22no—
137#121×C151—21no—
138#121×C151—21no—
139#121×C151D411yescharacteristic, complemented
140#121×C151D411yescharacteristic, complemented
141#120×C151—22no—
142#120×C151—22no—
143#120×C151—22no—
144#120×C151—21no—
145#120×C151—22no—
146#120×C151—48no—
147C4×Q8×C151—21no—
148C4×D4×C151—22no—
149C4×D4×C151—22no—
150C4×D4×C151—21no—
151C4×D4×C151—22no—
152C4×D4×C151—21no—
153C4×D4×C151—21no—
154#117×C151—21no—
155#117×C151C2311yescharacteristic
156C2×C4⋊C4×C151—21no—
157C2×C4⋊C4×C151C2311yescharacteristic
158C2×C22⋊C4×C151—22no—
159C2×C22⋊C4×C151—24no—
160C2×C22⋊C4×C151—21no—
161C2×C22⋊C4×C151D412yes—
162C2×C42×C151C2312yes—
163#104×C151—24no—
164#104×C151—24no—
165#104×C151—42no—
166#102×C151—22no—
167#102×C151—22no—
168#100×C151—24no—
169C22⋊C8×C151—21no—
170C22⋊C8×C151—21no—
171#95×C151—21no—
172C24×C151—22no—
173C24×C151—22no—
174C24×C151—21no—
175C24×C151—44no—
176C24×C151—44no—
177C24×C151—41no—
178C24×C151—41no—
179C24×C151—82no—
180C24×C151C2×D411yescharacteristic
181C24×C151C2×D412yes—
182#41×C151—22no—
183#41×C151—22no—
184#41×C151—22no—
185#41×C151—22no—
186#41×C151—22no—
187#41×C151—22no—
188#41×C151—22no—
189#41×C151—44no—
190#41×C151—41no—
191#41×C151—41no—
192#41×C151—44no—
193#41×C151—44no—
194#41×C151—42no—
195#41×C151—42no—
196#41×C151C2×D414yes—
197C2×Q8×C151—21no—
198C2×Q8×C151—22no—
199C2×Q8×C151—41no—
200C2×Q8×C151C2×D411yescharacteristic
201C2×Q8×C151C2×D411yescharacteristic
202C2×Q8×C151C2×D411yescharacteristic
203C2×D4×C151—21no—
204C2×D4×C151—24no—
205C2×D4×C151—24no—
206C2×D4×C151—22no—
207C2×D4×C151—22no—
208C2×D4×C151—22no—
209C2×D4×C151—22no—
210C2×D4×C151—21no—
211C2×D4×C151—21no—
212C2×D4×C151—21no—
213C2×D4×C151—21no—
214C2×D4×C151—21no—
215C2×D4×C151—22no—
216C2×D4×C151—22no—
217C2×D4×C151—22no—
218C2×D4×C151—21no—
219C2×D4×C151—22no—
220C2×D4×C151—21no—
221C2×D4×C151—22no—
222C2×D4×C151—22no—
223C2×D4×C151—22no—
224C2×D4×C151—22no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—22no—
228C2×D4×C151—22no—
229C2×D4×C151—22no—
230C2×D4×C151—41no—
231C2×D4×C151—44no—
232C2×D4×C151—44no—
233C2×D4×C151—44no—
234C2×D4×C151—44no—
235C2×D4×C151—42no—
236C2×D4×C151—42no—
237C2×D4×C151—48no—
238C2×D4×C151—44no—
239C2×D4×C151—48no—
240C2×D4×C151—42no—
241C2×D4×C151—42no—
242C2×D4×C151—44no—
243C2×D4×C151—48no—
244C2×D4×C151—41no—
245C2×D4×C151—41no—
246C2×D4×C151—84no—
247C2×D4×C151—84no—
248C2×D4×C151C2×D411yescharacteristic
249C2×D4×C151C2×D411yescharacteristic
250C2×D4×C151C2×D411yescharacteristic
251C2×D4×C151C2×D414yescomplemented
252C22×C4×C151—21no—
253C22×C4×C151—22no—
254C22×C4×C151—22no—
255C22×C4×C151—22no—
256C22×C4×C151—21no—
257C22×C4×C151—22no—
258C22×C4×C151—22no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—44no—
264C22×C4×C151C2×D411yescharacteristic
265C22×C4×C151C2×D411yescharacteristic
266C22×C4×C151C2×D411yescharacteristic
267C22×C4×C151C2×D411yescharacteristic
268C22×C4×C151C2×D411yescharacteristic
269C22×C4×C151C2×D412yes—
270C22×C4×C151C2411yescharacteristic
271SD16×C151—28no—
272SD16×C151—28no—
273SD16×C151—44no—
274D8×C151—28no—
275D8×C151—28no—
276D8×C151—44no—
277M16×C151—24no—
278M16×C151—22no—
279M16×C151—22no—
280M16×C151—22no—
281M16×C151C2×D414yescomplemented
282C2×C8×C151—24no—
283C2×C8×C151—22no—
284C2×C8×C151—22no—
285C4⋊C4×C151—22no—
286C4⋊C4×C151—22no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151—21no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151C2×D411yescharacteristic
292C4⋊C4×C151C2×D411yescharacteristic
293C22⋊C4×C151—22no—
294C22⋊C4×C151—22no—
295C22⋊C4×C151—24no—
296C22⋊C4×C151—22no—
297C22⋊C4×C151—22no—
298C22⋊C4×C151—22no—
299C22⋊C4×C151—21no—
300C22⋊C4×C151—21no—
301C22⋊C4×C151—21no—
302C22⋊C4×C151—21no—
303C22⋊C4×C151—22no—
304C22⋊C4×C151—22no—
305C22⋊C4×C151—21no—
306C22⋊C4×C151—48no—
307C42×C151—22no—
308C42×C151—21no—
309C42×C151—22no—
310C42×C151—22no—
311C23×C151—21no—
312C23×C151—22no—
313C23×C151—22no—
314C23×C151—21no—
315C23×C151—22no—
316C23×C151—21no—
317C23×C151—24no—
318C23×C151—24no—
319C23×C151—41no—
320C23×C151—42no—
321C23×C151—44no—
322C23×C151—44no—
323C23×C151—44no—
324C23×C151—44no—
325C23×C151—44no—
326C23×C151—42no—
327C23×C151—42no—
328C23×C151—42no—
329C23×C151—42no—
330C23×C151—42no—
331C23×C151—81no—
332C23×C151—82no—
333C23×C151—82no—
334C23×C151—82no—
335C23×C151—82no—
336C23×C151—82no—
337C23×C151—816no—
338C23×C151—82no—
339C23×C151#12011yescharacteristic
340C23×C151#12011yescharacteristic
341C23×C151C22×D411yescharacteristic
342Q8×C151—21no—
343Q8×C151—21no—
344Q8×C151—21no—
345Q8×C151—22no—
346Q8×C151—42no—
347Q8×C151#12012yescomplemented
348D4×C151—24no—
349D4×C151—21no—
350D4×C151—24no—
351D4×C151—21no—
352D4×C151—21no—
353D4×C151—22no—
354D4×C151—24no—
355D4×C151—42no—
356D4×C151—42no—
357D4×C151—44no—
358D4×C151—44no—
359D4×C151—44no—
360D4×C151—42no—
361D4×C151—44no—
362D4×C151—42no—
363D4×C151—42no—
364D4×C151—44no—
365D4×C151—42no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—42no—
369D4×C151—42no—
370D4×C151—42no—
371D4×C151—81no—
372D4×C151—82no—
373D4×C151—82no—
374D4×C151—82no—
375D4×C151—82no—
376D4×C151—816no—
377D4×C151#12012yescomplemented
378C2×C4×C151—21no—
379C2×C4×C151—22no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—24no—
385C2×C4×C151—22no—
386C2×C4×C151—22no—
387C2×C4×C151—24no—
388C2×C4×C151—21no—
389C2×C4×C151—21no—
390C2×C4×C151—21no—
391C2×C4×C151—22no—
392C2×C4×C151—21no—
393C2×C4×C151—42no—
394C2×C4×C151—42no—
395C2×C4×C151—42no—
396C2×C4×C151—44no—
397C2×C4×C151—42no—
398C2×C4×C151—42no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—42no—
402C2×C4×C151—42no—
403C2×C4×C151—82no—
404C2×C4×C151#12011yescharacteristic
405C2×C4×C151#12011yescharacteristic
406C2×C4×C151C22×D411yescharacteristic
407C2×C4×C151C22×D412yes—
408C2×C4×C151C22×D411yescharacteristic
409C2×C4×C151H(5,𝔽2)12yes—
410C8×C151—24no—
411C8×C151—42no—
412C22×C151—21no—
413C22×C151—21no—
414C22×C151—21no—
415C22×C151—21no—
416C22×C151—21no—
417C22×C151—22no—
418C22×C151—21no—
419C22×C151—21no—
420C22×C151—44no—
421C22×C151—48no—
422C22×C151—41no—
423C22×C151—41no—
424C22×C151—41no—
425C22×C151—41no—
426C22×C151—42no—
427C22×C151—44no—
428C22×C151—42no—
429C22×C151—41no—
430C22×C151—41no—
431C22×C151—41no—
432C22×C151—42no—
433C22×C151—41no—
434C22×C151—84no—
435C22×C151—84no—
436C22×C151—84no—
437C22×C151—88no—
438C22×C151—88no—
439C22×C151—82no—
440C22×C151—82no—
441C22×C151—164no—
442C22×C151#45312yescomplemented
443C22×C151C2×#12011yescharacteristic
444C22×C151D4212yes—
445C4×C151—21no—
446C4×C151—21no—
447C4×C151—22no—
448C4×C151—44no—
449C4×C151—41no—
450C4×C151—41no—
451C4×C151—42no—
452C4×C151—41no—
453C4×C151—41no—
454C4×C151C2×#12011yescharacteristic
455C4×C151#53411yescharacteristic
456C4×C151D4212yes—
457C2×C151—22no—
458C2×C151—22no—
459C2×C151—41no—
460C2×C151—42no—
461C2×C151—81no—
462C2×C151—84no—
463C2×C151—82no—
464C2×C151—81no—
465C2×C151#240311yescharacteristic
466C2×C151C2×#45311yescharacteristic
467C2×C151#302111yescharacteristic
468#23876C15111yesmaximal, characteristic, direct product factor, Sylow
469C151#2387611yescharacteristic, direct product factor, Sylow
470C22×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
471#3488C2×C15111yescharacteristic, complemented
472C2×#453C2×C15112yescomplemented
473#3003C2×C15111yescharacteristic, complemented
474#2433C2×C15111yescharacteristic, complemented
475#2006C2×C15112yescomplemented
476#2002C2×C15112yescomplemented
477#1900C2×C15111yescharacteristic, complemented
478#1883C2×C15112yescomplemented
479#1871C2×C15111yescharacteristic, complemented
480#1789C2×C15111yescharacteristic, complemented
481C2×H(5,𝔽2)C22×C15111yescharacteristic, complemented
482C22×#41C22×C15111yescharacteristic
483C23×D4C22×C15111yescharacteristic, complemented
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—21no—
486C2×AGL(1,ℤ/8)—28no—
487C2×AGL(1,ℤ/8)C22×C15112yes—
488C2×AGL(1,ℤ/8)C22×C15112yescomplemented
489C2×AGL(1,ℤ/8)C22×C15112yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C15111yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C15111yescharacteristic, complemented
501#535—21no—
502#535C22×C15111yescharacteristic, complemented
503C2×#127C22×C15112yescomplemented
504#525—21no—
505#525C22×C15111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C15111yescharacteristic
508C2×#120—22no—
509#520C22×C15111yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C15112yescomplemented
516C2×#104C22×C15112yescomplemented
517C2×#104C22×C15112yescomplemented
518#418C22×C15112yescomplemented
519C2×#100C22×C15112yescomplemented
520#407C22×C15111yescharacteristic, complemented
521#392—22no—
522#390C22×C15112yescomplemented
523C4×C22⋊C4C22×C15111yescharacteristic, complemented
524#343C22×C15112yescomplemented
525#339C22×C15112yescomplemented
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C15111yescharacteristic, complemented
536C2×#41D4×C15111yescharacteristic, complemented
537C2×#41C23×C15111yescharacteristic
538C2×#41C23×C15111yescharacteristic
539C2×#41C23×C15111yescharacteristic
540C22×Q8D4×C15111yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C15112yes—
555C22×D4D4×C15111yescharacteristic, complemented
556C22×D4C23×C15111yescharacteristic
557C22×D4C23×C15112yes—
558C23×C4—21no—
559C23×C4C23×C15111yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C15118yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C15112yes—
579C2×M16C23×C15112yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C15111yescharacteristic, complemented
593C22⋊Q8D4×C15111yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C15111yescharacteristic, complemented
609#121D4×C15111yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C15111yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C15111yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C15112yes—
631C2×C42C23×C15112yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C15111yescharacteristic
650C24C2×D4×C15112yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C15114yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C15111yescharacteristic
670C2×Q8C2×D4×C15111yescharacteristic
671C2×Q8C2×D4×C15111yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C15111yescharacteristic
718C2×D4C2×D4×C15111yescharacteristic
719C2×D4C2×D4×C15111yescharacteristic
720C2×D4C2×D4×C15114yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C15111yescharacteristic
734C22×C4C2×D4×C15111yescharacteristic
735C22×C4C2×D4×C15111yescharacteristic
736C22×C4C2×D4×C15111yescharacteristic
737C22×C4C2×D4×C15111yescharacteristic
738C22×C4C2×D4×C15112yes—
739C22×C4C24×C15111yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C15114yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C15111yescharacteristic
761C4⋊C4C2×D4×C15111yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C15111yescharacteristic
809C23#120×C15111yescharacteristic
810C23C22×D4×C15111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C15112yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C15112yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C15111yescharacteristic
874C2×C4#120×C15111yescharacteristic
875C2×C4C22×D4×C15111yescharacteristic
876C2×C4C22×D4×C15112yes—
877C2×C4C22×D4×C15111yescharacteristic
878C2×C4H(5,𝔽2)×C15112yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C15112yescomplemented
912C22C2×#120×C15111yescharacteristic
913C22D42×C15112yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C15111yescharacteristic
924C4#534×C15111yescharacteristic
925C4D42×C15112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2#2403×C15111yescharacteristic
935C2C2×#453×C15111yescharacteristic
936C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
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
1. C22×AGL(1,ℤ/8)×C151C2semidirect
2. #3488×C151C2semidirect
3. C2×#453×C151C2semidirect
4. #3003×C151C2semidirect
5. #2433×C151C2semidirect
6. #2006×C151C2semidirect
7. #2002×C151C2semidirect
8. #1900×C151C2semidirect
9. #1883×C151C2semidirect
10. #1871×C151C2semidirect
11. #1789×C151C2semidirect
12. C2×H(5,𝔽2)×C151C22semidirect
14. C23×D4×C151C22semidirect
19. C2×AGL(1,ℤ/8)×C151C22semidirect
20. C2×AGL(1,ℤ/8)×C151C22semidirect
23. C22×M16×C151C22semidirect
31. #537×C151C22semidirect
33. #535×C151C22semidirect
34. C2×#127×C151C22semidirect
40. #520×C151C22semidirect
46. C2×#104×C151C22semidirect
47. C2×#104×C151C22semidirect
48. C2×#104×C151C22semidirect
49. #418×C151C22semidirect
50. C2×#100×C151C22semidirect
51. #407×C151C22semidirect
53. #390×C151C22semidirect
54. C4×C22⋊C4×C151C22semidirect
55. #343×C151C22semidirect
56. #339×C151C22semidirect
66. C2×#41×C151D4semidirect
67. C2×#41×C151D4semidirect
71. C22×Q8×C151D4semidirect
86. C22×D4×C151D4semidirect
98. AGL(1,ℤ/8)×C151D4semidirect
123. C22⋊Q8×C151D4semidirect
124. C22⋊Q8×C151D4semidirect
139. #121×C151D4semidirect
140. #121×C151D4semidirect
251. C2×D4×C151C2×D4semidirect
281. M16×C151C2×D4semidirect
347. Q8×C151#120semidirect
377. D4×C151#120semidirect
442. C22×C151#453semidirect
468. #23876C151direct (N × H)
469. C151#23876direct (N × H)
470. C22×AGL(1,ℤ/8)C2×C151semidirect
471. #3488C2×C151semidirect
472. C2×#453C2×C151semidirect
473. #3003C2×C151semidirect
474. #2433C2×C151semidirect
475. #2006C2×C151semidirect
476. #2002C2×C151semidirect
477. #1900C2×C151semidirect
478. #1883C2×C151semidirect
479. #1871C2×C151semidirect
480. #1789C2×C151semidirect
481. C2×H(5,𝔽2)C22×C151semidirect
483. C23×D4C22×C151semidirect
488. C2×AGL(1,ℤ/8)C22×C151semidirect
489. C2×AGL(1,ℤ/8)C22×C151semidirect
492. C22×M16C22×C151semidirect
500. #537C22×C151semidirect
502. #535C22×C151semidirect
503. C2×#127C22×C151semidirect
509. #520C22×C151semidirect
515. C2×#104C22×C151semidirect
516. C2×#104C22×C151semidirect
517. C2×#104C22×C151semidirect
518. #418C22×C151semidirect
519. C2×#100C22×C151semidirect
520. #407C22×C151semidirect
522. #390C22×C151semidirect
523. C4×C22⋊C4C22×C151semidirect
524. #343C22×C151semidirect
525. #339C22×C151semidirect
535. C2×#41D4×C151semidirect
536. C2×#41D4×C151semidirect
540. C22×Q8D4×C151semidirect
555. C22×D4D4×C151semidirect
567. AGL(1,ℤ/8)D4×C151semidirect
592. C22⋊Q8D4×C151semidirect
593. C22⋊Q8D4×C151semidirect
608. #121D4×C151semidirect
609. #121D4×C151semidirect
720. C2×D4C2×D4×C151semidirect
750. M16C2×D4×C151semidirect
816. Q8#120×C151semidirect
846. D4#120×C151semidirect
911. C22#453×C151semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1512
#3488×C1512
C2×#453×C1512
#3003×C1512
#2433×C1512
#2006×C1512
#2002×C1512
#1900×C1512
#1883×C1512
#1871×C1512
#1789×C1512
#23876151