Finite Group Databasebeta

← C151×#23681 #50328606

Subgroups — C151×#23681 #50328606

Order 38656.

880 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q16×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic
3C4×#124×C151C211yesmaximal, characteristic
4#2295×C151C211yesmaximal, characteristic, complemented
5#2085×C151C211yesmaximal, characteristic, complemented
6#2074×C151C211yesmaximal, characteristic, complemented
7#2067×C151C211yesmaximal, characteristic
8#2066×C151C211yesmaximal, characteristic, complemented
9#2056×C151C211yesmaximal, characteristic, complemented
10#2055×C151C211yesmaximal, characteristic
11#2042×C151C211yesmaximal, characteristic
12#2015×C151C211yesmaximal, characteristic
13C4×C4⋊C8×C151C211yesmaximal, characteristic, complemented
14C4×#103×C151C211yesmaximal, characteristic, complemented
15C4×#102×C151C211yesmaximal, characteristic
16C22×Q16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C4×Q16×C151—24no—
23C4×SD16×C151—24no—
24C2×#107×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C4×C8×C151C2211yescharacteristic
37C2×C4×C8×C151C2211yescharacteristic
38#391×C151C2211yescharacteristic
39#391×C151C2211yescharacteristic
40#391×C151C2211yescharacteristic
41#390×C151C2211yescharacteristic
42#389×C151C2211yescharacteristic
43#389×C151C2211yescharacteristic
44#388×C151—21no—
45#388×C151—21no—
46#387×C151—21no—
47#387×C151—21no—
48#382×C151C2211yescharacteristic
49C4×C4⋊C4×C151—21no—
50C4×C4⋊C4×C151C2211yescharacteristic
51C4×C22⋊C4×C151—21no—
52C4×C22⋊C4×C151—21no—
53#376×C151—21no—
54C43×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151C2311yescharacteristic
64C23×C4×C151—21no—
65C2×Q16×C151—22no—
66C2×Q16×C151—22no—
67C2×Q16×C151—22no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75#124×C151—22no—
76#124×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151—22no—
79C4×Q8×C151—22no—
80C4×Q8×C151D414yes—
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151—21no—
100C2×C42×C151D411yescharacteristic
101C2×C42×C151D411yescharacteristic
102C2×C42×C151D411yescharacteristic
103C2×C42×C151D411yescharacteristic
104C2×C42×C151C2311yescharacteristic
105C2×C42×C151C2311yescharacteristic
106C2×C42×C151C2311yescharacteristic
107#107×C151—22no—
108#106×C151—22no—
109C4⋊C8×C151—22no—
110C4⋊C8×C151—22no—
111#103×C151—22no—
112#103×C151—22no—
113#103×C151—22no—
114#103×C151—22no—
115#103×C151—22no—
116#102×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119C4×C8×C151—22no—
120C4×C8×C151—22no—
121#95×C151—21no—
122#95×C151—21no—
123#95×C151—21no—
124#95×C151—21no—
125#95×C151—21no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132C24×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151C2×D412yes—
144C2×Q8×C151#4112yes—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151#4112yes—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—42no—
159C22×C4×C151—42no—
160C22×C4×C151—42no—
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2411yescharacteristic
168Q16×C151—28no—
169SD16×C151—28no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151#4112yes—
181C2×C8×C151#4112yes—
182C4⋊C4×C151—24no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—42no—
193C4⋊C4×C151—42no—
194C4⋊C4×C151—42no—
195C4⋊C4×C151C2×D412yes—
196C22⋊C4×C151—24no—
197C22⋊C4×C151—24no—
198C22⋊C4×C151—42no—
199C22⋊C4×C151—42no—
200C22⋊C4×C151—42no—
201C42×C151—24no—
202C42×C151—22no—
203C42×C151—22no—
204C42×C151—22no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—41no—
210C42×C151—42no—
211C42×C151—42no—
212C42×C151C2×D412yes—
213C42×C151#4112yes—
214C23×C151—22no—
215C23×C151—41no—
216C23×C151—41no—
217C23×C151—41no—
218C23×C151—41no—
219C23×C151—41no—
220C23×C151—41no—
221C23×C151C22×D411yescharacteristic
222Q8×C151—22no—
223Q8×C151—22no—
224Q8×C151—22no—
225Q8×C151—22no—
226Q8×C151—41no—
227Q8×C151—41no—
228Q8×C151—41no—
229Q8×C151—41no—
230D4×C151—22no—
231D4×C151—22no—
232D4×C151—41no—
233D4×C151—41no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—22no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—84no—
269C2×C4×C151#12112yes—
270C2×C4×C151#12112yes—
271C2×C4×C151#13512yes—
272C2×C4×C151#13512yes—
273C2×C4×C151#13712yes—
274C2×C4×C151C22×D411yescharacteristic
275C2×C4×C151C2×#4111yescharacteristic
276C2×C4×C151C2×#4111yescharacteristic
277C2×C4×C151C2×#4111yescharacteristic
278C2×C4×C151C2×#4111yescharacteristic
279C2×C4×C151C2×#4111yescharacteristic
280C8×C151—22no—
281C8×C151—22no—
282C8×C151—41no—
283C8×C151—41no—
284C22×C151—42no—
285C22×C151—42no—
286C22×C151—42no—
287C22×C151—81no—
288C22×C151—81no—
289C22×C151—81no—
290C22×C151—81no—
291C22×C151C2×#12111yescharacteristic
292C22×C151#52511yescharacteristic
293C22×C151#53211yescharacteristic
294C22×C151C2×#13511yescharacteristic
295C22×C151C2×#13511yescharacteristic
296C22×C151C2×#13711yescharacteristic
297C22×C151#57511yescharacteristic
298C4×C151—22no—
299C4×C151—22no—
300C4×C151—41no—
301C4×C151—41no—
302C4×C151—42no—
303C4×C151—42no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—81no—
307C4×C151—81no—
308C4×C151—81no—
309C4×C151—81no—
310C4×C151#46414yes—
311C4×C151#52511yescharacteristic
312C4×C151#52511yescharacteristic
313C4×C151#52911yescharacteristic
314C4×C151#52911yescharacteristic
315C2×C151—82no—
316C2×C151#239211yescharacteristic
317C2×C151C2×#46411yescharacteristic
318C2×C151#303511yescharacteristic
319C2×C151#310211yescharacteristic
320C2×C151#310711yescharacteristic
321C2×C151#316811yescharacteristic
322C2×C151#317211yescharacteristic
323#23681C15111yesmaximal, characteristic, direct product factor, Sylow
324C151#2368111yescharacteristic, direct product factor, Sylow
325C2×C4×Q16C2×C15111yescharacteristic, complemented
326C2×C4×SD16C2×C15111yescharacteristic
327C4×#124C2×C15111yescharacteristic
328#2295C2×C15111yescharacteristic, complemented
329#2085C2×C15111yescharacteristic, complemented
330#2074C2×C15111yescharacteristic, complemented
331#2067C2×C15111yescharacteristic
332#2066C2×C15111yescharacteristic, complemented
333#2056C2×C15111yescharacteristic, complemented
334#2055C2×C15111yescharacteristic
335#2042C2×C15111yescharacteristic
336#2015C2×C15111yescharacteristic
337C4×C4⋊C8C2×C15111yescharacteristic, complemented
338C4×#103C2×C15111yescharacteristic, complemented
339C4×#102C2×C15111yescharacteristic
340C22×Q16C22×C15111yescharacteristic
341C22×SD16C22×C15111yescharacteristic
342C2×#124C22×C15111yescharacteristic
343C2×C4×Q8C22×C15111yescharacteristic
344C2×C4×Q8C22×C15111yescharacteristic
345C2×C4×D4C22×C15111yescharacteristic
346C4×Q16—24no—
347C4×SD16—24no—
348C2×#107C22×C15111yescharacteristic
349C2×#106C22×C15111yescharacteristic
350C2×C4⋊C8C22×C15111yescharacteristic
351C2×C4⋊C8C22×C15111yescharacteristic
352C2×#103C22×C15111yescharacteristic
353C2×#103C22×C15111yescharacteristic
354C2×#103C22×C15111yescharacteristic
355C2×#103C22×C15111yescharacteristic
356C2×#103C22×C15111yescharacteristic
357C2×#102C22×C15111yescharacteristic
358C2×#102C22×C15111yescharacteristic
359C2×#102C22×C15111yescharacteristic
360C2×C4×C8C22×C15111yescharacteristic
361C2×C4×C8C22×C15111yescharacteristic
362#391C22×C15111yescharacteristic
363#391C22×C15111yescharacteristic
364#391C22×C15111yescharacteristic
365#390C22×C15111yescharacteristic
366#389C22×C15111yescharacteristic
367#389C22×C15111yescharacteristic
368#388—21no—
369#388—21no—
370#387—21no—
371#387—21no—
372#382C22×C15111yescharacteristic
373C4×C4⋊C4—21no—
374C4×C4⋊C4C22×C15111yescharacteristic
375C4×C22⋊C4—21no—
376C4×C22⋊C4—21no—
377#376—21no—
378C43C22×C15111yescharacteristic
379#340C22×C15111yescharacteristic
380#340C22×C15111yescharacteristic
381#340C22×C15111yescharacteristic
382#340C22×C15111yescharacteristic
383#336C22×C15111yescharacteristic
384#336C22×C15111yescharacteristic
385C22×Q8C23×C15111yescharacteristic
386C22×Q8C23×C15111yescharacteristic
387C22×D4C23×C15111yescharacteristic
388C23×C4—21no—
389C2×Q16—22no—
390C2×Q16—22no—
391C2×Q16—22no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—22no—
395C22×C8C23×C15111yescharacteristic
396C22×C8C23×C15111yescharacteristic
397C22×C8C23×C15111yescharacteristic
398C22×C8C23×C15111yescharacteristic
399#124—22no—
400#124—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8D4×C15114yes—
405C4×D4—22no—
406C4×D4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4C23×C15111yescharacteristic
412C2×C4⋊C4C23×C15111yescharacteristic
413C2×C4⋊C4C23×C15111yescharacteristic
414C2×C4⋊C4C23×C15111yescharacteristic
415C2×C4⋊C4C23×C15111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42D4×C15111yescharacteristic
425C2×C42D4×C15111yescharacteristic
426C2×C42D4×C15111yescharacteristic
427C2×C42D4×C15111yescharacteristic
428C2×C42C23×C15111yescharacteristic
429C2×C42C23×C15111yescharacteristic
430C2×C42C23×C15111yescharacteristic
431#107—22no—
432#106—22no—
433C4⋊C8—22no—
434C4⋊C8—22no—
435#103—22no—
436#103—22no—
437#103—22no—
438#103—22no—
439#103—22no—
440#102—22no—
441#102—22no—
442#102—22no—
443C4×C8—22no—
444C4×C8—22no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456C24—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C2×D4×C15112yes—
468C2×Q8#41×C15112yes—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4#41×C15112yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4C2×D4×C15111yescharacteristic
486C22×C4C2×D4×C15111yescharacteristic
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4C2×D4×C15111yescharacteristic
490C22×C4C2×D4×C15111yescharacteristic
491C22×C4C24×C15111yescharacteristic
492Q16—28no—
493SD16—28no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8#41×C15112yes—
505C2×C8#41×C15112yes—
506C4⋊C4—24no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4C2×D4×C15112yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C42—24no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—41no—
534C42—42no—
535C42—42no—
536C42C2×D4×C15112yes—
537C42#41×C15112yes—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23C22×D4×C15111yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554D4—22no—
555D4—22no—
556D4—41no—
557D4—41no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—84no—
593C2×C4#121×C15112yes—
594C2×C4#121×C15112yes—
595C2×C4#135×C15112yes—
596C2×C4#135×C15112yes—
597C2×C4#137×C15112yes—
598C2×C4C22×D4×C15111yescharacteristic
599C2×C4C2×#41×C15111yescharacteristic
600C2×C4C2×#41×C15111yescharacteristic
601C2×C4C2×#41×C15111yescharacteristic
602C2×C4C2×#41×C15111yescharacteristic
603C2×C4C2×#41×C15111yescharacteristic
604C8—22no—
605C8—22no—
606C8—41no—
607C8—41no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22C2×#121×C15111yescharacteristic
616C22#525×C15111yescharacteristic
617C22#532×C15111yescharacteristic
618C22C2×#135×C15111yescharacteristic
619C22C2×#135×C15111yescharacteristic
620C22C2×#137×C15111yescharacteristic
621C22#575×C15111yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4#464×C15114yes—
635C4#525×C15111yescharacteristic
636C4#525×C15111yescharacteristic
637C4#529×C15111yescharacteristic
638C4#529×C15111yescharacteristic
639C2—82no—
640C2#2392×C15111yescharacteristic
641C2C2×#464×C15111yescharacteristic
642C2#3035×C15111yescharacteristic
643C2#3102×C15111yescharacteristic
644C2#3107×C15111yescharacteristic
645C2#3168×C15111yescharacteristic
646C2#3172×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
socleC23×C151C22×D4
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q16×C151C2semidirect
4. #2295×C151C2semidirect
5. #2085×C151C2semidirect
6. #2074×C151C2semidirect
8. #2066×C151C2semidirect
9. #2056×C151C2semidirect
13. C4×C4⋊C8×C151C2semidirect
14. C4×#103×C151C2semidirect
323. #23681C151direct (N × H)
324. C151#23681direct (N × H)
325. C2×C4×Q16C2×C151semidirect
328. #2295C2×C151semidirect
329. #2085C2×C151semidirect
330. #2074C2×C151semidirect
332. #2066C2×C151semidirect
333. #2056C2×C151semidirect
337. C4×C4⋊C8C2×C151semidirect
338. C4×#103C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q16×C1512
C2×C4×SD16×C1512
C4×#124×C1512
#2295×C1512
#2085×C1512
#2074×C1512
#2067×C1512
#2066×C1512
#2056×C1512
#2055×C1512
#2042×C1512
#2015×C1512
C4×C4⋊C8×C1512
C4×#103×C1512
C4×#102×C1512
#23681151