Finite Group Databasebeta

← C151×#24387 #50329312

Subgroups — C151×#24387 #50329312

Order 38656.

1626 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
2C2×#468×C151C212yesmaximal, complemented
3C2×#448×C151C211yesmaximal, characteristic, complemented
4C2×#407×C151C211yesmaximal, characteristic, complemented
5#2847×C151C211yesmaximal, characteristic
6#2036×C151C212yesmaximal, complemented
7#2000×C151C212yesmaximal, complemented
8#1894×C151C212yesmaximal, complemented
9#1874×C151C211yesmaximal, characteristic, complemented
10#1852×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C24×C4×C151C2211yescharacteristic
14C22×SD16×C151C2212yescomplemented
15C22×M16×C151C2212yes—
16C2×C22⋊Q8×C151—21no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—28no—
19C2×C22⋊Q8×C151C2212yes—
20C2×C22⋊Q8×C151C2212yes—
21C2×#121×C151C2211yescharacteristic
22C2×#121×C151C2211yescharacteristic
23C2×#121×C151C2211yescharacteristic
24C2×#120×C151—21no—
25C22×C4⋊C4×C151—21no—
26C22×C4⋊C4×C151C2211yescharacteristic
27C22×C22⋊C4×C151—21no—
28#468×C151—28no—
29#448×C151—24no—
30C2×#107×C151C2212yescomplemented
31C2×#103×C151C2212yescomplemented
32C2×#103×C151C2212yescomplemented
33C2×#103×C151C2212yescomplemented
34C2×#102×C151C2212yescomplemented
35#407×C151—24no—
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2212yes—
38C2×C22⋊C8×C151C2211yescharacteristic
39#386×C151—21no—
40#386×C151—21no—
41#386×C151—21no—
42#380×C151C2211yescharacteristic
43#380×C151C2211yescharacteristic
44#380×C151C2211yescharacteristic
45#340×C151C2212yescomplemented
46#340×C151C2212yescomplemented
47C25×C151D411yescharacteristic
48C22×Q8×C151—21no—
49C22×Q8×C151—24no—
50C22×Q8×C151—22no—
51C22×Q8×C151—22no—
52C22×Q8×C151—42no—
53C22×Q8×C151C2312yes—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151—21no—
57C22×D4×C151C2311yescharacteristic
58C23×C4×C151—22no—
59C23×C4×C151—24no—
60C23×C4×C151—22no—
61C23×C4×C151—21no—
62C23×C4×C151—21no—
63C23×C4×C151—42no—
64C23×C4×C151D411yescharacteristic
65C23×C4×C151D411yescharacteristic
66C23×C4×C151D411yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C2×SD16×C151—24no—
71C2×SD16×C151—24no—
72C2×SD16×C151—42no—
73C2×M16×C151—24no—
74C2×M16×C151—24no—
75C2×M16×C151—42no—
76C22×C8×C151C2312yes—
77C22×C8×C151C2312yes—
78C22⋊Q8×C151—28no—
79C22⋊Q8×C151—28no—
80C22⋊Q8×C151—24no—
81C22⋊Q8×C151—24no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151D418yescomplemented
84#121×C151—22no—
85#121×C151—24no—
86#121×C151—22no—
87#121×C151—42no—
88#120×C151—44no—
89C2×C4⋊C4×C151—28no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—24no—
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2312yes—
98C2×C22⋊C4×C151—28no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—22no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107#107×C151—24no—
108#103×C151—24no—
109#103×C151—24no—
110#103×C151—42no—
111#102×C151—24no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—24no—
114C22⋊C8×C151D414yescomplemented
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—21no—
118C24×C151—22no—
119C24×C151—22no—
120C24×C151—22no—
121C24×C151—22no—
122C24×C151—22no—
123C24×C151—21no—
124C24×C151—41no—
125C24×C151—41no—
126C24×C151C2×D411yescharacteristic
127C24×C151C2×D411yescharacteristic
128C24×C151C2×D411yescharacteristic
129C2×Q8×C151—24no—
130C2×Q8×C151—22no—
131C2×Q8×C151—22no—
132C2×Q8×C151—22no—
133C2×Q8×C151—22no—
134C2×Q8×C151—22no—
135C2×Q8×C151—48no—
136C2×Q8×C151—48no—
137C2×Q8×C151—42no—
138C2×Q8×C151—42no—
139C2×Q8×C151C2×D414yes—
140C2×D4×C151—22no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—22no—
144C2×D4×C151—42no—
145C2×D4×C151—42no—
146C2×D4×C151—42no—
147C2×D4×C151—42no—
148C2×D4×C151—42no—
149C2×D4×C151—42no—
150C2×D4×C151—42no—
151C2×D4×C151—42no—
152C2×D4×C151—42no—
153C22×C4×C151—22no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151—24no—
159C22×C4×C151—24no—
160C22×C4×C151—22no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—21no—
169C22×C4×C151—22no—
170C22×C4×C151—21no—
171C22×C4×C151—22no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—41no—
176C22×C4×C151—41no—
177C22×C4×C151—41no—
178C22×C4×C151—48no—
179C22×C4×C151—48no—
180C22×C4×C151—42no—
181C22×C4×C151—42no—
182C22×C4×C151—42no—
183C22×C4×C151—42no—
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D414yes—
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D412yes—
189C22×C4×C151#4112yes—
190C22×C4×C151C2411yescharacteristic
191SD16×C151—48no—
192M16×C151—48no—
193C2×C8×C151—22no—
194C2×C8×C151—22no—
195C2×C8×C151—22no—
196C2×C8×C151—22no—
197C2×C8×C151—22no—
198C2×C8×C151C2×D414yes—
199C4⋊C4×C151—24no—
200C4⋊C4×C151—28no—
201C4⋊C4×C151—28no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—22no—
207C4⋊C4×C151C2×D414yes—
208C22⋊C4×C151—28no—
209C22⋊C4×C151—28no—
210C22⋊C4×C151—42no—
211C22⋊C4×C151—42no—
212C22⋊C4×C151—42no—
213C22⋊C4×C151—42no—
214C22⋊C4×C151—42no—
215C22⋊C4×C151—42no—
216C23×C151—21no—
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—21no—
220C23×C151—28no—
221C23×C151—21no—
222C23×C151—21no—
223C23×C151—21no—
224C23×C151—21no—
225C23×C151—21no—
226C23×C151—21no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—44no—
234C23×C151—44no—
235C23×C151—44no—
236C23×C151—44no—
237C23×C151—44no—
238C23×C151—44no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151#12012yes—
247C23×C151#12112yes—
248C23×C151AGL(1,ℤ/8)12yes—
249C23×C151#13712yes—
250C23×C151#13712yes—
251C23×C151C22×D411yescharacteristic
252Q8×C151—24no—
253Q8×C151—24no—
254Q8×C151—48no—
255Q8×C151—42no—
256Q8×C151—42no—
257D4×C151—42no—
258D4×C151—42no—
259D4×C151—84no—
260D4×C151—84no—
261D4×C151—84no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—24no—
267C2×C4×C151—24no—
268C2×C4×C151—24no—
269C2×C4×C151—24no—
270C2×C4×C151—24no—
271C2×C4×C151—24no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—44no—
276C2×C4×C151—44no—
277C2×C4×C151—44no—
278C2×C4×C151—48no—
279C2×C4×C151—48no—
280C2×C4×C151—42no—
281C2×C4×C151—42no—
282C2×C4×C151—42no—
283C2×C4×C151—42no—
284C2×C4×C151—42no—
285C2×C4×C151—42no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151#12012yes—
296C2×C4×C151#12112yes—
297C2×C4×C151C22×D411yescharacteristic
298C2×C4×C151C22×D412yes—
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C151H(5,𝔽2)12yes—
301C8×C151—24no—
302C8×C151—42no—
303C22×C151—22no—
304C22×C151—22no—
305C22×C151—22no—
306C22×C151—22no—
307C22×C151—22no—
308C22×C151—22no—
309C22×C151—22no—
310C22×C151—22no—
311C22×C151—22no—
312C22×C151—22no—
313C22×C151—22no—
314C22×C151—22no—
315C22×C151—416no—
316C22×C151—41no—
317C22×C151—41no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—41no—
323C22×C151—41no—
324C22×C151—81no—
325C22×C151—81no—
326C22×C151—81no—
327C22×C151—81no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—81no—
331C22×C151#46814yescomplemented
332C22×C151C2×#12011yescharacteristic
333C22×C151C2×#12111yescharacteristic
334C22×C151#53411yescharacteristic
335C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C151C2×#13711yescharacteristic
337C22×C151C2×#13711yescharacteristic
338C22×C151#57511yescharacteristic
339C4×C151—22no—
340C4×C151—22no—
341C4×C151—41no—
342C4×C151—44no—
343C4×C151—44no—
344C4×C151—81no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151D4212yes—
348C4×C151#54612yes—
349C2×C151—24no—
350C2×C151—42no—
351C2×C151—42no—
352C2×C151—161no—
353C2×C151#241011yescharacteristic
354C2×C151#300411yescharacteristic
355C2×C151#300611yescharacteristic
356C2×C151C2×#46811yescharacteristic
357C2×C151#305611yescharacteristic
358C2×C151#319311yescharacteristic
359C2×C151#319611yescharacteristic
360#24387C15111yesmaximal, characteristic, direct product factor, Sylow
361C151#2438711yescharacteristic, direct product factor, Sylow
362C22×C22⋊Q8C2×C15111yescharacteristic, complemented
363C2×#468C2×C15112yescomplemented
364C2×#448C2×C15111yescharacteristic, complemented
365C2×#407C2×C15111yescharacteristic, complemented
366#2847C2×C15111yescharacteristic
367#2036C2×C15112yescomplemented
368#2000C2×C15112yescomplemented
369#1894C2×C15112yescomplemented
370#1874C2×C15111yescharacteristic, complemented
371#1852C2×C15111yescharacteristic, complemented
372#1787C2×C15111yescharacteristic, complemented
373C23×Q8C22×C15111yescharacteristic
374C24×C4C22×C15111yescharacteristic
375C22×SD16C22×C15112yescomplemented
376C22×M16C22×C15112yes—
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—28no—
380C2×C22⋊Q8C22×C15112yes—
381C2×C22⋊Q8C22×C15112yes—
382C2×#121C22×C15111yescharacteristic
383C2×#121C22×C15111yescharacteristic
384C2×#121C22×C15111yescharacteristic
385C2×#120—21no—
386C22×C4⋊C4—21no—
387C22×C4⋊C4C22×C15111yescharacteristic
388C22×C22⋊C4—21no—
389#468—28no—
390#448—24no—
391C2×#107C22×C15112yescomplemented
392C2×#103C22×C15112yescomplemented
393C2×#103C22×C15112yescomplemented
394C2×#103C22×C15112yescomplemented
395C2×#102C22×C15112yescomplemented
396#407—24no—
397C2×C22⋊C8C22×C15111yescharacteristic
398C2×C22⋊C8C22×C15112yes—
399C2×C22⋊C8C22×C15111yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#380C22×C15111yescharacteristic
404#380C22×C15111yescharacteristic
405#380C22×C15111yescharacteristic
406#340C22×C15112yescomplemented
407#340C22×C15112yescomplemented
408C25D4×C15111yescharacteristic
409C22×Q8—24no—
410C22×Q8—21no—
411C22×Q8—22no—
412C22×Q8—22no—
413C22×Q8—42no—
414C22×Q8C23×C15112yes—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C23×C15111yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—22no—
422C23×C4—24no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4D4×C15111yescharacteristic
426C23×C4D4×C15111yescharacteristic
427C23×C4D4×C15111yescharacteristic
428C23×C4C23×C15111yescharacteristic
429C23×C4C23×C15111yescharacteristic
430C23×C4C23×C15111yescharacteristic
431C2×SD16—24no—
432C2×SD16—24no—
433C2×SD16—42no—
434C2×M16—24no—
435C2×M16—24no—
436C2×M16—42no—
437C22×C8C23×C15112yes—
438C22×C8C23×C15112yes—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8—24no—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8D4×C15118yescomplemented
445#121—22no—
446#121—22no—
447#121—24no—
448#121—42no—
449#120—44no—
450C2×C4⋊C4—28no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4C23×C15111yescharacteristic
456C2×C4⋊C4C23×C15111yescharacteristic
457C2×C4⋊C4C23×C15111yescharacteristic
458C2×C4⋊C4C23×C15112yes—
459C2×C22⋊C4—28no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468#107—24no—
469#103—24no—
470#103—24no—
471#103—42no—
472#102—24no—
473C22⋊C8—22no—
474C22⋊C8—24no—
475C22⋊C8D4×C15114yescomplemented
476#95—21no—
477#95—21no—
478#95—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—41no—
486C24—41no—
487C24C2×D4×C15111yescharacteristic
488C24C2×D4×C15111yescharacteristic
489C24C2×D4×C15111yescharacteristic
490C2×Q8—24no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—48no—
497C2×Q8—48no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8C2×D4×C15114yes—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C2×D4×C15114yes—
548C22×C4C2×D4×C15111yescharacteristic
549C22×C4C2×D4×C15112yes—
550C22×C4#41×C15112yes—
551C22×C4C24×C15111yescharacteristic
552SD16—48no—
553M16—48no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8C2×D4×C15114yes—
560C4⋊C4—24no—
561C4⋊C4—28no—
562C4⋊C4—28no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—22no—
568C4⋊C4C2×D4×C15114yes—
569C22⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—28no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23#120×C15112yes—
608C23#121×C15112yes—
609C23AGL(1,ℤ/8)×C15112yes—
610C23#137×C15112yes—
611C23#137×C15112yes—
612C23C22×D4×C15111yescharacteristic
613Q8—24no—
614Q8—24no—
615Q8—48no—
616Q8—42no—
617Q8—42no—
618D4—42no—
619D4—42no—
620D4—84no—
621D4—84no—
622D4—84no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—48no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4#120×C15112yes—
657C2×C4#121×C15112yes—
658C2×C4C22×D4×C15111yescharacteristic
659C2×C4C22×D4×C15112yes—
660C2×C4C2×#41×C15111yescharacteristic
661C2×C4H(5,𝔽2)×C15112yes—
662C8—24no—
663C8—42no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—416no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22#468×C15114yescomplemented
693C22C2×#120×C15111yescharacteristic
694C22C2×#121×C15111yescharacteristic
695C22#534×C15111yescharacteristic
696C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
697C22C2×#137×C15111yescharacteristic
698C22C2×#137×C15111yescharacteristic
699C22#575×C15111yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—44no—
704C4—44no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4D42×C15112yes—
709C4#546×C15112yes—
710C2—24no—
711C2—42no—
712C2—42no—
713C2—161no—
714C2#2410×C15111yescharacteristic
715C2#3004×C15111yescharacteristic
716C2#3006×C15111yescharacteristic
717C2C2×#468×C15111yescharacteristic
718C2#3056×C15111yescharacteristic
719C2#3193×C15111yescharacteristic
720C2#3196×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2847×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
1. C22×C22⋊Q8×C151C2semidirect
2. C2×#468×C151C2semidirect
3. C2×#448×C151C2semidirect
4. C2×#407×C151C2semidirect
6. #2036×C151C2semidirect
7. #2000×C151C2semidirect
8. #1894×C151C2semidirect
9. #1874×C151C2semidirect
10. #1852×C151C2semidirect
11. #1787×C151C2semidirect
14. C22×SD16×C151C22semidirect
30. C2×#107×C151C22semidirect
31. C2×#103×C151C22semidirect
32. C2×#103×C151C22semidirect
33. C2×#103×C151C22semidirect
34. C2×#102×C151C22semidirect
45. #340×C151C22semidirect
46. #340×C151C22semidirect
83. C22⋊Q8×C151D4semidirect
114. C22⋊C8×C151D4semidirect
331. C22×C151#468semidirect
360. #24387C151direct (N × H)
361. C151#24387direct (N × H)
362. C22×C22⋊Q8C2×C151semidirect
363. C2×#468C2×C151semidirect
364. C2×#448C2×C151semidirect
365. C2×#407C2×C151semidirect
367. #2036C2×C151semidirect
368. #2000C2×C151semidirect
369. #1894C2×C151semidirect
370. #1874C2×C151semidirect
371. #1852C2×C151semidirect
372. #1787C2×C151semidirect
375. C22×SD16C22×C151semidirect
391. C2×#107C22×C151semidirect
392. C2×#103C22×C151semidirect
393. C2×#103C22×C151semidirect
394. C2×#103C22×C151semidirect
395. C2×#102C22×C151semidirect
406. #340C22×C151semidirect
407. #340C22×C151semidirect
444. C22⋊Q8D4×C151semidirect
475. C22⋊C8D4×C151semidirect
692. C22#468×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1512
C2×#468×C1512
C2×#448×C1512
C2×#407×C1512
#2847×C1512
#2036×C1512
#2000×C1512
#1894×C1512
#1874×C1512
#1852×C1512
#1787×C1512
#24387151