Finite Group Databasebeta

← C4×#15689369 #26222907

Subgroups — C4×#15689369 #26222907

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689369C211yesmaximal, characteristic
2C2×C4×#10625325C211yesmaximal, characteristic, complemented
3C4×#13094003C211yesmaximal, characteristic, complemented
4C4×#13093998C211yesmaximal, characteristic
5#20244269C211yesmaximal, characteristic, complemented
6#20244126C211yesmaximal, characteristic, complemented
7#20244085C211yesmaximal, characteristic, complemented
8#20244078C211yesmaximal, characteristic, complemented
9#20243826C211yesmaximal, characteristic
10#20243821C211yesmaximal, characteristic, complemented
11#20243421C211yesmaximal, characteristic, complemented
12C4×#13093958C211yesmaximal, characteristic, complemented
13C4×#13093949C211yesmaximal, characteristic, complemented
14C4×#13093946C211yesmaximal, characteristic, complemented
15C2×C4×M16×C47C211yesmaximal, characteristic, complemented
16C22×#10625325C2211yescharacteristic
17C2×#13094003C2211yescharacteristic
18C2×#13093998C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×C22⋊D47—21no—
22#15689369C418yesdirect product factor
23C4×#10625325—24no—
24C2×#13093958C2211yescharacteristic
25C2×#13093958C2211yescharacteristic
26C2×#13093956C2211yescharacteristic
27C2×#13093949C2211yescharacteristic
28C2×#13093949C2211yescharacteristic
29C2×#13093949C2211yescharacteristic
30C2×#13093946C2211yescharacteristic
31C2×#13093946C2211yescharacteristic
32C2×#13093946C2211yescharacteristic
33#15689029C2211yescharacteristic
34#15689025C2211yescharacteristic
35#15689021C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689014—21no—
38#15689007—21no—
39#15689002—21no—
40#15688996—21no—
41#15688983C2211yescharacteristic
42#15688983C2211yescharacteristic
43C4×Dic47⋊C4—21no—
44C4×C4⋊Dic47C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46C4×(C2×D47)⋊C4—21no—
47C4×C22⋊Dic47—21no—
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688886C2211yescharacteristic
54C22×M16×C47C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C22×C42×C47C2211yescharacteristic
57C4×M16×C47—24no—
58C2×#97×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×C4×C8×C47C2211yescharacteristic
61C2×C4×C8×C47C2211yescharacteristic
62C22×Dic94C2311yescharacteristic
63C22×D188C2311yescharacteristic
64C22×C22⋊D47—21no—
65C22×C4×D47—21no—
66C2×#10625325—22no—
67C2×#10625325—22no—
68C2×#10625325C2×C414yescomplemented
69#13094003—22no—
70#13094003C2×C414yescomplemented
71#13093998—22no—
72#13093998C2×C414yes—
73C4×Dic94—22no—
74C4×Dic94—22no—
75C4×D188—22no—
76C4×D188—22no—
77C4×C22⋊D47—44no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×C22⋊Dic47—21no—
89C2×C22⋊Dic47—21no—
90C2×C22⋊Dic47—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—21no—
97C2×C4×Dic47—21no—
98#13093958—22no—
99#13093958C2×C414yescomplemented
100#13093956—22no—
101#13093949—22no—
102#13093949—22no—
103#13093949C2×C414yescomplemented
104#13093946—22no—
105#13093946—22no—
106#13093946C2×C414yescomplemented
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C47⋊#95—21no—
113C47⋊#95—21no—
114C47⋊#95—21no—
115C23×C4×C47D411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C2×M16×C47—22no—
119C2×M16×C47—22no—
120C2×M16×C47—22no—
121C2×M16×C47—22no—
122C2×M16×C47—22no—
123C2×M16×C47C2×C414yescomplemented
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C2×C42×C47—22no—
129C2×C42×C47—22no—
130C2×C42×C47D411yescharacteristic
131C2×C42×C47D411yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2311yescharacteristic
134#97×C47—22no—
135#97×C47—22no—
136C4×C8×C47—22no—
137C4×C8×C47D414yescomplemented
138C24×C47C2×D411yescharacteristic
139C23×D47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—41no—
149C22×C4×C47—41no—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47#4112yes—
157C22×C4×C47C2411yescharacteristic
158C2×C22⋊D47—24no—
159C2×C22⋊D47—42no—
160C2×C22⋊D47—42no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C2×D188—21no—
169C2×D188—21no—
170C2×D188—21no—
171C2×D188—21no—
172C2×D188—21no—
173C2×D188C22×C412yes—
174C2×C4×D47—42no—
175C2×C4×D47—42no—
176C2×C4×D47—42no—
177C2×Dic94—21no—
178C2×Dic94—21no—
179C2×Dic94—21no—
180C2×Dic94—21no—
181C2×Dic94—21no—
182C2×Dic94C22×C412yes—
183M16×C47—28no—
184M16×C47—28no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47C22×C412yes—
192C2×C8×C47C22×C412yes—
193C2×C8×C47C2×D412yes—
194C2×C8×C47C2×D412yes—
195C2×C8×C47#4112yes—
196C2×C8×C47#4112yes—
197C42×C47—22no—
198C42×C47—22no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47C2×D412yes—
202C42×C47#4112yes—
203C22⋊Dic47—24no—
204C22⋊Dic47—42no—
205C22⋊Dic47—42no—
206(C2×D47)⋊C4—24no—
207(C2×D47)⋊C4—42no—
208(C2×D47)⋊C4—42no—
209(C2×D47)⋊C4—42no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47C22×C412yes—
221C4⋊Dic47C22×C412yes—
222Dic47⋊C4—24no—
223Dic47⋊C4—42no—
224Dic47⋊C4—42no—
225Dic47⋊C4—42no—
226C4×Dic47—42no—
227C4×Dic47—42no—
228C4×Dic47—42no—
229#10625325—28no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47C4×D412yes—
237C23×C47C22×D411yescharacteristic
238C22×D47—22no—
239C22×D47—41no—
240C22×D47—41no—
241C22×D47—41no—
242C22×D47—41no—
243C22×D47—41no—
244C22×D47—41no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—44no—
260C2×C4×C47—44no—
261C2×C4×C47C4×D412yes—
262C2×C4×C47#12112yes—
263C2×C4×C47#12112yes—
264C2×C4×C47AGL(1,ℤ/8)12yes—
265C2×C4×C47#13712yes—
266C2×C4×C47C23×C411yescharacteristic
267C2×C4×C47C22×D411yescharacteristic
268C2×C4×C47C2×#4111yescharacteristic
269C2×C4×C47C2×#4111yescharacteristic
270C2×C4×C47C2×#4111yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C22⋊D47—48no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294D188—22no—
295D188—22no—
296D188—41no—
297D188—41no—
298C4×D47—84no—
299Dic94—22no—
300Dic94—22no—
301Dic94—41no—
302Dic94—41no—
303C8×C47—22no—
304C8×C47—22no—
305C8×C47—22no—
306C8×C47C4×D414yescomplemented
307C4×#468—471nomaximal, Sylow
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47C2×C4×D411yescharacteristic
316C22×C47C2×#12111yescharacteristic
317C22×C47#53211yescharacteristic
318C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C47C2×#13711yescharacteristic
320C22×C47#57511yescharacteristic
321C22×C47#57511yescharacteristic
322C2×D47—42no—
323C2×D47—42no—
324C2×D47—42no—
325C2×D47—81no—
326C2×D47—81no—
327C2×D47—81no—
328C2×D47—81no—
329C4×C47—22no—
330C4×C47—22no—
331C4×C47—41no—
332C4×C47—41no—
333C4×C47#46814yescomplemented
334C4×C47C2×C4×D411yescharacteristic
335C4×C47C4×#4111yescharacteristic
336C4×C47#52511yescharacteristic
337C4×C47#52911yescharacteristic
338Dic47—42no—
339Dic47—42no—
340Dic47—42no—
341Dic47—81no—
342Dic47—81no—
343Dic47—81no—
344Dic47—81no—
345C2×#468—471no—
346C2×C4×SD16—471no—
347C2×C4×M16D4711yescharacteristic, complemented
348C4×C22⋊Q8—471no—
349C4×#121—471no—
350#1973—471no—
351#1943—471no—
352#1936—471no—
353#1935—471no—
354#1895—471no—
355#1894—471no—
356#1809—471no—
357C4×#107—471no—
358C4×#103—471no—
359C4×#102—471no—
360C2×C47—42no—
361C2×C47C4×#12111yescharacteristic
362C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
363C2×C47C4×#13711yescharacteristic
364C2×C47C2×#46811yescharacteristic
365C2×C47#305411yescharacteristic
366C2×C47#317111yescharacteristic
367C2×C47#317211yescharacteristic
368D47—82no—
369C22×SD16—471no—
370C22×M16C2×D4711yescharacteristic
371C22×M16C2×D4711yescharacteristic
372C2×C22⋊Q8—471no—
373C2×#121—471no—
374C2×C4×Q8—471no—
375C2×C4×D4—471no—
376C2×C4×D4—941no—
377C22×C42C2×D4711yescharacteristic
378#468—478no—
379C4×SD16—944no—
380C2×#107—471no—
381C2×#107—471no—
382C2×#106—471no—
383C2×#103—471no—
384C2×#103—471no—
385C2×#103—471no—
386C2×#102—471no—
387C2×#102—471no—
388C2×#102—471no—
389C4×M16—24no—
390C2×#97C2×D4711yescharacteristic
391C2×#97C2×D4711yescharacteristic
392C2×C4×C8C2×D4711yescharacteristic
393C2×C4×C8C2×D4711yescharacteristic
394#391—471no—
395#390—471no—
396#389—471no—
397#389—471no—
398#388—941no—
399#387—941no—
400#386—941no—
401#385—941no—
402#380—471no—
403#380—471no—
404C4×C4⋊C4—471no—
405C4×C4⋊C4—471no—
406C4×C4⋊C4—941no—
407C4×C22⋊C4—941no—
408C4×C22⋊C4—941no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415C47C4×#46811yescharacteristic, complemented, Sylow
416C22×Q8—471no—
417C22×D4—471no—
418C22×D4—941no—
419C23×C4—941no—
420C23×C4D18811yescharacteristic
421C23×C4D18811yescharacteristic
422C23×C4C22×D4711yescharacteristic
423C2×SD16—474no—
424C2×SD16—942no—
425C2×SD16—942no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16C4×D4714yescomplemented
432C22×C8C22×D4711yescharacteristic
433C22×C8C22×D4711yescharacteristic
434C22×C8C22×D4711yescharacteristic
435C22×C8C22×D4711yescharacteristic
436C22⋊Q8—474no—
437C22⋊Q8—942no—
438#121—474no—
439#121—942no—
440C4×Q8—942no—
441C4×Q8—942no—
442C4×D4—942no—
443C4×D4—942no—
444C4×D4—1884no—
445C2×C4⋊C4—471no—
446C2×C4⋊C4—471no—
447C2×C4⋊C4—471no—
448C2×C4⋊C4—471no—
449C2×C4⋊C4—471no—
450C2×C4⋊C4—471no—
451C2×C4⋊C4—941no—
452C2×C4⋊C4—941no—
453C2×C4⋊C4—941no—
454C2×C4⋊C4—941no—
455C2×C22⋊C4—941no—
456C2×C22⋊C4—941no—
457C2×C22⋊C4—941no—
458C2×C22⋊C4—941no—
459C2×C22⋊C4—941no—
460C2×C22⋊C4—941no—
461C2×C22⋊C4—941no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—941no—
465C2×C42—941no—
466C2×C42—941no—
467C2×C42D18811yescharacteristic
468C2×C42D18811yescharacteristic
469C2×C42C22×D4711yescharacteristic
470C2×C42C22×D4711yescharacteristic
471#107—474no—
472#107—942no—
473#106—942no—
474#103—474no—
475#103—942no—
476#103—942no—
477#102—474no—
478#102—942no—
479#102—942no—
480#97—22no—
481#97—22no—
482C4×C8—22no—
483C4×C8C22⋊D4714yescomplemented
484#95—941no—
485#95—941no—
486#95—941no—
487#95—941no—
488#95—941no—
489#95—941no—
490#95—941no—
491#95—941no—
492C24—941no—
493C24C2×D18811yescharacteristic
494C2×Q8—472no—
495C2×Q8—941no—
496C2×Q8—941no—
497C2×Q8—941no—
498C2×Q8—941no—
499C2×Q8—941no—
500C2×D4—472no—
501C2×D4—944no—
502C2×D4—941no—
503C2×D4—941no—
504C2×D4—941no—
505C2×D4—941no—
506C2×D4—941no—
507C2×D4—1882no—
508C2×D4—1882no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—941no—
520C22×C4—941no—
521C22×C4—941no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—1882no—
527C22×C4—1882no—
528C22×C4—1882no—
529C22×C4C2×C4×D4712yes—
530C22×C4C2×D18811yescharacteristic
531C22×C4C2×D18811yescharacteristic
532C22×C4C2×D18811yescharacteristic
533C22×C4C2×D18811yescharacteristic
534C22×C4C2×D18811yescharacteristic
535C22×C4#1062535012yes—
536C22×C4C23×D4711yescharacteristic
537SD16—948no—
538M16—28no—
539M16—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C2×C4×D4712yes—
547C2×C8C2×C4×D4712yes—
548C2×C8#1062535012yes—
549C2×C8#1062535012yes—
550C2×C8C2×C22⋊D4712yes—
551C2×C8C2×C22⋊D4712yes—
552C4⋊C4—472no—
553C4⋊C4—472no—
554C4⋊C4—944no—
555C4⋊C4—941no—
556C4⋊C4—941no—
557C4⋊C4—941no—
558C4⋊C4—941no—
559C4⋊C4—941no—
560C4⋊C4—941no—
561C4⋊C4—941no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—1882no—
566C4⋊C4—1882no—
567C4⋊C4—1882no—
568C22⋊C4—944no—
569C22⋊C4—944no—
570C22⋊C4—1882no—
571C22⋊C4—1882no—
572C22⋊C4—1882no—
573C22⋊C4—1882no—
574C22⋊C4—1882no—
575C42—22no—
576C42—22no—
577C42—21no—
578C42—21no—
579C42—1882no—
580C42—1882no—
581C42—1882no—
582C42#1062535012yes—
583C42C2×C22⋊D4712yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—942no—
591C23—1881no—
592C23—1881no—
593C23—1881no—
594C23—1881no—
595C23—1881no—
596C23—1881no—
597C23C4×D18812yes—
598C23C22×D18811yescharacteristic
599Q8—942no—
600Q8—942no—
601Q8—1881no—
602Q8—1881no—
603D4—942no—
604D4—942no—
605D4—1888no—
606D4—1881no—
607D4—1881no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—942no—
625C2×C4—942no—
626C2×C4—942no—
627C2×C4—3764no—
628C2×C4—1881no—
629C2×C4—1881no—
630C2×C4—1881no—
631C2×C4—1881no—
632C2×C4—1881no—
633C2×C4—1881no—
634C2×C4—1881no—
635C2×C4—1881no—
636C2×C4—1881no—
637C2×C4—1881no—
638C2×C4—1881no—
639C2×C4—1881no—
640C2×C4—1881no—
641C2×C4—1881no—
642C2×C4—1881no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4C4×D18812yes—
647C2×C4#1309399812yes—
648C2×C4#1309399812yes—
649C2×C4#1309405212yes—
650C2×C4#1309405712yes—
651C2×C4C22×C4×D4711yescharacteristic
652C2×C4C22×C22⋊D4711yescharacteristic
653C2×C4C2×#1062535011yescharacteristic
654C2×C4C2×#1062535011yescharacteristic
655C2×C4C2×#1062535011yescharacteristic
656C2×C4C2×#1062535011yescharacteristic
657C8—22no—
658C8—22no—
659C8—22no—
660C8C4×C22⋊D4714yescomplemented
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—3761no—
669C22—3761no—
670C22—3761no—
671C22—3761no—
672C22—1882no—
673C22—1882no—
674C22—1882no—
675C22C2×C4×D18811yescharacteristic
676C22C2×#1309399811yescharacteristic
677C22#1568967311yescharacteristic
678C22C2×#1309405211yescharacteristic
679C22C2×#1309405711yescharacteristic
680C22#1568992311yescharacteristic
681C22#1568992311yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—3761no—
687C4—3761no—
688C4—3761no—
689C4—3761no—
690C4—1882no—
691C4—1882no—
692C4—1882no—
693C4#1568936914yesdirect product factor
694C4C2×C4×C22⋊D4711yescharacteristic
695C4C4×#1062535011yescharacteristic
696C4#1568963411yescharacteristic
697C4#1568965711yescharacteristic
698C2—42no—
699C2—3762no—
700C2C4×#1309399811yescharacteristic
701C2C4×#1309405211yescharacteristic
702C2C4×#1309405711yescharacteristic
703C2C2×#1568936911yescharacteristic
704C2#2025299711yescharacteristic
705C2#2025398311yescharacteristic
706C2#2025399411yescharacteristic
subgroupG/H
centerC22×C4C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×M16×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C4×#468
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625325C2semidirect
3. C4×#13094003C2semidirect
5. #20244269C2semidirect
6. #20244126C2semidirect
7. #20244085C2semidirect
8. #20244078C2semidirect
10. #20243821C2semidirect
11. #20243421C2semidirect
12. C4×#13093958C2semidirect
13. C4×#13093949C2semidirect
14. C4×#13093946C2semidirect
15. C2×C4×M16×C47C2semidirect
22. #15689369C4direct (N × H)
68. C2×#10625325C2×C4semidirect
70. #13094003C2×C4semidirect
99. #13093958C2×C4semidirect
103. #13093949C2×C4semidirect
106. #13093946C2×C4semidirect
123. C2×M16×C47C2×C4semidirect
137. C4×C8×C47D4semidirect
306. C8×C47C4×D4semidirect
333. C4×C47#468semidirect
347. C2×C4×M16D47semidirect
415. C47C4×#468semidirect
431. C2×M16C4×D47semidirect
483. C4×C8C22⋊D47semidirect
660. C8C4×C22⋊D47semidirect
693. C4#15689369direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893692
C2×C4×#106253252
C4×#130940032
C4×#130939982
#202442692
#202441262
#202440852
#202440782
#202438262
#202438212
#202434212
C4×#130939582
C4×#130939492
C4×#130939462
C2×C4×M16×C472
C4×#46847