Finite Group Databasebeta

← #26121562

Subgroups — #26121562

Order 12032.

1510 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
1C22×M16×D47C211yesmaximal, characteristic
2#20245767C211yesmaximal, characteristic
3C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
4C2×#15688884C211yesmaximal, characteristic, complemented
5C2×#15688883C211yesmaximal, characteristic, complemented
6C2×#15688882C211yesmaximal, characteristic, complemented
7C2×C47×#339C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625324—21no—
11C2×M16×D47—22no—
12C2×M16×D47—22no—
13C2×M16×D47—22no—
14C2×M16×D47—22no—
15C2×M16×D47—22no—
16C2×M16×D47C414yescomplemented
17C22×C8×D47—21no—
18C2×#13093983C2211yescharacteristic
19C22×(C2×D47)⋊C4—21no—
20C22×C4×Dic47C2211yescharacteristic
21#15688984—21no—
22#15688980C412yescomplemented
23#15688980C412yescomplemented
24#15688978—21no—
25C4×(C2×D47)⋊C4—21no—
26C4×(C2×D47)⋊C4—21no—
27C4×(C2×D47)⋊C4—22no—
28C4×(C2×D47)⋊C4C414yescomplemented
29C2×C47⋊#95—21no—
30#15688884—22no—
31#15688883—22no—
32#15688882—22no—
33C22×M16×C47C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C47×#339—22no—
37C24×D47D411yescharacteristic
38C23×Dic47—21no—
39C23×Dic47D411yescharacteristic
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47—21no—
47C22×C4×D47—21no—
48C22×C4×D47C2×C412yes—
49C22×C4×D47C2×C412yes—
50C22×C4×D47C2×C411yescharacteristic
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D412yes—
54C22×C4×D47D411yescharacteristic
55C22×C4×D47Q812yes—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329C2×C412yes—
60C2×#10625329D412yes—
61C2×#10625329D412yes—
62C2×#10625324—24no—
63C2×#10625324—24no—
64C2×#10625324—24no—
65M16×D47—28no—
66M16×D47—28no—
67M16×D47—28no—
68M16×D47—28no—
69C22×C47⋊C8—21no—
70C2×C8×D47—24no—
71C2×C8×D47—24no—
72C2×C8×D47—24no—
73#13093983—21no—
74#13093983—21no—
75#13093983—21no—
76#13093983—21no—
77C2×C4⋊Dic47C2×C412yes—
78C2×C22⋊Dic47—21no—
79C2×(C2×D47)⋊C4—28no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47C2×C412yes—
90C47⋊#95—24no—
91C47⋊#95—22no—
92C47⋊#95—22no—
93C23×C4×C47—21no—
94C23×C4×C47C2311yescharacteristic
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47—21no—
98C2×M16×C47C2×C412yes—
99C2×M16×C47D412yes—
100C2×M16×C47D412yes—
101C22×C8×C47—21no—
102#117×C47—21no—
103#117×C47—21no—
104#117×C47—21no—
105#117×C47—21no—
106C2×C4⋊C4×C47C2×C412yes—
107C2×C22⋊C4×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47C2×C412yes—
115C24×C47C2×D411yescharacteristic
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—24no—
121C23×D47—42no—
122C23×D47C22⋊C411yescharacteristic
123C23×D47C22⋊C412yes—
124C23×D47C22⋊C411yescharacteristic
125C23×D47C4⋊C412yes—
126C22×C4×C47—24no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—42no—
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×Q811yescharacteristic
142C22×C4×C47#4111yescharacteristic
143C22×C4×C47#4111yescharacteristic
144C22×C4×C47#4111yescharacteristic
145C22×C4×C47#4111yescharacteristic
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—24no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—42no—
154C22×Dic47—41no—
155C22×Dic47—41no—
156C22×Dic47C22⋊C412yes—
157C22×Dic47C22⋊C411yescharacteristic
158C22×Dic47C22⋊C411yescharacteristic
159C22×Dic47C4⋊C412yes—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—22no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—22no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—22no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—22no—
185C2×C4×D47—22no—
186C2×C4×D47—21no—
187C2×C4×D47—22no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—22no—
191C2×C4×D47—21no—
192C2×C4×D47C4212yes—
193C2×C4×D47C4212yes—
194C2×C4×D47C22⋊C412yes—
195C2×C4×D47C22⋊C412yes—
196C2×C4×D47C4⋊C412yes—
197C2×C4×D47C4⋊C412yes—
198C2×C4×D47C4⋊C412yes—
199C2×C4×D47C4⋊C412yes—
200M16×C47—22no—
201M16×C47—22no—
202M16×C47—22no—
203M16×C47C22⋊C414yescomplemented
204C2×C8×C47—22no—
205C2×C8×C47—22no—
206C2×C8×C47—22no—
207C4⋊C4×C47—22no—
208C4⋊C4×C47—22no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C42×C47—22no—
212C42×C47—22no—
213C42×C47—41no—
214C42×C47—41no—
215C42×C47—41no—
216C42×C47—41no—
217C22⋊Dic47—41no—
218C22⋊Dic47—41no—
219(C2×D47)⋊C4—216no—
220(C2×D47)⋊C4—44no—
221(C2×D47)⋊C4—44no—
222C4⋊Dic47—22no—
223C4⋊Dic47—22no—
224C4×Dic47—22no—
225C4×Dic47—22no—
226C4×Dic47—41no—
227C4×Dic47—41no—
228C4×Dic47—41no—
229C4×Dic47—41no—
230#10625329—22no—
231#10625329—22no—
232#10625329—22no—
233#10625329C22⋊C414yescomplemented
234C2×C47⋊C8—22no—
235C2×C47⋊C8—22no—
236C2×C47⋊C8—22no—
237#10625324—216no—
238C8×D47—216no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47C2×C22⋊C411yescharacteristic
242C23×C47C2×C22⋊C411yescharacteristic
243C23×C47C2×C4⋊C411yescharacteristic
244C23×C47#12111yescharacteristic
245C23×C47#12111yescharacteristic
246C23×C47#12111yescharacteristic
247C23×C47#12111yescharacteristic
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—21no—
255C22×D47—22no—
256C22×D47—21no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—24no—
260C22×D47—24no—
261C22×D47—42no—
262C22×D47—42no—
263C22×D47—44no—
264C22×D47—44no—
265C22×D47—44no—
266C22×D47—44no—
267C22×D47#9512yes—
268C22×D47#9512yes—
269C22×D47#10414yes—
270C2×C4×C47—24no—
271C2×C4×C47—44no—
272C2×C4×C47—44no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47C2×C4211yescharacteristic
279C2×C4×C47C2×C22⋊C411yescharacteristic
280C2×C4×C47C2×C22⋊C411yescharacteristic
281C2×C4×C47C2×C22⋊C411yescharacteristic
282C2×C4×C47C2×C4⋊C411yescharacteristic
283C2×C4×C47C2×C4⋊C411yescharacteristic
284C2×C4×C47#11711yescharacteristic
285C2×C4×C47#11711yescharacteristic
286C2×C4×C47C4×D411yescharacteristic
287C2×C4×C47C4×D411yescharacteristic
288C2×C4×C47C4×D411yescharacteristic
289C2×C4×C47C4×D411yescharacteristic
290C2×C4×C47C4×D411yescharacteristic
291C2×C4×C47C4×D411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C4×D411yescharacteristic
294C2×C4×C47#12011yescharacteristic
295C2×C4×C47#12011yescharacteristic
296C2×C4×C47#12011yescharacteristic
297C2×C4×C47#12011yescharacteristic
298C2×C4×C47C22⋊Q811yescharacteristic
299C2×C4×C47C22⋊Q811yescharacteristic
300C2×C4×C47C22⋊Q811yescharacteristic
301C2×C4×C47C22⋊Q811yescharacteristic
302C2×C4×C47#12311yescharacteristic
303C2×C4×C47#12311yescharacteristic
304C2×C4×C47#12311yescharacteristic
305C2×C4×C47#12311yescharacteristic
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—22no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—24no—
315C2×Dic47—44no—
316C2×Dic47—44no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47#9512yes—
323C2×Dic47#9512yes—
324C4×D47—22no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—22no—
340C8×C47—24no—
341C47⋊C8—24no—
342#10732—471nomaximal, Sylow
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—21no—
351C22×C47C2×#9511yescharacteristic
352C22×C47#38011yescharacteristic
353C22×C47#38011yescharacteristic
354C22×C47#38611yescharacteristic
355C22×C47#38611yescharacteristic
356C22×C47#38611yescharacteristic
357C22×C47#38611yescharacteristic
358C22×C47C2×#10412yes—
359C22×C47#42112yes—
360C2×D47—24no—
361C2×D47—24no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—44no—
368C2×D47—44no—
369C2×D47—44no—
370C2×D47—44no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47#33914yescomplemented
374C4×C47—44no—
375C4×C47—82no—
376C4×C47C4×C22⋊C411yescharacteristic
377C4×C47C4×C22⋊C411yescharacteristic
378C4×C47#37911yescharacteristic
379C4×C47#38111yescharacteristic
380C4×C47#38511yescharacteristic
381C4×C47#38511yescharacteristic
382C4×C47#38511yescharacteristic
383C4×C47#38511yescharacteristic
384Dic47—22no—
385Dic47—22no—
386Dic47—44no—
387Dic47—82no—
388C23×M16—471no—
389#2280—471no—
390C2×C4×C22⋊C4—471no—
391C2×#339—471no—
392C2×#339—471no—
393C2×#339—471no—
394C2×#339D4711yescharacteristic, complemented
395C2×C47—21no—
396C2×C47—21no—
397C2×C47—21no—
398C2×C47—21no—
399C2×C47C22⋊#9511yescharacteristic
400C2×C47C2×#33911yescharacteristic
401C2×C47#173311yescharacteristic
402C2×C47#187112yes—
403C2×C47#187112yes—
404D47—24no—
405D47—42no—
406C24×C4—471no—
407C22×M16—471no—
408C22×M16—474no—
409C22×M16—941no—
410C22×M16—942no—
411C22×M16—942no—
412C22×M16—942no—
413C22×M16—942no—
414C22×M16—942no—
415C22×M16C2×D4711yescharacteristic
416C23×C8—941no—
417C2×#117—471no—
418C2×#117C2×D4711yescharacteristic
419C22×C22⋊C4—941no—
420C22×C42—471no—
421C22×C42C2×D4711yescharacteristic
422#381—941no—
423#380—472no—
424#380—472no—
425#379—941no—
426C4×C22⋊C4—474no—
427C4×C22⋊C4—942no—
428C4×C22⋊C4—941no—
429C4×C22⋊C4—941no—
430C2×#95—941no—
431#339—22no—
432#339—942no—
433#339—942no—
434#339—942no—
435C47#1073211yescharacteristic, complemented, Sylow
436C25—471no—
437C23×C4—21no—
438C23×C4—471no—
439C23×C4—472no—
440C23×C4—472no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—472no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—472no—
447C23×C4—941no—
448C23×C4—941no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4—941no—
452C23×C4—941no—
453C23×C4—941no—
454C23×C4—941no—
455C23×C4—941no—
456C23×C4C22×D4711yescharacteristic
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—472no—
461C2×M16—472no—
462C2×M16—472no—
463C2×M16—944no—
464C2×M16—944no—
465C2×M16—944no—
466C2×M16—948no—
467C2×M16—948no—
468C2×M16—948no—
469C2×M16—941no—
470C2×M16—941no—
471C2×M16—941no—
472C2×M16—948no—
473C2×M16C4×D4712yes—
474C2×M16D18812yes—
475C2×M16C22⋊D4712yes—
476C22×C8—21no—
477C22×C8—944no—
478C22×C8—944no—
479C22×C8—944no—
480C22×C8—941no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—21no—
485#117—941no—
486#117—941no—
487#117—941no—
488#117—941no—
489C2×C4⋊C4—472no—
490C2×C4⋊C4C4×D4712yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—944no—
493C2×C22⋊C4—948no—
494C2×C22⋊C4—942no—
495C2×C22⋊C4—942no—
496C2×C22⋊C4—941no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—472no—
504C2×C42—941no—
505C2×C42—941no—
506C2×C42—941no—
507C2×C42—941no—
508C2×C42—941no—
509C2×C42—941no—
510C2×C42C4×D4712yes—
511#95—944no—
512#95—942no—
513#95—942no—
514C24—471no—
515C24—471no—
516C24—472no—
517C24—472no—
518C24—944no—
519C24—941no—
520C24—941no—
521C24—941no—
522C24—941no—
523C24—1882no—
524C24D4×D4711yescharacteristic
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—472no—
532C22×C4—471no—
533C22×C4—471no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—472no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
542C22×C4—472no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—942no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—942no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—942no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—942no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—942no—
568C22×C4—941no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—942no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—944no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—1882no—
583C22×C4—1881no—
584C22×C4—1881no—
585C22×C4C2×C4×D4711yescharacteristic
586C22×C4C2×C4×D4711yescharacteristic
587C22×C4C2×C4×D4711yescharacteristic
588C22×C4C2×D18811yescharacteristic
589C22×C4#1062535011yescharacteristic
590C22×C4#1062535011yescharacteristic
591C22×C4D4×D4711yescharacteristic
592C22×C4D4×D4711yescharacteristic
593C22×C4D4×D4711yescharacteristic
594C22×C4D4×D4711yescharacteristic
595C22×C4#1062535211yescharacteristic
596C22×C4Q8×D4711yescharacteristic
597C22×C4#1062535411yescharacteristic
598C22×C4C2×C22⋊D4711yescharacteristic
599M16—22no—
600M16—22no—
601M16—22no—
602M16—474no—
603M16—9416no—
604M16—942no—
605M16—942no—
606M16—942no—
607M16(C2×D47)⋊C414yescomplemented
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—9416no—
612C2×C8—942no—
613C2×C8—942no—
614C2×C8—942no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—942no—
618C4⋊C4—942no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—9416no—
622C22⋊C4—1884no—
623C22⋊C4—1884no—
624C22⋊C4—1881no—
625C22⋊C4—1881no—
626C42—22no—
627C42—22no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—942no—
633C42—942no—
634C42—1881no—
635C42—1881no—
636C42—1881no—
637C42—1881no—
638C23—22no—
639C23—22no—
640C23—472no—
641C23—474no—
642C23—472no—
643C23—944no—
644C23—944no—
645C23—941no—
646C23—941no—
647C23—942no—
648C23—942no—
649C23—942no—
650C23—942no—
651C23—941no—
652C23—942no—
653C23—941no—
654C23—942no—
655C23—942no—
656C23—1882no—
657C23—1882no—
658C23—1884no—
659C23—1884no—
660C23—1884no—
661C23—1884no—
662C23C22⋊C4×D4711yescharacteristic
663C23C22⋊C4×D4711yescharacteristic
664C23C4⋊C4×D4711yescharacteristic
665C23#1309399511yescharacteristic
666C23#1309399711yescharacteristic
667C23#1309399711yescharacteristic
668C23#1309399911yescharacteristic
669C2×C4—24no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—472no—
678C2×C4—472no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—942no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—944no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1884no—
709C2×C4—1884no—
710C2×C4—1882no—
711C2×C4C42×D4711yescharacteristic
712C2×C4C22⋊C4×D4711yescharacteristic
713C2×C4C22⋊C4×D4711yescharacteristic
714C2×C4C2×(C2×D47)⋊C411yescharacteristic
715C2×C4C4⋊C4×D4711yescharacteristic
716C2×C4C4⋊C4×D4711yescharacteristic
717C2×C4#1309398111yescharacteristic
718C2×C4#1309398211yescharacteristic
719C2×C4(C22⋊D47)⋊C411yescharacteristic
720C2×C4(C22⋊D47)⋊C411yescharacteristic
721C2×C4C4×C22⋊D4711yescharacteristic
722C2×C4C4×C22⋊D4711yescharacteristic
723C2×C4#1309398611yescharacteristic
724C2×C4#1309398611yescharacteristic
725C2×C4C4×D18811yescharacteristic
726C2×C4C4×D18811yescharacteristic
727C2×C4#1309399211yescharacteristic
728C2×C4#1309399211yescharacteristic
729C2×C4#1309399411yescharacteristic
730C2×C4#1309399411yescharacteristic
731C2×C4#1309400011yescharacteristic
732C2×C4#1309400211yescharacteristic
733C2×C4#1309400211yescharacteristic
734C2×C4#1309400411yescharacteristic
735C2×C4#1309400611yescharacteristic
736C2×C4#1309400611yescharacteristic
737C2×C4#1309400911yescharacteristic
738C2×C4#1309400911yescharacteristic
739C8—24no—
740C8—944no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—474no—
750C22—942no—
751C22—942no—
752C22—944no—
753C22—944no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—1884no—
758C22—1884no—
759C22—1884no—
760C22—1884no—
761C22—1882no—
762C22—1882no—
763C22#95×D4711yescharacteristic
764C22#1568898011yescharacteristic
765C22#1568898211yescharacteristic
766C22#1568899911yescharacteristic
767C22#1568899911yescharacteristic
768C22#1568900111yescharacteristic
769C22#1568900111yescharacteristic
770C22#104×D4712yes—
771C22#1568913812yes—
772C4—44no—
773C4—82no—
774C4—942no—
775C4—942no—
776C4—3762no—
777C4—1884no—
778C4#1568897011yescharacteristic
779C4C4×(C2×D47)⋊C411yescharacteristic
780C4#1568897811yescharacteristic
781C4#1568898511yescharacteristic
782C4#1568899411yescharacteristic
783C4#1568899411yescharacteristic
784C4#1568899711yescharacteristic
785C4#1568899711yescharacteristic
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—944no—
791C2—1882no—
792C2(C2×D47)⋊#9511yescharacteristic
793C2#339×D4711yescharacteristic
794C2#2024309611yescharacteristic
795C2#2024368712yes—
796C2#2024368912yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#339C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC2×#339D47
hypocenterC47#10732
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#15688884C2semidirect
5. C2×#15688883C2semidirect
6. C2×#15688882C2semidirect
7. C2×C47×#339C2semidirect
16. C2×M16×D47C4semidirect
22. #15688980C4semidirect
23. #15688980C4semidirect
28. C4×(C2×D47)⋊C4C4semidirect
203. M16×C47C22⋊C4semidirect
233. #10625329C22⋊C4semidirect
373. C2×D47#339semidirect
394. C2×#339D47semidirect
435. C47#10732semidirect
607. M16(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
#202457672
C2×C4×(C2×D47)⋊C42
C2×#156888842
C2×#156888832
C2×#156888822
C2×C47×#3392
#1073247