Finite Group Databasebeta

← #26121508

Subgroups — #26121508

Order 12032.

1414 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3#20245767C211yesmaximal, characteristic
4C2×#15688880C211yesmaximal, characteristic, complemented
5C2×#15688879C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C2×C47×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C2×#13093982—21no—
13C2×#13093981C412yescomplemented
14C2×#13093980—21no—
15#117×D47—22no—
16#117×D47—22no—
17#117×D47—22no—
18#117×D47—22no—
19C2×C4⋊C4×D47—21no—
20C2×C22⋊C4×D47—21no—
21C2×C42×D47C412yescomplemented
22#15689086—22no—
23#15689086—21no—
24#15689086—21no—
25C2×(C2×D47)⋊C8C414yescomplemented
26#15688984—21no—
27#15688980—22no—
28#15688978—21no—
29C4×(C2×D47)⋊C4C414yescomplemented
30#15688880—22no—
31#15688879—22no—
32#15688879—22no—
33C22×M16×C47C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C47×H(3,ℤ/4)—22no—
37C24×D47D411yescharacteristic
38C23×Dic47D411yescharacteristic
39C22×C4×D47—21no—
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—22no—
48C22×C4×D47C2×C412yes—
49C22×C4×D47C2×C412yes—
50C22×C4×D47C2×C411yescharacteristic
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47D412yes—
53C22×C4×D47D411yescharacteristic
54C22×C4×D47D411yescharacteristic
55C22×C4×D47Q812yes—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C22×C47⋊C8C2×C412yescomplemented
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983—21no—
69#13093983D412yes—
70#13093983D412yes—
71#13093982—24no—
72#13093982—24no—
73#13093981—24no—
74#13093981—24no—
75#13093980—24no—
76#13093980—24no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×Dic47⋊C4—22no—
80C4⋊C4×D47—24no—
81C4⋊C4×D47—24no—
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—24no—
86C22⋊C4×D47—24no—
87C22⋊C4×D47—24no—
88C2×C4×Dic47—22no—
89C2×C4×Dic47C2×C412yes—
90C2×C4×Dic47C2×C412yescomplemented
91C42×D47—24no—
92C42×D47—24no—
93(C2×D47)⋊C8—24no—
94(C2×D47)⋊C8—24no—
95C47⋊#95—24no—
96C23×C4×C47C2311yescharacteristic
97C2×M16×C47—21no—
98C2×M16×C47—21no—
99C2×M16×C47—21no—
100C2×M16×C47—21no—
101C2×M16×C47—21no—
102C2×M16×C47—21no—
103C22×C8×C47C2×C412yescomplemented
104#117×C47—21no—
105#117×C47—21no—
106#117×C47—21no—
107#117×C47—21no—
108#117×C47—21no—
109#117×C47—21no—
110#117×C47D412yes—
111#117×C47D412yes—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C42×C47C2×C412yes—
117C2×C42×C47C2×C412yescomplemented
118C24×C47C2×D411yescharacteristic
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—21no—
123C23×D47—44no—
124C23×D47C22⋊C411yescharacteristic
125C23×D47C22⋊C412yes—
126C23×D47C22⋊C411yescharacteristic
127C23×D47C4⋊C412yes—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×Q811yescharacteristic
140C22×C4×C47#4111yescharacteristic
141C22×C4×C47#4111yescharacteristic
142C22×C4×C47#4111yescharacteristic
143C22×C4×C47#4111yescharacteristic
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47C22⋊C412yes—
151C22×Dic47C22⋊C411yescharacteristic
152C22×Dic47C22⋊C411yescharacteristic
153C22×Dic47C4⋊C412yes—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—28no—
187C2×C4×D47—48no—
188C2×C4×D47C4212yes—
189C2×C4×D47C4212yes—
190C2×C4×D47C22⋊C412yes—
191C2×C4×D47C22⋊C412yes—
192C2×C4×D47C4⋊C412yes—
193C2×C4×D47C4⋊C412yes—
194C2×C4×D47C4⋊C412yes—
195C2×C4×D47C4⋊C412yes—
196M16×C47—41no—
197M16×C47—41no—
198M16×C47—41no—
199M16×C47—41no—
200C2×C8×C47—22no—
201C2×C8×C47—22no—
202C2×C8×C47—22no—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—22no—
205C4⋊C4×C47—41no—
206C4⋊C4×C47—41no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C42×C47—22no—
212C42×C47—22no—
213C42×C47—22no—
214C42×C47C22⋊C414yescomplemented
215C22⋊Dic47—22no—
216C22⋊Dic47—22no—
217C22⋊Dic47—41no—
218C22⋊Dic47—41no—
219(C2×D47)⋊C4—28no—
220(C2×D47)⋊C4—48no—
221C4⋊Dic47—22no—
222C4⋊Dic47—22no—
223C4⋊Dic47—41no—
224C4⋊Dic47—41no—
225Dic47⋊C4—28no—
226C4×Dic47—28no—
227C4×Dic47—22no—
228C4×Dic47—22no—
229C4×Dic47—22no—
230C4×Dic47C22⋊C414yescomplemented
231#10625329—41no—
232#10625329—41no—
233#10625329—41no—
234#10625329—41no—
235C2×C47⋊C8—22no—
236C2×C47⋊C8—22no—
237C2×C47⋊C8—22no—
238C23×C47—42no—
239C23×C47C2×C22⋊C411yescharacteristic
240C23×C47C2×C22⋊C411yescharacteristic
241C23×C47C2×C4⋊C411yescharacteristic
242C23×C47#12011yescharacteristic
243C23×C47#12011yescharacteristic
244C23×C47#12311yescharacteristic
245C23×C47#12311yescharacteristic
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—24no—
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—24no—
256C22×D47—24no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47—42no—
260C22×D47—44no—
261C22×D47—44no—
262C22×D47—44no—
263C22×D47—44no—
264C22×D47#9512yes—
265C22×D47#9512yes—
266C2×C4×C47—24no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47—42no—
270C2×C4×C47C2×C4211yescharacteristic
271C2×C4×C47C2×C22⋊C411yescharacteristic
272C2×C4×C47C2×C22⋊C411yescharacteristic
273C2×C4×C47C2×C22⋊C411yescharacteristic
274C2×C4×C47C2×C4⋊C411yescharacteristic
275C2×C4×C47C2×C4⋊C411yescharacteristic
276C2×C4×C47#11711yescharacteristic
277C2×C4×C47#11711yescharacteristic
278C2×C4×C47C4×D411yescharacteristic
279C2×C4×C47C4×D411yescharacteristic
280C2×C4×C47C4×D411yescharacteristic
281C2×C4×C47C4×D411yescharacteristic
282C2×C4×C47C4×D411yescharacteristic
283C2×C4×C47C4×D411yescharacteristic
284C2×C4×C47C4×D411yescharacteristic
285C2×C4×C47C4×D411yescharacteristic
286C2×C4×C47#12011yescharacteristic
287C2×C4×C47#12011yescharacteristic
288C2×C4×C47#12111yescharacteristic
289C2×C4×C47#12111yescharacteristic
290C2×C4×C47#12111yescharacteristic
291C2×C4×C47#12111yescharacteristic
292C2×C4×C47C22⋊Q811yescharacteristic
293C2×C4×C47C22⋊Q811yescharacteristic
294C2×C4×C47C22⋊Q811yescharacteristic
295C2×C4×C47C22⋊Q811yescharacteristic
296C2×C4×C47#12311yescharacteristic
297C2×C4×C47#12311yescharacteristic
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—24no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—42no—
310C2×Dic47#9512yes—
311C2×Dic47#9512yes—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—22no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—416no—
329C8×C47—42no—
330C47⋊C8—42no—
331#10716—471nomaximal, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47C2×#9511yescharacteristic
340C22×C47#37911yescharacteristic
341C22×C47#38111yescharacteristic
342C22×C47#38511yescharacteristic
343C22×C47#38511yescharacteristic
344C22×C47#38611yescharacteristic
345C22×C47#38611yescharacteristic
346C2×D47—24no—
347C2×D47—24no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—44no—
354C2×D47—44no—
355C2×D47—44no—
356C2×D47—44no—
357C2×D47—42no—
358C2×D47—42no—
359C2×D47H(3,ℤ/4)14yescomplemented
360C4×C47—44no—
361C4×C47—82no—
362C4×C47C4×C22⋊C411yescharacteristic
363C4×C47C4×C22⋊C411yescharacteristic
364C4×C47#38011yescharacteristic
365C4×C47#38011yescharacteristic
366C4×C47#38511yescharacteristic
367C4×C47#38511yescharacteristic
368C4×C47#38611yescharacteristic
369C4×C47#38611yescharacteristic
370Dic47—22no—
371Dic47—22no—
372Dic47—44no—
373Dic47—82no—
374C22×#117—471no—
375C2×#407—471no—
376#2280—471no—
377C2×H(3,ℤ/4)—471no—
378C2×H(3,ℤ/4)—471no—
379C2×H(3,ℤ/4)—471no—
380C2×H(3,ℤ/4)D4711yescharacteristic, complemented
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47C22⋊#9511yescharacteristic
388C2×C47C2×H(3,ℤ/4)12yes—
389D47—24no—
390D47—42no—
391C24×C4—471no—
392C22×M16—471no—
393C22×M16C2×D4711yescharacteristic
394C2×#117—471no—
395C2×#117—471no—
396C2×#117—472no—
397C2×#117—941no—
398C2×#117—941no—
399C2×#117—942no—
400C2×#117—942no—
401C2×#117—942no—
402C2×#117—942no—
403C2×#117C2×D4711yescharacteristic
404C2×#117C2×D4711yescharacteristic
405C22×C4⋊C4—941no—
406C22×C22⋊C4—941no—
407C22×C42—472no—
408#407—941no—
409#407—941no—
410#407—942no—
411C2×C22⋊C8—474no—
412#381—941no—
413#380—942no—
414#379—941no—
415C4×C22⋊C4—474no—
416H(3,ℤ/4)—22no—
417H(3,ℤ/4)—942no—
418H(3,ℤ/4)—942no—
419H(3,ℤ/4)—942no—
420C47#1071611yescharacteristic, complemented, Sylow
421C25—471no—
422C23×C4—471no—
423C23×C4—471no—
424C23×C4—472no—
425C23×C4—472no—
426C23×C4—471no—
427C23×C4—471no—
428C23×C4—471no—
429C23×C4—472no—
430C23×C4—472no—
431C23×C4—942no—
432C23×C4—941no—
433C23×C4—941no—
434C23×C4—941no—
435C23×C4—941no—
436C23×C4—941no—
437C23×C4—941no—
438C23×C4—941no—
439C23×C4—941no—
440C23×C4C22×D4711yescharacteristic
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—941no—
448C2×M16—941no—
449C2×M16—941no—
450C2×M16—941no—
451C2×M16—941no—
452C2×M16—941no—
453C22×C8—472no—
454C22×C8C4×D4712yescomplemented
455#117—21no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—472no—
462#117—472no—
463#117—944no—
464#117—944no—
465#117—944no—
466#117—944no—
467#117—944no—
468#117—941no—
469#117—941no—
470#117—941no—
471#117—941no—
472#117—941no—
473#117—941no—
474#117—944no—
475#117D18812yes—
476#117C22⋊D4712yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—944no—
480C2×C4⋊C4—944no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—941no—
483C2×C4⋊C4—941no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4—944no—
488C2×C22⋊C4—942no—
489C2×C22⋊C4—941no—
490C2×C22⋊C4—944no—
491C2×C22⋊C4—941no—
492C2×C42—472no—
493C2×C42—472no—
494C2×C42—944no—
495C2×C42—942no—
496C2×C42—944no—
497C2×C42C4×D4712yes—
498C2×C42C4×D4712yescomplemented
499C22⋊C8—944no—
500C22⋊C8—944no—
501#95—944no—
502C24—471no—
503C24—472no—
504C24—472no—
505C24—471no—
506C24—941no—
507C24—941no—
508C24—941no—
509C24—941no—
510C24—1884no—
511C24D4×D4711yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—472no—
515C22×C4—471no—
516C22×C4—471no—
517C22×C4—472no—
518C22×C4—472no—
519C22×C4—472no—
520C22×C4—472no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—472no—
526C22×C4—948no—
527C22×C4—941no—
528C22×C4—941no—
529C22×C4—941no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4—941no—
550C22×C4—941no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—1888no—
566C22×C4C2×C4×D4711yescharacteristic
567C22×C4C2×C4×D4711yescharacteristic
568C22×C4C2×C4×D4711yescharacteristic
569C22×C4C2×D18811yescharacteristic
570C22×C4#1062535011yescharacteristic
571C22×C4#1062535011yescharacteristic
572C22×C4D4×D4711yescharacteristic
573C22×C4D4×D4711yescharacteristic
574C22×C4D4×D4711yescharacteristic
575C22×C4D4×D4711yescharacteristic
576C22×C4#1062535211yescharacteristic
577C22×C4Q8×D4711yescharacteristic
578C22×C4#1062535411yescharacteristic
579C22×C4C2×C22⋊D4711yescharacteristic
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—1881no—
585M16—1881no—
586M16—1881no—
587M16—1881no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—942no—
592C2×C8—942no—
593C2×C8—942no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—948no—
599C4⋊C4—942no—
600C4⋊C4—942no—
601C4⋊C4—1881no—
602C4⋊C4—1881no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—948no—
608C22⋊C4—942no—
609C22⋊C4—942no—
610C22⋊C4—1888no—
611C22⋊C4—1881no—
612C22⋊C4—1881no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—474no—
617C42—948no—
618C42—942no—
619C42—942no—
620C42—942no—
621C42(C2×D47)⋊C414yescomplemented
622C23—42no—
623C23—472no—
624C23—472no—
625C23—944no—
626C23—944no—
627C23—944no—
628C23—941no—
629C23—941no—
630C23—941no—
631C23—941no—
632C23—942no—
633C23—942no—
634C23—942no—
635C23—942no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23—1884no—
640C23—1884no—
641C23—1884no—
642C23—1884no—
643C23C22⋊C4×D4711yescharacteristic
644C23C22⋊C4×D4711yescharacteristic
645C23C4⋊C4×D4711yescharacteristic
646C23#1309399211yescharacteristic
647C23#1309399411yescharacteristic
648C23#1309400611yescharacteristic
649C23#1309400911yescharacteristic
650C2×C4—24no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—472no—
655C2×C4—472no—
656C2×C4—941no—
657C2×C4—941no—
658C2×C4—941no—
659C2×C4—941no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—944no—
681C2×C4—18816no—
682C2×C4—1884no—
683C2×C4—1882no—
684C2×C4—1884no—
685C2×C4C42×D4711yescharacteristic
686C2×C4C22⋊C4×D4711yescharacteristic
687C2×C4C22⋊C4×D4711yescharacteristic
688C2×C4C2×(C2×D47)⋊C411yescharacteristic
689C2×C4C4⋊C4×D4711yescharacteristic
690C2×C4C4⋊C4×D4711yescharacteristic
691C2×C4#1309398111yescharacteristic
692C2×C4#1309398211yescharacteristic
693C2×C4(C22⋊D47)⋊C411yescharacteristic
694C2×C4(C22⋊D47)⋊C411yescharacteristic
695C2×C4C4×C22⋊D4711yescharacteristic
696C2×C4C4×C22⋊D4711yescharacteristic
697C2×C4#1309398611yescharacteristic
698C2×C4#1309398611yescharacteristic
699C2×C4C4×D18811yescharacteristic
700C2×C4C4×D18811yescharacteristic
701C2×C4#1309399211yescharacteristic
702C2×C4#1309399411yescharacteristic
703C2×C4#1309399511yescharacteristic
704C2×C4#1309399711yescharacteristic
705C2×C4#1309399711yescharacteristic
706C2×C4#1309399911yescharacteristic
707C2×C4#1309400011yescharacteristic
708C2×C4#1309400211yescharacteristic
709C2×C4#1309400211yescharacteristic
710C2×C4#1309400411yescharacteristic
711C2×C4#1309400611yescharacteristic
712C2×C4#1309400911yescharacteristic
713C8—42no—
714C8—1882no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—474no—
723C22—944no—
724C22—944no—
725C22—942no—
726C22—942no—
727C22—942no—
728C22—942no—
729C22—942no—
730C22—1884no—
731C22—1884no—
732C22—1884no—
733C22—1884no—
734C22—1882no—
735C22—1882no—
736C22#95×D4711yescharacteristic
737C22#1568897811yescharacteristic
738C22#1568898511yescharacteristic
739C22#1568899411yescharacteristic
740C22#1568899711yescharacteristic
741C22#1568899911yescharacteristic
742C22#1568900111yescharacteristic
743C4—44no—
744C4—82no—
745C4—942no—
746C4—942no—
747C4—3762no—
748C4—1884no—
749C4#1568897011yescharacteristic
750C4C4×(C2×D47)⋊C411yescharacteristic
751C4#1568898011yescharacteristic
752C4#1568898211yescharacteristic
753C4#1568899411yescharacteristic
754C4#1568899711yescharacteristic
755C4#1568899911yescharacteristic
756C4#1568900111yescharacteristic
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—944no—
764C2—1882no—
765C2(C2×D47)⋊#9511yescharacteristic
766C2H(3,ℤ/4)×D4712yes—
subgroupG/H
centerC2×C4C42×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC22×C47C2×#95
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47#10716
LCSG ▷ C2×C4×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#15688880C2semidirect
5. C2×#15688879C2semidirect
6. C2×#15688879C2semidirect
7. C2×C47×H(3,ℤ/4)C2semidirect
13. C2×#13093981C4semidirect
21. C2×C42×D47C4semidirect
25. C2×(C2×D47)⋊C8C4semidirect
29. C4×(C2×D47)⋊C4C4semidirect
62. C22×C47⋊C8C2×C4semidirect
90. C2×C4×Dic47C2×C4semidirect
103. C22×C8×C47C2×C4semidirect
117. C2×C42×C47C2×C4semidirect
214. C42×C47C22⋊C4semidirect
230. C4×Dic47C22⋊C4semidirect
359. C2×D47H(3,ℤ/4)semidirect
380. C2×H(3,ℤ/4)D47semidirect
420. C47#10716semidirect
454. C22×C8C4×D47semidirect
498. C2×C42C4×D47semidirect
621. C42(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
C2×#156890862
#202457672
C2×#156888802
C2×#156888792
C2×C47×H(3,ℤ/4)2
#1071647