Finite Group Databasebeta

← #26121504

Subgroups — #26121504

Order 12032.

1534 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625324C211yesmaximal, characteristic
2C22×(C2×D47)⋊C8C211yesmaximal, characteristic
3C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
4C2×#15688878C211yesmaximal, characteristic, complemented
5C2×#15688877C211yesmaximal, characteristic, complemented
6C2×#15688877C211yesmaximal, characteristic, complemented
7C2×C47×#336C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625324—22no—
10C22×#10625324—22no—
11C22×#10625324—22no—
12C22×#10625324—22no—
13C22×#10625324—22no—
14C22×#10625324—22no—
15C22×#10625324C414yescomplemented
16C23×C47⋊C8C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C22×(C2×D47)⋊C4C412yes—
19C22×C4×Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C8—22no—
21C2×(C2×D47)⋊C8—22no—
22C2×(C2×D47)⋊C8C414yescomplemented
23C4×(C2×D47)⋊C4—22no—
24C4×(C2×D47)⋊C4—22no—
25C2×C47⋊#95C412yes—
26#15688878—22no—
27#15688877—22no—
28#15688877—22no—
29C23×C8×C47C2211yescharacteristic
30C23×C8×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C47×#336—22no—
33C24×D47C2×C411yescharacteristic
34C23×Dic47C2×C412yes—
35C23×Dic47C2×C411yescharacteristic
36C22×C4×D47—21no—
37C22×C4×D47—21no—
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47C2×C412yes—
45C22×C4×D47C2×C412yes—
46C22×C4×D47D412yes—
47C22×C4×D47D412yes—
48C22×C4×D47D412yes—
49C22×C4×D47Q812yes—
50C2×#10625324—28no—
51C2×#10625324—28no—
52C2×#10625324—28no—
53C2×#10625324—28no—
54C2×#10625324—28no—
55C2×#10625324—28no—
56C2×#10625324—28no—
57C22×C47⋊C8—21no—
58C22×C47⋊C8—21no—
59C22×C47⋊C8—21no—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63C22×C47⋊C8—21no—
64C22×C47⋊C8—21no—
65C22×C47⋊C8—21no—
66C22×C47⋊C8—21no—
67C22×C47⋊C8C2×C412yes—
68C22×C47⋊C8C2×C412yes—
69C22×C47⋊C8D412yes—
70C22×C47⋊C8D412yes—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×C4×Dic47—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80(C2×D47)⋊C8—28no—
81C47⋊#95—24no—
82C23×C4×C47C2×C412yes—
83C23×C4×C47C2311yescharacteristic
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C22×C8×C47—21no—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C22×C8×C47—21no—
93C22×C8×C47—21no—
94C22×C8×C47C2×C412yes—
95C22×C8×C47C2×C412yes—
96C22×C8×C47D412yes—
97C22×C8×C47D412yes—
98C2×C42×C47—21no—
99C2×C42×C47—21no—
100C2×C42×C47—21no—
101C2×C42×C47—21no—
102C2×C42×C47—21no—
103C2×C42×C47—21no—
104C24×C47C22×C411yescharacteristic
105C23×D47—21no—
106C23×D47—21no—
107C23×D47—21no—
108C23×D47—21no—
109C23×D47—22no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—22no—
113C23×D47C4212yes—
114C23×D47C22⋊C412yes—
115C23×D47C4⋊C412yes—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47M1614yescomplemented
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×Q811yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×C4×C47#4111yescharacteristic
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47C4212yes—
148C22×Dic47C22⋊C412yes—
149C22×Dic47C4⋊C412yes—
150C22×Dic47M1614yescomplemented
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
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—22no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47C22⋊C414yes—
176C2×C4×D47C22⋊C414yes—
177C2×C4×D47C4⋊C414yes—
178C2×C4×D47C4⋊C414yes—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—22no—
182C2×C8×C47—22no—
183C2×C8×C47—22no—
184C2×C8×C47—22no—
185C2×C8×C47—22no—
186C2×C8×C47—22no—
187C2×C8×C47—22no—
188C2×C8×C47—41no—
189C2×C8×C47—41no—
190C2×C8×C47—41no—
191C2×C8×C47—41no—
192C2×C8×C47C22⋊C414yescomplemented
193C42×C47—41no—
194C42×C47—41no—
195C42×C47—41no—
196C42×C47—41no—
197(C2×D47)⋊C4—216no—
198C4×Dic47—41no—
199C4×Dic47—41no—
200C4×Dic47—41no—
201C4×Dic47—41no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C2×C47⋊C8—22no—
210C2×C47⋊C8—22no—
211C2×C47⋊C8—41no—
212C2×C47⋊C8—41no—
213C2×C47⋊C8—41no—
214C2×C47⋊C8—41no—
215C2×C47⋊C8C22⋊C414yescomplemented
216#10625324—232no—
217C23×C47C2×C4211yescharacteristic
218C23×C47C2×C22⋊C411yescharacteristic
219C23×C47C2×C4⋊C411yescharacteristic
220C23×C47C4×D411yescharacteristic
221C23×C47C4×D411yescharacteristic
222C23×C47C4×D411yescharacteristic
223C23×C47C4×D411yescharacteristic
224C23×C47C2×M1612yes—
225C23×C47C2×M1612yes—
226C23×C47#13112yes—
227C23×C47#13112yes—
228C22×D47—22no—
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—22no—
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—24no—
239C22×D47—24no—
240C22×D47—24no—
241C22×D47—24no—
242C22×D47—42no—
243C22×D47—42no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47#9514yes—
251C2×C4×C47—24no—
252C2×C4×C47—24no—
253C2×C4×C47—24no—
254C2×C4×C47—42no—
255C2×C4×C47—42no—
256C2×C4×C47—42no—
257C2×C4×C47—42no—
258C2×C4×C47C2×C22⋊C411yescharacteristic
259C2×C4×C47C2×C22⋊C411yescharacteristic
260C2×C4×C47C2×C22⋊C411yescharacteristic
261C2×C4×C47C2×C22⋊C411yescharacteristic
262C2×C4×C47C2×C4⋊C411yescharacteristic
263C2×C4×C47C2×C4⋊C411yescharacteristic
264C2×C4×C47#11711yescharacteristic
265C2×C4×C47#11711yescharacteristic
266C2×C4×C47C4×D411yescharacteristic
267C2×C4×C47C4×D411yescharacteristic
268C2×C4×C47C4×D411yescharacteristic
269C2×C4×C47C4×D411yescharacteristic
270C2×C4×C47#12011yescharacteristic
271C2×C4×C47#12011yescharacteristic
272C2×C4×C47#12011yescharacteristic
273C2×C4×C47#12011yescharacteristic
274C2×C4×C47#12111yescharacteristic
275C2×C4×C47#12111yescharacteristic
276C2×C4×C47#12111yescharacteristic
277C2×C4×C47#12111yescharacteristic
278C2×C4×C47C22⋊Q811yescharacteristic
279C2×C4×C47C22⋊Q811yescharacteristic
280C2×C4×C47C22⋊Q811yescharacteristic
281C2×C4×C47C22⋊Q811yescharacteristic
282C2×C4×C47#12311yescharacteristic
283C2×C4×C47#12311yescharacteristic
284C2×C4×C47#12311yescharacteristic
285C2×C4×C47#12311yescharacteristic
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—24no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47#9514yes—
300C4×D47—24no—
301C4×D47—24no—
302C4×D47—24no—
303C4×D47—24no—
304C4×D47—24no—
305C4×D47—24no—
306C4×D47—24no—
307C4×D47—24no—
308C8×C47—24no—
309C8×C47—42no—
310C47⋊C8—24no—
311C47⋊C8—42no—
312#10715—471nomaximal, Sylow
313C22×C47C2×#9511yescharacteristic
314C22×C47C4×C22⋊C411yescharacteristic
315C22×C47C4×C22⋊C411yescharacteristic
316C22×C47#38511yescharacteristic
317C22×C47#38511yescharacteristic
318C22×C47#38611yescharacteristic
319C22×C47#38611yescharacteristic
320C22×C47C4×M1611yescharacteristic
321C22×C47C4×M1611yescharacteristic
322C22×C47#40511yescharacteristic
323C22×C47#40511yescharacteristic
324C22×C47#40712yes—
325C22×C47#40812yes—
326C22×C47#42312yes—
327C22×C47#42412yes—
328C22×C47#43512yes—
329C22×C47#43512yes—
330C22×C47#43512yes—
331C22×C47#43512yes—
332C22×C47#43612yes—
333C22×C47#43612yes—
334C22×C47#43612yes—
335C22×C47#43612yes—
336C2×D47—24no—
337C2×D47—24no—
338C2×D47—24no—
339C2×D47—44no—
340C2×D47—44no—
341C2×D47—44no—
342C2×D47—44no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—42no—
347C4×C47—44no—
348C4×C47#37911yescharacteristic
349C4×C47#38011yescharacteristic
350C4×C47#38011yescharacteristic
351C4×C47#38111yescharacteristic
352C4×C47#38511yescharacteristic
353C4×C47#38511yescharacteristic
354C4×C47#38611yescharacteristic
355C4×C47#38611yescharacteristic
356Dic47—24no—
357Dic47—44no—
358C23×M16—471no—
359C22×C22⋊C8—471no—
360C2×C4×C22⋊C4—471no—
361C2×#336—471no—
362C2×#336—471no—
363C2×#336—471no—
364C2×#336D4711yescharacteristic, complemented
365C2×C47C22⋊#9511yescharacteristic
366C2×C47#172811yescharacteristic
367C2×C47#172911yescharacteristic
368C2×C47#175311yescharacteristic
369C2×C47#175311yescharacteristic
370C2×C47#175311yescharacteristic
371C2×C47#175311yescharacteristic
372C2×C47#185112yes—
373C2×C47#185112yes—
374C2×C47#187012yes—
375C2×C47#187012yes—
376D47—44no—
377C24×C4—471no—
378C22×M16—474no—
379C22×M16—942no—
380C22×M16—942no—
381C22×M16—942no—
382C22×M16—942no—
383C22×M16—942no—
384C22×M16—942no—
385C23×C8—471no—
386C23×C8—471no—
387C23×C8C2×D4711yescharacteristic
388C23×C8C2×D4711yescharacteristic
389C22×C22⋊C4—472no—
390C22×C42—471no—
391C22×C42C2×D4711yescharacteristic
392C2×C22⋊C8—474no—
393C2×C22⋊C8—942no—
394C2×C22⋊C8—942no—
395C4×C22⋊C4—942no—
396C4×C22⋊C4—942no—
397C2×#95—472no—
398#336—22no—
399#336—942no—
400#336—942no—
401#336—942no—
402C47#1071511yescharacteristic, complemented, Sylow
403C25—471no—
404C23×C4—471no—
405C23×C4—472no—
406C23×C4—472no—
407C23×C4—472no—
408C23×C4—472no—
409C23×C4—472no—
410C23×C4—472no—
411C23×C4—472no—
412C23×C4—941no—
413C23×C4—941no—
414C23×C4—941no—
415C23×C4—941no—
416C23×C4—941no—
417C23×C4—941no—
418C23×C4—941no—
419C23×C4—941no—
420C23×C4C4×D4712yes—
421C23×C4C22×D4711yescharacteristic
422C2×M16—948no—
423C2×M16—948no—
424C2×M16—948no—
425C2×M16—948no—
426C2×M16—948no—
427C2×M16—948no—
428C2×M16—948no—
429C22×C8—21no—
430C22×C8—21no—
431C22×C8—21no—
432C22×C8—21no—
433C22×C8—21no—
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—21no—
437C22×C8—21no—
438C22×C8—21no—
439C22×C8—472no—
440C22×C8—472no—
441C22×C8—472no—
442C22×C8—472no—
443C22×C8—941no—
444C22×C8—941no—
445C22×C8—941no—
446C22×C8—941no—
447C22×C8—941no—
448C22×C8—941no—
449C22×C8—941no—
450C22×C8—941no—
451C22×C8—941no—
452C22×C8—941no—
453C22×C8C4×D4712yes—
454C22×C8C4×D4712yes—
455C22×C8D18812yes—
456C22×C8C22⋊D4712yes—
457C2×C22⋊C4—944no—
458C2×C22⋊C4—944no—
459C2×C22⋊C4—944no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—941no—
467C2×C42—941no—
468C2×C42—941no—
469C2×C42—941no—
470C2×C42—941no—
471C2×C42—941no—
472C22⋊C8—948no—
473#95—944no—
474C24—472no—
475C24—472no—
476C24—472no—
477C24—941no—
478C24—941no—
479C24—941no—
480C24—941no—
481C24—942no—
482C24—942no—
483C24—942no—
484C24—942no—
485C24C2×C4×D4711yescharacteristic
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—472no—
493C22×C4—472no—
494C22×C4—472no—
495C22×C4—474no—
496C22×C4—474no—
497C22×C4—474no—
498C22×C4—474no—
499C22×C4—474no—
500C22×C4—941no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—942no—
518C22×C4—942no—
519C22×C4—942no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—942no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4#1062532414yescomplemented
535C22×C4C2×C4×D4711yescharacteristic
536C22×C4C2×C4×D4711yescharacteristic
537C22×C4C2×D18811yescharacteristic
538C22×C4#1062535011yescharacteristic
539C22×C4#1062535011yescharacteristic
540C22×C4D4×D4711yescharacteristic
541C22×C4D4×D4711yescharacteristic
542C22×C4D4×D4711yescharacteristic
543C22×C4D4×D4711yescharacteristic
544C22×C4D4×D4711yescharacteristic
545C22×C4#1062535211yescharacteristic
546C22×C4Q8×D4711yescharacteristic
547C22×C4#1062535411yescharacteristic
548C22×C4C2×C22⋊D4711yescharacteristic
549M16—9432no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—474no—
564C2×C8—942no—
565C2×C8—942no—
566C2×C8—942no—
567C2×C8—942no—
568C2×C8—942no—
569C2×C8—942no—
570C2×C8—942no—
571C2×C8—942no—
572C2×C8—942no—
573C2×C8—1881no—
574C2×C8—1881no—
575C2×C8—1881no—
576C2×C8—1881no—
577C2×C8(C2×D47)⋊C414yescomplemented
578C22⋊C4—9416no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—1881no—
584C42—1881no—
585C42—1881no—
586C42—1881no—
587C23—474no—
588C23—942no—
589C23—942no—
590C23—942no—
591C23—942no—
592C23—942no—
593C23—942no—
594C23—942no—
595C23—942no—
596C23—942no—
597C23—942no—
598C23—944no—
599C23—944no—
600C23—944no—
601C23—944no—
602C23—1882no—
603C23—1882no—
604C23—1882no—
605C23—1882no—
606C23—1882no—
607C23—1882no—
608C23—1882no—
609C23—1882no—
610C23C42×D4711yescharacteristic
611C23C22⋊C4×D4711yescharacteristic
612C23C4⋊C4×D4711yescharacteristic
613C23(C22⋊D47)⋊C411yescharacteristic
614C23C4×C22⋊D4711yescharacteristic
615C23#1309398611yescharacteristic
616C23C4×D18811yescharacteristic
617C23M16×D4712yes—
618C23C2×#1062532412yes—
619C23#1309403012yes—
620C23#1309403212yes—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—474no—
629C2×C4—942no—
630C2×C4—942no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—944no—
636C2×C4—944no—
637C2×C4—944no—
638C2×C4—944no—
639C2×C4—944no—
640C2×C4—944no—
641C2×C4—944no—
642C2×C4—944no—
643C2×C4—944no—
644C2×C4—944no—
645C2×C4—944no—
646C2×C4—1882no—
647C2×C4—1882no—
648C2×C4—1882no—
649C2×C4—1882no—
650C2×C4C22⋊C4×D4711yescharacteristic
651C2×C4C22⋊C4×D4711yescharacteristic
652C2×C4C22⋊C4×D4711yescharacteristic
653C2×C4C2×(C2×D47)⋊C411yescharacteristic
654C2×C4C4⋊C4×D4711yescharacteristic
655C2×C4C4⋊C4×D4711yescharacteristic
656C2×C4#1309398111yescharacteristic
657C2×C4#1309398211yescharacteristic
658C2×C4(C22⋊D47)⋊C411yescharacteristic
659C2×C4C4×C22⋊D4711yescharacteristic
660C2×C4#1309398611yescharacteristic
661C2×C4C4×D18811yescharacteristic
662C2×C4#1309399211yescharacteristic
663C2×C4#1309399211yescharacteristic
664C2×C4#1309399411yescharacteristic
665C2×C4#1309399411yescharacteristic
666C2×C4#1309399511yescharacteristic
667C2×C4#1309399711yescharacteristic
668C2×C4#1309399711yescharacteristic
669C2×C4#1309399911yescharacteristic
670C2×C4#1309400011yescharacteristic
671C2×C4#1309400211yescharacteristic
672C2×C4#1309400211yescharacteristic
673C2×C4#1309400411yescharacteristic
674C2×C4#1309400611yescharacteristic
675C2×C4#1309400611yescharacteristic
676C2×C4#1309400911yescharacteristic
677C2×C4#1309400911yescharacteristic
678C8—24no—
679C8—42no—
680C8—944no—
681C8—1882no—
682C22—944no—
683C22—944no—
684C22—944no—
685C22—1884no—
686C22—1884no—
687C22—1882no—
688C22—1882no—
689C22—1884no—
690C22—1882no—
691C22—1884no—
692C22—1882no—
693C22#95×D4711yescharacteristic
694C22#1568897011yescharacteristic
695C22C4×(C2×D47)⋊C411yescharacteristic
696C22#1568899411yescharacteristic
697C22#1568899711yescharacteristic
698C22#1568899911yescharacteristic
699C22#1568900111yescharacteristic
700C22C4×#1062532411yescharacteristic
701C22#1568907511yescharacteristic
702C22#1568907711yescharacteristic
703C22#1568908011yescharacteristic
704C22#1568908512yes—
705C22#1568908812yes—
706C22#1568914512yes—
707C22#1568914812yes—
708C22#1568919112yes—
709C22#1568919312yes—
710C22#1568919412yes—
711C22#1568919612yes—
712C22#1568919812yes—
713C22#1568919912yes—
714C22#1568920012yes—
715C22#1568920212yes—
716C4—44no—
717C4—944no—
718C4—1884no—
719C4#1568897811yescharacteristic
720C4#1568898011yescharacteristic
721C4#1568898211yescharacteristic
722C4#1568898511yescharacteristic
723C4#1568899411yescharacteristic
724C4#1568899711yescharacteristic
725C4#1568899911yescharacteristic
726C4#1568900111yescharacteristic
727C2—1884no—
728C2(C2×D47)⋊#9511yescharacteristic
729C2#2024308011yescharacteristic
730C2#2024308311yescharacteristic
731C2#2024316811yescharacteristic
732C2#2024317011yescharacteristic
733C2#2024317111yescharacteristic
734C2#2024317311yescharacteristic
735C2#2024356912yes—
736C2#2024357212yes—
737C2#2024368212yes—
738C2#2024368412yes—
subgroupG/H
center, FrattiniC23×C4C22×D47
commutatorC23×C47C2×C42
FittingC2×C47×#336C2
socleC24×C47C22×C4
prime radicalC24×D47C2×C4
cosocleC23×C4×C47C23
hypercenterC2×#336D47
hypocenterC47#10715
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×#15688878C2semidirect
5. C2×#15688877C2semidirect
6. C2×#15688877C2semidirect
7. C2×C47×#336C2semidirect
15. C22×#10625324C4semidirect
22. C2×(C2×D47)⋊C8C4semidirect
122. C22×C4×C47M16semidirect
150. C22×Dic47M16semidirect
192. C2×C8×C47C22⋊C4semidirect
215. C2×C47⋊C8C22⋊C4semidirect
364. C2×#336D47semidirect
402. C47#10715semidirect
534. C22×C4#10625324semidirect
577. C2×C8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×#106253242
C22×(C2×D47)⋊C82
C2×C4×(C2×D47)⋊C42
C2×#156888782
C2×#156888772
C2×C47×#3362
#1071547