Finite Group Databasebeta

← C2×#20253579 #27084516

Subgroups — C2×#20253579 #27084516

Order 12032.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689747C211yesmaximal, characteristic, complemented
2C2×#15689595C211yesmaximal, characteristic, complemented
3#20253579C2116yesmaximal, direct product factor
4C2×#15689466C211yesmaximal, characteristic, complemented
5C2×#15689450C211yesmaximal, characteristic, complemented
6C2×#15689410C211yesmaximal, characteristic, complemented
7C2×#15689339C211yesmaximal, characteristic, complemented
8C2×#15689338C211yesmaximal, characteristic, complemented
9C2×#15689275C211yesmaximal, characteristic, complemented
10C2×#15689258C211yesmaximal, characteristic
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689214C211yesmaximal, characteristic, complemented
14C2×#15689205C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#474C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×D376C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22#15689747—24no—
23#15689747C2218yescomplemented
24C2×#13094019—21no—
25C2×#13094013—21no—
26C2×#13094012C2211yescharacteristic, complemented
27C2×#13094009—21no—
28C2×#13094004C2211yescharacteristic
29C2×#13094000—21no—
30C2×#13093999C2211yescharacteristic
31#15689595—24no—
32#15689595C2218yescomplemented
33C2×#13093989C2211yescharacteristic, complemented
34C2×C4×D188C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×#13093986C2211yescharacteristic, complemented
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981C2211yescharacteristic
42C22×(C2×D47)⋊C4—21no—
43C2×C22⋊C4×D47—21no—
44#15689466C2218yescomplemented
45#15689450C2218yescomplemented
46#15689410C2218yescomplemented
47#15689339C2218yescomplemented
48#15689338C2218yescomplemented
49#15689275C2218yescomplemented
50#15689258C2218yes—
51#15689232C2218yescomplemented
52#15689222C2218yescomplemented
53#15689214C2218yescomplemented
54#15689205C2218yescomplemented
55#15689183C2218yescomplemented
56C2×#13093955C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic, complemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C2×C4⋊Q8×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#474C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#107×C47C2211yescharacteristic, complemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C22⋊D47—21no—
83C2×D4×D47—24no—
84C2×D4×D47—24no—
85C2×D4×D47—22no—
86C2×D4×D47C2314yes—
87C23×Dic47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47C2311yescharacteristic
92C2×#10625325—24no—
93C2×#10625325C2314yes—
94C2×#10625335—24no—
95C2×#10625335C2314yes—
96C2×D376—24no—
97C2×D376C2314yes—
98C2×#10625334—24no—
99C2×#10625334C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102#13094019—28no—
103#13094013—28no—
104#13094012—22no—
105#13094012C2314yescomplemented
106#13094009—28no—
107#13094004—22no—
108#13094004C2314yes—
109#13094000—28no—
110#13093999—22no—
111#13093999C2314yes—
112#13093989—22no—
113#13093989C2314yescomplemented
114C4×D188—22no—
115C4×D188C2314yes—
116D4×Dic47—22no—
117D4×Dic47C2314yes—
118#13093986—22no—
119#13093986—22no—
120#13093986C2314yes—
121#13093986C2314yescomplemented
122C4×C22⋊D47—28no—
123(C22⋊D47)⋊C4—28no—
124#13093982—22no—
125#13093982C2314yes—
126#13093981D414yes—
127#13093981C2314yes—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—28no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×(C2×D47)⋊C4D411yescharacteristic
145C22⋊C4×D47—28no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093955C2314yescomplemented
150#13093955C2314yescomplemented
151C4⋊(C47⋊C8)C2314yescomplemented
152#13093949C2314yescomplemented
153#13093947C2314yescomplemented
154#13093946C2314yescomplemented
155#13093944C2314yes—
156#13093944C2314yes—
157#13093944C2314yescomplemented
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093934C2314yescomplemented
161C8×Dic47C2314yescomplemented
162C22×Q8×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4⋊Q8×C47—22no—
168C4⋊Q8×C47C2314yescomplemented
169C4×D4×C47—22no—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yescomplemented
178#107×C47C2314yescomplemented
179C4⋊C8×C47C2314yescomplemented
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47—28no—
185C23×D47—24no—
186C23×D47—21no—
187C23×D47—82no—
188C23×D47—82no—
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—24no—
191C2×Q8×C47—82no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47#4114yes—
195C2×D4×C47C2412yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—24no—
200C22×C4×C47—82no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—28no—
205C2×C22⋊D47—24no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—82no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213D4×D47—216no—
214D4×D47—28no—
215D4×D47—28no—
216C2×D188—21no—
217C2×D188—22no—
218C2×D188—22no—
219C2×D188—22no—
220C2×D188—21no—
221C2×D188—24no—
222C2×D188—82no—
223C2×D188#4114yes—
224C2×D188C2412yes—
225C2×D188C2412yes—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—82no—
232C2×C4×D47—82no—
233C2×C4×D47—82no—
234C2×C4×D47C2×D412yes—
235C2×C4×D47C2412yes—
236C2×Dic94—22no—
237C2×Dic94—22no—
238C2×Dic94—21no—
239C2×Dic94C2412yes—
240C2×C8×C47—22no—
241C2×C8×C47—22no—
242C2×C8×C47C2412yes—
243C2×C8×C47C2412yes—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47C2412yes—
249C4⋊C4×C47C2412yes—
250C4⋊C4×C47C2412yes—
251C22⋊C4×C47—24no—
252C42×C47C2×D412yes—
253C42×C47C2412yes—
254C22⋊Dic47—24no—
255#10625335—28no—
256#10625334—28no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4C2×D414yes—
266(C2×D47)⋊C4C2×D414yes—
267C4⋊Dic47—21no—
268C4⋊Dic47—24no—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4C2×D414yes—
272Dic47⋊C4C2×D414yes—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47C2×D412yes—
276C4×Dic47C2412yes—
277C2×C47⋊C8—22no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8C2412yes—
280C2×C47⋊C8C2412yes—
281D376—28no—
282#10625325—28no—
283C23×C47—24no—
284C23×C47—22no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47C22×D411yescharacteristic
288C22×D47—22no—
289C22×D47—24no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—216no—
294C22×D47—22no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47—84no—
301C22×D47—84no—
302C22×D47—816no—
303C22×D47C22×D412yes—
304Q8×C47—84no—
305D4×C47—24no—
306D4×C47—22no—
307D4×C47C2×#4114yes—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—84no—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2×#4112yes—
322C2×C4×C47C2511yescharacteristic
323C22⋊D47—216no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—84no—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335D188—24no—
336D188—22no—
337D188—22no—
338D188—22no—
339D188—42no—
340D188—84no—
341D188C2×#4114yes—
342C4×D47—24no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—84no—
346C4×D47—84no—
347C4×D47—84no—
348Dic94—22no—
349Dic94—22no—
350Dic94—42no—
351C8×C47—22no—
352C8×C47—22no—
353C47⋊C8—22no—
354C47⋊C8—22no—
355C2×#3118—471nomaximal, Sylow
356C22×C47—24no—
357C22×C47—48no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47#52512yes—
361C22×C47#57612yes—
362C22×C47#57712yes—
363C22×C47C23×D411yescharacteristic
364C2×D47—22no—
365C2×D47—24no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—44no—
369C2×D47—48no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—816no—
376C2×D47—84no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47#52512yes—
383C4×C47C22×#4111yescharacteristic
384C4×C47C22×#4111yescharacteristic
385Dic47—22no—
386Dic47—22no—
387Dic47—22no—
388Dic47—42no—
389Dic47—42no—
390C2×#542—471no—
391C2×#518—471no—
392#3118—4716no—
393C2×#485—471no—
394C2×#482—471no—
395C2×#476—471no—
396C2×#474D4711yescharacteristic, complemented
397C2×#463—471no—
398C2×#463—471no—
399C2×#450—471no—
400C2×#447—471no—
401C2×#442—471no—
402C2×#440—471no—
403C2×C4×SD16—471no—
404C2×C4×D8—471no—
405C2×#433—471no—
406C2×C47—44no—
407C2×C47#311814yescomplemented
408C2×C47C2×#52511yescharacteristic
409C2×C47C2×#57611yescharacteristic
410C2×C47C2×#57711yescharacteristic
411D47—42no—
412D47—44no—
413D47—82no—
414C23×D4—471no—
415C22×SD16—471no—
416C22×SD16—471no—
417C22×D8—471no—
418C22×D8—471no—
419#542—478no—
420#542—944no—
421C2×C4⋊Q8C2×D4711yescharacteristic, complemented
422C2×#126—941no—
423C2×#124—471no—
424C2×#124—941no—
425C2×#123—941no—
426C2×C22⋊Q8—471no—
427C2×C22⋊Q8—941no—
428C2×#121—471no—
429#518—478no—
430#518—944no—
431C2×C4×Q8—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—941no—
437C2×C4×D4—941no—
438C2×C4×D4C2×D4711yescharacteristic
439C2×#117—471no—
440C2×#117—471no—
441C22×C22⋊C4—941no—
442C22×C22⋊C4—941no—
443#485—478no—
444#482—478no—
445#476—478no—
446#474C2×D4718yescomplemented
447#463—478no—
448#463—478no—
449#450—478no—
450#447—478no—
451#442—478no—
452#440—478no—
453C4×SD16—478no—
454C4×D8—478no—
455#433—478no—
456C2×#107C2×D4711yescharacteristic, complemented
457C2×#107C2×D4711yescharacteristic, complemented
458C2×#106—471no—
459C2×#106—471no—
460C2×C4⋊C8—471no—
461C2×C4⋊C8C2×D4711yescharacteristic, complemented
462C2×#103—471no—
463C2×#103—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×#102—471no—
468C2×#102C2×D4711yescharacteristic
469C2×#102C2×D4711yescharacteristic
470C2×C22⋊C8—471no—
471C2×C22⋊C8—471no—
472C2×#97—471no—
473C2×C4×C8—471no—
474C47C2×#311811yescharacteristic, complemented, Sylow
475C25—941no—
476C22×Q8—21no—
477C22×Q8—471no—
478C22×D4—474no—
479C22×D4—471no—
480C22×D4—471no—
481C22×D4—941no—
482C22×D4—942no—
483C22×D4—941no—
484C22×D4—944no—
485C22×D4—944no—
486C22×D4C22×D4711yescharacteristic
487C23×C4—21no—
488C23×C4—471no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C23×C4—941no—
493C2×SD16—474no—
494C2×SD16—474no—
495C2×SD16—944no—
496C2×SD16—944no—
497C2×D8—474no—
498C2×D8—474no—
499C2×D8—944no—
500C2×D8—944no—
501C22×C8—471no—
502C22×C8—471no—
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8C22×D4714yescomplemented
507#126—948no—
508#124—474no—
509#124—948no—
510#124—942no—
511#123—948no—
512C22⋊Q8—474no—
513C22⋊Q8—942no—
514C22⋊Q8—948no—
515#121—474no—
516#121—942no—
517C4×Q8—474no—
518C4×Q8—942no—
519C4×D4—22no—
520C4×D4—474no—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—942no—
525C4×D4—942no—
526C4×D4—942no—
527C4×D4—948no—
528C4×D4—948no—
529C4×D4—942no—
530C4×D4C22×D4714yes—
531#117—474no—
532#117—474no—
533#117—474no—
534#117—942no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4C22×D4711yescharacteristic
542C2×C4⋊C4C22×D4711yescharacteristic
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—471no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—948no—
548C2×C22⋊C4—948no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C42—471no—
559C2×C42—941no—
560C2×C42—941no—
561C2×C42C22×D4711yescharacteristic
562#107C22×D4714yescomplemented
563#107C22×D4714yescomplemented
564#106—474no—
565#106—474no—
566C4⋊C8—474no—
567C4⋊C8C22×D4714yescomplemented
568#103—474no—
569#103—474no—
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574#102C22×D4714yes—
575#102C22×D4714yes—
576C22⋊C8—474no—
577C22⋊C8—474no—
578#97—474no—
579C4×C8—474no—
580C24—21no—
581C24—471no—
582C24—944no—
583C24—948no—
584C24—941no—
585C24—941no—
586C24—3762no—
587C24—3762no—
588C2×Q8—24no—
589C2×Q8—82no—
590C2×Q8—472no—
591C2×Q8—941no—
592C2×Q8—942no—
593C2×Q8—942no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—474no—
597C2×D4—472no—
598C2×D4—472no—
599C2×D4—944no—
600C2×D4—944no—
601C2×D4—948no—
602C2×D4—9416no—
603C2×D4—948no—
604C2×D4—948no—
605C2×D4—941no—
606C2×D4—941no—
607C2×D4—942no—
608C2×D4—942no—
609C2×D4—942no—
610C2×D4—3762no—
611C2×D4#1062535414yes—
612C2×D4C23×D4712yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—944no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—944no—
631C22×C4—3762no—
632C22×C4—3762no—
633C22×C4—3762no—
634C22×C4—3762no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638SD16—948no—
639SD16—948no—
640D8—948no—
641D8—948no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8C23×D4712yes—
649C2×C8C23×D4712yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—474no—
655C4⋊C4—474no—
656C4⋊C4—472no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—941no—
660C4⋊C4C23×D4712yes—
661C4⋊C4C23×D4712yes—
662C4⋊C4C23×D4712yes—
663C22⋊C4—24no—
664C22⋊C4—474no—
665C22⋊C4—474no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C42—472no—
676C42—472no—
677C42—944no—
678C42—944no—
679C42D4×D4712yes—
680C42C23×D4712yes—
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—472no—
686C23—9416no—
687C23—942no—
688C23—944no—
689C23—942no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—3764no—
694C23—3764no—
695C23—37616no—
696C23—1882no—
697C23—1882no—
698C23—1882no—
699C23—1882no—
700C23—1882no—
701C23C2×D4×D4711yescharacteristic
702Q8—84no—
703Q8—942no—
704Q8—942no—
705Q8—1882no—
706D4—24no—
707D4—22no—
708D4—474no—
709D4—9416no—
710D4—944no—
711D4—942no—
712D4—942no—
713D4—942no—
714D4—3764no—
715D4—1882no—
716D4C2×#1062535414yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—472no—
727C2×C4—472no—
728C2×C4—472no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—944no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—3764no—
738C2×C4—3764no—
739C2×C4—3764no—
740C2×C4—3764no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4C2×D4×D4712yes—
744C2×C4C2×D4×D4712yes—
745C2×C4C2×D4×D4711yescharacteristic
746C2×C4#41×D4712yes—
747C2×C4C2×#1062535412yes—
748C2×C4C24×D4711yescharacteristic
749C8—22no—
750C8—22no—
751C8—942no—
752C8—942no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—942no—
758C22—942no—
759C22—942no—
760C22—944no—
761C22—37616no—
762C22—3764no—
763C22—1882no—
764C22—1882no—
765C22—1882no—
766C22—1882no—
767C22—1882no—
768C22—1884no—
769C22—1888no—
770C22#1568963612yes—
771C22#1568992412yes—
772C22#1568993212yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—942no—
780C4—942no—
781C4—942no—
782C4—1882no—
783C4—1882no—
784C4#1568963612yes—
785C4C2×#41×D4711yescharacteristic
786C4C22×#1062535411yescharacteristic
787C2—44no—
788C2—3762no—
789C2—1882no—
790C2—1884no—
791C2#2025357914yesdirect product factor
792C2C2×#1568963611yescharacteristic
793C2C2×#1568992411yescharacteristic
794C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#474C2
socleC23×C47C22×D4
prime radicalC2×#15689258C2
hypercenterC2×#474D47
hypocenterC47C2×#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#15689747C2semidirect
2. C2×#15689595C2semidirect
3. #20253579C2direct (N × H)
4. C2×#15689466C2semidirect
5. C2×#15689450C2semidirect
6. C2×#15689410C2semidirect
7. C2×#15689339C2semidirect
8. C2×#15689338C2semidirect
9. C2×#15689275C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689214C2semidirect
14. C2×#15689205C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#474C2semidirect
23. #15689747C22semidirect
26. C2×#13094012C22semidirect
32. #15689595C22semidirect
33. C2×#13093989C22semidirect
37. C2×#13093986C22semidirect
44. #15689466C22semidirect
45. #15689450C22semidirect
46. #15689410C22semidirect
47. #15689339C22semidirect
48. #15689338C22semidirect
49. #15689275C22semidirect
51. #15689232C22semidirect
52. #15689222C22semidirect
53. #15689214C22semidirect
54. #15689205C22semidirect
55. #15689183C22semidirect
56. C2×#13093955C22semidirect
57. C2×#13093955C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093947C22semidirect
61. C2×#13093946C22semidirect
64. C2×#13093944C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
69. C2×C4⋊Q8×C47C22semidirect
71. C47×#474C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#107×C47C22semidirect
74. C2×C4⋊C8×C47C22semidirect
105. #13094012C23semidirect
113. #13093989C23semidirect
121. #13093986C23semidirect
149. #13093955C23semidirect
150. #13093955C23semidirect
151. C4⋊(C47⋊C8)C23semidirect
152. #13093949C23semidirect
153. #13093947C23semidirect
154. #13093946C23semidirect
157. #13093944C23semidirect
160. #13093934C23semidirect
161. C8×Dic47C23semidirect
168. C4⋊Q8×C47C23semidirect
177. #107×C47C23semidirect
178. #107×C47C23semidirect
179. C4⋊C8×C47C23semidirect
396. C2×#474D47semidirect
407. C2×C47#3118semidirect
421. C2×C4⋊Q8C2×D47semidirect
446. #474C2×D47semidirect
456. C2×#107C2×D47semidirect
457. C2×#107C2×D47semidirect
461. C2×C4⋊C8C2×D47semidirect
474. C47C2×#3118semidirect
506. C4⋊Q8C22×D47semidirect
562. #107C22×D47semidirect
563. #107C22×D47semidirect
567. C4⋊C8C22×D47semidirect
791. C2#20253579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897472
C2×#156895952
#202535792
C2×#156894662
C2×#156894502
C2×#156894102
C2×#156893392
C2×#156893382
C2×#156892752
C2×#156892582
C2×#156892322
C2×#156892222
C2×#156892142
C2×#156892052
C2×#156891832
C2×C47×#4742
C2×#311847