Finite Group Databasebeta

← C47×#24362 #26064060

Subgroups — C47×#24362 #26064060

Order 12032.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C47C211yesmaximal, characteristic, complemented
2C2×C47×#464C211yesmaximal, characteristic, complemented
3C2×C47×#460C211yesmaximal, characteristic, complemented
4C2×C47×#449C211yesmaximal, characteristic, complemented
5C47×#2431C211yesmaximal, characteristic, complemented
6C47×#2341C211yesmaximal, characteristic, complemented
7C47×#2055C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2012C211yesmaximal, characteristic, complemented
10C47×#2011C211yesmaximal, characteristic, complemented
11C47×#1893C211yesmaximal, characteristic, complemented
12C47×#1880C211yesmaximal, characteristic, complemented
13C47×#1878C211yesmaximal, characteristic, complemented
14C47×#1850C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C2×#135×C47—24no—
19C2×#135×C47—24no—
20C2×#135×C47—24no—
21C22×Q16×C47C2211yescharacteristic
22C22×SD16×C47C2211yescharacteristic
23C22×SD16×C47C2211yescharacteristic
24C22×SD16×C47C2211yescharacteristic
25C22×D8×C47C2211yescharacteristic
26C22×D8×C47C2211yescharacteristic
27C23×C8×C47C2211yescharacteristic
28C2×#127×C47C2211yescharacteristic
29C2×#124×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C2×C4×Q8×C47C2211yescharacteristic
32C2×C4×Q8×C47C2211yescharacteristic
33C47×#464—24no—
34C47×#460—24no—
35C47×#449—24no—
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×C4⋊C8×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C47×#392—21no—
48C47×#392—21no—
49C47×#391C2211yescharacteristic
50C47×#390—21no—
51C47×#390—21no—
52C47×#390C2211yescharacteristic
53C47×#390C2211yescharacteristic
54C47×#390C2211yescharacteristic
55C47×#386—21no—
56C47×#386—21no—
57C47×#380—21no—
58C47×#380C2211yescharacteristic
59C4×C22⋊C4×C47—21no—
60C4×C22⋊C4×C47C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#336C2211yescharacteristic
64C47×#336C2211yescharacteristic
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47—41no—
76C2×#41×C47D414yescomplemented
77C22×Q8×C47C2311yescharacteristic
78C22×Q8×C47C2311yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47—21no—
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47C2311yescharacteristic
90#135×C47—232no—
91C2×Q16×C47—22no—
92C2×Q16×C47—22no—
93C2×Q16×C47D414yescomplemented
94C2×SD16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47—22no—
99C2×SD16×C47—22no—
100C2×SD16×C47—22no—
101C2×SD16×C47—22no—
102C2×SD16×C47D414yescomplemented
103C2×D8×C47—22no—
104C2×D8×C47—22no—
105C2×D8×C47—22no—
106C2×D8×C47—22no—
107C2×D8×C47—41no—
108C2×D8×C47—41no—
109C22×C8×C47—22no—
110C22×C8×C47—22no—
111C22×C8×C47—22no—
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116#127×C47—22no—
117#127×C47—41no—
118#124×C47—22no—
119#124×C47—41no—
120#121×C47—22no—
121#121×C47—22no—
122C4×Q8×C47—22no—
123C4×Q8×C47—22no—
124C4×Q8×C47—41no—
125C4×Q8×C47—41no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47D411yescharacteristic
142C2×C22⋊C4×C47D411yescharacteristic
143C2×C42×C47—21no—
144C2×C42×C47—21no—
145C2×C42×C47C2311yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C4⋊C8×C47—22no—
148C4⋊C8×C47—22no—
149#103×C47—22no—
150#103×C47—22no—
151#103×C47—41no—
152#102×C47—22no—
153#102×C47—22no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—41no—
157C22⋊C8×C47—22no—
158#95×C47—21no—
159#95×C47—21no—
160#95×C47—21no—
161#95×C47D411yescharacteristic
162#95×C47D411yescharacteristic
163C24×C47—21no—
164C24×C47—21no—
165C24×C47—21no—
166C24×C47C2×D411yescharacteristic
167#41×C47—28no—
168#41×C47—28no—
169#41×C47—44no—
170#41×C47—44no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47C2×D412yes—
184C2×Q8×C47C2×D412yes—
185C2×Q8×C47C2×D412yes—
186C2×Q8×C47C2×D412yes—
187C2×D4×C47—24no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47—42no—
207C2×D4×C47—42no—
208C2×D4×C47—42no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—81no—
215C2×D4×C47—81no—
216C2×D4×C47—81no—
217C2×D4×C47—81no—
218C2×D4×C47C2×D412yes—
219C2×D4×C47C2×D412yes—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—24no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—42no—
231C22×C4×C47—42no—
232C22×C4×C47—42no—
233C22×C4×C47—42no—
234C22×C4×C47—42no—
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D412yes—
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47#4112yes—
242C22×C4×C47C2411yescharacteristic
243Q16×C47—28no—
244SD16×C47—28no—
245SD16×C47—28no—
246SD16×C47—44no—
247D8×C47—28no—
248D8×C47—44no—
249C2×C8×C47—28no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47C2×D412yes—
261C2×C8×C47C2×D412yes—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—42no—
269C4⋊C4×C47—42no—
270C22⋊C4×C47—22no—
271C22⋊C4×C47—41no—
272C22⋊C4×C47—42no—
273C22⋊C4×C47—42no—
274C22⋊C4×C47—42no—
275C22⋊C4×C47—42no—
276C22⋊C4×C47—42no—
277C22⋊C4×C47—81no—
278C22⋊C4×C47—81no—
279C22⋊C4×C47—81no—
280C22⋊C4×C47—81no—
281C22⋊C4×C47—81no—
282C42×C47—21no—
283C42×C47—21no—
284C42×C47—21no—
285C42×C47—21no—
286C42×C47—42no—
287C42×C47—42no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47#12112yes—
316C23×C47C22×D411yescharacteristic
317Q8×C47—22no—
318Q8×C47—22no—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—22no—
322Q8×C47—41no—
323Q8×C47—41no—
324Q8×C47#12014yes—
325D4×C47—22no—
326D4×C47—22no—
327D4×C47—22no—
328D4×C47—22no—
329D4×C47—48no—
330D4×C47—48no—
331D4×C47—41no—
332D4×C47—41no—
333D4×C47—41no—
334D4×C47—41no—
335D4×C47—41no—
336D4×C47—41no—
337D4×C47—41no—
338D4×C47—41no—
339D4×C47—84no—
340D4×C47—84no—
341D4×C47—84no—
342C2×C4×C47—22no—
343C2×C4×C47—21no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—21no—
354C2×C4×C47—21no—
355C2×C4×C47—21no—
356C2×C4×C47—22no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—48no—
364C2×C4×C47—48no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47#12112yes—
377C2×C4×C47#13512yescomplemented
378C2×C4×C47C22×D411yescharacteristic
379C2×C4×C47C22×D411yescharacteristic
380C2×C4×C47C22×D411yescharacteristic
381C2×C4×C47C2×#4111yescharacteristic
382C2×C4×C47H(5,𝔽2)11yescharacteristic
383C2×C4×C47H(5,𝔽2)11yescharacteristic
384C8×C47—22no—
385C8×C47—22no—
386C8×C47—41no—
387C8×C47—41no—
388#24362C4711yesmaximal, characteristic, direct product factor, Sylow
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47—81no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47—81no—
415C22×C47—81no—
416C22×C47—81no—
417C22×C47C2×#12111yescharacteristic
418C22×C47D4211yescharacteristic
419C22×C47D4211yescharacteristic
420C22×C47C2×#13511yescharacteristic
421C22×C47#57511yescharacteristic
422C22×C47#57611yescharacteristic
423C22×C47#57711yescharacteristic
424C4×C47—22no—
425C4×C47—24no—
426C4×C47—22no—
427C4×C47—42no—
428C4×C47—41no—
429C4×C47—41no—
430C4×C47—41no—
431C4×C47—81no—
432C4×C47—81no—
433C4×C47—81no—
434C4×C47C2×#12011yescharacteristic
435C4×C47#53411yescharacteristic
436C4×C47#54611yescharacteristic
437C4×C47#54611yescharacteristic
438C22×#135C2×C4711yescharacteristic, complemented
439C2×#464C2×C4711yescharacteristic, complemented
440C2×#460C2×C4711yescharacteristic, complemented
441C2×#449C2×C4711yescharacteristic, complemented
442#2431C2×C4711yescharacteristic, complemented
443#2341C2×C4711yescharacteristic, complemented
444#2055C2×C4711yescharacteristic, complemented
445#2054C2×C4711yescharacteristic, complemented
446#2012C2×C4711yescharacteristic, complemented
447#2011C2×C4711yescharacteristic, complemented
448#1893C2×C4711yescharacteristic, complemented
449#1880C2×C4711yescharacteristic, complemented
450#1878C2×C4711yescharacteristic, complemented
451#1850C2×C4711yescharacteristic, complemented
452#1788C2×C4711yescharacteristic, complemented
453C2×C47—42no—
454C2×C47—82no—
455C2×C47—82no—
456C2×C47—161no—
457C2×C47#241011yescharacteristic
458C2×C47#303511yescharacteristic
459C2×C47#304511yescharacteristic
460C2×C47#326811yescharacteristic
461C2×C47#327111yescharacteristic
462C2×C47#328211yescharacteristic
463C2×C47#328711yescharacteristic
464C22×#41C22×C4711yescharacteristic
465C22×#41C22×C4711yescharacteristic
466C2×#135—24no—
467C2×#135—24no—
468C2×#135—24no—
469C22×Q16C22×C4711yescharacteristic
470C22×SD16C22×C4711yescharacteristic
471C22×SD16C22×C4711yescharacteristic
472C22×SD16C22×C4711yescharacteristic
473C22×D8C22×C4711yescharacteristic
474C22×D8C22×C4711yescharacteristic
475C23×C8C22×C4711yescharacteristic
476C2×#127C22×C4711yescharacteristic
477C2×#124C22×C4711yescharacteristic
478C2×#121C22×C4711yescharacteristic
479C2×C4×Q8C22×C4711yescharacteristic
480C2×C4×Q8C22×C4711yescharacteristic
481#464—24no—
482#460—24no—
483#449—24no—
484C2×C4⋊C8C22×C4711yescharacteristic
485C2×C4⋊C8C22×C4711yescharacteristic
486C2×#103C22×C4711yescharacteristic
487C2×#103C22×C4711yescharacteristic
488C2×#103C22×C4711yescharacteristic
489C2×#102C22×C4711yescharacteristic
490C2×#102C22×C4711yescharacteristic
491C2×#102C22×C4711yescharacteristic
492C2×#102C22×C4711yescharacteristic
493C2×#102C22×C4711yescharacteristic
494C2×C22⋊C8C22×C4711yescharacteristic
495#392—21no—
496#392—21no—
497#391C22×C4711yescharacteristic
498#390—21no—
499#390—21no—
500#390C22×C4711yescharacteristic
501#390C22×C4711yescharacteristic
502#390C22×C4711yescharacteristic
503#386—21no—
504#386—21no—
505#380—21no—
506#380C22×C4711yescharacteristic
507C4×C22⋊C4—21no—
508C4×C22⋊C4C22×C4711yescharacteristic
509#340C22×C4711yescharacteristic
510#340C22×C4711yescharacteristic
511#336C22×C4711yescharacteristic
512#336C22×C4711yescharacteristic
513C47#2436211yescharacteristic, direct product factor, Sylow
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41D4×C4714yescomplemented
526C22×Q8C23×C4711yescharacteristic
527C22×Q8C23×C4711yescharacteristic
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C23×C4711yescharacteristic
534C22×D4C23×C4711yescharacteristic
535C22×D4C23×C4711yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C4711yescharacteristic
539#135—232no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16D4×C4714yescomplemented
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16D4×C4714yescomplemented
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8C23×C4711yescharacteristic
562C22×C8C23×C4711yescharacteristic
563C22×C8C23×C4711yescharacteristic
564C22×C8C23×C4711yescharacteristic
565#127—22no—
566#127—41no—
567#124—22no—
568#124—41no—
569#121—22no—
570#121—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4C23×C4711yescharacteristic
578C2×C4⋊C4C23×C4711yescharacteristic
579C2×C4⋊C4C23×C4711yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C4711yescharacteristic
591C2×C22⋊C4D4×C4711yescharacteristic
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C23×C4711yescharacteristic
595C2×C42C23×C4711yescharacteristic
596C4⋊C8—22no—
597C4⋊C8—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95D4×C4711yescharacteristic
611#95D4×C4711yescharacteristic
612C24—21no—
613C24—21no—
614C24—21no—
615C24C2×D4×C4711yescharacteristic
616#41—28no—
617#41—28no—
618#41—44no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×D4×C4712yes—
633C2×Q8C2×D4×C4712yes—
634C2×Q8C2×D4×C4712yes—
635C2×Q8C2×D4×C4712yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C4712yes—
668C2×D4C2×D4×C4712yes—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4C2×D4×C4711yescharacteristic
685C22×C4C2×D4×C4711yescharacteristic
686C22×C4C2×D4×C4711yescharacteristic
687C22×C4C2×D4×C4711yescharacteristic
688C22×C4C2×D4×C4712yes—
689C22×C4C2×D4×C4711yescharacteristic
690C22×C4#41×C4712yes—
691C22×C4C24×C4711yescharacteristic
692Q16—28no—
693SD16—28no—
694SD16—28no—
695SD16—44no—
696D8—28no—
697D8—44no—
698C2×C8—28no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8C2×D4×C4712yes—
710C2×C8C2×D4×C4712yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—42no—
736C42—42no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23#121×C4712yes—
765C23C22×D4×C4711yescharacteristic
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8#120×C4714yes—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4—84no—
790D4—84no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4#121×C4712yes—
826C2×C4#135×C4712yescomplemented
827C2×C4C22×D4×C4711yescharacteristic
828C2×C4C22×D4×C4711yescharacteristic
829C2×C4C22×D4×C4711yescharacteristic
830C2×C4C2×#41×C4711yescharacteristic
831C2×C4H(5,𝔽2)×C4711yescharacteristic
832C2×C4H(5,𝔽2)×C4711yescharacteristic
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×#121×C4711yescharacteristic
866C22D42×C4711yescharacteristic
867C22D42×C4711yescharacteristic
868C22C2×#135×C4711yescharacteristic
869C22C47×#57511yescharacteristic
870C22C47×#57611yescharacteristic
871C22C47×#57711yescharacteristic
872C4—22no—
873C4—24no—
874C4—22no—
875C4—41no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C2×#120×C4711yescharacteristic
883C4C47×#53411yescharacteristic
884C4C47×#54611yescharacteristic
885C4C47×#54611yescharacteristic
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2C47×#241011yescharacteristic
891C2C47×#303511yescharacteristic
892C2C47×#304511yescharacteristic
893C2C47×#326811yescharacteristic
894C2C47×#327111yescharacteristic
895C2C47×#328211yescharacteristic
896C2C47×#328711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C47C2semidirect
2. C2×C47×#464C2semidirect
3. C2×C47×#460C2semidirect
4. C2×C47×#449C2semidirect
5. C47×#2431C2semidirect
6. C47×#2341C2semidirect
7. C47×#2055C2semidirect
8. C47×#2054C2semidirect
9. C47×#2012C2semidirect
10. C47×#2011C2semidirect
11. C47×#1893C2semidirect
12. C47×#1880C2semidirect
13. C47×#1878C2semidirect
14. C47×#1850C2semidirect
15. C47×#1788C2semidirect
76. C2×#41×C47D4semidirect
93. C2×Q16×C47D4semidirect
102. C2×SD16×C47D4semidirect
377. C2×C4×C47#135semidirect
388. #24362C47direct (N × H)
438. C22×#135C2×C47semidirect
439. C2×#464C2×C47semidirect
440. C2×#460C2×C47semidirect
441. C2×#449C2×C47semidirect
442. #2431C2×C47semidirect
443. #2341C2×C47semidirect
444. #2055C2×C47semidirect
445. #2054C2×C47semidirect
446. #2012C2×C47semidirect
447. #2011C2×C47semidirect
448. #1893C2×C47semidirect
449. #1880C2×C47semidirect
450. #1878C2×C47semidirect
451. #1850C2×C47semidirect
452. #1788C2×C47semidirect
513. C47#24362direct (N × H)
525. C2×#41D4×C47semidirect
542. C2×Q16D4×C47semidirect
551. C2×SD16D4×C47semidirect
826. C2×C4#135×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C472
C2×C47×#4642
C2×C47×#4602
C2×C47×#4492
C47×#24312
C47×#23412
C47×#20552
C47×#20542
C47×#20122
C47×#20112
C47×#18932
C47×#18802
C47×#18782
C47×#18502
C47×#17882
#2436247