Finite Group Databasebeta

← C2×C47×#3271 #26100727

Subgroups — C2×C47×#3271 #26100727

Order 12032.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C47C211yesmaximal, characteristic, complemented
2C22×#135×C47C211yesmaximal, characteristic, complemented
3C2×C47×#550C211yesmaximal, characteristic, complemented
4C2×C47×#548C211yesmaximal, characteristic, complemented
5C47×#3271C2116yesmaximal, direct product factor
6C2×C47×#496C211yesmaximal, characteristic, complemented
7C2×C47×#469C211yesmaximal, characteristic, complemented
8C2×C47×#465C211yesmaximal, characteristic, complemented
9C2×C47×#464C211yesmaximal, characteristic, complemented
10C2×C47×#460C211yesmaximal, characteristic, complemented
11C2×C47×#452C211yesmaximal, characteristic, complemented
12C2×C47×#449C211yesmaximal, characteristic, complemented
13C2×C47×#449C211yesmaximal, characteristic, complemented
14C2×C47×#448C211yesmaximal, characteristic, complemented
15C2×C47×#441C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#41×C47C2211yescharacteristic
18C22×#41×C47C2211yescharacteristic
19C22×#41×C47C2211yescharacteristic
20C23×Q8×C47C2211yescharacteristic
21C2×#137×C47—28no—
22C2×#137×C47C2218yescomplemented
23C2×#135×C47—28no—
24C2×#135×C47C2218yescomplemented
25C22×Q16×C47C2211yescharacteristic
26C22×Q16×C47C2211yescharacteristic
27C22×SD16×C47C2211yescharacteristic
28C22×SD16×C47C2211yescharacteristic
29C22×SD16×C47C2211yescharacteristic
30C22×SD16×C47C2211yescharacteristic
31C22×SD16×C47C2211yescharacteristic
32C22×D8×C47C2211yescharacteristic
33C22×D8×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C23×C8×C47C2211yescharacteristic
36C47×#550—24no—
37C47×#550C2218yescomplemented
38C47×#548—24no—
39C47×#548C2218yescomplemented
40C2×#127×C47—21no—
41C2×#127×C47C2211yescharacteristic
42C2×#124×C47—21no—
43C2×#124×C47C2211yescharacteristic
44C2×C22⋊Q8×C47—21no—
45C2×C22⋊Q8×C47C2211yescharacteristic
46C2×#121×C47—21no—
47C2×#121×C47—21no—
48C2×#121×C47—21no—
49C2×#121×C47C2211yescharacteristic
50C2×#121×C47C2211yescharacteristic
51C2×#121×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C2×C4×D4×C47—21no—
55C2×C4×D4×C47—21no—
56C2×C4×D4×C47C2211yescharacteristic
57C47×#496C2218yescomplemented
58C47×#469C2218yescomplemented
59C47×#465C2218yescomplemented
60C47×#464C2218yescomplemented
61C47×#460C2218yescomplemented
62C47×#452C2218yescomplemented
63C47×#449C2218yescomplemented
64C47×#449C2218yescomplemented
65C47×#448C2218yescomplemented
66C47×#441C2218yescomplemented
67C47×#435C2218yescomplemented
68C2×#106×C47C2211yescharacteristic
69C2×C4⋊C8×C47C2211yescharacteristic
70C2×#103×C47C2211yescharacteristic
71C2×#103×C47C2211yescharacteristic
72C2×#103×C47C2211yescharacteristic
73C2×#102×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×C22⋊C8×C47C2211yescharacteristic
78C2×#97×C47C2211yescharacteristic
79C2×#41×C47—22no—
80C2×#41×C47—22no—
81C2×#41×C47—22no—
82C2×#41×C47—24no—
83C2×#41×C47—24no—
84C2×#41×C47—24no—
85C2×#41×C47—42no—
86C2×#41×C47—42no—
87C2×#41×C47—42no—
88C2×#41×C47C2314yes—
89C2×#41×C47C2314yes—
90C2×#41×C47C2314yes—
91C22×Q8×C47—21no—
92C22×Q8×C47—22no—
93C22×Q8×C47—24no—
94C22×Q8×C47—42no—
95C22×Q8×C47C2311yescharacteristic
96C22×Q8×C47C2314yes—
97C22×Q8×C47C2311yescharacteristic
98C22×Q8×C47C2311yescharacteristic
99C22×D4×C47—21no—
100C22×D4×C47—21no—
101C22×D4×C47—21no—
102C22×D4×C47—21no—
103C22×D4×C47—21no—
104C22×D4×C47—21no—
105C22×D4×C47—21no—
106C22×D4×C47—21no—
107C22×D4×C47D411yescharacteristic
108C22×D4×C47C2311yescharacteristic
109C22×D4×C47C2311yescharacteristic
110C22×D4×C47C2311yescharacteristic
111C23×C4×C47—21no—
112C23×C4×C47—21no—
113C23×C4×C47—21no—
114C23×C4×C47—21no—
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117#137×C47—232no—
118#135×C47—232no—
119C2×Q16×C47—24no—
120C2×Q16×C47D418yescomplemented
121C2×Q16×C47C2314yes—
122C2×Q16×C47C2314yes—
123C2×SD16×C47—24no—
124C2×SD16×C47—24no—
125C2×SD16×C47—24no—
126C2×SD16×C47—24no—
127C2×SD16×C47—42no—
128C2×SD16×C47C2314yes—
129C2×SD16×C47C2314yes—
130C2×SD16×C47C2314yes—
131C2×SD16×C47C2314yes—
132C2×SD16×C47C2314yes—
133C2×D8×C47—24no—
134C2×D8×C47—42no—
135C2×D8×C47C2314yes—
136C2×D8×C47C2314yes—
137C2×M16×C47—24no—
138C2×M16×C47C2314yes—
139C22×C8×C47—24no—
140C22×C8×C47C2314yes—
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143C22×C8×C47C2311yescharacteristic
144C22×C8×C47C2311yescharacteristic
145#127×C47—28no—
146#127×C47—22no—
147#127×C47C2314yes—
148#124×C47—28no—
149#124×C47—22no—
150#124×C47C2314yes—
151C22⋊Q8×C47—22no—
152C22⋊Q8×C47—28no—
153C22⋊Q8×C47C2314yes—
154#121×C47—28no—
155#121×C47—22no—
156#121×C47—22no—
157#121×C47—22no—
158#121×C47—28no—
159#121×C47—28no—
160#121×C47C2314yes—
161#121×C47C2314yes—
162#121×C47C2314yes—
163C4×Q8×C47—22no—
164C4×Q8×C47—22no—
165C4×Q8×C47C2314yes—
166C4×Q8×C47C2314yes—
167C4×D4×C47—28no—
168C4×D4×C47—28no—
169C4×D4×C47D414yes—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47D411yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47D411yescharacteristic
184C2×C22⋊C4×C47D411yescharacteristic
185C2×C42×C47—21no—
186C2×C42×C47—21no—
187C2×C42×C47C2311yescharacteristic
188#106×C47C2314yes—
189C4⋊C8×C47C2314yes—
190#103×C47C2314yes—
191#103×C47C2314yes—
192#103×C47C2314yes—
193#102×C47C2314yes—
194#102×C47C2314yes—
195#102×C47C2314yes—
196C22⋊C8×C47C2314yes—
197C22⋊C8×C47C2314yes—
198#97×C47C2314yes—
199C24×C47—21no—
200C24×C47—21no—
201C24×C47—21no—
202C24×C47C2×D411yescharacteristic
203C24×C47C2×D411yescharacteristic
204#41×C47—28no—
205#41×C47—28no—
206#41×C47—28no—
207#41×C47—44no—
208#41×C47—44no—
209#41×C47—44no—
210#41×C47—48no—
211#41×C47—48no—
212#41×C47—48no—
213C2×Q8×C47—21no—
214C2×Q8×C47—21no—
215C2×Q8×C47—24no—
216C2×Q8×C47—21no—
217C2×Q8×C47—22no—
218C2×Q8×C47—22no—
219C2×Q8×C47—28no—
220C2×Q8×C47—22no—
221C2×Q8×C47—22no—
222C2×Q8×C47—44no—
223C2×Q8×C47—44no—
224C2×Q8×C47—48no—
225C2×Q8×C47C2×D414yes—
226C2×Q8×C47C2×D414yes—
227C2×Q8×C47C2412yes—
228C2×Q8×C47C2412yes—
229C2×Q8×C47C2412yes—
230C2×D4×C47—24no—
231C2×D4×C47—24no—
232C2×D4×C47—24no—
233C2×D4×C47—24no—
234C2×D4×C47—24no—
235C2×D4×C47—24no—
236C2×D4×C47—22no—
237C2×D4×C47—22no—
238C2×D4×C47—22no—
239C2×D4×C47—24no—
240C2×D4×C47—21no—
241C2×D4×C47—21no—
242C2×D4×C47—21no—
243C2×D4×C47—24no—
244C2×D4×C47—22no—
245C2×D4×C47—22no—
246C2×D4×C47—22no—
247C2×D4×C47—42no—
248C2×D4×C47—44no—
249C2×D4×C47—44no—
250C2×D4×C47—44no—
251C2×D4×C47—44no—
252C2×D4×C47—44no—
253C2×D4×C47—82no—
254C2×D4×C47—82no—
255C2×D4×C47—82no—
256C2×D4×C47C2×D414yes—
257C2×D4×C47C2412yes—
258C2×D4×C47C2412yes—
259C2×D4×C47C2412yes—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—22no—
263C22×C4×C47—22no—
264C22×C4×C47—22no—
265C22×C4×C47—22no—
266C22×C4×C47—24no—
267C22×C4×C47—21no—
268C22×C4×C47—21no—
269C22×C4×C47—21no—
270C22×C4×C47—24no—
271C22×C4×C47—24no—
272C22×C4×C47—24no—
273C22×C4×C47—44no—
274C22×C4×C47—44no—
275C22×C4×C47—44no—
276C22×C4×C47—44no—
277C22×C4×C47C2×D412yes—
278C22×C4×C47C2×D412yes—
279C22×C4×C47C2×D411yescharacteristic
280C22×C4×C47C2×D411yescharacteristic
281C22×C4×C47C2×D411yescharacteristic
282C22×C4×C47C2×D411yescharacteristic
283C22×C4×C47C2412yes—
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286Q16×C47—28no—
287Q16×C47C2×D4116yescomplemented
288SD16×C47—28no—
289SD16×C47—28no—
290SD16×C47—28no—
291SD16×C47—28no—
292SD16×C47—44no—
293D8×C47—28no—
294D8×C47—44no—
295M16×C47—28no—
296C2×C8×C47—22no—
297C2×C8×C47—22no—
298C2×C8×C47—22no—
299C2×C8×C47—28no—
300C2×C8×C47C2×D414yes—
301C2×C8×C47C2412yes—
302C2×C8×C47C2412yes—
303C2×C8×C47C2412yes—
304C2×C8×C47C2412yes—
305C4⋊C4×C47—24no—
306C4⋊C4×C47—24no—
307C4⋊C4×C47—24no—
308C4⋊C4×C47—21no—
309C4⋊C4×C47—21no—
310C4⋊C4×C47C2×D414yes—
311C4⋊C4×C47C2412yes—
312C4⋊C4×C47C2412yes—
313C22⋊C4×C47—24no—
314C22⋊C4×C47—24no—
315C22⋊C4×C47—24no—
316C22⋊C4×C47—24no—
317C22⋊C4×C47—24no—
318C22⋊C4×C47—24no—
319C22⋊C4×C47C2×D414yes—
320C22⋊C4×C47C2×D414yes—
321C42×C47—24no—
322C42×C47—24no—
323C42×C47C2×D412yes—
324C42×C47C2412yes—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—22no—
333C23×C47—22no—
334C23×C47—42no—
335C23×C47—42no—
336C23×C47—42no—
337C23×C47—42no—
338C23×C47—42no—
339C23×C47—42no—
340C23×C47—42no—
341C23×C47—42no—
342C23×C47—42no—
343C23×C47C22×D412yes—
344C23×C47C22×D412yes—
345C23×C47C22×D411yescharacteristic
346Q8×C47—24no—
347Q8×C47—24no—
348Q8×C47—22no—
349Q8×C47—22no—
350Q8×C47—22no—
351Q8×C47—22no—
352Q8×C47—48no—
353Q8×C47—42no—
354Q8×C47C22×D414yes—
355Q8×C47C22×D414yes—
356D4×C47—22no—
357D4×C47—22no—
358D4×C47—22no—
359D4×C47—22no—
360D4×C47—22no—
361D4×C47—22no—
362D4×C47—44no—
363D4×C47—48no—
364D4×C47—48no—
365D4×C47—48no—
366D4×C47—48no—
367D4×C47—48no—
368D4×C47—42no—
369D4×C47—42no—
370D4×C47—42no—
371D4×C47—84no—
372D4×C47—84no—
373D4×C47—84no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—24no—
377C2×C4×C47—24no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—24no—
383C2×C4×C47—24no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—48no—
392C2×C4×C47—48no—
393C2×C4×C47—48no—
394C2×C4×C47—48no—
395C2×C4×C47—42no—
396C2×C4×C47—42no—
397C2×C4×C47—42no—
398C2×C4×C47C22×D412yes—
399C2×C4×C47C22×D412yes—
400C2×C4×C47C22×D412yes—
401C2×C4×C47C22×D412yes—
402C2×C4×C47C22×D411yescharacteristic
403C2×C4×C47C22×D412yes—
404C2×C4×C47H(5,𝔽2)12yes—
405C2×C4×C47C2511yescharacteristic
406C8×C47—22no—
407C8×C47—22no—
408C8×C47—22no—
409C8×C47C22×D414yes—
410C2×#3271C4711yesmaximal, characteristic, direct product factor, Sylow
411C22×C47—22no—
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—22no—
417C22×C47—44no—
418C22×C47—44no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—42no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—84no—
429C22×C47—84no—
430C22×C47—84no—
431C22×C47D4212yes—
432C22×C47#57512yes—
433C22×C47#57712yes—
434C22×C47C23×D411yescharacteristic
435C4×C47—22no—
436C4×C47—22no—
437C4×C47—24no—
438C4×C47—24no—
439C4×C47—22no—
440C4×C47—22no—
441C4×C47—42no—
442C4×C47—42no—
443C4×C47—42no—
444C4×C47D4212yes—
445C4×C47C23×D411yescharacteristic
446C4×C47C2×H(5,𝔽2)11yescharacteristic
447C22×#137C2×C4711yescharacteristic, complemented
448C22×#135C2×C4711yescharacteristic, complemented
449C2×#550C2×C4711yescharacteristic, complemented
450C2×#548C2×C4711yescharacteristic, complemented
451#3271C2×C47116yesdirect product factor
452C2×#496C2×C4711yescharacteristic, complemented
453C2×#469C2×C4711yescharacteristic, complemented
454C2×#465C2×C4711yescharacteristic, complemented
455C2×#464C2×C4711yescharacteristic, complemented
456C2×#460C2×C4711yescharacteristic, complemented
457C2×#452C2×C4711yescharacteristic, complemented
458C2×#449C2×C4711yescharacteristic, complemented
459C2×#449C2×C4711yescharacteristic, complemented
460C2×#448C2×C4711yescharacteristic, complemented
461C2×#441C2×C4711yescharacteristic, complemented
462C2×#435C2×C4711yescharacteristic, complemented
463C2×C47—42no—
464C2×C47—42no—
465C2×C47—82no—
466C2×C47—82no—
467C2×C47—82no—
468C2×C47#327114yesdirect product factor
469C2×C47C2×D4211yescharacteristic
470C2×C47C2×#57511yescharacteristic
471C2×C47C2×#57711yescharacteristic
472C22×#41C22×C4711yescharacteristic
473C22×#41C22×C4711yescharacteristic
474C22×#41C22×C4711yescharacteristic
475C23×Q8C22×C4711yescharacteristic
476C2×#137—28no—
477C2×#137C22×C4718yescomplemented
478C2×#135—28no—
479C2×#135C22×C4718yescomplemented
480C22×Q16C22×C4711yescharacteristic
481C22×Q16C22×C4711yescharacteristic
482C22×SD16C22×C4711yescharacteristic
483C22×SD16C22×C4711yescharacteristic
484C22×SD16C22×C4711yescharacteristic
485C22×SD16C22×C4711yescharacteristic
486C22×SD16C22×C4711yescharacteristic
487C22×D8C22×C4711yescharacteristic
488C22×D8C22×C4711yescharacteristic
489C22×M16C22×C4711yescharacteristic
490C23×C8C22×C4711yescharacteristic
491#550—24no—
492#550C22×C4718yescomplemented
493#548—24no—
494#548C22×C4718yescomplemented
495C2×#127—21no—
496C2×#127C22×C4711yescharacteristic
497C2×#124—21no—
498C2×#124C22×C4711yescharacteristic
499C2×C22⋊Q8—21no—
500C2×C22⋊Q8C22×C4711yescharacteristic
501C2×#121—21no—
502C2×#121—21no—
503C2×#121—21no—
504C2×#121C22×C4711yescharacteristic
505C2×#121C22×C4711yescharacteristic
506C2×#121C22×C4711yescharacteristic
507C2×C4×Q8C22×C4711yescharacteristic
508C2×C4×Q8C22×C4711yescharacteristic
509C2×C4×D4—21no—
510C2×C4×D4—21no—
511C2×C4×D4C22×C4711yescharacteristic
512#496C22×C4718yescomplemented
513#469C22×C4718yescomplemented
514#465C22×C4718yescomplemented
515#464C22×C4718yescomplemented
516#460C22×C4718yescomplemented
517#452C22×C4718yescomplemented
518#449C22×C4718yescomplemented
519#449C22×C4718yescomplemented
520#448C22×C4718yescomplemented
521#441C22×C4718yescomplemented
522#435C22×C4718yescomplemented
523C2×#106C22×C4711yescharacteristic
524C2×C4⋊C8C22×C4711yescharacteristic
525C2×#103C22×C4711yescharacteristic
526C2×#103C22×C4711yescharacteristic
527C2×#103C22×C4711yescharacteristic
528C2×#102C22×C4711yescharacteristic
529C2×#102C22×C4711yescharacteristic
530C2×#102C22×C4711yescharacteristic
531C2×C22⋊C8C22×C4711yescharacteristic
532C2×C22⋊C8C22×C4711yescharacteristic
533C2×#97C22×C4711yescharacteristic
534C47C2×#327111yescharacteristic, direct product factor, Sylow
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—24no—
539C2×#41—24no—
540C2×#41—24no—
541C2×#41—42no—
542C2×#41—42no—
543C2×#41—42no—
544C2×#41C23×C4714yes—
545C2×#41C23×C4714yes—
546C2×#41C23×C4714yes—
547C22×Q8—21no—
548C22×Q8—22no—
549C22×Q8—24no—
550C22×Q8—42no—
551C22×Q8C23×C4711yescharacteristic
552C22×Q8C23×C4714yes—
553C22×Q8C23×C4711yescharacteristic
554C22×Q8C23×C4711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4D4×C4711yescharacteristic
564C22×D4C23×C4711yescharacteristic
565C22×D4C23×C4711yescharacteristic
566C22×D4C23×C4711yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C4711yescharacteristic
572C23×C4C23×C4711yescharacteristic
573#137—232no—
574#135—232no—
575C2×Q16—24no—
576C2×Q16D4×C4718yescomplemented
577C2×Q16C23×C4714yes—
578C2×Q16C23×C4714yes—
579C2×SD16—24no—
580C2×SD16—24no—
581C2×SD16—24no—
582C2×SD16—24no—
583C2×SD16—42no—
584C2×SD16C23×C4714yes—
585C2×SD16C23×C4714yes—
586C2×SD16C23×C4714yes—
587C2×SD16C23×C4714yes—
588C2×SD16C23×C4714yes—
589C2×D8—24no—
590C2×D8—42no—
591C2×D8C23×C4714yes—
592C2×D8C23×C4714yes—
593C2×M16—24no—
594C2×M16C23×C4714yes—
595C22×C8—24no—
596C22×C8C23×C4711yescharacteristic
597C22×C8C23×C4714yes—
598C22×C8C23×C4711yescharacteristic
599C22×C8C23×C4711yescharacteristic
600C22×C8C23×C4711yescharacteristic
601#127—28no—
602#127—22no—
603#127C23×C4714yes—
604#124—28no—
605#124—22no—
606#124C23×C4714yes—
607C22⋊Q8—22no—
608C22⋊Q8—28no—
609C22⋊Q8C23×C4714yes—
610#121—28no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—28no—
615#121—28no—
616#121C23×C4714yes—
617#121C23×C4714yes—
618#121C23×C4714yes—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8C23×C4714yes—
622C4×Q8C23×C4714yes—
623C4×D4—28no—
624C4×D4—28no—
625C4×D4D4×C4714yes—
626C4×D4C23×C4714yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4D4×C4711yescharacteristic
631C2×C4⋊C4C23×C4711yescharacteristic
632C2×C4⋊C4C23×C4711yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4D4×C4711yescharacteristic
640C2×C22⋊C4D4×C4711yescharacteristic
641C2×C42—21no—
642C2×C42—21no—
643C2×C42C23×C4711yescharacteristic
644#106C23×C4714yes—
645C4⋊C8C23×C4714yes—
646#103C23×C4714yes—
647#103C23×C4714yes—
648#103C23×C4714yes—
649#102C23×C4714yes—
650#102C23×C4714yes—
651#102C23×C4714yes—
652C22⋊C8C23×C4714yes—
653C22⋊C8C23×C4714yes—
654#97C23×C4714yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C2×D4×C4711yescharacteristic
659C24C2×D4×C4711yescharacteristic
660#41—28no—
661#41—28no—
662#41—28no—
663#41—44no—
664#41—44no—
665#41—44no—
666#41—48no—
667#41—48no—
668#41—48no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—24no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—28no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—48no—
681C2×Q8C2×D4×C4714yes—
682C2×Q8C2×D4×C4714yes—
683C2×Q8C24×C4712yes—
684C2×Q8C24×C4712yes—
685C2×Q8C24×C4712yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—24no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—24no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—42no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—82no—
710C2×D4—82no—
711C2×D4—82no—
712C2×D4C2×D4×C4714yes—
713C2×D4C24×C4712yes—
714C2×D4C24×C4712yes—
715C2×D4C24×C4712yes—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4C2×D4×C4711yescharacteristic
734C22×C4C2×D4×C4711yescharacteristic
735C22×C4C2×D4×C4711yescharacteristic
736C22×C4C2×D4×C4711yescharacteristic
737C22×C4C2×D4×C4712yes—
738C22×C4C2×D4×C4712yes—
739C22×C4C24×C4712yes—
740C22×C4C24×C4712yes—
741C22×C4C24×C4711yescharacteristic
742Q16—28no—
743Q16C2×D4×C47116yescomplemented
744SD16—28no—
745SD16—28no—
746SD16—28no—
747SD16—28no—
748SD16—44no—
749D8—28no—
750D8—44no—
751M16—28no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—28no—
756C2×C8C2×D4×C4714yes—
757C2×C8C24×C4712yes—
758C2×C8C24×C4712yes—
759C2×C8C24×C4712yes—
760C2×C8C24×C4712yes—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4C2×D4×C4714yes—
767C4⋊C4C24×C4712yes—
768C4⋊C4C24×C4712yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4C2×D4×C4714yes—
776C22⋊C4C2×D4×C4714yes—
777C42—24no—
778C42—24no—
779C42C2×D4×C4712yes—
780C42C24×C4712yes—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23C22×D4×C4712yes—
800C23C22×D4×C4712yes—
801C23C22×D4×C4711yescharacteristic
802Q8—24no—
803Q8—24no—
804Q8—22no—
805Q8—22no—
806Q8—22no—
807Q8—22no—
808Q8—48no—
809Q8—42no—
810Q8C22×D4×C4714yes—
811Q8C22×D4×C4714yes—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—48no—
823D4—48no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—84no—
828D4—84no—
829D4—84no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—48no—
848C2×C4—48no—
849C2×C4—48no—
850C2×C4—48no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4C22×D4×C4712yes—
855C2×C4C22×D4×C4712yes—
856C2×C4C22×D4×C4712yes—
857C2×C4C22×D4×C4712yes—
858C2×C4C22×D4×C4711yescharacteristic
859C2×C4C22×D4×C4712yes—
860C2×C4H(5,𝔽2)×C4712yes—
861C2×C4C25×C4711yescharacteristic
862C8—22no—
863C8—22no—
864C8—22no—
865C8C22×D4×C4714yes—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—84no—
884C22—84no—
885C22—84no—
886C22D42×C4712yes—
887C22C47×#57512yes—
888C22C47×#57712yes—
889C22C23×D4×C4711yescharacteristic
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—24no—
895C4—24no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4D42×C4712yes—
900C4C23×D4×C4711yescharacteristic
901C4C2×H(5,𝔽2)×C4711yescharacteristic
902C2—42no—
903C2—42no—
904C2—82no—
905C2—82no—
906C2—82no—
907C2C47×#327114yesdirect product factor
908C2C2×D42×C4711yescharacteristic
909C2C2×C47×#57511yescharacteristic
910C2C2×C47×#57711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC2×C4C25×C47
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C47C2semidirect
2. C22×#135×C47C2semidirect
3. C2×C47×#550C2semidirect
4. C2×C47×#548C2semidirect
5. C47×#3271C2direct (N × H)
6. C2×C47×#496C2semidirect
7. C2×C47×#469C2semidirect
8. C2×C47×#465C2semidirect
9. C2×C47×#464C2semidirect
10. C2×C47×#460C2semidirect
11. C2×C47×#452C2semidirect
12. C2×C47×#449C2semidirect
13. C2×C47×#449C2semidirect
14. C2×C47×#448C2semidirect
15. C2×C47×#441C2semidirect
16. C2×C47×#435C2semidirect
22. C2×#137×C47C22semidirect
24. C2×#135×C47C22semidirect
37. C47×#550C22semidirect
39. C47×#548C22semidirect
57. C47×#496C22semidirect
58. C47×#469C22semidirect
59. C47×#465C22semidirect
60. C47×#464C22semidirect
61. C47×#460C22semidirect
62. C47×#452C22semidirect
63. C47×#449C22semidirect
64. C47×#449C22semidirect
65. C47×#448C22semidirect
66. C47×#441C22semidirect
67. C47×#435C22semidirect
120. C2×Q16×C47D4semidirect
287. Q16×C47C2×D4semidirect
410. C2×#3271C47direct (N × H)
447. C22×#137C2×C47semidirect
448. C22×#135C2×C47semidirect
449. C2×#550C2×C47semidirect
450. C2×#548C2×C47semidirect
451. #3271C2×C47direct (N × H)
452. C2×#496C2×C47semidirect
453. C2×#469C2×C47semidirect
454. C2×#465C2×C47semidirect
455. C2×#464C2×C47semidirect
456. C2×#460C2×C47semidirect
457. C2×#452C2×C47semidirect
458. C2×#449C2×C47semidirect
459. C2×#449C2×C47semidirect
460. C2×#448C2×C47semidirect
461. C2×#441C2×C47semidirect
462. C2×#435C2×C47semidirect
468. C2×C47#3271direct (N × H)
477. C2×#137C22×C47semidirect
479. C2×#135C22×C47semidirect
492. #550C22×C47semidirect
494. #548C22×C47semidirect
512. #496C22×C47semidirect
513. #469C22×C47semidirect
514. #465C22×C47semidirect
515. #464C22×C47semidirect
516. #460C22×C47semidirect
517. #452C22×C47semidirect
518. #449C22×C47semidirect
519. #449C22×C47semidirect
520. #448C22×C47semidirect
521. #441C22×C47semidirect
522. #435C22×C47semidirect
534. C47C2×#3271direct (N × H)
576. C2×Q16D4×C47semidirect
743. Q16C2×D4×C47semidirect
907. C2C47×#3271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#137×C472
C22×#135×C472
C2×C47×#5502
C2×C47×#5482
C47×#32712
C2×C47×#4962
C2×C47×#4692
C2×C47×#4652
C2×C47×#4642
C2×C47×#4602
C2×C47×#4522
C2×C47×#4492
C2×C47×#4482
C2×C47×#4412
C2×C47×#4352
C2×#327147