Finite Group Databasebeta

← C47×#17597 #26057295

Subgroups — C47×#17597 #26057295

Order 12032.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3519C211yesmaximal, characteristic
2C47×#2974C211yesmaximal, characteristic, complemented
3C47×#2318C211yesmaximal, characteristic, complemented
4C47×#1521C211yesmaximal, characteristic, complemented
5C47×#1519C211yesmaximal, characteristic, complemented
6C47×#1517C211yesmaximal, characteristic, complemented
7C47×#1516C211yesmaximal, characteristic, complemented
8C47×#1514C211yesmaximal, characteristic, complemented
9C47×#1513C211yesmaximal, characteristic, complemented
10C47×#1512C211yesmaximal, characteristic, complemented
11C47×#1510C211yesmaximal, characteristic, complemented
12C47×#1507C211yesmaximal, characteristic, complemented
13C47×#1504C211yesmaximal, characteristic, complemented
14C47×#1501C211yesmaximal, characteristic, complemented
15C2×C47×#327C211yesmaximal, characteristic, complemented
16C47×#555C411yescharacteristic, complemented
17C47×#554C411yescharacteristic, complemented
18C47×#553—21no—
19C47×#553C411yescharacteristic, complemented
20C47×#553C411yescharacteristic, complemented
21C47×#550C411yescharacteristic, complemented
22C47×#546—21no—
23C47×#546—21no—
24C47×#546C411yescharacteristic, complemented
25C47×#546C411yescharacteristic, complemented
26D42×C47—21no—
27D42×C47C411yescharacteristic, complemented
28C47×#540—21no—
29C47×#538—21no—
30C47×#538—21no—
31C47×#532C2211yescharacteristic
32C47×#529C2211yescharacteristic
33C47×#525C2211yescharacteristic
34C47×#525C2211yescharacteristic
35C2×#121×C47C2211yescharacteristic
36C2×#121×C47C2211yescharacteristic
37C47×#518—21no—
38C2×C4×D4×C47C2211yescharacteristic
39C47×#436—21no—
40C47×#435—21no—
41C47×#435—21no—
42C8×D4×C47—21no—
43C47×#432C2211yescharacteristic, complemented
44C47×#431C2211yescharacteristic, complemented
45C47×#407C2211yescharacteristic, complemented
46C47×#407C2211yescharacteristic, complemented
47C2×C22⋊C8×C47C2211yescharacteristic, complemented
48C2×C22⋊C8×C47C2211yescharacteristic, complemented
49C47×#388—21no—
50C47×#387—21no—
51C47×#386—21no—
52C47×#385—21no—
53C47×#383C2211yescharacteristic, complemented
54C47×#382C2211yescharacteristic, complemented
55C47×#381C2211yescharacteristic, complemented
56C47×#380C2211yescharacteristic, complemented
57C4×C22⋊C4×C47C2211yescharacteristic, complemented
58C2×#95×C47C2211yescharacteristic, complemented
59C47×#328C2211yescharacteristic, complemented
60C47×#328C2211yescharacteristic, complemented
61C47×#328C2211yescharacteristic, complemented
62C47×#328C2211yescharacteristic, complemented
63C47×#327C2211yescharacteristic
64C47×#327C2211yescharacteristic
65C47×#327C2211yescharacteristic
66C47×#327C2211yescharacteristic
67C47×#327C2211yescharacteristic, complemented
68C47×#327C2211yescharacteristic, complemented
69C47×#327C2211yescharacteristic, complemented
70C47×#327C2211yescharacteristic, complemented
71C47×#327C2211yescharacteristic, complemented
72C47×#327C2211yescharacteristic, complemented
73C47×#327C2211yescharacteristic, complemented
74C47×#327C2211yescharacteristic, complemented
75C2×#41×C47—21no—
76C2×#41×C47C2×C411yescharacteristic
77C2×#41×C47C2×C411yescharacteristic, complemented
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47C2×C411yescharacteristic
82C22×D4×C47C2×C411yescharacteristic, complemented
83C22×D4×C47D411yescharacteristic
84C23×C4×C47—21no—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C4⋊Q8×C47C2×C411yescharacteristic, complemented
92#127×C47—21no—
93#127×C47C2×C411yescharacteristic, complemented
94#126×C47—21no—
95#126×C47—21no—
96#126×C47—21no—
97#125×C47—21no—
98#125×C47C2×C411yescharacteristic, complemented
99#124×C47—21no—
100#124×C47—21no—
101#124×C47—21no—
102#124×C47C2×C411yescharacteristic, complemented
103#123×C47—21no—
104#123×C47—21no—
105#123×C47—21no—
106#123×C47—21no—
107#123×C47—21no—
108#123×C47—21no—
109#123×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47C2×C411yescharacteristic
113C22⋊Q8×C47C2×C411yescharacteristic, complemented
114C22⋊Q8×C47C2311yescharacteristic
115#121×C47—21no—
116#121×C47—21no—
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47C2×C411yescharacteristic
129#121×C47C2×C411yescharacteristic
130#121×C47C2×C411yescharacteristic
131#121×C47C2×C411yescharacteristic, complemented
132#121×C47C2×C411yescharacteristic, complemented
133#121×C47C2×C411yescharacteristic, complemented
134#121×C47C2311yescharacteristic
135#121×C47C2311yescharacteristic
136#121×C47C2311yescharacteristic
137#120×C47—21no—
138#120×C47—21no—
139#120×C47—21no—
140#120×C47—21no—
141#120×C47—21no—
142#120×C47—21no—
143C4×Q8×C47C2×C411yescharacteristic, complemented
144C4×D4×C47—21no—
145C4×D4×C47—21no—
146C4×D4×C47—21no—
147C4×D4×C47—21no—
148C4×D4×C47—21no—
149C4×D4×C47—21no—
150C4×D4×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47—21no—
153C4×D4×C47—21no—
154C4×D4×C47C2×C411yescharacteristic
155C4×D4×C47C2×C411yescharacteristic
156C4×D4×C47C2×C411yescharacteristic
157C4×D4×C47C2×C411yescharacteristic
158C4×D4×C47C2×C411yescharacteristic, complemented
159C4×D4×C47C2×C411yescharacteristic, complemented
160C4×D4×C47C2×C411yescharacteristic, complemented
161C4×D4×C47D411yescharacteristic
162C4×D4×C47D411yescharacteristic
163C4×D4×C47D411yescharacteristic
164C4×D4×C47D411yescharacteristic
165#117×C47—21no—
166#117×C47—21no—
167#117×C47C2×C411yescharacteristic
168#117×C47C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2×C411yescharacteristic
172C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C47D411yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47D411yescharacteristic
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C42×C47—21no—
184C2×C42×C47C2311yescharacteristic
185C4⋊C8×C47—21no—
186C4⋊C8×C47—21no—
187C22⋊C8×C47—21no—
188C22⋊C8×C47—21no—
189C22⋊C8×C47—21no—
190C22⋊C8×C47—21no—
191C22⋊C8×C47C2311yescharacteristic
192C22⋊C8×C47C2311yescharacteristic
193C22⋊C8×C47C2311yescharacteristic
194C22⋊C8×C47C2311yescharacteristic
195#97×C47—21no—
196C4×C8×C47—21no—
197#95×C47—21no—
198#95×C47—21no—
199#95×C47—21no—
200#95×C47—21no—
201#95×C47—21no—
202#95×C47C2311yescharacteristic
203#95×C47C2311yescharacteristic
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47—21no—
208C24×C47C2×D411yescharacteristic
209C24×C47C2×D411yescharacteristic
210#41×C47—81no—
211#41×C47—81no—
212#41×C47—81no—
213#41×C47—81no—
214C2×Q8×C47—21no—
215C2×Q8×C47C22×C411yescharacteristic
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—42no—
232C2×D4×C47—44no—
233C2×D4×C47—81no—
234C2×D4×C47—81no—
235C2×D4×C47—81no—
236C2×D4×C47—81no—
237C2×D4×C47—81no—
238C2×D4×C47—81no—
239C2×D4×C47C22⋊C411yescharacteristic
240C2×D4×C47C22⋊C411yescharacteristic
241C2×D4×C47C22⋊C411yescharacteristic
242C2×D4×C47C22⋊C411yescharacteristic
243C2×D4×C47C22×C411yescharacteristic
244C2×D4×C47C22×C411yescharacteristic
245C2×D4×C47C22×C411yescharacteristic
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—42no—
258C22×C4×C47—81no—
259C22×C4×C47—81no—
260C22×C4×C47—81no—
261C22×C4×C47—81no—
262C22×C4×C47C22×C411yescharacteristic
263C22×C4×C47C22×C411yescharacteristic
264C22×C4×C47C22×C411yescharacteristic
265C22×C4×C47C22×C411yescharacteristic
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D411yescharacteristic
273C22×C4×C47C2×D411yescharacteristic
274C22×C4×C47C2411yescharacteristic
275M16×C47—81no—
276M16×C47—81no—
277C2×C8×C47—21no—
278C2×C8×C47—21no—
279C2×C8×C47—21no—
280C2×C8×C47—21no—
281C2×C8×C47—81no—
282C2×C8×C47—81no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47—81no—
293C4⋊C4×C47—81no—
294C4⋊C4×C47C22⋊C411yescharacteristic
295C4⋊C4×C47C22⋊C411yescharacteristic
296C4⋊C4×C47C22⋊C411yescharacteristic
297C4⋊C4×C47C22⋊C411yescharacteristic
298C4⋊C4×C47C22×C411yescharacteristic
299C4⋊C4×C47C22×C411yescharacteristic
300C4⋊C4×C47C22×C411yescharacteristic
301C4⋊C4×C47C22×C411yescharacteristic
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—21no—
312C22⋊C4×C47—21no—
313C22⋊C4×C47—21no—
314C22⋊C4×C47—21no—
315C22⋊C4×C47—21no—
316C22⋊C4×C47—21no—
317C22⋊C4×C47—21no—
318C22⋊C4×C47—21no—
319C22⋊C4×C47—21no—
320C22⋊C4×C47—21no—
321C22⋊C4×C47—42no—
322C22⋊C4×C47—81no—
323C22⋊C4×C47—81no—
324C22⋊C4×C47C22⋊C411yescharacteristic
325C22⋊C4×C47C22⋊C411yescharacteristic
326C22⋊C4×C47C22⋊C411yescharacteristic
327C22⋊C4×C47C22⋊C411yescharacteristic
328C22⋊C4×C47C22⋊C411yescharacteristic
329C22⋊C4×C47C22⋊C411yescharacteristic
330C22⋊C4×C47C22⋊C411yescharacteristic
331C22⋊C4×C47C22⋊C411yescharacteristic
332C42×C47—21no—
333C42×C47—21no—
334C42×C47—21no—
335C42×C47—81no—
336C42×C47C22×C411yescharacteristic
337C42×C47C22×C411yescharacteristic
338C42×C47C2×D411yescharacteristic
339C42×C47C2×D411yescharacteristic
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—22no—
343C23×C47—21no—
344C23×C47—21no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—21no—
348C23×C47—41no—
349C23×C47—41no—
350C23×C47—41no—
351C23×C47—42no—
352C23×C47—42no—
353C23×C47—81no—
354C23×C47—81no—
355C23×C47—81no—
356C23×C47—81no—
357C23×C47C2×C22⋊C411yescharacteristic
358C23×C47C2×C22⋊C411yescharacteristic
359C23×C47C2×C22⋊C411yescharacteristic
360C23×C47C2×C22⋊C411yescharacteristic
361C23×C47C22×D411yescharacteristic
362Q8×C47—41no—
363Q8×C47—81no—
364D4×C47—22no—
365D4×C47—22no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—42no—
372D4×C47—42no—
373D4×C47—41no—
374D4×C47—41no—
375D4×C47—41no—
376D4×C47—41no—
377D4×C47—41no—
378D4×C47—41no—
379D4×C47—42no—
380D4×C47—81no—
381D4×C47—81no—
382D4×C47—81no—
383D4×C47—81no—
384D4×C47—81no—
385D4×C47—81no—
386D4×C47—81no—
387D4×C47—81no—
388D4×C47—81no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—42no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—41no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47—41no—
421C2×C4×C47—81no—
422C2×C4×C47—81no—
423C2×C4×C47—81no—
424C2×C4×C47—81no—
425C2×C4×C47—81no—
426C2×C4×C47—81no—
427C2×C4×C47—84no—
428C2×C4×C47C2×C22⋊C411yescharacteristic
429C2×C4×C47C2×C22⋊C411yescharacteristic
430C2×C4×C47C2×C22⋊C411yescharacteristic
431C2×C4×C47C2×C22⋊C411yescharacteristic
432C2×C4×C47C2×C22⋊C411yescharacteristic
433C2×C4×C47C2×C22⋊C411yescharacteristic
434C2×C4×C47C2×C22⋊C411yescharacteristic
435C2×C4×C47C2×C22⋊C411yescharacteristic
436C2×C4×C47C23×C411yescharacteristic
437C2×C4×C47C22×D411yescharacteristic
438C8×C47—41no—
439C8×C47—41no—
440C8×C47—41no—
441C8×C47—41no—
442#17597C4711yesmaximal, characteristic, direct product factor, Sylow
443C22×C47—21no—
444C22×C47—21no—
445C22×C47—21no—
446C22×C47—21no—
447C22×C47—21no—
448C22×C47—21no—
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—42no—
457C22×C47—42no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47—41no—
462C22×C47—41no—
463C22×C47—41no—
464C22×C47—41no—
465C22×C47—41no—
466C22×C47—41no—
467C22×C47—81no—
468C22×C47—81no—
469C22×C47—162no—
470C22×C47—162no—
471C22×C47#42112yes—
472C22×C47C22×C22⋊C411yescharacteristic
473C22×C47#57611yescharacteristic
474C22×C47#57711yescharacteristic
475C4×C47—21no—
476C4×C47—21no—
477C4×C47—21no—
478C4×C47—21no—
479C4×C47—21no—
480C4×C47—21no—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—41no—
486C4×C47—41no—
487C4×C47—41no—
488C4×C47—41no—
489C4×C47—41no—
490C4×C47—81no—
491C4×C47—81no—
492C4×C47—81no—
493C4×C47—81no—
494#3519C2×C4711yescharacteristic
495#2974C2×C4711yescharacteristic, complemented
496#2318C2×C4711yescharacteristic, complemented
497#1521C2×C4711yescharacteristic, complemented
498#1519C2×C4711yescharacteristic, complemented
499#1517C2×C4711yescharacteristic, complemented
500#1516C2×C4711yescharacteristic, complemented
501#1514C2×C4711yescharacteristic, complemented
502#1513C2×C4711yescharacteristic, complemented
503#1512C2×C4711yescharacteristic, complemented
504#1510C2×C4711yescharacteristic, complemented
505#1507C2×C4711yescharacteristic, complemented
506#1504C2×C4711yescharacteristic, complemented
507#1501C2×C4711yescharacteristic, complemented
508C2×#327C2×C4711yescharacteristic, complemented
509C2×C47—21no—
510C2×C47—21no—
511C2×C47—22no—
512C2×C47—41no—
513C2×C47—41no—
514C2×C47—41no—
515C2×C47—81no—
516C2×C47—81no—
517C2×C47—81no—
518C2×C47#288311yescharacteristic
519C2×C47#289711yescharacteristic
520C2×C47C2×#42111yescharacteristic
521#555C4×C4711yescharacteristic, complemented
522#554C4×C4711yescharacteristic, complemented
523#553—21no—
524#553C4×C4711yescharacteristic, complemented
525#553C4×C4711yescharacteristic, complemented
526#550C4×C4711yescharacteristic, complemented
527#546—21no—
528#546—21no—
529#546C4×C4711yescharacteristic, complemented
530#546C4×C4711yescharacteristic, complemented
531D42—21no—
532D42C4×C4711yescharacteristic, complemented
533#540—21no—
534#538—21no—
535#538—21no—
536#532C22×C4711yescharacteristic
537#529C22×C4711yescharacteristic
538#525C22×C4711yescharacteristic
539#525C22×C4711yescharacteristic
540C2×#121C22×C4711yescharacteristic
541C2×#121C22×C4711yescharacteristic
542#518—21no—
543C2×C4×D4C22×C4711yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C22×C4711yescharacteristic, complemented
549#431C22×C4711yescharacteristic, complemented
550#407C22×C4711yescharacteristic, complemented
551#407C22×C4711yescharacteristic, complemented
552C2×C22⋊C8C22×C4711yescharacteristic, complemented
553C2×C22⋊C8C22×C4711yescharacteristic, complemented
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C22×C4711yescharacteristic, complemented
559#382C22×C4711yescharacteristic, complemented
560#381C22×C4711yescharacteristic, complemented
561#380C22×C4711yescharacteristic, complemented
562C4×C22⋊C4C22×C4711yescharacteristic, complemented
563C2×#95C22×C4711yescharacteristic, complemented
564#328C22×C4711yescharacteristic, complemented
565#328C22×C4711yescharacteristic, complemented
566#328C22×C4711yescharacteristic, complemented
567#328C22×C4711yescharacteristic, complemented
568#327C22×C4711yescharacteristic
569#327C22×C4711yescharacteristic
570#327C22×C4711yescharacteristic
571#327C22×C4711yescharacteristic
572#327C22×C4711yescharacteristic, complemented
573#327C22×C4711yescharacteristic, complemented
574#327C22×C4711yescharacteristic, complemented
575#327C22×C4711yescharacteristic, complemented
576#327C22×C4711yescharacteristic, complemented
577#327C22×C4711yescharacteristic, complemented
578#327C22×C4711yescharacteristic, complemented
579#327C22×C4711yescharacteristic, complemented
580C47#1759711yescharacteristic, direct product factor, Sylow
581C2×#41—21no—
582C2×#41C2×C4×C4711yescharacteristic
583C2×#41C2×C4×C4711yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×C4×C4711yescharacteristic
588C22×D4C2×C4×C4711yescharacteristic, complemented
589C22×D4D4×C4711yescharacteristic
590C23×C4—21no—
591C23×C4C23×C4711yescharacteristic
592C23×C4C23×C4711yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8C2×C4×C4711yescharacteristic, complemented
598#127—21no—
599#127C2×C4×C4711yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×C4×C4711yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×C4×C4711yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×C4×C4711yescharacteristic
619C22⋊Q8C2×C4×C4711yescharacteristic, complemented
620C22⋊Q8C23×C4711yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×C4×C4711yescharacteristic
635#121C2×C4×C4711yescharacteristic
636#121C2×C4×C4711yescharacteristic
637#121C2×C4×C4711yescharacteristic, complemented
638#121C2×C4×C4711yescharacteristic, complemented
639#121C2×C4×C4711yescharacteristic, complemented
640#121C23×C4711yescharacteristic
641#121C23×C4711yescharacteristic
642#121C23×C4711yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×C4×C4711yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×C4×C4711yescharacteristic
661C4×D4C2×C4×C4711yescharacteristic
662C4×D4C2×C4×C4711yescharacteristic
663C4×D4C2×C4×C4711yescharacteristic
664C4×D4C2×C4×C4711yescharacteristic, complemented
665C4×D4C2×C4×C4711yescharacteristic, complemented
666C4×D4C2×C4×C4711yescharacteristic, complemented
667C4×D4D4×C4711yescharacteristic
668C4×D4D4×C4711yescharacteristic
669C4×D4D4×C4711yescharacteristic
670C4×D4D4×C4711yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×C4×C4711yescharacteristic
674#117C2×C4×C4711yescharacteristic, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C2×C4×C4711yescharacteristic
678C2×C4⋊C4C2×C4×C4711yescharacteristic, complemented
679C2×C4⋊C4D4×C4711yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4D4×C4711yescharacteristic
688C2×C22⋊C4D4×C4711yescharacteristic
689C2×C42—21no—
690C2×C42C23×C4711yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C23×C4711yescharacteristic
698C22⋊C8C23×C4711yescharacteristic
699C22⋊C8C23×C4711yescharacteristic
700C22⋊C8C23×C4711yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C23×C4711yescharacteristic
709#95C23×C4711yescharacteristic
710#95C23×C4711yescharacteristic
711#95C23×C4711yescharacteristic
712C24—21no—
713C24—21no—
714C24C2×D4×C4711yescharacteristic
715C24C2×D4×C4711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C4711yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C4711yescharacteristic
746C2×D4C22⋊C4×C4711yescharacteristic
747C2×D4C22⋊C4×C4711yescharacteristic
748C2×D4C22⋊C4×C4711yescharacteristic
749C2×D4C22×C4×C4711yescharacteristic
750C2×D4C22×C4×C4711yescharacteristic
751C2×D4C22×C4×C4711yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C4711yescharacteristic
769C22×C4C22×C4×C4711yescharacteristic
770C22×C4C22×C4×C4711yescharacteristic
771C22×C4C22×C4×C4711yescharacteristic
772C22×C4C2×D4×C4711yescharacteristic
773C22×C4C2×D4×C4711yescharacteristic
774C22×C4C2×D4×C4711yescharacteristic
775C22×C4C2×D4×C4711yescharacteristic
776C22×C4C2×D4×C4711yescharacteristic
777C22×C4C2×D4×C4711yescharacteristic
778C22×C4C2×D4×C4711yescharacteristic
779C22×C4C2×D4×C4711yescharacteristic
780C22×C4C24×C4711yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C4711yescharacteristic
801C4⋊C4C22⋊C4×C4711yescharacteristic
802C4⋊C4C22⋊C4×C4711yescharacteristic
803C4⋊C4C22⋊C4×C4711yescharacteristic
804C4⋊C4C22×C4×C4711yescharacteristic
805C4⋊C4C22×C4×C4711yescharacteristic
806C4⋊C4C22×C4×C4711yescharacteristic
807C4⋊C4C22×C4×C4711yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C4711yescharacteristic
831C22⋊C4C22⋊C4×C4711yescharacteristic
832C22⋊C4C22⋊C4×C4711yescharacteristic
833C22⋊C4C22⋊C4×C4711yescharacteristic
834C22⋊C4C22⋊C4×C4711yescharacteristic
835C22⋊C4C22⋊C4×C4711yescharacteristic
836C22⋊C4C22⋊C4×C4711yescharacteristic
837C22⋊C4C22⋊C4×C4711yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C4711yescharacteristic
843C42C22×C4×C4711yescharacteristic
844C42C2×D4×C4711yescharacteristic
845C42C2×D4×C4711yescharacteristic
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C4711yescharacteristic
864C23C2×C22⋊C4×C4711yescharacteristic
865C23C2×C22⋊C4×C4711yescharacteristic
866C23C2×C22⋊C4×C4711yescharacteristic
867C23C22×D4×C4711yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—42no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C4711yescharacteristic
935C2×C4C2×C22⋊C4×C4711yescharacteristic
936C2×C4C2×C22⋊C4×C4711yescharacteristic
937C2×C4C2×C22⋊C4×C4711yescharacteristic
938C2×C4C2×C22⋊C4×C4711yescharacteristic
939C2×C4C2×C22⋊C4×C4711yescharacteristic
940C2×C4C2×C22⋊C4×C4711yescharacteristic
941C2×C4C2×C22⋊C4×C4711yescharacteristic
942C2×C4C23×C4×C4711yescharacteristic
943C2×C4C22×D4×C4711yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C47×#42112yes—
977C22C22×C22⋊C4×C4711yescharacteristic
978C22C47×#57611yescharacteristic
979C22C47×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C47×#288311yescharacteristic
1009C2C47×#289711yescharacteristic
1010C2C2×C47×#42111yescharacteristic
subgroupG/H
center, socleC22×C47C22×C22⋊C4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2974C2semidirect
3. C47×#2318C2semidirect
4. C47×#1521C2semidirect
5. C47×#1519C2semidirect
6. C47×#1517C2semidirect
7. C47×#1516C2semidirect
8. C47×#1514C2semidirect
9. C47×#1513C2semidirect
10. C47×#1512C2semidirect
11. C47×#1510C2semidirect
12. C47×#1507C2semidirect
13. C47×#1504C2semidirect
14. C47×#1501C2semidirect
15. C2×C47×#327C2semidirect
16. C47×#555C4semidirect
17. C47×#554C4semidirect
19. C47×#553C4semidirect
20. C47×#553C4semidirect
21. C47×#550C4semidirect
24. C47×#546C4semidirect
25. C47×#546C4semidirect
27. D42×C47C4semidirect
43. C47×#432C22semidirect
44. C47×#431C22semidirect
45. C47×#407C22semidirect
46. C47×#407C22semidirect
47. C2×C22⋊C8×C47C22semidirect
48. C2×C22⋊C8×C47C22semidirect
53. C47×#383C22semidirect
54. C47×#382C22semidirect
55. C47×#381C22semidirect
56. C47×#380C22semidirect
57. C4×C22⋊C4×C47C22semidirect
58. C2×#95×C47C22semidirect
59. C47×#328C22semidirect
60. C47×#328C22semidirect
61. C47×#328C22semidirect
62. C47×#328C22semidirect
67. C47×#327C22semidirect
68. C47×#327C22semidirect
69. C47×#327C22semidirect
70. C47×#327C22semidirect
71. C47×#327C22semidirect
72. C47×#327C22semidirect
73. C47×#327C22semidirect
74. C47×#327C22semidirect
77. C2×#41×C47C2×C4semidirect
82. C22×D4×C47C2×C4semidirect
91. C4⋊Q8×C47C2×C4semidirect
93. #127×C47C2×C4semidirect
98. #125×C47C2×C4semidirect
102. #124×C47C2×C4semidirect
113. C22⋊Q8×C47C2×C4semidirect
131. #121×C47C2×C4semidirect
132. #121×C47C2×C4semidirect
133. #121×C47C2×C4semidirect
143. C4×Q8×C47C2×C4semidirect
158. C4×D4×C47C2×C4semidirect
159. C4×D4×C47C2×C4semidirect
160. C4×D4×C47C2×C4semidirect
168. #117×C47C2×C4semidirect
172. C2×C4⋊C4×C47C2×C4semidirect
442. #17597C47direct (N × H)
495. #2974C2×C47semidirect
496. #2318C2×C47semidirect
497. #1521C2×C47semidirect
498. #1519C2×C47semidirect
499. #1517C2×C47semidirect
500. #1516C2×C47semidirect
501. #1514C2×C47semidirect
502. #1513C2×C47semidirect
503. #1512C2×C47semidirect
504. #1510C2×C47semidirect
505. #1507C2×C47semidirect
506. #1504C2×C47semidirect
507. #1501C2×C47semidirect
508. C2×#327C2×C47semidirect
521. #555C4×C47semidirect
522. #554C4×C47semidirect
524. #553C4×C47semidirect
525. #553C4×C47semidirect
526. #550C4×C47semidirect
529. #546C4×C47semidirect
530. #546C4×C47semidirect
532. D42C4×C47semidirect
548. #432C22×C47semidirect
549. #431C22×C47semidirect
550. #407C22×C47semidirect
551. #407C22×C47semidirect
552. C2×C22⋊C8C22×C47semidirect
553. C2×C22⋊C8C22×C47semidirect
558. #383C22×C47semidirect
559. #382C22×C47semidirect
560. #381C22×C47semidirect
561. #380C22×C47semidirect
562. C4×C22⋊C4C22×C47semidirect
563. C2×#95C22×C47semidirect
564. #328C22×C47semidirect
565. #328C22×C47semidirect
566. #328C22×C47semidirect
567. #328C22×C47semidirect
572. #327C22×C47semidirect
573. #327C22×C47semidirect
574. #327C22×C47semidirect
575. #327C22×C47semidirect
576. #327C22×C47semidirect
577. #327C22×C47semidirect
578. #327C22×C47semidirect
579. #327C22×C47semidirect
580. C47#17597direct (N × H)
583. C2×#41C2×C4×C47semidirect
588. C22×D4C2×C4×C47semidirect
597. C4⋊Q8C2×C4×C47semidirect
599. #127C2×C4×C47semidirect
604. #125C2×C4×C47semidirect
608. #124C2×C4×C47semidirect
619. C22⋊Q8C2×C4×C47semidirect
637. #121C2×C4×C47semidirect
638. #121C2×C4×C47semidirect
639. #121C2×C4×C47semidirect
649. C4×Q8C2×C4×C47semidirect
664. C4×D4C2×C4×C47semidirect
665. C4×D4C2×C4×C47semidirect
666. C4×D4C2×C4×C47semidirect
674. #117C2×C4×C47semidirect
678. C2×C4⋊C4C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35192
C47×#29742
C47×#23182
C47×#15212
C47×#15192
C47×#15172
C47×#15162
C47×#15142
C47×#15132
C47×#15122
C47×#15102
C47×#15072
C47×#15042
C47×#15012
C2×C47×#3272
#1759747