Finite Group Databasebeta

← C47×#26926 #26066624

Subgroups — C47×#26926 #26066624

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#480C211yesmaximal, characteristic, complemented
2C2×C47×#459C211yesmaximal, characteristic, complemented
3C47×#2428C211yesmaximal, characteristic, complemented
4C47×#2361C211yesmaximal, characteristic, complemented
5C47×#2086C211yesmaximal, characteristic, complemented
6C47×#2041C211yesmaximal, characteristic, complemented
7C47×#1999C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1970C211yesmaximal, characteristic, complemented
10C47×#1925C211yesmaximal, characteristic, complemented
11C47×#1923C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1874C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×#127×C47C2211yescharacteristic
19C2×#121×C47—21no—
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×#121×C47C2211yescharacteristic
23C2×C4×D4×C47—21no—
24C2×C4×D4×C47C2211yescharacteristic
25C2×C4×D4×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C47×#480—24no—
28C47×#459—24no—
29C2×#107×C47C2211yescharacteristic
30C2×#107×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×C22⋊C8×C47C2211yescharacteristic
41C2×C22⋊C8×C47C2211yescharacteristic
42C2×C4×C8×C47C2211yescharacteristic
43C47×#394—21no—
44C47×#392—21no—
45C47×#390C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#388—21no—
50C47×#386—21no—
51C47×#386—21no—
52C47×#385—21no—
53C4×C4⋊C4×C47C2211yescharacteristic
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C23×C4×C47—21no—
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47C2311yescharacteristic
73C2×D8×C47—22no—
74C2×D8×C47—22no—
75C2×D8×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—41no—
78C2×D8×C47—41no—
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83#127×C47—22no—
84#127×C47—41no—
85#121×C47—22no—
86#121×C47—22no—
87#121×C47—22no—
88#121×C47—22no—
89#121×C47—41no—
90#121×C47—41no—
91#121×C47—44no—
92C4×D4×C47—22no—
93C4×D4×C47—22no—
94C4×D4×C47—41no—
95C4×D4×C47—41no—
96C4×D4×C47—44no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—41no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47D411yescharacteristic
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C42×C47—21no—
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#107×C47—22no—
122#107×C47—22no—
123C4⋊C8×C47—22no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—22no—
129#102×C47—41no—
130#102×C47—41no—
131#102×C47D414yescomplemented
132C22⋊C8×C47—22no—
133C22⋊C8×C47—41no—
134C4×C8×C47—41no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47D411yescharacteristic
139#95×C47D411yescharacteristic
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47C2×D411yescharacteristic
144C2×D4×C47—24no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—42no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—81no—
172C2×D4×C47—81no—
173C2×D4×C47—81no—
174C2×D4×C47—81no—
175C2×D4×C47C2×D412yes—
176C2×D4×C47#4112yes—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—42no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47—42no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—81no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203D8×C47—44no—
204D8×C47—44no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47C2×D412yes—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—42no—
225C4⋊C4×C47—42no—
226C4⋊C4×C47—42no—
227C4⋊C4×C47C2×D412yes—
228C4⋊C4×C47#4112yes—
229C4⋊C4×C47#4112yes—
230C22⋊C4×C47—24no—
231C22⋊C4×C47—41no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—81no—
239C22⋊C4×C47—81no—
240C22⋊C4×C47D814yescomplemented
241C42×C47—21no—
242C42×C47—21no—
243C42×C47—21no—
244C42×C47—21no—
245C42×C47—42no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47C2×D812yes—
274C23×C47C22×D411yescharacteristic
275D4×C47—22no—
276D4×C47—22no—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—48no—
280D4×C47—41no—
281D4×C47—41no—
282D4×C47—41no—
283D4×C47—41no—
284D4×C47—41no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—84no—
289D4×C47—84no—
290D4×C47—84no—
291D4×C47—84no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—21no—
302C2×C4×C47—22no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—84no—
325C2×C4×C47—84no—
326C2×C4×C47—84no—
327C2×C4×C47C2×D812yes—
328C2×C4×C47C2×D812yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C8×C47—22no—
336C8×C47—41no—
337C8×C47—41no—
338C8×C47—41no—
339#26926C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—81no—
359C22×C47—81no—
360C22×C47—81no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47#52511yescharacteristic
369C22×C47D4211yescharacteristic
370C22×C47#54611yescharacteristic
371C22×C47C22×D811yescharacteristic
372C22×C47#57511yescharacteristic
373C22×C47#57611yescharacteristic
374C22×C47#57711yescharacteristic
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—42no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—41no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47#53211yescharacteristic
386C4×C47#54011yescharacteristic
387C4×C47#54611yescharacteristic
388C4×C47#55311yescharacteristic
389C2×#480C2×C4711yescharacteristic, complemented
390C2×#459C2×C4711yescharacteristic, complemented
391#2428C2×C4711yescharacteristic, complemented
392#2361C2×C4711yescharacteristic, complemented
393#2086C2×C4711yescharacteristic, complemented
394#2041C2×C4711yescharacteristic, complemented
395#1999C2×C4711yescharacteristic, complemented
396#1999C2×C4711yescharacteristic, complemented
397#1970C2×C4711yescharacteristic, complemented
398#1925C2×C4711yescharacteristic, complemented
399#1923C2×C4711yescharacteristic, complemented
400#1879C2×C4711yescharacteristic, complemented
401#1874C2×C4711yescharacteristic, complemented
402#1862C2×C4711yescharacteristic, complemented
403C4×#102C2×C4711yescharacteristic, complemented
404C2×C47—42no—
405C2×C47—82no—
406C2×C47—82no—
407C2×C47—161no—
408C2×C47#246411yescharacteristic
409C2×C47#310011yescharacteristic
410C2×C47#311911yescharacteristic
411C2×C47#327511yescharacteristic
412C2×C47D4×D811yescharacteristic
413C2×C47#329411yescharacteristic
414C2×C47#330911yescharacteristic
415C22×D8C22×C4711yescharacteristic
416C22×D8C22×C4711yescharacteristic
417C2×#127C22×C4711yescharacteristic
418C2×#121—21no—
419C2×#121C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×#121C22×C4711yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4C22×C4711yescharacteristic
424C2×C4×D4C22×C4711yescharacteristic
425C22×C4⋊C4C22×C4711yescharacteristic
426#480—24no—
427#459—24no—
428C2×#107C22×C4711yescharacteristic
429C2×#107C22×C4711yescharacteristic
430C2×C4⋊C8C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432C2×#102C22×C4711yescharacteristic
433C2×#102C22×C4711yescharacteristic
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×#102C22×C4711yescharacteristic
437C2×#102C22×C4711yescharacteristic
438C2×#102C22×C4711yescharacteristic
439C2×C22⋊C8C22×C4711yescharacteristic
440C2×C22⋊C8C22×C4711yescharacteristic
441C2×C4×C8C22×C4711yescharacteristic
442#394—21no—
443#392—21no—
444#390C22×C4711yescharacteristic
445#390C22×C4711yescharacteristic
446#389C22×C4711yescharacteristic
447#389C22×C4711yescharacteristic
448#388—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452C4×C4⋊C4C22×C4711yescharacteristic
453C4×C22⋊C4C22×C4711yescharacteristic
454#340C22×C4711yescharacteristic
455#340C22×C4711yescharacteristic
456#340C22×C4711yescharacteristic
457#340C22×C4711yescharacteristic
458#336C22×C4711yescharacteristic
459#336C22×C4711yescharacteristic
460C47#2692611yescharacteristic, direct product factor, Sylow
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C4711yescharacteristic
467C22×D4C23×C4711yescharacteristic
468C22×D4C23×C4711yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C4711yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C22×C8C23×C4711yescharacteristic
480C22×C8C23×C4711yescharacteristic
481C22×C8C23×C4711yescharacteristic
482C22×C8C23×C4711yescharacteristic
483#127—22no—
484#127—41no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#121—44no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C4×D4—44no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C4711yescharacteristic
503C2×C4⋊C4C23×C4711yescharacteristic
504C2×C4⋊C4C23×C4711yescharacteristic
505C2×C4⋊C4C23×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C4711yescharacteristic
517C2×C22⋊C4D4×C4711yescharacteristic
518C2×C42—21no—
519C2×C42C23×C4711yescharacteristic
520C2×C42C23×C4711yescharacteristic
521#107—22no—
522#107—22no—
523C4⋊C8—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—41no—
530#102—41no—
531#102D4×C4714yescomplemented
532C22⋊C8—22no—
533C22⋊C8—41no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95D4×C4711yescharacteristic
539#95D4×C4711yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24C2×D4×C4711yescharacteristic
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C2×D4×C4712yes—
576C2×D4#41×C4712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C22×C4C2×D4×C4711yescharacteristic
600C22×C4C2×D4×C4711yescharacteristic
601C22×C4C2×D4×C4711yescharacteristic
602C22×C4C24×C4711yescharacteristic
603D8—44no—
604D8—44no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8C2×D4×C4712yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C4712yes—
628C4⋊C4#41×C4712yes—
629C4⋊C4#41×C4712yes—
630C22⋊C4—24no—
631C22⋊C4—41no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4D8×C4714yescomplemented
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23C2×D8×C4712yes—
674C23C22×D4×C4711yescharacteristic
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—48no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×D8×C4712yes—
728C2×C4C2×D8×C4712yes—
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C2×#41×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4C2×#41×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C2×C4H(5,𝔽2)×C4711yescharacteristic
735C8—22no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C47×#52511yescharacteristic
768C22D42×C4711yescharacteristic
769C22C47×#54611yescharacteristic
770C22C22×D8×C4711yescharacteristic
771C22C47×#57511yescharacteristic
772C22C47×#57611yescharacteristic
773C22C47×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—41no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4C47×#53211yescharacteristic
785C4C47×#54011yescharacteristic
786C4C47×#54611yescharacteristic
787C4C47×#55311yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C47×#246411yescharacteristic
793C2C47×#310011yescharacteristic
794C2C47×#311911yescharacteristic
795C2C47×#327511yescharacteristic
796C2D4×D8×C4711yescharacteristic
797C2C47×#329411yescharacteristic
798C2C47×#330911yescharacteristic
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. C2×C47×#480C2semidirect
2. C2×C47×#459C2semidirect
3. C47×#2428C2semidirect
4. C47×#2361C2semidirect
5. C47×#2086C2semidirect
6. C47×#2041C2semidirect
7. C47×#1999C2semidirect
8. C47×#1999C2semidirect
9. C47×#1970C2semidirect
10. C47×#1925C2semidirect
11. C47×#1923C2semidirect
12. C47×#1879C2semidirect
13. C47×#1874C2semidirect
14. C47×#1862C2semidirect
15. C4×#102×C47C2semidirect
131. #102×C47D4semidirect
240. C22⋊C4×C47D8semidirect
339. #26926C47direct (N × H)
389. C2×#480C2×C47semidirect
390. C2×#459C2×C47semidirect
391. #2428C2×C47semidirect
392. #2361C2×C47semidirect
393. #2086C2×C47semidirect
394. #2041C2×C47semidirect
395. #1999C2×C47semidirect
396. #1999C2×C47semidirect
397. #1970C2×C47semidirect
398. #1925C2×C47semidirect
399. #1923C2×C47semidirect
400. #1879C2×C47semidirect
401. #1874C2×C47semidirect
402. #1862C2×C47semidirect
403. C4×#102C2×C47semidirect
460. C47#26926direct (N × H)
531. #102D4×C47semidirect
640. C22⋊C4D8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4802
C2×C47×#4592
C47×#24282
C47×#23612
C47×#20862
C47×#20412
C47×#19992
C47×#19702
C47×#19252
C47×#19232
C47×#18792
C47×#18742
C47×#18622
C4×#102×C472
#2692647