Finite Group Databasebeta

← C47×#22056 #26061754

Subgroups — C47×#22056 #26061754

Order 12032.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#447C211yesmaximal, characteristic
2C47×#2324C211yesmaximal, characteristic, complemented
3C47×#2309C211yesmaximal, characteristic, complemented
4C47×#1972C211yesmaximal, characteristic, complemented
5C47×#1970C211yesmaximal, characteristic, complemented
6C47×#1936C211yesmaximal, characteristic, complemented
7C47×#1934C211yesmaximal, characteristic, complemented
8C47×#1926C211yesmaximal, characteristic, complemented
9C47×#1925C211yesmaximal, characteristic, complemented
10C47×#1879C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C47×#1786C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic, complemented
21C2×#117×C47C2211yescharacteristic
22C2×#117×C47C2211yescharacteristic
23C47×#447C418yescomplemented
24C2×#107×C47C2211yescharacteristic, complemented
25C2×#106×C47C2211yescharacteristic, complemented
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#102×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic, complemented
33C2×#102×C47C2211yescharacteristic, complemented
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×#97×C47C2211yescharacteristic, complemented
37C2×C4×C8×C47C2211yescharacteristic, complemented
38C47×#390—21no—
39C47×#390—21no—
40C47×#390—21no—
41C47×#390C2211yescharacteristic
42C47×#390C2211yescharacteristic
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#390C2211yescharacteristic, complemented
46C47×#389C2211yescharacteristic, complemented
47C47×#388—21no—
48C47×#386—21no—
49C47×#385—21no—
50C47×#380C2211yescharacteristic
51C47×#379—21no—
52C47×#379—21no—
53C4×C4⋊C4×C47C2211yescharacteristic, complemented
54C47×#340C2211yescharacteristic, complemented
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#336C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C25×C47—21no—
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47—22no—
64C22×D4×C47—41no—
65C22×D4×C47—41no—
66C22×D4×C47—41no—
67C22×D4×C47—41no—
68C22×D4×C47C2×C414yescomplemented
69C22×D4×C47C2311yescharacteristic
70C22×D4×C47C2311yescharacteristic
71C22×D4×C47C2311yescharacteristic
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74C2×D8×C47—41no—
75C2×D8×C47—41no—
76C2×D8×C47—41no—
77C2×D8×C47—41no—
78C2×D8×C47C2×C414yes—
79C2×D8×C47C2×C414yes—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84#121×C47—22no—
85#121×C47C2×C414yes—
86C4×D4×C47—41no—
87C4×D4×C47—41no—
88#117×C47—41no—
89#117×C47—41no—
90#117×C47—41no—
91#117×C47—41no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47D411yescharacteristic
94C2×C4⋊C4×C47D411yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
115C2×C22⋊C4×C47D411yescharacteristic
116C2×C42×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120#107×C47—41no—
121#106×C47—41no—
122#102×C47—41no—
123#102×C47—41no—
124#102×C47—41no—
125#102×C47—41no—
126#102×C47—41no—
127#102×C47—41no—
128#102×C47C2×C414yescomplemented
129#102×C47C2×C414yescomplemented
130C22⋊C8×C47—22no—
131C22⋊C8×C47C2×C414yescomplemented
132#97×C47—41no—
133C4×C8×C47—41no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137C24×C47—21no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—24no—
141C24×C47—42no—
142C24×C47—42no—
143C24×C47—81no—
144C24×C47—81no—
145C24×C47—81no—
146C24×C47—81no—
147C24×C47C2×D411yescharacteristic
148C2×D4×C47—24no—
149C2×D4×C47—24no—
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—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—44no—
166C2×D4×C47—44no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—44no—
170C2×D4×C47—44no—
171C2×D4×C47—81no—
172C2×D4×C47—81no—
173C2×D4×C47C22×C412yes—
174C2×D4×C47C22×C412yes—
175C2×D4×C47C22×C412yes—
176C22×C4×C47—21no—
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—42no—
186C22×C4×C47—81no—
187C22×C4×C47—81no—
188C22×C4×C47C22×C412yes—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47#4112yes—
195C22×C4×C47C2411yescharacteristic
196D8×C47—44no—
197D8×C47—44no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47C22×C412yes—
209C2×C8×C47C22×C412yes—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—41no—
220C4⋊C4×C47—41no—
221C4⋊C4×C47—81no—
222C4⋊C4×C47C22×C412yes—
223C22⋊C4×C47—24no—
224C22⋊C4×C47—41no—
225C22⋊C4×C47—41no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—81no—
229C22⋊C4×C47—81no—
230C22⋊C4×C47—81no—
231C22⋊C4×C47—81no—
232C22⋊C4×C47—81no—
233C22⋊C4×C47—81no—
234C22⋊C4×C47—81no—
235C22⋊C4×C47—81no—
236C22⋊C4×C47—81no—
237C22⋊C4×C47—81no—
238C22⋊C4×C47—81no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47—21no—
243C42×C47—42no—
244C42×C47—81no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—48no—
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×C47—84no—
274C23×C47—84no—
275C23×C47—84no—
276C23×C47—84no—
277C23×C47—84no—
278C23×C47—84no—
279C23×C47C4×D412yes—
280C23×C47C22×D411yescharacteristic
281D4×C47—22no—
282D4×C47—22no—
283D4×C47—22no—
284D4×C47—22no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—48no—
288D4×C47—41no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—84no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
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—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—84no—
329C2×C4×C47C4×D412yes—
330C2×C4×C47C23×C411yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47H(5,𝔽2)11yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C2×C4×C47H(5,𝔽2)11yescharacteristic
336C8×C47—22no—
337C8×C47—22no—
338C8×C47—41no—
339C8×C47—41no—
340#22056C4711yesmaximal, characteristic, direct product factor, Sylow
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—816no—
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—81no—
369C22×C47—81no—
370C22×C47C2×C4×D411yescharacteristic
371C22×C47#53411yescharacteristic
372C22×C47#53511yescharacteristic
373C22×C47#57611yescharacteristic
374C22×C47#57611yescharacteristic
375C22×C47#57611yescharacteristic
376C22×C47#57711yescharacteristic
377C4×C47—22no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—41no—
382C4×C47—42no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47—81no—
386C4×C47—81no—
387C4×C47#51811yescharacteristic
388C4×C47#51811yescharacteristic
389C4×C47#53811yescharacteristic
390C4×C47#53811yescharacteristic
391C2×#447C2×C4711yescharacteristic
392#2324C2×C4711yescharacteristic, complemented
393#2309C2×C4711yescharacteristic, complemented
394#1972C2×C4711yescharacteristic, complemented
395#1970C2×C4711yescharacteristic, complemented
396#1936C2×C4711yescharacteristic, complemented
397#1934C2×C4711yescharacteristic, complemented
398#1926C2×C4711yescharacteristic, complemented
399#1925C2×C4711yescharacteristic, complemented
400#1879C2×C4711yescharacteristic, complemented
401#1879C2×C4711yescharacteristic, complemented
402#1875C2×C4711yescharacteristic, complemented
403#1854C2×C4711yescharacteristic, complemented
404#1786C2×C4711yescharacteristic, complemented
405#1750C2×C4711yescharacteristic, complemented
406C2×C47—42no—
407C2×C47—82no—
408C2×C47—82no—
409C2×C47—82no—
410C2×C47#232111yescharacteristic
411C2×C47#294611yescharacteristic
412C2×C47#294811yescharacteristic
413C2×C47#319811yescharacteristic
414C2×C47#319911yescharacteristic
415C2×C47#322011yescharacteristic
416C2×C47#322411yescharacteristic
417C23×D4C22×C4711yescharacteristic
418C22×D8C22×C4711yescharacteristic
419C22×D8C22×C4711yescharacteristic
420C2×#121C22×C4711yescharacteristic
421C2×C4×D4C22×C4711yescharacteristic, complemented
422C2×#117C22×C4711yescharacteristic
423C2×#117C22×C4711yescharacteristic
424#447C4×C4718yescomplemented
425C2×#107C22×C4711yescharacteristic, complemented
426C2×#106C22×C4711yescharacteristic, complemented
427C2×#102C22×C4711yescharacteristic
428C2×#102C22×C4711yescharacteristic
429C2×#102C22×C4711yescharacteristic
430C2×#102C22×C4711yescharacteristic
431C2×#102C22×C4711yescharacteristic
432C2×#102C22×C4711yescharacteristic
433C2×#102C22×C4711yescharacteristic, complemented
434C2×#102C22×C4711yescharacteristic, complemented
435C2×C22⋊C8C22×C4711yescharacteristic
436C2×C22⋊C8C22×C4711yescharacteristic
437C2×#97C22×C4711yescharacteristic, complemented
438C2×C4×C8C22×C4711yescharacteristic, complemented
439#390—21no—
440#390—21no—
441#390—21no—
442#390C22×C4711yescharacteristic
443#390C22×C4711yescharacteristic
444#390C22×C4711yescharacteristic
445#390C22×C4711yescharacteristic
446#390C22×C4711yescharacteristic, complemented
447#389C22×C4711yescharacteristic, complemented
448#388—21no—
449#386—21no—
450#385—21no—
451#380C22×C4711yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4C22×C4711yescharacteristic, complemented
455#340C22×C4711yescharacteristic, complemented
456#340C22×C4711yescharacteristic, complemented
457#340C22×C4711yescharacteristic, complemented
458#340C22×C4711yescharacteristic, complemented
459#336C22×C4711yescharacteristic, complemented
460#336C22×C4711yescharacteristic, complemented
461C47#2205611yescharacteristic, direct product factor, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C4714yescomplemented
471C22×D4C23×C4711yescharacteristic
472C22×D4C23×C4711yescharacteristic
473C22×D4C23×C4711yescharacteristic
474C23×C4—21no—
475C23×C4C23×C4711yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C4714yes—
481C2×D8C2×C4×C4714yes—
482C22×C8C23×C4711yescharacteristic
483C22×C8C23×C4711yescharacteristic
484C22×C8C23×C4711yescharacteristic
485C22×C8C23×C4711yescharacteristic
486#121—22no—
487#121C2×C4×C4714yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C4711yescharacteristic
496C2×C4⋊C4D4×C4711yescharacteristic
497C2×C4⋊C4C23×C4711yescharacteristic
498C2×C4⋊C4C23×C4711yescharacteristic
499C2×C4⋊C4C23×C4711yescharacteristic
500C2×C4⋊C4C23×C4711yescharacteristic
501C2×C4⋊C4C23×C4711yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
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×C42—21no—
520C2×C42C23×C4711yescharacteristic
521C2×C42C23×C4711yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C4714yescomplemented
531#102C2×C4×C4714yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C4714yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C4711yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
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—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C4712yes—
576C2×D4C22×C4×C4712yes—
577C2×D4C22×C4×C4712yes—
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—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C4712yes—
591C22×C4C2×D4×C4711yescharacteristic
592C22×C4C2×D4×C4711yescharacteristic
593C22×C4C2×D4×C4711yescharacteristic
594C22×C4C2×D4×C4711yescharacteristic
595C22×C4C2×D4×C4711yescharacteristic
596C22×C4#41×C4712yes—
597C22×C4C24×C4711yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C4712yes—
611C2×C8C22×C4×C4712yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C4712yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
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—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C4712yes—
682C23C22×D4×C4711yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
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—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C4712yes—
732C2×C4C23×C4×C4711yescharacteristic
733C2×C4C2×#41×C4711yescharacteristic
734C2×C4H(5,𝔽2)×C4711yescharacteristic
735C2×C4H(5,𝔽2)×C4711yescharacteristic
736C2×C4H(5,𝔽2)×C4711yescharacteristic
737C2×C4H(5,𝔽2)×C4711yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C4711yescharacteristic
772C22C47×#53411yescharacteristic
773C22C47×#53511yescharacteristic
774C22C47×#57611yescharacteristic
775C22C47×#57611yescharacteristic
776C22C47×#57611yescharacteristic
777C22C47×#57711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4C47×#51811yescharacteristic
789C4C47×#51811yescharacteristic
790C4C47×#53811yescharacteristic
791C4C47×#53811yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C47×#232111yescharacteristic
797C2C47×#294611yescharacteristic
798C2C47×#294811yescharacteristic
799C2C47×#319811yescharacteristic
800C2C47×#319911yescharacteristic
801C2C47×#322011yescharacteristic
802C2C47×#322411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2324C2semidirect
3. C47×#2309C2semidirect
4. C47×#1972C2semidirect
5. C47×#1970C2semidirect
6. C47×#1936C2semidirect
7. C47×#1934C2semidirect
8. C47×#1926C2semidirect
9. C47×#1925C2semidirect
10. C47×#1879C2semidirect
11. C47×#1879C2semidirect
12. C47×#1875C2semidirect
13. C47×#1854C2semidirect
14. C47×#1786C2semidirect
15. C47×#1750C2semidirect
20. C2×C4×D4×C47C22semidirect
23. C47×#447C4semidirect
24. C2×#107×C47C22semidirect
25. C2×#106×C47C22semidirect
32. C2×#102×C47C22semidirect
33. C2×#102×C47C22semidirect
36. C2×#97×C47C22semidirect
37. C2×C4×C8×C47C22semidirect
45. C47×#390C22semidirect
46. C47×#389C22semidirect
53. C4×C4⋊C4×C47C22semidirect
54. C47×#340C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#336C22semidirect
59. C47×#336C22semidirect
68. C22×D4×C47C2×C4semidirect
128. #102×C47C2×C4semidirect
129. #102×C47C2×C4semidirect
131. C22⋊C8×C47C2×C4semidirect
340. #22056C47direct (N × H)
392. #2324C2×C47semidirect
393. #2309C2×C47semidirect
394. #1972C2×C47semidirect
395. #1970C2×C47semidirect
396. #1936C2×C47semidirect
397. #1934C2×C47semidirect
398. #1926C2×C47semidirect
399. #1925C2×C47semidirect
400. #1879C2×C47semidirect
401. #1879C2×C47semidirect
402. #1875C2×C47semidirect
403. #1854C2×C47semidirect
404. #1786C2×C47semidirect
405. #1750C2×C47semidirect
421. C2×C4×D4C22×C47semidirect
424. #447C4×C47semidirect
425. C2×#107C22×C47semidirect
426. C2×#106C22×C47semidirect
433. C2×#102C22×C47semidirect
434. C2×#102C22×C47semidirect
437. C2×#97C22×C47semidirect
438. C2×C4×C8C22×C47semidirect
446. #390C22×C47semidirect
447. #389C22×C47semidirect
454. C4×C4⋊C4C22×C47semidirect
455. #340C22×C47semidirect
456. #340C22×C47semidirect
457. #340C22×C47semidirect
458. #340C22×C47semidirect
459. #336C22×C47semidirect
460. #336C22×C47semidirect
461. C47#22056direct (N × H)
470. C22×D4C2×C4×C47semidirect
530. #102C2×C4×C47semidirect
531. #102C2×C4×C47semidirect
533. C22⋊C8C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4472
C47×#23242
C47×#23092
C47×#19722
C47×#19702
C47×#19362
C47×#19342
C47×#19262
C47×#19252
C47×#18792
C47×#18752
C47×#18542
C47×#17862
C47×#17502
#2205647