Finite Group Databasebeta

← C47×#13789 #26053487

Subgroups — C47×#13789 #26053487

Order 12032.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#388C211yesmaximal, characteristic
2C2×C47×#388C211yesmaximal, characteristic
3C2×C47×#385C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
6C47×#1437C211yesmaximal, characteristic
7C47×#1437C211yesmaximal, characteristic
8C47×#1436C211yesmaximal, characteristic, complemented
9C47×#1436C211yesmaximal, characteristic, complemented
10C47×#1436C211yesmaximal, characteristic, complemented
11C47×#1436C211yesmaximal, characteristic, complemented
12C47×C4⋊#95C211yesmaximal, characteristic, complemented
13C47×#1434C211yesmaximal, characteristic, complemented
14C47×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C47C211yesmaximal, characteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47C2211yescharacteristic
22C22×C22⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C42×C47C2211yescharacteristic
28C22×C42×C47C2211yescharacteristic
29C22×C42×C47C2211yescharacteristic
30C22×C42×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C47×#388C418yescomplemented
34C47×#388C418yescomplemented
35C47×#385C418yescomplemented
36C4×C4⋊C4×C47—24no—
37C4×C22⋊C4×C47—24no—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2211yescharacteristic
42C2×#95×C47C2211yescharacteristic
43C2×#95×C47C2211yescharacteristic
44C2×#95×C47C2211yescharacteristic
45C2×#95×C47C2211yescharacteristic
46C2×#95×C47C2211yescharacteristic
47C2×#95×C47C2211yescharacteristic
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C25×C47C2311yescharacteristic
57C23×C4×C47—22no—
58C23×C4×C47—22no—
59C23×C4×C47—41no—
60C23×C4×C47—41no—
61C23×C4×C47—41no—
62C23×C4×C47—41no—
63C23×C4×C47C2×C414yes—
64C23×C4×C47C2311yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47—41no—
83C2×C4⋊C4×C47—41no—
84C2×C4⋊C4×C47—41no—
85C2×C4⋊C4×C47—41no—
86C2×C4⋊C4×C47C2×C414yes—
87C2×C4⋊C4×C47C2×C414yes—
88C2×C4⋊C4×C47C2×C414yescomplemented
89C2×C4⋊C4×C47C2×C414yescomplemented
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47—22no—
93C2×C22⋊C4×C47—22no—
94C2×C22⋊C4×C47—41no—
95C2×C22⋊C4×C47—41no—
96C2×C22⋊C4×C47—41no—
97C2×C22⋊C4×C47—41no—
98C2×C22⋊C4×C47—41no—
99C2×C22⋊C4×C47—41no—
100C2×C22⋊C4×C47C2×C414yes—
101C2×C22⋊C4×C47C2×C414yes—
102C2×C22⋊C4×C47C2×C414yes—
103C2×C22⋊C4×C47C2×C414yes—
104C2×C22⋊C4×C47C2×C414yes—
105C2×C22⋊C4×C47C2×C414yes—
106C2×C22⋊C4×C47C2×C414yes—
107C2×C22⋊C4×C47C2×C414yes—
108C2×C42×C47—22no—
109C2×C42×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47—22no—
112C2×C42×C47—22no—
113C2×C42×C47—41no—
114C2×C42×C47—41no—
115C2×C42×C47—41no—
116C2×C42×C47—41no—
117C2×C42×C47—41no—
118C2×C42×C47—41no—
119C2×C42×C47—41no—
120C2×C42×C47—41no—
121C2×C42×C47—41no—
122C2×C42×C47—41no—
123C2×C42×C47C2×C414yescomplemented
124C2×C42×C47C2×C414yescomplemented
125C2×C42×C47D414yes—
126#95×C47—22no—
127#95×C47—22no—
128#95×C47—22no—
129#95×C47—22no—
130#95×C47—22no—
131#95×C47—22no—
132#95×C47—41no—
133#95×C47—41no—
134#95×C47—41no—
135#95×C47—41no—
136#95×C47—41no—
137#95×C47—41no—
138#95×C47C2×C414yes—
139#95×C47C2×C414yes—
140#95×C47C2×C414yescomplemented
141#95×C47C2×C414yescomplemented
142#95×C47C2×C414yescomplemented
143#95×C47C2×C414yescomplemented
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C22×C412yes—
157C24×C47C22×C412yes—
158C24×C47C22×C412yes—
159C24×C47C2411yescharacteristic
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
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—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—28no—
235C22×C4×C47—44no—
236C22×C4×C47—44no—
237C22×C4×C47—44no—
238C22×C4×C47—44no—
239C22×C4×C47—44no—
240C22×C4×C47—44no—
241C22×C4×C47C22×C412yes—
242C22×C4×C47C22×C412yes—
243C22×C4×C47C22×C412yes—
244C22×C4×C47C22×C412yes—
245C22×C4×C47C22×C412yes—
246C22×C4×C47C22×C412yes—
247C22×C4×C47C22×C412yes—
248C22×C4×C47C22×C412yes—
249C22×C4×C47C22×C412yes—
250C22×C4×C47C22×C412yes—
251C22×C4×C47C22×C412yes—
252C22×C4×C47C22×C412yes—
253C22×C4×C47C22×C412yes—
254C22×C4×C47C22×C412yes—
255C22×C4×C47C22×C412yes—
256C22×C4×C47C22×C412yes—
257C22×C4×C47C22×C412yes—
258C22×C4×C47C22×C412yes—
259C22×C4×C47C2×D412yes—
260C22×C4×C47C2×D412yes—
261C22×C4×C47C2×D412yes—
262C22×C4×C47#4112yes—
263C22×C4×C47#4112yes—
264C22×C4×C47#4112yes—
265C4⋊C4×C47—28no—
266C4⋊C4×C47—28no—
267C4⋊C4×C47—44no—
268C4⋊C4×C47—44no—
269C22⋊C4×C47—28no—
270C22⋊C4×C47—28no—
271C22⋊C4×C47—44no—
272C22⋊C4×C47—44no—
273C22⋊C4×C47—44no—
274C22⋊C4×C47C42116yescomplemented
275C42×C47—28no—
276C42×C47—44no—
277C42×C47—44no—
278C42×C47—44no—
279C42×C47—44no—
280C42×C47—44no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47C2×C4214yes—
316C23×C47C23×C411yescharacteristic
317C23×C47C23×C411yescharacteristic
318C23×C47C23×C411yescharacteristic
319C23×C47C22×D411yescharacteristic
320C23×C47C2×#4111yescharacteristic
321C23×C47C2×#4111yescharacteristic
322C23×C47C2×#4111yescharacteristic
323C23×C47H(5,𝔽2)11yescharacteristic
324C23×C47H(5,𝔽2)11yescharacteristic
325C23×C47H(5,𝔽2)11yescharacteristic
326C23×C47H(5,𝔽2)11yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C472−1+411yescharacteristic
329C23×C472−1+411yescharacteristic
330C23×C472−1+411yescharacteristic
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—416no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
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—41no—
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—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47C2×C4214yes—
426C2×C4×C47C2×C4214yes—
427C2×C4×C47C4×D414yes—
428C2×C4×C47C4×D414yes—
429C2×C4×C47C4×D414yes—
430#13789C4711yesmaximal, characteristic, direct product factor, Sylow
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47C22×C4211yescharacteristic
447C22×C47C2×C4×D411yescharacteristic
448C22×C47C2×C4×D411yescharacteristic
449C22×C47C2×C4×D411yescharacteristic
450C22×C47C4×#4111yescharacteristic
451C22×C47C4×#4111yescharacteristic
452C22×C47C4×#4111yescharacteristic
453C22×C47#51811yescharacteristic
454C22×C47#51811yescharacteristic
455C22×C47#51811yescharacteristic
456C22×C47#51811yescharacteristic
457C22×C47#51911yescharacteristic
458C22×C47#52011yescharacteristic
459C22×C47#52011yescharacteristic
460C22×C47#52011yescharacteristic
461C22×C47#52011yescharacteristic
462C22×C47#52011yescharacteristic
463C22×C47#52011yescharacteristic
464C22×C47#52011yescharacteristic
465C22×C47#53411yescharacteristic
466C22×C47#53511yescharacteristic
467C22×C47#53611yescharacteristic
468C22×C47#53711yescharacteristic
469C22×C47#53811yescharacteristic
470C22×C47#53811yescharacteristic
471C22×C47#53811yescharacteristic
472C22×C47#53911yescharacteristic
473C22×C47#53911yescharacteristic
474C22×C47#53911yescharacteristic
475C22×C47#54011yescharacteristic
476C22×C47#54111yescharacteristic
477C22×C47#54211yescharacteristic
478C22×C47#54211yescharacteristic
479C22×C47#54211yescharacteristic
480C22×C47#54211yescharacteristic
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—24no—
484C4×C47—24no—
485C4×C47—24no—
486C4×C47—42no—
487C4×C47—42no—
488C4×C47—42no—
489C4×C47—42no—
490C4×C47—42no—
491C4×C47—42no—
492C4×C47—42no—
493C4×C47—42no—
494C4×C47—42no—
495C2×#388C2×C4711yescharacteristic
496C2×#388C2×C4711yescharacteristic
497C2×#385C2×C4711yescharacteristic
498C2×C4×C4⋊C4C2×C4711yescharacteristic, complemented
499C2×C4×C22⋊C4C2×C4711yescharacteristic
500#1437C2×C4711yescharacteristic
501#1437C2×C4711yescharacteristic
502#1436C2×C4711yescharacteristic, complemented
503#1436C2×C4711yescharacteristic, complemented
504#1436C2×C4711yescharacteristic, complemented
505#1436C2×C4711yescharacteristic, complemented
506C4⋊#95C2×C4711yescharacteristic, complemented
507#1434C2×C4711yescharacteristic, complemented
508C22⋊#95C2×C4711yescharacteristic
509C4×#95C2×C4711yescharacteristic, complemented
510C2×C47—44no—
511C2×C47C42×D411yescharacteristic
512C2×C47#227411yescharacteristic
513C2×C47#227511yescharacteristic
514C2×C47#232111yescharacteristic
515C2×C47#232211yescharacteristic
516C2×C47#232311yescharacteristic
517C2×C47#232411yescharacteristic
518C2×C47#232511yescharacteristic
519C2×C47#232611yescharacteristic
520C2×C47#233211yescharacteristic
521C2×C47#233411yescharacteristic
522C2×C47#233411yescharacteristic
523C2×C47#233511yescharacteristic
524C2×C47#233511yescharacteristic
525C2×C47#233711yescharacteristic
526C24×C4C22×C4711yescharacteristic
527C22×C4⋊C4C22×C4711yescharacteristic
528C22×C4⋊C4C22×C4711yescharacteristic
529C22×C4⋊C4C22×C4711yescharacteristic
530C22×C4⋊C4C22×C4711yescharacteristic
531C22×C22⋊C4C22×C4711yescharacteristic
532C22×C22⋊C4C22×C4711yescharacteristic
533C22×C22⋊C4C22×C4711yescharacteristic
534C22×C22⋊C4C22×C4711yescharacteristic
535C22×C22⋊C4C22×C4711yescharacteristic
536C22×C22⋊C4C22×C4711yescharacteristic
537C22×C42C22×C4711yescharacteristic
538C22×C42C22×C4711yescharacteristic
539C22×C42C22×C4711yescharacteristic
540C22×C42C22×C4711yescharacteristic
541C22×C42C22×C4711yescharacteristic
542C22×C42C22×C4711yescharacteristic
543#388C4×C4718yescomplemented
544#388C4×C4718yescomplemented
545#385C4×C4718yescomplemented
546C4×C4⋊C4—24no—
547C4×C22⋊C4—24no—
548C2×#95C22×C4711yescharacteristic
549C2×#95C22×C4711yescharacteristic
550C2×#95C22×C4711yescharacteristic
551C2×#95C22×C4711yescharacteristic
552C2×#95C22×C4711yescharacteristic
553C2×#95C22×C4711yescharacteristic
554C2×#95C22×C4711yescharacteristic
555C2×#95C22×C4711yescharacteristic
556C2×#95C22×C4711yescharacteristic
557C2×#95C22×C4711yescharacteristic
558C2×#95C22×C4711yescharacteristic
559C2×#95C22×C4711yescharacteristic
560C2×#95C22×C4711yescharacteristic
561C2×#95C22×C4711yescharacteristic
562C2×#95C22×C4711yescharacteristic
563C2×#95C22×C4711yescharacteristic
564C2×#95C22×C4711yescharacteristic
565C2×#95C22×C4711yescharacteristic
566C47#1378911yescharacteristic, direct product factor, Sylow
567C25C23×C4711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C4714yes—
575C23×C4C23×C4711yescharacteristic
576C23×C4C23×C4711yescharacteristic
577C23×C4C23×C4711yescharacteristic
578C23×C4C23×C4711yescharacteristic
579C23×C4C23×C4711yescharacteristic
580C23×C4C23×C4711yescharacteristic
581C23×C4C23×C4711yescharacteristic
582C23×C4C23×C4711yescharacteristic
583C23×C4C23×C4711yescharacteristic
584C23×C4C23×C4711yescharacteristic
585C23×C4C23×C4711yescharacteristic
586C23×C4C23×C4711yescharacteristic
587C23×C4C23×C4711yescharacteristic
588C23×C4C23×C4711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×C4×C4714yes—
598C2×C4⋊C4C2×C4×C4714yes—
599C2×C4⋊C4C2×C4×C4714yescomplemented
600C2×C4⋊C4C2×C4×C4714yescomplemented
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4C2×C4×C4714yes—
612C2×C22⋊C4C2×C4×C4714yes—
613C2×C22⋊C4C2×C4×C4714yes—
614C2×C22⋊C4C2×C4×C4714yes—
615C2×C22⋊C4C2×C4×C4714yes—
616C2×C22⋊C4C2×C4×C4714yes—
617C2×C22⋊C4C2×C4×C4714yes—
618C2×C22⋊C4C2×C4×C4714yes—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42C2×C4×C4714yescomplemented
635C2×C42C2×C4×C4714yescomplemented
636C2×C42D4×C4714yes—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95C2×C4×C4714yes—
650#95C2×C4×C4714yes—
651#95C2×C4×C4714yescomplemented
652#95C2×C4×C4714yescomplemented
653#95C2×C4×C4714yescomplemented
654#95C2×C4×C4714yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C4712yes—
668C24C22×C4×C4712yes—
669C24C22×C4×C4712yes—
670C24C24×C4711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—28no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4C22×C4×C4712yes—
753C22×C4C22×C4×C4712yes—
754C22×C4C22×C4×C4712yes—
755C22×C4C22×C4×C4712yes—
756C22×C4C22×C4×C4712yes—
757C22×C4C22×C4×C4712yes—
758C22×C4C22×C4×C4712yes—
759C22×C4C22×C4×C4712yes—
760C22×C4C22×C4×C4712yes—
761C22×C4C22×C4×C4712yes—
762C22×C4C22×C4×C4712yes—
763C22×C4C22×C4×C4712yes—
764C22×C4C22×C4×C4712yes—
765C22×C4C22×C4×C4712yes—
766C22×C4C22×C4×C4712yes—
767C22×C4C22×C4×C4712yes—
768C22×C4C22×C4×C4712yes—
769C22×C4C22×C4×C4712yes—
770C22×C4C2×D4×C4712yes—
771C22×C4C2×D4×C4712yes—
772C22×C4C2×D4×C4712yes—
773C22×C4#41×C4712yes—
774C22×C4#41×C4712yes—
775C22×C4#41×C4712yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4C42×C47116yescomplemented
786C42—28no—
787C42—44no—
788C42—44no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C42×C4714yes—
827C23C23×C4×C4711yescharacteristic
828C23C23×C4×C4711yescharacteristic
829C23C23×C4×C4711yescharacteristic
830C23C22×D4×C4711yescharacteristic
831C23C2×#41×C4711yescharacteristic
832C23C2×#41×C4711yescharacteristic
833C23C2×#41×C4711yescharacteristic
834C23H(5,𝔽2)×C4711yescharacteristic
835C23H(5,𝔽2)×C4711yescharacteristic
836C23H(5,𝔽2)×C4711yescharacteristic
837C23H(5,𝔽2)×C4711yescharacteristic
838C23H(5,𝔽2)×C4711yescharacteristic
839C232−1+4×C4711yescharacteristic
840C232−1+4×C4711yescharacteristic
841C232−1+4×C4711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—416no—
900C2×C4—41no—
901C2×C4—41no—
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—41no—
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—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4C2×C42×C4714yes—
937C2×C4C2×C42×C4714yes—
938C2×C4C4×D4×C4714yes—
939C2×C4C4×D4×C4714yes—
940C2×C4C4×D4×C4714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C42×C4711yescharacteristic
957C22C2×C4×D4×C4711yescharacteristic
958C22C2×C4×D4×C4711yescharacteristic
959C22C2×C4×D4×C4711yescharacteristic
960C22C4×#41×C4711yescharacteristic
961C22C4×#41×C4711yescharacteristic
962C22C4×#41×C4711yescharacteristic
963C22C47×#51811yescharacteristic
964C22C47×#51811yescharacteristic
965C22C47×#51811yescharacteristic
966C22C47×#51811yescharacteristic
967C22C47×#51911yescharacteristic
968C22C47×#52011yescharacteristic
969C22C47×#52011yescharacteristic
970C22C47×#52011yescharacteristic
971C22C47×#52011yescharacteristic
972C22C47×#52011yescharacteristic
973C22C47×#52011yescharacteristic
974C22C47×#52011yescharacteristic
975C22C47×#53411yescharacteristic
976C22C47×#53511yescharacteristic
977C22C47×#53611yescharacteristic
978C22C47×#53711yescharacteristic
979C22C47×#53811yescharacteristic
980C22C47×#53811yescharacteristic
981C22C47×#53811yescharacteristic
982C22C47×#53911yescharacteristic
983C22C47×#53911yescharacteristic
984C22C47×#53911yescharacteristic
985C22C47×#54011yescharacteristic
986C22C47×#54111yescharacteristic
987C22C47×#54211yescharacteristic
988C22C47×#54211yescharacteristic
989C22C47×#54211yescharacteristic
990C22C47×#54211yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C2—44no—
1006C2C42×D4×C4711yescharacteristic
1007C2C47×#227411yescharacteristic
1008C2C47×#227511yescharacteristic
1009C2C47×#232111yescharacteristic
1010C2C47×#232211yescharacteristic
1011C2C47×#232311yescharacteristic
1012C2C47×#232411yescharacteristic
1013C2C47×#232511yescharacteristic
1014C2C47×#232611yescharacteristic
1015C2C47×#233211yescharacteristic
1016C2C47×#233411yescharacteristic
1017C2C47×#233411yescharacteristic
1018C2C47×#233511yescharacteristic
1019C2C47×#233511yescharacteristic
1020C2C47×#233711yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutatorC22C22×C42×C47
Frattini, cosocleC24C24×C47
prime radicalC25×C47C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊C4×C47C2semidirect
8. C47×#1436C2semidirect
9. C47×#1436C2semidirect
10. C47×#1436C2semidirect
11. C47×#1436C2semidirect
12. C47×C4⋊#95C2semidirect
13. C47×#1434C2semidirect
15. C4×#95×C47C2semidirect
33. C47×#388C4semidirect
34. C47×#388C4semidirect
35. C47×#385C4semidirect
88. C2×C4⋊C4×C47C2×C4semidirect
89. C2×C4⋊C4×C47C2×C4semidirect
123. C2×C42×C47C2×C4semidirect
124. C2×C42×C47C2×C4semidirect
140. #95×C47C2×C4semidirect
141. #95×C47C2×C4semidirect
142. #95×C47C2×C4semidirect
143. #95×C47C2×C4semidirect
274. C22⋊C4×C47C42semidirect
430. #13789C47direct (N × H)
498. C2×C4×C4⋊C4C2×C47semidirect
502. #1436C2×C47semidirect
503. #1436C2×C47semidirect
504. #1436C2×C47semidirect
505. #1436C2×C47semidirect
506. C4⋊#95C2×C47semidirect
507. #1434C2×C47semidirect
509. C4×#95C2×C47semidirect
543. #388C4×C47semidirect
544. #388C4×C47semidirect
545. #385C4×C47semidirect
566. C47#13789direct (N × H)
599. C2×C4⋊C4C2×C4×C47semidirect
600. C2×C4⋊C4C2×C4×C47semidirect
634. C2×C42C2×C4×C47semidirect
635. C2×C42C2×C4×C47semidirect
651. #95C2×C4×C47semidirect
652. #95C2×C4×C47semidirect
653. #95C2×C4×C47semidirect
654. #95C2×C4×C47semidirect
785. C22⋊C4C42×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3882
C2×C47×#3852
C2×C4×C4⋊C4×C472
C2×C4×C22⋊C4×C472
C47×#14372
C47×#14362
C47×C4⋊#952
C47×#14342
C47×C22⋊#952
C4×#95×C472
#1378947