Finite Group Databasebeta

← C47×#22558 #26062256

Subgroups — C47×#22558 #26062256

Order 12032.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#433C211yesmaximal, characteristic, complemented
2C22×C22⋊C8×C47C211yesmaximal, characteristic
3C47×#2280C211yesmaximal, characteristic
4C47×#1924C211yesmaximal, characteristic, complemented
5C47×#1924C211yesmaximal, characteristic, complemented
6C47×#1923C211yesmaximal, characteristic, complemented
7C47×#1923C211yesmaximal, characteristic, complemented
8C47×#1850C211yesmaximal, characteristic, complemented
9C47×#1850C211yesmaximal, characteristic, complemented
10C47×#1818C211yesmaximal, characteristic, complemented
11C47×#1798C211yesmaximal, characteristic, complemented
12C47×#1779C211yesmaximal, characteristic
13C47×#1752C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C2×#117×C47C2211yescharacteristic
21C47×#433—24no—
22C2×C4⋊C8×C47C2211yescharacteristic, complemented
23C2×C4⋊C8×C47C2211yescharacteristic, complemented
24C2×C4⋊C8×C47C2211yescharacteristic, complemented
25C2×C4⋊C8×C47C2211yescharacteristic, complemented
26C2×C22⋊C8×C47—24no—
27C2×C22⋊C8×C47C2211yescharacteristic
28C2×C22⋊C8×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×C22⋊C8×C47C2211yescharacteristic
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C2×#97×C47C2211yescharacteristic, complemented
38C2×#97×C47C2211yescharacteristic, complemented
39C2×C4×C8×C47C2211yescharacteristic, complemented
40C2×C4×C8×C47C2211yescharacteristic, complemented
41C47×#381C411yescharacteristic
42C47×#381C411yescharacteristic
43C47×#380C411yescharacteristic
44C47×#380C411yescharacteristic
45C47×#380C411yescharacteristic
46C47×#380C411yescharacteristic
47C47×#379C411yescharacteristic
48C47×#379C411yescharacteristic
49C4×C22⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C4×C22⋊C4×C47C2211yescharacteristic
52C4×C22⋊C4×C47C2211yescharacteristic
53C47×#336C2211yescharacteristic, complemented
54C47×#336C2211yescharacteristic, complemented
55C47×#336C2211yescharacteristic, complemented
56C47×#336C2211yescharacteristic, complemented
57C47×#336C2211yescharacteristic, complemented
58C47×#336C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C25×C47C2×C411yescharacteristic
62C23×C4×C47—22no—
63C23×C4×C47—22no—
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47—41no—
67C23×C4×C47—41no—
68C23×C4×C47C2×C411yescharacteristic
69C23×C4×C47C2×C411yescharacteristic
70C23×C4×C47C2×C411yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C22×C8×C47—22no—
75C22×C8×C47—22no—
76C22×C8×C47—22no—
77C22×C8×C47—22no—
78C22×C8×C47—41no—
79C22×C8×C47—41no—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88#117×C47—22no—
89#117×C47—22no—
90#117×C47—41no—
91#117×C47—41no—
92C2×C4⋊C4×C47C2×C411yescharacteristic
93C2×C4⋊C4×C47C2×C411yescharacteristic
94C2×C4⋊C4×C47C2×C411yescharacteristic
95C2×C4⋊C4×C47C2×C411yescharacteristic
96C2×C22⋊C4×C47C2×C411yescharacteristic
97C2×C22⋊C4×C47C2×C411yescharacteristic
98C2×C22⋊C4×C47C2×C411yescharacteristic
99C2×C22⋊C4×C47C2×C411yescharacteristic
100C2×C22⋊C4×C47C2×C411yescharacteristic
101C2×C22⋊C4×C47C2×C411yescharacteristic
102C2×C22⋊C4×C47C2×C411yescharacteristic
103C2×C22⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47C2×C411yescharacteristic
106C2×C22⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47C2×C411yescharacteristic
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C4⋊C8×C47—22no—
113C4⋊C8×C47—22no—
114C4⋊C8×C47—41no—
115C4⋊C8×C47—41no—
116C22⋊C8×C47—22no—
117C22⋊C8×C47—22no—
118C22⋊C8×C47—22no—
119C22⋊C8×C47—22no—
120C22⋊C8×C47—22no—
121C22⋊C8×C47—22no—
122C22⋊C8×C47—22no—
123C22⋊C8×C47—41no—
124C22⋊C8×C47—41no—
125C22⋊C8×C47D414yes—
126#97×C47—22no—
127#97×C47—41no—
128C4×C8×C47—22no—
129C4×C8×C47—41no—
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132#95×C47C2×C411yescharacteristic
133#95×C47C2×C411yescharacteristic
134#95×C47C2×C411yescharacteristic
135#95×C47C2×C411yescharacteristic
136#95×C47C2×C411yescharacteristic
137#95×C47C2×C411yescharacteristic
138C24×C47—22no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—22no—
143C24×C47—41no—
144C24×C47—41no—
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C411yescharacteristic
147C24×C47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
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—41no—
169C22×C4×C47—41no—
170C22×C4×C47—41no—
171C22×C4×C47—44no—
172C22×C4×C47—44no—
173C22×C4×C47—44no—
174C22×C4×C47—44no—
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C2×D412yes—
187C22×C4×C47#4112yes—
188C22×C4×C47#4112yes—
189C22×C4×C47#4112yes—
190C22×C4×C47C2411yescharacteristic
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
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×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—44no—
214C2×C8×C47—44no—
215C2×C8×C47C2×D412yes—
216C2×C8×C47C2×D412yes—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—41no—
220C4⋊C4×C47—41no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—22no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—41no—
230C22⋊C4×C47—41no—
231C22⋊C4×C47—41no—
232C22⋊C4×C47—41no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—28no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—44no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47#11712yes—
265C23×C47C4×D412yes—
266C23×C47#13112yes—
267C23×C47#13112yes—
268C23×C47#13112yes—
269C23×C47C23×C411yescharacteristic
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
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—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47#11712yes—
317C2×C4×C47C4×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47C2×#4111yescharacteristic
322C2×C4×C47H(5,𝔽2)11yescharacteristic
323C2×C4×C47H(5,𝔽2)11yescharacteristic
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—41no—
327C8×C47—41no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47—41no—
331C8×C47—41no—
332#22558C4711yesmaximal, characteristic, direct product factor, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—416no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47#43314yescomplemented
355C22×C47C2×#11711yescharacteristic
356C22×C47C2×C4×D411yescharacteristic
357C22×C47#51811yescharacteristic
358C22×C47C2×#13111yescharacteristic
359C22×C47C2×#13111yescharacteristic
360C22×C47C2×#13111yescharacteristic
361C22×C47#56811yescharacteristic
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47—41no—
367C4×C47—41no—
368C4×C47—41no—
369C4×C47—41no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47#54611yescharacteristic
374C4×C47#54611yescharacteristic
375C4×C47#55111yescharacteristic
376C4×C47#55111yescharacteristic
377C2×#433C2×C4711yescharacteristic, complemented
378C22×C22⋊C8C2×C4711yescharacteristic
379#2280C2×C4711yescharacteristic
380#1924C2×C4711yescharacteristic, complemented
381#1924C2×C4711yescharacteristic, complemented
382#1923C2×C4711yescharacteristic, complemented
383#1923C2×C4711yescharacteristic, complemented
384#1850C2×C4711yescharacteristic, complemented
385#1850C2×C4711yescharacteristic, complemented
386#1818C2×C4711yescharacteristic, complemented
387#1798C2×C4711yescharacteristic, complemented
388#1779C2×C4711yescharacteristic
389#1752C2×C4711yescharacteristic, complemented
390C8×C22⋊C4C2×C4711yescharacteristic, complemented
391#1750C2×C4711yescharacteristic, complemented
392C2×C47—24no—
393C2×C47—42no—
394C2×C47—42no—
395C2×C47#234211yescharacteristic
396C2×C47C2×#43311yescharacteristic
397C2×C47#292411yescharacteristic
398C2×C47#292911yescharacteristic
399C2×C47#293311yescharacteristic
400C2×C47#297611yescharacteristic
401C2×C47#297711yescharacteristic
402C24×C4C22×C4711yescharacteristic
403C23×C8C22×C4711yescharacteristic
404C23×C8C22×C4711yescharacteristic
405C2×#117C22×C4711yescharacteristic
406C2×#117C22×C4711yescharacteristic
407#433—24no—
408C2×C4⋊C8C22×C4711yescharacteristic, complemented
409C2×C4⋊C8C22×C4711yescharacteristic, complemented
410C2×C4⋊C8C22×C4711yescharacteristic, complemented
411C2×C4⋊C8C22×C4711yescharacteristic, complemented
412C2×C22⋊C8—24no—
413C2×C22⋊C8C22×C4711yescharacteristic
414C2×C22⋊C8C22×C4711yescharacteristic
415C2×C22⋊C8C22×C4711yescharacteristic
416C2×C22⋊C8C22×C4711yescharacteristic
417C2×C22⋊C8C22×C4711yescharacteristic
418C2×C22⋊C8C22×C4711yescharacteristic
419C2×C22⋊C8C22×C4711yescharacteristic
420C2×C22⋊C8C22×C4711yescharacteristic
421C2×C22⋊C8C22×C4711yescharacteristic
422C2×C22⋊C8C22×C4711yescharacteristic
423C2×#97C22×C4711yescharacteristic, complemented
424C2×#97C22×C4711yescharacteristic, complemented
425C2×C4×C8C22×C4711yescharacteristic, complemented
426C2×C4×C8C22×C4711yescharacteristic, complemented
427#381C4×C4711yescharacteristic
428#381C4×C4711yescharacteristic
429#380C4×C4711yescharacteristic
430#380C4×C4711yescharacteristic
431#380C4×C4711yescharacteristic
432#380C4×C4711yescharacteristic
433#379C4×C4711yescharacteristic
434#379C4×C4711yescharacteristic
435C4×C22⋊C4C22×C4711yescharacteristic
436C4×C22⋊C4C22×C4711yescharacteristic
437C4×C22⋊C4C22×C4711yescharacteristic
438C4×C22⋊C4C22×C4711yescharacteristic
439#336C22×C4711yescharacteristic, complemented
440#336C22×C4711yescharacteristic, complemented
441#336C22×C4711yescharacteristic, complemented
442#336C22×C4711yescharacteristic, complemented
443#336C22×C4711yescharacteristic, complemented
444#336C22×C4711yescharacteristic, complemented
445#336C22×C4711yescharacteristic, complemented
446#336C22×C4711yescharacteristic, complemented
447C47#2255811yescharacteristic, direct product factor, Sylow
448C25C2×C4×C4711yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C2×C4×C4711yescharacteristic
456C23×C4C2×C4×C4711yescharacteristic
457C23×C4C2×C4×C4711yescharacteristic
458C23×C4C23×C4711yescharacteristic
459C23×C4C23×C4711yescharacteristic
460C23×C4C23×C4711yescharacteristic
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—41no—
467C22×C8C23×C4711yescharacteristic
468C22×C8C23×C4711yescharacteristic
469C22×C8C23×C4711yescharacteristic
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473C22×C8C23×C4711yescharacteristic
474C22×C8C23×C4711yescharacteristic
475#117—22no—
476#117—22no—
477#117—41no—
478#117—41no—
479C2×C4⋊C4C2×C4×C4711yescharacteristic
480C2×C4⋊C4C2×C4×C4711yescharacteristic
481C2×C4⋊C4C2×C4×C4711yescharacteristic
482C2×C4⋊C4C2×C4×C4711yescharacteristic
483C2×C22⋊C4C2×C4×C4711yescharacteristic
484C2×C22⋊C4C2×C4×C4711yescharacteristic
485C2×C22⋊C4C2×C4×C4711yescharacteristic
486C2×C22⋊C4C2×C4×C4711yescharacteristic
487C2×C22⋊C4C2×C4×C4711yescharacteristic
488C2×C22⋊C4C2×C4×C4711yescharacteristic
489C2×C22⋊C4C2×C4×C4711yescharacteristic
490C2×C22⋊C4C2×C4×C4711yescharacteristic
491C2×C22⋊C4C2×C4×C4711yescharacteristic
492C2×C22⋊C4C2×C4×C4711yescharacteristic
493C2×C22⋊C4C2×C4×C4711yescharacteristic
494C2×C22⋊C4C2×C4×C4711yescharacteristic
495C2×C42C23×C4711yescharacteristic
496C2×C42C23×C4711yescharacteristic
497C2×C42C23×C4711yescharacteristic
498C2×C42C23×C4711yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—41no—
502C4⋊C8—41no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512C22⋊C8D4×C4714yes—
513#97—22no—
514#97—41no—
515C4×C8—22no—
516C4×C8—41no—
517#95C2×C4×C4711yescharacteristic
518#95C2×C4×C4711yescharacteristic
519#95C2×C4×C4711yescharacteristic
520#95C2×C4×C4711yescharacteristic
521#95C2×C4×C4711yescharacteristic
522#95C2×C4×C4711yescharacteristic
523#95C2×C4×C4711yescharacteristic
524#95C2×C4×C4711yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24C22×C4×C4711yescharacteristic
533C24C22×C4×C4711yescharacteristic
534C24C22×C4×C4711yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4C22×C4×C4711yescharacteristic
563C22×C4C22×C4×C4711yescharacteristic
564C22×C4C22×C4×C4711yescharacteristic
565C22×C4C22×C4×C4711yescharacteristic
566C22×C4C22×C4×C4711yescharacteristic
567C22×C4C22×C4×C4711yescharacteristic
568C22×C4C22×C4×C4711yescharacteristic
569C22×C4C22×C4×C4711yescharacteristic
570C22×C4C22×C4×C4711yescharacteristic
571C22×C4C22×C4×C4711yescharacteristic
572C22×C4C22×C4×C4711yescharacteristic
573C22×C4C2×D4×C4712yes—
574C22×C4#41×C4712yes—
575C22×C4#41×C4712yes—
576C22×C4#41×C4712yes—
577C22×C4C24×C4711yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—44no—
601C2×C8—44no—
602C2×C8C2×D4×C4712yes—
603C2×C8C2×D4×C4712yes—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—28no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23#117×C4712yes—
652C23C4×D4×C4712yes—
653C23#131×C4712yes—
654C23#131×C4712yes—
655C23#131×C4712yes—
656C23C23×C4×C4711yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4#117×C4712yes—
704C2×C4C4×D4×C4712yes—
705C2×C4C22×D4×C4711yescharacteristic
706C2×C4C2×#41×C4711yescharacteristic
707C2×C4C2×#41×C4711yescharacteristic
708C2×C4C2×#41×C4711yescharacteristic
709C2×C4H(5,𝔽2)×C4711yescharacteristic
710C2×C4H(5,𝔽2)×C4711yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22C47×#43314yescomplemented
741C22C2×#117×C4711yescharacteristic
742C22C2×C4×D4×C4711yescharacteristic
743C22C47×#51811yescharacteristic
744C22C2×#131×C4711yescharacteristic
745C22C2×#131×C4711yescharacteristic
746C22C2×#131×C4711yescharacteristic
747C22C47×#56811yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4C47×#54611yescharacteristic
760C4C47×#54611yescharacteristic
761C4C47×#55111yescharacteristic
762C4C47×#55111yescharacteristic
763C2—24no—
764C2—42no—
765C2—42no—
766C2C47×#234211yescharacteristic
767C2C2×C47×#43311yescharacteristic
768C2C47×#292411yescharacteristic
769C2C47×#292911yescharacteristic
770C2C47×#293311yescharacteristic
771C2C47×#297611yescharacteristic
772C2C47×#297711yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC25×C47C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#433C2semidirect
4. C47×#1924C2semidirect
5. C47×#1924C2semidirect
6. C47×#1923C2semidirect
7. C47×#1923C2semidirect
8. C47×#1850C2semidirect
9. C47×#1850C2semidirect
10. C47×#1818C2semidirect
11. C47×#1798C2semidirect
13. C47×#1752C2semidirect
14. C8×C22⋊C4×C47C2semidirect
15. C47×#1750C2semidirect
22. C2×C4⋊C8×C47C22semidirect
23. C2×C4⋊C8×C47C22semidirect
24. C2×C4⋊C8×C47C22semidirect
25. C2×C4⋊C8×C47C22semidirect
37. C2×#97×C47C22semidirect
38. C2×#97×C47C22semidirect
39. C2×C4×C8×C47C22semidirect
40. C2×C4×C8×C47C22semidirect
53. C47×#336C22semidirect
54. C47×#336C22semidirect
55. C47×#336C22semidirect
56. C47×#336C22semidirect
57. C47×#336C22semidirect
58. C47×#336C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
332. #22558C47direct (N × H)
354. C22×C47#433semidirect
377. C2×#433C2×C47semidirect
380. #1924C2×C47semidirect
381. #1924C2×C47semidirect
382. #1923C2×C47semidirect
383. #1923C2×C47semidirect
384. #1850C2×C47semidirect
385. #1850C2×C47semidirect
386. #1818C2×C47semidirect
387. #1798C2×C47semidirect
389. #1752C2×C47semidirect
390. C8×C22⋊C4C2×C47semidirect
391. #1750C2×C47semidirect
408. C2×C4⋊C8C22×C47semidirect
409. C2×C4⋊C8C22×C47semidirect
410. C2×C4⋊C8C22×C47semidirect
411. C2×C4⋊C8C22×C47semidirect
423. C2×#97C22×C47semidirect
424. C2×#97C22×C47semidirect
425. C2×C4×C8C22×C47semidirect
426. C2×C4×C8C22×C47semidirect
439. #336C22×C47semidirect
440. #336C22×C47semidirect
441. #336C22×C47semidirect
442. #336C22×C47semidirect
443. #336C22×C47semidirect
444. #336C22×C47semidirect
445. #336C22×C47semidirect
446. #336C22×C47semidirect
447. C47#22558direct (N × H)
740. C22C47×#433semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4332
C22×C22⋊C8×C472
C47×#22802
C47×#19242
C47×#19232
C47×#18502
C47×#18182
C47×#17982
C47×#17792
C47×#17522
C8×C22⋊C4×C472
C47×#17502
#2255847