Finite Group Databasebeta

← C47×#21855 #26061553

Subgroups — C47×#21855 #26061553

Order 12032.

1128 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×#529C211yesmaximal, characteristic
2C2×C47×#433C211yesmaximal, characteristic, complemented
3C2×C47×#424C211yesmaximal, characteristic, complemented
4C47×#1985C211yesmaximal, characteristic, complemented
5C47×#1984C211yesmaximal, characteristic, complemented
6C47×#1955C211yesmaximal, characteristic, complemented
7C47×#1954C211yesmaximal, characteristic, complemented
8C47×#1870C211yesmaximal, characteristic, complemented
9C47×#1870C211yesmaximal, characteristic, complemented
10C47×#1869C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1798C211yesmaximal, characteristic, complemented
13C47×#1798C211yesmaximal, characteristic, complemented
14C47×#1797C211yesmaximal, characteristic, complemented
15C47×#1797C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C47×#529—24no—
19C47×#529—24no—
20C2×#126×C47C411yescharacteristic
21C2×#126×C47C411yescharacteristic
22C2×#125×C47C411yescharacteristic
23C2×#124×C47C411yescharacteristic
24C2×#123×C47C411yescharacteristic
25C2×#123×C47C411yescharacteristic
26C2×C22⋊Q8×C47C411yescharacteristic
27C2×#121×C47C411yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×C4×D4×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C47×#433—24no—
36C47×#424—24no—
37C2×C4⋊C8×C47C2211yescharacteristic
38C2×C4⋊C8×C47C2211yescharacteristic
39C2×C4⋊C8×C47C2211yescharacteristic
40C2×C4⋊C8×C47C2211yescharacteristic
41C2×C4⋊C8×C47C2211yescharacteristic
42C2×C4⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic
50C2×C22⋊C8×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×#97×C47C2211yescharacteristic
54C2×C4×C8×C47C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2×C411yescharacteristic
64C22×D4×C47C2×C411yescharacteristic
65C22×D4×C47C2×C411yescharacteristic
66C22×D4×C47C2×C411yescharacteristic
67C23×C4×C47C2×C411yescharacteristic
68C23×C4×C47C2×C411yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C2×M16×C47—22no—
73C2×M16×C47—41no—
74C2×M16×C47—41no—
75C22×C8×C47—22no—
76C22×C8×C47—41no—
77C22×C8×C47—41no—
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86#126×C47—24no—
87#126×C47—24no—
88#125×C47—24no—
89#124×C47—24no—
90#123×C47—24no—
91#123×C47—24no—
92C22⋊Q8×C47—24no—
93#121×C47—24no—
94C4×Q8×C47—22no—
95C4×Q8×C47—22no—
96C4×D4×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99C4×D4×C47—22no—
100C4×D4×C47—22no—
101C4×D4×C47—22no—
102#117×C47—22no—
103#117×C47—22no—
104#117×C47D414yes—
105#117×C47D414yes—
106C2×C4⋊C4×C47C2×C411yescharacteristic
107C2×C4⋊C4×C47C2×C411yescharacteristic
108C2×C4⋊C4×C47C2×C411yescharacteristic
109C2×C4⋊C4×C47C2×C411yescharacteristic
110C2×C4⋊C4×C47C2×C411yescharacteristic
111C2×C4⋊C4×C47C2×C411yescharacteristic
112C2×C4⋊C4×C47C2×C411yescharacteristic
113C2×C4⋊C4×C47C2×C411yescharacteristic
114C2×C4⋊C4×C47C2×C411yescharacteristic
115C2×C4⋊C4×C47C2×C411yescharacteristic
116C2×C22⋊C4×C47C2×C411yescharacteristic
117C2×C22⋊C4×C47C2×C411yescharacteristic
118C2×C22⋊C4×C47C2×C411yescharacteristic
119C2×C22⋊C4×C47C2×C411yescharacteristic
120C2×C22⋊C4×C47C2×C411yescharacteristic
121C2×C22⋊C4×C47C2×C411yescharacteristic
122C2×C22⋊C4×C47C2×C411yescharacteristic
123C2×C22⋊C4×C47C2×C411yescharacteristic
124C2×C22⋊C4×C47C2×C411yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C42×C47—22no—
127C2×C42×C47—22no—
128C2×C42×C47C2×C411yescharacteristic
129C2×C42×C47C2×C411yescharacteristic
130C2×C42×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2311yescharacteristic
134C4⋊C8×C47—22no—
135C4⋊C8×C47—22no—
136C4⋊C8×C47—22no—
137C4⋊C8×C47—22no—
138C4⋊C8×C47—22no—
139C4⋊C8×C47—22no—
140C22⋊C8×C47—22no—
141C22⋊C8×C47—22no—
142C22⋊C8×C47—41no—
143C22⋊C8×C47—41no—
144C22⋊C8×C47—41no—
145C22⋊C8×C47—41no—
146C22⋊C8×C47—41no—
147C22⋊C8×C47—41no—
148C22⋊C8×C47—41no—
149C22⋊C8×C47—41no—
150#97×C47—22no—
151C4×C8×C47—22no—
152C24×C47C22×C411yescharacteristic
153C24×C47C22×C411yescharacteristic
154C24×C47C22×C411yescharacteristic
155C2×Q8×C47—22no—
156C2×Q8×C47—22no—
157C2×Q8×C47—41no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
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—41no—
188C22×C4×C47—41no—
189C22×C4×C47C22×C411yescharacteristic
190C22×C4×C47C22×C411yescharacteristic
191C22×C4×C47C22×C411yescharacteristic
192C22×C4×C47C22×C411yescharacteristic
193C22×C4×C47C22×C411yescharacteristic
194C22×C4×C47C22×C411yescharacteristic
195C22×C4×C47C22×C411yescharacteristic
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C22×C411yescharacteristic
198C22×C4×C47C22×C411yescharacteristic
199C22×C4×C47C22×C411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2411yescharacteristic
203M16×C47—44no—
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—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—44no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—22no—
231C4⋊C4×C47—22no—
232C4⋊C4×C47—22no—
233C4⋊C4×C47—22no—
234C4⋊C4×C47—22no—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—22no—
237C4⋊C4×C47C22⋊C414yes—
238C4⋊C4×C47C22⋊C414yes—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47C22⋊C414yes—
248C22⋊C4×C47C22⋊C414yes—
249C42×C47—22no—
250C42×C47—22no—
251C42×C47—21no—
252C42×C47—21no—
253C42×C47—21no—
254C42×C47—21no—
255C42×C47C2×D412yes—
256C42×C47C2×D412yes—
257C42×C47C2×D412yes—
258C42×C47C2×D412yes—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47C2×C22⋊C412yes—
279C23×C47#13112yes—
280C23×C47C23×C411yescharacteristic
281Q8×C47—44no—
282D4×C47—44no—
283D4×C47—44no—
284D4×C47—44no—
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—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
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—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—44no—
317C2×C4×C47—44no—
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×C47C2×C22⋊C412yes—
327C2×C4×C47C2×C22⋊C412yes—
328C2×C4×C47C2×C22⋊C412yes—
329C2×C4×C47C2×C22⋊C412yes—
330C2×C4×C47C2×C22⋊C412yes—
331C2×C4×C47#13112yes—
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C2×C4×C47H(5,𝔽2)11yescharacteristic
336C2×C4×C472−1+411yescharacteristic
337C2×C4×C472−1+411yescharacteristic
338C8×C47—41no—
339C8×C47—41no—
340C8×C47—41no—
341C8×C47—41no—
342C8×C47—41no—
343C8×C47—41no—
344C8×C47—41no—
345C8×C47—41no—
346#21855C4711yesmaximal, characteristic, direct product factor, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47C22×C22⋊C411yescharacteristic
369C22×C47#52011yescharacteristic
370C22×C47#52011yescharacteristic
371C22×C47C2×#13111yescharacteristic
372C22×C47C2×#13111yescharacteristic
373C22×C47#56811yescharacteristic
374C22×C47#56811yescharacteristic
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47—22no—
381C4×C47—41no—
382C4×C47—41no—
383C4×C47—41no—
384C4×C47—41no—
385C4×C47—41no—
386C4×C47#53511yescharacteristic
387C4×C47#53611yescharacteristic
388C4×C47#53711yescharacteristic
389C4×C47#53711yescharacteristic
390C2×#529C2×C4711yescharacteristic
391C2×#433C2×C4711yescharacteristic, complemented
392C2×#424C2×C4711yescharacteristic, complemented
393#1985C2×C4711yescharacteristic, complemented
394#1984C2×C4711yescharacteristic, complemented
395#1955C2×C4711yescharacteristic, complemented
396#1954C2×C4711yescharacteristic, complemented
397#1870C2×C4711yescharacteristic, complemented
398#1870C2×C4711yescharacteristic, complemented
399#1869C2×C4711yescharacteristic, complemented
400#1869C2×C4711yescharacteristic, complemented
401#1798C2×C4711yescharacteristic, complemented
402#1798C2×C4711yescharacteristic, complemented
403#1797C2×C4711yescharacteristic, complemented
404#1797C2×C4711yescharacteristic, complemented
405C2×C47—42no—
406C2×C47—42no—
407C2×C47—81no—
408C2×C47#231111yescharacteristic
409C2×C47#288011yescharacteristic
410C2×C47#288011yescharacteristic
411C2×C47#299211yescharacteristic
412C2×C47#299311yescharacteristic
413C2×C47#299411yescharacteristic
414C2×C47#299511yescharacteristic
415C22×M16C22×C4711yescharacteristic
416C23×C8C22×C4711yescharacteristic
417#529—24no—
418#529—24no—
419C2×#126C4×C4711yescharacteristic
420C2×#126C4×C4711yescharacteristic
421C2×#125C4×C4711yescharacteristic
422C2×#124C4×C4711yescharacteristic
423C2×#123C4×C4711yescharacteristic
424C2×#123C4×C4711yescharacteristic
425C2×C22⋊Q8C4×C4711yescharacteristic
426C2×#121C4×C4711yescharacteristic
427C2×C4×Q8C22×C4711yescharacteristic
428C2×C4×D4C22×C4711yescharacteristic
429C2×C4×D4C22×C4711yescharacteristic
430C2×C4×D4C22×C4711yescharacteristic
431C2×#117C22×C4711yescharacteristic
432C2×#117C22×C4711yescharacteristic
433C22×C42C22×C4711yescharacteristic
434#433—24no—
435#424—24no—
436C2×C4⋊C8C22×C4711yescharacteristic
437C2×C4⋊C8C22×C4711yescharacteristic
438C2×C4⋊C8C22×C4711yescharacteristic
439C2×C4⋊C8C22×C4711yescharacteristic
440C2×C4⋊C8C22×C4711yescharacteristic
441C2×C4⋊C8C22×C4711yescharacteristic
442C2×C22⋊C8C22×C4711yescharacteristic
443C2×C22⋊C8C22×C4711yescharacteristic
444C2×C22⋊C8C22×C4711yescharacteristic
445C2×C22⋊C8C22×C4711yescharacteristic
446C2×C22⋊C8C22×C4711yescharacteristic
447C2×C22⋊C8C22×C4711yescharacteristic
448C2×C22⋊C8C22×C4711yescharacteristic
449C2×C22⋊C8C22×C4711yescharacteristic
450C2×C22⋊C8C22×C4711yescharacteristic
451C2×C22⋊C8C22×C4711yescharacteristic
452C2×#97C22×C4711yescharacteristic
453C2×C4×C8C22×C4711yescharacteristic
454#336C22×C4711yescharacteristic
455#336C22×C4711yescharacteristic
456#336C22×C4711yescharacteristic
457#336C22×C4711yescharacteristic
458#336C22×C4711yescharacteristic
459#336C22×C4711yescharacteristic
460#336C22×C4711yescharacteristic
461#336C22×C4711yescharacteristic
462C47#2185511yescharacteristic, direct product factor, Sylow
463C22×Q8C2×C4×C4711yescharacteristic
464C22×D4C2×C4×C4711yescharacteristic
465C22×D4C2×C4×C4711yescharacteristic
466C22×D4C2×C4×C4711yescharacteristic
467C23×C4C2×C4×C4711yescharacteristic
468C23×C4C2×C4×C4711yescharacteristic
469C23×C4C23×C4711yescharacteristic
470C23×C4C23×C4711yescharacteristic
471C23×C4C23×C4711yescharacteristic
472C2×M16—22no—
473C2×M16—41no—
474C2×M16—41no—
475C22×C8—22no—
476C22×C8—41no—
477C22×C8—41no—
478C22×C8C23×C4711yescharacteristic
479C22×C8C23×C4711yescharacteristic
480C22×C8C23×C4711yescharacteristic
481C22×C8C23×C4711yescharacteristic
482C22×C8C23×C4711yescharacteristic
483C22×C8C23×C4711yescharacteristic
484C22×C8C23×C4711yescharacteristic
485C22×C8C23×C4711yescharacteristic
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117D4×C4714yes—
505#117D4×C4714yes—
506C2×C4⋊C4C2×C4×C4711yescharacteristic
507C2×C4⋊C4C2×C4×C4711yescharacteristic
508C2×C4⋊C4C2×C4×C4711yescharacteristic
509C2×C4⋊C4C2×C4×C4711yescharacteristic
510C2×C4⋊C4C2×C4×C4711yescharacteristic
511C2×C4⋊C4C2×C4×C4711yescharacteristic
512C2×C4⋊C4C2×C4×C4711yescharacteristic
513C2×C4⋊C4C2×C4×C4711yescharacteristic
514C2×C4⋊C4C2×C4×C4711yescharacteristic
515C2×C4⋊C4C2×C4×C4711yescharacteristic
516C2×C22⋊C4C2×C4×C4711yescharacteristic
517C2×C22⋊C4C2×C4×C4711yescharacteristic
518C2×C22⋊C4C2×C4×C4711yescharacteristic
519C2×C22⋊C4C2×C4×C4711yescharacteristic
520C2×C22⋊C4C2×C4×C4711yescharacteristic
521C2×C22⋊C4C2×C4×C4711yescharacteristic
522C2×C22⋊C4C2×C4×C4711yescharacteristic
523C2×C22⋊C4C2×C4×C4711yescharacteristic
524C2×C22⋊C4C2×C4×C4711yescharacteristic
525C2×C22⋊C4C2×C4×C4711yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×C4×C4711yescharacteristic
529C2×C42C2×C4×C4711yescharacteristic
530C2×C42C23×C4711yescharacteristic
531C2×C42C23×C4711yescharacteristic
532C2×C42C23×C4711yescharacteristic
533C2×C42C23×C4711yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—22no—
537C4⋊C8—22no—
538C4⋊C8—22no—
539C4⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#97—22no—
551C4×C8—22no—
552C24C22×C4×C4711yescharacteristic
553C24C22×C4×C4711yescharacteristic
554C24C22×C4×C4711yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
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—41no—
588C22×C4—41no—
589C22×C4C22×C4×C4711yescharacteristic
590C22×C4C22×C4×C4711yescharacteristic
591C22×C4C22×C4×C4711yescharacteristic
592C22×C4C22×C4×C4711yescharacteristic
593C22×C4C22×C4×C4711yescharacteristic
594C22×C4C22×C4×C4711yescharacteristic
595C22×C4C22×C4×C4711yescharacteristic
596C22×C4C22×C4×C4711yescharacteristic
597C22×C4C22×C4×C4711yescharacteristic
598C22×C4C22×C4×C4711yescharacteristic
599C22×C4C22×C4×C4711yescharacteristic
600C22×C4C2×D4×C4712yes—
601C22×C4C2×D4×C4712yes—
602C22×C4C24×C4711yescharacteristic
603M16—44no—
604C2×C8—21no—
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×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—44no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊C4×C4714yes—
638C4⋊C4C22⋊C4×C4714yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊C4×C4714yes—
648C22⋊C4C22⋊C4×C4714yes—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42C2×D4×C4712yes—
656C42C2×D4×C4712yes—
657C42C2×D4×C4712yes—
658C42C2×D4×C4712yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊C4×C4712yes—
679C23#131×C4712yes—
680C23C23×C4×C4711yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
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—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
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—44no—
717C2×C4—44no—
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×C4C2×C22⋊C4×C4712yes—
727C2×C4C2×C22⋊C4×C4712yes—
728C2×C4C2×C22⋊C4×C4712yes—
729C2×C4C2×C22⋊C4×C4712yes—
730C2×C4C2×C22⋊C4×C4712yes—
731C2×C4#131×C4712yes—
732C2×C4C22×D4×C4711yescharacteristic
733C2×C4C22×D4×C4711yescharacteristic
734C2×C4H(5,𝔽2)×C4711yescharacteristic
735C2×C4H(5,𝔽2)×C4711yescharacteristic
736C2×C42−1+4×C4711yescharacteristic
737C2×C42−1+4×C4711yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊C4×C4711yescharacteristic
768C22C47×#52011yescharacteristic
769C22C47×#52011yescharacteristic
770C22C2×#131×C4711yescharacteristic
771C22C2×#131×C4711yescharacteristic
772C22C47×#56811yescharacteristic
773C22C47×#56811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4C47×#53511yescharacteristic
786C4C47×#53611yescharacteristic
787C4C47×#53711yescharacteristic
788C4C47×#53711yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2C47×#231111yescharacteristic
793C2C47×#288011yescharacteristic
794C2C47×#288011yescharacteristic
795C2C47×#299211yescharacteristic
796C2C47×#299311yescharacteristic
797C2C47×#299411yescharacteristic
798C2C47×#299511yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC2×#121×C47C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#433C2semidirect
3. C2×C47×#424C2semidirect
4. C47×#1985C2semidirect
5. C47×#1984C2semidirect
6. C47×#1955C2semidirect
7. C47×#1954C2semidirect
8. C47×#1870C2semidirect
9. C47×#1870C2semidirect
10. C47×#1869C2semidirect
11. C47×#1869C2semidirect
12. C47×#1798C2semidirect
13. C47×#1798C2semidirect
14. C47×#1797C2semidirect
15. C47×#1797C2semidirect
346. #21855C47direct (N × H)
391. C2×#433C2×C47semidirect
392. C2×#424C2×C47semidirect
393. #1985C2×C47semidirect
394. #1984C2×C47semidirect
395. #1955C2×C47semidirect
396. #1954C2×C47semidirect
397. #1870C2×C47semidirect
398. #1870C2×C47semidirect
399. #1869C2×C47semidirect
400. #1869C2×C47semidirect
401. #1798C2×C47semidirect
402. #1798C2×C47semidirect
403. #1797C2×C47semidirect
404. #1797C2×C47semidirect
462. C47#21855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5292
C2×C47×#4332
C2×C47×#4242
C47×#19852
C47×#19842
C47×#19552
C47×#19542
C47×#18702
C47×#18692
C47×#17982
C47×#17972
#2185547