Finite Group Databasebeta

← C47×#22472 #26062170

Subgroups — C47×#22472 #26062170

Order 12032.

1162 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×#529C211yesmaximal, characteristic
2C2×C47×#436C211yesmaximal, characteristic, complemented
3C2×C47×#435C211yesmaximal, characteristic, complemented
4C47×#1985C211yesmaximal, characteristic, complemented
5C47×#1984C211yesmaximal, characteristic, complemented
6C47×#1870C211yesmaximal, characteristic, complemented
7C47×#1870C211yesmaximal, characteristic, complemented
8C47×#1870C211yesmaximal, characteristic, complemented
9C47×#1869C211yesmaximal, characteristic, complemented
10C47×#1818C211yesmaximal, characteristic, complemented
11C47×#1817C211yesmaximal, characteristic, complemented
12C47×#1798C211yesmaximal, characteristic, complemented
13C47×#1750C211yesmaximal, characteristic, complemented
14C47×#1729C211yesmaximal, characteristic, complemented
15C47×#1728C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C47×#529—24no—
21C47×#529—24no—
22C2×#126×C47C411yescharacteristic
23C2×#126×C47C411yescharacteristic
24C2×#125×C47C411yescharacteristic
25C2×#124×C47C411yescharacteristic
26C2×#123×C47C411yescharacteristic
27C2×#123×C47C411yescharacteristic
28C2×C22⋊Q8×C47C411yescharacteristic
29C2×#121×C47C411yescharacteristic
30C2×C4×Q8×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C47×#436—24no—
38C47×#435—24no—
39C2×C4⋊C8×C47C2211yescharacteristic
40C2×C4⋊C8×C47C2211yescharacteristic
41C2×C22⋊C8×C47C2211yescharacteristic
42C2×C22⋊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×#97×C47C2211yescharacteristic
50C2×C4×C8×C47C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
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—22no—
74C2×M16×C47—22no—
75C2×M16×C47—22no—
76C2×M16×C47—22no—
77C2×M16×C47—22no—
78C2×M16×C47—41no—
79C2×M16×C47—41no—
80C2×M16×C47—41no—
81C22×C8×C47—22no—
82C22×C8×C47—22no—
83C22×C8×C47—41no—
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C22×C8×C47C2311yescharacteristic
92#126×C47—24no—
93#126×C47—24no—
94#125×C47—24no—
95#124×C47—24no—
96#123×C47—24no—
97#123×C47—24no—
98C22⋊Q8×C47—24no—
99#121×C47—24no—
100C4×Q8×C47—22no—
101C4×Q8×C47—22no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106C4×D4×C47D414yes—
107C4×D4×C47D414yes—
108#117×C47—22no—
109#117×C47—22no—
110#117×C47—22no—
111#117×C47—22no—
112C2×C4⋊C4×C47C2×C411yescharacteristic
113C2×C4⋊C4×C47C2×C411yescharacteristic
114C2×C4⋊C4×C47C2×C411yescharacteristic
115C2×C4⋊C4×C47C2×C411yescharacteristic
116C2×C4⋊C4×C47C2×C411yescharacteristic
117C2×C4⋊C4×C47C2×C411yescharacteristic
118C2×C4⋊C4×C47C2×C411yescharacteristic
119C2×C4⋊C4×C47C2×C411yescharacteristic
120C2×C4⋊C4×C47C2×C411yescharacteristic
121C2×C4⋊C4×C47C2×C411yescharacteristic
122C2×C22⋊C4×C47C2×C411yescharacteristic
123C2×C22⋊C4×C47C2×C411yescharacteristic
124C2×C22⋊C4×C47C2×C411yescharacteristic
125C2×C22⋊C4×C47C2×C411yescharacteristic
126C2×C22⋊C4×C47C2×C411yescharacteristic
127C2×C22⋊C4×C47C2×C411yescharacteristic
128C2×C22⋊C4×C47C2×C411yescharacteristic
129C2×C22⋊C4×C47C2×C411yescharacteristic
130C2×C22⋊C4×C47C2×C411yescharacteristic
131C2×C22⋊C4×C47C2×C411yescharacteristic
132C2×C42×C47—22no—
133C2×C42×C47—22no—
134C2×C42×C47C2×C411yescharacteristic
135C2×C42×C47C2×C411yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C2×C42×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C4⋊C8×C47—22no—
141C4⋊C8×C47—22no—
142C22⋊C8×C47—22no—
143C22⋊C8×C47—22no—
144C22⋊C8×C47—22no—
145C22⋊C8×C47—22no—
146C22⋊C8×C47—22no—
147C22⋊C8×C47—22no—
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—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47C22⋊C414yes—
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—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
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—41no—
185C22×C4×C47—41no—
186C22×C4×C47—41no—
187C22×C4×C47C22×C411yescharacteristic
188C22×C4×C47C22×C411yescharacteristic
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×C47C2×D412yes—
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2411yescharacteristic
203M16×C47—44no—
204M16×C47—44no—
205M16×C47—44no—
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—
229C2×C8×C47#4112yes—
230C2×C8×C47#4112yes—
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×C47—22no—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—22no—
240C4⋊C4×C47C22⋊C414yes—
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×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47C22⋊C414yes—
250C22⋊C4×C47C22⋊C414yes—
251C42×C47—22no—
252C42×C47—22no—
253C42×C47—21no—
254C42×C47—21no—
255C42×C47—21no—
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47C2×D412yes—
260C42×C47C2×D412yes—
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×C47—21no—
279C23×C47—21no—
280C23×C47C2×C22⋊C412yes—
281C23×C47C2×C22⋊C412yes—
282C23×C47C23×C411yescharacteristic
283Q8×C47—44no—
284D4×C47—44no—
285D4×C47—44no—
286D4×C47—44no—
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—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
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—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—44no—
324C2×C4×C47—44no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47C2×C22⋊C412yes—
330C2×C4×C47C2×C22⋊C412yes—
331C2×C4×C47C2×C22⋊C412yes—
332C2×C4×C47C2×C22⋊C412yes—
333C2×C4×C47#13112yes—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C2×C4×C47C2×#4111yescharacteristic
338C2×C4×C47H(5,𝔽2)11yescharacteristic
339C2×C4×C472−1+411yescharacteristic
340C8×C47—22no—
341C8×C47—22no—
342C8×C47—41no—
343C8×C47—41no—
344C8×C47—41no—
345C8×C47—41no—
346C8×C47—41no—
347C8×C47—41no—
348#22472C4711yesmaximal, characteristic, direct product factor, Sylow
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
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×C47—41no—
369C22×C47—41no—
370C22×C47C22×C22⋊C411yescharacteristic
371C22×C47C4×#4111yescharacteristic
372C22×C47#52011yescharacteristic
373C22×C47C2×#13111yescharacteristic
374C22×C47#56811yescharacteristic
375C22×C47#56811yescharacteristic
376C22×C47#56811yescharacteristic
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47—22no—
381C4×C47—22no—
382C4×C47—41no—
383C4×C47—41no—
384C4×C47—41no—
385C4×C47—41no—
386C4×C47—41no—
387C4×C47—41no—
388C4×C47#54611yescharacteristic
389C4×C47#54611yescharacteristic
390C4×C47#54711yescharacteristic
391C4×C47#54711yescharacteristic
392C2×#529C2×C4711yescharacteristic
393C2×#436C2×C4711yescharacteristic, complemented
394C2×#435C2×C4711yescharacteristic, complemented
395#1985C2×C4711yescharacteristic, complemented
396#1984C2×C4711yescharacteristic, complemented
397#1870C2×C4711yescharacteristic, complemented
398#1870C2×C4711yescharacteristic, complemented
399#1870C2×C4711yescharacteristic, complemented
400#1869C2×C4711yescharacteristic, complemented
401#1818C2×C4711yescharacteristic, complemented
402#1817C2×C4711yescharacteristic, complemented
403#1798C2×C4711yescharacteristic, complemented
404#1750C2×C4711yescharacteristic, complemented
405#1729C2×C4711yescharacteristic, complemented
406#1728C2×C4711yescharacteristic, complemented
407C2×C47—42no—
408C2×C47—42no—
409C2×C47—81no—
410C2×C47#233911yescharacteristic
411C2×C47#287911yescharacteristic
412C2×C47#288011yescharacteristic
413C2×C47#296711yescharacteristic
414C2×C47#296911yescharacteristic
415C2×C47#299311yescharacteristic
416C2×C47#299511yescharacteristic
417C22×M16C22×C4711yescharacteristic
418C22×M16C22×C4711yescharacteristic
419C22×M16C22×C4711yescharacteristic
420C23×C8C22×C4711yescharacteristic
421#529—24no—
422#529—24no—
423C2×#126C4×C4711yescharacteristic
424C2×#126C4×C4711yescharacteristic
425C2×#125C4×C4711yescharacteristic
426C2×#124C4×C4711yescharacteristic
427C2×#123C4×C4711yescharacteristic
428C2×#123C4×C4711yescharacteristic
429C2×C22⋊Q8C4×C4711yescharacteristic
430C2×#121C4×C4711yescharacteristic
431C2×C4×Q8C22×C4711yescharacteristic
432C2×C4×D4C22×C4711yescharacteristic
433C2×C4×D4C22×C4711yescharacteristic
434C2×C4×D4C22×C4711yescharacteristic
435C2×#117C22×C4711yescharacteristic
436C2×#117C22×C4711yescharacteristic
437C22×C42C22×C4711yescharacteristic
438#436—24no—
439#435—24no—
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×#97C22×C4711yescharacteristic
451C2×C4×C8C22×C4711yescharacteristic
452#336C22×C4711yescharacteristic
453#336C22×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
462#336C22×C4711yescharacteristic
463#336C22×C4711yescharacteristic
464C47#2247211yescharacteristic, direct product factor, Sylow
465C22×Q8C2×C4×C4711yescharacteristic
466C22×D4C2×C4×C4711yescharacteristic
467C22×D4C2×C4×C4711yescharacteristic
468C22×D4C2×C4×C4711yescharacteristic
469C23×C4C2×C4×C4711yescharacteristic
470C23×C4C2×C4×C4711yescharacteristic
471C23×C4C23×C4711yescharacteristic
472C23×C4C23×C4711yescharacteristic
473C23×C4C23×C4711yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—41no—
481C2×M16—41no—
482C2×M16—41no—
483C22×C8—22no—
484C22×C8—22no—
485C22×C8—41no—
486C22×C8C23×C4711yescharacteristic
487C22×C8C23×C4711yescharacteristic
488C22×C8C23×C4711yescharacteristic
489C22×C8C23×C4711yescharacteristic
490C22×C8C23×C4711yescharacteristic
491C22×C8C23×C4711yescharacteristic
492C22×C8C23×C4711yescharacteristic
493C22×C8C23×C4711yescharacteristic
494#126—24no—
495#126—24no—
496#125—24no—
497#124—24no—
498#123—24no—
499#123—24no—
500C22⋊Q8—24no—
501#121—24no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4D4×C4714yes—
509C4×D4D4×C4714yes—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—22no—
514C2×C4⋊C4C2×C4×C4711yescharacteristic
515C2×C4⋊C4C2×C4×C4711yescharacteristic
516C2×C4⋊C4C2×C4×C4711yescharacteristic
517C2×C4⋊C4C2×C4×C4711yescharacteristic
518C2×C4⋊C4C2×C4×C4711yescharacteristic
519C2×C4⋊C4C2×C4×C4711yescharacteristic
520C2×C4⋊C4C2×C4×C4711yescharacteristic
521C2×C4⋊C4C2×C4×C4711yescharacteristic
522C2×C4⋊C4C2×C4×C4711yescharacteristic
523C2×C4⋊C4C2×C4×C4711yescharacteristic
524C2×C22⋊C4C2×C4×C4711yescharacteristic
525C2×C22⋊C4C2×C4×C4711yescharacteristic
526C2×C22⋊C4C2×C4×C4711yescharacteristic
527C2×C22⋊C4C2×C4×C4711yescharacteristic
528C2×C22⋊C4C2×C4×C4711yescharacteristic
529C2×C22⋊C4C2×C4×C4711yescharacteristic
530C2×C22⋊C4C2×C4×C4711yescharacteristic
531C2×C22⋊C4C2×C4×C4711yescharacteristic
532C2×C22⋊C4C2×C4×C4711yescharacteristic
533C2×C22⋊C4C2×C4×C4711yescharacteristic
534C2×C42—22no—
535C2×C42—22no—
536C2×C42C2×C4×C4711yescharacteristic
537C2×C42C2×C4×C4711yescharacteristic
538C2×C42C23×C4711yescharacteristic
539C2×C42C23×C4711yescharacteristic
540C2×C42C23×C4711yescharacteristic
541C2×C42C23×C4711yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—22no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—41no—
551C22⋊C8—41no—
552#97—22no—
553C4×C8—22no—
554C24C22×C4×C4711yescharacteristic
555C24C22×C4×C4711yescharacteristic
556C24C22×C4×C4711yescharacteristic
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—41no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4C22⋊C4×C4714yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
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×C4C2×D4×C4712yes—
603C22×C4C2×D4×C4712yes—
604C22×C4C24×C4711yescharacteristic
605M16—44no—
606M16—44no—
607M16—44no—
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—21no—
629C2×C8—21no—
630C2×C8—44no—
631C2×C8#41×C4712yes—
632C2×C8#41×C4712yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4C22⋊C4×C4714yes—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4C22⋊C4×C4714yes—
652C22⋊C4C22⋊C4×C4714yes—
653C42—22no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42C2×D4×C4712yes—
662C42C2×D4×C4712yes—
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—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23C2×C22⋊C4×C4712yes—
683C23C2×C22⋊C4×C4712yes—
684C23C23×C4×C4711yescharacteristic
685Q8—44no—
686D4—44no—
687D4—44no—
688D4—44no—
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—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
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—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4C2×C22⋊C4×C4712yes—
732C2×C4C2×C22⋊C4×C4712yes—
733C2×C4C2×C22⋊C4×C4712yes—
734C2×C4C2×C22⋊C4×C4712yes—
735C2×C4#131×C4712yes—
736C2×C4C22×D4×C4711yescharacteristic
737C2×C4C22×D4×C4711yescharacteristic
738C2×C4C2×#41×C4711yescharacteristic
739C2×C4C2×#41×C4711yescharacteristic
740C2×C4H(5,𝔽2)×C4711yescharacteristic
741C2×C42−1+4×C4711yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C22×C22⋊C4×C4711yescharacteristic
772C22C4×#41×C4711yescharacteristic
773C22C47×#52011yescharacteristic
774C22C2×#131×C4711yescharacteristic
775C22C47×#56811yescharacteristic
776C22C47×#56811yescharacteristic
777C22C47×#56811yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4C47×#54611yescharacteristic
790C4C47×#54611yescharacteristic
791C4C47×#54711yescharacteristic
792C4C47×#54711yescharacteristic
793C2—42no—
794C2—42no—
795C2—81no—
796C2C47×#233911yescharacteristic
797C2C47×#287911yescharacteristic
798C2C47×#288011yescharacteristic
799C2C47×#296711yescharacteristic
800C2C47×#296911yescharacteristic
801C2C47×#299311yescharacteristic
802C2C47×#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×#436C2semidirect
3. C2×C47×#435C2semidirect
4. C47×#1985C2semidirect
5. C47×#1984C2semidirect
6. C47×#1870C2semidirect
7. C47×#1870C2semidirect
8. C47×#1870C2semidirect
9. C47×#1869C2semidirect
10. C47×#1818C2semidirect
11. C47×#1817C2semidirect
12. C47×#1798C2semidirect
13. C47×#1750C2semidirect
14. C47×#1729C2semidirect
15. C47×#1728C2semidirect
348. #22472C47direct (N × H)
393. C2×#436C2×C47semidirect
394. C2×#435C2×C47semidirect
395. #1985C2×C47semidirect
396. #1984C2×C47semidirect
397. #1870C2×C47semidirect
398. #1870C2×C47semidirect
399. #1870C2×C47semidirect
400. #1869C2×C47semidirect
401. #1818C2×C47semidirect
402. #1817C2×C47semidirect
403. #1798C2×C47semidirect
404. #1750C2×C47semidirect
405. #1729C2×C47semidirect
406. #1728C2×C47semidirect
464. C47#22472direct (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×#4362
C2×C47×#4352
C47×#19852
C47×#19842
C47×#18702
C47×#18692
C47×#18182
C47×#18172
C47×#17982
C47×#17502
C47×#17292
C47×#17282
#2247247