Finite Group Databasebeta

← C47×#22173 #26061871

Subgroups — C47×#22173 #26061871

Order 12032.

920 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#435C211yesmaximal, characteristic, complemented
2C2×C8×D4×C47C211yesmaximal, characteristic, complemented
3C47×#2392C211yesmaximal, characteristic
4C47×#1924C211yesmaximal, characteristic, complemented
5C47×#1923C211yesmaximal, characteristic, complemented
6C47×#1917C211yesmaximal, characteristic, complemented
7C47×#1916C211yesmaximal, characteristic, complemented
8C47×#1870C211yesmaximal, characteristic, complemented
9C47×#1870C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1851C211yesmaximal, characteristic, complemented
13C47×#1850C211yesmaximal, characteristic, complemented
14C47×#1798C211yesmaximal, characteristic, complemented
15C47×#1729C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C23×C8×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×#117×C47C2211yescharacteristic
24C47×#435—24no—
25C8×D4×C47—24no—
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊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×C22⋊C8×C47C2211yescharacteristic
38C2×#97×C47C2211yescharacteristic
39C2×C4×C8×C47C2211yescharacteristic
40C47×#398C411yescharacteristic
41C47×#397C411yescharacteristic
42C47×#396C411yescharacteristic
43C47×#396C411yescharacteristic
44C47×#394C411yescharacteristic
45C47×#394C411yescharacteristic
46C47×#394C411yescharacteristic
47C47×#392C411yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C4×C22⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×D4×C47C2×C411yescharacteristic
62C22×D4×C47C2×C411yescharacteristic
63C22×D4×C47C2×C411yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C23×C4×C47C2311yescharacteristic
66C23×C4×C47C2311yescharacteristic
67C2×M16×C47—22no—
68C2×M16×C47—22no—
69C2×M16×C47—41no—
70C2×M16×C47—41no—
71C2×M16×C47—41no—
72C2×M16×C47—41no—
73C22×C8×C47—22no—
74C22×C8×C47—41no—
75C22×C8×C47—41no—
76C22×C8×C47—41no—
77C22×C8×C47—41no—
78C22×C8×C47D414yescomplemented
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87C4×D4×C47—22no—
88C4×D4×C47—22no—
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91C4×D4×C47—41no—
92C4×D4×C47—41no—
93#117×C47—41no—
94#117×C47—41no—
95C2×C4⋊C4×C47C2×C411yescharacteristic
96C2×C4⋊C4×C47C2×C411yescharacteristic
97C2×C4⋊C4×C47C2×C411yescharacteristic
98C2×C4⋊C4×C47C2×C411yescharacteristic
99C2×C4⋊C4×C47C2×C411yescharacteristic
100C2×C4⋊C4×C47C2×C411yescharacteristic
101C2×C4⋊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×C22⋊C4×C47C2×C411yescharacteristic
109C2×C22⋊C4×C47C2×C411yescharacteristic
110C2×C22⋊C4×C47C2×C411yescharacteristic
111C2×C22⋊C4×C47C2×C411yescharacteristic
112C2×C22⋊C4×C47C2×C411yescharacteristic
113C2×C22⋊C4×C47C2×C411yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C4⋊C8×C47—22no—
119C4⋊C8×C47—22no—
120C4⋊C8×C47—41no—
121C4⋊C8×C47—41no—
122C22⋊C8×C47—22no—
123C22⋊C8×C47—22no—
124C22⋊C8×C47—22no—
125C22⋊C8×C47—22no—
126C22⋊C8×C47—41no—
127C22⋊C8×C47—41no—
128C22⋊C8×C47—41no—
129C22⋊C8×C47—41no—
130#97×C47—22no—
131C4×C8×C47—22no—
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×C47C22×C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141C2×D4×C47—22no—
142C2×D4×C47—22no—
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—41no—
147C2×D4×C47—41no—
148C2×D4×C47—41no—
149C2×D4×C47—41no—
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—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
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×C47C22×C411yescharacteristic
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C2×D412yes—
178C22×C4×C47#4112yes—
179C22×C4×C47C2411yescharacteristic
180M16×C47—44no—
181M16×C47—44no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
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—44no—
205C2×C8×C47—44no—
206C2×C8×C47C2×D412yes—
207C2×C8×C47C2×D412yes—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—22no—
210C4⋊C4×C47—22no—
211C4⋊C4×C47—41no—
212C4⋊C4×C47—41no—
213C4⋊C4×C47—41no—
214C4⋊C4×C47—41no—
215C22⋊C4×C47—22no—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—41no—
223C22⋊C4×C47—41no—
224C22⋊C4×C47—41no—
225C22⋊C4×C47—41no—
226C22⋊C4×C47—41no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
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×C47C4×D412yes—
255C23×C47#13112yes—
256C23×C47C23×C411yescharacteristic
257D4×C47—28no—
258D4×C47—44no—
259D4×C47—44no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
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—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47C4×D412yes—
304C2×C4×C47#13112yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47H(5,𝔽2)11yescharacteristic
308C2×C4×C47H(5,𝔽2)11yescharacteristic
309C2×C4×C47H(5,𝔽2)11yescharacteristic
310C2×C4×C472−1+411yescharacteristic
311C8×C47—22no—
312C8×C47—22no—
313C8×C47—41no—
314C8×C47—41no—
315C8×C47—41no—
316C8×C47—41no—
317C8×C47—41no—
318C8×C47—41no—
319#22173C4711yesmaximal, characteristic, direct product factor, Sylow
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47C2×C4×D411yescharacteristic
342C22×C47#51811yescharacteristic
343C22×C47#52011yescharacteristic
344C22×C47C2×#13111yescharacteristic
345C22×C47C2×#13111yescharacteristic
346C22×C47#56811yescharacteristic
347C22×C47#56811yescharacteristic
348C4×C47—22no—
349C4×C47—22no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—41no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47#53411yescharacteristic
360C4×C47#53711yescharacteristic
361C4×C47#53811yescharacteristic
362C4×C47#53911yescharacteristic
363C2×#435C2×C4711yescharacteristic, complemented
364C2×C8×D4C2×C4711yescharacteristic, complemented
365#2392C2×C4711yescharacteristic
366#1924C2×C4711yescharacteristic, complemented
367#1923C2×C4711yescharacteristic, complemented
368#1917C2×C4711yescharacteristic, complemented
369#1916C2×C4711yescharacteristic, complemented
370#1870C2×C4711yescharacteristic, complemented
371#1870C2×C4711yescharacteristic, complemented
372#1870C2×C4711yescharacteristic, complemented
373#1869C2×C4711yescharacteristic, complemented
374#1851C2×C4711yescharacteristic, complemented
375#1850C2×C4711yescharacteristic, complemented
376#1798C2×C4711yescharacteristic, complemented
377#1729C2×C4711yescharacteristic, complemented
378C2×C47—42no—
379C2×C47—42no—
380C2×C47—81no—
381C2×C47#232511yescharacteristic
382C2×C47#292911yescharacteristic
383C2×C47#293011yescharacteristic
384C2×C47#297611yescharacteristic
385C2×C47#298111yescharacteristic
386C2×C47#299211yescharacteristic
387C2×C47#299311yescharacteristic
388C22×M16C22×C4711yescharacteristic
389C22×M16C22×C4711yescharacteristic
390C23×C8C22×C4711yescharacteristic
391C23×C8C22×C4711yescharacteristic
392C2×C4×D4C22×C4711yescharacteristic
393C2×C4×D4C22×C4711yescharacteristic
394C2×C4×D4C22×C4711yescharacteristic
395C2×#117C22×C4711yescharacteristic
396#435—24no—
397C8×D4—24no—
398C2×C4⋊C8C22×C4711yescharacteristic
399C2×C4⋊C8C22×C4711yescharacteristic
400C2×C4⋊C8C22×C4711yescharacteristic
401C2×C4⋊C8C22×C4711yescharacteristic
402C2×C22⋊C8C22×C4711yescharacteristic
403C2×C22⋊C8C22×C4711yescharacteristic
404C2×C22⋊C8C22×C4711yescharacteristic
405C2×C22⋊C8C22×C4711yescharacteristic
406C2×C22⋊C8C22×C4711yescharacteristic
407C2×C22⋊C8C22×C4711yescharacteristic
408C2×C22⋊C8C22×C4711yescharacteristic
409C2×C22⋊C8C22×C4711yescharacteristic
410C2×#97C22×C4711yescharacteristic
411C2×C4×C8C22×C4711yescharacteristic
412#398C4×C4711yescharacteristic
413#397C4×C4711yescharacteristic
414#396C4×C4711yescharacteristic
415#396C4×C4711yescharacteristic
416#394C4×C4711yescharacteristic
417#394C4×C4711yescharacteristic
418#394C4×C4711yescharacteristic
419#392C4×C4711yescharacteristic
420C4×C4⋊C4C22×C4711yescharacteristic
421C4×C22⋊C4C22×C4711yescharacteristic
422C4×C22⋊C4C22×C4711yescharacteristic
423#336C22×C4711yescharacteristic
424#336C22×C4711yescharacteristic
425#336C22×C4711yescharacteristic
426#336C22×C4711yescharacteristic
427#336C22×C4711yescharacteristic
428#336C22×C4711yescharacteristic
429#336C22×C4711yescharacteristic
430#336C22×C4711yescharacteristic
431#336C22×C4711yescharacteristic
432#336C22×C4711yescharacteristic
433C47#2217311yescharacteristic, direct product factor, Sylow
434C22×D4C2×C4×C4711yescharacteristic
435C22×D4C2×C4×C4711yescharacteristic
436C22×D4C2×C4×C4711yescharacteristic
437C23×C4C23×C4711yescharacteristic
438C23×C4C23×C4711yescharacteristic
439C23×C4C23×C4711yescharacteristic
440C2×M16—22no—
441C2×M16—22no—
442C2×M16—41no—
443C2×M16—41no—
444C2×M16—41no—
445C2×M16—41no—
446C22×C8—22no—
447C22×C8—41no—
448C22×C8—41no—
449C22×C8—41no—
450C22×C8—41no—
451C22×C8D4×C4714yescomplemented
452C22×C8C23×C4711yescharacteristic
453C22×C8C23×C4711yescharacteristic
454C22×C8C23×C4711yescharacteristic
455C22×C8C23×C4711yescharacteristic
456C22×C8C23×C4711yescharacteristic
457C22×C8C23×C4711yescharacteristic
458C22×C8C23×C4711yescharacteristic
459C22×C8C23×C4711yescharacteristic
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466#117—41no—
467#117—41no—
468C2×C4⋊C4C2×C4×C4711yescharacteristic
469C2×C4⋊C4C2×C4×C4711yescharacteristic
470C2×C4⋊C4C2×C4×C4711yescharacteristic
471C2×C4⋊C4C2×C4×C4711yescharacteristic
472C2×C4⋊C4C2×C4×C4711yescharacteristic
473C2×C4⋊C4C2×C4×C4711yescharacteristic
474C2×C4⋊C4C2×C4×C4711yescharacteristic
475C2×C22⋊C4C2×C4×C4711yescharacteristic
476C2×C22⋊C4C2×C4×C4711yescharacteristic
477C2×C22⋊C4C2×C4×C4711yescharacteristic
478C2×C22⋊C4C2×C4×C4711yescharacteristic
479C2×C22⋊C4C2×C4×C4711yescharacteristic
480C2×C22⋊C4C2×C4×C4711yescharacteristic
481C2×C22⋊C4C2×C4×C4711yescharacteristic
482C2×C22⋊C4C2×C4×C4711yescharacteristic
483C2×C22⋊C4C2×C4×C4711yescharacteristic
484C2×C22⋊C4C2×C4×C4711yescharacteristic
485C2×C22⋊C4C2×C4×C4711yescharacteristic
486C2×C22⋊C4C2×C4×C4711yescharacteristic
487C2×C42C23×C4711yescharacteristic
488C2×C42C23×C4711yescharacteristic
489C2×C42C23×C4711yescharacteristic
490C2×C42C23×C4711yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—41no—
494C4⋊C8—41no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—41no—
501C22⋊C8—41no—
502C22⋊C8—41no—
503#97—22no—
504C4×C8—22no—
505#95C2×C4×C4711yescharacteristic
506#95C2×C4×C4711yescharacteristic
507#95C2×C4×C4711yescharacteristic
508#95C2×C4×C4711yescharacteristic
509#95C2×C4×C4711yescharacteristic
510#95C2×C4×C4711yescharacteristic
511C24C22×C4×C4711yescharacteristic
512C24C22×C4×C4711yescharacteristic
513C24C22×C4×C4711yescharacteristic
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C22×C4×C4711yescharacteristic
540C22×C4C22×C4×C4711yescharacteristic
541C22×C4C22×C4×C4711yescharacteristic
542C22×C4C22×C4×C4711yescharacteristic
543C22×C4C22×C4×C4711yescharacteristic
544C22×C4C22×C4×C4711yescharacteristic
545C22×C4C22×C4×C4711yescharacteristic
546C22×C4C22×C4×C4711yescharacteristic
547C22×C4C22×C4×C4711yescharacteristic
548C22×C4C22×C4×C4711yescharacteristic
549C22×C4C22×C4×C4711yescharacteristic
550C22×C4C2×D4×C4712yes—
551C22×C4#41×C4712yes—
552C22×C4C24×C4711yescharacteristic
553M16—44no—
554M16—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8—44no—
579C2×C8C2×D4×C4712yes—
580C2×C8C2×D4×C4712yes—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23C4×D4×C4712yes—
628C23#131×C4712yes—
629C23C23×C4×C4711yescharacteristic
630D4—28no—
631D4—44no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4C4×D4×C4712yes—
677C2×C4#131×C4712yes—
678C2×C4C22×D4×C4711yescharacteristic
679C2×C4C2×#41×C4711yescharacteristic
680C2×C4H(5,𝔽2)×C4711yescharacteristic
681C2×C4H(5,𝔽2)×C4711yescharacteristic
682C2×C4H(5,𝔽2)×C4711yescharacteristic
683C2×C42−1+4×C4711yescharacteristic
684C8—22no—
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22C2×C4×D4×C4711yescharacteristic
714C22C47×#51811yescharacteristic
715C22C47×#52011yescharacteristic
716C22C2×#131×C4711yescharacteristic
717C22C2×#131×C4711yescharacteristic
718C22C47×#56811yescharacteristic
719C22C47×#56811yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4C47×#53411yescharacteristic
732C4C47×#53711yescharacteristic
733C4C47×#53811yescharacteristic
734C4C47×#53911yescharacteristic
735C2—42no—
736C2—42no—
737C2—81no—
738C2C47×#232511yescharacteristic
739C2C47×#292911yescharacteristic
740C2C47×#293011yescharacteristic
741C2C47×#297611yescharacteristic
742C2C47×#298111yescharacteristic
743C2C47×#299211yescharacteristic
744C2C47×#299311yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C23×C4
prime radicalC47×#392C4
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×#435C2semidirect
2. C2×C8×D4×C47C2semidirect
4. C47×#1924C2semidirect
5. C47×#1923C2semidirect
6. C47×#1917C2semidirect
7. C47×#1916C2semidirect
8. C47×#1870C2semidirect
9. C47×#1870C2semidirect
10. C47×#1870C2semidirect
11. C47×#1869C2semidirect
12. C47×#1851C2semidirect
13. C47×#1850C2semidirect
14. C47×#1798C2semidirect
15. C47×#1729C2semidirect
78. C22×C8×C47D4semidirect
319. #22173C47direct (N × H)
363. C2×#435C2×C47semidirect
364. C2×C8×D4C2×C47semidirect
366. #1924C2×C47semidirect
367. #1923C2×C47semidirect
368. #1917C2×C47semidirect
369. #1916C2×C47semidirect
370. #1870C2×C47semidirect
371. #1870C2×C47semidirect
372. #1870C2×C47semidirect
373. #1869C2×C47semidirect
374. #1851C2×C47semidirect
375. #1850C2×C47semidirect
376. #1798C2×C47semidirect
377. #1729C2×C47semidirect
433. C47#22173direct (N × H)
451. C22×C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4352
C2×C8×D4×C472
C47×#23922
C47×#19242
C47×#19232
C47×#19172
C47×#19162
C47×#18702
C47×#18692
C47×#18512
C47×#18502
C47×#17982
C47×#17292
#2217347