Finite Group Databasebeta

← C47×#22336 #26062034

Subgroups — C47×#22336 #26062034

Order 12032.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2392C211yesmaximal, characteristic
2C47×#1955C211yesmaximal, characteristic, complemented
3C47×#1954C211yesmaximal, characteristic, complemented
4C47×#1923C211yesmaximal, characteristic, complemented
5C47×#1923C211yesmaximal, characteristic, complemented
6C47×#1917C211yesmaximal, characteristic, complemented
7C47×#1916C211yesmaximal, characteristic, complemented
8C47×#1870C211yesmaximal, characteristic, complemented
9C47×#1870C211yesmaximal, characteristic, complemented
10C47×#1869C211yesmaximal, characteristic, complemented
11C47×#1869C211yesmaximal, characteristic, complemented
12C47×#1818C211yesmaximal, characteristic, complemented
13C47×#1753C211yesmaximal, characteristic, complemented
14C47×#1752C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×#117×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C22⋊C8×C47C2211yescharacteristic
25C2×C22⋊C8×C47C2211yescharacteristic
26C2×C22⋊C8×C47C2211yescharacteristic
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×#97×C47C2211yescharacteristic
35C2×#97×C47C2211yescharacteristic
36C2×C4×C8×C47C2211yescharacteristic
37C2×C4×C8×C47C2211yescharacteristic
38C47×#398C411yescharacteristic
39C47×#397C411yescharacteristic
40C47×#396C411yescharacteristic
41C47×#396C411yescharacteristic
42C47×#394C411yescharacteristic
43C47×#394C411yescharacteristic
44C47×#394C411yescharacteristic
45C47×#392C411yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C22⋊C4×C47C2211yescharacteristic
48C4×C22⋊C4×C47C2211yescharacteristic
49C47×#336C2211yescharacteristic
50C47×#336C2211yescharacteristic
51C47×#336C2211yescharacteristic
52C47×#336C2211yescharacteristic
53C47×#336C2211yescharacteristic
54C47×#336C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×D4×C47C2×C411yescharacteristic
60C22×D4×C47C2×C411yescharacteristic
61C22×D4×C47C2×C411yescharacteristic
62C23×C4×C47C2311yescharacteristic
63C23×C4×C47C2311yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C2×M16×C47—22no—
66C2×M16×C47—41no—
67C2×M16×C47—41no—
68C22×C8×C47—22no—
69C22×C8×C47—41no—
70C22×C8×C47—41no—
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C4×D4×C47—41no—
80C4×D4×C47—41no—
81C4×D4×C47—41no—
82C4×D4×C47—41no—
83C4×D4×C47—41no—
84C4×D4×C47—41no—
85#117×C47—41no—
86#117×C47—41no—
87C2×C4⋊C4×C47C2×C411yescharacteristic
88C2×C4⋊C4×C47C2×C411yescharacteristic
89C2×C4⋊C4×C47C2×C411yescharacteristic
90C2×C4⋊C4×C47C2×C411yescharacteristic
91C2×C4⋊C4×C47C2×C411yescharacteristic
92C2×C4⋊C4×C47C2×C411yescharacteristic
93C2×C4⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2×C411yescharacteristic
95C2×C22⋊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×C42×C47C2311yescharacteristic
107C2×C42×C47C2311yescharacteristic
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C4⋊C8×C47—41no—
111C4⋊C8×C47—41no—
112C22⋊C8×C47—22no—
113C22⋊C8×C47—22no—
114C22⋊C8×C47—22no—
115C22⋊C8×C47—22no—
116C22⋊C8×C47—41no—
117C22⋊C8×C47—41no—
118C22⋊C8×C47—41no—
119C22⋊C8×C47—41no—
120C22⋊C8×C47—41no—
121C22⋊C8×C47—41no—
122#97×C47—41no—
123#97×C47—41no—
124C4×C8×C47—41no—
125C4×C8×C47—41no—
126#95×C47C2×C411yescharacteristic
127#95×C47C2×C411yescharacteristic
128#95×C47C2×C411yescharacteristic
129#95×C47C2×C411yescharacteristic
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132C24×C47C22×C411yescharacteristic
133C24×C47C22×C411yescharacteristic
134C24×C47C22×C411yescharacteristic
135C2×D4×C47—22no—
136C2×D4×C47—22no—
137C2×D4×C47—22no—
138C2×D4×C47—41no—
139C2×D4×C47—41no—
140C2×D4×C47—41no—
141C2×D4×C47—41no—
142C2×D4×C47—41no—
143C2×D4×C47—41no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
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—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C22×C411yescharacteristic
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×C47C2411yescharacteristic
174M16×C47—44no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
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—44no—
198C2×C8×C47#4112yes—
199C2×C8×C47#4112yes—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—41no—
202C4⋊C4×C47—41no—
203C4⋊C4×C47—41no—
204C4⋊C4×C47—41no—
205C4⋊C4×C47—41no—
206C4⋊C4×C47—41no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—41no—
210C22⋊C4×C47—41no—
211C22⋊C4×C47—41no—
212C22⋊C4×C47—41no—
213C22⋊C4×C47—41no—
214C22⋊C4×C47—41no—
215C22⋊C4×C47—41no—
216C22⋊C4×C47—41no—
217C22⋊C4×C47—41no—
218C22⋊C4×C47—41no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×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#13112yes—
248C23×C47C23×C411yescharacteristic
249D4×C47—44no—
250D4×C47—44no—
251D4×C47—44no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
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—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47#13112yes—
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47H(5,𝔽2)11yescharacteristic
300C2×C4×C47H(5,𝔽2)11yescharacteristic
301C2×C4×C47H(5,𝔽2)11yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C8×C47—22no—
304C8×C47—22no—
305C8×C47—41no—
306C8×C47—41no—
307C8×C47—41no—
308C8×C47—41no—
309C8×C47—41no—
310C8×C47—41no—
311#22336C4711yesmaximal, characteristic, direct product factor, Sylow
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—41no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47C4×#4111yescharacteristic
334C22×C47#51811yescharacteristic
335C22×C47#51811yescharacteristic
336C22×C47C2×#13111yescharacteristic
337C22×C47C2×#13111yescharacteristic
338C22×C47#56811yescharacteristic
339C22×C47#56811yescharacteristic
340C4×C47—22no—
341C4×C47—41no—
342C4×C47—41no—
343C4×C47—41no—
344C4×C47—41no—
345C4×C47—41no—
346C4×C47—41no—
347C4×C47—41no—
348C4×C47—41no—
349C4×C47—41no—
350C4×C47—41no—
351C4×C47#53811yescharacteristic
352C4×C47#53811yescharacteristic
353C4×C47#54011yescharacteristic
354C4×C47#54011yescharacteristic
355#2392C2×C4711yescharacteristic
356#1955C2×C4711yescharacteristic, complemented
357#1954C2×C4711yescharacteristic, complemented
358#1923C2×C4711yescharacteristic, complemented
359#1923C2×C4711yescharacteristic, complemented
360#1917C2×C4711yescharacteristic, complemented
361#1916C2×C4711yescharacteristic, complemented
362#1870C2×C4711yescharacteristic, complemented
363#1870C2×C4711yescharacteristic, complemented
364#1869C2×C4711yescharacteristic, complemented
365#1869C2×C4711yescharacteristic, complemented
366#1818C2×C4711yescharacteristic, complemented
367#1753C2×C4711yescharacteristic, complemented
368#1752C2×C4711yescharacteristic, complemented
369#1750C2×C4711yescharacteristic, complemented
370C2×C47—42no—
371C2×C47—81no—
372C2×C47—81no—
373C2×C47#233311yescharacteristic
374C2×C47#296811yescharacteristic
375C2×C47#296911yescharacteristic
376C2×C47#297611yescharacteristic
377C2×C47#297711yescharacteristic
378C2×C47#297811yescharacteristic
379C2×C47#298111yescharacteristic
380C22×M16C22×C4711yescharacteristic
381C23×C8C22×C4711yescharacteristic
382C2×C4×D4C22×C4711yescharacteristic
383C2×C4×D4C22×C4711yescharacteristic
384C2×C4×D4C22×C4711yescharacteristic
385C2×#117C22×C4711yescharacteristic
386C2×C4⋊C8C22×C4711yescharacteristic
387C2×C4⋊C8C22×C4711yescharacteristic
388C2×C22⋊C8C22×C4711yescharacteristic
389C2×C22⋊C8C22×C4711yescharacteristic
390C2×C22⋊C8C22×C4711yescharacteristic
391C2×C22⋊C8C22×C4711yescharacteristic
392C2×C22⋊C8C22×C4711yescharacteristic
393C2×C22⋊C8C22×C4711yescharacteristic
394C2×C22⋊C8C22×C4711yescharacteristic
395C2×C22⋊C8C22×C4711yescharacteristic
396C2×C22⋊C8C22×C4711yescharacteristic
397C2×C22⋊C8C22×C4711yescharacteristic
398C2×#97C22×C4711yescharacteristic
399C2×#97C22×C4711yescharacteristic
400C2×C4×C8C22×C4711yescharacteristic
401C2×C4×C8C22×C4711yescharacteristic
402#398C4×C4711yescharacteristic
403#397C4×C4711yescharacteristic
404#396C4×C4711yescharacteristic
405#396C4×C4711yescharacteristic
406#394C4×C4711yescharacteristic
407#394C4×C4711yescharacteristic
408#394C4×C4711yescharacteristic
409#392C4×C4711yescharacteristic
410C4×C4⋊C4C22×C4711yescharacteristic
411C4×C22⋊C4C22×C4711yescharacteristic
412C4×C22⋊C4C22×C4711yescharacteristic
413#336C22×C4711yescharacteristic
414#336C22×C4711yescharacteristic
415#336C22×C4711yescharacteristic
416#336C22×C4711yescharacteristic
417#336C22×C4711yescharacteristic
418#336C22×C4711yescharacteristic
419#336C22×C4711yescharacteristic
420#336C22×C4711yescharacteristic
421#336C22×C4711yescharacteristic
422#336C22×C4711yescharacteristic
423C47#2233611yescharacteristic, direct product factor, Sylow
424C22×D4C2×C4×C4711yescharacteristic
425C22×D4C2×C4×C4711yescharacteristic
426C22×D4C2×C4×C4711yescharacteristic
427C23×C4C23×C4711yescharacteristic
428C23×C4C23×C4711yescharacteristic
429C23×C4C23×C4711yescharacteristic
430C2×M16—22no—
431C2×M16—41no—
432C2×M16—41no—
433C22×C8—22no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8C23×C4711yescharacteristic
437C22×C8C23×C4711yescharacteristic
438C22×C8C23×C4711yescharacteristic
439C22×C8C23×C4711yescharacteristic
440C22×C8C23×C4711yescharacteristic
441C22×C8C23×C4711yescharacteristic
442C22×C8C23×C4711yescharacteristic
443C22×C8C23×C4711yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×C4×C4711yescharacteristic
453C2×C4⋊C4C2×C4×C4711yescharacteristic
454C2×C4⋊C4C2×C4×C4711yescharacteristic
455C2×C4⋊C4C2×C4×C4711yescharacteristic
456C2×C4⋊C4C2×C4×C4711yescharacteristic
457C2×C4⋊C4C2×C4×C4711yescharacteristic
458C2×C4⋊C4C2×C4×C4711yescharacteristic
459C2×C22⋊C4C2×C4×C4711yescharacteristic
460C2×C22⋊C4C2×C4×C4711yescharacteristic
461C2×C22⋊C4C2×C4×C4711yescharacteristic
462C2×C22⋊C4C2×C4×C4711yescharacteristic
463C2×C22⋊C4C2×C4×C4711yescharacteristic
464C2×C22⋊C4C2×C4×C4711yescharacteristic
465C2×C22⋊C4C2×C4×C4711yescharacteristic
466C2×C22⋊C4C2×C4×C4711yescharacteristic
467C2×C22⋊C4C2×C4×C4711yescharacteristic
468C2×C22⋊C4C2×C4×C4711yescharacteristic
469C2×C22⋊C4C2×C4×C4711yescharacteristic
470C2×C22⋊C4C2×C4×C4711yescharacteristic
471C2×C42C23×C4711yescharacteristic
472C2×C42C23×C4711yescharacteristic
473C2×C42C23×C4711yescharacteristic
474C2×C42C23×C4711yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487#97—41no—
488#97—41no—
489C4×C8—41no—
490C4×C8—41no—
491#95C2×C4×C4711yescharacteristic
492#95C2×C4×C4711yescharacteristic
493#95C2×C4×C4711yescharacteristic
494#95C2×C4×C4711yescharacteristic
495#95C2×C4×C4711yescharacteristic
496#95C2×C4×C4711yescharacteristic
497C24C22×C4×C4711yescharacteristic
498C24C22×C4×C4711yescharacteristic
499C24C22×C4×C4711yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C4711yescharacteristic
528C22×C4C22×C4×C4711yescharacteristic
529C22×C4C22×C4×C4711yescharacteristic
530C22×C4C22×C4×C4711yescharacteristic
531C22×C4C22×C4×C4711yescharacteristic
532C22×C4C22×C4×C4711yescharacteristic
533C22×C4C22×C4×C4711yescharacteristic
534C22×C4C22×C4×C4711yescharacteristic
535C22×C4C22×C4×C4711yescharacteristic
536C22×C4C22×C4×C4711yescharacteristic
537C22×C4C22×C4×C4711yescharacteristic
538C22×C4C24×C4711yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8#41×C4712yes—
564C2×C8#41×C4712yes—
565C4⋊C4—22no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#131×C4712yes—
613C23C23×C4×C4711yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
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—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4#131×C4712yes—
662C2×C4C2×#41×C4711yescharacteristic
663C2×C4C2×#41×C4711yescharacteristic
664C2×C4H(5,𝔽2)×C4711yescharacteristic
665C2×C4H(5,𝔽2)×C4711yescharacteristic
666C2×C4H(5,𝔽2)×C4711yescharacteristic
667C2×C4H(5,𝔽2)×C4711yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22C4×#41×C4711yescharacteristic
698C22C47×#51811yescharacteristic
699C22C47×#51811yescharacteristic
700C22C2×#131×C4711yescharacteristic
701C22C2×#131×C4711yescharacteristic
702C22C47×#56811yescharacteristic
703C22C47×#56811yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4C47×#53811yescharacteristic
716C4C47×#53811yescharacteristic
717C4C47×#54011yescharacteristic
718C4C47×#54011yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2C47×#233311yescharacteristic
723C2C47×#296811yescharacteristic
724C2C47×#296911yescharacteristic
725C2C47×#297611yescharacteristic
726C2C47×#297711yescharacteristic
727C2C47×#297811yescharacteristic
728C2C47×#298111yescharacteristic
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
2. C47×#1955C2semidirect
3. C47×#1954C2semidirect
4. C47×#1923C2semidirect
5. C47×#1923C2semidirect
6. C47×#1917C2semidirect
7. C47×#1916C2semidirect
8. C47×#1870C2semidirect
9. C47×#1870C2semidirect
10. C47×#1869C2semidirect
11. C47×#1869C2semidirect
12. C47×#1818C2semidirect
13. C47×#1753C2semidirect
14. C47×#1752C2semidirect
15. C47×#1750C2semidirect
311. #22336C47direct (N × H)
356. #1955C2×C47semidirect
357. #1954C2×C47semidirect
358. #1923C2×C47semidirect
359. #1923C2×C47semidirect
360. #1917C2×C47semidirect
361. #1916C2×C47semidirect
362. #1870C2×C47semidirect
363. #1870C2×C47semidirect
364. #1869C2×C47semidirect
365. #1869C2×C47semidirect
366. #1818C2×C47semidirect
367. #1753C2×C47semidirect
368. #1752C2×C47semidirect
369. #1750C2×C47semidirect
423. C47#22336direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#23922
C47×#19552
C47×#19542
C47×#19232
C47×#19172
C47×#19162
C47×#18702
C47×#18692
C47×#18182
C47×#17532
C47×#17522
C47×#17502
#2233647