Finite Group Databasebeta

← C47×#29896 #26069594

Subgroups — C47×#29896 #26069594

Order 12032.

1056 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2847C211yesmaximal, characteristic
2C47×#2280C211yesmaximal, characteristic, complemented
3C47×#2077C211yesmaximal, characteristic, complemented
4C47×#2077C211yesmaximal, characteristic, complemented
5C47×#2076C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#1875C211yesmaximal, characteristic, complemented
12C47×#1875C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C47×#1854C211yesmaximal, characteristic, complemented
15C47×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C2×#121×C47C2211yescharacteristic
18C2×#121×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×#120×C47—21no—
21C2×#117×C47C2211yescharacteristic
22C2×#117×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic, complemented
24C2×#107×C47C2211yescharacteristic, complemented
25C2×#106×C47C2211yescharacteristic, complemented
26C2×#106×C47C2211yescharacteristic, complemented
27C2×#102×C47C2211yescharacteristic, complemented
28C2×#102×C47C2211yescharacteristic, complemented
29C2×#102×C47C2211yescharacteristic, complemented
30C2×#102×C47C2211yescharacteristic, complemented
31C2×C22⋊C8×C47C2211yescharacteristic
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2211yescharacteristic
37C47×#386—21no—
38C47×#386—21no—
39C47×#386—21no—
40C47×#381—21no—
41C47×#380C2211yescharacteristic
42C47×#380C2211yescharacteristic
43C47×#380C2211yescharacteristic
44C47×#380C2211yescharacteristic
45C47×#380C2211yescharacteristic
46C47×#380C2211yescharacteristic
47C47×#380C2211yescharacteristic
48C47×#379—21no—
49C4×C22⋊C4×C47—21no—
50C4×C22⋊C4×C47—21no—
51C47×#340C2211yescharacteristic, complemented
52C47×#340C2211yescharacteristic, complemented
53C47×#340C2211yescharacteristic, complemented
54C47×#340C2211yescharacteristic, complemented
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C25×C47D411yescharacteristic
60C22×D4×C47—21no—
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47C2311yescharacteristic
64C23×C4×C47—22no—
65C23×C4×C47—22no—
66C23×C4×C47—41no—
67C23×C4×C47—41no—
68C23×C4×C47—41no—
69C23×C4×C47—41no—
70C23×C4×C47D411yescharacteristic
71C23×C4×C47D411yescharacteristic
72C23×C4×C47D411yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80#121×C47—22no—
81#121×C47—22no—
82#121×C47—41no—
83#121×C47—41no—
84#121×C47—41no—
85#121×C47—41no—
86#120×C47—44no—
87#117×C47—41no—
88#117×C47—41no—
89#117×C47—41no—
90#117×C47—41no—
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112#107×C47—41no—
113#107×C47—41no—
114#106×C47—41no—
115#106×C47—41no—
116#102×C47—41no—
117#102×C47—41no—
118#102×C47—41no—
119#102×C47—41no—
120C22⋊C8×C47—22no—
121C22⋊C8×C47—22no—
122C22⋊C8×C47—41no—
123C22⋊C8×C47—41no—
124C22⋊C8×C47—41no—
125C22⋊C8×C47—41no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132#95×C47—21no—
133C24×C47—22no—
134C24×C47—22no—
135C24×C47—22no—
136C24×C47—21no—
137C24×C47—41no—
138C24×C47—41no—
139C24×C47—41no—
140C24×C47—41no—
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—42no—
151C2×D4×C47—42no—
152C2×D4×C47—42no—
153C2×D4×C47—42no—
154C2×D4×C47—42no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47—42no—
158C2×D4×C47—42no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—21no—
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—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—41no—
186C22×C4×C47—41no—
187C22×C4×C47—41no—
188C22×C4×C47—41no—
189C22×C4×C47—41no—
190C22×C4×C47—41no—
191C22×C4×C47—44no—
192C22×C4×C47—44no—
193C22×C4×C47—44no—
194C22×C4×C47—44no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47#4112yes—
199C22×C4×C47#4112yes—
200C22×C4×C47C2411yescharacteristic
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—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—42no—
239C42×C47—42no—
240C42×C47—42no—
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×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47#12312yes—
274C23×C47#13512yes—
275C23×C47AGL(1,ℤ/8)12yes—
276C23×C47C22×D411yescharacteristic
277D4×C47—41no—
278D4×C47—41no—
279D4×C47—41no—
280D4×C47—41no—
281D4×C47—84no—
282D4×C47—84no—
283D4×C47—84no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
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—44no—
297C2×C4×C47—44no—
298C2×C4×C47—44no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
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×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47#12312yes—
329C2×C4×C47C2×#4111yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47H(5,𝔽2)11yescharacteristic
332C2×C4×C47H(5,𝔽2)11yescharacteristic
333C2×C4×C47H(5,𝔽2)11yescharacteristic
334C2×C4×C47H(5,𝔽2)11yescharacteristic
335C8×C47—41no—
336C8×C47—41no—
337C8×C47—41no—
338C8×C47—41no—
339#29896C4711yesmaximal, characteristic, direct product factor, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—416no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
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—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47C2×#12311yescharacteristic
370C22×C47#53411yescharacteristic
371C22×C47#53411yescharacteristic
372C22×C47C2×#13511yescharacteristic
373C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C47#57511yescharacteristic
375C22×C47#57511yescharacteristic
376C4×C47—22no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—81no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47—81no—
383C4×C47—81no—
384C4×C47—81no—
385C4×C47—81no—
386C4×C47#53811yescharacteristic
387C4×C47#53811yescharacteristic
388C4×C47#53811yescharacteristic
389C4×C47#53811yescharacteristic
390#2847C2×C4711yescharacteristic
391#2280C2×C4711yescharacteristic, complemented
392#2077C2×C4711yescharacteristic, complemented
393#2077C2×C4711yescharacteristic, complemented
394#2076C2×C4711yescharacteristic, complemented
395#2075C2×C4711yescharacteristic, complemented
396#2034C2×C4711yescharacteristic, complemented
397#2034C2×C4711yescharacteristic, complemented
398#2033C2×C4711yescharacteristic, complemented
399#2033C2×C4711yescharacteristic, complemented
400#1875C2×C4711yescharacteristic, complemented
401#1875C2×C4711yescharacteristic, complemented
402#1854C2×C4711yescharacteristic, complemented
403#1854C2×C4711yescharacteristic, complemented
404#1779C2×C4711yescharacteristic, complemented
405C2×C47—42no—
406C2×C47—42no—
407C2×C47—42no—
408C2×C47—161no—
409C2×C47#262211yescharacteristic
410C2×C47#309111yescharacteristic
411C2×C47#309411yescharacteristic
412C2×C47#318811yescharacteristic
413C2×C47#319111yescharacteristic
414C2×C47#319411yescharacteristic
415C2×C47#319711yescharacteristic
416C24×C4C22×C4711yescharacteristic
417C2×#121C22×C4711yescharacteristic
418C2×#121C22×C4711yescharacteristic
419C2×#121C22×C4711yescharacteristic
420C2×#120—21no—
421C2×#117C22×C4711yescharacteristic
422C2×#117C22×C4711yescharacteristic
423C2×#107C22×C4711yescharacteristic, complemented
424C2×#107C22×C4711yescharacteristic, complemented
425C2×#106C22×C4711yescharacteristic, complemented
426C2×#106C22×C4711yescharacteristic, complemented
427C2×#102C22×C4711yescharacteristic, complemented
428C2×#102C22×C4711yescharacteristic, complemented
429C2×#102C22×C4711yescharacteristic, complemented
430C2×#102C22×C4711yescharacteristic, complemented
431C2×C22⋊C8C22×C4711yescharacteristic
432C2×C22⋊C8C22×C4711yescharacteristic
433C2×C22⋊C8C22×C4711yescharacteristic
434C2×C22⋊C8C22×C4711yescharacteristic
435C2×C22⋊C8C22×C4711yescharacteristic
436C2×C22⋊C8C22×C4711yescharacteristic
437#386—21no—
438#386—21no—
439#386—21no—
440#381—21no—
441#380C22×C4711yescharacteristic
442#380C22×C4711yescharacteristic
443#380C22×C4711yescharacteristic
444#380C22×C4711yescharacteristic
445#380C22×C4711yescharacteristic
446#380C22×C4711yescharacteristic
447#380C22×C4711yescharacteristic
448#379—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451#340C22×C4711yescharacteristic, complemented
452#340C22×C4711yescharacteristic, complemented
453#340C22×C4711yescharacteristic, complemented
454#340C22×C4711yescharacteristic, complemented
455#340C22×C4711yescharacteristic, complemented
456#340C22×C4711yescharacteristic, complemented
457#340C22×C4711yescharacteristic, complemented
458#340C22×C4711yescharacteristic, complemented
459C47#2989611yescharacteristic, direct product factor, Sylow
460C25D4×C4711yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C4711yescharacteristic
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—41no—
468C23×C4—41no—
469C23×C4—41no—
470C23×C4—41no—
471C23×C4D4×C4711yescharacteristic
472C23×C4D4×C4711yescharacteristic
473C23×C4D4×C4711yescharacteristic
474C23×C4C23×C4711yescharacteristic
475C23×C4C23×C4711yescharacteristic
476C23×C4C23×C4711yescharacteristic
477C22×C8C23×C4711yescharacteristic
478C22×C8C23×C4711yescharacteristic
479C22×C8C23×C4711yescharacteristic
480C22×C8C23×C4711yescharacteristic
481#121—22no—
482#121—22no—
483#121—41no—
484#121—41no—
485#121—41no—
486#121—41no—
487#120—44no—
488#117—41no—
489#117—41no—
490#117—41no—
491#117—41no—
492C2×C4⋊C4C23×C4711yescharacteristic
493C2×C4⋊C4C23×C4711yescharacteristic
494C2×C4⋊C4C23×C4711yescharacteristic
495C2×C4⋊C4C23×C4711yescharacteristic
496C2×C4⋊C4C23×C4711yescharacteristic
497C2×C4⋊C4C23×C4711yescharacteristic
498C2×C4⋊C4C23×C4711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C42—21no—
512C2×C42—21no—
513#107—41no—
514#107—41no—
515#106—41no—
516#106—41no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—41no—
524C22⋊C8—41no—
525C22⋊C8—41no—
526C22⋊C8—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24C2×D4×C4711yescharacteristic
543C24C2×D4×C4711yescharacteristic
544C24C2×D4×C4711yescharacteristic
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
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—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—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4C2×D4×C4711yescharacteristic
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C22×C4#41×C4712yes—
600C22×C4#41×C4712yes—
601C22×C4C24×C4711yescharacteristic
602C2×C8—21no—
603C2×C8—21no—
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—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C42—42no—
641C42—42no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23#123×C4712yes—
675C23#135×C4712yes—
676C23AGL(1,ℤ/8)×C4712yes—
677C23C22×D4×C4711yescharacteristic
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
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×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4#123×C4712yes—
730C2×C4C2×#41×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4H(5,𝔽2)×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C2×C4H(5,𝔽2)×C4711yescharacteristic
735C2×C4H(5,𝔽2)×C4711yescharacteristic
736C8—41no—
737C8—41no—
738C8—41no—
739C8—41no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—416no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×#123×C4711yescharacteristic
770C22C47×#53411yescharacteristic
771C22C47×#53411yescharacteristic
772C22C2×#135×C4711yescharacteristic
773C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
774C22C47×#57511yescharacteristic
775C22C47×#57511yescharacteristic
776C4—22no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C47×#53811yescharacteristic
787C4C47×#53811yescharacteristic
788C4C47×#53811yescharacteristic
789C4C47×#53811yescharacteristic
790C2—42no—
791C2—42no—
792C2—42no—
793C2—161no—
794C2C47×#262211yescharacteristic
795C2C47×#309111yescharacteristic
796C2C47×#309411yescharacteristic
797C2C47×#318811yescharacteristic
798C2C47×#319111yescharacteristic
799C2C47×#319411yescharacteristic
800C2C47×#319711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2280C2semidirect
3. C47×#2077C2semidirect
4. C47×#2077C2semidirect
5. C47×#2076C2semidirect
6. C47×#2075C2semidirect
7. C47×#2034C2semidirect
8. C47×#2034C2semidirect
9. C47×#2033C2semidirect
10. C47×#2033C2semidirect
11. C47×#1875C2semidirect
12. C47×#1875C2semidirect
13. C47×#1854C2semidirect
14. C47×#1854C2semidirect
15. C47×#1779C2semidirect
23. C2×#107×C47C22semidirect
24. C2×#107×C47C22semidirect
25. C2×#106×C47C22semidirect
26. C2×#106×C47C22semidirect
27. C2×#102×C47C22semidirect
28. C2×#102×C47C22semidirect
29. C2×#102×C47C22semidirect
30. C2×#102×C47C22semidirect
51. C47×#340C22semidirect
52. C47×#340C22semidirect
53. C47×#340C22semidirect
54. C47×#340C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
339. #29896C47direct (N × H)
391. #2280C2×C47semidirect
392. #2077C2×C47semidirect
393. #2077C2×C47semidirect
394. #2076C2×C47semidirect
395. #2075C2×C47semidirect
396. #2034C2×C47semidirect
397. #2034C2×C47semidirect
398. #2033C2×C47semidirect
399. #2033C2×C47semidirect
400. #1875C2×C47semidirect
401. #1875C2×C47semidirect
402. #1854C2×C47semidirect
403. #1854C2×C47semidirect
404. #1779C2×C47semidirect
423. C2×#107C22×C47semidirect
424. C2×#107C22×C47semidirect
425. C2×#106C22×C47semidirect
426. C2×#106C22×C47semidirect
427. C2×#102C22×C47semidirect
428. C2×#102C22×C47semidirect
429. C2×#102C22×C47semidirect
430. C2×#102C22×C47semidirect
451. #340C22×C47semidirect
452. #340C22×C47semidirect
453. #340C22×C47semidirect
454. #340C22×C47semidirect
455. #340C22×C47semidirect
456. #340C22×C47semidirect
457. #340C22×C47semidirect
458. #340C22×C47semidirect
459. C47#29896direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28472
C47×#22802
C47×#20772
C47×#20762
C47×#20752
C47×#20342
C47×#20332
C47×#18752
C47×#18542
C47×#17792
#2989647