Finite Group Databasebeta

← C2×#20246058 #26375007

Subgroups — C2×#20246058 #26375007

Order 12032.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic
2C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20246058C2116yesmaximal, direct product factor
5C2×#15689021C211yesmaximal, characteristic, complemented
6C2×#15689018C211yesmaximal, characteristic, complemented
7C2×#15689017C211yesmaximal, characteristic, complemented
8C2×#15689010C211yesmaximal, characteristic, complemented
9C2×#15689006C211yesmaximal, characteristic, complemented
10C2×#15688999C211yesmaximal, characteristic
11C2×#15688998C211yesmaximal, characteristic, complemented
12C2×#15688997C211yesmaximal, characteristic, complemented
13C2×#15688995C211yesmaximal, characteristic, complemented
14C2×#15688985C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13094006C4116yescomplemented
23C2×#13094006C2218yes—
24C2×(C22⋊D47)⋊C4—28no—
25C2×(C22⋊D47)⋊C4C2218yes—
26C22×C4⋊Dic47C2211yescharacteristic
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C2×C4⋊C4×D47—28no—
35C2×C4⋊C4×D47C2218yescomplemented
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689021C2218yescomplemented
44#15689018C2218yescomplemented
45#15689017C2218yescomplemented
46#15689010C2218yescomplemented
47#15689006C2218yescomplemented
48#15688999C2218yes—
49#15688998C2218yescomplemented
50#15688997C2218yescomplemented
51#15688995C2218yescomplemented
52#15688985C2218yescomplemented
53C4×(C2×D47)⋊C4C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47—24no—
76C23×Dic47—42no—
77C23×Dic47—42no—
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2314yes—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47—42no—
92C22×C4×D47—42no—
93C22×C4×D47C2×C418yescomplemented
94C22×C4×D47D418yes—
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98#13094006C2×C4164yescomplemented
99(C22⋊D47)⋊C4—232no—
100C2×C4⋊Dic47—24no—
101C2×C4⋊Dic47—42no—
102C2×C4⋊Dic47C2×C418yescomplemented
103C2×C4⋊Dic47C2314yes—
104C2×C4⋊Dic47C2314yes—
105C2×C4⋊Dic47C2314yes—
106C2×Dic47⋊C4—24no—
107C2×Dic47⋊C4—24no—
108C2×Dic47⋊C4—24no—
109C2×Dic47⋊C4—42no—
110C2×Dic47⋊C4C2×C418yescomplemented
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2314yes—
116C4⋊C4×D47—232no—
117C2×C22⋊Dic47—42no—
118C2×C22⋊Dic47C2×C418yescomplemented
119C2×C22⋊Dic47C2314yes—
120C2×C22⋊Dic47C2314yes—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4C2×C418yescomplemented
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×C4×Dic47—24no—
128C2×C4×Dic47—42no—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C25×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—24no—
147C2×C4⋊C4×C47C2314yes—
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—42no—
150C2×C22⋊C4×C47C2×C418yescomplemented
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47—42no—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47C22×C414yes—
172C23×D47C2×D414yes—
173C23×D47#4114yes—
174C23×D47C2412yes—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C2×D414yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—232no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47C22×C4116yes—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—28no—
221C22×Dic47—44no—
222C22×Dic47—44no—
223C22×Dic47—416no—
224C22×Dic47C22×C414yes—
225C22×Dic47C22×C414yes—
226C22×Dic47C22×C414yes—
227C22×Dic47C2×D414yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—416no—
240C2×C4×D47—44no—
241C2×C4×D47—44no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47—416no—
245C2×C4×D47C22×C4116yescomplemented
246C2×C4×D47C2×D4116yes—
247C4⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C22⋊C4×C47—44no—
250C22⋊C4×C47C22×C4116yescomplemented
251C42×C47—44no—
252C22⋊Dic47—44no—
253C22⋊Dic47C22×C4116yescomplemented
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4C22×C4116yescomplemented
257C4⋊Dic47—28no—
258C4⋊Dic47—44no—
259C4⋊Dic47C22×C4116yescomplemented
260Dic47⋊C4—28no—
261Dic47⋊C4—28no—
262Dic47⋊C4—28no—
263Dic47⋊C4—44no—
264Dic47⋊C4C22×C4116yescomplemented
265C4×Dic47—28no—
266C4×Dic47—44no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47H(5,𝔽2)12yes—
285C23×C47H(5,𝔽2)12yes—
286C23×C472−1+412yes—
287C23×C472−1+412yes—
288C23×C47C2511yescharacteristic
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47C4×D4116yes—
300C22×D47C23×C414yes—
301C22×D47C22×D414yes—
302C22×D47C2×#4114yes—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47—44no—
324C2×C4×C47C23×C414yes—
325C2×C4×C47C23×C414yes—
326C2×C4×C47C22×D414yes—
327C22⋊D47—232no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—28no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—416no—
350C2×Dic47—44no—
351C2×Dic47—44no—
352C2×Dic47—44no—
353C2×Dic47C23×C414yes—
354C2×Dic47C23×C414yes—
355C2×Dic47C23×C414yes—
356C2×Dic47C22×D414yes—
357C4×D47—232no—
358C4×D47—416no—
359C4×D47—416no—
360C2×#2322—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—416no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47C2×C4×D414yes—
370C22×C47#52014yes—
371C22×C47#52014yes—
372C22×C47#53414yes—
373C22×C47#53614yes—
374C22×C47#53914yes—
375C22×C47#53914yes—
376C22×C47C24×C411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C2×H(5,𝔽2)11yescharacteristic
380C22×C47C2×H(5,𝔽2)11yescharacteristic
381C22×C47C2×2−1+411yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C2×D47—232no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—24no—
390C2×D47C2×C4×D418yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—42no—
402Dic47—42no—
403Dic47—42no—
404C22×#123—471no—
405C22×C4×D4—471no—
406C23×C4⋊C4—471no—
407#2322—4716no—
408C2×#389—471no—
409C2×#389—471no—
410C2×#388—471no—
411C2×#388D4711yescharacteristic, complemented
412C2×#387—471no—
413C2×#387—471no—
414C2×#386—471no—
415C2×#385—471no—
416C2×#385—471no—
417C2×#385—471no—
418C2×#381—471no—
419C2×C4×C22⋊C4—471no—
420C2×C47—44no—
421C2×C47#232218yescomplemented
422C2×C47C22×C4×D411yescharacteristic
423C2×C47C2×#52011yescharacteristic
424C2×C47C2×#52011yescharacteristic
425C2×C47C2×#53411yescharacteristic
426C2×C47C2×#53611yescharacteristic
427C2×C47C2×#53911yescharacteristic
428C2×C47C2×#53911yescharacteristic
429D47—28no—
430C23×D4—471no—
431C24×C4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4—471no—
435C2×#123—4716no—
436C2×#123—478no—
437C2×C4×D4—478no—
438C2×C4×D4—948no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—478no—
448C22×C4⋊C4—948no—
449C22×C4⋊C4C2×D4711yescharacteristic
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4C2×D4711yescharacteristic
456C22×C22⋊C4C2×D4711yescharacteristic
457C22×C22⋊C4C2×D4711yescharacteristic
458C22×C42—471no—
459C22×C42—471no—
460C22×C42C2×D4711yescharacteristic
461#389—478no—
462#389—478no—
463#388—478no—
464#388C2×D4718yescomplemented
465#387—478no—
466#387—478no—
467#386—478no—
468#385—478no—
469#385—478no—
470#385—478no—
471#381—478no—
472C4×C22⋊C4—478no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—471no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×#232211yescharacteristic, complemented, Sylow
484C25—471no—
485C25C22×D4711yescharacteristic
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—478no—
495C23×C4—474no—
496C23×C4—478no—
497C23×C4—474no—
498C23×C4—471no—
499C23×C4—471no—
500C23×C4—471no—
501C23×C4—474no—
502C23×C4—474no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—1882no—
508C23×C4—1882no—
509C23×C4—1882no—
510C23×C4—1882no—
511C23×C4—1882no—
512C23×C4—1882no—
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519#123—4764no—
520C4×D4—9432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—478no—
523C2×C4⋊C4—478no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—474no—
532C2×C4⋊C4—9432no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4—944no—
536C2×C4⋊C4—944no—
537C2×C4⋊C4—1882no—
538C2×C4⋊C4—1882no—
539C2×C4⋊C4C22×D4714yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—478no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—478no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4—474no—
549C2×C22⋊C4—944no—
550C2×C22⋊C4—944no—
551C2×C22⋊C4—1882no—
552C2×C22⋊C4C4×D4718yescomplemented
553C2×C22⋊C4C22×D4714yes—
554C2×C22⋊C4C22×D4714yes—
555C2×C22⋊C4C22×D4714yes—
556C2×C42—42no—
557C2×C42—474no—
558C2×C42—474no—
559C2×C42—944no—
560C2×C42—1882no—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95C22×D4714yes—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—474no—
579C24—474no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C2×C4×D4714yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—4716no—
590C2×D4—948no—
591C2×D4—9432no—
592C2×D4—948no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—474no—
611C22×C4—474no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—472no—
616C22×C4—4716no—
617C22×C4—4716no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—948no—
622C22×C4—9432no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—948no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—18816no—
644C22×C4—1884no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4—1884no—
648C22×C4—18816no—
649C22×C4—1884no—
650C22×C4—1884no—
651C22×C4—18816no—
652C22×C4C2×C4×D4714yes—
653C22×C4C2×C4×D4714yes—
654C22×C4D4×D4714yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—28no—
662C4⋊C4—4716no—
663C4⋊C4—4716no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—948no—
668C4⋊C4—1884no—
669C4⋊C4—1884no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—4716no—
673C22⋊C4—4716no—
674C22⋊C4—948no—
675C22⋊C4—948no—
676C22⋊C4—1884no—
677C22⋊C4C2×C4×D47116yescomplemented
678C42—44no—
679C42—948no—
680C42—1884no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4716no—
695C23—474no—
696C23—474no—
697C23—474no—
698C23—948no—
699C23—948no—
700C23—948no—
701C23—948no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—942no—
706C23—948no—
707C23—948no—
708C23C22×C4×D4714yes—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#1309406912yes—
713C23#1309407012yes—
714C23#1309407112yes—
715C23#1309407112yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—9432no—
744C2×C4—948no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—948no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—18816no—
766C2×C4—18816no—
767C2×C4—18816no—
768C2×C4—1884no—
769C2×C4—1884no—
770C2×C4—1884no—
771C2×C4C22×C4×D4714yes—
772C2×C4C22×C4×D4714yes—
773C2×C4C2×D4×D4714yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—478no—
783C22—9432no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22—944no—
789C22—944no—
790C22C4×D4×D4714yes—
791C22#1568960214yes—
792C22#1568960314yes—
793C22#1568968114yes—
794C22#1568969314yes—
795C22#1568971414yes—
796C22#1568971614yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#1309406911yescharacteristic
801C22C2×#1309407011yescharacteristic
802C22C2×#1309407111yescharacteristic
803C22C2×#1309407111yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—944no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—1882no—
815C4—1882no—
816C4—1882no—
817C2—44no—
818C2—948no—
819C2#2024605818yesdirect product factor
820C2C2×C4×D4×D4711yescharacteristic
821C2C2×#1568960211yescharacteristic
822C2C2×#1568960311yescharacteristic
823C2C2×#1568968111yescharacteristic
824C2C2×#1568969311yescharacteristic
825C2C2×#1568971411yescharacteristic
826C2C2×#1568971611yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2322
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D47C2semidirect
4. #20246058C2direct (N × H)
5. C2×#15689021C2semidirect
6. C2×#15689018C2semidirect
7. C2×#15689017C2semidirect
8. C2×#15689010C2semidirect
9. C2×#15689006C2semidirect
11. C2×#15688998C2semidirect
12. C2×#15688997C2semidirect
13. C2×#15688995C2semidirect
14. C2×#15688985C2semidirect
15. C2×C4×(C2×D47)⋊C4C2semidirect
16. C2×C47×#388C2semidirect
22. C2×#13094006C4semidirect
35. C2×C4⋊C4×D47C22semidirect
43. #15689021C22semidirect
44. #15689018C22semidirect
45. #15689017C22semidirect
46. #15689010C22semidirect
47. #15689006C22semidirect
49. #15688998C22semidirect
50. #15688997C22semidirect
51. #15688995C22semidirect
52. #15688985C22semidirect
53. C4×(C2×D47)⋊C4C22semidirect
67. C47×#388C22semidirect
93. C22×C4×D47C2×C4semidirect
98. #13094006C2×C4semidirect
102. C2×C4⋊Dic47C2×C4semidirect
110. C2×Dic47⋊C4C2×C4semidirect
118. C2×C22⋊Dic47C2×C4semidirect
123. C2×(C2×D47)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
245. C2×C4×D47C22×C4semidirect
250. C22⋊C4×C47C22×C4semidirect
253. C22⋊Dic47C22×C4semidirect
256. (C2×D47)⋊C4C22×C4semidirect
259. C4⋊Dic47C22×C4semidirect
264. Dic47⋊C4C22×C4semidirect
411. C2×#388D47semidirect
421. C2×C47#2322semidirect
464. #388C2×D47semidirect
483. C47C2×#2322semidirect
552. C2×C22⋊C4C4×D47semidirect
677. C22⋊C4C2×C4×D47semidirect
819. C2#20246058direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×(C22⋊D47)⋊C42
C22×C4⋊C4×D472
#202460582
C2×#156890212
C2×#156890182
C2×#156890172
C2×#156890102
C2×#156890062
C2×#156889992
C2×#156889982
C2×#156889972
C2×#156889952
C2×#156889852
C2×C4×(C2×D47)⋊C42
C2×C47×#3882
C2×#232247