Finite Group Databasebeta

← C22⋊C4×(C2×D47)⋊C4 #26137678

Subgroups — C22⋊C4×(C2×D47)⋊C4 #26137678

Order 12032.

4254 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D47)⋊C4C211yesmaximal, characteristic
2C22×C22⋊C4×D47C211yesmaximal, characteristic
3C2×#15688978C211yesmaximal, characteristic
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C212yesmaximal, complemented
6#20241626C212yesmaximal, complemented
7#20241624C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic, complemented
9#20241610C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
12C25×D47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C23×C4×D47C2212yes—
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2211yescharacteristic
17C22×(C2×D47)⋊C4—28no—
18C22×(C2×D47)⋊C4C418yescomplemented
19C22×(C2×D47)⋊C4C2211yescharacteristic
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C2×C22⋊C4×D47—24no—
27C2×C22⋊C4×D47—24no—
28C2×C22⋊C4×D47C418yescomplemented
29C22×C4×Dic47C2212yescomplemented
30#15688978C418yescomplemented
31C22⋊C4×Dic47—24no—
32C4×(C2×D47)⋊C4—28no—
33C2×C47⋊#95C2212yescomplemented
34C2×C47⋊#95C2212yescomplemented
35C2×C47⋊#95C2212yescomplemented
36C2×C47⋊#95C2212yescomplemented
37C2×C47⋊#95C2212yescomplemented
38C24×C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C42×C47C2212yescomplemented
42C4×C22⋊C4×C47—24no—
43C2×#95×C47C2212yescomplemented
44C24×D47—22no—
45C24×D47—22no—
46C24×D47—22no—
47C24×D47—22no—
48C24×D47—24no—
49C24×D47—24no—
50C24×D47—42no—
51C24×D47—42no—
52C24×D47C2×C414yes—
53C24×D47C2×C414yes—
54C24×D47C2×C414yes—
55C24×D47C2311yescharacteristic
56C24×D47C2311yescharacteristic
57C23×Dic47—22no—
58C23×Dic47—22no—
59C23×Dic47—24no—
60C23×Dic47—42no—
61C23×Dic47C2×C414yescomplemented
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2312yes—
64C23×Dic47C2312yes—
65C23×Dic47C2311yescharacteristic
66C22×C4×D47—24no—
67C22×C4×D47—24no—
68C22×C4×D47—24no—
69C22×C4×D47—24no—
70C22×C4×D47—42no—
71C22×C4×D47—42no—
72C22×C4×D47C2×C418yescomplemented
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47—22no—
75C2×C22⋊Dic47—22no—
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47C2×C414yes—
78C2×C22⋊Dic47C2×C414yescomplemented
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—232no—
87C2×(C2×D47)⋊C4—42no—
88C2×(C2×D47)⋊C4—42no—
89C2×(C2×D47)⋊C4C2×C414yes—
90C2×(C2×D47)⋊C4C2×C414yes—
91C2×(C2×D47)⋊C4C2×C418yescomplemented
92C2×(C2×D47)⋊C4C2×C418yescomplemented
93C2×(C2×D47)⋊C4C2×C414yescomplemented
94C2×(C2×D47)⋊C4C2×C414yescomplemented
95C2×(C2×D47)⋊C4C2×C418yescomplemented
96C2×(C2×D47)⋊C4D418yes—
97C22⋊C4×D47—232no—
98C2×C4×Dic47—24no—
99C2×C4×Dic47—24no—
100C2×C4×Dic47—42no—
101C47⋊#95—24no—
102C47⋊#95—24no—
103C47⋊#95—24no—
104C47⋊#95—42no—
105C47⋊#95—42no—
106C25×C47C2311yescharacteristic
107C23×C4×C47—22no—
108C23×C4×C47—22no—
109C23×C4×C47—24no—
110C23×C4×C47—42no—
111C23×C4×C47C2×C414yescomplemented
112C23×C4×C47C2312yes—
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2312yes—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47C2×C414yes—
119C2×C22⋊C4×C47C2×C414yescomplemented
120C2×C22⋊C4×C47D414yes—
121C2×C22⋊C4×C47D414yes—
122C2×C42×C47—24no—
123C2×C42×C47—24no—
124C2×C42×C47—42no—
125#95×C47—24no—
126C24×C47—22no—
127C24×C47—22no—
128C24×C47—22no—
129C24×C47—22no—
130C24×C47C22×C412yes—
131C24×C47C22×C412yes—
132C24×C47C22×C412yes—
133C24×C47C2×D412yes—
134C24×C47C2×D412yes—
135C24×C47#4112yes—
136C24×C47#4112yes—
137C24×C47C2411yescharacteristic
138C23×D47—21no—
139C23×D47—21no—
140C23×D47—21no—
141C23×D47—21no—
142C23×D47—22no—
143C23×D47—22no—
144C23×D47—28no—
145C23×D47—28no—
146C23×D47—28no—
147C23×D47—28no—
148C23×D47—28no—
149C23×D47—28no—
150C23×D47—22no—
151C23×D47—21no—
152C23×D47—21no—
153C23×D47—22no—
154C23×D47—21no—
155C23×D47—21no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—28no—
159C23×D47—28no—
160C23×D47—216no—
161C23×D47—216no—
162C23×D47—48no—
163C23×D47—48no—
164C23×D47—44no—
165C23×D47—44no—
166C23×D47—48no—
167C23×D47—48no—
168C23×D47—48no—
169C23×D47—48no—
170C23×D47—48no—
171C23×D47—48no—
172C23×D47—48no—
173C23×D47—48no—
174C23×D47C42116yescomplemented
175C23×D47C22×C412yes—
176C23×D47C22×C412yes—
177C23×D47C22×C412yes—
178C23×D47C22×C412yes—
179C23×D47C22×C412yes—
180C23×D47C22×C412yes—
181C23×D47C2×D414yes—
182C23×D47#4114yes—
183C22×C4×C47—21no—
184C22×C4×C47—22no—
185C22×C4×C47—21no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—28no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—28no—
202C22×C4×C47—44no—
203C22×C4×C47—48no—
204C22×C4×C47—48no—
205C22×C4×C47C22×C414yes—
206C22×C4×C47C22×C412yes—
207C22×C4×C47C22×C414yes—
208C22×C4×C47C22×C412yes—
209C22×C4×C47C2×D414yes—
210C22×C4×C47C2×D414yes—
211C22×C4×C47C2×D414yes—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—22no—
215C22×Dic47—28no—
216C22×Dic47—22no—
217C22×Dic47—21no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—21no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—28no—
233C22×Dic47—44no—
234C22×Dic47—48no—
235C22×Dic47—48no—
236C22×Dic47C22×C412yes—
237C22×Dic47C22×C414yes—
238C22×Dic47C22×C414yes—
239C22×Dic47C22×C412yes—
240C22×Dic47C2×D414yes—
241C2×C4×D47—216no—
242C2×C4×D47—216no—
243C2×C4×D47—48no—
244C2×C4×D47—48no—
245C2×C4×D47—48no—
246C2×C4×D47—48no—
247C2×C4×D47—48no—
248C22⋊C4×C47—28no—
249C22⋊C4×C47C22⋊C4116yescomplemented
250C42×C47—48no—
251C22⋊Dic47—28no—
252C22⋊Dic47—28no—
253(C2×D47)⋊C4—28no—
254(C2×D47)⋊C4—216no—
255(C2×D47)⋊C4—216no—
256(C2×D47)⋊C4—28no—
257(C2×D47)⋊C4—28no—
258(C2×D47)⋊C4—48no—
259(C2×D47)⋊C4C22⋊C4116yesdirect product factor
260C4×Dic47—48no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—24no—
264C23×C47—24no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—24no—
268C23×C47—24no—
269C23×C47—24no—
270C23×C47—24no—
271C23×C47—24no—
272C23×C47—24no—
273C23×C47—24no—
274C23×C47—24no—
275C23×C47—24no—
276C23×C47—24no—
277C23×C47C2×C4214yes—
278C23×C47C2×C22⋊C414yes—
279C23×C47#11714yes—
280C23×C47C4×D414yes—
281C23×C47C4×D414yes—
282C23×C47C4×D414yes—
283C23×C47C4×D414yes—
284C23×C47C23×C411yescharacteristic
285C23×C47C23×C411yescharacteristic
286C23×C47C23×C411yescharacteristic
287C23×C47C22×D412yes—
288C23×C47C22×D411yescharacteristic
289C23×C47C22×D411yescharacteristic
290C23×C47C2×#4112yes—
291C23×C47C2×#4111yescharacteristic
292C23×C47C2×#4111yescharacteristic
293C23×C47H(5,𝔽2)12yes—
294C23×C47H(5,𝔽2)12yes—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—24no—
302C22×D47—24no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—24no—
306C22×D47—24no—
307C22×D47—24no—
308C22×D47—24no—
309C22×D47—24no—
310C22×D47—24no—
311C22×D47—24no—
312C22×D47—24no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—24no—
318C22×D47—24no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—24no—
324C22×D47—24no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—232no—
328C22×D47—232no—
329C22×D47—416no—
330C22×D47—432no—
331C22×D47—416no—
332C22×D47—416no—
333C22×D47—416no—
334C22×D47—416no—
335C22×D47—432no—
336C22×D47—432no—
337C22×D47—432no—
338C22×D47—42no—
339C22×D47—42no—
340C22×D47—42no—
341C22×D47—42no—
342C22×D47—42no—
343C22×D47—42no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47C2×C4214yes—
347C22×D47C2×C4214yes—
348C22×D47C2×C22⋊C414yes—
349C22×D47#11714yes—
350C22×D47C4×D418yes—
351C22×D47C4×D418yes—
352C2×C4×C47—24no—
353C2×C4×C47—22no—
354C2×C4×C47—24no—
355C2×C4×C47—22no—
356C2×C4×C47—24no—
357C2×C4×C47—24no—
358C2×C4×C47—24no—
359C2×C4×C47—24no—
360C2×C4×C47—24no—
361C2×C4×C47—24no—
362C2×C4×C47—22no—
363C2×C4×C47—24no—
364C2×C4×C47—24no—
365C2×C4×C47—22no—
366C2×C4×C47—24no—
367C2×C4×C47—22no—
368C2×C4×C47—416no—
369C2×C4×C47—42no—
370C2×C4×C47—42no—
371C2×C4×C47—42no—
372C2×C4×C47—42no—
373C2×C4×C47—42no—
374C2×C4×C47—42no—
375C2×C4×C47C2×C22⋊C414yescomplemented
376C2×C4×C47C2×C22⋊C418yescomplemented
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—24no—
380C2×Dic47—24no—
381C2×Dic47—22no—
382C2×Dic47—24no—
383C2×Dic47—24no—
384C2×Dic47—24no—
385C2×Dic47—24no—
386C2×Dic47—22no—
387C2×Dic47—24no—
388C2×Dic47—24no—
389C2×Dic47—22no—
390C2×Dic47—416no—
391C2×Dic47—42no—
392C2×Dic47—42no—
393C2×Dic47—42no—
394C2×Dic47—42no—
395C2×Dic47—42no—
396C2×Dic47—42no—
397C2×Dic47—42no—
398C2×Dic47—42no—
399C2×Dic47—42no—
400C2×Dic47—42no—
401C2×Dic47C2×C22⋊C414yescomplemented
402C4×D47—432no—
403C22⋊C42—471nomaximal, Sylow
404C22×C47—24no—
405C22×C47—24no—
406C22×C47—28no—
407C22×C47—28no—
408C22×C47—24no—
409C22×C47—24no—
410C22×C47—28no—
411C22×C47—28no—
412C22×C47—24no—
413C22×C47—24no—
414C22×C47C4×C22⋊C418yescomplemented
415C22×C47C22×C4211yescharacteristic
416C22×C47C22×C22⋊C411yescharacteristic
417C22×C47C22×C22⋊C411yescharacteristic
418C22×C47C2×#11711yescharacteristic
419C22×C47C2×#11711yescharacteristic
420C22×C47C2×C4×D412yes—
421C22×C47C2×C4×D412yes—
422C22×C47C2×C4×D411yescharacteristic
423C22×C47C2×C4×D411yescharacteristic
424C22×C47C2×C4×D411yescharacteristic
425C22×C47C2×C4×D411yescharacteristic
426C22×C47#51812yes—
427C22×C47#51812yes—
428C22×C47#51811yescharacteristic
429C22×C47#51811yescharacteristic
430C22×C47D4212yes—
431C22×C47D4212yes—
432C22×C47#54612yes—
433C22×C47#54612yes—
434C22×C47#54612yes—
435C22×C47#54612yes—
436C22×C47#55112yes—
437C22×C47#55112yes—
438C2×D47—28no—
439C2×D47—24no—
440C2×D47—24no—
441C2×D47—24no—
442C2×D47—24no—
443C2×D47—28no—
444C2×D47—28no—
445C2×D47—28no—
446C2×D47—24no—
447C2×D47—24no—
448C2×D47—24no—
449C2×D47—24no—
450C2×D47—24no—
451C2×D47—464no—
452C2×D47—44no—
453C2×D47—42no—
454C2×D47—42no—
455C2×D47—44no—
456C2×D47—42no—
457C2×D47—42no—
458C2×D47—44no—
459C2×D47—44no—
460C2×D47C4×C22⋊C418yescomplemented
461C4×C47—28no—
462C4×C47—24no—
463C4×C47—42no—
464C4×C47—44no—
465Dic47—24no—
466Dic47—44no—
467Dic47—42no—
468Dic47—44no—
469C23×C22⋊C4—471no—
470C23×C22⋊C4—471no—
471C2×#379—471no—
472C2×C4×C22⋊C4—472no—
473C2×C4×C22⋊C4—471no—
474C2×C4×C22⋊C4D4711yescharacteristic, complemented
475#1437—472no—
476#1437—472no—
477C22⋊#95—472no—
478C22⋊#95—471no—
479C22⋊#95—471no—
480C2×C47—28no—
481C2×C47C2×C4×C22⋊C411yescharacteristic
482C2×C47C2×C4×C22⋊C411yescharacteristic
483C2×C47#227311yescharacteristic
484C2×C47D4×C22⋊C412yes—
485C2×C47D4×C22⋊C411yescharacteristic
486C2×C47D4×C22⋊C411yescharacteristic
487C2×C47#234212yes—
488C2×C47#234211yescharacteristic
489C2×C47#234211yescharacteristic
490C2×C47#235812yes—
491C2×C47#235812yes—
492D47—28no—
493D47—44no—
494C26—471no—
495C24×C4—471no—
496C24×C4—472no—
497C24×C4C2×D4711yescharacteristic
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4—471no—
501C22×C22⋊C4—478no—
502C22×C22⋊C4—471no—
503C22×C22⋊C4—471no—
504C22×C22⋊C4—472no—
505C22×C22⋊C4—471no—
506C22×C22⋊C4—472no—
507C22×C22⋊C4—472no—
508C22×C22⋊C4—478no—
509C22×C22⋊C4—948no—
510C22×C22⋊C4—944no—
511C22×C22⋊C4—944no—
512C22×C22⋊C4C2×D4711yescharacteristic
513C22×C22⋊C4C2×D4711yescharacteristic
514C22×C42—472no—
515C22×C42C2×D4712yescomplemented
516#379—478no—
517C4×C22⋊C4—24no—
518C4×C22⋊C4—948no—
519C4×C22⋊C4—944no—
520C2×#95—472no—
521C2×#95—472no—
522C2×#95—472no—
523C2×#95—472no—
524C2×#95—472no—
525C2×#95C2×D4712yescomplemented
526C47C22⋊C4211yescharacteristic, complemented, Sylow
527C25—471no—
528C25—471no—
529C25—474no—
530C25—474no—
531C25—474no—
532C25—944no—
533C25—944no—
534C25—942no—
535C25—942no—
536C25—942no—
537C25—942no—
538C25—1882no—
539C25—1882no—
540C25C22×D4711yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—471no—
546C23×C4—472no—
547C23×C4—472no—
548C23×C4—471no—
549C23×C4—474no—
550C23×C4—478no—
551C23×C4—944no—
552C23×C4—944no—
553C23×C4—944no—
554C23×C4—942no—
555C23×C4—942no—
556C23×C4—944no—
557C23×C4—944no—
558C23×C4—1882no—
559C23×C4—1882no—
560C23×C4—1882no—
561C23×C4C4×D4714yescomplemented
562C23×C4C22×D4712yes—
563C23×C4C22×D4711yescharacteristic
564C23×C4C22×D4712yes—
565C23×C4C22×D4711yescharacteristic
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—474no—
569C2×C22⋊C4—478no—
570C2×C22⋊C4—474no—
571C2×C22⋊C4—474no—
572C2×C22⋊C4—474no—
573C2×C22⋊C4—474no—
574C2×C22⋊C4—474no—
575C2×C22⋊C4—478no—
576C2×C22⋊C4—478no—
577C2×C22⋊C4—478no—
578C2×C22⋊C4—9432no—
579C2×C22⋊C4—944no—
580C2×C22⋊C4—944no—
581C2×C22⋊C4—944no—
582C2×C22⋊C4—944no—
583C2×C22⋊C4—942no—
584C2×C22⋊C4—942no—
585C2×C22⋊C4—942no—
586C2×C22⋊C4—942no—
587C2×C22⋊C4—944no—
588C2×C22⋊C4—944no—
589C2×C22⋊C4—944no—
590C2×C22⋊C4—9432no—
591C2×C22⋊C4—1882no—
592C2×C22⋊C4—1882no—
593C2×C22⋊C4C4×D4714yes—
594C2×C22⋊C4C4×D4714yescomplemented
595C2×C22⋊C4D18814yes—
596C2×C22⋊C4C22⋊D4714yes—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—42no—
600C2×C42—944no—
601C2×C42—944no—
602C2×C42—1882no—
603#95—24no—
604#95—944no—
605#95—944no—
606#95—944no—
607#95—1882no—
608#95—1882no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—472no—
614C24—472no—
615C24—472no—
616C24—474no—
617C24—474no—
618C24—472no—
619C24—472no—
620C24—472no—
621C24—4716no—
622C24—948no—
623C24—948no—
624C24—9416no—
625C24—9416no—
626C24—941no—
627C24—941no—
628C24—941no—
629C24—941no—
630C24—942no—
631C24—942no—
632C24—948no—
633C24—948no—
634C24—948no—
635C24—948no—
636C24—948no—
637C24—948no—
638C24—942no—
639C24—941no—
640C24—941no—
641C24—942no—
642C24—941no—
643C24—941no—
644C24—942no—
645C24—942no—
646C24—1888no—
647C24—1888no—
648C24—1884no—
649C24—1884no—
650C24—1888no—
651C24—1888no—
652C24—1888no—
653C24—1888no—
654C24—1888no—
655C24—1888no—
656C24—1888no—
657C24—1888no—
658C24C2×C4×D4712yes—
659C24C2×C4×D4712yes—
660C24C2×C4×D4712yes—
661C24C2×D18812yes—
662C24#1062535012yes—
663C24#1062535012yes—
664C24C2×C22⋊D4712yes—
665C24C23×D4711yescharacteristic
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—28no—
685C22×C4—44no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—472no—
689C22×C4—474no—
690C22×C4—474no—
691C22×C4—472no—
692C22×C4—474no—
693C22×C4—9416no—
694C22×C4—948no—
695C22×C4—941no—
696C22×C4—941no—
697C22×C4—942no—
698C22×C4—948no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—941no—
704C22×C4—942no—
705C22×C4—942no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—941no—
710C22×C4—942no—
711C22×C4—942no—
712C22×C4—942no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—9416no—
716C22×C4—1888no—
717C22×C4—1888no—
718C22×C4—1888no—
719C22×C4—1888no—
720C22×C4—1888no—
721C22×C4—1884no—
722C22×C4—1888no—
723C22×C4—1888no—
724C22×C4C2×C4×D4714yes—
725C22×C4C2×C4×D4712yes—
726C22×C4C2×C4×D4712yes—
727C22×C4C2×C4×D4714yes—
728C22×C4C2×D18814yes—
729C22×C4D4×D4714yes—
730C22×C4C2×C22⋊D4714yes—
731C22⋊C4—28no—
732C22⋊C4—4716no—
733C22⋊C4—948no—
734C22⋊C4—9416no—
735C22⋊C4—948no—
736C22⋊C4—948no—
737C22⋊C4—948no—
738C22⋊C4—948no—
739C22⋊C4—9416no—
740C22⋊C4—1888no—
741C22⋊C4(C2×D47)⋊C4116yesdirect product factor
742C42—48no—
743C42—1888no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—22no—
753C23—22no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—22no—
759C23—22no—
760C23—474no—
761C23—474no—
762C23—474no—
763C23—478no—
764C23—478no—
765C23—474no—
766C23—9432no—
767C23—944no—
768C23—944no—
769C23—944no—
770C23—944no—
771C23—944no—
772C23—944no—
773C23—944no—
774C23—944no—
775C23—942no—
776C23—942no—
777C23—942no—
778C23—942no—
779C23—942no—
780C23—942no—
781C23—944no—
782C23—944no—
783C23—942no—
784C23—942no—
785C23—9432no—
786C23—942no—
787C23—942no—
788C23—942no—
789C23—942no—
790C23—944no—
791C23—944no—
792C23—942no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—944no—
797C23—944no—
798C23—942no—
799C23—942no—
800C23—18816no—
801C23—18832no—
802C23—18832no—
803C23—18832no—
804C23—18816no—
805C23—18816no—
806C23—18832no—
807C23—18816no—
808C23—18816no—
809C23—1882no—
810C23—1882no—
811C23—1882no—
812C23—1882no—
813C23—1882no—
814C23—1882no—
815C23—1882no—
816C23—1882no—
817C23C42×D4714yes—
818C23C2×(C2×D47)⋊C414yes—
819C23#1309398114yes—
820C23C4×C22⋊D4714yes—
821C23C4×C22⋊D4714yes—
822C23C4×D18814yes—
823C23C4×D18814yes—
824C23C22×C4×D4711yescharacteristic
825C23C22×C4×D4711yescharacteristic
826C23C22×C4×D4711yescharacteristic
827C23C2×D4×D4712yes—
828C23C22×C22⋊D4711yescharacteristic
829C23C22×D18811yescharacteristic
830C23#41×D4712yes—
831C23C2×#1062535011yescharacteristic
832C23C2×#1062535011yescharacteristic
833C23#1309406912yes—
834C23#1309407012yes—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—474no—
859C2×C4—944no—
860C2×C4—944no—
861C2×C4—942no—
862C2×C4—942no—
863C2×C4—942no—
864C2×C4—944no—
865C2×C4—944no—
866C2×C4—944no—
867C2×C4—944no—
868C2×C4—942no—
869C2×C4—944no—
870C2×C4—944no—
871C2×C4—942no—
872C2×C4—18832no—
873C2×C4—18816no—
874C2×C4—1882no—
875C2×C4—1882no—
876C2×C4—1882no—
877C2×C4—1882no—
878C2×C4—1882no—
879C2×C4—1882no—
880C2×C4—1882no—
881C2×C4—1882no—
882C2×C4—1882no—
883C2×C4—1882no—
884C2×C4C22⋊C4×D4714yescomplemented
885C2×C4C2×(C2×D47)⋊C418yescomplemented
886C22—28no—
887C22—28no—
888C22—28no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—478no—
897C22—948no—
898C22—948no—
899C22—948no—
900C22—944no—
901C22—944no—
902C22—944no—
903C22—948no—
904C22—944no—
905C22—944no—
906C22—944no—
907C22—944no—
908C22—944no—
909C22—944no—
910C22—18864no—
911C22—1884no—
912C22—1884no—
913C22—1884no—
914C22—1882no—
915C22—1882no—
916C22—1884no—
917C22—1882no—
918C22—1882no—
919C22C4×(C2×D47)⋊C418yescomplemented
920C22C2×C42×D4711yescharacteristic
921C22C2×C22⋊C4×D4711yescharacteristic
922C22C22×(C2×D47)⋊C411yescharacteristic
923C22#117×D4711yescharacteristic
924C22C2×#1309398111yescharacteristic
925C22C4×D4×D4712yes—
926C22C4×D4×D4712yes—
927C22C2×C4×C22⋊D4711yescharacteristic
928C22C2×C4×C22⋊D4711yescharacteristic
929C22C2×C4×D18811yescharacteristic
930C22C2×C4×D18811yescharacteristic
931C22#1568959512yes—
932C22#1568959512yes—
933C22#1568959611yescharacteristic
934C22#1568959711yescharacteristic
935C22D4×C22⋊D4712yes—
936C22D4×D18812yes—
937C22#1568976112yes—
938C22#1568976312yes—
939C22#1568976812yes—
940C22#1568976912yes—
941C22#1568979712yes—
942C22#1568980212yes—
943C4—28no—
944C4—24no—
945C4—44no—
946C4—42no—
947C4—944no—
948C4—1884no—
949C4—1884no—
950C4—1882no—
951C2—28no—
952C2—948no—
953C2—1884no—
954C2C4×C22⋊C4×D4711yescharacteristic
955C2C2×C4×(C2×D47)⋊C411yescharacteristic
956C2#2024574011yescharacteristic
957C2D4×(C2×D47)⋊C412yes—
958C2C22⋊C4×C22⋊D4711yescharacteristic
959C2C22⋊C4×D18811yescharacteristic
960C2#2024623112yes—
961C2#2024623811yescharacteristic
962C2#2024624011yescharacteristic
963C2#2024636512yes—
964C2#2024637012yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C22⋊C42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic47C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. #20241626C2semidirect
7. #20241624C2semidirect
8. #20241611C2semidirect
9. #20241610C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C2×C4×C22⋊C4×C47C2semidirect
18. C22×(C2×D47)⋊C4C4semidirect
28. C2×C22⋊C4×D47C4semidirect
29. C22×C4×Dic47C22semidirect
30. #15688978C4semidirect
33. C2×C47⋊#95C22semidirect
34. C2×C47⋊#95C22semidirect
35. C2×C47⋊#95C22semidirect
36. C2×C47⋊#95C22semidirect
37. C2×C47⋊#95C22semidirect
41. C22×C42×C47C22semidirect
43. C2×#95×C47C22semidirect
61. C23×Dic47C2×C4semidirect
72. C22×C4×D47C2×C4semidirect
78. C2×C22⋊Dic47C2×C4semidirect
91. C2×(C2×D47)⋊C4C2×C4semidirect
92. C2×(C2×D47)⋊C4C2×C4semidirect
93. C2×(C2×D47)⋊C4C2×C4semidirect
94. C2×(C2×D47)⋊C4C2×C4semidirect
95. C2×(C2×D47)⋊C4C2×C4semidirect
111. C23×C4×C47C2×C4semidirect
119. C2×C22⋊C4×C47C2×C4semidirect
174. C23×D47C42semidirect
249. C22⋊C4×C47C22⋊C4semidirect
259. (C2×D47)⋊C4C22⋊C4direct (N × H)
375. C2×C4×C47C2×C22⋊C4semidirect
376. C2×C4×C47C2×C22⋊C4semidirect
401. C2×Dic47C2×C22⋊C4semidirect
414. C22×C47C4×C22⋊C4semidirect
460. C2×D47C4×C22⋊C4semidirect
474. C2×C4×C22⋊C4D47semidirect
515. C22×C42C2×D47semidirect
525. C2×#95C2×D47semidirect
526. C47C22⋊C42semidirect
561. C23×C4C4×D47semidirect
594. C2×C22⋊C4C4×D47semidirect
741. C22⋊C4(C2×D47)⋊C4direct (N × H)
884. C2×C4C22⋊C4×D47semidirect
885. C2×C4C2×(C2×D47)⋊C4semidirect
919. C22C4×(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D47)⋊C42
C22×C22⋊C4×D472
C2×#156889782
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
#202416262
#202416242
#202416112
#202416102
(C2×D47)⋊#952
C2×C4×C22⋊C4×C472
C22⋊C4247