Finite Group Databasebeta

← #26137677

Subgroups — #26137677

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×C22⋊Dic47C211yesmaximal, characteristic, complemented
6C2×#15688970C212yesmaximal, complemented
7#20241624C212yesmaximal, complemented
8#20241624C212yesmaximal, complemented
9#20241610C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×C22⋊#95C211yesmaximal, 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
30C22×C4×Dic47C2212yescomplemented
31#15688978C418yescomplemented
32C22⋊C4×Dic47—24no—
33C4×C22⋊Dic47—24no—
34#15688970—28no—
35C2×C47⋊#95C2212yescomplemented
36C2×C47⋊#95C2212yescomplemented
37C2×C47⋊#95C2212yescomplemented
38C2×C47⋊#95C2212yescomplemented
39C24×C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2211yescharacteristic
42C2×#95×C47C2212yescomplemented
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×Dic47C2311yescharacteristic
65C23×Dic47C2312yes—
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⋊Dic47C2×C414yes—
76C2×C22⋊Dic47C2×C414yescomplemented
77C2×C22⋊Dic47D414yes—
78C2×C22⋊Dic47D414yes—
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—24no—
101C2×C4×Dic47—24no—
102C2×C4×Dic47—42no—
103C2×C4×Dic47—42no—
104C47⋊#95—24no—
105C47⋊#95—24no—
106C47⋊#95—24no—
107C47⋊#95—42no—
108C25×C47C2311yescharacteristic
109C23×C4×C47—22no—
110C23×C4×C47—22no—
111C23×C4×C47—24no—
112C23×C4×C47—42no—
113C23×C4×C47C2×C414yescomplemented
114C23×C4×C47C2312yes—
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2312yes—
117C23×C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—22no—
120C2×C22⋊C4×C47—22no—
121C2×C22⋊C4×C47—22no—
122C2×C22⋊C4×C47C2×C414yes—
123C2×C22⋊C4×C47C2×C414yescomplemented
124#95×C47—24no—
125#95×C47—42no—
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—21no—
185C22×C4×C47—22no—
186C22×C4×C47—28no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—21no—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—21no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—28no—
204C22×C4×C47—44no—
205C22×C4×C47—48no—
206C22×C4×C47—48no—
207C22×C4×C47C22×C414yes—
208C22×C4×C47C22×C414yes—
209C22×C4×C47C22×C412yes—
210C22×C4×C47C22×C412yes—
211C22×C4×C47C2×D414yes—
212C22×Dic47—22no—
213C22×Dic47—21no—
214C22×Dic47—22no—
215C22×Dic47—21no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—28no—
220C22×Dic47—21no—
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—28no—
231C22×Dic47—44no—
232C22×Dic47—48no—
233C22×Dic47—48no—
234C22×Dic47C22×C412yes—
235C22×Dic47C22×C414yes—
236C22×Dic47C22×C412yes—
237C22×Dic47C22×C414yes—
238C22×Dic47C2×D414yes—
239C22×Dic47C2×D414yes—
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×C47—28no—
250C22⋊Dic47—28no—
251C22⋊Dic47C22⋊C4116yescomplemented
252(C2×D47)⋊C4—28no—
253(C2×D47)⋊C4—216no—
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—216no—
256(C2×D47)⋊C4—28no—
257(C2×D47)⋊C4—48no—
258(C2×D47)⋊C4C22⋊C4116yescomplemented
259C4×Dic47—48no—
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—22no—
353C2×C4×C47—22no—
354C2×C4×C47—24no—
355C2×C4×C47—24no—
356C2×C4×C47—22no—
357C2×C4×C47—24no—
358C2×C4×C47—24no—
359C2×C4×C47—24no—
360C2×C4×C47—24no—
361C2×C4×C47—22no—
362C2×C4×C47—24no—
363C2×C4×C47—24no—
364C2×C4×C47—22no—
365C2×C4×C47—416no—
366C2×C4×C47—42no—
367C2×C4×C47—42no—
368C2×C4×C47—42no—
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×C47—42no—
376C2×C4×C47C2×C22⋊C414yescomplemented
377C2×Dic47—24no—
378C2×Dic47—22no—
379C2×Dic47—24no—
380C2×Dic47—22no—
381C2×Dic47—24no—
382C2×Dic47—24no—
383C2×Dic47—24no—
384C2×Dic47—24no—
385C2×Dic47—24no—
386C2×Dic47—24no—
387C2×Dic47—22no—
388C2×Dic47—24no—
389C2×Dic47—24no—
390C2×Dic47—22no—
391C2×Dic47—24no—
392C2×Dic47—22no—
393C2×Dic47—416no—
394C2×Dic47—42no—
395C2×Dic47—42no—
396C2×Dic47—42no—
397C2×Dic47—42no—
398C2×Dic47—42no—
399C2×Dic47—42no—
400C2×Dic47C2×C22⋊C414yescomplemented
401C2×Dic47C2×C22⋊C418yescomplemented
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—42no—
453C2×D47—44no—
454C2×D47—42no—
455C2×D47—42no—
456C2×D47—42no—
457C2×D47—44no—
458C2×D47—44no—
459C2×D47—44no—
460C2×D47C4×C22⋊C418yescomplemented
461C4×C47—24no—
462C4×C47—44no—
463C4×C47—42no—
464C4×C47—44no—
465Dic47—28no—
466Dic47—24no—
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⋊C4—471no—
475#1437—472no—
476#1437—472no—
477C22⋊#95—472no—
478C22⋊#95—471no—
479C22⋊#95D4711yescharacteristic, complemented
480C2×C47—28no—
481C2×C47C2×C4×C22⋊C411yescharacteristic
482C2×C47C2×C4×C22⋊C411yescharacteristic
483C2×C47#227311yescharacteristic
484C2×C47D4×C22⋊C411yescharacteristic
485C2×C47D4×C22⋊C412yes—
486C2×C47D4×C22⋊C411yescharacteristic
487C2×C47#234211yescharacteristic
488C2×C47#234211yescharacteristic
489C2×C47#234212yes—
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—944no—
510C22×C22⋊C4—944no—
511C22×C22⋊C4—948no—
512C22×C22⋊C4C2×D4711yescharacteristic
513C22×C22⋊C4C2×D4711yescharacteristic
514C22×C42—472no—
515C22×C42—472no—
516#379—478no—
517C4×C22⋊C4—948no—
518C4×C22⋊C4—944no—
519C4×C22⋊C4—944no—
520C2×#95—472no—
521C2×#95—472no—
522C2×#95—472no—
523C2×#95—472no—
524C2×#95C2×D4712yescomplemented
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—472no—
546C23×C4—471no—
547C23×C4—472no—
548C23×C4—471no—
549C23×C4—474no—
550C23×C4—478no—
551C23×C4—944no—
552C23×C4—944no—
553C23×C4—944no—
554C23×C4—944no—
555C23×C4—944no—
556C23×C4—942no—
557C23×C4—942no—
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—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—474no—
571C2×C22⋊C4—474no—
572C2×C22⋊C4—474no—
573C2×C22⋊C4—474no—
574C2×C22⋊C4—478no—
575C2×C22⋊C4—474no—
576C2×C22⋊C4—474no—
577C2×C22⋊C4—474no—
578C2×C22⋊C4—478no—
579C2×C22⋊C4—474no—
580C2×C22⋊C4—478no—
581C2×C22⋊C4—478no—
582C2×C22⋊C4—9432no—
583C2×C22⋊C4—9432no—
584C2×C22⋊C4—944no—
585C2×C22⋊C4—944no—
586C2×C22⋊C4—944no—
587C2×C22⋊C4—944no—
588C2×C22⋊C4—944no—
589C2×C22⋊C4—944no—
590C2×C22⋊C4—942no—
591C2×C22⋊C4—942no—
592C2×C22⋊C4—944no—
593C2×C22⋊C4—1882no—
594C2×C22⋊C4—1882no—
595C2×C22⋊C4C4×D4714yes—
596C2×C22⋊C4C4×D4714yescomplemented
597C2×C42—944no—
598C2×C42—944no—
599C2×C42—944no—
600C2×C42—944no—
601C2×C42—1882no—
602C2×C42—1882no—
603#95—24no—
604#95—42no—
605#95—944no—
606#95—944no—
607#95—944no—
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—
661C24D4×D4712yes—
662C24D4×D4712yes—
663C24#1062535212yes—
664C24#1062535412yes—
665C24C23×D4711yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—28no—
687C22×C4—44no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—474no—
691C22×C4—472no—
692C22×C4—474no—
693C22×C4—474no—
694C22×C4—474no—
695C22×C4—474no—
696C22×C4—472no—
697C22×C4—9416no—
698C22×C4—9416no—
699C22×C4—948no—
700C22×C4—942no—
701C22×C4—941no—
702C22×C4—942no—
703C22×C4—941no—
704C22×C4—942no—
705C22×C4—942no—
706C22×C4—942no—
707C22×C4—948no—
708C22×C4—941no—
709C22×C4—942no—
710C22×C4—942no—
711C22×C4—942no—
712C22×C4—942no—
713C22×C4—942no—
714C22×C4—941no—
715C22×C4—942no—
716C22×C4—942no—
717C22×C4—942no—
718C22×C4—1888no—
719C22×C4—1888no—
720C22×C4—1888no—
721C22×C4—1888no—
722C22×C4—1888no—
723C22×C4—1884no—
724C22×C4—1888no—
725C22×C4—1888no—
726C22×C4C2×C4×D4714yes—
727C22×C4C2×C4×D4712yes—
728C22×C4C2×C4×D4714yes—
729C22×C4C2×C4×D4712yes—
730C22×C4D4×D4714yes—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—4716no—
734C22⋊C4—4716no—
735C22⋊C4—9416no—
736C22⋊C4—948no—
737C22⋊C4—9416no—
738C22⋊C4—948no—
739C22⋊C4—948no—
740C22⋊C4—948no—
741C22⋊C4—1888no—
742C42—1888no—
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—18816no—
804C23—18832no—
805C23—18816no—
806C23—18816no—
807C23—18816no—
808C23—18832no—
809C23—1882no—
810C23—1882no—
811C23—1882no—
812C23—1882no—
813C23—1882no—
814C23—1882no—
815C23—1882no—
816C23—1882no—
817C23C42×D4714yes—
818C23C22⋊C4×D4714yes—
819C23#1309398214yes—
820C23(C22⋊D47)⋊C414yes—
821C23(C22⋊D47)⋊C414yes—
822C23#1309398614yes—
823C23#1309398614yes—
824C23C22×C4×D4711yescharacteristic
825C23C22×C4×D4711yescharacteristic
826C23C22×C4×D4711yescharacteristic
827C23C2×D4×D4711yescharacteristic
828C23C2×D4×D4712yes—
829C23C2×D4×D4711yescharacteristic
830C23#41×D4712yes—
831C23C2×#1062535211yescharacteristic
832C23C2×#1062535411yescharacteristic
833C23#1309406912yes—
834C23#1309407012yes—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—416no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—478no—
860C2×C4—474no—
861C2×C4—944no—
862C2×C4—944no—
863C2×C4—944no—
864C2×C4—944no—
865C2×C4—944no—
866C2×C4—944no—
867C2×C4—944no—
868C2×C4—942no—
869C2×C4—944no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—944no—
873C2×C4—944no—
874C2×C4—942no—
875C2×C4—944no—
876C2×C4—942no—
877C2×C4—18832no—
878C2×C4—18816no—
879C2×C4—1882no—
880C2×C4—1882no—
881C2×C4—1882no—
882C2×C4—1882no—
883C2×C4—1882no—
884C2×C4—1882no—
885C2×C4C22⋊C4×D4714yescomplemented
886C22—28no—
887C22—28no—
888C22—24no—
889C22—28no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—28no—
895C22—24no—
896C22—478no—
897C22—948no—
898C22—948no—
899C22—944no—
900C22—948no—
901C22—944no—
902C22—944no—
903C22—944no—
904C22—944no—
905C22—948no—
906C22—944no—
907C22—944no—
908C22—944no—
909C22—944no—
910C22—18864no—
911C22—1884no—
912C22—1884no—
913C22—1882no—
914C22—1884no—
915C22—1882no—
916C22—1882no—
917C22—1882no—
918C22—1884no—
919C22#1568897018yescomplemented
920C22C2×C42×D4711yescharacteristic
921C22C2×C22⋊C4×D4711yescharacteristic
922C22C2×C22⋊C4×D4711yescharacteristic
923C22#117×D4711yescharacteristic
924C22C2×#1309398211yescharacteristic
925C22C4×D4×D4712yes—
926C22C4×D4×D4712yes—
927C22C2×(C22⋊D47)⋊C411yescharacteristic
928C22C2×(C22⋊D47)⋊C411yescharacteristic
929C22C2×#1309398611yescharacteristic
930C22C2×#1309398611yescharacteristic
931C22#1568959512yes—
932C22#1568959512yes—
933C22#1568959611yescharacteristic
934C22#1568959711yescharacteristic
935C22#1568975512yes—
936C22#1568975712yes—
937C22#1568976012yes—
938C22#1568976212yes—
939C22#1568976412yes—
940C22#1568976512yes—
941C22#1568979612yes—
942C22#1568980012yes—
943C4—24no—
944C4—44no—
945C4—42no—
946C4—44no—
947C4—948no—
948C4—944no—
949C4—1884no—
950C4—1882no—
951C2—28no—
952C2—948no—
953C2—1884no—
954C2C4×C22⋊C4×D4711yescharacteristic
955C2C2×#1568897011yescharacteristic
956C2#2024574011yescharacteristic
957C2#2024620411yescharacteristic
958C2#2024620612yes—
959C2#2024620811yescharacteristic
960C2#2024623011yescharacteristic
961C2#2024623411yescharacteristic
962C2#2024623512yes—
963C2#2024636412yes—
964C2#2024636812yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC25×D47C22
hypercenterC22⋊#95D47
hypocenterC47C22⋊C42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic47C2semidirect
5. C2×C4×C22⋊Dic47C2semidirect
6. C2×#15688970C2semidirect
7. #20241624C2semidirect
8. #20241624C2semidirect
9. #20241610C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
18. C22×(C2×D47)⋊C4C4semidirect
28. C2×C22⋊C4×D47C4semidirect
29. C22×C4×Dic47C22semidirect
30. C22×C4×Dic47C22semidirect
31. #15688978C4semidirect
35. C2×C47⋊#95C22semidirect
36. C2×C47⋊#95C22semidirect
37. C2×C47⋊#95C22semidirect
38. C2×C47⋊#95C22semidirect
42. C2×#95×C47C22semidirect
43. C2×#95×C47C22semidirect
61. C23×Dic47C2×C4semidirect
72. C22×C4×D47C2×C4semidirect
76. 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
113. C23×C4×C47C2×C4semidirect
123. C2×C22⋊C4×C47C2×C4semidirect
174. C23×D47C42semidirect
251. C22⋊Dic47C22⋊C4semidirect
258. (C2×D47)⋊C4C22⋊C4semidirect
376. C2×C4×C47C2×C22⋊C4semidirect
400. C2×Dic47C2×C22⋊C4semidirect
401. C2×Dic47C2×C22⋊C4semidirect
414. C22×C47C4×C22⋊C4semidirect
460. C2×D47C4×C22⋊C4semidirect
479. C22⋊#95D47semidirect
524. C2×#95C2×D47semidirect
525. C2×#95C2×D47semidirect
526. C47C22⋊C42semidirect
561. C23×C4C4×D47semidirect
596. C2×C22⋊C4C4×D47semidirect
885. C2×C4C22⋊C4×D47semidirect
919. C22#15688970semidirect

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×C22⋊Dic472
C2×#156889702
#202416242
#202416102
(C2×D47)⋊#952
C47×C22⋊#952
C22⋊C4247