Finite Group Databasebeta

← #26137776

Subgroups — #26137776

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C2×#15689002C211yesmaximal, characteristic
3C2×#15689000C211yesmaximal, characteristic
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6C22×C47⋊#95C211yesmaximal, characteristic, complemented
7#20241626C211yesmaximal, characteristic, complemented
8#20241624C211yesmaximal, characteristic, complemented
9#20241623C211yesmaximal, characteristic, complemented
10#20241621C211yesmaximal, characteristic, complemented
11#20241612C211yesmaximal, characteristic, complemented
12#20241610C211yesmaximal, characteristic, complemented
13(C2×D47)⋊#95C211yesmaximal, characteristic, complemented
14C4×C47⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C23×C22⋊D47C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×(C22⋊D47)⋊C4—24no—
21C2×(C22⋊D47)⋊C4—24no—
22C2×(C22⋊D47)⋊C4C418yescomplemented
23C22×Dic47⋊C4C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33#15689002C418yescomplemented
34#15689000C418yescomplemented
35C22⋊C4×Dic47—24no—
36C4×(C2×D47)⋊C4—24no—
37C2×C47⋊#95—24no—
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C24×C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C22⋊C4×C47C2211yescharacteristic
55C22×C42×C47C2211yescharacteristic
56C22×C42×C47C2211yescharacteristic
57C4×C22⋊C4×C47—24no—
58C2×#95×C47C2211yescharacteristic
59C2×#95×C47C2211yescharacteristic
60C24×D47C2311yescharacteristic
61C22×C22⋊D47—22no—
62C22×C22⋊D47—22no—
63C22×C22⋊D47—22no—
64C22×C22⋊D47—22no—
65C22×C22⋊D47C2×C414yes—
66C22×C22⋊D47C2×C414yes—
67C22×C22⋊D47C2×C414yes—
68C23×Dic47—22no—
69C23×Dic47—22no—
70C23×Dic47—22no—
71C23×Dic47—22no—
72C23×Dic47—22no—
73C23×Dic47—22no—
74C23×Dic47—22no—
75C23×Dic47—22no—
76C23×Dic47—41no—
77C23×Dic47—41no—
78C23×Dic47—41no—
79C23×Dic47—41no—
80C23×Dic47C2×C414yes—
81C23×Dic47C2×C414yescomplemented
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C22×C4×D47—22no—
90C22×C4×D47—22no—
91C22×C4×D47—22no—
92C22×C4×D47—22no—
93C22×C4×D47—41no—
94C22×C4×D47—41no—
95C22×C4×D47C2×C414yescomplemented
96(C22⋊D47)⋊C4—232no—
97C2×Dic47⋊C4—22no—
98C2×Dic47⋊C4—22no—
99C2×Dic47⋊C4C2×C414yescomplemented
100C2×C22⋊Dic47—22no—
101C2×C22⋊Dic47—22no—
102C2×C22⋊Dic47C2×C414yescomplemented
103C2×(C2×D47)⋊C4—22no—
104C2×(C2×D47)⋊C4—22no—
105C2×(C2×D47)⋊C4—22no—
106C2×(C2×D47)⋊C4—22no—
107C2×(C2×D47)⋊C4—22no—
108C2×(C2×D47)⋊C4—22no—
109C2×(C2×D47)⋊C4—41no—
110C2×(C2×D47)⋊C4—41no—
111C2×(C2×D47)⋊C4—41no—
112C2×(C2×D47)⋊C4—41no—
113C2×(C2×D47)⋊C4C2×C414yescomplemented
114C2×(C2×D47)⋊C4C2×C414yescomplemented
115C2×(C2×D47)⋊C4C2×C414yescomplemented
116C2×(C2×D47)⋊C4C2×C414yescomplemented
117C2×(C2×D47)⋊C4C2×C414yescomplemented
118C2×C4×Dic47—22no—
119C2×C4×Dic47—22no—
120C2×C4×Dic47—22no—
121C2×C4×Dic47—22no—
122C2×C4×Dic47—22no—
123C2×C4×Dic47—22no—
124C2×C4×Dic47—41no—
125C2×C4×Dic47—41no—
126C2×C4×Dic47C2×C414yescomplemented
127C47⋊#95—22no—
128C47⋊#95—22no—
129C47⋊#95—22no—
130C47⋊#95—22no—
131C47⋊#95—22no—
132C47⋊#95—22no—
133C47⋊#95—22no—
134C47⋊#95—41no—
135C47⋊#95—41no—
136C47⋊#95C2×C414yescomplemented
137C47⋊#95C2×C414yescomplemented
138C47⋊#95C2×C414yescomplemented
139C47⋊#95C2×C414yescomplemented
140C47⋊#95D414yescomplemented
141C25×C47C2311yescharacteristic
142C23×C4×C47—22no—
143C23×C4×C47—22no—
144C23×C4×C47—22no—
145C23×C4×C47—22no—
146C23×C4×C47—41no—
147C23×C4×C47—41no—
148C23×C4×C47C2×C414yescomplemented
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C2×C22⋊C4×C47—22no—
156C2×C22⋊C4×C47—22no—
157C2×C22⋊C4×C47C2×C414yes—
158C2×C22⋊C4×C47C2×C414yescomplemented
159C2×C22⋊C4×C47D414yes—
160C2×C22⋊C4×C47D414yes—
161C2×C42×C47—22no—
162C2×C42×C47—22no—
163C2×C42×C47—22no—
164C2×C42×C47—22no—
165C2×C42×C47—41no—
166C2×C42×C47—41no—
167#95×C47—22no—
168#95×C47—22no—
169C24×C47—21no—
170C24×C47—21no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—21no—
174C24×C47—21no—
175C24×C47—21no—
176C24×C47—21no—
177C24×C47C22×C412yes—
178C24×C47C22×C412yes—
179C24×C47C22×C412yes—
180C24×C47C2×D412yes—
181C24×C47C2×D412yes—
182C24×C47#4112yes—
183C24×C47#4112yes—
184C24×C47C2411yescharacteristic
185C23×D47—21no—
186C23×D47—21no—
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—21no—
193C23×D47—21no—
194C23×D47—21no—
195C23×D47—21no—
196C23×D47—21no—
197C23×D47C22×C412yes—
198C23×D47C22×C412yes—
199C23×D47C22×C412yes—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—28no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—28no—
232C22×C4×C47—44no—
233C22×C4×C47—44no—
234C22×C4×C47—44no—
235C22×C4×C47—44no—
236C22×C4×C47—44no—
237C22×C4×C47C22×C412yes—
238C22×C4×C47C22×C412yes—
239C22×C4×C47C22×C412yes—
240C22×C4×C47C22×C412yes—
241C22×C4×C47C22×C412yes—
242C22×C4×C47C22×C412yes—
243C22×C4×C47C2×D412yes—
244C22×C4×C47C2×D412yes—
245C22×C4×C47C2×D412yes—
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D412yes—
248C22×C4×C47#4112yes—
249C2×C22⋊D47—28no—
250C2×C22⋊D47—28no—
251C2×C22⋊D47—28no—
252C2×C22⋊D47—28no—
253C2×C22⋊D47—28no—
254C2×C22⋊D47—28no—
255C2×C22⋊D47C42116yescomplemented
256C22×Dic47—21no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47—21no—
262C22×Dic47—21no—
263C22×Dic47—21no—
264C22×Dic47—21no—
265C22×Dic47—21no—
266C22×Dic47—21no—
267C22×Dic47—21no—
268C22×Dic47—28no—
269C22×Dic47—28no—
270C22×Dic47—21no—
271C22×Dic47—21no—
272C22×Dic47—21no—
273C22×Dic47—21no—
274C22×Dic47—21no—
275C22×Dic47—21no—
276C22×Dic47—21no—
277C22×Dic47—21no—
278C22×Dic47—21no—
279C22×Dic47—21no—
280C22×Dic47—21no—
281C22×Dic47—21no—
282C22×Dic47—21no—
283C22×Dic47—21no—
284C22×Dic47—21no—
285C22×Dic47—21no—
286C22×Dic47—21no—
287C22×Dic47—21no—
288C22×Dic47—21no—
289C22×Dic47—21no—
290C22×Dic47—21no—
291C22×Dic47—21no—
292C22×Dic47—21no—
293C22×Dic47—21no—
294C22×Dic47—28no—
295C22×Dic47—28no—
296C22×Dic47—44no—
297C22×Dic47—44no—
298C22×Dic47—44no—
299C22×Dic47—44no—
300C22×Dic47—44no—
301C22×Dic47—44no—
302C22×Dic47—44no—
303C22×Dic47—44no—
304C22×Dic47—44no—
305C22×Dic47—44no—
306C22×Dic47C22×C412yes—
307C22×Dic47C22×C412yes—
308C22×Dic47C22×C412yes—
309C22×Dic47C22×C412yes—
310C22×Dic47C22×C412yes—
311C22×Dic47C22×C412yes—
312C22×Dic47C22×C412yes—
313C22×Dic47C22×C412yes—
314C22×Dic47C22×C412yes—
315C22×Dic47C2×D412yes—
316C22×Dic47C2×D412yes—
317C22×Dic47#4112yes—
318C22×Dic47#4112yes—
319C2×C4×D47—28no—
320C2×C4×D47—28no—
321C2×C4×D47—44no—
322C2×C4×D47—44no—
323C2×C4×D47—44no—
324C2×C4×D47—44no—
325C2×C4×D47—44no—
326C22⋊C4×C47—28no—
327C22⋊C4×C47C22⋊C4116yescomplemented
328C42×C47—44no—
329C42×C47—44no—
330C22⋊Dic47—28no—
331(C2×D47)⋊C4—28no—
332(C2×D47)⋊C4—28no—
333(C2×D47)⋊C4—28no—
334(C2×D47)⋊C4—44no—
335(C2×D47)⋊C4—44no—
336Dic47⋊C4—28no—
337C4×Dic47—28no—
338C4×Dic47—44no—
339C4×Dic47—44no—
340C23×C47—22no—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—22no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—22no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—22no—
365C23×C47—22no—
366C23×C47—22no—
367C23×C47—22no—
368C23×C47C2×C4214yes—
369C23×C47C2×C22⋊C414yes—
370C23×C47#11714yes—
371C23×C47C4×D414yes—
372C23×C47C4×D414yes—
373C23×C47C4×D414yes—
374C23×C47C4×D414yes—
375C23×C47C23×C411yescharacteristic
376C23×C47C23×C411yescharacteristic
377C23×C47C23×C411yescharacteristic
378C23×C47C22×D411yescharacteristic
379C23×C47C22×D411yescharacteristic
380C23×C47C22×D411yescharacteristic
381C23×C47C2×#4111yescharacteristic
382C23×C47C2×#4111yescharacteristic
383C23×C47C2×#4111yescharacteristic
384C23×C47C2×#4111yescharacteristic
385C23×C47C2×#4111yescharacteristic
386C23×C47H(5,𝔽2)11yescharacteristic
387C23×C47H(5,𝔽2)11yescharacteristic
388C23×C47H(5,𝔽2)11yescharacteristic
389C23×C472−1+411yescharacteristic
390C22×D47—22no—
391C22×D47—22no—
392C22×D47—22no—
393C22×D47—22no—
394C22×D47—22no—
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—22no—
402C22×D47—22no—
403C22×D47—22no—
404C22×D47—22no—
405C22×D47—22no—
406C22×D47—22no—
407C22×D47—22no—
408C22×D47—41no—
409C22×D47—41no—
410C22×D47—41no—
411C22×D47—41no—
412C22×D47—41no—
413C22×D47—41no—
414C22×D47—41no—
415C22×D47—41no—
416C22×D47—41no—
417C22×D47—41no—
418C22×D47—41no—
419C22×D47—41no—
420C22×D47—41no—
421C22×D47—41no—
422C22×D47—41no—
423C22×D47—41no—
424C22×D47C2×C4214yes—
425C2×C4×C47—22no—
426C2×C4×C47—22no—
427C2×C4×C47—22no—
428C2×C4×C47—22no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—22no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—22no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—416no—
453C2×C4×C47—41no—
454C2×C4×C47—41no—
455C2×C4×C47—41no—
456C2×C4×C47—41no—
457C2×C4×C47—41no—
458C2×C4×C47—41no—
459C2×C4×C47—41no—
460C2×C4×C47—41no—
461C2×C4×C47—41no—
462C2×C4×C47—41no—
463C2×C4×C47—41no—
464C2×C4×C47—41no—
465C2×C4×C47C2×C22⋊C414yes—
466C2×C4×C47C2×C22⋊C414yes—
467C2×C4×C47C4×D414yescomplemented
468C22⋊D47—232no—
469C2×Dic47—22no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—22no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—416no—
500C2×Dic47—416no—
501C2×Dic47—41no—
502C2×Dic47—41no—
503C2×Dic47—41no—
504C2×Dic47—41no—
505C2×Dic47—41no—
506C2×Dic47—41no—
507C2×Dic47—41no—
508C2×Dic47—41no—
509C2×Dic47—41no—
510C2×Dic47—41no—
511C2×Dic47—41no—
512C2×Dic47—41no—
513C2×Dic47—41no—
514C2×Dic47—41no—
515C2×Dic47—41no—
516C2×Dic47—41no—
517C2×Dic47C2×C4214yes—
518C2×Dic47C4×D414yes—
519C2×Dic47C4×D414yescomplemented
520C4×D47—416no—
521#13813—471nomaximal, Sylow
522C22×C47—24no—
523C22×C47—24no—
524C22×C47—24no—
525C22×C47—24no—
526C22×C47—24no—
527C22×C47—24no—
528C22×C47—24no—
529C22×C47—24no—
530C22×C47—24no—
531C22×C47—24no—
532C22×C47—24no—
533C22×C47—24no—
534C22×C47—24no—
535C22×C47—24no—
536C22×C47C4×C22⋊C418yescomplemented
537C22×C47C22×C4211yescharacteristic
538C22×C47C22×C22⋊C411yescharacteristic
539C22×C47C2×#11711yescharacteristic
540C22×C47C2×C4×D411yescharacteristic
541C22×C47C2×C4×D411yescharacteristic
542C22×C47C2×C4×D411yescharacteristic
543C22×C47C2×C4×D411yescharacteristic
544C22×C47C2×C4×D411yescharacteristic
545C22×C47C2×C4×D411yescharacteristic
546C22×C47C2×C4×D411yescharacteristic
547C22×C47C4×#4111yescharacteristic
548C22×C47C4×#4111yescharacteristic
549C22×C47C4×#4111yescharacteristic
550C22×C47#51811yescharacteristic
551C22×C47#51811yescharacteristic
552C22×C47#51811yescharacteristic
553C22×C47#52011yescharacteristic
554C22×C47#52011yescharacteristic
555C22×C47#52011yescharacteristic
556C22×C47D4211yescharacteristic
557C22×C47D4211yescharacteristic
558C22×C47#54611yescharacteristic
559C22×C47#54611yescharacteristic
560C22×C47#54611yescharacteristic
561C22×C47#54611yescharacteristic
562C22×C47#54611yescharacteristic
563C22×C47#54711yescharacteristic
564C22×C47#54711yescharacteristic
565C22×C47#54811yescharacteristic
566C22×C47#55111yescharacteristic
567C22×C47#55111yescharacteristic
568C22×C47#55211yescharacteristic
569C22×C47#55311yescharacteristic
570C22×C47#55311yescharacteristic
571C22×C47#55311yescharacteristic
572C2×D47—24no—
573C2×D47—24no—
574C2×D47—24no—
575C2×D47—42no—
576C2×D47—42no—
577C2×D47—42no—
578C2×D47—42no—
579C2×D47—42no—
580C2×D47—42no—
581C2×D47—42no—
582C2×D47—42no—
583C2×D47—42no—
584C2×D47—42no—
585C2×D47—42no—
586C2×D47—42no—
587C4×C47—24no—
588C4×C47—24no—
589C4×C47—24no—
590C4×C47—42no—
591C4×C47—42no—
592C4×C47—42no—
593Dic47—24no—
594Dic47—24no—
595Dic47—24no—
596Dic47—42no—
597Dic47—42no—
598Dic47—42no—
599Dic47—42no—
600C22×C4×D4—471no—
601C2×#386—471no—
602C2×#386—471no—
603C2×C4×C22⋊C4—471no—
604C2×C4×C22⋊C4—471no—
605C2×C4×C22⋊C4D4711yescharacteristic, complemented
606C22×#95—471no—
607#1437—471no—
608#1437—471no—
609#1436—471no—
610#1436—471no—
611#1434—471no—
612C22⋊#95—471no—
613C22⋊#95—471no—
614C4×#95—471no—
615C2×C47—28no—
616C2×C47C2×C4×C22⋊C411yescharacteristic
617C2×C47C42×D411yescharacteristic
618C2×C47#227511yescharacteristic
619C2×C47D4×C22⋊C411yescharacteristic
620C2×C47#233911yescharacteristic
621C2×C47#235211yescharacteristic
622C2×C47#235311yescharacteristic
623C2×C47#235811yescharacteristic
624C2×C47#235811yescharacteristic
625C2×C47#235911yescharacteristic
626C2×C47#235911yescharacteristic
627C2×C47#236111yescharacteristic
628C2×C47#236111yescharacteristic
629C2×C47#236411yescharacteristic
630C2×C47#236411yescharacteristic
631D47—44no—
632C23×D4—471no—
633C24×C4—471no—
634C24×C4—471no—
635C24×C4—471no—
636C24×C4C2×D4711yescharacteristic
637C2×C4×D4—478no—
638C2×C4×D4—944no—
639C2×C4×D4—944no—
640C22×C4⋊C4—471no—
641C22×C22⋊C4—471no—
642C22×C22⋊C4—471no—
643C22×C22⋊C4—471no—
644C22×C22⋊C4—471no—
645C22×C22⋊C4—471no—
646C22×C22⋊C4—471no—
647C22×C22⋊C4C2×D4711yescharacteristic
648C22×C22⋊C4C2×D4711yescharacteristic
649C22×C42—471no—
650C22×C42—471no—
651C22×C42—471no—
652C22×C42C2×D4711yescharacteristic
653C22×C42C2×D4711yescharacteristic
654#386—478no—
655#386—478no—
656C4×C22⋊C4—24no—
657C4×C22⋊C4—944no—
658C4×C22⋊C4—944no—
659C2×#95—471no—
660C2×#95—471no—
661C2×#95—471no—
662C2×#95—471no—
663C2×#95—471no—
664C2×#95—471no—
665C2×#95—471no—
666C2×#95—471no—
667C2×#95—471no—
668C2×#95—471no—
669C2×#95—471no—
670C2×#95—471no—
671C2×#95—471no—
672C2×#95—471no—
673C2×#95—944no—
674C2×#95C2×D4711yescharacteristic
675C2×#95C2×D4711yescharacteristic
676C47#1381311yescharacteristic, complemented, Sylow
677C25—471no—
678C25C22×D4711yescharacteristic
679C22×D4—474no—
680C22×D4—474no—
681C22×D4—474no—
682C22×D4—942no—
683C22×D4—942no—
684C22×D4—942no—
685C22×D4—942no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—471no—
693C23×C4—471no—
694C23×C4—471no—
695C23×C4—471no—
696C23×C4—471no—
697C23×C4—471no—
698C23×C4—471no—
699C23×C4—474no—
700C23×C4—474no—
701C23×C4—474no—
702C23×C4—942no—
703C23×C4—942no—
704C23×C4—942no—
705C23×C4—942no—
706C23×C4—942no—
707C23×C4—942no—
708C23×C4—942no—
709C23×C4—942no—
710C23×C4—942no—
711C23×C4—942no—
712C23×C4—942no—
713C23×C4—942no—
714C23×C4—1881no—
715C23×C4—1881no—
716C23×C4—1881no—
717C23×C4—1881no—
718C23×C4—1881no—
719C23×C4—1881no—
720C23×C4C4×D4714yescomplemented
721C23×C4C22×D4711yescharacteristic
722C23×C4C22×D4711yescharacteristic
723C23×C4C22×D4711yescharacteristic
724C23×C4C22×D4711yescharacteristic
725C23×C4C22×D4711yescharacteristic
726C23×C4C22×D4711yescharacteristic
727C4×D4—9432no—
728C2×C4⋊C4—474no—
729C2×C4⋊C4—942no—
730C2×C4⋊C4—942no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—474no—
734C2×C22⋊C4—474no—
735C2×C22⋊C4—474no—
736C2×C22⋊C4—474no—
737C2×C22⋊C4—474no—
738C2×C22⋊C4—474no—
739C2×C22⋊C4—942no—
740C2×C22⋊C4—942no—
741C2×C22⋊C4—942no—
742C2×C22⋊C4—942no—
743C2×C22⋊C4—942no—
744C2×C22⋊C4—942no—
745C2×C22⋊C4—942no—
746C2×C22⋊C4—942no—
747C2×C22⋊C4—1881no—
748C2×C22⋊C4—1881no—
749C2×C22⋊C4—1881no—
750C2×C22⋊C4—1881no—
751C2×C22⋊C4C4×D4714yes—
752C2×C22⋊C4C4×D4714yescomplemented
753C2×C22⋊C4D18814yes—
754C2×C22⋊C4C22⋊D4714yes—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—41no—
760C2×C42—41no—
761C2×C42—474no—
762C2×C42—942no—
763C2×C42—942no—
764C2×C42—942no—
765C2×C42—942no—
766C2×C42—942no—
767C2×C42—942no—
768C2×C42—1881no—
769C2×C42—1881no—
770#95—22no—
771#95—22no—
772#95—474no—
773#95—474no—
774#95—474no—
775#95—474no—
776#95—474no—
777#95—942no—
778#95—942no—
779#95—942no—
780#95—942no—
781#95—942no—
782#95—942no—
783#95—942no—
784#95—1881no—
785#95—1881no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—472no—
795C24—472no—
796C24—472no—
797C24—941no—
798C24—941no—
799C24—941no—
800C24—941no—
801C24—941no—
802C24—941no—
803C24—941no—
804C24—941no—
805C24—941no—
806C24—941no—
807C24—941no—
808C24—941no—
809C24C2×C4×D4712yes—
810C24C2×C4×D4712yes—
811C24C2×C4×D4712yes—
812C24C2×D18812yes—
813C24#1062535012yes—
814C24#1062535012yes—
815C24C2×C22⋊D4712yes—
816C24C23×D4711yescharacteristic
817C2×D4—4716no—
818C2×D4—948no—
819C2×D4—948no—
820C2×D4—948no—
821C2×D4—948no—
822C2×D4—948no—
823C2×D4—948no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—28no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—472no—
862C22×C4—472no—
863C22×C4—472no—
864C22×C4—472no—
865C22×C4—472no—
866C22×C4—472no—
867C22×C4—472no—
868C22×C4—472no—
869C22×C4—472no—
870C22×C4—472no—
871C22×C4—472no—
872C22×C4—472no—
873C22×C4—472no—
874C22×C4—948no—
875C22×C4—948no—
876C22×C4—948no—
877C22×C4—941no—
878C22×C4—941no—
879C22×C4—941no—
880C22×C4—941no—
881C22×C4—941no—
882C22×C4—941no—
883C22×C4—941no—
884C22×C4—941no—
885C22×C4—941no—
886C22×C4—941no—
887C22×C4—941no—
888C22×C4—941no—
889C22×C4—948no—
890C22×C4—948no—
891C22×C4—941no—
892C22×C4—941no—
893C22×C4—941no—
894C22×C4—941no—
895C22×C4—941no—
896C22×C4—941no—
897C22×C4—941no—
898C22×C4—941no—
899C22×C4—941no—
900C22×C4—941no—
901C22×C4—941no—
902C22×C4—941no—
903C22×C4—941no—
904C22×C4—941no—
905C22×C4—941no—
906C22×C4—941no—
907C22×C4—941no—
908C22×C4—941no—
909C22×C4—941no—
910C22×C4—941no—
911C22×C4—941no—
912C22×C4—941no—
913C22×C4—941no—
914C22×C4—941no—
915C22×C4—948no—
916C22×C4—1884no—
917C22×C4—1884no—
918C22×C4—1884no—
919C22×C4—1884no—
920C22×C4—1884no—
921C22×C4—1884no—
922C22×C4—1884no—
923C22×C4—1884no—
924C22×C4—1884no—
925C22×C4—1884no—
926C22×C4—1884no—
927C22×C4—1884no—
928C22×C4—1884no—
929C22×C4—1884no—
930C22×C4—1884no—
931C22×C4C2×C4×D4712yes—
932C22×C4C2×C4×D4712yes—
933C22×C4C2×C4×D4712yes—
934C22×C4C2×C4×D4712yes—
935C22×C4C2×C4×D4712yes—
936C22×C4C2×C4×D4712yes—
937C22×C4C2×D18812yes—
938C22×C4C2×D18812yes—
939C22×C4D4×D4712yes—
940C22×C4#1062535212yes—
941C22×C4C2×C22⋊D4712yes—
942C22×C4C2×C22⋊D4712yes—
943C4⋊C4—948no—
944C22⋊C4—28no—
945C22⋊C4—948no—
946C22⋊C4—948no—
947C22⋊C4—948no—
948C22⋊C4—948no—
949C22⋊C4—1884no—
950C22⋊C4—1884no—
951C22⋊C4(C2×D47)⋊C4116yescomplemented
952C42—44no—
953C42—44no—
954C42—948no—
955C42—1884no—
956C42—1884no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—474no—
986C23—942no—
987C23—942no—
988C23—942no—
989C23—942no—
990C23—942no—
991C23—942no—
992C23—942no—
993C23—942no—
994C23—942no—
995C23—942no—
996C23—942no—
997C23—942no—
998C23—942no—
999C23—942no—
1000C23—942no—
1001C23—942no—
1002C23—942no—
1003C23—942no—
1004C23—1881no—
1005C23—1881no—
1006C23—1881no—
1007C23—1881no—
1008C23—1881no—
1009C23—1881no—
1010C23—1881no—
1011C23—1881no—
1012C23—1881no—
1013C23—1881no—
1014C23—1881no—
1015C23—1881no—
1016C23—1881no—
1017C23—1881no—
1018C23—1881no—
1019C23—1881no—
1020C23C42×D4714yes—
1021C23C2×(C2×D47)⋊C414yes—
1022C23#1309398114yes—
1023C23C4×C22⋊D4714yes—
1024C23C4×C22⋊D4714yes—
1025C23C4×D18814yes—
1026C23C4×D18814yes—
1027C23C22×C4×D4711yescharacteristic
1028C23C22×C4×D4711yescharacteristic
1029C23C22×C4×D4711yescharacteristic
1030C23C2×D4×D4711yescharacteristic
1031C23C22×C22⋊D4711yescharacteristic
1032C23C22×D18811yescharacteristic
1033C23#41×D4711yescharacteristic
1034C23#41×D4711yescharacteristic
1035C23C2×#1062535211yescharacteristic
1036C23C2×#1062535011yescharacteristic
1037C23C2×#1062535011yescharacteristic
1038C23#1309406911yescharacteristic
1039C23#1309406911yescharacteristic
1040C23#1309407011yescharacteristic
1041C23#1309407111yescharacteristic
1042D4—9432no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—474no—
1084C2×C4—474no—
1085C2×C4—474no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—942no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—942no—
1108C2×C4—942no—
1109C2×C4—942no—
1110C2×C4—942no—
1111C2×C4—942no—
1112C2×C4—942no—
1113C2×C4—942no—
1114C2×C4—942no—
1115C2×C4—942no—
1116C2×C4—18816no—
1117C2×C4—18816no—
1118C2×C4—18816no—
1119C2×C4—1881no—
1120C2×C4—1881no—
1121C2×C4—1881no—
1122C2×C4—1881no—
1123C2×C4—1881no—
1124C2×C4—1881no—
1125C2×C4—1881no—
1126C2×C4—1881no—
1127C2×C4—1881no—
1128C2×C4—1881no—
1129C2×C4—1881no—
1130C2×C4—1881no—
1131C2×C4—1881no—
1132C2×C4—1881no—
1133C2×C4—1881no—
1134C2×C4—1881no—
1135C2×C4C2×(C2×D47)⋊C414yes—
1136C2×C4C2×(C2×D47)⋊C414yes—
1137C2×C4(C22⋊D47)⋊C414yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—944no—
1153C22—944no—
1154C22—944no—
1155C22—1882no—
1156C22—1882no—
1157C22—1882no—
1158C22—1882no—
1159C22—1882no—
1160C22—1882no—
1161C22—1882no—
1162C22—1882no—
1163C22—1882no—
1164C22—1882no—
1165C22—1882no—
1166C22—1882no—
1167C22C4×(C2×D47)⋊C418yescomplemented
1168C22C2×C42×D4711yescharacteristic
1169C22C22×(C2×D47)⋊C411yescharacteristic
1170C22C2×#1309398111yescharacteristic
1171C22C4×D4×D4711yescharacteristic
1172C22C4×D4×D4711yescharacteristic
1173C22C2×(C22⋊D47)⋊C411yescharacteristic
1174C22C2×C4×C22⋊D4711yescharacteristic
1175C22C2×C4×C22⋊D4711yescharacteristic
1176C22C2×C4×D18811yescharacteristic
1177C22C2×C4×D18811yescharacteristic
1178C22C4×#1062535211yescharacteristic
1179C22C4×#1062535211yescharacteristic
1180C22#1568959111yescharacteristic
1181C22#1568959511yescharacteristic
1182C22#1568959511yescharacteristic
1183C22#1568959611yescharacteristic
1184C22#1568960211yescharacteristic
1185C22#1568960211yescharacteristic
1186C22#1568960311yescharacteristic
1187C22D4×C22⋊D4711yescharacteristic
1188C22D4×D18811yescharacteristic
1189C22#1568976111yescharacteristic
1190C22#1568976311yescharacteristic
1191C22#1568976711yescharacteristic
1192C22#1568976811yescharacteristic
1193C22#1568976811yescharacteristic
1194C22#1568977211yescharacteristic
1195C22#1568977711yescharacteristic
1196C22#1568978211yescharacteristic
1197C22#1568979711yescharacteristic
1198C22#1568979911yescharacteristic
1199C22#1568980611yescharacteristic
1200C22#1568981911yescharacteristic
1201C22#1568982211yescharacteristic
1202C22#1568982211yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—944no—
1210C4—944no—
1211C4—944no—
1212C4—1882no—
1213C4—1882no—
1214C4—1882no—
1215C4—1882no—
1216C2—28no—
1217C2—1884no—
1218C2C2×C4×(C2×D47)⋊C411yescharacteristic
1219C2C4×(C22⋊D47)⋊C411yescharacteristic
1220C2#2024574711yescharacteristic
1221C2D4×(C2×D47)⋊C411yescharacteristic
1222C2#2024621311yescharacteristic
1223C2#2024631111yescharacteristic
1224C2#2024632211yescharacteristic
1225C2#2024636711yescharacteristic
1226C2#2024637011yescharacteristic
1227C2#2024638011yescharacteristic
1228C2#2024638211yescharacteristic
1229C2#2024640211yescharacteristic
1230C2#2024640511yescharacteristic
1231C2#2024643311yescharacteristic
1232C2#2024643811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13813
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. C22×C47⋊#95C2semidirect
7. #20241626C2semidirect
8. #20241624C2semidirect
9. #20241623C2semidirect
10. #20241621C2semidirect
11. #20241612C2semidirect
12. #20241610C2semidirect
13. (C2×D47)⋊#95C2semidirect
14. C4×C47⋊#95C2semidirect
15. C2×C4×C22⋊C4×C47C2semidirect
22. C2×(C22⋊D47)⋊C4C4semidirect
33. #15689002C4semidirect
34. #15689000C4semidirect
81. C23×Dic47C2×C4semidirect
95. C22×C4×D47C2×C4semidirect
99. C2×Dic47⋊C4C2×C4semidirect
102. C2×C22⋊Dic47C2×C4semidirect
113. C2×(C2×D47)⋊C4C2×C4semidirect
114. C2×(C2×D47)⋊C4C2×C4semidirect
115. C2×(C2×D47)⋊C4C2×C4semidirect
116. C2×(C2×D47)⋊C4C2×C4semidirect
117. C2×(C2×D47)⋊C4C2×C4semidirect
126. C2×C4×Dic47C2×C4semidirect
136. C47⋊#95C2×C4semidirect
137. C47⋊#95C2×C4semidirect
138. C47⋊#95C2×C4semidirect
139. C47⋊#95C2×C4semidirect
140. C47⋊#95D4semidirect
148. C23×C4×C47C2×C4semidirect
158. C2×C22⋊C4×C47C2×C4semidirect
255. C2×C22⋊D47C42semidirect
327. C22⋊C4×C47C22⋊C4semidirect
467. C2×C4×C47C4×D4semidirect
519. C2×Dic47C4×D4semidirect
536. C22×C47C4×C22⋊C4semidirect
605. C2×C4×C22⋊C4D47semidirect
676. C47#13813semidirect
720. C23×C4C4×D47semidirect
752. C2×C22⋊C4C4×D47semidirect
951. C22⋊C4(C2×D47)⋊C4semidirect
1137. C2×C4(C22⋊D47)⋊C4semidirect
1167. C22C4×(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C2×#156890022
C2×#156890002
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C22×C47⋊#952
#202416262
#202416242
#202416232
#202416212
#202416122
#202416102
(C2×D47)⋊#952
C4×C47⋊#952
C2×C4×C22⋊C4×C472
#1381347