Finite Group Databasebeta

← D47×#2413 #26384972

Subgroups — D47×#2413 #26384972

Order 12032.

3570 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D47C211yesmaximal, characteristic
2C2×#123×D47C211yesmaximal, characteristic
3C2×#117×D47C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246798C211yesmaximal, characteristic, complemented
6#20246797C211yesmaximal, characteristic, complemented
7#20246796C211yesmaximal, characteristic, complemented
8#20246795C211yesmaximal, characteristic, complemented
9#20246794C212yesmaximal, complemented
10#20246793C211yesmaximal, characteristic, complemented
11#20246792C212yesmaximal, complemented
12#20246791C211yesmaximal, characteristic, complemented
13#20246790C212yesmaximal, complemented
14#20246789C211yesmaximal, characteristic, complemented
15#20246788C212yesmaximal, complemented
16#398×D47C212yesmaximal, complemented
17#396×D47C212yesmaximal, complemented
18#389×D47C212yesmaximal, complemented
19#388×D47C212yesmaximal, complemented
20#386×D47C211yesmaximal, characteristic
21#385×D47C211yesmaximal, characteristic, complemented
22#381×D47C211yesmaximal, characteristic, complemented
23C47×#2413C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic
28C2×#13094009C2211yescharacteristic
29C2×#13094009C2212yes—
30C2×#13094009C2211yescharacteristic
31C2×#13094008C2211yescharacteristic
32C2×#13094008C2211yescharacteristic
33C2×#13094007C2211yescharacteristic
34C2×#13094007C2211yescharacteristic
35C2×#13094006C2211yescharacteristic
36C2×#13094006C2212yes—
37C2×#13094006C2211yescharacteristic
38C2×#13094005C2211yescharacteristic
39C2×#13094005C2211yescharacteristic
40#123×D47—28no—
41#123×D47—28no—
42C2×#13093983C2211yescharacteristic, complemented
43C2×#13093982C2212yescomplemented
44C2×#13093981C2212yescomplemented
45C2×#13093980C2211yescharacteristic, complemented
46C2×#13093980C2211yescharacteristic, complemented
47#117×D47—28no—
48C22×C4⋊Dic47C2211yescharacteristic, complemented
49C22×Dic47⋊C4C2211yescharacteristic, complemented
50C22×Dic47⋊C4C2211yescharacteristic, complemented
51C2×C4⋊C4×D47—28no—
52C2×C4⋊C4×D47C2212yes—
53C2×C4⋊C4×D47C2212yes—
54C2×C4⋊C4×D47C2212yes—
55C2×C4⋊C4×D47C2212yes—
56C2×C4⋊C4×D47C2211yescharacteristic
57C2×C4⋊C4×D47C2212yes—
58C2×C4⋊C4×D47C2211yescharacteristic
59C2×C4⋊C4×D47C2212yescomplemented
60C2×C4⋊C4×D47C2212yescomplemented
61C2×C22⋊C4×D47C2211yescharacteristic
62C2×C22⋊C4×D47C2211yescharacteristic
63C2×C22⋊C4×D47C2212yes—
64C2×C22⋊C4×D47C2211yescharacteristic
65C2×C22⋊C4×D47C2212yes—
66C2×C22⋊C4×D47C2211yescharacteristic
67C2×C22⋊C4×D47C2211yescharacteristic
68C2×C42×D47C2212yes—
69#15689057C2212yescomplemented
70#15689057C2212yescomplemented
71#15689056C2212yescomplemented
72#15689056C2212yescomplemented
73#15689055C2212yescomplemented
74#15689054C2212yescomplemented
75#15689053C2212yescomplemented
76#15689047C2212yescomplemented
77#15689046C2212yescomplemented
78#15689046C2212yescomplemented
79#15689046C2212yescomplemented
80#15689045C2212yescomplemented
81#15689045C2212yescomplemented
82#15689045C2212yescomplemented
83#15689022C2212yescomplemented
84#15689021C2212yescomplemented
85#15689020C2212yescomplemented
86#15689020C2212yescomplemented
87#15689019C2212yescomplemented
88#15689018C2212yescomplemented
89#15689018C2212yescomplemented
90#15689017C2212yescomplemented
91#15689016C2212yescomplemented
92#15689015C2212yescomplemented
93#15689014C2212yescomplemented
94#15689013C2212yescomplemented
95#15689012C2212yescomplemented
96#15689011C2212yescomplemented
97#15689003C2211yescharacteristic
98#15689002C2211yescharacteristic
99#15689001C2212yes—
100#15689000C2211yescharacteristic
101#15688999C2212yes—
102#15688998C2211yescharacteristic, complemented
103#15688997C2212yescomplemented
104#15688996C2211yescharacteristic, complemented
105#15688995C2211yescharacteristic, complemented
106#15688994C2212yescomplemented
107#15688986C2211yescharacteristic, complemented
108#15688985C2212yescomplemented
109#15688985C2212yescomplemented
110#15688984C2211yescharacteristic, complemented
111#15688984C2211yescharacteristic, complemented
112#95×D47C2212yes—
113#95×D47C2212yes—
114#95×D47C2212yes—
115#95×D47C2212yes—
116C2×#123×C47C2211yescharacteristic
117C2×#123×C47C2211yescharacteristic
118C2×#117×C47C2211yescharacteristic, complemented
119C22×C4⋊C4×C47C2211yescharacteristic, complemented
120C47×#398C2212yescomplemented
121C47×#396C2212yescomplemented
122C47×#389C2212yescomplemented
123C47×#388C2212yescomplemented
124C47×#386C2211yescharacteristic
125C47×#385C2211yescharacteristic, complemented
126C47×#381C2211yescharacteristic, complemented
127C24×D47C2311yescharacteristic
128C24×D47C2311yescharacteristic
129C22×D188C2311yescharacteristic
130C22×C22⋊D47C2311yescharacteristic
131C22×C22⋊D47C2311yescharacteristic
132C2×D4×D47—24no—
133C2×D4×D47—24no—
134C2×D4×D47—24no—
135C23×Dic47C2311yescharacteristic
136C23×Dic47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C22×C4×D47—24no—
139C22×C4×D47—24no—
140C22×C4×D47—24no—
141C22×C4×D47—28no—
142C22×C4×D47—24no—
143C22×C4×D47—24no—
144C22×C4×D47—24no—
145C22×C4×D47D418yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2312yes—
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2312yes—
152C22×C4×D47C2312yes—
153C22×C4×D47C2312yes—
154C22×C4×D47C2311yescharacteristic
155C22×C4×D47C2311yescharacteristic
156C22×C4×D47C2311yescharacteristic
157C22×C4×D47C2311yescharacteristic
158C22×C4×D47C2312yes—
159#13094009—24no—
160#13094009—24no—
161#13094009—28no—
162#13094008—24no—
163#13094008—24no—
164#13094007—24no—
165#13094007—24no—
166#13094006—24no—
167#13094006—24no—
168#13094006—28no—
169#13094005—24no—
170#13094005—24no—
171#13093983—24no—
172#13093982—28no—
173#13093981—28no—
174#13093980—24no—
175#13093980—24no—
176C2×C4⋊Dic47—24no—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2311yescharacteristic
180C2×C4⋊Dic47C2312yes—
181C2×C4⋊Dic47C2312yes—
182C2×C4⋊Dic47C2312yes—
183C2×C4⋊Dic47C2311yescharacteristic
184C2×Dic47⋊C4—24no—
185C2×Dic47⋊C4—24no—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2312yes—
190C2×Dic47⋊C4C2311yescharacteristic
191C2×Dic47⋊C4C2312yes—
192C2×Dic47⋊C4C2312yes—
193C2×Dic47⋊C4C2311yescharacteristic
194C2×Dic47⋊C4C2312yes—
195C2×Dic47⋊C4C2312yes—
196C2×Dic47⋊C4C2312yes—
197C2×Dic47⋊C4C2312yes—
198C2×Dic47⋊C4C2311yescharacteristic
199C2×Dic47⋊C4C2311yescharacteristic
200C4⋊C4×D47—28no—
201C4⋊C4×D47—28no—
202C4⋊C4×D47—28no—
203C4⋊C4×D47—28no—
204C4⋊C4×D47—28no—
205C4⋊C4×D47—24no—
206C4⋊C4×D47—24no—
207C4⋊C4×D47—28no—
208C4⋊C4×D47—28no—
209C2×C22⋊Dic47C2311yescharacteristic
210C2×C22⋊Dic47C2311yescharacteristic
211C2×C22⋊Dic47C2312yes—
212C2×C22⋊Dic47C2311yescharacteristic
213C2×C22⋊Dic47C2312yes—
214C2×C22⋊Dic47C2311yescharacteristic
215C2×C22⋊Dic47C2311yescharacteristic
216C2×(C2×D47)⋊C4C2311yescharacteristic
217C2×(C2×D47)⋊C4C2311yescharacteristic
218C2×(C2×D47)⋊C4C2312yes—
219C2×(C2×D47)⋊C4C2312yes—
220C2×(C2×D47)⋊C4C2312yes—
221C2×(C2×D47)⋊C4C2311yescharacteristic
222C2×(C2×D47)⋊C4C2312yes—
223C2×(C2×D47)⋊C4C2311yescharacteristic
224C2×(C2×D47)⋊C4C2312yes—
225C2×(C2×D47)⋊C4C2311yescharacteristic
226C2×(C2×D47)⋊C4C2311yescharacteristic
227C2×(C2×D47)⋊C4C2312yes—
228C22⋊C4×D47—24no—
229C22⋊C4×D47—24no—
230C22⋊C4×D47—24no—
231C22⋊C4×D47—24no—
232C22⋊C4×D47—28no—
233C22⋊C4×D47—28no—
234C22⋊C4×D47D418yes—
235C2×C4×Dic47C2312yes—
236C2×C4×Dic47C2312yes—
237C2×C4×Dic47C2312yes—
238C42×D47—28no—
239C47⋊#95C2312yes—
240C47⋊#95C2312yes—
241C47⋊#95C2312yes—
242C47⋊#95C2312yes—
243C47⋊#95C2312yes—
244C47⋊#95C2312yes—
245C47⋊#95C2312yes—
246C47⋊#95C2312yes—
247C47⋊#95C2312yes—
248C47⋊#95C2312yes—
249C47⋊#95C2312yes—
250C47⋊#95C2312yes—
251C22×D4×C47C2311yescharacteristic
252C23×C4×C47C2311yescharacteristic
253C23×C4×C47C2311yescharacteristic
254C23×C4×C47C2311yescharacteristic
255#123×C47—24no—
256#123×C47—24no—
257#117×C47—24no—
258C2×C4⋊C4×C47—24no—
259C2×C4⋊C4×C47C2312yes—
260C2×C4⋊C4×C47C2312yes—
261C2×C4⋊C4×C47C2311yescharacteristic
262C2×C4⋊C4×C47C2312yes—
263C2×C4⋊C4×C47C2312yes—
264C2×C4⋊C4×C47C2312yes—
265C2×C4⋊C4×C47C2311yescharacteristic
266C2×C22⋊C4×C47C2311yescharacteristic
267C2×C22⋊C4×C47C2311yescharacteristic
268C2×C22⋊C4×C47C2312yes—
269C2×C22⋊C4×C47C2312yes—
270C2×C22⋊C4×C47C2311yescharacteristic
271C2×C22⋊C4×C47C2311yescharacteristic
272C2×C22⋊C4×C47C2311yescharacteristic
273C2×C42×C47C2312yes—
274#95×C47C2312yes—
275#95×C47C2312yes—
276#95×C47C2312yes—
277#95×C47C2312yes—
278C24×C47C2411yescharacteristic
279C24×C47C2411yescharacteristic
280C23×D47—24no—
281C23×D47—24no—
282C23×D47—22no—
283C23×D47—22no—
284C23×D47—24no—
285C23×D47—22no—
286C23×D47—24no—
287C23×D47C2×D414yes—
288C23×D47C2×D414yes—
289C23×D47#4114yes—
290C23×D47C2411yescharacteristic
291C23×D47C2411yescharacteristic
292C23×D47C2411yescharacteristic
293C2×D4×C47—22no—
294C2×D4×C47—22no—
295C2×D4×C47—22no—
296C22×C4×C47—22no—
297C22×C4×C47—22no—
298C22×C4×C47—22no—
299C22×C4×C47—24no—
300C22×C4×C47—22no—
301C22×C4×C47—22no—
302C22×C4×C47—22no—
303C22×C4×C47C2×D414yes—
304C22×C4×C47C2412yes—
305C22×C4×C47C2411yescharacteristic
306C22×C4×C47C2411yescharacteristic
307C22×C4×C47C2412yes—
308C22×C4×C47C2411yescharacteristic
309C22×C4×C47C2411yescharacteristic
310C22×C4×C47C2412yes—
311C22×C4×C47C2411yescharacteristic
312C22×C4×C47C2412yes—
313C2×C22⋊D47—22no—
314C2×C22⋊D47—22no—
315C2×C22⋊D47—22no—
316C2×C22⋊D47—22no—
317C2×C22⋊D47—22no—
318C2×C22⋊D47—22no—
319C22×Dic47—22no—
320C22×Dic47—22no—
321C22×Dic47—22no—
322C22×Dic47—24no—
323C22×Dic47—22no—
324C22×Dic47—22no—
325C22×Dic47—22no—
326C22×Dic47C2×D414yes—
327C22×Dic47C2411yescharacteristic
328C22×Dic47C2412yes—
329C22×Dic47C2411yescharacteristic
330C22×Dic47C2412yes—
331C22×Dic47C2411yescharacteristic
332C22×Dic47C2412yes—
333C22×Dic47C2411yescharacteristic
334C22×Dic47C2411yescharacteristic
335C22×Dic47C2412yes—
336D4×D47—416no—
337C2×D188—22no—
338C2×D188—22no—
339C2×D188—22no—
340C2×C4×D47—232no—
341C2×C4×D47—232no—
342C2×C4×D47—22no—
343C2×C4×D47—24no—
344C2×C4×D47—22no—
345C2×C4×D47—24no—
346C2×C4×D47—22no—
347C2×C4×D47—22no—
348C2×C4×D47—24no—
349C2×C4×D47—22no—
350C2×C4×D47—22no—
351C2×C4×D47—22no—
352C2×C4×D47—22no—
353C2×C4×D47—24no—
354C2×C4×D47—24no—
355C2×C4×D47—24no—
356C2×C4×D47—24no—
357C2×C4×D47—24no—
358C2×C4×D47—22no—
359C2×C4×D47—22no—
360C2×C4×D47—24no—
361C2×C4×D47—24no—
362C2×C4×D47—24no—
363C2×C4×D47—22no—
364C2×C4×D47—22no—
365C2×C4×D47—24no—
366C2×C4×D47—24no—
367C2×C4×D47—24no—
368C2×C4×D47—24no—
369C2×C4×D47—24no—
370C2×C4×D47—22no—
371C2×C4×D47—24no—
372C2×C4×D47—24no—
373C2×C4×D47—416no—
374C2×C4×D47C2×D418yes—
375C2×C4×D47C2×D414yes—
376C2×C4×D47C2×D414yes—
377C2×C4×D47C2×D414yes—
378C2×C4×D47C2×D414yes—
379C2×C4×D47#4118yes—
380C4⋊C4×C47—24no—
381C4⋊C4×C47—24no—
382C4⋊C4×C47—24no—
383C4⋊C4×C47—24no—
384C4⋊C4×C47—22no—
385C4⋊C4×C47—22no—
386C4⋊C4×C47—24no—
387C22⋊C4×C47—22no—
388C22⋊C4×C47—22no—
389C22⋊C4×C47—24no—
390C22⋊C4×C47—22no—
391C22⋊C4×C47—22no—
392C22⋊C4×C47—24no—
393C22⋊C4×C47C2×D414yes—
394C42×C47—24no—
395C22⋊Dic47—22no—
396C22⋊Dic47—22no—
397C22⋊Dic47—22no—
398C22⋊Dic47—22no—
399C22⋊Dic47—24no—
400C22⋊Dic47—24no—
401C22⋊Dic47C2×D414yes—
402(C2×D47)⋊C4—24no—
403(C2×D47)⋊C4—22no—
404(C2×D47)⋊C4—22no—
405(C2×D47)⋊C4—22no—
406(C2×D47)⋊C4—22no—
407(C2×D47)⋊C4—24no—
408(C2×D47)⋊C4—24no—
409(C2×D47)⋊C4—24no—
410(C2×D47)⋊C4—22no—
411(C2×D47)⋊C4—22no—
412(C2×D47)⋊C4—24no—
413(C2×D47)⋊C4C2×D418yes—
414C4⋊Dic47—24no—
415C4⋊Dic47—24no—
416C4⋊Dic47—24no—
417C4⋊Dic47—24no—
418C4⋊Dic47—22no—
419C4⋊Dic47—22no—
420C4⋊Dic47—24no—
421Dic47⋊C4—24no—
422Dic47⋊C4—24no—
423Dic47⋊C4—24no—
424Dic47⋊C4—22no—
425Dic47⋊C4—22no—
426Dic47⋊C4—24no—
427Dic47⋊C4—24no—
428Dic47⋊C4—24no—
429Dic47⋊C4—24no—
430Dic47⋊C4—22no—
431Dic47⋊C4—22no—
432Dic47⋊C4—24no—
433Dic47⋊C4—24no—
434Dic47⋊C4—24no—
435C4×Dic47—24no—
436C4×Dic47—24no—
437C4×Dic47—24no—
438C23×C47—22no—
439C23×C47—22no—
440C23×C47—21no—
441C23×C47—21no—
442C23×C47—22no—
443C23×C47—21no—
444C23×C47—22no—
445C23×C47C22×D412yes—
446C23×C47C22×D412yes—
447C23×C47C2×#4112yes—
448C23×C47C2511yescharacteristic
449C22×D47—22no—
450C22×D47—22no—
451C22×D47—28no—
452C22×D47—28no—
453C22×D47—216no—
454C22×D47—216no—
455C22×D47—21no—
456C22×D47—21no—
457C22×D47—22no—
458C22×D47—21no—
459C22×D47—22no—
460C22×D47—44no—
461C22×D47—44no—
462C22×D47—44no—
463C22×D47—48no—
464C22×D47—48no—
465C22×D47#121116yes—
466C22×D47C22×D412yes—
467C22×D47C22×D412yes—
468C22×D47C22×D412yes—
469C22×D47C22×D412yes—
470C22×D47C2×#4112yes—
471C22×D47C2×#4112yes—
472C22×D47C2×#4114yes—
473C22×D472−1+414yes—
474D4×C47—44no—
475C2×C4×C47—28no—
476C2×C4×C47—28no—
477C2×C4×C47—21no—
478C2×C4×C47—21no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—21no—
482C2×C4×C47—21no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—22no—
487C2×C4×C47—21no—
488C2×C4×C47—21no—
489C2×C4×C47—22no—
490C2×C4×C47—21no—
491C2×C4×C47—21no—
492C2×C4×C47—22no—
493C2×C4×C47—22no—
494C2×C4×C47—22no—
495C2×C4×C47—21no—
496C2×C4×C47—22no—
497C2×C4×C47—22no—
498C2×C4×C47—44no—
499C2×C4×C47C22×D414yes—
500C2×C4×C47C22×D412yes—
501C2×C4×C47C22×D412yes—
502C2×C4×C47C2×#4114yes—
503C22⋊D47—44no—
504C22⋊D47—44no—
505C2×Dic47—28no—
506C2×Dic47—28no—
507C2×Dic47—21no—
508C2×Dic47—21no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—21no—
512C2×Dic47—21no—
513C2×Dic47—22no—
514C2×Dic47—22no—
515C2×Dic47—22no—
516C2×Dic47—22no—
517C2×Dic47—21no—
518C2×Dic47—21no—
519C2×Dic47—21no—
520C2×Dic47—21no—
521C2×Dic47—22no—
522C2×Dic47—22no—
523C2×Dic47—22no—
524C2×Dic47—22no—
525C2×Dic47—21no—
526C2×Dic47—22no—
527C2×Dic47—22no—
528C2×Dic47—44no—
529C2×Dic47C22×D414yes—
530C2×Dic47C22×D412yes—
531C2×Dic47C22×D412yes—
532C2×Dic47C2×#4114yes—
533D188—44no—
534C4×D47—216no—
535C4×D47—28no—
536C4×D47—28no—
537C4×D47—28no—
538C4×D47—28no—
539C4×D47—216no—
540C4×D47—216no—
541C4×D47—48no—
542C4×D47—48no—
543C4×D47—44no—
544C4×D47—44no—
545C4×D47—44no—
546C4×D47—48no—
547C2×#2413—471nomaximal, Sylow
548C22×C47—22no—
549C22×C47—22no—
550C22×C47—24no—
551C22×C47—24no—
552C22×C47—41no—
553C22×C47—41no—
554C22×C47—41no—
555C22×C47—42no—
556C22×C47—42no—
557C22×C47C2×#12114yes—
558C22×C47C23×D411yescharacteristic
559C22×C47C23×D411yescharacteristic
560C22×C47C22×#4111yescharacteristic
561C22×C47C22×#4112yes—
562C22×C47C2×2−1+412yes—
563C2×D47—22no—
564C2×D47—22no—
565C2×D47—24no—
566C2×D47—24no—
567C2×D47—232no—
568C2×D47—41no—
569C2×D47—41no—
570C2×D47—41no—
571C2×D47—42no—
572C2×D47—42no—
573C2×D47—88no—
574C2×D47C2×#12114yes—
575C2×D47C2×#12114yes—
576C2×D47#52514yes—
577C2×D47#53614yes—
578C2×D47#54718yes—
579C2×D47#55218yes—
580C4×C47—22no—
581C4×C47—22no—
582C4×C47—24no—
583C4×C47—24no—
584C4×C47—42no—
585C4×C47—41no—
586C4×C47—41no—
587C4×C47—41no—
588C4×C47—42no—
589Dic47—22no—
590Dic47—22no—
591Dic47—24no—
592Dic47—24no—
593Dic47—42no—
594Dic47—41no—
595Dic47—41no—
596Dic47—41no—
597Dic47—42no—
598C22×#123—471no—
599C22×#123—471no—
600C22×#117—471no—
601C23×C4⋊C4—471no—
602#2413—472no—
603#2413—472no—
604#2413—472no—
605#2413—472no—
606#2413—471no—
607#2413—471no—
608#2413—471no—
609#2413—471no—
610#2413—471no—
611#2413—471no—
612#2413—471no—
613#2413D4711yescharacteristic, direct product factor
614C2×#398—472no—
615C2×#396—472no—
616C2×#389—472no—
617C2×#388—472no—
618C2×#386—471no—
619C2×#385—471no—
620C2×#381—471no—
621C2×C47—24no—
622C2×C47—81no—
623C2×C47C22×#12111yescharacteristic
624C2×C47C2×#52511yescharacteristic
625C2×C47C2×#53611yescharacteristic
626C2×C47C2×#54712yes—
627C2×C47C2×#55212yes—
628D47—24no—
629D47—81no—
630D47#241318yesdirect product factor
631C23×D4—471no—
632C24×C4—471no—
633C24×C4—471no—
634C24×C4—471no—
635C2×#123—471no—
636C2×#123—471no—
637C2×#123—471no—
638C2×#123—471no—
639C2×#123—472no—
640C2×#123—471no—
641C2×#123—471no—
642C2×#123—472no—
643C2×#123—471no—
644C2×#123—471no—
645C2×#123—471no—
646C2×#123—471no—
647C2×#123—948no—
648C2×#123—948no—
649C2×#123C2×D4711yescharacteristic
650C2×#123C2×D4711yescharacteristic
651C2×#117—471no—
652C2×#117—472no—
653C2×#117—471no—
654C2×#117—471no—
655C2×#117—472no—
656C2×#117—948no—
657C2×#117C2×D4711yescharacteristic, complemented
658C22×C4⋊C4—471no—
659C22×C4⋊C4—471no—
660C22×C4⋊C4—471no—
661C22×C4⋊C4—472no—
662C22×C4⋊C4—472no—
663C22×C4⋊C4—472no—
664C22×C4⋊C4—471no—
665C22×C4⋊C4—472no—
666C22×C4⋊C4—472no—
667C22×C4⋊C4—472no—
668C22×C4⋊C4—472no—
669C22×C4⋊C4—471no—
670C22×C4⋊C4—948no—
671C22×C4⋊C4C2×D4711yescharacteristic, complemented
672C22×C22⋊C4—471no—
673C22×C22⋊C4—471no—
674C22×C22⋊C4—472no—
675C22×C22⋊C4—472no—
676C22×C22⋊C4—471no—
677C22×C22⋊C4—471no—
678C22×C22⋊C4—471no—
679C22×C42—472no—
680#398—472no—
681#398—472no—
682#398—472no—
683#398—472no—
684#398—472no—
685#398—472no—
686#398—472no—
687#398C2×D4712yescomplemented
688#396—472no—
689#396—472no—
690#396—472no—
691#396—472no—
692#396—472no—
693#396—472no—
694#396—472no—
695#396C2×D4712yescomplemented
696#389—472no—
697#389—472no—
698#389—472no—
699#389—472no—
700#389—472no—
701#389—472no—
702#389—472no—
703#389C2×D4712yescomplemented
704#388—472no—
705#388—472no—
706#388—472no—
707#388—472no—
708#388—472no—
709#388—472no—
710#388—472no—
711#388C2×D4712yescomplemented
712#386—471no—
713#386—471no—
714#386—472no—
715#386—471no—
716#386—472no—
717#386C2×D4711yescharacteristic
718#385—471no—
719#385—472no—
720#385—471no—
721#385—471no—
722#385—472no—
723#385C2×D4711yescharacteristic, complemented
724#381—471no—
725#381—471no—
726#381—471no—
727#381—472no—
728#381—472no—
729#381C2×D4711yescharacteristic, complemented
730C2×#95—472no—
731C2×#95—472no—
732C2×#95—472no—
733C2×#95—472no—
734C47C2×#241311yescharacteristic, complemented, Sylow
735C25—471no—
736C25—471no—
737C22×D4—471no—
738C22×D4—471no—
739C22×D4—471no—
740C22×D4—944no—
741C22×D4—944no—
742C22×D4—944no—
743C22×D4C22×D4711yescharacteristic
744C23×C4—471no—
745C23×C4—478no—
746C23×C4—472no—
747C23×C4—471no—
748C23×C4—472no—
749C23×C4—471no—
750C23×C4—471no—
751C23×C4—471no—
752C23×C4—471no—
753C23×C4—471no—
754C23×C4—471no—
755C23×C4—471no—
756C23×C4—472no—
757C23×C4—472no—
758C23×C4—471no—
759C23×C4—472no—
760C23×C4—472no—
761C23×C4—948no—
762C23×C4—944no—
763C23×C4—944no—
764C23×C4—944no—
765C23×C4—944no—
766C23×C4—944no—
767C23×C4—944no—
768C23×C4C22×D4711yescharacteristic
769C23×C4C22×D4711yescharacteristic
770C23×C4C22×D4711yescharacteristic
771#123—24no—
772#123—24no—
773#123—948no—
774#123—944no—
775#123—944no—
776#123—944no—
777#123—948no—
778#123—944no—
779#123—944no—
780#123—944no—
781#123—944no—
782#123—944no—
783#123—944no—
784#123—944no—
785#117—24no—
786#117—948no—
787#117—944no—
788#117—948no—
789#117—944no—
790#117—944no—
791C2×C4⋊C4—24no—
792C2×C4⋊C4—472no—
793C2×C4⋊C4—472no—
794C2×C4⋊C4—472no—
795C2×C4⋊C4—472no—
796C2×C4⋊C4—472no—
797C2×C4⋊C4—472no—
798C2×C4⋊C4—472no—
799C2×C4⋊C4—472no—
800C2×C4⋊C4—472no—
801C2×C4⋊C4—471no—
802C2×C4⋊C4—471no—
803C2×C4⋊C4—472no—
804C2×C4⋊C4—472no—
805C2×C4⋊C4—471no—
806C2×C4⋊C4—471no—
807C2×C4⋊C4—471no—
808C2×C4⋊C4—472no—
809C2×C4⋊C4—471no—
810C2×C4⋊C4—472no—
811C2×C4⋊C4—472no—
812C2×C4⋊C4—472no—
813C2×C4⋊C4—948no—
814C2×C4⋊C4—948no—
815C2×C4⋊C4—948no—
816C2×C4⋊C4—948no—
817C2×C4⋊C4—948no—
818C2×C4⋊C4—948no—
819C2×C4⋊C4—944no—
820C2×C4⋊C4—944no—
821C2×C4⋊C4—948no—
822C2×C4⋊C4—944no—
823C2×C4⋊C4—944no—
824C2×C4⋊C4—944no—
825C2×C4⋊C4C22×D4712yes—
826C2×C4⋊C4C22×D4712yes—
827C2×C4⋊C4C22×D4712yes—
828C2×C4⋊C4C22×D4711yescharacteristic
829C2×C4⋊C4C22×D4712yes—
830C2×C4⋊C4C22×D4711yescharacteristic
831C2×C4⋊C4C22×D4712yes—
832C2×C22⋊C4—471no—
833C2×C22⋊C4—472no—
834C2×C22⋊C4—478no—
835C2×C22⋊C4—471no—
836C2×C22⋊C4—471no—
837C2×C22⋊C4—471no—
838C2×C22⋊C4—472no—
839C2×C22⋊C4—471no—
840C2×C22⋊C4—472no—
841C2×C22⋊C4—472no—
842C2×C22⋊C4—471no—
843C2×C22⋊C4—471no—
844C2×C22⋊C4—471no—
845C2×C22⋊C4—471no—
846C2×C22⋊C4—472no—
847C2×C22⋊C4—472no—
848C2×C22⋊C4—471no—
849C2×C22⋊C4—471no—
850C2×C22⋊C4—472no—
851C2×C22⋊C4—472no—
852C2×C22⋊C4—948no—
853C2×C22⋊C4—944no—
854C2×C22⋊C4—944no—
855C2×C22⋊C4—948no—
856C2×C22⋊C4—944no—
857C2×C22⋊C4—944no—
858C2×C22⋊C4C22×D4711yescharacteristic
859C2×C22⋊C4C22×D4711yescharacteristic
860C2×C22⋊C4C22×D4711yescharacteristic
861C2×C22⋊C4C22×D4712yes—
862C2×C22⋊C4C22×D4711yescharacteristic
863C2×C22⋊C4C22×D4712yes—
864C2×C22⋊C4C22×D4711yescharacteristic
865C2×C42—472no—
866C2×C42—472no—
867C2×C42—472no—
868C2×C42—948no—
869C2×C42C22×D4712yes—
870#95—472no—
871#95—472no—
872#95—472no—
873#95—472no—
874#95—472no—
875#95—472no—
876#95—472no—
877#95—472no—
878#95—472no—
879#95—472no—
880#95—472no—
881#95—472no—
882#95C22×D4712yes—
883#95C22×D4712yes—
884#95C22×D4712yes—
885#95C22×D4712yes—
886C24—471no—
887C24—474no—
888C24—474no—
889C24—474no—
890C24—471no—
891C24—471no—
892C24—944no—
893C24—944no—
894C24—942no—
895C24—942no—
896C24—944no—
897C24—942no—
898C24—944no—
899C24C23×D4711yescharacteristic
900C24C23×D4711yescharacteristic
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—942no—
905C2×D4—942no—
906C2×D4—942no—
907C2×D4—942no—
908C2×D4—942no—
909C2×D4—942no—
910C2×D4—942no—
911C2×D4—942no—
912C2×D4—942no—
913C2×D4—18816no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—474no—
922C22×C4—472no—
923C22×C4—472no—
924C22×C4—471no—
925C22×C4—471no—
926C22×C4—478no—
927C22×C4—474no—
928C22×C4—474no—
929C22×C4—474no—
930C22×C4—474no—
931C22×C4—478no—
932C22×C4—471no—
933C22×C4—472no—
934C22×C4—471no—
935C22×C4—472no—
936C22×C4—471no—
937C22×C4—944no—
938C22×C4—942no—
939C22×C4—944no—
940C22×C4—942no—
941C22×C4—944no—
942C22×C4—944no—
943C22×C4—942no—
944C22×C4—942no—
945C22×C4—944no—
946C22×C4—9432no—
947C22×C4—944no—
948C22×C4—942no—
949C22×C4—942no—
950C22×C4—942no—
951C22×C4—942no—
952C22×C4—9432no—
953C22×C4—944no—
954C22×C4—942no—
955C22×C4—942no—
956C22×C4—944no—
957C22×C4—944no—
958C22×C4—944no—
959C22×C4—944no—
960C22×C4—942no—
961C22×C4—942no—
962C22×C4—944no—
963C22×C4—944no—
964C22×C4—944no—
965C22×C4—944no—
966C22×C4—944no—
967C22×C4—944no—
968C22×C4—942no—
969C22×C4—944no—
970C22×C4—942no—
971C22×C4—942no—
972C22×C4—942no—
973C22×C4—944no—
974C22×C4—942no—
975C22×C4—942no—
976C22×C4—942no—
977C22×C4—18816no—
978C22×C4D4×D4714yes—
979C22×C4C23×D4711yescharacteristic
980C22×C4C23×D4712yes—
981C22×C4C23×D4711yescharacteristic
982C22×C4C23×D4712yes—
983C22×C4C23×D4711yescharacteristic
984C22×C4C23×D4712yes—
985C22×C4C23×D4711yescharacteristic
986C22×C4C23×D4711yescharacteristic
987C22×C4C23×D4712yes—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—944no—
996C4⋊C4—944no—
997C4⋊C4—944no—
998C4⋊C4—944no—
999C4⋊C4—944no—
1000C4⋊C4—944no—
1001C4⋊C4—942no—
1002C4⋊C4—942no—
1003C4⋊C4—944no—
1004C4⋊C4—944no—
1005C4⋊C4—944no—
1006C4⋊C4—944no—
1007C4⋊C4—942no—
1008C4⋊C4—942no—
1009C4⋊C4—944no—
1010C4⋊C4—944no—
1011C4⋊C4—944no—
1012C4⋊C4—942no—
1013C4⋊C4—942no—
1014C4⋊C4—944no—
1015C4⋊C4—944no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—474no—
1023C22⋊C4—478no—
1024C22⋊C4—944no—
1025C22⋊C4—942no—
1026C22⋊C4—942no—
1027C22⋊C4—944no—
1028C22⋊C4—944no—
1029C22⋊C4—942no—
1030C22⋊C4—942no—
1031C22⋊C4—944no—
1032C22⋊C4—944no—
1033C22⋊C4—942no—
1034C22⋊C4—942no—
1035C22⋊C4—942no—
1036C22⋊C4—942no—
1037C22⋊C4—942no—
1038C22⋊C4—942no—
1039C22⋊C4—944no—
1040C22⋊C4—944no—
1041C22⋊C4D4×D4714yes—
1042C42—24no—
1043C42—944no—
1044C42—944no—
1045C42—944no—
1046C23—22no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—21no—
1052C23—22no—
1053C23—472no—
1054C23—472no—
1055C23—474no—
1056C23—472no—
1057C23—474no—
1058C23—4716no—
1059C23—472no—
1060C23—472no—
1061C23—472no—
1062C23—948no—
1063C23—9416no—
1064C23—9416no—
1065C23—948no—
1066C23—942no—
1067C23—942no—
1068C23—941no—
1069C23—941no—
1070C23—942no—
1071C23—941no—
1072C23—942no—
1073C23—1884no—
1074C23—1888no—
1075C23—1884no—
1076C23—1888no—
1077C23—1884no—
1078C23C2×D4×D4712yes—
1079C23C2×D4×D4712yes—
1080C23#41×D4712yes—
1081C23C24×D4711yescharacteristic
1082D4—44no—
1083D4—1884no—
1084D4—1884no—
1085D4—1884no—
1086C2×C4—28no—
1087C2×C4—28no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—44no—
1110C2×C4—474no—
1111C2×C4—472no—
1112C2×C4—472no—
1113C2×C4—474no—
1114C2×C4—9416no—
1115C2×C4—948no—
1116C2×C4—948no—
1117C2×C4—948no—
1118C2×C4—948no—
1119C2×C4—9416no—
1120C2×C4—9416no—
1121C2×C4—948no—
1122C2×C4—948no—
1123C2×C4—941no—
1124C2×C4—941no—
1125C2×C4—942no—
1126C2×C4—942no—
1127C2×C4—941no—
1128C2×C4—941no—
1129C2×C4—942no—
1130C2×C4—942no—
1131C2×C4—942no—
1132C2×C4—941no—
1133C2×C4—941no—
1134C2×C4—942no—
1135C2×C4—942no—
1136C2×C4—941no—
1137C2×C4—941no—
1138C2×C4—942no—
1139C2×C4—942no—
1140C2×C4—942no—
1141C2×C4—941no—
1142C2×C4—942no—
1143C2×C4—942no—
1144C2×C4—1888no—
1145C2×C4—1884no—
1146C2×C4—1884no—
1147C2×C4—1888no—
1148C2×C4—1888no—
1149C2×C4—1884no—
1150C2×C4—1884no—
1151C2×C4C2×D4×D4714yes—
1152C2×C4C2×D4×D4712yes—
1153C2×C4C2×D4×D4712yes—
1154C2×C4#41×D4714yes—
1155C22—24no—
1156C22—22no—
1157C22—24no—
1158C22—22no—
1159C22—42no—
1160C22—41no—
1161C22—41no—
1162C22—42no—
1163C22—41no—
1164C22—478no—
1165C22—474no—
1166C22—474no—
1167C22—478no—
1168C22—474no—
1169C22—474no—
1170C22—9432no—
1171C22—944no—
1172C22—942no—
1173C22—944no—
1174C22—942no—
1175C22—3768no—
1176C22—1882no—
1177C22—1881no—
1178C22—1881no—
1179C22—1882no—
1180C22—1881no—
1181C22#121×D4714yes—
1182C22C22×D4×D4711yescharacteristic
1183C22C22×D4×D4711yescharacteristic
1184C22C2×#41×D4712yes—
1185C22C2×#41×D4711yescharacteristic
1186C222−1+4×D4712yes—
1187C4—24no—
1188C4—22no—
1189C4—22no—
1190C4—24no—
1191C4—42no—
1192C4—42no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—944no—
1197C4—942no—
1198C4—942no—
1199C4—944no—
1200C4—1882no—
1201C4—1882no—
1202C4—1881no—
1203C4—1881no—
1204C4—1881no—
1205C2—24no—
1206C2—81no—
1207C2—478no—
1208C2—944no—
1209C2—3761no—
1210C2C2×#121×D4711yescharacteristic
1211C2#525×D4711yescharacteristic
1212C2#536×D4711yescharacteristic
1213C2#547×D4712yes—
1214C2#552×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2413C2
prime radicalC22×D4×D47C22
hypercenter#2413D47
hypocenterC47C2×#2413
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2413

Complements

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

NH ≅ G/Ntype
3. C2×#117×D47C2semidirect
4. C22×C4⋊C4×D47C2semidirect
5. #20246798C2semidirect
6. #20246797C2semidirect
7. #20246796C2semidirect
8. #20246795C2semidirect
9. #20246794C2semidirect
10. #20246793C2semidirect
11. #20246792C2semidirect
12. #20246791C2semidirect
13. #20246790C2semidirect
14. #20246789C2semidirect
15. #20246788C2semidirect
16. #398×D47C2semidirect
17. #396×D47C2semidirect
18. #389×D47C2semidirect
19. #388×D47C2semidirect
21. #385×D47C2semidirect
22. #381×D47C2semidirect
23. C47×#2413C2semidirect
42. C2×#13093983C22semidirect
43. C2×#13093982C22semidirect
44. C2×#13093981C22semidirect
45. C2×#13093980C22semidirect
46. C2×#13093980C22semidirect
48. C22×C4⋊Dic47C22semidirect
49. C22×Dic47⋊C4C22semidirect
50. C22×Dic47⋊C4C22semidirect
59. C2×C4⋊C4×D47C22semidirect
60. C2×C4⋊C4×D47C22semidirect
69. #15689057C22semidirect
70. #15689057C22semidirect
71. #15689056C22semidirect
72. #15689056C22semidirect
73. #15689055C22semidirect
74. #15689054C22semidirect
75. #15689053C22semidirect
76. #15689047C22semidirect
77. #15689046C22semidirect
78. #15689046C22semidirect
79. #15689046C22semidirect
80. #15689045C22semidirect
81. #15689045C22semidirect
82. #15689045C22semidirect
83. #15689022C22semidirect
84. #15689021C22semidirect
85. #15689020C22semidirect
86. #15689020C22semidirect
87. #15689019C22semidirect
88. #15689018C22semidirect
89. #15689018C22semidirect
90. #15689017C22semidirect
91. #15689016C22semidirect
92. #15689015C22semidirect
93. #15689014C22semidirect
94. #15689013C22semidirect
95. #15689012C22semidirect
96. #15689011C22semidirect
102. #15688998C22semidirect
103. #15688997C22semidirect
104. #15688996C22semidirect
105. #15688995C22semidirect
106. #15688994C22semidirect
107. #15688986C22semidirect
108. #15688985C22semidirect
109. #15688985C22semidirect
110. #15688984C22semidirect
111. #15688984C22semidirect
118. C2×#117×C47C22semidirect
119. C22×C4⋊C4×C47C22semidirect
120. C47×#398C22semidirect
121. C47×#396C22semidirect
122. C47×#389C22semidirect
123. C47×#388C22semidirect
125. C47×#385C22semidirect
126. C47×#381C22semidirect
613. #2413D47direct (N × H)
630. D47#2413direct (N × H)
657. C2×#117C2×D47semidirect
671. C22×C4⋊C4C2×D47semidirect
687. #398C2×D47semidirect
695. #396C2×D47semidirect
703. #389C2×D47semidirect
711. #388C2×D47semidirect
723. #385C2×D47semidirect
729. #381C2×D47semidirect
734. C47C2×#2413semidirect

Maximal subgroups

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

subgroupindex
C2×#123×D472
C2×#117×D472
C22×C4⋊C4×D472
#202467982
#202467972
#202467962
#202467952
#202467942
#202467932
#202467922
#202467912
#202467902
#202467892
#202467882
#398×D472
#396×D472
#389×D472
#388×D472
#386×D472
#385×D472
#381×D472
C47×#24132
C2×#241347