Finite Group Databasebeta

← D47×#2431 #26384607

Subgroups — D47×#2431 #26384607

Order 12032.

6278 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D47C211yesmaximal, characteristic, complemented
2C2×#127×D47C211yesmaximal, characteristic, complemented
3C2×#124×D47C211yesmaximal, characteristic, complemented
4C2×#121×D47C211yesmaximal, characteristic, complemented
5#20247010C211yesmaximal, characteristic, complemented
6#20247009C211yesmaximal, characteristic, complemented
7#20247008C211yesmaximal, characteristic, complemented
8#20247007C211yesmaximal, characteristic, complemented
9#20247006C211yesmaximal, characteristic, complemented
10#20247005C214yesmaximal, complemented
11#20247004C211yesmaximal, characteristic, complemented
12#20247003C211yesmaximal, characteristic, complemented
13#20247002C214yesmaximal, complemented
14#392×D47C214yesmaximal, complemented
15#391×D47C211yesmaximal, characteristic, complemented
16#390×D47C211yesmaximal, characteristic, complemented
17#386×D47C214yesmaximal, complemented
18C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
19C47×#2431C211yesmaximal, characteristic, complemented
20C22×#10625354C2211yescharacteristic, complemented
21C22×#10625350C2212yescomplemented
22C22×#10625350C2211yescharacteristic, complemented
23C22×#10625352C2212yescomplemented
24C22×#10625352C2211yescharacteristic, complemented
25C2×#41×D47—28no—
26C2×#41×D47—28no—
27C2×#41×D47—28no—
28C22×Q8×D47C2211yescharacteristic
29C22×D4×D47C2212yes—
30C22×D4×D47C2211yescharacteristic
31C22×D4×D47C2214yes—
32C22×D4×D47C2211yescharacteristic
33C22×D4×D47C2212yes—
34C23×C4×D47C2212yes—
35C23×C4×D47C2211yescharacteristic
36C2×#13094021C2211yescharacteristic, complemented
37C2×#13094020C2214yescomplemented
38C2×#13094020C2211yescharacteristic, complemented
39C2×#13094020C2211yescharacteristic, complemented
40#127×D47—28no—
41C2×#13094013C2211yescharacteristic, complemented
42C2×#13094012C2211yescharacteristic, complemented
43C2×#13094011C2211yescharacteristic, complemented
44C2×#13094010C2214yescomplemented
45#124×D47—28no—
46C2×#13093999C2211yescharacteristic, complemented
47C2×#13093998C2211yescharacteristic, complemented
48C2×#13093997C2212yescomplemented
49C2×#13093996C2212yescomplemented
50C2×#13093995C2211yescharacteristic, complemented
51#121×D47—28no—
52C2×C4⋊C4×D47C2211yescharacteristic
53C2×C22⋊C4×D47C2212yes—
54C2×C22⋊C4×D47C2214yes—
55C2×C22⋊C4×D47C2212yes—
56C2×C22⋊C4×D47C2214yes—
57C2×C42×D47C2211yescharacteristic
58C2×C42×D47C2211yescharacteristic
59#15689033C2214yescomplemented
60#15689032C2214yescomplemented
61#15689032C2214yescomplemented
62#15689032C2214yescomplemented
63#15689031C2214yescomplemented
64#15689031C2214yescomplemented
65#15689031C2214yescomplemented
66#15689030C2211yescharacteristic, complemented
67#15689029C2211yescharacteristic, complemented
68#15689028C2211yescharacteristic, complemented
69#15689027C2214yescomplemented
70#15689026C2211yescharacteristic, complemented
71#15689025C2211yescharacteristic, complemented
72#15689024C2211yescharacteristic, complemented
73#15689023C2214yescomplemented
74#15689003C2214yescomplemented
75#15689002C2214yescomplemented
76#15689001C2214yescomplemented
77#15689001C2214yescomplemented
78#15689000C2214yescomplemented
79#15688999C2214yescomplemented
80#15688999C2214yescomplemented
81C22⋊C4×Dic47C2212yescomplemented
82C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
83C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
84C4×C22⋊Dic47C2211yescharacteristic, complemented
85#15688970C2212yescomplemented
86#95×D47C2212yes—
87#95×D47C2214yes—
88C22×#41×C47C2211yescharacteristic, complemented
89C2×#127×C47C2211yescharacteristic, complemented
90C2×#124×C47C2211yescharacteristic, complemented
91C2×#121×C47C2211yescharacteristic, complemented
92C47×#392C2214yescomplemented
93C47×#391C2211yescharacteristic, complemented
94C47×#390C2211yescharacteristic, complemented
95C47×#386C2214yescomplemented
96C4×C22⋊C4×C47C2211yescharacteristic, complemented
97C24×D47C2312yes—
98C24×D47C2311yescharacteristic
99C24×D47C2312yes—
100C2×#10625354—24no—
101C2×#10625354—24no—
102C2×#10625354—24no—
103C2×#10625350—24no—
104C2×#10625350—28no—
105C2×#10625350—24no—
106C2×#10625350—28no—
107C2×#10625350—28no—
108C2×#10625350—24no—
109C2×#10625352—24no—
110C2×#10625352—28no—
111C2×#10625352—28no—
112C2×#10625352—24no—
113C2×#10625352—28no—
114C2×#10625352—24no—
115#41×D47—2128no—
116C22×Dic94C2312yes—
117C22×Dic94C2311yescharacteristic
118C2×Q8×D47—24no—
119C2×Q8×D47—24no—
120C2×Q8×D47D418yescomplemented
121C22×D188C2312yes—
122C22×D188C2311yescharacteristic
123C22×D188C2314yes—
124C22×D188C2311yescharacteristic
125C22×D188C2312yes—
126C22×C22⋊D47C2312yes—
127C22×C22⋊D47C2312yes—
128C22×C22⋊D47C2312yes—
129C22×C22⋊D47C2314yes—
130C22×C22⋊D47C2314yes—
131C22×C22⋊D47C2312yes—
132C22×C22⋊D47C2312yes—
133C22×C22⋊D47C2312yes—
134C2×D4×D47—28no—
135C2×D4×D47—28no—
136C2×D4×D47—28no—
137C2×D4×D47—216no—
138C2×D4×D47—28no—
139C2×D4×D47—24no—
140C2×D4×D47—24no—
141C2×D4×D47—24no—
142C2×D4×D47—24no—
143C2×D4×D47—24no—
144C2×D4×D47—216no—
145C2×D4×D47—48no—
146C2×D4×D47—48no—
147C2×D4×D47D418yescomplemented
148C23×Dic47C2312yes—
149C23×Dic47C2311yescharacteristic
150C22×C4×D47—28no—
151C22×C4×D47—28no—
152C22×C4×D47—28no—
153C22×C4×D47—24no—
154C22×C4×D47—24no—
155C22×C4×D47D418yescomplemented
156C22×C4×D47C2312yes—
157C22×C4×D47C2312yes—
158C22×C4×D47C2312yes—
159C22×C4×D47C2312yes—
160C22×C4×D47C2311yescharacteristic
161C22×C4×D47C2312yes—
162C22×C4×D47C2311yescharacteristic
163C22×C4×D47C2311yescharacteristic
164C22×C4×D47C2312yes—
165C22×C4×D47C2311yescharacteristic
166#13094021—24no—
167#13094020—24no—
168#13094020—216no—
169#13094020—24no—
170#13094013—24no—
171#13094012—24no—
172#13094011—24no—
173#13094010—216no—
174#13093999—24no—
175#13093998—24no—
176#13093997—28no—
177#13093996—28no—
178#13093995—24no—
179C2×C4⋊Dic47C2311yescharacteristic
180C2×Dic47⋊C4C2312yes—
181C4⋊C4×D47—24no—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2314yes—
185C2×C22⋊Dic47C2314yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2312yes—
189C2×(C2×D47)⋊C4C2314yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2314yes—
192C2×(C2×D47)⋊C4C2314yes—
193C2×(C2×D47)⋊C4C2314yes—
194C22⋊C4×D47—28no—
195C22⋊C4×D47—216no—
196C22⋊C4×D47—28no—
197C22⋊C4×D47—48no—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2311yescharacteristic
202C42×D47—24no—
203C42×D47—24no—
204C47⋊#95C2312yes—
205C47⋊#95C2312yes—
206C47⋊#95C2312yes—
207C47⋊#95C2314yes—
208C47⋊#95C2314yes—
209C47⋊#95C2314yes—
210C2×#41×C47—24no—
211C2×#41×C47—24no—
212C2×#41×C47—24no—
213C22×Q8×C47C2311yescharacteristic
214C22×D4×C47C2312yes—
215C22×D4×C47C2311yescharacteristic
216C22×D4×C47C2314yes—
217C22×D4×C47C2311yescharacteristic
218C22×D4×C47C2312yes—
219C23×C4×C47C2312yes—
220C23×C4×C47C2311yescharacteristic
221#127×C47—24no—
222#124×C47—24no—
223#121×C47—24no—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C22⋊C4×C47C2312yes—
226C2×C22⋊C4×C47C2312yes—
227C2×C22⋊C4×C47C2314yes—
228C2×C22⋊C4×C47C2314yes—
229C2×C42×C47C2311yescharacteristic
230C2×C42×C47C2311yescharacteristic
231#95×C47C2312yes—
232#95×C47C2314yes—
233C24×C47C2412yes—
234C24×C47C2411yescharacteristic
235C24×C47C2412yes—
236C23×D47—24no—
237C23×D47—22no—
238C23×D47—24no—
239C23×D47—22no—
240C23×D47—24no—
241C23×D47—28no—
242C23×D47—28no—
243C23×D47—24no—
244C23×D47—24no—
245C23×D47—24no—
246C23×D47—24no—
247C23×D47—28no—
248C23×D47—28no—
249C23×D47C2×D418yes—
250C23×D47C2×D414yes—
251C23×D47C2412yes—
252C23×D47C2411yescharacteristic
253C23×D47C2412yes—
254C23×D47C2411yescharacteristic
255#41×C47—232no—
256C2×Q8×C47—22no—
257C2×Q8×C47—22no—
258C2×Q8×C47C2×D414yescomplemented
259C2×D4×C47—24no—
260C2×D4×C47—24no—
261C2×D4×C47—24no—
262C2×D4×C47—28no—
263C2×D4×C47—24no—
264C2×D4×C47—22no—
265C2×D4×C47—22no—
266C2×D4×C47—22no—
267C2×D4×C47—22no—
268C2×D4×C47—22no—
269C2×D4×C47—28no—
270C2×D4×C47—44no—
271C2×D4×C47—44no—
272C2×D4×C47C2×D414yescomplemented
273C22×C4×C47—24no—
274C22×C4×C47—24no—
275C22×C4×C47—24no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47C2×D414yescomplemented
279C22×C4×C47C2412yes—
280C22×C4×C47C2412yes—
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2412yes—
283C22×C4×C47C2412yes—
284C22×C4×C47C2411yescharacteristic
285C2×C22⋊D47—24no—
286C2×C22⋊D47—24no—
287C2×C22⋊D47—24no—
288C2×C22⋊D47—24no—
289C2×C22⋊D47—24no—
290C2×C22⋊D47—28no—
291C2×C22⋊D47—24no—
292C2×C22⋊D47—28no—
293C2×C22⋊D47—24no—
294C2×C22⋊D47—24no—
295C2×C22⋊D47—24no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—24no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—28no—
301C2×C22⋊D47—28no—
302C2×C22⋊D47—44no—
303C2×C22⋊D47—44no—
304C2×C22⋊D47—44no—
305C2×C22⋊D47—44no—
306C2×C22⋊D47C2×D418yescomplemented
307C22×Dic47—24no—
308C22×Dic47—24no—
309C22×Dic47—24no—
310C22×Dic47—22no—
311C22×Dic47—22no—
312C22×Dic47C2×D414yescomplemented
313C22×Dic47C2412yes—
314C22×Dic47C2412yes—
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2411yescharacteristic
319#10625354—232no—
320Q8×D47—232no—
321#10625352—232no—
322#10625352—264no—
323D4×D47—264no—
324D4×D47—232no—
325D4×D47—464no—
326D4×D47—432no—
327D4×D47—416no—
328#10625350—232no—
329#10625350—264no—
330C2×D188—24no—
331C2×D188—24no—
332C2×D188—24no—
333C2×D188—22no—
334C2×D188—22no—
335C2×D188—24no—
336C2×D188—28no—
337C2×D188—22no—
338C2×D188—22no—
339C2×D188—22no—
340C2×D188—28no—
341C2×D188—44no—
342C2×D188—44no—
343C2×D188C2×D414yescomplemented
344C2×C4×D47—264no—
345C2×C4×D47—24no—
346C2×C4×D47—22no—
347C2×C4×D47—22no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—24no—
351C2×C4×D47—24no—
352C2×C4×D47—24no—
353C2×C4×D47—24no—
354C2×C4×D47—22no—
355C2×C4×D47—22no—
356C2×C4×D47—24no—
357C2×C4×D47—24no—
358C2×C4×D47—24no—
359C2×C4×D47—22no—
360C2×C4×D47—22no—
361C2×C4×D47—232no—
362C2×C4×D47—24no—
363C2×C4×D47—24no—
364C2×C4×D47—24no—
365C2×C4×D47—24no—
366C2×C4×D47—28no—
367C2×C4×D47C2×D414yes—
368C2×C4×D47C2×D418yes—
369C2×C4×D47C2×D414yes—
370C2×C4×D47C2×D414yes—
371C2×C4×D47C2×D414yes—
372C2×C4×D47C2×D414yescomplemented
373C2×C4×D47C2×D414yescomplemented
374C2×C4×D47#4118yescomplemented
375C2×Dic94—22no—
376C2×Dic94—22no—
377C2×Dic94—24no—
378C2×Dic94—24no—
379C2×Dic94C2×D418yescomplemented
380C2×Dic94C2×D414yescomplemented
381C4⋊C4×C47—22no—
382C22⋊C4×C47—24no—
383C22⋊C4×C47—28no—
384C22⋊C4×C47—24no—
385C22⋊C4×C47—44no—
386C42×C47—22no—
387C42×C47—22no—
388C22⋊Dic47—24no—
389C22⋊Dic47—28no—
390C22⋊Dic47—24no—
391C22⋊Dic47—44no—
392(C2×D47)⋊C4—24no—
393(C2×D47)⋊C4—28no—
394(C2×D47)⋊C4—24no—
395(C2×D47)⋊C4—24no—
396(C2×D47)⋊C4—28no—
397(C2×D47)⋊C4—24no—
398(C2×D47)⋊C4—44no—
399(C2×D47)⋊C4—44no—
400C4⋊Dic47—22no—
401Dic47⋊C4—24no—
402C4×Dic47—22no—
403C4×Dic47—22no—
404C4×Dic47—24no—
405C4×Dic47—24no—
406C23×C47—22no—
407C23×C47—21no—
408C23×C47—22no—
409C23×C47—21no—
410C23×C47—22no—
411C23×C47—24no—
412C23×C47—24no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—24no—
418C23×C47—24no—
419C23×C47C22×D414yes—
420C23×C47C22×D412yes—
421C23×C47C2511yescharacteristic
422C22×D47—22no—
423C22×D47—21no—
424C22×D47—22no—
425C22×D47—21no—
426C22×D47—22no—
427C22×D47—24no—
428C22×D47—24no—
429C22×D47—22no—
430C22×D47—216no—
431C22×D47—28no—
432C22×D47—28no—
433C22×D47—28no—
434C22×D47—232no—
435C22×D47—22no—
436C22×D47—22no—
437C22×D47—22no—
438C22×D47—24no—
439C22×D47—24no—
440C22×D47—48no—
441C22×D47—48no—
442C22×D47—48no—
443C22×D47—48no—
444C22×D47—416no—
445C22×D47—48no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47—416no—
449C22×D47—416no—
450C22×D47C22×D414yes—
451C22×D47C22×D412yes—
452C22×D47C22×D412yes—
453C22×D47C22×D412yes—
454C22×D47C22×D412yes—
455C22×D47C2×#4114yes—
456C22×D47H(5,𝔽2)14yes—
457Q8×C47—28no—
458D4×C47—216no—
459D4×C47—28no—
460D4×C47—416no—
461D4×C47—48no—
462D4×C47—44no—
463C2×C4×C47—216no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—22no—
470C2×C4×C47—28no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—24no—
476C2×C4×C47C22×D414yes—
477C2×C4×C47C22×D412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C22×D412yes—
480C2×C4×C47C22×D412yes—
481C2×C4×C47C2×#4114yescomplemented
482C22⋊D47—216no—
483C22⋊D47—216no—
484C22⋊D47—216no—
485C22⋊D47—416no—
486C22⋊D47—416no—
487C22⋊D47—48no—
488C22⋊D47—48no—
489C22⋊D47—48no—
490C2×Dic47—216no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—21no—
495C2×Dic47—21no—
496C2×Dic47—22no—
497C2×Dic47—28no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—24no—
503C2×Dic47C22×D414yes—
504C2×Dic47C22×D412yes—
505C2×Dic47C22×D412yes—
506C2×Dic47C22×D412yes—
507C2×Dic47C22×D412yes—
508C2×Dic47C2×#4114yescomplemented
509D188—216no—
510D188—28no—
511D188—416no—
512D188—48no—
513D188—44no—
514C4×D47—216no—
515C4×D47—216no—
516C4×D47—28no—
517C4×D47—216no—
518C4×D47—216no—
519C4×D47—28no—
520C4×D47—28no—
521C4×D47—48no—
522C4×D47—48no—
523C4×D47#120116yes—
524Dic94—28no—
525Dic94—216no—
526C2×#2431—471nomaximal, Sylow
527C22×C47—24no—
528C22×C47—22no—
529C22×C47—22no—
530C22×C47—22no—
531C22×C47—28no—
532C22×C47—42no—
533C22×C47—42no—
534C22×C47—42no—
535C22×C47—42no—
536C22×C47—44no—
537C22×C47—42no—
538C22×C47—42no—
539C22×C47—42no—
540C22×C47—44no—
541C22×C47—44no—
542C22×C47C23×D411yescharacteristic
543C22×C47C23×D411yescharacteristic
544C22×C47C23×D411yescharacteristic
545C22×C47C22×#4112yes—
546C22×C47C2×H(5,𝔽2)12yes—
547C2×D47—24no—
548C2×D47—22no—
549C2×D47—22no—
550C2×D47—22no—
551C2×D47—28no—
552C2×D47—42no—
553C2×D47—42no—
554C2×D47—42no—
555C2×D47—42no—
556C2×D47—44no—
557C2×D47—416no—
558C2×D47—432no—
559C2×D47—42no—
560C2×D47—42no—
561C2×D47—42no—
562C2×D47—44no—
563C2×D47—44no—
564C2×D47—816no—
565C2×D47C2×#12014yes—
566C2×D47#53214yes—
567C2×D47#53514yes—
568C2×D47#54618yes—
569C2×D47#55018yes—
570C4×C47—24no—
571C4×C47—22no—
572C4×C47—24no—
573C4×C47—42no—
574C4×C47—42no—
575C4×C47C2×#12014yes—
576Dic47—24no—
577Dic47—22no—
578Dic47—24no—
579Dic47—42no—
580Dic47—42no—
581Dic47C2×#12014yes—
582C23×#41—471no—
583C22×#127—471no—
584C22×#124—471no—
585C22×#121—471no—
586#2431—474no—
587#2431—471no—
588#2431—471no—
589#2431—474no—
590#2431—471no—
591#2431—471no—
592#2431—471no—
593#2431—471no—
594#2431—471no—
595#2431D4711yescharacteristic, direct product factor
596C2×#392—474no—
597C2×#391—471no—
598C2×#390—471no—
599C2×#386—474no—
600C2×C4×C22⋊C4—471no—
601C2×C47—42no—
602C2×C47—44no—
603C2×C47—82no—
604C2×C47C22×#12011yescharacteristic
605C2×C47C2×#53211yescharacteristic
606C2×C47C2×#53511yescharacteristic
607C2×C47C2×#54612yes—
608C2×C47C2×#55012yes—
609D47—42no—
610D47—44no—
611D47—82no—
612D47#243118yesdirect product factor
613C22×#41—471no—
614C22×#41—472no—
615C22×#41—471no—
616C22×#41—472no—
617C22×#41—471no—
618C22×#41—948no—
619C22×#41—948no—
620C22×#41—948no—
621C22×#41C2×D4711yescharacteristic, complemented
622C23×Q8—471no—
623C23×D4—471no—
624C23×D4—472no—
625C23×D4—471no—
626C23×D4—474no—
627C23×D4—472no—
628C24×C4—471no—
629C24×C4—472no—
630C2×#127—474no—
631C2×#127—471no—
632C2×#127—471no—
633C2×#127—471no—
634C2×#127—948no—
635C2×#127C2×D4711yescharacteristic, complemented
636C2×#124—471no—
637C2×#124—471no—
638C2×#124—474no—
639C2×#124—471no—
640C2×#124—948no—
641C2×#124C2×D4711yescharacteristic, complemented
642C2×#121—471no—
643C2×#121—472no—
644C2×#121—471no—
645C2×#121—471no—
646C2×#121—472no—
647C2×#121—948no—
648C2×#121C2×D4711yescharacteristic, complemented
649C22×C4⋊C4—471no—
650C22×C22⋊C4—472no—
651C22×C22⋊C4—474no—
652C22×C22⋊C4—472no—
653C22×C22⋊C4—474no—
654C22×C42—471no—
655C22×C42—471no—
656#392—474no—
657#392—474no—
658#392—474no—
659#392—474no—
660#392—474no—
661#392—474no—
662#392—474no—
663#392C2×D4714yescomplemented
664#391—471no—
665#391—471no—
666#391—471no—
667#391—474no—
668#391C2×D4711yescharacteristic, complemented
669#390—471no—
670#390—471no—
671#390—474no—
672#390—471no—
673#390C2×D4711yescharacteristic, complemented
674#386—474no—
675#386—474no—
676#386—474no—
677#386—474no—
678#386—474no—
679#386—474no—
680#386—474no—
681#386C2×D4714yescomplemented
682C4×C22⋊C4—471no—
683C4×C22⋊C4—472no—
684C4×C22⋊C4—471no—
685C4×C22⋊C4—471no—
686C4×C22⋊C4—472no—
687C4×C22⋊C4C2×D4711yescharacteristic, complemented
688C2×#95—474no—
689C2×#95—472no—
690C47C2×#243111yescharacteristic, complemented, Sylow
691C25—471no—
692C25—472no—
693C25—472no—
694C2×#41—24no—
695C2×#41—24no—
696C2×#41—24no—
697C2×#41—948no—
698C2×#41—948no—
699C2×#41—944no—
700C2×#41—948no—
701C2×#41—944no—
702C2×#41—948no—
703C2×#41—944no—
704C2×#41—944no—
705C2×#41—948no—
706C2×#41—948no—
707C2×#41—944no—
708C2×#41—944no—
709C2×#41—94128no—
710C2×#41—944no—
711C2×#41—944no—
712C2×#41—944no—
713C22×Q8—478no—
714C22×Q8—472no—
715C22×Q8—471no—
716C22×Q8—944no—
717C22×Q8—944no—
718C22×Q8C22×D4711yescharacteristic
719C22×D4—472no—
720C22×D4—478no—
721C22×D4—472no—
722C22×D4—472no—
723C22×D4—472no—
724C22×D4—474no—
725C22×D4—474no—
726C22×D4—472no—
727C22×D4—472no—
728C22×D4—471no—
729C22×D4—471no—
730C22×D4—472no—
731C22×D4—474no—
732C22×D4—472no—
733C22×D4—944no—
734C22×D4—944no—
735C22×D4—948no—
736C22×D4—944no—
737C22×D4—944no—
738C22×D4—944no—
739C22×D4—9416no—
740C22×D4—948no—
741C22×D4—948no—
742C22×D4—948no—
743C22×D4—9416no—
744C22×D4—1888no—
745C22×D4—1888no—
746C22×D4C22×D4711yescharacteristic
747C22×D4C22×D4712yes—
748C22×D4C22×D4714yes—
749C22×D4C22×D4711yescharacteristic
750C22×D4C22×D4712yes—
751C23×C4—471no—
752C23×C4—471no—
753C23×C4—478no—
754C23×C4—471no—
755C23×C4—472no—
756C23×C4—472no—
757C23×C4—471no—
758C23×C4—471no—
759C23×C4—472no—
760C23×C4—472no—
761C23×C4—472no—
762C23×C4—472no—
763C23×C4—472no—
764C23×C4—944no—
765C23×C4—944no—
766C23×C4—948no—
767C23×C4—948no—
768C23×C4—948no—
769C23×C4C22×D4712yes—
770C23×C4C22×D4711yescharacteristic
771#127—24no—
772#127—944no—
773#127—9416no—
774#127—944no—
775#127—944no—
776#124—24no—
777#124—944no—
778#124—9416no—
779#124—944no—
780#124—944no—
781#121—24no—
782#121—948no—
783#121—944no—
784#121—944no—
785#121—948no—
786#121—944no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—944no—
790C2×C4⋊C4C22×D4711yescharacteristic
791C2×C22⋊C4—472no—
792C2×C22⋊C4—474no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—474no—
797C2×C22⋊C4—474no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—474no—
801C2×C22⋊C4—474no—
802C2×C22⋊C4—474no—
803C2×C22⋊C4—948no—
804C2×C22⋊C4—9416no—
805C2×C22⋊C4—948no—
806C2×C22⋊C4—1888no—
807C2×C22⋊C4C22×D4712yes—
808C2×C22⋊C4C22×D4714yes—
809C2×C22⋊C4C22×D4712yes—
810C2×C22⋊C4C22×D4714yes—
811C2×C42—472no—
812C2×C42—471no—
813C2×C42—472no—
814C2×C42—471no—
815C2×C42—944no—
816C2×C42—944no—
817C2×C42C22×D4711yescharacteristic
818C2×C42C22×D4711yescharacteristic
819#95—472no—
820#95—472no—
821#95—472no—
822#95—474no—
823#95—474no—
824#95—474no—
825#95C22×D4712yes—
826#95C22×D4714yes—
827C24—471no—
828C24—474no—
829C24—478no—
830C24—471no—
831C24—472no—
832C24—472no—
833C24—944no—
834C24—948no—
835C24—942no—
836C24—944no—
837C24—944no—
838C24—942no—
839C24—948no—
840C24—944no—
841C24—944no—
842C24—944no—
843C24—944no—
844C24—948no—
845C24—948no—
846C24C23×D4712yes—
847C24C23×D4711yescharacteristic
848C24C23×D4712yes—
849#41—232no—
850#41—9464no—
851#41—9432no—
852#41—9464no—
853#41—9432no—
854#41—9432no—
855C2×Q8—22no—
856C2×Q8—22no—
857C2×Q8—478no—
858C2×Q8—474no—
859C2×Q8—944no—
860C2×Q8—944no—
861C2×Q8—9432no—
862C2×Q8—942no—
863C2×Q8—942no—
864C2×Q8D4×D4714yescomplemented
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—28no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—28no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—478no—
879C2×D4—474no—
880C2×D4—944no—
881C2×D4—944no—
882C2×D4—944no—
883C2×D4—948no—
884C2×D4—9432no—
885C2×D4—944no—
886C2×D4—944no—
887C2×D4—944no—
888C2×D4—944no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—948no—
893C2×D4—948no—
894C2×D4—9464no—
895C2×D4—944no—
896C2×D4—944no—
897C2×D4—944no—
898C2×D4—944no—
899C2×D4—944no—
900C2×D4—948no—
901C2×D4—944no—
902C2×D4—948no—
903C2×D4—944no—
904C2×D4—942no—
905C2×D4—942no—
906C2×D4—942no—
907C2×D4—942no—
908C2×D4—942no—
909C2×D4—948no—
910C2×D4—1884no—
911C2×D4—1884no—
912C2×D4—18816no—
913C2×D4—18864no—
914C2×D4—1884no—
915C2×D4—1884no—
916C2×D4—1884no—
917C2×D4—1884no—
918C2×D4—18832no—
919C2×D4D4×D4714yescomplemented
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—471no—
926C22×C4—474no—
927C22×C4—474no—
928C22×C4—474no—
929C22×C4—474no—
930C22×C4—472no—
931C22×C4—471no—
932C22×C4—472no—
933C22×C4—474no—
934C22×C4—478no—
935C22×C4—474no—
936C22×C4—474no—
937C22×C4—478no—
938C22×C4—472no—
939C22×C4—472no—
940C22×C4—942no—
941C22×C4—942no—
942C22×C4—944no—
943C22×C4—944no—
944C22×C4—9432no—
945C22×C4—944no—
946C22×C4—942no—
947C22×C4—942no—
948C22×C4—944no—
949C22×C4—944no—
950C22×C4—944no—
951C22×C4—944no—
952C22×C4—944no—
953C22×C4—9464no—
954C22×C4—944no—
955C22×C4—944no—
956C22×C4—944no—
957C22×C4—944no—
958C22×C4—948no—
959C22×C4—942no—
960C22×C4—942no—
961C22×C4—944no—
962C22×C4—944no—
963C22×C4—944no—
964C22×C4—944no—
965C22×C4—944no—
966C22×C4—942no—
967C22×C4—942no—
968C22×C4D4×D4714yescomplemented
969C22×C4C23×D4712yes—
970C22×C4C23×D4712yes—
971C22×C4C23×D4711yescharacteristic
972C22×C4C23×D4712yes—
973C22×C4C23×D4712yes—
974C22×C4C23×D4711yescharacteristic
975C4⋊C4—22no—
976C4⋊C4—944no—
977C4⋊C4—942no—
978C22⋊C4—24no—
979C22⋊C4—28no—
980C22⋊C4—24no—
981C22⋊C4—44no—
982C22⋊C4—944no—
983C22⋊C4—944no—
984C22⋊C4—948no—
985C22⋊C4—944no—
986C22⋊C4—944no—
987C22⋊C4—948no—
988C22⋊C4—944no—
989C22⋊C4—948no—
990C22⋊C4—944no—
991C22⋊C4—1884no—
992C22⋊C4—1884no—
993C22⋊C4—1884no—
994C42—22no—
995C42—22no—
996C42—944no—
997C42—944no—
998C42—942no—
999C42—942no—
1000C23—21no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—24no—
1013C23—472no—
1014C23—472no—
1015C23—472no—
1016C23—474no—
1017C23—474no—
1018C23—472no—
1019C23—474no—
1020C23—948no—
1021C23—9416no—
1022C23—948no—
1023C23—9432no—
1024C23—948no—
1025C23—941no—
1026C23—941no—
1027C23—942no—
1028C23—942no—
1029C23—942no—
1030C23—944no—
1031C23—944no—
1032C23—942no—
1033C23—942no—
1034C23—942no—
1035C23—942no—
1036C23—944no—
1037C23—944no—
1038C23—18816no—
1039C23—1888no—
1040C23—1888no—
1041C23—18816no—
1042C23—1888no—
1043C23—1888no—
1044C23—1888no—
1045C23—18816no—
1046C23—1888no—
1047C23—1888no—
1048C23C2×D4×D4714yes—
1049C23C2×D4×D4712yes—
1050C23C24×D4711yescharacteristic
1051Q8—28no—
1052Q8—9416no—
1053Q8—948no—
1054D4—216no—
1055D4—28no—
1056D4—416no—
1057D4—48no—
1058D4—44no—
1059D4—9416no—
1060D4—9416no—
1061D4—9416no—
1062D4—9416no—
1063D4—948no—
1064D4—18816no—
1065D4—1888no—
1066D4—1888no—
1067D4—18816no—
1068D4—18816no—
1069D4—1888no—
1070D4—1888no—
1071D4—1884no—
1072C2×C4—216no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—28no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—472no—
1086C2×C4—472no—
1087C2×C4—472no—
1088C2×C4—4716no—
1089C2×C4—472no—
1090C2×C4—474no—
1091C2×C4—474no—
1092C2×C4—948no—
1093C2×C4—948no—
1094C2×C4—9416no—
1095C2×C4—9416no—
1096C2×C4—9416no—
1097C2×C4—9416no—
1098C2×C4—948no—
1099C2×C4—9416no—
1100C2×C4—942no—
1101C2×C4—941no—
1102C2×C4—941no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—942no—
1106C2×C4—948no—
1107C2×C4—942no—
1108C2×C4—942no—
1109C2×C4—942no—
1110C2×C4—942no—
1111C2×C4—944no—
1112C2×C4—1888no—
1113C2×C4—1888no—
1114C2×C4C2×D4×D4712yes—
1115C2×C4C2×D4×D4714yes—
1116C2×C4C2×D4×D4712yes—
1117C2×C4C2×D4×D4712yes—
1118C2×C4C2×D4×D4712yes—
1119C2×C4#41×D4714yescomplemented
1120C22—28no—
1121C22—24no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—42no—
1126C22—42no—
1127C22—44no—
1128C22—42no—
1129C22—42no—
1130C22—44no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—478no—
1136C22—474no—
1137C22—478no—
1138C22—474no—
1139C22—474no—
1140C22—948no—
1141C22—942no—
1142C22—944no—
1143C22—942no—
1144C22—942no—
1145C22—37616no—
1146C22—18816no—
1147C22—18832no—
1148C22—1884no—
1149C22—1882no—
1150C22—1884no—
1151C22—1882no—
1152C22—1882no—
1153C22—1882no—
1154C22—1882no—
1155C22—1884no—
1156C22—1882no—
1157C22—1882no—
1158C22C22×D4×D4711yescharacteristic
1159C22C22×D4×D4711yescharacteristic
1160C22C22×D4×D4711yescharacteristic
1161C22C2×#41×D4712yes—
1162C22H(5,𝔽2)×D4712yes—
1163C4—24no—
1164C4—22no—
1165C4—24no—
1166C4—42no—
1167C4—42no—
1168C4—474no—
1169C4—944no—
1170C4—942no—
1171C4—944no—
1172C4—1882no—
1173C4—1882no—
1174C4#120×D4714yes—
1175C2—44no—
1176C2—42no—
1177C2—82no—
1178C2—478no—
1179C2—3762no—
1180C2—1884no—
1181C2—1882no—
1182C2C2×#120×D4711yescharacteristic
1183C2#532×D4711yescharacteristic
1184C2#535×D4711yescharacteristic
1185C2#546×D4712yes—
1186C2#550×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2431C2
hypercenter#2431D47
hypocenterC47C2×#2431
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C22×#41×D47C2semidirect
2. C2×#127×D47C2semidirect
3. C2×#124×D47C2semidirect
4. C2×#121×D47C2semidirect
5. #20247010C2semidirect
6. #20247009C2semidirect
7. #20247008C2semidirect
8. #20247007C2semidirect
9. #20247006C2semidirect
10. #20247005C2semidirect
11. #20247004C2semidirect
12. #20247003C2semidirect
13. #20247002C2semidirect
14. #392×D47C2semidirect
15. #391×D47C2semidirect
16. #390×D47C2semidirect
17. #386×D47C2semidirect
18. C4×C22⋊C4×D47C2semidirect
19. C47×#2431C2semidirect
20. C22×#10625354C22semidirect
21. C22×#10625350C22semidirect
22. C22×#10625350C22semidirect
23. C22×#10625352C22semidirect
24. C22×#10625352C22semidirect
36. C2×#13094021C22semidirect
37. C2×#13094020C22semidirect
38. C2×#13094020C22semidirect
39. C2×#13094020C22semidirect
41. C2×#13094013C22semidirect
42. C2×#13094012C22semidirect
43. C2×#13094011C22semidirect
44. C2×#13094010C22semidirect
46. C2×#13093999C22semidirect
47. C2×#13093998C22semidirect
48. C2×#13093997C22semidirect
49. C2×#13093996C22semidirect
50. C2×#13093995C22semidirect
59. #15689033C22semidirect
60. #15689032C22semidirect
61. #15689032C22semidirect
62. #15689032C22semidirect
63. #15689031C22semidirect
64. #15689031C22semidirect
65. #15689031C22semidirect
66. #15689030C22semidirect
67. #15689029C22semidirect
68. #15689028C22semidirect
69. #15689027C22semidirect
70. #15689026C22semidirect
71. #15689025C22semidirect
72. #15689024C22semidirect
73. #15689023C22semidirect
74. #15689003C22semidirect
75. #15689002C22semidirect
76. #15689001C22semidirect
77. #15689001C22semidirect
78. #15689000C22semidirect
79. #15688999C22semidirect
80. #15688999C22semidirect
81. C22⋊C4×Dic47C22semidirect
82. C4×(C2×D47)⋊C4C22semidirect
83. C4×(C2×D47)⋊C4C22semidirect
84. C4×C22⋊Dic47C22semidirect
85. #15688970C22semidirect
88. C22×#41×C47C22semidirect
89. C2×#127×C47C22semidirect
90. C2×#124×C47C22semidirect
91. C2×#121×C47C22semidirect
92. C47×#392C22semidirect
93. C47×#391C22semidirect
94. C47×#390C22semidirect
95. C47×#386C22semidirect
96. C4×C22⋊C4×C47C22semidirect
120. C2×Q8×D47D4semidirect
147. C2×D4×D47D4semidirect
155. C22×C4×D47D4semidirect
258. C2×Q8×C47C2×D4semidirect
272. C2×D4×C47C2×D4semidirect
278. C22×C4×C47C2×D4semidirect
306. C2×C22⋊D47C2×D4semidirect
312. C22×Dic47C2×D4semidirect
343. C2×D188C2×D4semidirect
372. C2×C4×D47C2×D4semidirect
373. C2×C4×D47C2×D4semidirect
374. C2×C4×D47#41semidirect
379. C2×Dic94C2×D4semidirect
380. C2×Dic94C2×D4semidirect
481. C2×C4×C47C2×#41semidirect
508. C2×Dic47C2×#41semidirect
595. #2431D47direct (N × H)
612. D47#2431direct (N × H)
621. C22×#41C2×D47semidirect
635. C2×#127C2×D47semidirect
641. C2×#124C2×D47semidirect
648. C2×#121C2×D47semidirect
663. #392C2×D47semidirect
668. #391C2×D47semidirect
673. #390C2×D47semidirect
681. #386C2×D47semidirect
687. C4×C22⋊C4C2×D47semidirect
690. C47C2×#2431semidirect
864. C2×Q8D4×D47semidirect
919. C2×D4D4×D47semidirect
968. C22×C4D4×D47semidirect
1119. C2×C4#41×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D472
C2×#127×D472
C2×#124×D472
C2×#121×D472
#202470102
#202470092
#202470082
#202470072
#202470062
#202470052
#202470042
#202470032
#202470022
#392×D472
#391×D472
#390×D472
#386×D472
C4×C22⋊C4×D472
C47×#24312
C2×#243147