Finite Group Databasebeta

← D47×#2610 #26387120

Subgroups — D47×#2610 #26387120

Order 12032.

3286 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
1C2×#124×D47C211yesmaximal, characteristic, complemented
2C2×#117×D47C211yesmaximal, characteristic, complemented
3#20249078C211yesmaximal, characteristic, complemented
4#20249077C211yesmaximal, characteristic, complemented
5#20249076C211yesmaximal, characteristic, complemented
6#20249075C211yesmaximal, characteristic, complemented
7#20249074C212yesmaximal, complemented
8#20249073C212yesmaximal, complemented
9#20249072C212yesmaximal, complemented
10#20249071C212yesmaximal, complemented
11#20249070C211yesmaximal, characteristic, complemented
12#20249069C211yesmaximal, characteristic, complemented
13#20249068C211yesmaximal, characteristic, complemented
14#395×D47C211yesmaximal, characteristic, complemented
15#394×D47C211yesmaximal, characteristic, complemented
16#393×D47C211yesmaximal, characteristic, complemented
17#392×D47C211yesmaximal, characteristic
18#390×D47C212yesmaximal, complemented
19#388×D47C212yesmaximal, complemented
20#388×D47C212yesmaximal, complemented
21#386×D47C212yesmaximal, complemented
22#376×D47C211yesmaximal, characteristic, complemented
23C47×#2610C211yesmaximal, characteristic, complemented
24C22×Q8×D47C2211yescharacteristic
25C22×D4×D47C2212yes—
26C22×D4×D47C2211yescharacteristic
27C23×C4×D47C2211yescharacteristic
28C2×#13094013C2211yescharacteristic, complemented
29C2×#13094012C2211yescharacteristic, complemented
30C2×#13094011C2211yescharacteristic, complemented
31C2×#13094010C2212yescomplemented
32C2×#13094010C2212yescomplemented
33#124×D47—28no—
34C2×#13093983C2211yescharacteristic, complemented
35C2×#13093982C2211yescharacteristic, complemented
36C2×#13093982C2211yescharacteristic, complemented
37C2×#13093981C2211yescharacteristic, complemented
38C2×#13093981C2211yescharacteristic, complemented
39C2×#13093980C2211yescharacteristic, complemented
40C2×#13093980C2211yescharacteristic, complemented
41#117×D47—28no—
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C4⋊C4×D47C2212yes—
45C2×C22⋊C4×D47C2211yescharacteristic
46C2×C22⋊C4×D47C2211yescharacteristic
47C2×C22⋊C4×D47C2212yes—
48C2×C22⋊C4×D47C2212yes—
49C2×C22⋊C4×D47C2212yes—
50C2×C22⋊C4×D47C2212yes—
51C2×C22⋊C4×D47C2212yes—
52C2×C22⋊C4×D47C2212yes—
53C2×C42×D47C2211yescharacteristic
54C2×C42×D47C2212yes—
55C2×C42×D47C2211yescharacteristic
56#15689044C2211yescharacteristic, complemented
57#15689044C2212yescomplemented
58#15689043C2212yescomplemented
59#15689043C2211yescharacteristic, complemented
60#15689042C2211yescharacteristic, complemented
61#15689041C2211yescharacteristic, complemented
62#15689040C2211yescharacteristic, complemented
63#15689039C2212yescomplemented
64#15689038C2212yescomplemented
65#15689037C2211yescharacteristic, complemented
66#15689036C2211yescharacteristic, complemented
67#15689036C2212yescomplemented
68#15689035C2211yescharacteristic, complemented
69#15689035C2212yescomplemented
70#15689034C2211yescharacteristic, complemented
71#15689033C2211yescharacteristic
72#15689032C2212yes—
73#15689032C2211yescharacteristic
74#15689031C2212yes—
75#15689031C2211yescharacteristic
76#15689026C2212yescomplemented
77#15689025C2212yescomplemented
78#15689024C2212yescomplemented
79#15689023C2212yescomplemented
80#15689023C2212yescomplemented
81#15689023C2212yescomplemented
82#15689023C2212yescomplemented
83#15689017C2212yescomplemented
84#15689017C2212yescomplemented
85#15689016C2212yescomplemented
86#15689016C2212yescomplemented
87#15689015C2212yescomplemented
88#15689015C2212yescomplemented
89#15689014C2212yescomplemented
90#15689014C2212yescomplemented
91#15689013C2212yescomplemented
92#15689013C2212yescomplemented
93#15689012C2212yescomplemented
94#15689012C2212yescomplemented
95#15689011C2212yescomplemented
96#15689011C2212yescomplemented
97#15689003C2212yescomplemented
98#15689002C2212yescomplemented
99#15689001C2212yescomplemented
100#15689001C2212yescomplemented
101#15689000C2212yescomplemented
102#15688999C2212yescomplemented
103#15688999C2212yescomplemented
104#15688969C2212yescomplemented
105#15688969C2211yescharacteristic, complemented
106#15688968C2211yescharacteristic, complemented
107#15688968C2212yescomplemented
108#15688968C2211yescharacteristic, complemented
109#95×D47C2212yes—
110#95×D47C2212yes—
111#95×D47C2211yescharacteristic
112#95×D47C2212yes—
113#95×D47C2211yescharacteristic
114C2×#124×C47C2211yescharacteristic, complemented
115C2×#117×C47C2211yescharacteristic, complemented
116C47×#395C2211yescharacteristic, complemented
117C47×#394C2211yescharacteristic, complemented
118C47×#393C2211yescharacteristic, complemented
119C47×#392C2211yescharacteristic
120C47×#390C2212yescomplemented
121C47×#388C2212yescomplemented
122C47×#388C2212yescomplemented
123C47×#386C2212yescomplemented
124C47×#376C2211yescharacteristic, complemented
125C24×D47C2312yes—
126C24×D47C2311yescharacteristic
127C22×Dic94C2312yes—
128C22×Dic94C2311yescharacteristic
129C2×Q8×D47—24no—
130C2×Q8×D47—44no—
131C22×D188C2312yes—
132C22×D188C2311yescharacteristic
133C22×C22⋊D47C2312yes—
134C22×C22⋊D47C2312yes—
135C22×C22⋊D47C2312yes—
136C2×D4×D47—28no—
137C2×D4×D47—24no—
138C2×D4×D47—28no—
139C2×D4×D47—44no—
140C2×D4×D47—44no—
141C23×Dic47C2311yescharacteristic
142C22×C4×D47—24no—
143C22×C4×D47—24no—
144C22×C4×D47—24no—
145C22×C4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2312yes—
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153C22×C4×D47C2311yescharacteristic
154C22×C4×D47C2312yes—
155C22×C4×D47C2311yescharacteristic
156#13094013—24no—
157#13094012—24no—
158#13094011—24no—
159#13094010—28no—
160#13094010—28no—
161#13093983—24no—
162#13093982—24no—
163#13093982—24no—
164#13093981—24no—
165#13093981—24no—
166#13093980—24no—
167#13093980—24no—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2312yes—
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C4⋊C4×D47—24no—
178C4⋊C4×D47—24no—
179C4⋊C4×D47—44no—
180C2×C22⋊Dic47C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2311yescharacteristic
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
188C2×(C2×D47)⋊C4C2312yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2311yescharacteristic
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C22⋊C4×D47—24no—
205C22⋊C4×D47—24no—
206C22⋊C4×D47—28no—
207C22⋊C4×D47—28no—
208C22⋊C4×D47—28no—
209C22⋊C4×D47—28no—
210C22⋊C4×D47—44no—
211C22⋊C4×D47—44no—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C42×D47—24no—
222C42×D47—28no—
223C42×D47D418yescomplemented
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2311yescharacteristic
228C47⋊#95C2312yes—
229C47⋊#95C2311yescharacteristic
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C22×Q8×C47C2311yescharacteristic
238C22×D4×C47C2312yes—
239C22×D4×C47C2311yescharacteristic
240C23×C4×C47C2311yescharacteristic
241#124×C47—24no—
242#117×C47—24no—
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2311yescharacteristic
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C42×C47C2312yes—
255C2×C42×C47C2311yescharacteristic
256C2×C42×C47C2311yescharacteristic
257#95×C47C2312yes—
258#95×C47C2311yescharacteristic
259#95×C47C2311yescharacteristic
260#95×C47C2312yes—
261#95×C47C2312yes—
262C24×C47C2412yes—
263C24×C47C2411yescharacteristic
264C23×D47—22no—
265C23×D47—22no—
266C23×D47—24no—
267C23×D47—24no—
268C23×D47—24no—
269C23×D47—24no—
270C23×D47—24no—
271C23×D47—24no—
272C23×D47—24no—
273C23×D47—24no—
274C23×D47—24no—
275C23×D47#4114yes—
276C23×D47C2412yes—
277C23×D47C2411yescharacteristic
278C23×D47C2411yescharacteristic
279C2×Q8×C47—22no—
280C2×Q8×C47—42no—
281C2×D4×C47—24no—
282C2×D4×C47—22no—
283C2×D4×C47—24no—
284C2×D4×C47—42no—
285C2×D4×C47—42no—
286C22×C4×C47—22no—
287C22×C4×C47—22no—
288C22×C4×C47—22no—
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2412yes—
292C22×C4×C47C2412yes—
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C22×C4×C47C2412yes—
297C22×C4×C47C2411yescharacteristic
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—24no—
301C2×C22⋊D47—24no—
302C2×C22⋊D47—24no—
303C2×C22⋊D47—42no—
304C2×C22⋊D47—42no—
305C2×C22⋊D47—42no—
306C2×C22⋊D47—42no—
307C22×Dic47—22no—
308C22×Dic47—22no—
309C22×Dic47—22no—
310C22×Dic47C2412yes—
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2412yes—
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2411yescharacteristic
317C22×Dic47C2412yes—
318C22×Dic47C2411yescharacteristic
319Q8×D47—416no—
320D4×D47—432no—
321D4×D47—416no—
322C2×D188—24no—
323C2×D188—22no—
324C2×D188—24no—
325C2×D188—42no—
326C2×D188—42no—
327C2×C4×D47—232no—
328C2×C4×D47—22no—
329C2×C4×D47—24no—
330C2×C4×D47—22no—
331C2×C4×D47—22no—
332C2×C4×D47—22no—
333C2×C4×D47—22no—
334C2×C4×D47—22no—
335C2×C4×D47—24no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—22no—
339C2×C4×D47—22no—
340C2×C4×D47—22no—
341C2×C4×D47—22no—
342C2×C4×D47—22no—
343C2×C4×D47—22no—
344C2×C4×D47—24no—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—24no—
348C2×C4×D47—24no—
349C2×C4×D47—24no—
350C2×C4×D47—24no—
351C2×C4×D47—24no—
352C2×C4×D47C2×D414yes—
353C2×C4×D47C2×D414yes—
354C2×C4×D47C2×D414yes—
355C2×C4×D47#4118yes—
356C2×C4×D47#4114yes—
357C2×Dic94—22no—
358C2×Dic94—24no—
359C2×Dic94—42no—
360C2×Dic94—42no—
361C2×Dic94—42no—
362C4⋊C4×C47—22no—
363C4⋊C4×C47—22no—
364C4⋊C4×C47—42no—
365C22⋊C4×C47—22no—
366C22⋊C4×C47—22no—
367C22⋊C4×C47—24no—
368C22⋊C4×C47—24no—
369C22⋊C4×C47—24no—
370C22⋊C4×C47—24no—
371C22⋊C4×C47—42no—
372C22⋊C4×C47—42no—
373C42×C47—22no—
374C42×C47—24no—
375C42×C47C2×D414yescomplemented
376C22⋊Dic47—22no—
377C22⋊Dic47—22no—
378C22⋊Dic47—24no—
379C22⋊Dic47—24no—
380C22⋊Dic47—24no—
381C22⋊Dic47—24no—
382C22⋊Dic47—42no—
383C22⋊Dic47—42no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—22no—
386(C2×D47)⋊C4—24no—
387(C2×D47)⋊C4—24no—
388(C2×D47)⋊C4—24no—
389(C2×D47)⋊C4—24no—
390(C2×D47)⋊C4—22no—
391(C2×D47)⋊C4—22no—
392(C2×D47)⋊C4—24no—
393(C2×D47)⋊C4—24no—
394(C2×D47)⋊C4—24no—
395(C2×D47)⋊C4—24no—
396(C2×D47)⋊C4—42no—
397(C2×D47)⋊C4—42no—
398(C2×D47)⋊C4—42no—
399(C2×D47)⋊C4—42no—
400C4⋊Dic47—22no—
401C4⋊Dic47—22no—
402C4⋊Dic47—42no—
403Dic47⋊C4—22no—
404Dic47⋊C4—22no—
405Dic47⋊C4—22no—
406Dic47⋊C4—22no—
407Dic47⋊C4—42no—
408Dic47⋊C4—42no—
409C4×Dic47—22no—
410C4×Dic47—24no—
411C4×Dic47—22no—
412C4×Dic47—22no—
413C4×Dic47—24no—
414C4×Dic47—24no—
415C4×Dic47C2×D414yescomplemented
416C4×Dic47C2×D414yescomplemented
417C4×Dic47C2×D414yescomplemented
418C23×C47—21no—
419C23×C47—21no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—22no—
423C23×C47—22no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47—22no—
428C23×C47—22no—
429C23×C47C2×#4112yes—
430C23×C47C2511yescharacteristic
431C22×D47—21no—
432C22×D47—21no—
433C22×D47—22no—
434C22×D47—22no—
435C22×D47—28no—
436C22×D47—216no—
437C22×D47—22no—
438C22×D47—22no—
439C22×D47—22no—
440C22×D47—22no—
441C22×D47—22no—
442C22×D47—22no—
443C22×D47—22no—
444C22×D47—44no—
445C22×D47—44no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47—48no—
449C22×D47—48no—
450C22×D47—48no—
451C22×D47—48no—
452C22×D47—48no—
453C22×D47—48no—
454C22×D47C22×D412yes—
455C22×D47C2×#4112yes—
456C22×D47C2×#4112yes—
457C22×D47C2×#4112yes—
458C22×D47C2×#4114yes—
459C22×D47H(5,𝔽2)14yes—
460Q8×C47—44no—
461D4×C47—48no—
462D4×C47—44no—
463C2×C4×C47—28no—
464C2×C4×C47—21no—
465C2×C4×C47—22no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—21no—
473C2×C4×C47—21no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47C22×D412yes—
483C2×C4×C47C22×D412yes—
484C2×C4×C47C22×D412yes—
485C2×C4×C47C2×#4114yes—
486C2×C4×C47C2×#4112yes—
487C22⋊D47—48no—
488C22⋊D47—48no—
489C22⋊D47—48no—
490C2×Dic47—28no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—21no—
494C2×Dic47—21no—
495C2×Dic47—21no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—21no—
500C2×Dic47—21no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47C22×D412yes—
510C2×Dic47C22×D412yes—
511C2×Dic47C22×D412yes—
512C2×Dic47C2×#4114yes—
513C2×Dic47C2×#4112yes—
514D188—48no—
515D188—44no—
516C4×D47—28no—
517C4×D47—28no—
518C4×D47—28no—
519C4×D47—28no—
520C4×D47—28no—
521C4×D47—28no—
522C4×D47—216no—
523C4×D47—44no—
524C4×D47—44no—
525C4×D47—48no—
526C4×D47—48no—
527Dic94—48no—
528Dic94—44no—
529C2×#2610—471nomaximal, Sylow
530C22×C47—22no—
531C22×C47—24no—
532C22×C47—41no—
533C22×C47—41no—
534C22×C47—42no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47—42no—
538C22×C47—42no—
539C22×C47—42no—
540C22×C47—42no—
541C22×C47—42no—
542C22×C47C23×D411yescharacteristic
543C22×C47C22×#4111yescharacteristic
544C22×C47C22×#4111yescharacteristic
545C22×C47C22×#4112yes—
546C22×C47C2×H(5,𝔽2)12yes—
547C2×D47—22no—
548C2×D47—24no—
549C2×D47—41no—
550C2×D47—41no—
551C2×D47—42no—
552C2×D47—416no—
553C2×D47—42no—
554C2×D47—42no—
555C2×D47—42no—
556C2×D47—42no—
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—42no—
560C2×D47—816no—
561C2×D47#52514yes—
562C2×D47#53214yes—
563C2×D47#53514yes—
564C2×D47#55118yes—
565C2×D47#55518yes—
566C4×C47—22no—
567C4×C47—22no—
568C4×C47—22no—
569C4×C47—22no—
570C4×C47—24no—
571C4×C47—41no—
572C4×C47—42no—
573C4×C47—41no—
574C4×C47—42no—
575Dic47—22no—
576Dic47—22no—
577Dic47—22no—
578Dic47—22no—
579Dic47—24no—
580Dic47—41no—
581Dic47—42no—
582Dic47—41no—
583Dic47—42no—
584C22×#124—471no—
585C22×#117—471no—
586#2610—471no—
587#2610—471no—
588#2610—471no—
589#2610—471no—
590#2610—472no—
591#2610—472no—
592#2610—472no—
593#2610—472no—
594#2610—471no—
595#2610—471no—
596#2610—471no—
597#2610D4711yescharacteristic, direct product factor
598C2×#395—471no—
599C2×#394—471no—
600C2×#393—471no—
601C2×#392—471no—
602C2×#390—472no—
603C2×#388—472no—
604C2×#388—472no—
605C2×#386—472no—
606C2×#376—471no—
607C2×C47—42no—
608C2×C47—82no—
609C2×C47C2×#52511yescharacteristic
610C2×C47C2×#53211yescharacteristic
611C2×C47C2×#53511yescharacteristic
612C2×C47C2×#55112yes—
613C2×C47C2×#55512yes—
614D47—42no—
615D47—82no—
616D47#261018yesdirect product factor
617C23×Q8—471no—
618C23×D4—472no—
619C23×D4—471no—
620C24×C4—471no—
621C2×#124—471no—
622C2×#124—471no—
623C2×#124—472no—
624C2×#124—472no—
625C2×#124—471no—
626C2×#124—948no—
627C2×#124C2×D4711yescharacteristic, complemented
628C2×#117—471no—
629C2×#117—471no—
630C2×#117—471no—
631C2×#117—471no—
632C2×#117—471no—
633C2×#117—471no—
634C2×#117—471no—
635C2×#117—948no—
636C2×#117C2×D4711yescharacteristic, complemented
637C22×C4⋊C4—471no—
638C22×C4⋊C4—471no—
639C22×C4⋊C4—472no—
640C22×C22⋊C4—471no—
641C22×C22⋊C4—472no—
642C22×C22⋊C4—472no—
643C22×C22⋊C4—471no—
644C22×C22⋊C4—472no—
645C22×C22⋊C4—472no—
646C22×C22⋊C4—472no—
647C22×C22⋊C4—472no—
648C22×C42—471no—
649C22×C42—471no—
650C22×C42—472no—
651#395—471no—
652#395—472no—
653#395—471no—
654#395—472no—
655#395—471no—
656#395C2×D4711yescharacteristic, complemented
657#394—471no—
658#394—471no—
659#394—472no—
660#394—472no—
661#394—471no—
662#394C2×D4711yescharacteristic, complemented
663#393—471no—
664#393—472no—
665#393—471no—
666#393—472no—
667#393—471no—
668#393C2×D4711yescharacteristic, complemented
669#392—472no—
670#392—471no—
671#392—472no—
672#392—471no—
673#392—471no—
674#392C2×D4711yescharacteristic
675#390—472no—
676#390—472no—
677#390—472no—
678#390—472no—
679#390—472no—
680#390—472no—
681#390—472no—
682#390C2×D4712yescomplemented
683#388—472no—
684#388—472no—
685#388—472no—
686#388—472no—
687#388—472no—
688#388—472no—
689#388—472no—
690#388—472no—
691#388—472no—
692#388—472no—
693#388—472no—
694#388—472no—
695#388—472no—
696#388—472no—
697#388C2×D4712yescomplemented
698#388C2×D4712yescomplemented
699#386—472no—
700#386—472no—
701#386—472no—
702#386—472no—
703#386—472no—
704#386—472no—
705#386—472no—
706#386C2×D4712yescomplemented
707#376—472no—
708#376—471no—
709#376—471no—
710#376—471no—
711#376—472no—
712#376C2×D4711yescharacteristic, complemented
713C2×#95—471no—
714C2×#95—471no—
715C2×#95—472no—
716C2×#95—472no—
717C2×#95—472no—
718C47C2×#261011yescharacteristic, complemented, Sylow
719C25—471no—
720C25—472no—
721C22×Q8—472no—
722C22×Q8—471no—
723C22×Q8—944no—
724C22×Q8—1884no—
725C22×Q8C22×D4711yescharacteristic
726C22×D4—472no—
727C22×D4—472no—
728C22×D4—472no—
729C22×D4—472no—
730C22×D4—471no—
731C22×D4—944no—
732C22×D4—948no—
733C22×D4—948no—
734C22×D4—1884no—
735C22×D4—1884no—
736C22×D4C22×D4712yes—
737C22×D4C22×D4711yescharacteristic
738C23×C4—471no—
739C23×C4—471no—
740C23×C4—471no—
741C23×C4—471no—
742C23×C4—472no—
743C23×C4—471no—
744C23×C4—471no—
745C23×C4—472no—
746C23×C4—471no—
747C23×C4—472no—
748C23×C4—471no—
749C23×C4—471no—
750C23×C4—944no—
751C23×C4—944no—
752C23×C4—944no—
753C23×C4C22×D4711yescharacteristic
754#124—24no—
755#124—948no—
756#124—948no—
757#124—944no—
758#124—944no—
759#124—944no—
760#117—24no—
761#117—944no—
762#117—944no—
763#117—944no—
764#117—944no—
765#117—944no—
766#117—944no—
767#117—944no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—471no—
772C2×C4⋊C4—471no—
773C2×C4⋊C4—471no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—944no—
778C2×C4⋊C4—944no—
779C2×C4⋊C4—1884no—
780C2×C4⋊C4C22×D4711yescharacteristic
781C2×C4⋊C4C22×D4711yescharacteristic
782C2×C4⋊C4C22×D4712yes—
783C2×C22⋊C4—471no—
784C2×C22⋊C4—471no—
785C2×C22⋊C4—472no—
786C2×C22⋊C4—472no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—472no—
798C2×C22⋊C4—472no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—944no—
808C2×C22⋊C4—944no—
809C2×C22⋊C4—948no—
810C2×C22⋊C4—948no—
811C2×C22⋊C4—948no—
812C2×C22⋊C4—948no—
813C2×C22⋊C4—1884no—
814C2×C22⋊C4—1884no—
815C2×C22⋊C4C22×D4711yescharacteristic
816C2×C22⋊C4C22×D4711yescharacteristic
817C2×C22⋊C4C22×D4712yes—
818C2×C22⋊C4C22×D4712yes—
819C2×C22⋊C4C22×D4712yes—
820C2×C22⋊C4C22×D4712yes—
821C2×C22⋊C4C22×D4712yes—
822C2×C22⋊C4C22×D4712yes—
823C2×C42—471no—
824C2×C42—471no—
825C2×C42—471no—
826C2×C42—478no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—471no—
830C2×C42—472no—
831C2×C42—472no—
832C2×C42—472no—
833C2×C42—944no—
834C2×C42—948no—
835C2×C42C22×D4711yescharacteristic
836C2×C42C22×D4712yes—
837C2×C42C22×D4711yescharacteristic
838#95—472no—
839#95—472no—
840#95—472no—
841#95—471no—
842#95—472no—
843#95—472no—
844#95—471no—
845#95—472no—
846#95—472no—
847#95—472no—
848#95—472no—
849#95—472no—
850#95—472no—
851#95C22×D4712yes—
852#95C22×D4711yescharacteristic
853#95C22×D4711yescharacteristic
854#95C22×D4712yes—
855#95C22×D4712yes—
856C24—471no—
857C24—474no—
858C24—471no—
859C24—472no—
860C24—942no—
861C24—944no—
862C24—942no—
863C24—944no—
864C24—944no—
865C24—944no—
866C24—944no—
867C24—944no—
868C24—944no—
869C24—944no—
870C24—944no—
871C24C23×D4712yes—
872C24C23×D4711yescharacteristic
873C2×Q8—22no—
874C2×Q8—42no—
875C2×Q8—944no—
876C2×Q8—942no—
877C2×Q8—1882no—
878C2×Q8—1882no—
879C2×Q8—1882no—
880C2×Q8—18816no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—24no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—944no—
887C2×D4—944no—
888C2×D4—944no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—942no—
893C2×D4—944no—
894C2×D4—1882no—
895C2×D4—1882no—
896C2×D4—18832no—
897C2×D4—18816no—
898C2×D4—1882no—
899C2×D4—1882no—
900C2×D4—1882no—
901C2×D4—1882no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—472no—
906C22×C4—471no—
907C22×C4—471no—
908C22×C4—471no—
909C22×C4—471no—
910C22×C4—474no—
911C22×C4—474no—
912C22×C4—474no—
913C22×C4—478no—
914C22×C4—474no—
915C22×C4—472no—
916C22×C4—471no—
917C22×C4—472no—
918C22×C4—471no—
919C22×C4—942no—
920C22×C4—942no—
921C22×C4—944no—
922C22×C4—942no—
923C22×C4—944no—
924C22×C4—942no—
925C22×C4—942no—
926C22×C4—942no—
927C22×C4—942no—
928C22×C4—942no—
929C22×C4—944no—
930C22×C4—944no—
931C22×C4—9432no—
932C22×C4—942no—
933C22×C4—942no—
934C22×C4—944no—
935C22×C4—944no—
936C22×C4—944no—
937C22×C4—944no—
938C22×C4—944no—
939C22×C4—944no—
940C22×C4—944no—
941C22×C4—944no—
942C22×C4—942no—
943C22×C4—942no—
944C22×C4—942no—
945C22×C4—942no—
946C22×C4—942no—
947C22×C4C23×D4712yes—
948C22×C4C23×D4711yescharacteristic
949C22×C4C23×D4712yes—
950C22×C4C23×D4711yescharacteristic
951C22×C4C23×D4711yescharacteristic
952C22×C4C23×D4711yescharacteristic
953C22×C4C23×D4711yescharacteristic
954C22×C4C23×D4712yes—
955C22×C4C23×D4711yescharacteristic
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—42no—
959C4⋊C4—942no—
960C4⋊C4—942no—
961C4⋊C4—942no—
962C4⋊C4—942no—
963C4⋊C4—942no—
964C4⋊C4—942no—
965C4⋊C4—1882no—
966C4⋊C4—1882no—
967C4⋊C4—1882no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—944no—
977C22⋊C4—944no—
978C22⋊C4—942no—
979C22⋊C4—942no—
980C22⋊C4—944no—
981C22⋊C4—944no—
982C22⋊C4—944no—
983C22⋊C4—944no—
984C22⋊C4—942no—
985C22⋊C4—942no—
986C22⋊C4—944no—
987C22⋊C4—944no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—944no—
991C22⋊C4—944no—
992C22⋊C4—944no—
993C22⋊C4—944no—
994C22⋊C4—1882no—
995C22⋊C4—1882no—
996C22⋊C4—1882no—
997C22⋊C4—1882no—
998C22⋊C4—1882no—
999C22⋊C4—1882no—
1000C42—22no—
1001C42—24no—
1002C42—474no—
1003C42—474no—
1004C42—474no—
1005C42—944no—
1006C42—944no—
1007C42—942no—
1008C42—942no—
1009C42—942no—
1010C42—944no—
1011C42D4×D4714yescomplemented
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—472no—
1024C23—472no—
1025C23—474no—
1026C23—472no—
1027C23—474no—
1028C23—472no—
1029C23—948no—
1030C23—9416no—
1031C23—941no—
1032C23—941no—
1033C23—942no—
1034C23—942no—
1035C23—942no—
1036C23—942no—
1037C23—942no—
1038C23—942no—
1039C23—942no—
1040C23—942no—
1041C23—942no—
1042C23—1888no—
1043C23—1888no—
1044C23—1888no—
1045C23—1888no—
1046C23—1888no—
1047C23—1888no—
1048C23—1888no—
1049C23—1884no—
1050C23—1888no—
1051C23—1884no—
1052C23#41×D4712yes—
1053C23C24×D4711yescharacteristic
1054Q8—44no—
1055Q8—1884no—
1056Q8—1888no—
1057D4—48no—
1058D4—44no—
1059D4—1888no—
1060D4—1884no—
1061D4—1888no—
1062D4—1888no—
1063D4—1888no—
1064C2×C4—28no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—472no—
1084C2×C4—472no—
1085C2×C4—472no—
1086C2×C4—474no—
1087C2×C4—472no—
1088C2×C4—948no—
1089C2×C4—948no—
1090C2×C4—948no—
1091C2×C4—9416no—
1092C2×C4—948no—
1093C2×C4—948no—
1094C2×C4—948no—
1095C2×C4—948no—
1096C2×C4—941no—
1097C2×C4—942no—
1098C2×C4—941no—
1099C2×C4—941no—
1100C2×C4—941no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—942no—
1104C2×C4—941no—
1105C2×C4—941no—
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—1884no—
1115C2×C4—1888no—
1116C2×C4—1884no—
1117C2×C4—1888no—
1118C2×C4C2×D4×D4712yes—
1119C2×C4C2×D4×D4712yes—
1120C2×C4C2×D4×D4712yes—
1121C2×C4#41×D4714yes—
1122C2×C4#41×D4712yes—
1123C22—22no—
1124C22—24no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—474no—
1136C22—478no—
1137C22—474no—
1138C22—478no—
1139C22—474no—
1140C22—942no—
1141C22—944no—
1142C22—37616no—
1143C22—18816no—
1144C22—1882no—
1145C22—1882no—
1146C22—1882no—
1147C22—1882no—
1148C22—1882no—
1149C22—1882no—
1150C22—1882no—
1151C22—1881no—
1152C22—1882no—
1153C22—1881no—
1154C22C22×D4×D4711yescharacteristic
1155C22C2×#41×D4711yescharacteristic
1156C22C2×#41×D4711yescharacteristic
1157C22C2×#41×D4712yes—
1158C22H(5,𝔽2)×D4712yes—
1159C4—22no—
1160C4—22no—
1161C4—24no—
1162C4—22no—
1163C4—22no—
1164C4—41no—
1165C4—42no—
1166C4—42no—
1167C4—41no—
1168C4—942no—
1169C4—942no—
1170C4—944no—
1171C4—942no—
1172C4—942no—
1173C4—1881no—
1174C4—1882no—
1175C4—1882no—
1176C4—1881no—
1177C2—42no—
1178C2—82no—
1179C2—478no—
1180C2—3762no—
1181C2—1882no—
1182C2#525×D4711yescharacteristic
1183C2#532×D4711yescharacteristic
1184C2#535×D4711yescharacteristic
1185C2#551×D4712yes—
1186C2#555×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2610C2
prime radical#392×D47C2
hypercenter#2610D47
hypocenterC47C2×#2610
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. C2×#124×D47C2semidirect
2. C2×#117×D47C2semidirect
3. #20249078C2semidirect
4. #20249077C2semidirect
5. #20249076C2semidirect
6. #20249075C2semidirect
7. #20249074C2semidirect
8. #20249073C2semidirect
9. #20249072C2semidirect
10. #20249071C2semidirect
11. #20249070C2semidirect
12. #20249069C2semidirect
13. #20249068C2semidirect
14. #395×D47C2semidirect
15. #394×D47C2semidirect
16. #393×D47C2semidirect
18. #390×D47C2semidirect
19. #388×D47C2semidirect
20. #388×D47C2semidirect
21. #386×D47C2semidirect
22. #376×D47C2semidirect
23. C47×#2610C2semidirect
28. C2×#13094013C22semidirect
29. C2×#13094012C22semidirect
30. C2×#13094011C22semidirect
31. C2×#13094010C22semidirect
32. C2×#13094010C22semidirect
34. C2×#13093983C22semidirect
35. C2×#13093982C22semidirect
36. C2×#13093982C22semidirect
37. C2×#13093981C22semidirect
38. C2×#13093981C22semidirect
39. C2×#13093980C22semidirect
40. C2×#13093980C22semidirect
56. #15689044C22semidirect
57. #15689044C22semidirect
58. #15689043C22semidirect
59. #15689043C22semidirect
60. #15689042C22semidirect
61. #15689041C22semidirect
62. #15689040C22semidirect
63. #15689039C22semidirect
64. #15689038C22semidirect
65. #15689037C22semidirect
66. #15689036C22semidirect
67. #15689036C22semidirect
68. #15689035C22semidirect
69. #15689035C22semidirect
70. #15689034C22semidirect
76. #15689026C22semidirect
77. #15689025C22semidirect
78. #15689024C22semidirect
79. #15689023C22semidirect
80. #15689023C22semidirect
81. #15689023C22semidirect
82. #15689023C22semidirect
83. #15689017C22semidirect
84. #15689017C22semidirect
85. #15689016C22semidirect
86. #15689016C22semidirect
87. #15689015C22semidirect
88. #15689015C22semidirect
89. #15689014C22semidirect
90. #15689014C22semidirect
91. #15689013C22semidirect
92. #15689013C22semidirect
93. #15689012C22semidirect
94. #15689012C22semidirect
95. #15689011C22semidirect
96. #15689011C22semidirect
97. #15689003C22semidirect
98. #15689002C22semidirect
99. #15689001C22semidirect
100. #15689001C22semidirect
101. #15689000C22semidirect
102. #15688999C22semidirect
103. #15688999C22semidirect
104. #15688969C22semidirect
105. #15688969C22semidirect
106. #15688968C22semidirect
107. #15688968C22semidirect
108. #15688968C22semidirect
114. C2×#124×C47C22semidirect
115. C2×#117×C47C22semidirect
116. C47×#395C22semidirect
117. C47×#394C22semidirect
118. C47×#393C22semidirect
120. C47×#390C22semidirect
121. C47×#388C22semidirect
122. C47×#388C22semidirect
123. C47×#386C22semidirect
124. C47×#376C22semidirect
223. C42×D47D4semidirect
375. C42×C47C2×D4semidirect
415. C4×Dic47C2×D4semidirect
416. C4×Dic47C2×D4semidirect
417. C4×Dic47C2×D4semidirect
597. #2610D47direct (N × H)
616. D47#2610direct (N × H)
627. C2×#124C2×D47semidirect
636. C2×#117C2×D47semidirect
656. #395C2×D47semidirect
662. #394C2×D47semidirect
668. #393C2×D47semidirect
682. #390C2×D47semidirect
697. #388C2×D47semidirect
698. #388C2×D47semidirect
706. #386C2×D47semidirect
712. #376C2×D47semidirect
718. C47C2×#2610semidirect
1011. C42D4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D472
C2×#117×D472
#202490782
#202490772
#202490762
#202490752
#202490742
#202490732
#202490722
#202490712
#202490702
#202490692
#202490682
#395×D472
#394×D472
#393×D472
#392×D472
#390×D472
#388×D472
#386×D472
#376×D472
C47×#26102
C2×#261047