Finite Group Databasebeta

← D47×#2662 #26383005

Subgroups — D47×#2662 #26383005

Order 12032.

3002 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D47C211yesmaximal, characteristic, complemented
2C2×#124×D47C211yesmaximal, characteristic, complemented
3#20249534C211yesmaximal, characteristic, complemented
4#20249533C211yesmaximal, characteristic, complemented
5#20249532C211yesmaximal, characteristic, complemented
6#20249531C212yesmaximal, complemented
7#20249530C211yesmaximal, characteristic, complemented
8#20249529C212yesmaximal, complemented
9#20249528C211yesmaximal, characteristic, complemented
10#20249527C211yesmaximal, characteristic, complemented
11#20249526C212yesmaximal, complemented
12#20249525C211yesmaximal, characteristic, complemented
13#20249524C212yesmaximal, complemented
14#396×D47C212yesmaximal, complemented
15#395×D47C211yesmaximal, characteristic, complemented
16#394×D47C212yesmaximal, complemented
17#394×D47C211yesmaximal, characteristic, complemented
18#393×D47C211yesmaximal, characteristic, complemented
19#392×D47C211yesmaximal, characteristic
20#390×D47C212yesmaximal, complemented
21#388×D47C212yesmaximal, complemented
22C4×C4⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2662C211yesmaximal, characteristic, complemented
24C22×Q8×D47C2211yescharacteristic
25C22×D4×D47C2212yes—
26C22×D4×D47C2211yescharacteristic
27C2×#13094019C2211yescharacteristic, complemented
28C2×#13094019C2211yescharacteristic, complemented
29C2×#13094019C2211yescharacteristic, complemented
30C2×#13094018C2211yescharacteristic, complemented
31C2×#13094017C2211yescharacteristic, complemented
32C2×#13094017C2211yescharacteristic, complemented
33C2×#13094017C2211yescharacteristic, complemented
34#126×D47—28no—
35C2×#13094013C2211yescharacteristic, complemented
36C2×#13094012C2211yescharacteristic, complemented
37C2×#13094011C2211yescharacteristic, complemented
38C2×#13094010C2212yescomplemented
39C2×#13094010C2212yescomplemented
40#124×D47—28no—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2212yes—
44C2×C4⋊C4×D47C2211yescharacteristic
45C2×C4⋊C4×D47C2212yes—
46C2×C22⋊C4×D47C2212yes—
47C2×C22⋊C4×D47C2211yescharacteristic
48C2×C22⋊C4×D47C2212yes—
49C2×C22⋊C4×D47C2211yescharacteristic
50C2×C22⋊C4×D47C2212yes—
51C2×C22⋊C4×D47C2211yescharacteristic
52C2×C22⋊C4×D47C2212yes—
53C2×C22⋊C4×D47C2212yes—
54C2×C22⋊C4×D47C2212yes—
55C2×C42×D47C2212yes—
56C2×C42×D47C2211yescharacteristic
57#15689047C2212yescomplemented
58#15689046C2212yescomplemented
59#15689046C2212yescomplemented
60#15689046C2212yescomplemented
61#15689045C2212yescomplemented
62#15689045C2212yescomplemented
63#15689045C2212yescomplemented
64#15689044C2212yescomplemented
65#15689044C2211yescharacteristic, complemented
66#15689043C2212yescomplemented
67#15689043C2211yescharacteristic, complemented
68#15689042C2211yescharacteristic, complemented
69#15689041C2211yescharacteristic, complemented
70#15689041C2212yescomplemented
71#15689040C2212yescomplemented
72#15689040C2211yescharacteristic, complemented
73#15689039C2212yescomplemented
74#15689039C2212yescomplemented
75#15689039C2212yescomplemented
76#15689038C2212yescomplemented
77#15689038C2212yescomplemented
78#15689038C2212yescomplemented
79#15689037C2211yescharacteristic, complemented
80#15689037C2212yescomplemented
81#15689036C2211yescharacteristic, complemented
82#15689036C2212yescomplemented
83#15689035C2212yescomplemented
84#15689035C2211yescharacteristic, complemented
85#15689034C2211yescharacteristic, complemented
86#15689033C2211yescharacteristic
87#15689032C2212yes—
88#15689032C2211yescharacteristic
89#15689031C2212yes—
90#15689031C2211yescharacteristic
91#15689026C2212yescomplemented
92#15689025C2212yescomplemented
93#15689024C2212yescomplemented
94#15689023C2212yescomplemented
95#15689023C2212yescomplemented
96#15689023C2212yescomplemented
97#15689023C2212yescomplemented
98#15689017C2212yescomplemented
99#15689016C2212yescomplemented
100#15689015C2212yescomplemented
101#15689014C2212yescomplemented
102#15689013C2212yescomplemented
103#15689012C2212yescomplemented
104#15689011C2212yescomplemented
105C4⋊C4×Dic47C2212yescomplemented
106C4×Dic47⋊C4C2212yescomplemented
107C4×C4⋊Dic47C2211yescharacteristic, complemented
108#15688974C2211yescharacteristic, complemented
109#15688974C2211yescharacteristic, complemented
110#95×D47C2211yescharacteristic
111#95×D47C2212yes—
112#95×D47C2212yes—
113#95×D47C2211yescharacteristic
114C2×#126×C47C2211yescharacteristic, complemented
115C2×#124×C47C2211yescharacteristic, complemented
116C47×#396C2212yescomplemented
117C47×#395C2211yescharacteristic, complemented
118C47×#394C2212yescomplemented
119C47×#394C2211yescharacteristic, complemented
120C47×#393C2211yescharacteristic, complemented
121C47×#392C2211yescharacteristic
122C47×#390C2212yescomplemented
123C47×#388C2212yescomplemented
124C4×C4⋊C4×C47C2211yescharacteristic, complemented
125C24×D47C2311yescharacteristic
126C24×D47C2312yes—
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—24no—
137C2×D4×D47—28no—
138C2×D4×D47—44no—
139C2×D4×D47—44no—
140C2×D4×D47—44no—
141C22×C4×D47C2312yes—
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2312yes—
150#13094019—24no—
151#13094019—24no—
152#13094019—24no—
153#13094018—24no—
154#13094017—24no—
155#13094017—24no—
156#13094017—24no—
157#13094013—24no—
158#13094012—24no—
159#13094011—24no—
160#13094010—28no—
161#13094010—28no—
162C2×C4⋊Dic47C2312yes—
163C2×C4⋊Dic47C2311yescharacteristic
164C2×C4⋊Dic47C2311yescharacteristic
165C2×C4⋊Dic47C2311yescharacteristic
166C2×C4⋊Dic47C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2311yescharacteristic
170C2×Dic47⋊C4C2311yescharacteristic
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—24no—
180C4⋊C4×D47—28no—
181C4⋊C4×D47—44no—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2311yescharacteristic
186C2×C22⋊Dic47C2311yescharacteristic
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2312yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2311yescharacteristic
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2311yescharacteristic
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C22⋊C4×D47—28no—
210C22⋊C4×D47—28no—
211C22⋊C4×D47—24no—
212C22⋊C4×D47—24no—
213C22⋊C4×D47—24no—
214C22⋊C4×D47—28no—
215C22⋊C4×D47—44no—
216C22⋊C4×D47—44no—
217C22⋊C4×D47—44no—
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2312yes—
220C2×C4×Dic47C2312yes—
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2311yescharacteristic
224C42×D47—44no—
225C42×D47D418yescomplemented
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2311yescharacteristic
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C22×Q8×C47C2311yescharacteristic
237C22×D4×C47C2312yes—
238C22×D4×C47C2311yescharacteristic
239#126×C47—24no—
240#124×C47—24no—
241C2×C4⋊C4×C47C2312yes—
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2311yescharacteristic
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C22⋊C4×C47C2312yes—
255C2×C42×C47C2312yes—
256C2×C42×C47C2311yescharacteristic
257#95×C47C2311yescharacteristic
258#95×C47C2311yescharacteristic
259#95×C47C2312yes—
260#95×C47C2312yes—
261C24×C47C2411yescharacteristic
262C24×C47C2412yes—
263C23×D47—22no—
264C23×D47—24no—
265C23×D47—24no—
266C23×D47—24no—
267C23×D47—24no—
268C23×D47—24no—
269C23×D47—24no—
270C23×D47—24no—
271C23×D47—24no—
272C23×D47—22no—
273C23×D47—22no—
274C23×D47—24no—
275C23×D47C2411yescharacteristic
276C23×D47C2412yes—
277C23×D47C2411yescharacteristic
278C2×Q8×C47—22no—
279C2×Q8×C47—42no—
280C2×D4×C47—22no—
281C2×D4×C47—24no—
282C2×D4×C47—42no—
283C2×D4×C47—42no—
284C2×D4×C47—42no—
285C22×C4×C47C2412yes—
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2412yes—
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2412yes—
294C2×C22⋊D47—24no—
295C2×C22⋊D47—24no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—42no—
298C2×C22⋊D47—42no—
299C2×C22⋊D47—42no—
300C2×C22⋊D47—42no—
301C2×C22⋊D47—42no—
302C2×C22⋊D47—42no—
303C22×Dic47C2412yes—
304C22×Dic47C2411yescharacteristic
305C22×Dic47C2411yescharacteristic
306C22×Dic47C2412yes—
307C22×Dic47C2411yescharacteristic
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2412yes—
312Q8×D47—416no—
313D4×D47—416no—
314D4×D47—432no—
315C2×D188—22no—
316C2×D188—24no—
317C2×D188—42no—
318C2×D188—42no—
319C2×D188—42no—
320C2×C4×D47—24no—
321C2×C4×D47—22no—
322C2×C4×D47—24no—
323C2×C4×D47—24no—
324C2×C4×D47—24no—
325C2×C4×D47—22no—
326C2×C4×D47—24no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—24no—
333C2×C4×D47—22no—
334C2×C4×D47—24no—
335C2×C4×D47—24no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—22no—
339C2×C4×D47C2×D414yes—
340C2×C4×D47C2×D414yes—
341C2×C4×D47C2×D414yes—
342C2×C4×D47#4118yes—
343C2×Dic94—22no—
344C2×Dic94—24no—
345C2×Dic94—42no—
346C2×Dic94—42no—
347C2×Dic94—42no—
348C4⋊C4×C47—22no—
349C4⋊C4×C47—22no—
350C4⋊C4×C47—22no—
351C4⋊C4×C47—24no—
352C4⋊C4×C47—42no—
353C22⋊C4×C47—24no—
354C22⋊C4×C47—24no—
355C22⋊C4×C47—22no—
356C22⋊C4×C47—22no—
357C22⋊C4×C47—22no—
358C22⋊C4×C47—24no—
359C22⋊C4×C47—42no—
360C22⋊C4×C47—42no—
361C22⋊C4×C47—42no—
362C42×C47—42no—
363C42×C47C2×D414yescomplemented
364C22⋊Dic47—24no—
365C22⋊Dic47—24no—
366C22⋊Dic47—22no—
367C22⋊Dic47—22no—
368C22⋊Dic47—22no—
369C22⋊Dic47—24no—
370C22⋊Dic47—42no—
371C22⋊Dic47—42no—
372C22⋊Dic47—42no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—24no—
375(C2×D47)⋊C4—22no—
376(C2×D47)⋊C4—22no—
377(C2×D47)⋊C4—22no—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—24no—
380(C2×D47)⋊C4—24no—
381(C2×D47)⋊C4—22no—
382(C2×D47)⋊C4—22no—
383(C2×D47)⋊C4—22no—
384(C2×D47)⋊C4—24no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4—42no—
388(C2×D47)⋊C4—42no—
389(C2×D47)⋊C4—42no—
390(C2×D47)⋊C4—42no—
391C4⋊Dic47—22no—
392C4⋊Dic47—22no—
393C4⋊Dic47—22no—
394C4⋊Dic47—24no—
395C4⋊Dic47—42no—
396Dic47⋊C4—22no—
397Dic47⋊C4—22no—
398Dic47⋊C4—22no—
399Dic47⋊C4—24no—
400Dic47⋊C4—22no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403Dic47⋊C4—24no—
404Dic47⋊C4—42no—
405Dic47⋊C4—42no—
406C4×Dic47—42no—
407C4×Dic47—42no—
408C4×Dic47—42no—
409C4×Dic47C2×D414yescomplemented
410C4×Dic47C2×D414yescomplemented
411C4×Dic47C2×D414yescomplemented
412C23×C47—21no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—22no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—21no—
422C23×C47—21no—
423C23×C47—22no—
424C23×C47C2511yescharacteristic
425C22×D47—21no—
426C22×D47—22no—
427C22×D47—22no—
428C22×D47—22no—
429C22×D47—22no—
430C22×D47—22no—
431C22×D47—22no—
432C22×D47—22no—
433C22×D47—22no—
434C22×D47—21no—
435C22×D47—21no—
436C22×D47—22no—
437C22×D47—44no—
438C22×D47—48no—
439C22×D47—48no—
440C22×D47—44no—
441C22×D47—44no—
442C22×D47—48no—
443C22×D47—48no—
444C22×D47—48no—
445C22×D47—48no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47—48no—
449C22×D47C22×D412yes—
450C22×D47C2×#4114yes—
451C22×D47H(5,𝔽2)14yes—
452C22×D47H(5,𝔽2)12yes—
453C22×D472−1+412yes—
454Q8×C47—44no—
455D4×C47—44no—
456D4×C47—48no—
457C2×C4×C47—22no—
458C2×C4×C47—21no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—21no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—21no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—21no—
476C2×C4×C47C22×D412yes—
477C2×C4×C47C22×D412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C2×#4114yes—
480C22⋊D47—48no—
481C22⋊D47—48no—
482C22⋊D47—48no—
483C2×Dic47—22no—
484C2×Dic47—21no—
485C2×Dic47—22no—
486C2×Dic47—22no—
487C2×Dic47—22no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—21no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—21no—
502C2×Dic47C22×D412yes—
503C2×Dic47C22×D412yes—
504C2×Dic47C22×D412yes—
505C2×Dic47C2×#4114yes—
506D188—44no—
507D188—48no—
508C4×D47—28no—
509C4×D47—28no—
510C4×D47—28no—
511C4×D47—216no—
512C4×D47—44no—
513C4×D47—44no—
514C4×D47—48no—
515C4×D47—44no—
516C4×D47—48no—
517Dic94—48no—
518Dic94—44no—
519C2×#2662—471nomaximal, Sylow
520C22×C47—41no—
521C22×C47—42no—
522C22×C47—42no—
523C22×C47—41no—
524C22×C47—41no—
525C22×C47—42no—
526C22×C47—42no—
527C22×C47—42no—
528C22×C47—42no—
529C22×C47—42no—
530C22×C47—42no—
531C22×C47—42no—
532C22×C47C23×D411yescharacteristic
533C22×C47C22×#4112yes—
534C22×C47C2×H(5,𝔽2)12yes—
535C22×C47C2×H(5,𝔽2)11yescharacteristic
536C22×C47C2×2−1+411yescharacteristic
537C2×D47—41no—
538C2×D47—42no—
539C2×D47—42no—
540C2×D47—41no—
541C2×D47—41no—
542C2×D47—42no—
543C2×D47—42no—
544C2×D47—42no—
545C2×D47—42no—
546C2×D47—42no—
547C2×D47—42no—
548C2×D47—42no—
549C2×D47—816no—
550C2×D47—88no—
551C2×D47#53214yes—
552C2×D47#53514yes—
553C2×D47#53714yes—
554C2×D47#53818yes—
555C2×D47#54218yes—
556C4×C47—22no—
557C4×C47—22no—
558C4×C47—22no—
559C4×C47—24no—
560C4×C47—41no—
561C4×C47—42no—
562C4×C47—41no—
563C4×C47—41no—
564C4×C47—42no—
565Dic47—22no—
566Dic47—22no—
567Dic47—22no—
568Dic47—24no—
569Dic47—41no—
570Dic47—42no—
571Dic47—41no—
572Dic47—41no—
573Dic47—42no—
574C22×#126—471no—
575C22×#124—471no—
576#2662—472no—
577#2662—471no—
578#2662—472no—
579#2662—471no—
580#2662—471no—
581#2662—471no—
582#2662—472no—
583#2662—472no—
584#2662—471no—
585#2662—471no—
586#2662—471no—
587#2662D4711yescharacteristic, direct product factor
588C2×#396—472no—
589C2×#395—471no—
590C2×#394—472no—
591C2×#394—471no—
592C2×#393—471no—
593C2×#392—471no—
594C2×#390—472no—
595C2×#388—472no—
596C2×C4×C4⋊C4—471no—
597C2×C47—82no—
598C2×C47—81no—
599C2×C47C2×#53211yescharacteristic
600C2×C47C2×#53511yescharacteristic
601C2×C47C2×#53711yescharacteristic
602C2×C47C2×#53812yes—
603C2×C47C2×#54212yes—
604D47—82no—
605D47—81no—
606D47#266218yesdirect product factor
607C23×Q8—471no—
608C23×D4—471no—
609C23×D4—472no—
610C2×#126—471no—
611C2×#126—471no—
612C2×#126—471no—
613C2×#126—471no—
614C2×#126—471no—
615C2×#126—471no—
616C2×#126—471no—
617C2×#126—948no—
618C2×#126C2×D4711yescharacteristic, complemented
619C2×#124—471no—
620C2×#124—471no—
621C2×#124—472no—
622C2×#124—472no—
623C2×#124—471no—
624C2×#124—948no—
625C2×#124C2×D4711yescharacteristic, complemented
626C22×C4⋊C4—471no—
627C22×C4⋊C4—472no—
628C22×C4⋊C4—471no—
629C22×C4⋊C4—471no—
630C22×C4⋊C4—472no—
631C22×C22⋊C4—471no—
632C22×C22⋊C4—472no—
633C22×C22⋊C4—471no—
634C22×C22⋊C4—472no—
635C22×C22⋊C4—472no—
636C22×C22⋊C4—471no—
637C22×C22⋊C4—472no—
638C22×C22⋊C4—472no—
639C22×C22⋊C4—472no—
640C22×C42—471no—
641C22×C42—472no—
642#396—472no—
643#396—472no—
644#396—472no—
645#396—472no—
646#396—472no—
647#396—472no—
648#396—472no—
649#396C2×D4712yescomplemented
650#395—471no—
651#395—472no—
652#395—471no—
653#395—472no—
654#395—471no—
655#395C2×D4711yescharacteristic, complemented
656#394—471no—
657#394—472no—
658#394—471no—
659#394—472no—
660#394—472no—
661#394—472no—
662#394—472no—
663#394—472no—
664#394—472no—
665#394—472no—
666#394—471no—
667#394—472no—
668#394C2×D4711yescharacteristic, complemented
669#394C2×D4712yescomplemented
670#393—471no—
671#393—472no—
672#393—471no—
673#393—472no—
674#393—471no—
675#393C2×D4711yescharacteristic, complemented
676#392—472no—
677#392—471no—
678#392—472no—
679#392—471no—
680#392—471no—
681#392C2×D4711yescharacteristic
682#390—472no—
683#390—472no—
684#390—472no—
685#390—472no—
686#390—472no—
687#390—472no—
688#390—472no—
689#390C2×D4712yescomplemented
690#388—472no—
691#388—472no—
692#388—472no—
693#388—472no—
694#388—472no—
695#388—472no—
696#388—472no—
697#388C2×D4712yescomplemented
698C4×C4⋊C4—472no—
699C4×C4⋊C4—471no—
700C4×C4⋊C4—472no—
701C4×C4⋊C4—471no—
702C4×C4⋊C4—471no—
703C4×C4⋊C4C2×D4711yescharacteristic, complemented
704C2×#95—471no—
705C2×#95—471no—
706C2×#95—472no—
707C2×#95—472no—
708C47C2×#266211yescharacteristic, complemented, Sylow
709C25—471no—
710C25—472no—
711C22×Q8—472no—
712C22×Q8—471no—
713C22×Q8—944no—
714C22×Q8—1884no—
715C22×Q8C22×D4711yescharacteristic
716C22×D4—472no—
717C22×D4—472no—
718C22×D4—472no—
719C22×D4—471no—
720C22×D4—472no—
721C22×D4—944no—
722C22×D4—948no—
723C22×D4—1884no—
724C22×D4—1884no—
725C22×D4—1884no—
726C22×D4C22×D4711yescharacteristic
727C22×D4C22×D4712yes—
728C23×C4—471no—
729C23×C4—471no—
730C23×C4—472no—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—471no—
734C23×C4—471no—
735C23×C4—472no—
736C23×C4—472no—
737#126—24no—
738#126—944no—
739#126—944no—
740#126—944no—
741#126—944no—
742#126—944no—
743#126—944no—
744#126—944no—
745#124—24no—
746#124—948no—
747#124—948no—
748#124—944no—
749#124—944no—
750#124—944no—
751C2×C4⋊C4—471no—
752C2×C4⋊C4—471no—
753C2×C4⋊C4—471no—
754C2×C4⋊C4—471no—
755C2×C4⋊C4—471no—
756C2×C4⋊C4—471no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—471no—
759C2×C4⋊C4—471no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—472no—
762C2×C4⋊C4—472no—
763C2×C4⋊C4—472no—
764C2×C4⋊C4—472no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—944no—
767C2×C4⋊C4—944no—
768C2×C4⋊C4—944no—
769C2×C4⋊C4—948no—
770C2×C4⋊C4—1884no—
771C2×C4⋊C4C22×D4711yescharacteristic
772C2×C4⋊C4C22×D4711yescharacteristic
773C2×C4⋊C4C22×D4711yescharacteristic
774C2×C4⋊C4C22×D4712yes—
775C2×C4⋊C4C22×D4712yes—
776C2×C22⋊C4—472no—
777C2×C22⋊C4—472no—
778C2×C22⋊C4—471no—
779C2×C22⋊C4—471no—
780C2×C22⋊C4—471no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—472no—
785C2×C22⋊C4—472no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—471no—
788C2×C22⋊C4—471no—
789C2×C22⋊C4—471no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—472no—
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—948no—
804C2×C22⋊C4—948no—
805C2×C22⋊C4—944no—
806C2×C22⋊C4—944no—
807C2×C22⋊C4—944no—
808C2×C22⋊C4—948no—
809C2×C22⋊C4—1884no—
810C2×C22⋊C4—1884no—
811C2×C22⋊C4—1884no—
812C2×C22⋊C4C22×D4712yes—
813C2×C22⋊C4C22×D4712yes—
814C2×C22⋊C4C22×D4711yescharacteristic
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×C42—471no—
822C2×C42—471no—
823C2×C42—471no—
824C2×C42—478no—
825C2×C42—472no—
826C2×C42—472no—
827C2×C42—472no—
828C2×C42—1884no—
829C2×C42C22×D4712yes—
830C2×C42C22×D4711yescharacteristic
831#95—471no—
832#95—472no—
833#95—472no—
834#95—471no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95C22×D4711yescharacteristic
842#95C22×D4711yescharacteristic
843#95C22×D4712yes—
844#95C22×D4712yes—
845C24—471no—
846C24—471no—
847C24—472no—
848C24—942no—
849C24—944no—
850C24—944no—
851C24—944no—
852C24—944no—
853C24—944no—
854C24—944no—
855C24—944no—
856C24—944no—
857C24—942no—
858C24—942no—
859C24—944no—
860C24C23×D4711yescharacteristic
861C24C23×D4712yes—
862C2×Q8—22no—
863C2×Q8—42no—
864C2×Q8—944no—
865C2×Q8—942no—
866C2×Q8—1882no—
867C2×Q8—1882no—
868C2×Q8—1882no—
869C2×Q8—18816no—
870C2×D4—22no—
871C2×D4—24no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—944no—
878C2×D4—942no—
879C2×D4—944no—
880C2×D4—1882no—
881C2×D4—1882no—
882C2×D4—1882no—
883C2×D4—18832no—
884C2×D4—18816no—
885C2×D4—1882no—
886C2×D4—1882no—
887C2×D4—1882no—
888C2×D4—1882no—
889C2×D4—1882no—
890C2×D4—1882no—
891C22×C4—472no—
892C22×C4—471no—
893C22×C4—471no—
894C22×C4—471no—
895C22×C4—474no—
896C22×C4—474no—
897C22×C4—474no—
898C22×C4—478no—
899C22×C4—472no—
900C22×C4—471no—
901C22×C4—471no—
902C22×C4—472no—
903C22×C4—471no—
904C22×C4—942no—
905C22×C4—944no—
906C22×C4—944no—
907C22×C4—944no—
908C22×C4—942no—
909C22×C4—944no—
910C22×C4—944no—
911C22×C4—944no—
912C22×C4—942no—
913C22×C4—942no—
914C22×C4—942no—
915C22×C4—944no—
916C22×C4—942no—
917C22×C4—944no—
918C22×C4—944no—
919C22×C4—944no—
920C22×C4—944no—
921C22×C4—944no—
922C22×C4—942no—
923C22×C4C23×D4712yes—
924C22×C4C23×D4711yescharacteristic
925C22×C4C23×D4711yescharacteristic
926C22×C4C23×D4712yes—
927C22×C4C23×D4711yescharacteristic
928C22×C4C23×D4711yescharacteristic
929C22×C4C23×D4711yescharacteristic
930C22×C4C23×D4711yescharacteristic
931C22×C4C23×D4712yes—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—24no—
936C4⋊C4—42no—
937C4⋊C4—944no—
938C4⋊C4—942no—
939C4⋊C4—942no—
940C4⋊C4—942no—
941C4⋊C4—944no—
942C4⋊C4—942no—
943C4⋊C4—942no—
944C4⋊C4—942no—
945C4⋊C4—942no—
946C4⋊C4—942no—
947C4⋊C4—942no—
948C4⋊C4—944no—
949C4⋊C4—1882no—
950C4⋊C4—1882no—
951C4⋊C4—1882no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—24no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—944no—
962C22⋊C4—944no—
963C22⋊C4—944no—
964C22⋊C4—942no—
965C22⋊C4—942no—
966C22⋊C4—942no—
967C22⋊C4—944no—
968C22⋊C4—944no—
969C22⋊C4—944no—
970C22⋊C4—942no—
971C22⋊C4—942no—
972C22⋊C4—942no—
973C22⋊C4—944no—
974C22⋊C4—944no—
975C22⋊C4—942no—
976C22⋊C4—942no—
977C22⋊C4—942no—
978C22⋊C4—944no—
979C22⋊C4—1882no—
980C22⋊C4—1882no—
981C22⋊C4—1882no—
982C22⋊C4—1882no—
983C22⋊C4—1882no—
984C22⋊C4—1882no—
985C22⋊C4—1882no—
986C22⋊C4—1882no—
987C22⋊C4—1882no—
988C42—42no—
989C42—474no—
990C42—474no—
991C42—474no—
992C42—1882no—
993C42—1882no—
994C42—1882no—
995C42D4×D4714yescomplemented
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—472no—
1009C23—474no—
1010C23—474no—
1011C23—472no—
1012C23—472no—
1013C23—941no—
1014C23—942no—
1015C23—942no—
1016C23—942no—
1017C23—942no—
1018C23—942no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—941no—
1023C23—941no—
1024C23—942no—
1025C23—1888no—
1026C23—1888no—
1027C23—1888no—
1028C23—1884no—
1029C23—1888no—
1030C23—1884no—
1031C23—1884no—
1032C23—1888no—
1033C23—1888no—
1034C23—1888no—
1035C23—1888no—
1036C23—1888no—
1037C23C24×D4711yescharacteristic
1038Q8—44no—
1039Q8—1884no—
1040Q8—1888no—
1041D4—44no—
1042D4—48no—
1043D4—1884no—
1044D4—1888no—
1045D4—1888no—
1046D4—1888no—
1047D4—1888no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—472no—
1068C2×C4—472no—
1069C2×C4—472no—
1070C2×C4—474no—
1071C2×C4—948no—
1072C2×C4—948no—
1073C2×C4—9416no—
1074C2×C4—948no—
1075C2×C4—942no—
1076C2×C4—941no—
1077C2×C4—942no—
1078C2×C4—942no—
1079C2×C4—942no—
1080C2×C4—941no—
1081C2×C4—942no—
1082C2×C4—941no—
1083C2×C4—941no—
1084C2×C4—941no—
1085C2×C4—942no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—941no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—941no—
1094C2×C4—1884no—
1095C2×C4—1884no—
1096C2×C4—1884no—
1097C2×C4—1888no—
1098C2×C4—1888no—
1099C2×C4C2×D4×D4712yes—
1100C2×C4C2×D4×D4712yes—
1101C2×C4C2×D4×D4712yes—
1102C2×C4#41×D4714yes—
1103C22—41no—
1104C22—42no—
1105C22—42no—
1106C22—41no—
1107C22—41no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—474no—
1116C22—474no—
1117C22—474no—
1118C22—478no—
1119C22—478no—
1120C22—37616no—
1121C22—3768no—
1122C22—1881no—
1123C22—1882no—
1124C22—1882no—
1125C22—1881no—
1126C22—1881no—
1127C22—1882no—
1128C22—1882no—
1129C22—1882no—
1130C22—1882no—
1131C22—1882no—
1132C22—1882no—
1133C22—1882no—
1134C22C22×D4×D4711yescharacteristic
1135C22C2×#41×D4712yes—
1136C22H(5,𝔽2)×D4712yes—
1137C22H(5,𝔽2)×D4711yescharacteristic
1138C222−1+4×D4711yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—22no—
1142C4—24no—
1143C4—41no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—942no—
1149C4—942no—
1150C4—942no—
1151C4—944no—
1152C4—1881no—
1153C4—1882no—
1154C4—1881no—
1155C4—1881no—
1156C4—1882no—
1157C2—82no—
1158C2—81no—
1159C2—478no—
1160C2—3762no—
1161C2—3761no—
1162C2#532×D4711yescharacteristic
1163C2#535×D4711yescharacteristic
1164C2#537×D4711yescharacteristic
1165C2#538×D4712yes—
1166C2#542×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2662C2
prime radical#392×D47C2
hypercenter#2662D47
hypocenterC47C2×#2662
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2662

Complements

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

NH ≅ G/Ntype
1. C2×#126×D47C2semidirect
2. C2×#124×D47C2semidirect
3. #20249534C2semidirect
4. #20249533C2semidirect
5. #20249532C2semidirect
6. #20249531C2semidirect
7. #20249530C2semidirect
8. #20249529C2semidirect
9. #20249528C2semidirect
10. #20249527C2semidirect
11. #20249526C2semidirect
12. #20249525C2semidirect
13. #20249524C2semidirect
14. #396×D47C2semidirect
15. #395×D47C2semidirect
16. #394×D47C2semidirect
17. #394×D47C2semidirect
18. #393×D47C2semidirect
20. #390×D47C2semidirect
21. #388×D47C2semidirect
22. C4×C4⋊C4×D47C2semidirect
23. C47×#2662C2semidirect
27. C2×#13094019C22semidirect
28. C2×#13094019C22semidirect
29. C2×#13094019C22semidirect
30. C2×#13094018C22semidirect
31. C2×#13094017C22semidirect
32. C2×#13094017C22semidirect
33. C2×#13094017C22semidirect
35. C2×#13094013C22semidirect
36. C2×#13094012C22semidirect
37. C2×#13094011C22semidirect
38. C2×#13094010C22semidirect
39. C2×#13094010C22semidirect
57. #15689047C22semidirect
58. #15689046C22semidirect
59. #15689046C22semidirect
60. #15689046C22semidirect
61. #15689045C22semidirect
62. #15689045C22semidirect
63. #15689045C22semidirect
64. #15689044C22semidirect
65. #15689044C22semidirect
66. #15689043C22semidirect
67. #15689043C22semidirect
68. #15689042C22semidirect
69. #15689041C22semidirect
70. #15689041C22semidirect
71. #15689040C22semidirect
72. #15689040C22semidirect
73. #15689039C22semidirect
74. #15689039C22semidirect
75. #15689039C22semidirect
76. #15689038C22semidirect
77. #15689038C22semidirect
78. #15689038C22semidirect
79. #15689037C22semidirect
80. #15689037C22semidirect
81. #15689036C22semidirect
82. #15689036C22semidirect
83. #15689035C22semidirect
84. #15689035C22semidirect
85. #15689034C22semidirect
91. #15689026C22semidirect
92. #15689025C22semidirect
93. #15689024C22semidirect
94. #15689023C22semidirect
95. #15689023C22semidirect
96. #15689023C22semidirect
97. #15689023C22semidirect
98. #15689017C22semidirect
99. #15689016C22semidirect
100. #15689015C22semidirect
101. #15689014C22semidirect
102. #15689013C22semidirect
103. #15689012C22semidirect
104. #15689011C22semidirect
105. C4⋊C4×Dic47C22semidirect
106. C4×Dic47⋊C4C22semidirect
107. C4×C4⋊Dic47C22semidirect
108. #15688974C22semidirect
109. #15688974C22semidirect
114. C2×#126×C47C22semidirect
115. C2×#124×C47C22semidirect
116. C47×#396C22semidirect
117. C47×#395C22semidirect
118. C47×#394C22semidirect
119. C47×#394C22semidirect
120. C47×#393C22semidirect
122. C47×#390C22semidirect
123. C47×#388C22semidirect
124. C4×C4⋊C4×C47C22semidirect
225. C42×D47D4semidirect
363. C42×C47C2×D4semidirect
409. C4×Dic47C2×D4semidirect
410. C4×Dic47C2×D4semidirect
411. C4×Dic47C2×D4semidirect
587. #2662D47direct (N × H)
606. D47#2662direct (N × H)
618. C2×#126C2×D47semidirect
625. C2×#124C2×D47semidirect
649. #396C2×D47semidirect
655. #395C2×D47semidirect
668. #394C2×D47semidirect
669. #394C2×D47semidirect
675. #393C2×D47semidirect
689. #390C2×D47semidirect
697. #388C2×D47semidirect
703. C4×C4⋊C4C2×D47semidirect
708. C47C2×#2662semidirect
995. C42D4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D472
C2×#124×D472
#202495342
#202495332
#202495322
#202495312
#202495302
#202495292
#202495282
#202495272
#202495262
#202495252
#202495242
#396×D472
#395×D472
#394×D472
#393×D472
#392×D472
#390×D472
#388×D472
C4×C4⋊C4×D472
C47×#26622
C2×#266247