Finite Group Databasebeta

← D47×#2636 #26382993

Subgroups — D47×#2636 #26382993

Order 12032.

3218 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D47C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20249292C212yesmaximal, complemented
4#20249291C212yesmaximal, complemented
5#20249290C212yesmaximal, complemented
6#20249289C212yesmaximal, complemented
7#20249288C211yesmaximal, characteristic, complemented
8#20249287C211yesmaximal, characteristic, complemented
9#20249286C211yesmaximal, characteristic, complemented
10#20249285C211yesmaximal, characteristic, complemented
11#20249284C211yesmaximal, characteristic, complemented
12#20249283C211yesmaximal, characteristic, complemented
13#20249282C211yesmaximal, characteristic, complemented
14#400×D47C211yesmaximal, characteristic, complemented
15#399×D47C211yesmaximal, characteristic, complemented
16#396×D47C212yesmaximal, complemented
17#394×D47C211yesmaximal, characteristic, complemented
18#394×D47C212yesmaximal, complemented
19#392×D47C211yesmaximal, characteristic
20#386×D47C212yesmaximal, complemented
21#385×D47C212yesmaximal, complemented
22#382×D47C211yesmaximal, characteristic, complemented
23C47×#2636C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C22×D4×D47C2212yes—
26C23×C4×D47C2212yes—
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×C4×D188C2211yescharacteristic, complemented
36C2×D4×Dic47C2211yescharacteristic, complemented
37C2×#13093986C2211yescharacteristic, complemented
38C2×C4×C22⋊D47C2212yescomplemented
39C2×(C22⋊D47)⋊C4C2212yescomplemented
40C4×D4×D47—28no—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C4⋊C4×D47C2211yescharacteristic
45C2×C4⋊C4×D47C2212yes—
46C2×C4⋊C4×D47C2212yes—
47C2×C22⋊C4×D47C2212yes—
48C2×C22⋊C4×D47C2211yescharacteristic
49C2×C22⋊C4×D47C2212yes—
50C2×C22⋊C4×D47C2211yescharacteristic
51C2×C22⋊C4×D47C2211yescharacteristic
52C2×C22⋊C4×D47C2212yes—
53C2×C22⋊C4×D47C2212yes—
54C2×C22⋊C4×D47C2212yes—
55C2×C42×D47C2211yescharacteristic
56#15689065C2212yescomplemented
57#15689064C2212yescomplemented
58#15689063C2211yescharacteristic, complemented
59#15689062C2211yescharacteristic, complemented
60#15689061C2211yescharacteristic, complemented
61#15689060C2211yescharacteristic, complemented
62#15689059C2211yescharacteristic, complemented
63#15689059C2212yescomplemented
64#15689058C2211yescharacteristic, complemented
65#15689058C2212yescomplemented
66#15689047C2212yescomplemented
67#15689046C2212yescomplemented
68#15689046C2212yescomplemented
69#15689046C2212yescomplemented
70#15689045C2212yescomplemented
71#15689045C2212yescomplemented
72#15689045C2212yescomplemented
73#15689041C2211yescharacteristic, complemented
74#15689041C2212yescomplemented
75#15689040C2211yescharacteristic, complemented
76#15689040C2212yescomplemented
77#15689039C2212yescomplemented
78#15689039C2212yescomplemented
79#15689039C2212yescomplemented
80#15689038C2212yescomplemented
81#15689038C2212yescomplemented
82#15689038C2212yescomplemented
83#15689037C2211yescharacteristic, complemented
84#15689037C2212yescomplemented
85#15689033C2211yescharacteristic
86#15689032C2211yescharacteristic
87#15689032C2212yes—
88#15689031C2211yescharacteristic
89#15689031C2212yes—
90#15689003C2212yescomplemented
91#15689002C2212yescomplemented
92#15689001C2212yescomplemented
93#15689001C2212yescomplemented
94#15689000C2212yescomplemented
95#15688999C2212yescomplemented
96#15688999C2212yescomplemented
97#15688998C2212yescomplemented
98#15688997C2212yescomplemented
99#15688997C2212yescomplemented
100#15688996C2212yescomplemented
101#15688995C2212yescomplemented
102#15688994C2212yescomplemented
103#15688994C2212yescomplemented
104#15688989C2211yescharacteristic, complemented
105#15688988C2212yescomplemented
106#15688987C2211yescharacteristic, complemented
107#15688987C2211yescharacteristic, complemented
108#15688987C2212yescomplemented
109#95×D47C2212yes—
110#95×D47C2211yescharacteristic
111#95×D47C2211yescharacteristic
112#95×D47C2212yes—
113#95×D47C2212yes—
114C2×#126×C47C2211yescharacteristic, complemented
115C2×C4×D4×C47C2211yescharacteristic, complemented
116C47×#400C2211yescharacteristic, complemented
117C47×#399C2211yescharacteristic, complemented
118C47×#396C2212yescomplemented
119C47×#394C2211yescharacteristic, complemented
120C47×#394C2212yescomplemented
121C47×#392C2211yescharacteristic
122C47×#386C2212yescomplemented
123C47×#385C2212yescomplemented
124C47×#382C2211yescharacteristic, complemented
125C24×D47C2311yescharacteristic
126C24×D47C2312yes—
127C22×D188C2311yescharacteristic
128C22×D188C2312yes—
129C22×C22⋊D47C2312yes—
130C22×C22⋊D47C2312yes—
131C22×C22⋊D47C2312yes—
132C2×D4×D47—28no—
133C2×D4×D47—28no—
134C2×D4×D47—24no—
135C2×D4×D47—44no—
136C2×D4×D47—44no—
137C23×Dic47C2312yes—
138C22×C4×D47—28no—
139C22×C4×D47—44no—
140C22×C4×D47—44no—
141C22×C4×D47C2312yes—
142C22×C4×D47C2311yescharacteristic
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145C22×C4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2312yes—
151C22×C4×D47C2312yes—
152#13094019—24no—
153#13094019—24no—
154#13094019—24no—
155#13094018—24no—
156#13094017—24no—
157#13094017—24no—
158#13094017—24no—
159C4×D188—24no—
160D4×Dic47—24no—
161#13093986—24no—
162C4×C22⋊D47—28no—
163(C22⋊D47)⋊C4—28no—
164C2×C4⋊Dic47C2311yescharacteristic
165C2×C4⋊Dic47C2311yescharacteristic
166C2×C4⋊Dic47C2311yescharacteristic
167C2×C4⋊Dic47C2311yescharacteristic
168C2×C4⋊Dic47C2312yes—
169C2×C4⋊Dic47C2312yes—
170C2×Dic47⋊C4C2311yescharacteristic
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2311yescharacteristic
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C4⋊C4×D47—24no—
182C4⋊C4×D47—24no—
183C4⋊C4×D47—24no—
184C4⋊C4×D47—24no—
185C4⋊C4×D47—44no—
186C4⋊C4×D47—44no—
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2311yescharacteristic
189C2×C22⋊Dic47C2311yescharacteristic
190C2×C22⋊Dic47C2311yescharacteristic
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2311yescharacteristic
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C2×(C2×D47)⋊C4C2311yescharacteristic
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2312yes—
210C2×(C2×D47)⋊C4C2312yes—
211C22⋊C4×D47—28no—
212C22⋊C4×D47—28no—
213C22⋊C4×D47—24no—
214C22⋊C4×D47—24no—
215C22⋊C4×D47—24no—
216C22⋊C4×D47—44no—
217C22⋊C4×D47—44no—
218C22⋊C4×D47—44no—
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2311yescharacteristic
222C42×D47D418yescomplemented
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2311yescharacteristic
229C47⋊#95C2311yescharacteristic
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C22×D4×C47C2311yescharacteristic
237C22×D4×C47C2312yes—
238C23×C4×C47C2312yes—
239#126×C47—24no—
240C4×D4×C47—24no—
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2312yes—
246C2×C4⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2311yescharacteristic
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2311yescharacteristic
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C22⋊C4×C47C2312yes—
255C2×C42×C47C2311yescharacteristic
256#95×C47C2312yes—
257#95×C47C2311yescharacteristic
258#95×C47C2311yescharacteristic
259#95×C47C2312yes—
260#95×C47C2312yes—
261C24×C47C2411yescharacteristic
262C24×C47C2412yes—
263C23×D47—24no—
264C23×D47—24no—
265C23×D47—24no—
266C23×D47—24no—
267C23×D47—24no—
268C23×D47—24no—
269C23×D47—22no—
270C23×D47—24no—
271C23×D47—24no—
272C23×D47—22no—
273C23×D47—22no—
274C23×D47#4118yes—
275C23×D47C2411yescharacteristic
276C23×D47C2412yes—
277C23×D47C2411yescharacteristic
278C2×D4×C47—24no—
279C2×D4×C47—24no—
280C2×D4×C47—22no—
281C2×D4×C47—42no—
282C2×D4×C47—42no—
283C22×C4×C47—24no—
284C22×C4×C47—42no—
285C22×C4×C47—42no—
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2412yes—
290C22×C4×C47C2412yes—
291C22×C4×C47C2412yes—
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C2×C22⋊D47—24no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—24no—
298C2×C22⋊D47—24no—
299C2×C22⋊D47—24no—
300C2×C22⋊D47—42no—
301C2×C22⋊D47—42no—
302C2×C22⋊D47—42no—
303C2×C22⋊D47—42no—
304C22×Dic47—24no—
305C22×Dic47—42no—
306C22×Dic47—42no—
307C22×Dic47C2412yes—
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2412yes—
311C22×Dic47C2412yes—
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2411yescharacteristic
315C22×Dic47C2411yescharacteristic
316D4×D47—232no—
317D4×D47—432no—
318C2×D188—24no—
319C2×D188—22no—
320C2×D188—24no—
321C2×D188—42no—
322C2×D188—42no—
323C2×C4×D47—24no—
324C2×C4×D47—22no—
325C2×C4×D47—24no—
326C2×C4×D47—22no—
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—24no—
334C2×C4×D47—22no—
335C2×C4×D47—24no—
336C2×C4×D47—24no—
337C2×C4×D47—24no—
338C2×C4×D47—24no—
339C2×C4×D47—24no—
340C2×C4×D47—24no—
341C2×C4×D47—24no—
342C2×C4×D47—22no—
343C2×C4×D47—24no—
344C2×C4×D47—24no—
345C2×C4×D47—432no—
346C2×C4×D47—42no—
347C2×C4×D47—42no—
348C2×C4×D47—42no—
349C2×C4×D47—42no—
350C2×C4×D47C2×D414yes—
351C2×C4×D47C2×D414yes—
352C2×C4×D47C2×D414yes—
353C4⋊C4×C47—22no—
354C4⋊C4×C47—22no—
355C4⋊C4×C47—22no—
356C4⋊C4×C47—22no—
357C4⋊C4×C47—42no—
358C4⋊C4×C47—42no—
359C22⋊C4×C47—24no—
360C22⋊C4×C47—24no—
361C22⋊C4×C47—22no—
362C22⋊C4×C47—22no—
363C22⋊C4×C47—22no—
364C22⋊C4×C47—42no—
365C22⋊C4×C47—42no—
366C22⋊C4×C47—42no—
367C42×C47C2×D414yescomplemented
368C22⋊Dic47—24no—
369C22⋊Dic47—24no—
370C22⋊Dic47—22no—
371C22⋊Dic47—22no—
372C22⋊Dic47—22no—
373C22⋊Dic47—42no—
374C22⋊Dic47—42no—
375C22⋊Dic47—42no—
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—24no—
378(C2×D47)⋊C4—24no—
379(C2×D47)⋊C4—22no—
380(C2×D47)⋊C4—22no—
381(C2×D47)⋊C4—22no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—22no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—22no—
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—
391(C2×D47)⋊C4—42no—
392C4⋊Dic47—22no—
393C4⋊Dic47—22no—
394C4⋊Dic47—22no—
395C4⋊Dic47—22no—
396C4⋊Dic47—42no—
397C4⋊Dic47—42no—
398Dic47⋊C4—22no—
399Dic47⋊C4—22no—
400Dic47⋊C4—22no—
401Dic47⋊C4—24no—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—22no—
405Dic47⋊C4—42no—
406Dic47⋊C4—42no—
407Dic47⋊C4—42no—
408Dic47⋊C4—42no—
409C4×Dic47C2×D414yescomplemented
410C4×Dic47C2×D414yescomplemented
411C4×Dic47C2×D414yescomplemented
412C23×C47—22no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—21no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—21no—
422C23×C47—21no—
423C23×C47C2×#4114yes—
424C23×C47C2511yescharacteristic
425C22×D47—22no—
426C22×D47—22no—
427C22×D47—22no—
428C22×D47—22no—
429C22×D47—22no—
430C22×D47—22no—
431C22×D47—216no—
432C22×D47—216no—
433C22×D47—216no—
434C22×D47—21no—
435C22×D47—22no—
436C22×D47—22no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—48no—
440C22×D47—48no—
441C22×D47—48no—
442C22×D47—48no—
443C22×D47—44no—
444C22×D47—44no—
445C22×D47—44no—
446C22×D47—48no—
447C22×D47—48no—
448C22×D47C22×D412yes—
449C22×D47C2×#4114yes—
450C22×D47C2×#4114yes—
451C22×D47H(5,𝔽2)14yes—
452C22×D47H(5,𝔽2)12yes—
453C22×D472−1+412yes—
454D4×C47—28no—
455D4×C47—48no—
456C2×C4×C47—22no—
457C2×C4×C47—21no—
458C2×C4×C47—22no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
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×C47—48no—
477C2×C4×C47C22×D412yes—
478C2×C4×C47C22×D412yes—
479C2×C4×C47C22×D412yes—
480C22⋊D47—216no—
481C22⋊D47—48no—
482C22⋊D47—48no—
483C2×Dic47—22no—
484C2×Dic47—21no—
485C2×Dic47—22no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—21no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—21no—
503C2×Dic47—48no—
504C2×Dic47C22×D412yes—
505C2×Dic47C22×D412yes—
506C2×Dic47C22×D412yes—
507D188—28no—
508D188—48no—
509C4×D47—28no—
510C4×D47—28no—
511C4×D47—28no—
512C4×D47—48no—
513C4×D47—48no—
514C4×D47—44no—
515C4×D47—44no—
516C4×D47—48no—
517C4×D47—44no—
518C4×D47—48no—
519C4×D47—48no—
520C2×#2636—471nomaximal, Sylow
521C22×C47—24no—
522C22×C47—24no—
523C22×C47—24no—
524C22×C47—42no—
525C22×C47—42no—
526C22×C47—42no—
527C22×C47—42no—
528C22×C47—41no—
529C22×C47—41no—
530C22×C47—41no—
531C22×C47—42no—
532C22×C47—42no—
533C22×C47C23×D411yescharacteristic
534C22×C47C22×#4112yes—
535C22×C47C2×H(5,𝔽2)12yes—
536C22×C47C2×H(5,𝔽2)11yescharacteristic
537C22×C47C2×2−1+411yescharacteristic
538C2×D47—24no—
539C2×D47—24no—
540C2×D47—24no—
541C2×D47—42no—
542C2×D47—42no—
543C2×D47—42no—
544C2×D47—42no—
545C2×D47—432no—
546C2×D47—41no—
547C2×D47—41no—
548C2×D47—41no—
549C2×D47—42no—
550C2×D47—42no—
551C2×D47—88no—
552C2×D47#52514yes—
553C2×D47#53514yes—
554C2×D47#53714yes—
555C2×D47#53818yes—
556C2×D47#53918yes—
557C4×C47—22no—
558C4×C47—22no—
559C4×C47—22no—
560C4×C47—41no—
561C4×C47—42no—
562C4×C47—41no—
563C4×C47—41no—
564C4×C47—42no—
565C4×C47—42no—
566Dic47—22no—
567Dic47—22no—
568Dic47—22no—
569Dic47—41no—
570Dic47—42no—
571Dic47—41no—
572Dic47—41no—
573Dic47—42no—
574Dic47—42no—
575C22×#126—471no—
576C22×C4×D4—471no—
577#2636—471no—
578#2636—471no—
579#2636—472no—
580#2636—471no—
581#2636—472no—
582#2636—471no—
583#2636—472no—
584#2636—472no—
585#2636—471no—
586#2636—471no—
587#2636—471no—
588#2636D4711yescharacteristic, direct product factor
589C2×#400—471no—
590C2×#399—471no—
591C2×#396—472no—
592C2×#394—472no—
593C2×#394—471no—
594C2×#392—471no—
595C2×#386—472no—
596C2×#385—472no—
597C2×#382—471no—
598C2×C47—44no—
599C2×C47—81no—
600C2×C47C2×#52511yescharacteristic
601C2×C47C2×#53511yescharacteristic
602C2×C47C2×#53711yescharacteristic
603C2×C47C2×#53812yes—
604C2×C47C2×#53912yes—
605D47—44no—
606D47—81no—
607D47#263618yesdirect product factor
608C23×D4—471no—
609C23×D4—472no—
610C24×C4—472no—
611C2×#126—471no—
612C2×#126—471no—
613C2×#126—471no—
614C2×#126—471no—
615C2×#126—471no—
616C2×#126—471no—
617C2×#126—471no—
618C2×#126—948no—
619C2×#126C2×D4711yescharacteristic, complemented
620C2×C4×D4—471no—
621C2×C4×D4—472no—
622C2×C4×D4—471no—
623C2×C4×D4—472no—
624C2×C4×D4—471no—
625C2×C4×D4—948no—
626C2×C4×D4C2×D4711yescharacteristic, complemented
627C22×C4⋊C4—471no—
628C22×C4⋊C4—471no—
629C22×C4⋊C4—471no—
630C22×C4⋊C4—471no—
631C22×C4⋊C4—472no—
632C22×C4⋊C4—472no—
633C22×C22⋊C4—471no—
634C22×C22⋊C4—471no—
635C22×C22⋊C4—472no—
636C22×C22⋊C4—472no—
637C22×C22⋊C4—471no—
638C22×C22⋊C4—472no—
639C22×C22⋊C4—472no—
640C22×C22⋊C4—472no—
641C22×C42—471no—
642#400—471no—
643#400—471no—
644#400—471no—
645#400—472no—
646#400—472no—
647#400C2×D4711yescharacteristic, complemented
648#399—472no—
649#399—471no—
650#399—472no—
651#399—471no—
652#399—471no—
653#399C2×D4711yescharacteristic, complemented
654#396—472no—
655#396—472no—
656#396—472no—
657#396—472no—
658#396—472no—
659#396—472no—
660#396—472no—
661#396C2×D4712yescomplemented
662#394—471no—
663#394—472no—
664#394—471no—
665#394—472no—
666#394—472no—
667#394—472no—
668#394—472no—
669#394—472no—
670#394—472no—
671#394—472no—
672#394—471no—
673#394—472no—
674#394C2×D4711yescharacteristic, complemented
675#394C2×D4712yescomplemented
676#392—472no—
677#392—471no—
678#392—472no—
679#392—471no—
680#392—471no—
681#392C2×D4711yescharacteristic
682#386—472no—
683#386—472no—
684#386—472no—
685#386—472no—
686#386—472no—
687#386—472no—
688#386—472no—
689#386C2×D4712yescomplemented
690#385—472no—
691#385—472no—
692#385—472no—
693#385—472no—
694#385—472no—
695#385—472no—
696#385—472no—
697#385C2×D4712yescomplemented
698#382—472no—
699#382—471no—
700#382—471no—
701#382—471no—
702#382—472no—
703#382C2×D4711yescharacteristic, complemented
704C2×#95—471no—
705C2×#95—471no—
706C2×#95—472no—
707C2×#95—472no—
708C2×#95—472no—
709C47C2×#263611yescharacteristic, complemented, Sylow
710C25—472no—
711C25—471no—
712C22×D4—472no—
713C22×D4—472no—
714C22×D4—472no—
715C22×D4—471no—
716C22×D4—472no—
717C22×D4—944no—
718C22×D4—948no—
719C22×D4—948no—
720C22×D4—1884no—
721C22×D4—1884no—
722C22×D4C22×D4711yescharacteristic
723C22×D4C22×D4712yes—
724C23×C4—471no—
725C23×C4—471no—
726C23×C4—471no—
727C23×C4—472no—
728C23×C4—471no—
729C23×C4—471no—
730C23×C4—471no—
731C23×C4—472no—
732C23×C4—472no—
733C23×C4—472no—
734C23×C4—472no—
735C23×C4—472no—
736C23×C4—948no—
737C23×C4—1884no—
738C23×C4—1884no—
739C23×C4C22×D4712yes—
740#126—24no—
741#126—944no—
742#126—944no—
743#126—944no—
744#126—944no—
745#126—944no—
746#126—944no—
747#126—944no—
748C4×D4—24no—
749C4×D4—948no—
750C4×D4—944no—
751C4×D4—948no—
752C4×D4—944no—
753C4×D4—944no—
754C2×C4⋊C4—472no—
755C2×C4⋊C4—471no—
756C2×C4⋊C4—471no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—471no—
759C2×C4⋊C4—471no—
760C2×C4⋊C4—471no—
761C2×C4⋊C4—471no—
762C2×C4⋊C4—471no—
763C2×C4⋊C4—471no—
764C2×C4⋊C4—471no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—472no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—944no—
772C2×C4⋊C4—944no—
773C2×C4⋊C4—944no—
774C2×C4⋊C4—944no—
775C2×C4⋊C4—1884no—
776C2×C4⋊C4—1884no—
777C2×C4⋊C4C22×D4711yescharacteristic
778C2×C4⋊C4C22×D4711yescharacteristic
779C2×C4⋊C4C22×D4711yescharacteristic
780C2×C4⋊C4C22×D4711yescharacteristic
781C2×C4⋊C4C22×D4712yes—
782C2×C4⋊C4C22×D4712yes—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—471no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—471no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—471no—
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—948no—
808C2×C22⋊C4—944no—
809C2×C22⋊C4—944no—
810C2×C22⋊C4—944no—
811C2×C22⋊C4—948no—
812C2×C22⋊C4—1884no—
813C2×C22⋊C4—1884no—
814C2×C22⋊C4—1884no—
815C2×C22⋊C4C22×D4712yes—
816C2×C22⋊C4C22×D4711yescharacteristic
817C2×C22⋊C4C22×D4711yescharacteristic
818C2×C22⋊C4C22×D4711yescharacteristic
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×C42C22×D4711yescharacteristic
828#95—472no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—471no—
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×D4712yes—
842#95C22×D4711yescharacteristic
843#95C22×D4711yescharacteristic
844#95C22×D4712yes—
845#95C22×D4712yes—
846C24—471no—
847C24—478no—
848C24—472no—
849C24—471no—
850C24—944no—
851C24—944no—
852C24—944no—
853C24—944no—
854C24—944no—
855C24—944no—
856C24—942no—
857C24—944no—
858C24—944no—
859C24—942no—
860C24—942no—
861C24C23×D4711yescharacteristic
862C24C23×D4712yes—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—944no—
869C2×D4—944no—
870C2×D4—944no—
871C2×D4—9432no—
872C2×D4—944no—
873C2×D4—944no—
874C2×D4—944no—
875C2×D4—944no—
876C2×D4—942no—
877C2×D4—1882no—
878C2×D4—1882no—
879C2×D4—1882no—
880C2×D4—1882no—
881C2×D4—1882no—
882C2×D4—1882no—
883C2×D4—18832no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—471no—
888C22×C4—471no—
889C22×C4—471no—
890C22×C4—474no—
891C22×C4—474no—
892C22×C4—474no—
893C22×C4—472no—
894C22×C4—471no—
895C22×C4—471no—
896C22×C4—472no—
897C22×C4—472no—
898C22×C4—471no—
899C22×C4—944no—
900C22×C4—942no—
901C22×C4—942no—
902C22×C4—944no—
903C22×C4—944no—
904C22×C4—942no—
905C22×C4—942no—
906C22×C4—942no—
907C22×C4—944no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—942no—
911C22×C4—944no—
912C22×C4—944no—
913C22×C4—944no—
914C22×C4—944no—
915C22×C4—944no—
916C22×C4—944no—
917C22×C4—944no—
918C22×C4—942no—
919C22×C4—944no—
920C22×C4—944no—
921C22×C4—944no—
922C22×C4—1882no—
923C22×C4—1882no—
924C22×C4—1882no—
925C22×C4—1882no—
926C22×C4—18832no—
927C22×C4—1882no—
928C22×C4—1882no—
929C22×C4C23×D4712yes—
930C22×C4C23×D4711yescharacteristic
931C22×C4C23×D4711yescharacteristic
932C22×C4C23×D4712yes—
933C22×C4C23×D4712yes—
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C22×C4C23×D4711yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—944no—
945C4⋊C4—942no—
946C4⋊C4—942no—
947C4⋊C4—942no—
948C4⋊C4—942no—
949C4⋊C4—942no—
950C4⋊C4—942no—
951C4⋊C4—942no—
952C4⋊C4—942no—
953C4⋊C4—942no—
954C4⋊C4—942no—
955C4⋊C4—1882no—
956C4⋊C4—1882no—
957C4⋊C4—1882no—
958C4⋊C4—1882no—
959C4⋊C4—1882no—
960C4⋊C4—1882no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—944no—
970C22⋊C4—942no—
971C22⋊C4—942no—
972C22⋊C4—942no—
973C22⋊C4—944no—
974C22⋊C4—944no—
975C22⋊C4—944no—
976C22⋊C4—942no—
977C22⋊C4—942no—
978C22⋊C4—942no—
979C22⋊C4—944no—
980C22⋊C4—944no—
981C22⋊C4—942no—
982C22⋊C4—942no—
983C22⋊C4—942no—
984C22⋊C4—1882no—
985C22⋊C4—1882no—
986C22⋊C4—1882no—
987C22⋊C4—1882no—
988C22⋊C4—1882no—
989C22⋊C4—1882no—
990C22⋊C4—1882no—
991C22⋊C4—1882no—
992C22⋊C4—1882no—
993C42—474no—
994C42—474no—
995C42—474no—
996C42D4×D4714yescomplemented
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—21no—
1008C23—472no—
1009C23—474no—
1010C23—474no—
1011C23—472no—
1012C23—472no—
1013C23—474no—
1014C23—9416no—
1015C23—9416no—
1016C23—9416no—
1017C23—942no—
1018C23—942no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—942no—
1023C23—941no—
1024C23—942no—
1025C23—942no—
1026C23—941no—
1027C23—941no—
1028C23—1888no—
1029C23—1884no—
1030C23—1884no—
1031C23—1884no—
1032C23—1888no—
1033C23—1888no—
1034C23—1888no—
1035C23—1888no—
1036C23—1888no—
1037C23#41×D4714yes—
1038C23C24×D4711yescharacteristic
1039D4—28no—
1040D4—48no—
1041D4—948no—
1042D4—9416no—
1043D4—1888no—
1044D4—1888no—
1045D4—1888no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—48no—
1067C2×C4—472no—
1068C2×C4—472no—
1069C2×C4—472no—
1070C2×C4—948no—
1071C2×C4—948no—
1072C2×C4—948no—
1073C2×C4—942no—
1074C2×C4—941no—
1075C2×C4—942no—
1076C2×C4—941no—
1077C2×C4—941no—
1078C2×C4—941no—
1079C2×C4—941no—
1080C2×C4—942no—
1081C2×C4—942no—
1082C2×C4—942no—
1083C2×C4—942no—
1084C2×C4—941no—
1085C2×C4—942no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—941no—
1093C2×C4—1888no—
1094C2×C4—1888no—
1095C2×C4—1884no—
1096C2×C4—1884no—
1097C2×C4—1884no—
1098C2×C4—1888no—
1099C2×C4—1888no—
1100C2×C4—1888no—
1101C2×C4—1888no—
1102C2×C4C2×D4×D4712yes—
1103C2×C4C2×D4×D4712yes—
1104C2×C4C2×D4×D4712yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—42no—
1116C22—42no—
1117C22—474no—
1118C22—474no—
1119C22—474no—
1120C22—478no—
1121C22—478no—
1122C22—944no—
1123C22—944no—
1124C22—944no—
1125C22—3768no—
1126C22—18832no—
1127C22—1881no—
1128C22—1881no—
1129C22—1881no—
1130C22—1882no—
1131C22—1882no—
1132C22—1882no—
1133C22—1882no—
1134C22—1882no—
1135C22—1882no—
1136C22C22×D4×D4711yescharacteristic
1137C22C2×#41×D4712yes—
1138C22H(5,𝔽2)×D4712yes—
1139C22H(5,𝔽2)×D4711yescharacteristic
1140C222−1+4×D4711yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—41no—
1145C4—42no—
1146C4—41no—
1147C4—41no—
1148C4—42no—
1149C4—42no—
1150C4—942no—
1151C4—942no—
1152C4—942no—
1153C4—1881no—
1154C4—1882no—
1155C4—1881no—
1156C4—1881no—
1157C4—1882no—
1158C4—1882no—
1159C2—44no—
1160C2—81no—
1161C2—478no—
1162C2—3761no—
1163C2—1884no—
1164C2#525×D4711yescharacteristic
1165C2#535×D4711yescharacteristic
1166C2#537×D4711yescharacteristic
1167C2#538×D4712yes—
1168C2#539×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2636C2
prime radical#392×D47C2
hypercenter#2636D47
hypocenterC47C2×#2636
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2636

Complements

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

NH ≅ G/Ntype
1. C2×#126×D47C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20249292C2semidirect
4. #20249291C2semidirect
5. #20249290C2semidirect
6. #20249289C2semidirect
7. #20249288C2semidirect
8. #20249287C2semidirect
9. #20249286C2semidirect
10. #20249285C2semidirect
11. #20249284C2semidirect
12. #20249283C2semidirect
13. #20249282C2semidirect
14. #400×D47C2semidirect
15. #399×D47C2semidirect
16. #396×D47C2semidirect
17. #394×D47C2semidirect
18. #394×D47C2semidirect
20. #386×D47C2semidirect
21. #385×D47C2semidirect
22. #382×D47C2semidirect
23. C47×#2636C2semidirect
27. C2×#13094019C22semidirect
28. C2×#13094019C22semidirect
29. C2×#13094019C22semidirect
30. C2×#13094018C22semidirect
31. C2×#13094017C22semidirect
32. C2×#13094017C22semidirect
33. C2×#13094017C22semidirect
35. C2×C4×D188C22semidirect
36. C2×D4×Dic47C22semidirect
37. C2×#13093986C22semidirect
38. C2×C4×C22⋊D47C22semidirect
39. C2×(C22⋊D47)⋊C4C22semidirect
56. #15689065C22semidirect
57. #15689064C22semidirect
58. #15689063C22semidirect
59. #15689062C22semidirect
60. #15689061C22semidirect
61. #15689060C22semidirect
62. #15689059C22semidirect
63. #15689059C22semidirect
64. #15689058C22semidirect
65. #15689058C22semidirect
66. #15689047C22semidirect
67. #15689046C22semidirect
68. #15689046C22semidirect
69. #15689046C22semidirect
70. #15689045C22semidirect
71. #15689045C22semidirect
72. #15689045C22semidirect
73. #15689041C22semidirect
74. #15689041C22semidirect
75. #15689040C22semidirect
76. #15689040C22semidirect
77. #15689039C22semidirect
78. #15689039C22semidirect
79. #15689039C22semidirect
80. #15689038C22semidirect
81. #15689038C22semidirect
82. #15689038C22semidirect
83. #15689037C22semidirect
84. #15689037C22semidirect
90. #15689003C22semidirect
91. #15689002C22semidirect
92. #15689001C22semidirect
93. #15689001C22semidirect
94. #15689000C22semidirect
95. #15688999C22semidirect
96. #15688999C22semidirect
97. #15688998C22semidirect
98. #15688997C22semidirect
99. #15688997C22semidirect
100. #15688996C22semidirect
101. #15688995C22semidirect
102. #15688994C22semidirect
103. #15688994C22semidirect
104. #15688989C22semidirect
105. #15688988C22semidirect
106. #15688987C22semidirect
107. #15688987C22semidirect
108. #15688987C22semidirect
114. C2×#126×C47C22semidirect
115. C2×C4×D4×C47C22semidirect
116. C47×#400C22semidirect
117. C47×#399C22semidirect
118. C47×#396C22semidirect
119. C47×#394C22semidirect
120. C47×#394C22semidirect
122. C47×#386C22semidirect
123. C47×#385C22semidirect
124. C47×#382C22semidirect
222. C42×D47D4semidirect
367. C42×C47C2×D4semidirect
409. C4×Dic47C2×D4semidirect
410. C4×Dic47C2×D4semidirect
411. C4×Dic47C2×D4semidirect
588. #2636D47direct (N × H)
607. D47#2636direct (N × H)
619. C2×#126C2×D47semidirect
626. C2×C4×D4C2×D47semidirect
647. #400C2×D47semidirect
653. #399C2×D47semidirect
661. #396C2×D47semidirect
674. #394C2×D47semidirect
675. #394C2×D47semidirect
689. #386C2×D47semidirect
697. #385C2×D47semidirect
703. #382C2×D47semidirect
709. C47C2×#2636semidirect
996. 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×C4×D4×D472
#202492922
#202492912
#202492902
#202492892
#202492882
#202492872
#202492862
#202492852
#202492842
#202492832
#202492822
#400×D472
#399×D472
#396×D472
#394×D472
#392×D472
#386×D472
#385×D472
#382×D472
C47×#26362
C2×#263647