Finite Group Databasebeta

← #26383119

Subgroups — #26383119

Order 12032.

2934 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×#15689653C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3#20249291C212yesmaximal, complemented
4#20249289C212yesmaximal, complemented
5#20249260C212yesmaximal, complemented
6#20249244C212yesmaximal, complemented
7#20249199C211yesmaximal, characteristic, complemented
8#20249197C211yesmaximal, characteristic, complemented
9#20249174C211yesmaximal, characteristic, complemented
10#20249172C211yesmaximal, characteristic, complemented
11#20249128C211yesmaximal, characteristic, complemented
12#20249126C211yesmaximal, characteristic, complemented
13#20249103C211yesmaximal, characteristic, complemented
14#20249102C211yesmaximal, characteristic, complemented
15#20246675C212yesmaximal, complemented
16#20246667C212yesmaximal, complemented
17#20246632C212yesmaximal, complemented
18#20246630C212yesmaximal, complemented
19C4×#13093994C211yesmaximal, characteristic, complemented
20C4×#13093993C211yesmaximal, characteristic, complemented
21C4×#13093992C211yesmaximal, characteristic, complemented
22#20245782C211yesmaximal, characteristic, complemented
23C4×#120×C47C211yesmaximal, characteristic, complemented
24C23×C22⋊D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689653—28no—
27C2×#13094019C2211yescharacteristic, complemented
28C2×#13094017C2211yescharacteristic, complemented
29C2×#13094014C2211yescharacteristic, complemented
30C2×#13094010C2211yescharacteristic, complemented
31C2×#13094008C2211yescharacteristic
32C2×#13094005C2211yescharacteristic
33C2×#13094001C2211yescharacteristic
34C2×#13093996C2211yescharacteristic
35C2×#13093994C2211yescharacteristic
36C2×#13093993C2211yescharacteristic
37C2×#13093992C2211yescharacteristic
38C2×C4×Dic94C2211yescharacteristic, complemented
39C2×C4×D188C2212yescomplemented
40C2×C4×C22⋊D47—28no—
41C2×C4×C22⋊D47C2212yes—
42C2×C4×C22⋊D47C2212yes—
43C2×C4×C22⋊D47C2212yes—
44C2×C4×C22⋊D47C2212yes—
45C2×C4×C22⋊D47C2211yescharacteristic
46C2×C4×C22⋊D47C2211yescharacteristic, complemented
47C2×C4×C22⋊D47C2212yescomplemented
48C2×C4×C22⋊D47C2212yescomplemented
49C2×#13093983C2211yescharacteristic, complemented
50C2×#13093981C2211yescharacteristic, complemented
51C22×Dic47⋊C4C2211yescharacteristic
52C22×C22⋊Dic47C2211yescharacteristic
53C22×(C2×D47)⋊C4C2211yescharacteristic
54C22×C4×Dic47C2211yescharacteristic
55#15689065C2212yescomplemented
56#15689064C2212yescomplemented
57#15689059C2212yescomplemented
58#15689059C2212yescomplemented
59#15689058C2212yescomplemented
60#15689058C2212yescomplemented
61#15689057C2212yescomplemented
62#15689056C2212yescomplemented
63#15689052C2212yescomplemented
64#15689052C2212yescomplemented
65#15689051C2212yescomplemented
66#15689051C2212yescomplemented
67#15689047C2212yescomplemented
68#15689046C2212yescomplemented
69#15689046C2212yescomplemented
70#15689045C2212yescomplemented
71#15689041C2212yescomplemented
72#15689039C2212yes—
73#15689039C2212yes—
74#15689038C2212yes—
75#15689038C2212yes—
76#15689038C2212yescomplemented
77#15689038C2212yescomplemented
78#15689037C2212yescomplemented
79#15689036C2212yescomplemented
80#15689035C2212yescomplemented
81#15689032C2212yes—
82#15689032C2212yes—
83#15689032C2212yescomplemented
84#15689031C2212yes—
85#15689031C2212yes—
86#15689031C2212yescomplemented
87#15689003C2211yescharacteristic
88#15689002C2211yescharacteristic
89#15689002C2212yescomplemented
90#15689001C2212yescomplemented
91#15689000C2211yescharacteristic
92#15688999C2212yescomplemented
93#15688998C2211yescharacteristic
94#15688997C2212yescomplemented
95#15688996C2211yescharacteristic
96#15688996C2212yescomplemented
97#15688995C2211yescharacteristic
98#15688994C2212yescomplemented
99#15688990C2212yescomplemented
100#15688987C2212yescomplemented
101#15688984C2211yescharacteristic
102#15688984C2211yescharacteristic
103#15688981C2211yescharacteristic
104#15688981C2211yescharacteristic
105#15688979C2211yescharacteristic
106#15688978C2211yescharacteristic
107#15688978C2211yescharacteristic
108C4×Dic47⋊C4C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yescomplemented
110C4×(C2×D47)⋊C4C2212yescomplemented
111C4×C22⋊Dic47C2211yescharacteristic
112C4×C22⋊Dic47C2212yescomplemented
113#15688969C2212yescomplemented
114C24×C4×C47C2211yescharacteristic
115C2×#120×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic
117C2×C4×D4×C47C2212yescomplemented
118C47×#386C2211yescharacteristic
119C47×#386C2212yescomplemented
120C47×#385C2211yescharacteristic
121C47×#385C2212yescomplemented
122C47×#379C2211yescharacteristic
123C4×C22⋊C4×C47C2211yescharacteristic
124C4×C22⋊C4×C47C2212yescomplemented
125C24×D47C2311yescharacteristic
126C22×Dic94C2311yescharacteristic
127C22×D188C2312yes—
128C22×C22⋊D47—24no—
129C22×C22⋊D47—24no—
130C22×C22⋊D47—24no—
131C22×C22⋊D47C2311yescharacteristic
132C22×C22⋊D47C2312yes—
133C22×C22⋊D47C2312yes—
134C22×C22⋊D47C2312yes—
135C22×C22⋊D47C2312yes—
136C22×C22⋊D47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C23×Dic47C2311yescharacteristic
139C23×Dic47C2311yescharacteristic
140C22×C4×D47—24no—
141C22×C4×D47—44no—
142C22×C4×D47C2312yes—
143C22×C4×D47C2311yescharacteristic
144C22×C4×D47C2312yes—
145#13094019—24no—
146#13094017—24no—
147#13094014—24no—
148#13094010—24no—
149#13094008—24no—
150#13094005—24no—
151#13094001—24no—
152#13093996—24no—
153#13093994—24no—
154#13093993—24no—
155#13093992—24no—
156C4×Dic94—24no—
157C4×D188—44no—
158C4×C22⋊D47—24no—
159C4×C22⋊D47—28no—
160C4×C22⋊D47—28no—
161C4×C22⋊D47—28no—
162C4×C22⋊D47—28no—
163C4×C22⋊D47—24no—
164C4×C22⋊D47—44no—
165C4×C22⋊D47—44no—
166#13093983—24no—
167#13093981—24no—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2312yes—
172C2×Dic47⋊C4—24no—
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2311yescharacteristic
176C2×Dic47⋊C4C2311yescharacteristic
177C2×Dic47⋊C4C2311yescharacteristic
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×C22⋊Dic47—24no—
186C2×C22⋊Dic47C2311yescharacteristic
187C2×C22⋊Dic47C2311yescharacteristic
188C2×C22⋊Dic47C2312yes—
189C2×C22⋊Dic47C2311yescharacteristic
190C2×C22⋊Dic47C2311yescharacteristic
191C2×C22⋊Dic47C2311yescharacteristic
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2311yescharacteristic
194C2×C22⋊Dic47C2312yes—
195C2×C22⋊Dic47C2312yes—
196C2×C22⋊Dic47C2312yes—
197C2×C22⋊Dic47C2312yes—
198C2×(C2×D47)⋊C4—24no—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2312yes—
205C2×(C2×D47)⋊C4C2311yescharacteristic
206C2×(C2×D47)⋊C4C2312yes—
207C2×(C2×D47)⋊C4C2312yes—
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2312yes—
210C2×(C2×D47)⋊C4C2312yes—
211C2×(C2×D47)⋊C4C2312yes—
212C2×(C2×D47)⋊C4C2312yes—
213C2×C4×Dic47D418yescomplemented
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C25×C47C2311yescharacteristic
234C22×D4×C47C2311yescharacteristic
235C22×D4×C47C2312yes—
236C23×C4×C47—24no—
237C23×C4×C47—44no—
238C23×C4×C47C2312yes—
239C23×C4×C47C2311yescharacteristic
240C23×C4×C47C2311yescharacteristic
241C23×C4×C47C2311yescharacteristic
242C23×C4×C47C2312yes—
243#120×C47—24no—
244C4×D4×C47—24no—
245C4×D4×C47—44no—
246C2×C4⋊C4×C47C2311yescharacteristic
247C2×C4⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2311yescharacteristic
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2311yescharacteristic
251C2×C22⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C22⋊C4×C47C2312yes—
255C2×C22⋊C4×C47C2312yes—
256C2×C42×C47C2312yes—
257C2×C42×C47C2311yescharacteristic
258#95×C47C2312yes—
259#95×C47C2312yes—
260#95×C47C2312yes—
261C24×C47—22no—
262C24×C47—22no—
263C24×C47—42no—
264C24×C47—42no—
265C24×C47#4114yes—
266C24×C47C2411yescharacteristic
267C24×C47C2412yes—
268C24×C47C2411yescharacteristic
269C23×D47—22no—
270C23×D47—22no—
271C23×D47—42no—
272C23×D47—42no—
273C23×D47#4114yes—
274C23×D47C2411yescharacteristic
275C23×D47C2412yes—
276C2×D4×C47—22no—
277C2×D4×C47—24no—
278C2×D4×C47—22no—
279C2×D4×C47—22no—
280C2×D4×C47—42no—
281C2×D4×C47—42no—
282C22×C4×C47—24no—
283C22×C4×C47—22no—
284C22×C4×C47—22no—
285C22×C4×C47—24no—
286C22×C4×C47—24no—
287C22×C4×C47—24no—
288C22×C4×C47—24no—
289C22×C4×C47—24no—
290C22×C4×C47—42no—
291C22×C4×C47—42no—
292C22×C4×C47—42no—
293C22×C4×C47—416no—
294C22×C4×C47C2×D414yes—
295C22×C4×C47C2412yes—
296C22×C4×C47C2411yescharacteristic
297C22×C4×C47C2412yes—
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2412yes—
301C22×C4×C47C2411yescharacteristic
302C22×C4×C47C2411yescharacteristic
303C2×C22⋊D47—232no—
304C2×C22⋊D47—24no—
305C2×C22⋊D47—24no—
306C2×C22⋊D47—24no—
307C2×C22⋊D47—24no—
308C2×C22⋊D47—22no—
309C2×C22⋊D47—24no—
310C2×C22⋊D47—22no—
311C2×C22⋊D47—22no—
312C2×C22⋊D47—24no—
313C2×C22⋊D47—24no—
314C2×C22⋊D47—24no—
315C2×C22⋊D47—22no—
316C2×C22⋊D47—42no—
317C2×C22⋊D47—42no—
318C2×C22⋊D47—42no—
319C2×C22⋊D47—42no—
320C2×C22⋊D47—42no—
321C22×Dic47—22no—
322C22×Dic47—22no—
323C22×Dic47—22no—
324C22×Dic47—42no—
325C22×Dic47—42no—
326C22×Dic47C2×D414yes—
327C22×Dic47C2×D414yes—
328C22×Dic47C2412yes—
329C22×Dic47C2412yes—
330C22×Dic47C2411yescharacteristic
331C22×Dic47C2411yescharacteristic
332C22×Dic47C2412yes—
333C22×Dic47C2411yescharacteristic
334C22×Dic47C2411yescharacteristic
335C22×Dic47C2411yescharacteristic
336C22×Dic47C2411yescharacteristic
337C22×Dic47C2411yescharacteristic
338C2×D188—24no—
339C2×D188—42no—
340C2×D188—42no—
341C2×C4×D47—22no—
342C2×C4×D47—24no—
343C2×C4×D47—24no—
344C2×C4×D47—24no—
345C2×C4×D47—24no—
346C2×C4×D47—24no—
347C2×C4×D47—42no—
348C2×C4×D47—42no—
349C2×C4×D47—416no—
350C2×Dic94—22no—
351C2×Dic94—42no—
352C4⋊C4×C47—22no—
353C4⋊C4×C47—42no—
354C22⋊C4×C47—22no—
355C22⋊C4×C47—24no—
356C22⋊C4×C47—22no—
357C22⋊C4×C47—22no—
358C22⋊C4×C47—22no—
359C22⋊C4×C47—42no—
360C22⋊C4×C47—42no—
361C22⋊C4×C47—42no—
362C42×C47—22no—
363C42×C47—24no—
364C22⋊Dic47—22no—
365C22⋊Dic47—22no—
366C22⋊Dic47—24no—
367C22⋊Dic47—22no—
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—22no—
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—42no—
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—
390C4⋊Dic47—22no—
391C4⋊Dic47—22no—
392C4⋊Dic47—22no—
393C4⋊Dic47—42no—
394Dic47⋊C4—22no—
395Dic47⋊C4—24no—
396Dic47⋊C4—24no—
397Dic47⋊C4—22no—
398Dic47⋊C4—22no—
399Dic47⋊C4—22no—
400Dic47⋊C4—22no—
401Dic47⋊C4—22no—
402Dic47⋊C4—42no—
403Dic47⋊C4—42no—
404Dic47⋊C4—42no—
405Dic47⋊C4—42no—
406C4×Dic47—22no—
407C4×Dic47—24no—
408C4×Dic47C2×D414yes—
409C4×Dic47C2×D414yes—
410C4×Dic47C2×D414yes—
411C4×Dic47C2×D414yes—
412C23×C47—22no—
413C23×C47—22no—
414C23×C47—28no—
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—21no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—48no—
427C23×C47—44no—
428C23×C47—44no—
429C23×C47—48no—
430C23×C47C22×D412yes—
431C23×C47C2×#4112yes—
432C23×C47C2×#4114yes—
433C23×C47C2×#4112yes—
434C23×C47C2511yescharacteristic
435C22×D47—28no—
436C22×D47—22no—
437C22×D47—22no—
438C22×D47—22no—
439C22×D47—22no—
440C22×D47—22no—
441C22×D47—22no—
442C22×D47—21no—
443C22×D47—21no—
444C22×D47—21no—
445C22×D47—22no—
446C22×D47—22no—
447C22×D47—48no—
448C22×D47—44no—
449C22×D47—44no—
450C22×D47—48no—
451C22×D47C2×#4114yes—
452D4×C47—48no—
453D4×C47—44no—
454C2×C4×C47—22no—
455C2×C4×C47—28no—
456C2×C4×C47—21no—
457C2×C4×C47—22no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—22no—
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—48no—
473C2×C4×C47—44no—
474C2×C4×C47—44no—
475C2×C4×C47—48no—
476C2×C4×C47C22×D412yes—
477C2×C4×C47C22×D412yes—
478C2×C4×C47H(5,𝔽2)14yes—
479C22⋊D47—216no—
480C22⋊D47—216no—
481C22⋊D47—44no—
482C22⋊D47—48no—
483C22⋊D47—48no—
484C22⋊D47—44no—
485C2×Dic47—28no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—21no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—22no—
498C2×Dic47—21no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—44no—
509C2×Dic47—44no—
510C2×Dic47C22×D412yes—
511C2×Dic47C22×D412yes—
512C2×Dic47C22×D412yes—
513C2×Dic47C22×D412yes—
514D188—48no—
515C4×D47—48no—
516C4×D47—44no—
517C4×D47—48no—
518Dic94—44no—
519#34593—471nomaximal, Sylow
520C22×C47—22no—
521C22×C47—22no—
522C22×C47—24no—
523C22×C47—24no—
524C22×C47—24no—
525C22×C47—24no—
526C22×C47—24no—
527C22×C47—416no—
528C22×C47—42no—
529C22×C47—42no—
530C22×C47—42no—
531C22×C47—42no—
532C22×C47—41no—
533C22×C47—41no—
534C22×C47—41no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47#52514yes—
538C22×C47C23×D411yescharacteristic
539C22×C47C22×#4111yescharacteristic
540C22×C47C22×#4111yescharacteristic
541C22×C47C2×H(5,𝔽2)12yes—
542C22×C47#58512yes—
543C2×D47—24no—
544C2×D47—24no—
545C2×D47—24no—
546C2×D47—416no—
547C2×D47—42no—
548C2×D47—42no—
549C2×D47—42no—
550C2×D47—42no—
551C2×D47—41no—
552C2×D47—41no—
553C2×D47—41no—
554C2×D47—42no—
555C2×D47—42no—
556C4×C47—22no—
557C4×C47—41no—
558C4×C47—41no—
559C4×C47—42no—
560C4×C47—41no—
561C4×C47—42no—
562C4×C47—42no—
563C4×C47#53514yes—
564Dic47—22no—
565Dic47—22no—
566Dic47—22no—
567Dic47—22no—
568Dic47—41no—
569Dic47—42no—
570Dic47—41no—
571Dic47—41no—
572Dic47—42no—
573Dic47—42no—
574C2×#529—471no—
575C22×C4×D4—471no—
576#2636—472no—
577#2636—472no—
578#2633—472no—
579#2631—472no—
580#2626—471no—
581#2626—471no—
582#2623—471no—
583#2623—471no—
584#2617—471no—
585#2617—471no—
586#2613—471no—
587#2613—471no—
588#2398—472no—
589#2397—472no—
590#2392—472no—
591#2392—472no—
592C4×#120—471no—
593C4×#120—471no—
594C4×#120—471no—
595C4×#120D4711yescharacteristic, complemented
596#2283—471no—
597C2×C47—24no—
598C2×C47—44no—
599C2×C47—81no—
600C2×C47C2×#52511yescharacteristic
601C2×C47C2×#53511yescharacteristic
602C2×C47#344911yescharacteristic
603C2×C47#345912yes—
604C2×C47#345912yes—
605D47—44no—
606D47—81no—
607C23×D4—471no—
608C24×C4—471no—
609C24×C4C2×D4711yescharacteristic
610#529—948no—
611C2×#126—471no—
612C2×#126—471no—
613C2×#125—471no—
614C2×#124—471no—
615C2×#123—471no—
616C2×#123—471no—
617C2×C22⋊Q8—471no—
618C2×#121—471no—
619C2×#120—471no—
620C2×#120—471no—
621C2×#120—471no—
622C2×#120C2×D4711yescharacteristic
623C2×C4×Q8—471no—
624C2×C4×D4—472no—
625C2×C4×D4—472no—
626C2×C4×D4—472no—
627C2×C4×D4—471no—
628C2×C4×D4—472no—
629C2×C4×D4—471no—
630C2×C4×D4—472no—
631C2×C4×D4—472no—
632C2×C4×D4—472no—
633C2×C4×D4—948no—
634C2×C4×D4C2×D4711yescharacteristic
635C2×C4×D4C2×D4712yescomplemented
636C2×#117—471no—
637C2×#117—471no—
638C22×C4⋊C4—471no—
639C22×C22⋊C4—471no—
640C22×C22⋊C4—471no—
641C22×C42—471no—
642#400—472no—
643#400—472no—
644#399—472no—
645#399—472no—
646#399—472no—
647#399—472no—
648#398—472no—
649#398—472no—
650#397—472no—
651#397—472no—
652#397—472no—
653#397—472no—
654#396—472no—
655#396—472no—
656#396—472no—
657#396—472no—
658#394—472no—
659#394—472no—
660#394—472no—
661#394—472no—
662#394—472no—
663#394—472no—
664#394—472no—
665#394—472no—
666#393—472no—
667#393—472no—
668#392—472no—
669#392—472no—
670#392—472no—
671#392—472no—
672#392—472no—
673#392—472no—
674#386—471no—
675#386—471no—
676#386—472no—
677#386—472no—
678#386—471no—
679#386—472no—
680#386C2×D4711yescharacteristic
681#386C2×D4712yescomplemented
682#385—471no—
683#385—472no—
684#385—472no—
685#385—471no—
686#385—471no—
687#385—472no—
688#385C2×D4711yescharacteristic
689#385C2×D4712yescomplemented
690#383—472no—
691#382—472no—
692#381—471no—
693#381—471no—
694#380—471no—
695#380—471no—
696#379—471no—
697#379—471no—
698#379—471no—
699#379C2×D4711yescharacteristic
700C4×C4⋊C4—472no—
701C4×C22⋊C4—471no—
702C4×C22⋊C4—472no—
703C4×C22⋊C4—472no—
704C4×C22⋊C4—472no—
705C4×C22⋊C4C2×D4711yescharacteristic
706C4×C22⋊C4C2×D4712yescomplemented
707#376—472no—
708C47#3459311yescharacteristic, complemented, Sylow
709C25—471no—
710C25C22×D4711yescharacteristic
711C22×Q8—471no—
712C22×D4—472no—
713C22×D4—472no—
714C22×D4—471no—
715C22×D4—472no—
716C22×D4—472no—
717C22×D4—471no—
718C22×D4—472no—
719C22×D4—944no—
720C22×D4—944no—
721C22×D4—944no—
722C22×D4C22×D4711yescharacteristic
723C22×D4C22×D4712yes—
724C23×C4—24no—
725C23×C4—44no—
726C23×C4—471no—
727C23×C4—471no—
728C23×C4—471no—
729C23×C4—471no—
730C23×C4—472no—
731C23×C4—472no—
732C23×C4—944no—
733C23×C4—1884no—
734C23×C4C22×D4711yescharacteristic
735C23×C4C22×D4712yes—
736C23×C4C22×D4711yescharacteristic
737C23×C4C22×D4711yescharacteristic
738C23×C4C22×D4712yes—
739#126—944no—
740#126—944no—
741#125—944no—
742#124—944no—
743#123—944no—
744#123—944no—
745C22⋊Q8—944no—
746#121—944no—
747#120—24no—
748#120—944no—
749#120—944no—
750#120—944no—
751C4×Q8—944no—
752C4×D4—24no—
753C4×D4—44no—
754C4×D4—948no—
755C4×D4—948no—
756C4×D4—948no—
757C4×D4—948no—
758C4×D4—944no—
759C4×D4—944no—
760C4×D4—1884no—
761C4×D4—1884no—
762C4×D4—1884no—
763#117—944no—
764#117—944no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—471no—
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—471no—
775C2×C4⋊C4—471no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—472no—
778C2×C4⋊C4—472no—
779C2×C4⋊C4—472no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—944no—
782C2×C4⋊C4C22×D4711yescharacteristic
783C2×C4⋊C4C22×D4712yes—
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—471no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—471no—
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—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—944no—
811C2×C22⋊C4—944no—
812C2×C22⋊C4C22×D4711yescharacteristic
813C2×C22⋊C4C22×D4711yescharacteristic
814C2×C22⋊C4C22×D4711yescharacteristic
815C2×C22⋊C4C22×D4711yescharacteristic
816C2×C22⋊C4C22×D4712yes—
817C2×C22⋊C4C22×D4712yes—
818C2×C22⋊C4C22×D4712yes—
819C2×C22⋊C4C22×D4712yes—
820C2×C42—478no—
821C2×C42—471no—
822C2×C42—471no—
823C2×C42—471no—
824C2×C42—471no—
825C2×C42—471no—
826C2×C42—472no—
827C2×C42C22×D4711yescharacteristic
828C2×C42C22×D4712yes—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95—472no—
842#95C22×D4712yes—
843#95C22×D4712yes—
844#95C22×D4712yes—
845C24—22no—
846C24—22no—
847C24—42no—
848C24—42no—
849C24—472no—
850C24—474no—
851C24—471no—
852C24—942no—
853C24—942no—
854C24—1882no—
855C24—1882no—
856C24#1062535014yes—
857C24C23×D4711yescharacteristic
858C24C23×D4712yes—
859C24C23×D4711yescharacteristic
860C2×Q8—942no—
861C2×Q8—1882no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—944no—
869C2×D4—944no—
870C2×D4—944no—
871C2×D4—942no—
872C2×D4—944no—
873C2×D4—944no—
874C2×D4—9432no—
875C2×D4—944no—
876C2×D4—944no—
877C2×D4—944no—
878C2×D4—942no—
879C2×D4—942no—
880C2×D4—944no—
881C2×D4—942no—
882C2×D4—1882no—
883C2×D4—1882no—
884C2×D4—1882no—
885C2×D4—1882no—
886C2×D4—1882no—
887C2×D4—1882no—
888C2×D4—1882no—
889C22×C4—24no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—416no—
901C22×C4—474no—
902C22×C4—471no—
903C22×C4—471no—
904C22×C4—471no—
905C22×C4—471no—
906C22×C4—474no—
907C22×C4—472no—
908C22×C4—472no—
909C22×C4—471no—
910C22×C4—471no—
911C22×C4—472no—
912C22×C4—471no—
913C22×C4—942no—
914C22×C4—942no—
915C22×C4—942no—
916C22×C4—942no—
917C22×C4—944no—
918C22×C4—944no—
919C22×C4—944no—
920C22×C4—944no—
921C22×C4—944no—
922C22×C4—1882no—
923C22×C4—1882no—
924C22×C4—18816no—
925C22×C4—1882no—
926C22×C4—1882no—
927C22×C4D4×D4714yes—
928C22×C4C23×D4712yes—
929C22×C4C23×D4712yes—
930C22×C4C23×D4711yescharacteristic
931C22×C4C23×D4711yescharacteristic
932C22×C4C23×D4712yes—
933C22×C4C23×D4711yescharacteristic
934C22×C4C23×D4711yescharacteristic
935C22×C4C23×D4711yescharacteristic
936C4⋊C4—22no—
937C4⋊C4—42no—
938C4⋊C4—944no—
939C4⋊C4—944no—
940C4⋊C4—942no—
941C4⋊C4—942no—
942C4⋊C4—942no—
943C4⋊C4—942no—
944C4⋊C4—942no—
945C4⋊C4—942no—
946C4⋊C4—942no—
947C4⋊C4—942no—
948C4⋊C4—942no—
949C4⋊C4—1882no—
950C4⋊C4—1882no—
951C4⋊C4—1882no—
952C4⋊C4—1882no—
953C4⋊C4—1882no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
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—944no—
971C22⋊C4—942no—
972C22⋊C4—942no—
973C22⋊C4—942no—
974C22⋊C4—942no—
975C22⋊C4—942no—
976C22⋊C4—944no—
977C22⋊C4—942no—
978C22⋊C4—942no—
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—22no—
989C42—24no—
990C42—474no—
991C42—474no—
992C42—474no—
993C42—474no—
994C42—942no—
995C42—944no—
996C23—22no—
997C23—22no—
998C23—28no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—22no—
1009C23—22no—
1010C23—48no—
1011C23—44no—
1012C23—48no—
1013C23—44no—
1014C23—474no—
1015C23—948no—
1016C23—942no—
1017C23—942no—
1018C23—942no—
1019C23—942no—
1020C23—942no—
1021C23—942no—
1022C23—941no—
1023C23—941no—
1024C23—941no—
1025C23—942no—
1026C23—942no—
1027C23—1888no—
1028C23—1884no—
1029C23—1888no—
1030C23—1884no—
1031C23C2×D4×D4712yes—
1032C23#41×D4712yes—
1033C23C2×#1062535014yes—
1034C23C2×#1062535012yes—
1035C23C24×D4711yescharacteristic
1036Q8—1884no—
1037D4—48no—
1038D4—44no—
1039D4—9416no—
1040D4—9416no—
1041D4—1888no—
1042D4—1884no—
1043D4—1888no—
1044D4—1888no—
1045D4—1884no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—48no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—472no—
1069C2×C4—472no—
1070C2×C4—472no—
1071C2×C4—472no—
1072C2×C4—948no—
1073C2×C4—941no—
1074C2×C4—941no—
1075C2×C4—941no—
1076C2×C4—941no—
1077C2×C4—942no—
1078C2×C4—942no—
1079C2×C4—941no—
1080C2×C4—941no—
1081C2×C4—941no—
1082C2×C4—942no—
1083C2×C4—942no—
1084C2×C4—941no—
1085C2×C4—942no—
1086C2×C4—941no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—1888no—
1096C2×C4—1884no—
1097C2×C4—1884no—
1098C2×C4—1884no—
1099C2×C4—1888no—
1100C2×C4C2×D4×D4712yes—
1101C2×C4C2×D4×D4712yes—
1102C2×C4#1309406914yes—
1103C22—24no—
1104C22—24no—
1105C22—22no—
1106C22—22no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—416no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22—944no—
1121C22—944no—
1122C22—944no—
1123C22—18816no—
1124C22—1882no—
1125C22—1882no—
1126C22—1881no—
1127C22—1881no—
1128C22—1881no—
1129C22—1882no—
1130C22—1882no—
1131C22—1882no—
1132C22—1882no—
1133C22#1568963214yes—
1134C22C22×D4×D4711yescharacteristic
1135C22C2×#41×D4711yescharacteristic
1136C22C22×#1062535011yescharacteristic
1137C22C2×#1309406912yes—
1138C22#1568995912yes—
1139C4—22no—
1140C4—42no—
1141C4—42no—
1142C4—41no—
1143C4—42no—
1144C4—41no—
1145C4—41no—
1146C4—942no—
1147C4—942no—
1148C4—942no—
1149C4—942no—
1150C4—1882no—
1151C4—1882no—
1152C4—1881no—
1153C4—1882no—
1154C4—1881no—
1155C4—1881no—
1156C4#1568968814yes—
1157C2—24no—
1158C2—44no—
1159C2—81no—
1160C2—3761no—
1161C2—1884no—
1162C2C2×#1568963211yescharacteristic
1163C2C2×#1568968811yescharacteristic
1164C2#2025671811yescharacteristic
1165C2#2025679512yes—
1166C2#2025679712yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC4×#120×C47C2
hypercenterC4×#120D47
hypocenterC47#34593
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#15689653C2semidirect
2. C22×C4×C22⋊D47C2semidirect
3. #20249291C2semidirect
4. #20249289C2semidirect
5. #20249260C2semidirect
6. #20249244C2semidirect
7. #20249199C2semidirect
8. #20249197C2semidirect
9. #20249174C2semidirect
10. #20249172C2semidirect
11. #20249128C2semidirect
12. #20249126C2semidirect
13. #20249103C2semidirect
14. #20249102C2semidirect
15. #20246675C2semidirect
16. #20246667C2semidirect
17. #20246632C2semidirect
18. #20246630C2semidirect
19. C4×#13093994C2semidirect
20. C4×#13093993C2semidirect
21. C4×#13093992C2semidirect
22. #20245782C2semidirect
23. C4×#120×C47C2semidirect
27. C2×#13094019C22semidirect
28. C2×#13094017C22semidirect
29. C2×#13094014C22semidirect
30. C2×#13094010C22semidirect
38. C2×C4×Dic94C22semidirect
39. C2×C4×D188C22semidirect
46. C2×C4×C22⋊D47C22semidirect
47. C2×C4×C22⋊D47C22semidirect
48. C2×C4×C22⋊D47C22semidirect
49. C2×#13093983C22semidirect
50. C2×#13093981C22semidirect
55. #15689065C22semidirect
56. #15689064C22semidirect
57. #15689059C22semidirect
58. #15689059C22semidirect
59. #15689058C22semidirect
60. #15689058C22semidirect
61. #15689057C22semidirect
62. #15689056C22semidirect
63. #15689052C22semidirect
64. #15689052C22semidirect
65. #15689051C22semidirect
66. #15689051C22semidirect
67. #15689047C22semidirect
68. #15689046C22semidirect
69. #15689046C22semidirect
70. #15689045C22semidirect
71. #15689041C22semidirect
76. #15689038C22semidirect
77. #15689038C22semidirect
78. #15689037C22semidirect
79. #15689036C22semidirect
80. #15689035C22semidirect
83. #15689032C22semidirect
86. #15689031C22semidirect
89. #15689002C22semidirect
90. #15689001C22semidirect
92. #15688999C22semidirect
94. #15688997C22semidirect
96. #15688996C22semidirect
98. #15688994C22semidirect
99. #15688990C22semidirect
100. #15688987C22semidirect
108. C4×Dic47⋊C4C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
110. C4×(C2×D47)⋊C4C22semidirect
112. C4×C22⋊Dic47C22semidirect
113. #15688969C22semidirect
117. C2×C4×D4×C47C22semidirect
119. C47×#386C22semidirect
121. C47×#385C22semidirect
124. C4×C22⋊C4×C47C22semidirect
213. C2×C4×Dic47D4semidirect
595. C4×#120D47semidirect
635. C2×C4×D4C2×D47semidirect
681. #386C2×D47semidirect
689. #385C2×D47semidirect
706. C4×C22⋊C4C2×D47semidirect
708. C47#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#156896532
C22×C4×C22⋊D472
#202492912
#202492892
#202492602
#202492442
#202491992
#202491972
#202491742
#202491722
#202491282
#202491262
#202491032
#202491022
#202466752
#202466672
#202466322
#202466302
C4×#130939942
C4×#130939932
C4×#130939922
#202457822
C4×#120×C472
#3459347