Finite Group Databasebeta

← #26389196

Subgroups — #26389196

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689708C212yesmaximal, complemented
2#20251738C211yesmaximal, characteristic, complemented
3#20251731C211yesmaximal, characteristic, complemented
4#20251670C211yesmaximal, characteristic, complemented
5#20249318C212yesmaximal, complemented
6#20249126C212yesmaximal, complemented
7#20248516C212yesmaximal, complemented
8#20248514C212yesmaximal, complemented
9#20248486C212yesmaximal, complemented
10#20248484C212yesmaximal, complemented
11#20247812C211yesmaximal, characteristic, complemented
12#20247806C211yesmaximal, characteristic, complemented
13#20247753C211yesmaximal, characteristic, complemented
14#20247747C211yesmaximal, characteristic, complemented
15#20246978C211yesmaximal, characteristic, complemented
16#20246972C211yesmaximal, characteristic, complemented
17#20246904C211yesmaximal, characteristic, complemented
18#20246898C211yesmaximal, characteristic, complemented
19#20246089C212yesmaximal, complemented
20#121×Dic47C211yesmaximal, characteristic, complemented
21#20245894C211yesmaximal, characteristic, complemented
22C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
23C47×#2847C211yesmaximal, characteristic, complemented
24#15689708—216no—
25C2×#13094023C2211yescharacteristic, complemented
26C2×#13094020C2211yescharacteristic, complemented
27C2×#13094017C2212yes—
28C2×#13094017C2212yes—
29C2×#13094011C2212yes—
30C2×#13094010C2212yes—
31C2×#13094006C2212yes—
32C2×#13094005C2212yes—
33C2×#13094001C2212yes—
34C2×#13093998C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093998C2211yescharacteristic
37C2×#13093996C2212yes—
38C2×#13093996C2212yes—
39C2×#13093996C2212yes—
40C2×#13093995C2212yes—
41C2×#13093993C2212yes—
42C2×D4×Dic47C2212yes—
43C2×D4×Dic47C2211yescharacteristic, complemented
44C2×#13093986C2211yescharacteristic, complemented
45C2×(C22⋊D47)⋊C4C2212yes—
46C22×C22⋊Dic47C2211yescharacteristic
47C22×C22⋊Dic47C2211yescharacteristic
48C22×C4×Dic47C2211yescharacteristic
49C22×C4×Dic47C2211yescharacteristic
50#15689065C2212yescomplemented
51#15689064C2212yescomplemented
52#15689052C2212yescomplemented
53#15689051C2212yes—
54#15689051C2212yes—
55#15689051C2212yescomplemented
56#15689039C2212yescomplemented
57#15689038C2212yes—
58#15689038C2212yes—
59#15689038C2212yescomplemented
60#15689037C2212yes—
61#15689037C2212yes—
62#15689036C2212yescomplemented
63#15689035C2212yescomplemented
64#15689031C2212yes—
65#15689031C2212yes—
66#15689027C2212yescomplemented
67#15689026C2211yescharacteristic, complemented
68#15689026C2211yescharacteristic, complemented
69#15689024C2211yescharacteristic, complemented
70#15689024C2211yescharacteristic, complemented
71#15689023C2212yescomplemented
72#15689023C2212yescomplemented
73#15689022C2211yescharacteristic, complemented
74#15689022C2211yescharacteristic, complemented
75#15689020C2212yescomplemented
76#15689019C2211yescharacteristic, complemented
77#15689019C2211yescharacteristic, complemented
78#15689017C2212yescomplemented
79#15689016C2212yescomplemented
80#15689012C2212yescomplemented
81#15689012C2212yescomplemented
82#15689010C2212yescomplemented
83#15689005C2212yescomplemented
84#15689003C2212yes—
85#15689002C2212yes—
86#15689002C2212yes—
87#15689002C2212yes—
88#15689000C2212yes—
89#15689000C2212yescomplemented
90#15688999C2212yescomplemented
91#15688997C2212yescomplemented
92#15688995C2212yescomplemented
93#15688992C2211yescharacteristic, complemented
94#15688992C2211yescharacteristic, complemented
95#15688983C2211yescharacteristic
96#15688983C2211yescharacteristic
97#15688983C2211yescharacteristic
98#15688981C2212yes—
99C4⋊C4×Dic47C2211yescharacteristic, complemented
100C4⋊C4×Dic47C2211yescharacteristic, complemented
101C22⋊C4×Dic47C2212yescomplemented
102C4×C22⋊Dic47C2211yescharacteristic
103C4×C22⋊Dic47C2211yescharacteristic
104C4×C22⋊Dic47C2211yescharacteristic
105C4×C22⋊Dic47C2211yescharacteristic
106C4×C22⋊Dic47C2211yescharacteristic
107C4×C22⋊Dic47C2211yescharacteristic
108C4×C22⋊Dic47C2211yescharacteristic
109C4×C22⋊Dic47C2211yescharacteristic
110#15688970C2212yescomplemented
111C2×C47⋊#95C2211yescharacteristic
112C2×C47⋊#95C2211yescharacteristic
113C24×C4×C47C2211yescharacteristic
114C2×#121×C47C2211yescharacteristic
115C2×#121×C47C2211yescharacteristic
116C2×#121×C47C2211yescharacteristic
117C2×#120×C47C2212yes—
118C47×#386C2212yes—
119C47×#386C2212yes—
120C47×#386C2212yes—
121C47×#380C2211yescharacteristic
122C47×#380C2211yescharacteristic
123C47×#380C2211yescharacteristic
124C22×Dic94C2312yes—
125C22×D188C2311yescharacteristic
126C22×C22⋊D47C2312yes—
127C22×C22⋊D47C2312yes—
128C22×C22⋊D47C2312yes—
129C22×C22⋊D47C2312yes—
130C22×C22⋊D47C2312yes—
131C23×Dic47C2311yescharacteristic
132C23×Dic47C2312yes—
133C23×Dic47C2311yescharacteristic
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C22×C4×D47C2312yes—
137#13094023—42no—
138#13094020—42no—
139#13094017—28no—
140#13094017—28no—
141#13094011—28no—
142#13094010—28no—
143#13094006—28no—
144#13094005—28no—
145#13094001—28no—
146#13093998—24no—
147#13093998—42no—
148#13093998—42no—
149#13093996—28no—
150#13093996—28no—
151#13093996—28no—
152#13093995—28no—
153#13093993—28no—
154D4×Dic47—28no—
155D4×Dic47—42no—
156#13093986—42no—
157(C22⋊D47)⋊C4—28no—
158C2×C4⋊Dic47C2311yescharacteristic
159C2×C4⋊Dic47C2311yescharacteristic
160C2×C4⋊Dic47C2311yescharacteristic
161C2×C4⋊Dic47C2312yes—
162C2×C4⋊Dic47C2312yes—
163C2×Dic47⋊C4C2312yes—
164C2×Dic47⋊C4C2312yes—
165C2×Dic47⋊C4C2312yes—
166C2×Dic47⋊C4C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×C22⋊Dic47—24no—
171C2×C22⋊Dic47D418yescomplemented
172C2×C22⋊Dic47C2311yescharacteristic
173C2×C22⋊Dic47C2311yescharacteristic
174C2×C22⋊Dic47C2311yescharacteristic
175C2×C22⋊Dic47C2311yescharacteristic
176C2×C22⋊Dic47C2312yes—
177C2×C22⋊Dic47C2312yes—
178C2×C22⋊Dic47C2312yes—
179C2×C22⋊Dic47C2312yes—
180C2×C22⋊Dic47C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2311yescharacteristic
186C2×C22⋊Dic47C2311yescharacteristic
187C2×C22⋊Dic47C2311yescharacteristic
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×C4×Dic47—42no—
197C2×C4×Dic47—42no—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2311yescharacteristic
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C47⋊#95C2311yescharacteristic
209C47⋊#95C2311yescharacteristic
210C47⋊#95C2311yescharacteristic
211C47⋊#95C2311yescharacteristic
212C47⋊#95C2311yescharacteristic
213C47⋊#95C2311yescharacteristic
214C47⋊#95C2311yescharacteristic
215C47⋊#95C2311yescharacteristic
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C25×C47C2311yescharacteristic
226C22×D4×C47C2312yes—
227C22×D4×C47C2311yescharacteristic
228C22×D4×C47C2312yes—
229C22×D4×C47C2312yes—
230C23×C4×C47—24no—
231C23×C4×C47—42no—
232C23×C4×C47—42no—
233C23×C4×C47C2311yescharacteristic
234C23×C4×C47C2311yescharacteristic
235C23×C4×C47C2311yescharacteristic
236C23×C4×C47C2311yescharacteristic
237C23×C4×C47C2311yescharacteristic
238C23×C4×C47C2311yescharacteristic
239#121×C47—24no—
240#121×C47—42no—
241#121×C47—42no—
242#120×C47—28no—
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252#95×C47C2312yes—
253#95×C47C2312yes—
254#95×C47C2312yes—
255C24×C47—22no—
256C24×C47—22no—
257C24×C47—41no—
258C24×C47—41no—
259C24×C47—41no—
260C24×C47—41no—
261C24×C47C2×D414yes—
262C24×C47C2412yes—
263C24×C47C2411yescharacteristic
264C24×C47C2411yescharacteristic
265C24×C47C2411yescharacteristic
266C23×D47C2412yes—
267C2×D4×C47—24no—
268C2×D4×C47—24no—
269C2×D4×C47—24no—
270C2×D4×C47—24no—
271C2×D4×C47—24no—
272C2×D4×C47—22no—
273C2×D4×C47—22no—
274C2×D4×C47—22no—
275C2×D4×C47—42no—
276C2×D4×C47—42no—
277C2×D4×C47—42no—
278C2×D4×C47—42no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—22no—
284C22×C4×C47—22no—
285C22×C4×C47—22no—
286C22×C4×C47—22no—
287C22×C4×C47—22no—
288C22×C4×C47—22no—
289C22×C4×C47—22no—
290C22×C4×C47—41no—
291C22×C4×C47—41no—
292C22×C4×C47—41no—
293C22×C4×C47—41no—
294C22×C4×C47—41no—
295C22×C4×C47—41no—
296C22×C4×C47—416no—
297C22×C4×C47#4114yes—
298C22×C4×C47C2412yes—
299C22×C4×C47C2412yes—
300C22×C4×C47C2412yes—
301C22×C4×C47C2411yescharacteristic
302C22×C4×C47C2411yescharacteristic
303C22×C4×C47C2411yescharacteristic
304C22×C4×C47C2411yescharacteristic
305C2×C22⋊D47—24no—
306C2×C22⋊D47—24no—
307C2×C22⋊D47—24no—
308C2×C22⋊D47—24no—
309C2×C22⋊D47—24no—
310C2×C22⋊D47—24no—
311C2×C22⋊D47—24no—
312C2×C22⋊D47—42no—
313C2×C22⋊D47—42no—
314C2×C22⋊D47—42no—
315C2×C22⋊D47—42no—
316C2×C22⋊D47—42no—
317C2×C22⋊D47—42no—
318C2×C22⋊D47—42no—
319C2×C22⋊D47—42no—
320C22×Dic47—22no—
321C22×Dic47—24no—
322C22×Dic47—41no—
323C22×Dic47—41no—
324C22×Dic47—41no—
325C22×Dic47—41no—
326C22×Dic47—41no—
327C22×Dic47—41no—
328C22×Dic47—41no—
329C22×Dic47—41no—
330C22×Dic47—42no—
331C22×Dic47—42no—
332C22×Dic47C2×D414yes—
333C22×Dic47C2×D414yes—
334C22×Dic47#4114yes—
335C22×Dic47C2411yescharacteristic
336C22×Dic47C2411yescharacteristic
337C22×Dic47C2412yes—
338C22×Dic47C2412yes—
339C22×Dic47C2412yes—
340C22×Dic47C2411yescharacteristic
341C22×Dic47C2411yescharacteristic
342C22×Dic47C2411yescharacteristic
343C22×Dic47C2411yescharacteristic
344C22×Dic47C2411yescharacteristic
345C22×Dic47C2411yescharacteristic
346C2×D188—22no—
347C2×D188—22no—
348C2×D188—22no—
349C2×C4×D47—24no—
350C2×C4×D47—42no—
351C2×C4×D47—42no—
352C2×Dic94—24no—
353C2×Dic94—42no—
354C2×Dic94—42no—
355C4⋊C4×C47—22no—
356C4⋊C4×C47—22no—
357C4⋊C4×C47—22no—
358C22⋊C4×C47—24no—
359C22⋊C4×C47—24no—
360C22⋊C4×C47—24no—
361C22⋊C4×C47—24no—
362C22⋊C4×C47—42no—
363C22⋊C4×C47—42no—
364C22⋊Dic47—24no—
365C22⋊Dic47—24no—
366C22⋊Dic47—24no—
367C22⋊Dic47—24no—
368C22⋊Dic47—24no—
369C22⋊Dic47—22no—
370C22⋊Dic47—22no—
371C22⋊Dic47—22no—
372C22⋊Dic47—22no—
373C22⋊Dic47—24no—
374C22⋊Dic47—42no—
375C22⋊Dic47—42no—
376C22⋊Dic47C2×D414yes—
377C22⋊Dic47C2×D414yes—
378C22⋊Dic47C2×D414yes—
379C22⋊Dic47C2×D414yes—
380(C2×D47)⋊C4—24no—
381(C2×D47)⋊C4—24no—
382(C2×D47)⋊C4—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—42no—
385(C2×D47)⋊C4—42no—
386(C2×D47)⋊C4—42no—
387(C2×D47)⋊C4—42no—
388C4⋊Dic47—22no—
389C4⋊Dic47—22no—
390C4⋊Dic47—22no—
391C4⋊Dic47—24no—
392C4⋊Dic47—24no—
393Dic47⋊C4—24no—
394Dic47⋊C4—24no—
395Dic47⋊C4—24no—
396Dic47⋊C4—24no—
397Dic47⋊C4—24no—
398Dic47⋊C4—42no—
399Dic47⋊C4—42no—
400C4×Dic47—22no—
401C4×Dic47—22no—
402C4×Dic47—22no—
403C4×Dic47—22no—
404C4×Dic47—24no—
405C4×Dic47—24no—
406C4×Dic47—41no—
407C4×Dic47—41no—
408C4×Dic47—41no—
409C4×Dic47—41no—
410C23×C47—21no—
411C23×C47—21no—
412C23×C47—21no—
413C23×C47—21no—
414C23×C47—28no—
415C23×C47—21no—
416C23×C47—21no—
417C23×C47—21no—
418C23×C47—21no—
419C23×C47—21no—
420C23×C47—21no—
421C23×C47—21no—
422C23×C47—21no—
423C23×C47—21no—
424C23×C47—21no—
425C23×C47—21no—
426C23×C47—21no—
427C23×C47—22no—
428C23×C47—22no—
429C23×C47—22no—
430C23×C47—22no—
431C23×C47—22no—
432C23×C47—22no—
433C23×C47—22no—
434C23×C47—44no—
435C23×C47—44no—
436C23×C47—44no—
437C23×C47—44no—
438C23×C47—44no—
439C23×C47—44no—
440C23×C47C22×D412yes—
441C23×C47C22×D412yes—
442C23×C47C22×D412yes—
443C23×C47C2×#4112yes—
444C23×C47C2×#4112yes—
445C23×C47C2511yescharacteristic
446C22×D47—22no—
447C22×D47—22no—
448C22×D47—22no—
449C22×D47—22no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47—22no—
453D4×C47—48no—
454D4×C47—44no—
455D4×C47—84no—
456D4×C47—84no—
457C2×C4×C47—21no—
458C2×C4×C47—21no—
459C2×C4×C47—28no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—21no—
466C2×C4×C47—21no—
467C2×C4×C47—22no—
468C2×C4×C47—21no—
469C2×C4×C47—21no—
470C2×C4×C47—22no—
471C2×C4×C47—21no—
472C2×C4×C47—21no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—44no—
476C2×C4×C47—44no—
477C2×C4×C47—44no—
478C2×C4×C47—44no—
479C2×C4×C47—44no—
480C2×C4×C47C2×#4112yes—
481C2×C4×C47C2×#4112yes—
482C2×C4×C47H(5,𝔽2)12yes—
483C2×C4×C47H(5,𝔽2)12yes—
484C22⋊D47—48no—
485C22⋊D47—84no—
486C22⋊D47—84no—
487C22⋊D47—84no—
488C22⋊D47—84no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—21no—
495C2×Dic47—21no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—21no—
499C2×Dic47—21no—
500C2×Dic47—21no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—21no—
507C2×Dic47—21no—
508C2×Dic47—21no—
509C2×Dic47—21no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—22no—
513C2×Dic47—21no—
514C2×Dic47—21no—
515C2×Dic47—22no—
516C2×Dic47—44no—
517C2×Dic47—44no—
518C2×Dic47—44no—
519C2×Dic47—44no—
520C2×Dic47—84no—
521C2×Dic47C22×D412yes—
522C2×Dic47C22×D412yes—
523C2×Dic47C22×D412yes—
524C2×Dic47C22×D412yes—
525C2×Dic47C2×#4112yes—
526C2×Dic47C2×#4112yes—
527D188—44no—
528C4×D47—84no—
529Dic94—84no—
530#35005—471nomaximal, Sylow
531C22×C47—22no—
532C22×C47—22no—
533C22×C47—22no—
534C22×C47—22no—
535C22×C47—22no—
536C22×C47—22no—
537C22×C47—22no—
538C22×C47—22no—
539C22×C47—22no—
540C22×C47—22no—
541C22×C47—22no—
542C22×C47—22no—
543C22×C47—416no—
544C22×C47—41no—
545C22×C47—41no—
546C22×C47—41no—
547C22×C47—41no—
548C22×C47—41no—
549C22×C47—41no—
550C22×C47—41no—
551C22×C47—41no—
552C22×C47—42no—
553C22×C47—42no—
554C22×C47—42no—
555C22×C47—42no—
556C22×C47—42no—
557C22×C47—42no—
558C22×C47—42no—
559C22×C47#53214yes—
560C22×C47C23×D411yescharacteristic
561C22×C47C22×#4111yescharacteristic
562C22×C47C22×#4111yescharacteristic
563C22×C47C2×H(5,𝔽2)11yescharacteristic
564C22×C47C2×H(5,𝔽2)11yescharacteristic
565C22×C47#58511yescharacteristic
566C22×C47#58511yescharacteristic
567C2×D47—42no—
568C2×D47—42no—
569C2×D47—42no—
570C2×D47—42no—
571C2×D47—42no—
572C2×D47—42no—
573C2×D47—42no—
574C4×C47—22no—
575C4×C47—42no—
576C4×C47—41no—
577C4×C47—41no—
578C4×C47—42no—
579C4×C47—42no—
580C4×C47#53814yescomplemented
581Dic47—22no—
582Dic47—22no—
583Dic47—22no—
584Dic47—22no—
585Dic47—22no—
586Dic47—22no—
587Dic47—42no—
588Dic47—42no—
589Dic47—42no—
590Dic47—41no—
591Dic47—41no—
592C2×#538—472no—
593#2857—471no—
594#2856—471no—
595#2847—471no—
596#2847D4711yescharacteristic, complemented
597#2639—472no—
598#2617—472no—
599#2559—472no—
600#2559—472no—
601#2557—472no—
602#2557—472no—
603#2496—471no—
604#2496—471no—
605#2491—471no—
606#2491—471no—
607#2428—471no—
608#2428—471no—
609#2422—471no—
610#2422—471no—
611#2325—472no—
612C4×#121—471no—
613C4×#121—471no—
614C2×C4×C22⋊C4—471no—
615C2×C47—24no—
616C2×C47—42no—
617C2×C47—42no—
618C2×C47—82no—
619C2×C47C2×#53211yescharacteristic
620C2×C47C2×#53811yescharacteristic
621C2×C47#345511yescharacteristic
622C2×C47#349611yescharacteristic
623C2×C47#349611yescharacteristic
624C2×C47#350511yescharacteristic
625C2×C47#350611yescharacteristic
626D47—82no—
627C24×C4C2×D4711yescharacteristic
628#538—9416no—
629C2×C4⋊Q8—471no—
630C2×#127—471no—
631C2×#126—472no—
632C2×#126—472no—
633C2×#124—472no—
634C2×#124—472no—
635C2×#123—472no—
636C2×#123—472no—
637C2×C22⋊Q8—472no—
638C2×#121—472no—
639C2×#121—472no—
640C2×#121—472no—
641C2×#121—472no—
642C2×#121—471no—
643C2×#121—471no—
644C2×#121—471no—
645C2×#121C2×D4711yescharacteristic
646C2×#121C2×D4711yescharacteristic
647C2×#121C2×D4711yescharacteristic
648C2×#120—472no—
649C2×#120C2×D4712yes—
650C2×C4×D4—472no—
651C2×C4×D4—471no—
652C2×C4×D4—471no—
653C2×C4×D4—472no—
654C22×C22⋊C4—471no—
655C22×C22⋊C4—471no—
656C22×C42—471no—
657C22×C42—471no—
658#400—472no—
659#400—472no—
660#397—472no—
661#397—472no—
662#397—472no—
663#397—472no—
664#394—472no—
665#394—472no—
666#394—472no—
667#394—472no—
668#394—472no—
669#394—472no—
670#393—472no—
671#393—472no—
672#392—472no—
673#392—472no—
674#391—472no—
675#390—471no—
676#390—471no—
677#390—471no—
678#390—471no—
679#390—472no—
680#390—472no—
681#389—471no—
682#389—471no—
683#389—471no—
684#389—471no—
685#389—472no—
686#388—472no—
687#388—472no—
688#388—472no—
689#388—472no—
690#387—472no—
691#387—472no—
692#386—472no—
693#386—472no—
694#386—472no—
695#386—472no—
696#386—472no—
697#386—472no—
698#386—472no—
699#386C2×D4712yes—
700#386C2×D4712yes—
701#386C2×D4712yes—
702#385—472no—
703#385—472no—
704#384—471no—
705#384—471no—
706#380—471no—
707#380—471no—
708#380—471no—
709#380—472no—
710#380C2×D4711yescharacteristic
711#380C2×D4711yescharacteristic
712#380C2×D4711yescharacteristic
713C4×C4⋊C4—471no—
714C4×C4⋊C4—471no—
715C4×C22⋊C4—471no—
716C4×C22⋊C4—471no—
717C4×C22⋊C4—471no—
718C4×C22⋊C4—471no—
719C4×C22⋊C4—471no—
720C4×C22⋊C4—471no—
721C4×C22⋊C4—471no—
722C4×C22⋊C4—471no—
723C4×C22⋊C4—472no—
724C4×C22⋊C4—472no—
725C2×#95—471no—
726C2×#95—471no—
727C47#3500511yescharacteristic, complemented, Sylow
728C25C22×D4711yescharacteristic
729C22×Q8—472no—
730C22×D4—472no—
731C22×D4—472no—
732C22×D4—472no—
733C22×D4—472no—
734C22×D4—472no—
735C22×D4—471no—
736C22×D4C22×D4712yes—
737C22×D4C22×D4711yescharacteristic
738C22×D4C22×D4712yes—
739C22×D4C22×D4712yes—
740C23×C4—24no—
741C23×C4—42no—
742C23×C4—42no—
743C23×C4—471no—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—472no—
748C23×C4—472no—
749C23×C4C22×D4711yescharacteristic
750C23×C4C22×D4711yescharacteristic
751C23×C4C22×D4711yescharacteristic
752C23×C4C22×D4711yescharacteristic
753C23×C4C22×D4711yescharacteristic
754C23×C4C22×D4711yescharacteristic
755C4⋊Q8—1882no—
756#127—1882no—
757#126—948no—
758#126—948no—
759#124—948no—
760#124—948no—
761#123—948no—
762#123—948no—
763C22⋊Q8—948no—
764#121—24no—
765#121—42no—
766#121—42no—
767#121—948no—
768#121—948no—
769#121—948no—
770#121—948no—
771#121—944no—
772#121—1882no—
773#121—1882no—
774#120—28no—
775#120—948no—
776C4×D4—948no—
777C4×D4—948no—
778C4×D4—1882no—
779C4×D4—1882no—
780C2×C4⋊C4—471no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—472no—
784C2×C4⋊C4—472no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—471no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—472no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4—472no—
792C2×C4⋊C4C22×D4711yescharacteristic
793C2×C4⋊C4C22×D4711yescharacteristic
794C2×C4⋊C4C22×D4711yescharacteristic
795C2×C22⋊C4—478no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—471no—
799C2×C22⋊C4—471no—
800C2×C22⋊C4—471no—
801C2×C22⋊C4—471no—
802C2×C22⋊C4—471no—
803C2×C22⋊C4—471no—
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—472no—
811C2×C22⋊C4—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—472no—
820C2×C22⋊C4—944no—
821C2×C22⋊C4C22×D4712yes—
822C2×C22⋊C4C22×D4712yes—
823C2×C22⋊C4C22×D4712yes—
824C2×C22⋊C4C22×D4712yes—
825C2×C22⋊C4C22×D4712yes—
826C2×C22⋊C4C22×D4712yes—
827C2×C42—472no—
828C2×C42—472no—
829C2×C42—471no—
830C2×C42—471no—
831C2×C42—471no—
832C2×C42—471no—
833C2×C42—471no—
834C2×C42—471no—
835C2×C42—471no—
836C2×C42—471no—
837C2×C42—1882no—
838C2×C42—1882no—
839#95—471no—
840#95—471no—
841#95—471no—
842#95—471no—
843#95—471no—
844#95—471no—
845#95—471no—
846#95—471no—
847#95—472no—
848#95—472no—
849#95—472no—
850#95—472no—
851#95—472no—
852#95—472no—
853#95—472no—
854#95—472no—
855#95—472no—
856#95C22×D4712yes—
857#95C22×D4712yes—
858#95C22×D4712yes—
859C24—22no—
860C24—22no—
861C24—41no—
862C24—41no—
863C24—41no—
864C24—41no—
865C24—472no—
866C24D4×D4714yes—
867C24C23×D4712yes—
868C24C23×D4711yescharacteristic
869C24C23×D4711yescharacteristic
870C24C23×D4711yescharacteristic
871C2×Q8—944no—
872C2×Q8—1882no—
873C2×Q8—1882no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—24no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—42no—
883C2×D4—42no—
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—944no—
893C2×D4—942no—
894C2×D4—942no—
895C2×D4—942no—
896C2×D4—1882no—
897C2×D4—1882no—
898C2×D4—1882no—
899C2×D4—1882no—
900C2×D4—1882no—
901C2×D4—1882no—
902C2×D4—1882no—
903C2×D4—1882no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—416no—
922C22×C4—471no—
923C22×C4—471no—
924C22×C4—471no—
925C22×C4—471no—
926C22×C4—471no—
927C22×C4—471no—
928C22×C4—474no—
929C22×C4—474no—
930C22×C4—474no—
931C22×C4—471no—
932C22×C4—471no—
933C22×C4—472no—
934C22×C4—472no—
935C22×C4—472no—
936C22×C4—944no—
937C22×C4—944no—
938C22×C4—942no—
939C22×C4—1882no—
940C22×C4—1882no—
941C22×C4—1882no—
942C22×C4—1882no—
943C22×C4—1881no—
944C22×C4—1881no—
945C22×C4—1881no—
946C22×C4—1881no—
947C22×C4—1881no—
948C22×C4—1881no—
949C22×C4—1881no—
950C22×C4—1881no—
951C22×C4#1062535214yes—
952C22×C4C23×D4711yescharacteristic
953C22×C4C23×D4711yescharacteristic
954C22×C4C23×D4712yes—
955C22×C4C23×D4712yes—
956C22×C4C23×D4712yes—
957C22×C4C23×D4711yescharacteristic
958C22×C4C23×D4711yescharacteristic
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—944no—
963C4⋊C4—944no—
964C4⋊C4—944no—
965C4⋊C4—944no—
966C4⋊C4—944no—
967C4⋊C4—944no—
968C4⋊C4—944no—
969C4⋊C4—942no—
970C4⋊C4—942no—
971C4⋊C4—942no—
972C4⋊C4—1882no—
973C4⋊C4—1882no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—474no—
981C22⋊C4—474no—
982C22⋊C4—474no—
983C22⋊C4—474no—
984C22⋊C4—944no—
985C22⋊C4—944no—
986C22⋊C4—944no—
987C22⋊C4—942no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—942no—
991C22⋊C4—944no—
992C22⋊C4—944no—
993C22⋊C4—944no—
994C22⋊C4—944no—
995C22⋊C4—944no—
996C22⋊C4—944no—
997C22⋊C4—944no—
998C22⋊C4—1882no—
999C22⋊C4—1882no—
1000C22⋊C4—1882no—
1001C22⋊C4—1882no—
1002C22⋊C4—1882no—
1003C22⋊C4—1882no—
1004C42—944no—
1005C42—944no—
1006C42—942no—
1007C42—942no—
1008C42—942no—
1009C42—942no—
1010C42—1881no—
1011C42—1881no—
1012C42—1881no—
1013C42—1881no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—28no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23—942no—
1045C23—942no—
1046C23—942no—
1047C23—942no—
1048C23—942no—
1049C23—942no—
1050C23—942no—
1051C23C2×D4×D4712yes—
1052C23C2×D4×D4712yes—
1053C23C2×D4×D4712yes—
1054C23#41×D4712yes—
1055C23C2×#1062535212yes—
1056C23C24×D4711yescharacteristic
1057Q8—3764no—
1058D4—48no—
1059D4—44no—
1060D4—84no—
1061D4—84no—
1062D4—3764no—
1063D4—3764no—
1064D4—3764no—
1065D4—3764no—
1066D4—1888no—
1067D4—1884no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—472no—
1092C2×C4—472no—
1093C2×C4—472no—
1094C2×C4—472no—
1095C2×C4—472no—
1096C2×C4—472no—
1097C2×C4—941no—
1098C2×C4—941no—
1099C2×C4—941no—
1100C2×C4—941no—
1101C2×C4—941no—
1102C2×C4—941no—
1103C2×C4—941no—
1104C2×C4—941no—
1105C2×C4—941no—
1106C2×C4—941no—
1107C2×C4—941no—
1108C2×C4—941no—
1109C2×C4—942no—
1110C2×C4—942no—
1111C2×C4—942no—
1112C2×C4—941no—
1113C2×C4—941no—
1114C2×C4—942no—
1115C2×C4—942no—
1116C2×C4—941no—
1117C2×C4—941no—
1118C2×C4—942no—
1119C2×C4—942no—
1120C2×C4—941no—
1121C2×C4—941no—
1122C2×C4—942no—
1123C2×C4—942no—
1124C2×C4—3764no—
1125C2×C4—3764no—
1126C2×C4—1884no—
1127C2×C4—1884no—
1128C2×C4—1884no—
1129C2×C4—1884no—
1130C2×C4C2×#1062535212yes—
1131C2×C4C2×#1062535212yes—
1132C2×C4#1309406912yes—
1133C2×C4#1309406912yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—22no—
1146C22—416no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—1882no—
1163C22—1882no—
1164C22—1882no—
1165C22—1882no—
1166C22—1882no—
1167C22—1882no—
1168C22—1882no—
1169C22#1568966814yes—
1170C22C22×D4×D4711yescharacteristic
1171C22C2×#41×D4711yescharacteristic
1172C22C22×#1062535211yescharacteristic
1173C22C2×#1309406911yescharacteristic
1174C22C2×#1309406911yescharacteristic
1175C22#1568995911yescharacteristic
1176C22#1568995911yescharacteristic
1177C4—22no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—41no—
1182C4—41no—
1183C4—942no—
1184C4—942no—
1185C4—942no—
1186C4—942no—
1187C4—942no—
1188C4—942no—
1189C4—1882no—
1190C4—1882no—
1191C4—1882no—
1192C4—1881no—
1193C4—1881no—
1194C4#1568970814yescomplemented
1195C2—24no—
1196C2—42no—
1197C2—42no—
1198C2—82no—
1199C2—3762no—
1200C2C2×#1568966811yescharacteristic
1201C2C2×#1568970811yescharacteristic
1202C2#2025677611yescharacteristic
1203C2#2025714511yescharacteristic
1204C2#2025714511yescharacteristic
1205C2#2025721611yescharacteristic
1206C2#2025723111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2847C2
hypercenter#2847D47
hypocenterC47#35005
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#15689708C2semidirect
2. #20251738C2semidirect
3. #20251731C2semidirect
4. #20251670C2semidirect
5. #20249318C2semidirect
6. #20249126C2semidirect
7. #20248516C2semidirect
8. #20248514C2semidirect
9. #20248486C2semidirect
10. #20248484C2semidirect
11. #20247812C2semidirect
12. #20247806C2semidirect
13. #20247753C2semidirect
14. #20247747C2semidirect
15. #20246978C2semidirect
16. #20246972C2semidirect
17. #20246904C2semidirect
18. #20246898C2semidirect
19. #20246089C2semidirect
20. #121×Dic47C2semidirect
21. #20245894C2semidirect
22. C2×C4×C22⋊Dic47C2semidirect
23. C47×#2847C2semidirect
25. C2×#13094023C22semidirect
26. C2×#13094020C22semidirect
43. C2×D4×Dic47C22semidirect
44. C2×#13093986C22semidirect
50. #15689065C22semidirect
51. #15689064C22semidirect
52. #15689052C22semidirect
55. #15689051C22semidirect
56. #15689039C22semidirect
59. #15689038C22semidirect
62. #15689036C22semidirect
63. #15689035C22semidirect
66. #15689027C22semidirect
67. #15689026C22semidirect
68. #15689026C22semidirect
69. #15689024C22semidirect
70. #15689024C22semidirect
71. #15689023C22semidirect
72. #15689023C22semidirect
73. #15689022C22semidirect
74. #15689022C22semidirect
75. #15689020C22semidirect
76. #15689019C22semidirect
77. #15689019C22semidirect
78. #15689017C22semidirect
79. #15689016C22semidirect
80. #15689012C22semidirect
81. #15689012C22semidirect
82. #15689010C22semidirect
83. #15689005C22semidirect
89. #15689000C22semidirect
90. #15688999C22semidirect
91. #15688997C22semidirect
92. #15688995C22semidirect
93. #15688992C22semidirect
94. #15688992C22semidirect
99. C4⋊C4×Dic47C22semidirect
100. C4⋊C4×Dic47C22semidirect
101. C22⋊C4×Dic47C22semidirect
110. #15688970C22semidirect
171. C2×C22⋊Dic47D4semidirect
580. C4×C47#538semidirect
596. #2847D47semidirect
727. C47#35005semidirect
1194. C4#15689708semidirect

Maximal subgroups

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

subgroupindex
C2×#156897082
#202517382
#202517312
#202516702
#202493182
#202491262
#202485162
#202485142
#202484862
#202484842
#202478122
#202478062
#202477532
#202477472
#202469782
#202469722
#202469042
#202468982
#202460892
#121×Dic472
#202458942
C2×C4×C22⋊Dic472
C47×#28472
#3500547