Finite Group Databasebeta

← #26382698

Subgroups — #26382698

Order 12032.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689632C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3#20249309C212yesmaximal, complemented
4#20249276C212yesmaximal, complemented
5#20249233C212yesmaximal, complemented
6#20249231C212yesmaximal, complemented
7#20249207C211yesmaximal, characteristic, complemented
8#20249197C211yesmaximal, characteristic, complemented
9#20249166C211yesmaximal, characteristic, complemented
10#20249165C211yesmaximal, characteristic, complemented
11#20249136C211yesmaximal, characteristic, complemented
12#20249126C211yesmaximal, characteristic, complemented
13#20249103C211yesmaximal, characteristic, complemented
14#20249102C211yesmaximal, characteristic, complemented
15#20246649C212yesmaximal, complemented
16#20246632C212yesmaximal, complemented
17#20246626C212yesmaximal, complemented
18#20246603C212yesmaximal, complemented
19C4×#13094008C211yesmaximal, characteristic, complemented
20C4×#13094005C211yesmaximal, characteristic, complemented
21C4×#13093993C211yesmaximal, characteristic, complemented
22#20245769C211yesmaximal, characteristic, complemented
23C4×#120×C47C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic, complemented
25C23×C22⋊D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27#15689632—28no—
28C2×#13094009C2211yescharacteristic, complemented
29C2×#13094008C2211yescharacteristic
30C2×#13094006C2211yescharacteristic, complemented
31C2×#13094005C2211yescharacteristic
32C2×#13094002C2211yescharacteristic, complemented
33C2×#13094001C2211yescharacteristic
34C2×#13093997C2211yescharacteristic, complemented
35C2×#13093996C2211yescharacteristic
36C2×#13093994C2211yescharacteristic
37C2×#13093993C2211yescharacteristic
38C2×#13093992C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic, complemented
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×#13093981C2211yescharacteristic, complemented
49C2×#13093981C2212yescomplemented
50C22×Dic47⋊C4C2211yescharacteristic
51C22×C22⋊Dic47C2211yescharacteristic
52C22×(C2×D47)⋊C4C2211yescharacteristic
53C22×C4×Dic47C2211yescharacteristic
54#15689064C2212yescomplemented
55#15689059C2212yescomplemented
56#15689057C2212yescomplemented
57#15689057C2212yescomplemented
58#15689054C2212yescomplemented
59#15689052C2212yescomplemented
60#15689052C2212yescomplemented
61#15689051C2212yescomplemented
62#15689050C2212yescomplemented
63#15689049C2212yescomplemented
64#15689047C2212yescomplemented
65#15689046C2212yescomplemented
66#15689046C2212yescomplemented
67#15689046C2212yescomplemented
68#15689043C2212yescomplemented
69#15689041C2212yescomplemented
70#15689040C2212yescomplemented
71#15689039C2212yes—
72#15689039C2212yes—
73#15689039C2212yescomplemented
74#15689038C2212yes—
75#15689038C2212yes—
76#15689038C2212yescomplemented
77#15689038C2212yescomplemented
78#15689038C2212yescomplemented
79#15689037C2212yescomplemented
80#15689035C2212yescomplemented
81#15689032C2212yes—
82#15689032C2212yes—
83#15689031C2212yes—
84#15689031C2212yes—
85#15689031C2212yescomplemented
86#15689015C2212yescomplemented
87#15689011C2212yescomplemented
88#15689008C2212yescomplemented
89#15689004C2212yescomplemented
90#15689003C2211yescharacteristic
91#15689002C2211yescharacteristic
92#15689002C2212yescomplemented
93#15689000C2211yescharacteristic
94#15688998C2211yescharacteristic
95#15688996C2211yescharacteristic
96#15688996C2212yescomplemented
97#15688995C2211yescharacteristic
98#15688985C2212yescomplemented
99#15688984C2211yescharacteristic
100#15688984C2211yescharacteristic
101#15688982C2212yescomplemented
102#15688981C2211yescharacteristic
103#15688981C2211yescharacteristic
104#15688979C2211yescharacteristic
105#15688978C2211yescharacteristic
106#15688978C2211yescharacteristic
107C4×Dic47⋊C4C2212yescomplemented
108C4×C4⋊Dic47C2212yescomplemented
109C4×(C2×D47)⋊C4C2212yescomplemented
110C4×(C2×D47)⋊C4C2212yescomplemented
111C4×C22⋊Dic47C2211yescharacteristic
112C4×C22⋊Dic47C2212yescomplemented
113C4×C22⋊Dic47C2212yescomplemented
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
126C2×#10625350—24no—
127C2×#10625350—44no—
128C22×Dic94C2311yescharacteristic
129C22×D188C2311yescharacteristic
130C22×D188C2311yescharacteristic
131C22×C22⋊D47—24no—
132C22×C22⋊D47—24no—
133C22×C22⋊D47—24no—
134C22×C22⋊D47C2311yescharacteristic
135C22×C22⋊D47C2312yes—
136C22×C22⋊D47C2312yes—
137C22×C22⋊D47C2312yes—
138C22×C22⋊D47C2311yescharacteristic
139C22×C22⋊D47C2311yescharacteristic
140C22×C22⋊D47C2311yescharacteristic
141C23×Dic47C2311yescharacteristic
142C23×Dic47C2311yescharacteristic
143C23×Dic47C2311yescharacteristic
144C22×C4×D47—44no—
145C22×C4×D47D418yescomplemented
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151#13094009—24no—
152#13094008—24no—
153#13094006—24no—
154#13094005—24no—
155#13094002—24no—
156#13094001—24no—
157#13093997—24no—
158#13093996—24no—
159#13093994—24no—
160#13093993—24no—
161#13093992—24no—
162C4×D188—24no—
163C4×C22⋊D47—24no—
164C4×C22⋊D47—28no—
165C4×C22⋊D47—28no—
166C4×C22⋊D47—28no—
167C4×C22⋊D47—28no—
168C4×C22⋊D47—24no—
169C4×C22⋊D47—44no—
170#13093981—24no—
171#13093981—44no—
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2312yes—
175C2×Dic47⋊C4—24no—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2311yescharacteristic
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2311yescharacteristic
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2311yescharacteristic
182C2×Dic47⋊C4C2311yescharacteristic
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×C22⋊Dic47—24no—
188C2×C22⋊Dic47C2311yescharacteristic
189C2×C22⋊Dic47C2311yescharacteristic
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2311yescharacteristic
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2311yescharacteristic
195C2×C22⋊Dic47C2312yes—
196C2×C22⋊Dic47C2312yes—
197C2×C22⋊Dic47C2312yes—
198C2×C22⋊Dic47C2312yes—
199C2×(C2×D47)⋊C4—24no—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2311yescharacteristic
204C2×(C2×D47)⋊C4C2311yescharacteristic
205C2×(C2×D47)⋊C4C2312yes—
206C2×(C2×D47)⋊C4C2311yescharacteristic
207C2×(C2×D47)⋊C4C2311yescharacteristic
208C2×(C2×D47)⋊C4C2312yes—
209C2×(C2×D47)⋊C4C2312yes—
210C2×(C2×D47)⋊C4C2312yes—
211C2×(C2×D47)⋊C4C2312yes—
212C2×(C2×D47)⋊C4C2312yes—
213C2×(C2×D47)⋊C4C2312yes—
214C2×(C2×D47)⋊C4C2312yes—
215C2×C4×Dic47—24no—
216C2×C4×Dic47C2312yes—
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2312yes—
219C2×C4×Dic47C2312yes—
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×C47C2311yescharacteristic
239C23×C4×C47C2312yes—
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#4114yescomplemented
266C24×C47C2411yescharacteristic
267C24×C47C2412yes—
268C24×C47C2411yescharacteristic
269C23×D47—22no—
270C23×D47—22no—
271C23×D47—42no—
272C23×D47—42no—
273C23×D47C2×D414yes—
274C23×D47C2411yescharacteristic
275C23×D47C2411yescharacteristic
276C23×D47C2411yescharacteristic
277C2×D4×C47—22no—
278C2×D4×C47—24no—
279C2×D4×C47—22no—
280C2×D4×C47—22no—
281C2×D4×C47—42no—
282C2×D4×C47—42no—
283C22×C4×C47—24no—
284C22×C4×C47—22no—
285C22×C4×C47—22no—
286C22×C4×C47—24no—
287C22×C4×C47—24no—
288C22×C4×C47—24no—
289C22×C4×C47—24no—
290C22×C4×C47—24no—
291C22×C4×C47—42no—
292C22×C4×C47—42no—
293C22×C4×C47—42no—
294C22×C4×C47—416no—
295C22×C4×C47C2×D414yes—
296C22×C4×C47C2412yes—
297C22×C4×C47C2411yescharacteristic
298C22×C4×C47C2412yes—
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C22×C4×C47C2412yes—
302C22×C4×C47C2411yescharacteristic
303C22×C4×C47C2411yescharacteristic
304C2×C22⋊D47—232no—
305C2×C22⋊D47—24no—
306C2×C22⋊D47—24no—
307C2×C22⋊D47—24no—
308C2×C22⋊D47—24no—
309C2×C22⋊D47—22no—
310C2×C22⋊D47—24no—
311C2×C22⋊D47—22no—
312C2×C22⋊D47—22no—
313C2×C22⋊D47—22no—
314C2×C22⋊D47—22no—
315C2×C22⋊D47—22no—
316C2×C22⋊D47—24no—
317C2×C22⋊D47—24no—
318C2×C22⋊D47—42no—
319C2×C22⋊D47—42no—
320C2×C22⋊D47—42no—
321C2×C22⋊D47—42no—
322C2×C22⋊D47—42no—
323C22×Dic47—22no—
324C22×Dic47—22no—
325C22×Dic47—22no—
326C22×Dic47—42no—
327C22×Dic47—42no—
328C22×Dic47C2×D414yes—
329C22×Dic47#4114yescomplemented
330C22×Dic47C2412yes—
331C22×Dic47C2412yes—
332C22×Dic47C2412yes—
333C22×Dic47C2411yescharacteristic
334C22×Dic47C2411yescharacteristic
335C22×Dic47C2411yescharacteristic
336C22×Dic47C2411yescharacteristic
337C22×Dic47C2411yescharacteristic
338C22×Dic47C2412yes—
339#10625350—416no—
340C2×D188—22no—
341C2×D188—22no—
342C2×D188—42no—
343C2×D188—42no—
344C2×C4×D47—24no—
345C2×C4×D47—24no—
346C2×C4×D47—22no—
347C2×C4×D47—24no—
348C2×C4×D47—416no—
349C2×C4×D47—42no—
350C2×C4×D47—42no—
351C2×C4×D47C2×D414yes—
352C2×C4×D47C2×D414yes—
353C2×C4×D47C2×D414yes—
354C2×C4×D47C2×D414yes—
355C2×Dic94—22no—
356C2×Dic94—42no—
357C4⋊C4×C47—22no—
358C4⋊C4×C47—42no—
359C22⋊C4×C47—22no—
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×C47—22no—
368C42×C47—24no—
369C22⋊Dic47—22no—
370C22⋊Dic47—24no—
371C22⋊Dic47—22no—
372C22⋊Dic47—22no—
373C22⋊Dic47—24no—
374C22⋊Dic47—24no—
375C22⋊Dic47—22no—
376C22⋊Dic47—24no—
377C22⋊Dic47—42no—
378C22⋊Dic47—42no—
379C22⋊Dic47—42no—
380(C2×D47)⋊C4—24no—
381(C2×D47)⋊C4—24no—
382(C2×D47)⋊C4—22no—
383(C2×D47)⋊C4—22no—
384(C2×D47)⋊C4—22no—
385(C2×D47)⋊C4—22no—
386(C2×D47)⋊C4—22no—
387(C2×D47)⋊C4—22no—
388(C2×D47)⋊C4—24no—
389(C2×D47)⋊C4—42no—
390(C2×D47)⋊C4—42no—
391(C2×D47)⋊C4—42no—
392(C2×D47)⋊C4—42no—
393(C2×D47)⋊C4—42no—
394(C2×D47)⋊C4—42no—
395C4⋊Dic47—22no—
396C4⋊Dic47—24no—
397C4⋊Dic47—42no—
398Dic47⋊C4—22no—
399Dic47⋊C4—24no—
400Dic47⋊C4—24no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—24no—
405Dic47⋊C4—42no—
406Dic47⋊C4—42no—
407Dic47⋊C4—42no—
408Dic47⋊C4—42no—
409C4×Dic47—24no—
410C4×Dic47—24no—
411C4×Dic47—22no—
412C4×Dic47—24no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—28no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—22no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—21no—
423C23×C47—21no—
424C23×C47—21no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47—48no—
428C23×C47—44no—
429C23×C47—44no—
430C23×C47—48no—
431C23×C47C22×D412yes—
432C23×C47C2×#4112yes—
433C23×C47C2×#4114yes—
434C23×C47C2×#4112yes—
435C23×C47C2511yescharacteristic
436C22×D47—28no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—21no—
440C22×D47—21no—
441C22×D47—22no—
442C22×D47—22no—
443C22×D47—22no—
444C22×D47—22no—
445C22×D47—21no—
446C22×D47—21no—
447C22×D47—21no—
448C22×D47—22no—
449C22×D47—22no—
450C22×D47—44no—
451C22×D47—44no—
452C22×D47—48no—
453C22×D47—48no—
454C22×D47C22×D412yes—
455C22×D47C22×D412yes—
456D4×C47—48no—
457D4×C47—44no—
458C2×C4×C47—22no—
459C2×C4×C47—28no—
460C2×C4×C47—22no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—22no—
466C2×C4×C47—21no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—48no—
477C2×C4×C47—44no—
478C2×C4×C47—44no—
479C2×C4×C47—48no—
480C2×C4×C47C22×D412yes—
481C2×C4×C47C22×D412yes—
482C2×C4×C47H(5,𝔽2)14yes—
483C22⋊D47—216no—
484C22⋊D47—216no—
485C22⋊D47—44no—
486C22⋊D47—44no—
487C22⋊D47—44no—
488C22⋊D47—48no—
489C22⋊D47—44no—
490C2×Dic47—28no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—21no—
499C2×Dic47—22no—
500C2×Dic47—21no—
501C2×Dic47—21no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—44no—
512C2×Dic47—44no—
513C2×Dic47C22×D412yes—
514C2×Dic47C22×D412yes—
515C2×Dic47C2×#4114yes—
516D188—44no—
517D188—44no—
518C4×D47—28no—
519C4×D47—28no—
520C4×D47—44no—
521C4×D47—44no—
522C4×D47—44no—
523Dic94—44no—
524#34562—471nomaximal, Sylow
525C22×C47—22no—
526C22×C47—22no—
527C22×C47—24no—
528C22×C47—24no—
529C22×C47—24no—
530C22×C47—24no—
531C22×C47—24no—
532C22×C47—416no—
533C22×C47—42no—
534C22×C47—42no—
535C22×C47—42no—
536C22×C47—42no—
537C22×C47—41no—
538C22×C47—41no—
539C22×C47—41no—
540C22×C47—42no—
541C22×C47—42no—
542C22×C47#52514yes—
543C22×C47C23×D411yescharacteristic
544C22×C47C22×#4111yescharacteristic
545C22×C47C22×#4111yescharacteristic
546C22×C47C2×H(5,𝔽2)12yes—
547C22×C47#58512yes—
548C2×D47—22no—
549C2×D47—22no—
550C2×D47—22no—
551C2×D47—22no—
552C2×D47—22no—
553C2×D47—22no—
554C2×D47—416no—
555C2×D47—42no—
556C2×D47—42no—
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—41no—
560C2×D47—41no—
561C2×D47—41no—
562C2×D47—42no—
563C2×D47—42no—
564C4×C47—22no—
565C4×C47—41no—
566C4×C47—41no—
567C4×C47—42no—
568C4×C47—41no—
569C4×C47—42no—
570C4×C47—42no—
571C4×C47#53414yes—
572Dic47—24no—
573Dic47—22no—
574Dic47—22no—
575Dic47—41no—
576Dic47—41no—
577Dic47—42no—
578Dic47—41no—
579Dic47—42no—
580Dic47—42no—
581C2×#525—471no—
582C22×C4×D4—471no—
583#2638—472no—
584#2635—472no—
585#2630—472no—
586#2630—472no—
587#2627—471no—
588#2626—471no—
589#2622—471no—
590#2622—471no—
591#2618—471no—
592#2617—471no—
593#2613—471no—
594#2613—471no—
595#2395—472no—
596#2392—472no—
597#2392—472no—
598#2388—472no—
599C4×#123—471no—
600C4×#123—471no—
601C4×#120—471no—
602C4×#120D4711yescharacteristic, complemented
603#2280—471no—
604C2×C47—24no—
605C2×C47—44no—
606C2×C47—81no—
607C2×C47C2×#52511yescharacteristic
608C2×C47C2×#53411yescharacteristic
609C2×C47#344911yescharacteristic
610C2×C47#345912yes—
611C2×C47#346012yes—
612D47—42no—
613D47—42no—
614D47—81no—
615C22×#41—471no—
616C23×D4—471no—
617C24×C4—471no—
618C24×C4C2×D4711yescharacteristic
619#525—948no—
620C2×#123—471no—
621C2×#123—471no—
622C2×#123—471no—
623C2×#123—471no—
624C2×C22⋊Q8—471no—
625C2×C22⋊Q8—471no—
626C2×#121—471no—
627C2×#121—471no—
628C2×#120—471no—
629C2×#120—471no—
630C2×#120—471no—
631C2×#120C2×D4711yescharacteristic
632C2×C4×D4—472no—
633C2×C4×D4—472no—
634C2×C4×D4—472no—
635C2×C4×D4—472no—
636C2×C4×D4—471no—
637C2×C4×D4—471no—
638C2×C4×D4—472no—
639C2×C4×D4—471no—
640C2×C4×D4—948no—
641C2×C4×D4C2×D4711yescharacteristic
642C2×C4×D4C2×D4712yescomplemented
643C2×#117—471no—
644C2×#117—472no—
645C22×C4⋊C4—471no—
646C22×C22⋊C4—471no—
647C22×C22⋊C4—471no—
648C22×C42—471no—
649#400—472no—
650#399—472no—
651#398—472no—
652#398—472no—
653#398—472no—
654#397—472no—
655#397—472no—
656#397—472no—
657#397—472no—
658#397—472no—
659#396—472no—
660#396—472no—
661#396—472no—
662#396—472no—
663#395—472no—
664#394—472no—
665#394—472no—
666#394—472no—
667#394—472no—
668#394—472no—
669#394—472no—
670#394—472no—
671#394—472no—
672#394—472no—
673#394—472no—
674#394—472no—
675#393—472no—
676#392—472no—
677#392—472no—
678#392—472no—
679#392—472no—
680#392—472no—
681#388—472no—
682#388—472no—
683#387—472no—
684#387—472no—
685#386—471no—
686#386—471no—
687#386—472no—
688#386—471no—
689#386C2×D4711yescharacteristic
690#386C2×D4712yescomplemented
691#385—471no—
692#385—472no—
693#385—471no—
694#385—471no—
695#385C2×D4711yescharacteristic
696#385C2×D4712yescomplemented
697#381—471no—
698#381—471no—
699#381—472no—
700#380—471no—
701#380—471no—
702#380—472no—
703#379—471no—
704#379—471no—
705#379—471no—
706#379C2×D4711yescharacteristic
707C4×C4⋊C4—472no—
708C4×C4⋊C4—472no—
709C4×C22⋊C4—471no—
710C4×C22⋊C4—472no—
711C4×C22⋊C4—472no—
712C4×C22⋊C4—472no—
713C4×C22⋊C4—472no—
714C4×C22⋊C4C2×D4711yescharacteristic
715C4×C22⋊C4C2×D4712yescomplemented
716C47#3456211yescharacteristic, complemented, Sylow
717C25—471no—
718C25C22×D4711yescharacteristic
719C2×#41—944no—
720C2×#41—1884no—
721C22×Q8—471no—
722C22×D4—472no—
723C22×D4—472no—
724C22×D4—471no—
725C22×D4—471no—
726C22×D4—472no—
727C22×D4—471no—
728C22×D4—471no—
729C22×D4—471no—
730C22×D4—471no—
731C22×D4—944no—
732C22×D4—944no—
733C22×D4—944no—
734C22×D4C22×D4711yescharacteristic
735C22×D4C22×D4712yes—
736C23×C4—24no—
737C23×C4—44no—
738C23×C4—471no—
739C23×C4—471no—
740C23×C4—471no—
741C23×C4—471no—
742C23×C4—478no—
743C23×C4—471no—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—471no—
747C23×C4—1884no—
748C23×C4C22×D4712yes—
749C23×C4C22×D4711yescharacteristic
750C23×C4C22×D4711yescharacteristic
751C23×C4C22×D4711yescharacteristic
752C23×C4C22×D4712yes—
753#123—944no—
754#123—944no—
755#123—944no—
756#123—944no—
757C22⋊Q8—944no—
758C22⋊Q8—944no—
759#121—944no—
760#121—944no—
761#120—24no—
762#120—944no—
763#120—944no—
764#120—944no—
765C4×D4—24no—
766C4×D4—44no—
767C4×D4—944no—
768C4×D4—948no—
769C4×D4—948no—
770C4×D4—948no—
771C4×D4—948no—
772C4×D4—944no—
773C4×D4—944no—
774C4×D4—1884no—
775#117—944no—
776#117—1884no—
777C2×C4⋊C4—472no—
778C2×C4⋊C4—472no—
779C2×C4⋊C4—471no—
780C2×C4⋊C4—471no—
781C2×C4⋊C4—471no—
782C2×C4⋊C4—471no—
783C2×C4⋊C4—471no—
784C2×C4⋊C4—472no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—472no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—472no—
789C2×C4⋊C4—472no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4—944no—
792C2×C4⋊C4C22×D4711yescharacteristic
793C2×C4⋊C4C22×D4712yes—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—471no—
799C2×C22⋊C4—472no—
800C2×C22⋊C4—471no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—471no—
805C2×C22⋊C4—471no—
806C2×C22⋊C4—471no—
807C2×C22⋊C4—471no—
808C2×C22⋊C4—471no—
809C2×C22⋊C4—471no—
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⋊C4—944no—
822C2×C22⋊C4C22×D4711yescharacteristic
823C2×C22⋊C4C22×D4711yescharacteristic
824C2×C22⋊C4C22×D4711yescharacteristic
825C2×C22⋊C4C22×D4712yes—
826C2×C22⋊C4C22×D4711yescharacteristic
827C2×C22⋊C4C22×D4712yes—
828C2×C22⋊C4C22×D4712yes—
829C2×C22⋊C4C22×D4712yes—
830C2×C42—472no—
831C2×C42—471no—
832C2×C42—472no—
833C2×C42—472no—
834C2×C42—944no—
835C2×C42C22×D4711yescharacteristic
836C2×C42C22×D4712yes—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95—472no—
842#95—472no—
843#95—472no—
844#95—472no—
845#95—472no—
846#95—472no—
847#95—472no—
848#95—472no—
849#95—472no—
850#95C22×D4712yes—
851#95C22×D4712yes—
852#95C22×D4712yes—
853C24—22no—
854C24—22no—
855C24—42no—
856C24—42no—
857C24—471no—
858C24—471no—
859C24—474no—
860C24—471no—
861C24—942no—
862C24—942no—
863C24—1882no—
864C24—1882no—
865C24#1062535014yescomplemented
866C24C23×D4711yescharacteristic
867C24C23×D4712yes—
868C24C23×D4711yescharacteristic
869#41—18816no—
870C2×Q8—942no—
871C2×Q8—1882no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—24no—
875C2×D4—22no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—942no—
879C2×D4—942no—
880C2×D4—944no—
881C2×D4—944no—
882C2×D4—942no—
883C2×D4—944no—
884C2×D4—944no—
885C2×D4—9432no—
886C2×D4—944no—
887C2×D4—944no—
888C2×D4—942no—
889C2×D4—942no—
890C2×D4—942no—
891C2×D4—942no—
892C2×D4—944no—
893C2×D4—942no—
894C2×D4—1882no—
895C2×D4—1882no—
896C2×D4—1882no—
897C2×D4—1882no—
898C2×D4—1882no—
899C2×D4—1882no—
900C2×D4—1882no—
901C22×C4—24no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—416no—
913C22×C4—474no—
914C22×C4—472no—
915C22×C4—471no—
916C22×C4—471no—
917C22×C4—474no—
918C22×C4—474no—
919C22×C4—474no—
920C22×C4—474no—
921C22×C4—474no—
922C22×C4—472no—
923C22×C4—472no—
924C22×C4—472no—
925C22×C4—471no—
926C22×C4—471no—
927C22×C4—471no—
928C22×C4—942no—
929C22×C4—942no—
930C22×C4—944no—
931C22×C4—944no—
932C22×C4—942no—
933C22×C4—942no—
934C22×C4—944no—
935C22×C4—18816no—
936C22×C4—1882no—
937C22×C4—1882no—
938C22×C4—1882no—
939C22×C4—1882no—
940C22×C4D4×D4714yes—
941C22×C4C23×D4712yes—
942C22×C4C23×D4711yescharacteristic
943C22×C4C23×D4712yes—
944C22×C4C23×D4711yescharacteristic
945C22×C4C23×D4711yescharacteristic
946C22×C4C23×D4712yes—
947C22×C4C23×D4711yescharacteristic
948C22×C4C23×D4711yescharacteristic
949C4⋊C4—22no—
950C4⋊C4—42no—
951C4⋊C4—944no—
952C4⋊C4—944no—
953C4⋊C4—942no—
954C4⋊C4—942no—
955C4⋊C4—942no—
956C4⋊C4—944no—
957C4⋊C4—942no—
958C4⋊C4—944no—
959C4⋊C4—942no—
960C4⋊C4—1882no—
961C4⋊C4—1882no—
962C4⋊C4—1882no—
963C4⋊C4—1882no—
964C4⋊C4—1882no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—24no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—942no—
974C22⋊C4—944no—
975C22⋊C4—944no—
976C22⋊C4—944no—
977C22⋊C4—942no—
978C22⋊C4—942no—
979C22⋊C4—942no—
980C22⋊C4—942no—
981C22⋊C4—944no—
982C22⋊C4—944no—
983C22⋊C4—942no—
984C22⋊C4—944no—
985C22⋊C4—942no—
986C22⋊C4—942no—
987C22⋊C4—944no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—1882no—
991C22⋊C4—1882no—
992C22⋊C4—1882no—
993C22⋊C4—1882no—
994C22⋊C4—1882no—
995C22⋊C4—1882no—
996C22⋊C4—1882no—
997C22⋊C4—1882no—
998C22⋊C4—1882no—
999C42—22no—
1000C42—24no—
1001C42—944no—
1002C42—944no—
1003C42—942no—
1004C42—944no—
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—22no—
1018C23—22no—
1019C23—48no—
1020C23—44no—
1021C23—48no—
1022C23—44no—
1023C23—472no—
1024C23—472no—
1025C23—948no—
1026C23—941no—
1027C23—941no—
1028C23—941no—
1029C23—941no—
1030C23—942no—
1031C23—942no—
1032C23—942no—
1033C23—942no—
1034C23—941no—
1035C23—941no—
1036C23—941no—
1037C23—942no—
1038C23—942no—
1039C23—1884no—
1040C23—1884no—
1041C23—1888no—
1042C23—1888no—
1043C23C2×D4×D4712yes—
1044C23#41×D4712yes—
1045C23C2×#1062535014yes—
1046C23C2×#1062535012yes—
1047C23C24×D4711yescharacteristic
1048Q8—1884no—
1049D4—48no—
1050D4—44no—
1051D4—9416no—
1052D4—9416no—
1053D4—1884no—
1054D4—1884no—
1055D4—1884no—
1056D4—1888no—
1057D4—1884no—
1058D4—1884no—
1059D4—1884no—
1060C2×C4—22no—
1061C2×C4—28no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—48no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—44no—
1082C2×C4—472no—
1083C2×C4—472no—
1084C2×C4—474no—
1085C2×C4—948no—
1086C2×C4—942no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—948no—
1091C2×C4—948no—
1092C2×C4—942no—
1093C2×C4—941no—
1094C2×C4—941no—
1095C2×C4—941no—
1096C2×C4—942no—
1097C2×C4—941no—
1098C2×C4—942no—
1099C2×C4—941no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—942no—
1103C2×C4—942no—
1104C2×C4—942no—
1105C2×C4—942no—
1106C2×C4—942no—
1107C2×C4—942no—
1108C2×C4—1884no—
1109C2×C4—1884no—
1110C2×C4—1884no—
1111C2×C4—1884no—
1112C2×C4—1884no—
1113C2×C4C2×D4×D4712yes—
1114C2×C4C2×D4×D4712yes—
1115C2×C4#1309406914yes—
1116C22—24no—
1117C22—24no—
1118C22—22no—
1119C22—22no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—416no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—942no—
1134C22—942no—
1135C22—942no—
1136C22—942no—
1137C22—942no—
1138C22—942no—
1139C22—18816no—
1140C22—1882no—
1141C22—1882no—
1142C22—1881no—
1143C22—1881no—
1144C22—1881no—
1145C22—1882no—
1146C22—1882no—
1147C22—1882no—
1148C22—1882no—
1149C22#1568963214yes—
1150C22C22×D4×D4711yescharacteristic
1151C22C2×#41×D4711yescharacteristic
1152C22C22×#1062535011yescharacteristic
1153C22C2×#1309406912yes—
1154C22#1568995912yes—
1155C4—22no—
1156C4—42no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—41no—
1162C4—944no—
1163C4—942no—
1164C4—942no—
1165C4—1882no—
1166C4—1882no—
1167C4—1881no—
1168C4—1881no—
1169C4—1882no—
1170C4—1881no—
1171C4#1568968314yes—
1172C2—24no—
1173C2—44no—
1174C2—81no—
1175C2—3761no—
1176C2—1882no—
1177C2—1882no—
1178C2C2×#1568963211yescharacteristic
1179C2C2×#1568968311yescharacteristic
1180C2#2025671811yescharacteristic
1181C2#2025679712yes—
1182C2#2025680612yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC4×#120×C47C2
hypercenterC4×#120D47
hypocenterC47#34562
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×#15689632C2semidirect
2. C22×C4×C22⋊D47C2semidirect
3. #20249309C2semidirect
4. #20249276C2semidirect
5. #20249233C2semidirect
6. #20249231C2semidirect
7. #20249207C2semidirect
8. #20249197C2semidirect
9. #20249166C2semidirect
10. #20249165C2semidirect
11. #20249136C2semidirect
12. #20249126C2semidirect
13. #20249103C2semidirect
14. #20249102C2semidirect
15. #20246649C2semidirect
16. #20246632C2semidirect
17. #20246626C2semidirect
18. #20246603C2semidirect
19. C4×#13094008C2semidirect
20. C4×#13094005C2semidirect
21. C4×#13093993C2semidirect
22. #20245769C2semidirect
23. C4×#120×C47C2semidirect
24. C22×#10625350C22semidirect
28. C2×#13094009C22semidirect
30. C2×#13094006C22semidirect
32. C2×#13094002C22semidirect
34. C2×#13093997C22semidirect
39. C2×C4×D188C22semidirect
46. C2×C4×C22⋊D47C22semidirect
47. C2×C4×C22⋊D47C22semidirect
48. C2×#13093981C22semidirect
49. C2×#13093981C22semidirect
54. #15689064C22semidirect
55. #15689059C22semidirect
56. #15689057C22semidirect
57. #15689057C22semidirect
58. #15689054C22semidirect
59. #15689052C22semidirect
60. #15689052C22semidirect
61. #15689051C22semidirect
62. #15689050C22semidirect
63. #15689049C22semidirect
64. #15689047C22semidirect
65. #15689046C22semidirect
66. #15689046C22semidirect
67. #15689046C22semidirect
68. #15689043C22semidirect
69. #15689041C22semidirect
70. #15689040C22semidirect
73. #15689039C22semidirect
76. #15689038C22semidirect
77. #15689038C22semidirect
78. #15689038C22semidirect
79. #15689037C22semidirect
80. #15689035C22semidirect
85. #15689031C22semidirect
86. #15689015C22semidirect
87. #15689011C22semidirect
88. #15689008C22semidirect
89. #15689004C22semidirect
92. #15689002C22semidirect
96. #15688996C22semidirect
98. #15688985C22semidirect
101. #15688982C22semidirect
107. C4×Dic47⋊C4C22semidirect
108. C4×C4⋊Dic47C22semidirect
109. C4×(C2×D47)⋊C4C22semidirect
110. C4×(C2×D47)⋊C4C22semidirect
112. C4×C22⋊Dic47C22semidirect
113. C4×C22⋊Dic47C22semidirect
117. C2×C4×D4×C47C22semidirect
119. C47×#386C22semidirect
121. C47×#385C22semidirect
124. C4×C22⋊C4×C47C22semidirect
145. C22×C4×D47D4semidirect
265. C24×C47#41semidirect
329. C22×Dic47#41semidirect
602. C4×#120D47semidirect
642. C2×C4×D4C2×D47semidirect
690. #386C2×D47semidirect
696. #385C2×D47semidirect
715. C4×C22⋊C4C2×D47semidirect
716. C47#34562semidirect
865. C24#10625350semidirect

Maximal subgroups

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

subgroupindex
C2×#156896322
C22×C4×C22⋊D472
#202493092
#202492762
#202492332
#202492312
#202492072
#202491972
#202491662
#202491652
#202491362
#202491262
#202491032
#202491022
#202466492
#202466322
#202466262
#202466032
C4×#130940082
C4×#130940052
C4×#130939932
#202457692
C4×#120×C472
#3456247