Finite Group Databasebeta

← #26384449

Subgroups — #26384449

Order 12032.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689654C211yesmaximal, characteristic, complemented
2C22×D4×Dic47C211yesmaximal, characteristic, complemented
3#20247631C212yesmaximal, complemented
4#20247447C212yesmaximal, complemented
5#20247288C212yesmaximal, complemented
6#20247263C211yesmaximal, characteristic, complemented
7#20247173C211yesmaximal, characteristic, complemented
8#20247113C211yesmaximal, characteristic, complemented
9#20247035C211yesmaximal, characteristic, complemented
10#20246967C211yesmaximal, characteristic, complemented
11#20246876C211yesmaximal, characteristic, complemented
12#20246846C212yesmaximal, complemented
13#20246839C211yesmaximal, characteristic, complemented
14#20246644C212yesmaximal, complemented
15#20246623C212yesmaximal, complemented
16#20245935C211yesmaximal, characteristic, complemented
17#20245916C211yesmaximal, characteristic, complemented
18#121×Dic47C211yesmaximal, characteristic, complemented
19#120×Dic47C212yesmaximal, complemented
20#20245850C211yesmaximal, characteristic, complemented
21#20245766C212yesmaximal, complemented
22C4×D4×Dic47C211yesmaximal, characteristic, complemented
23C47×#2408C211yesmaximal, characteristic
24C24×Dic47C2212yes—
25#15689654—28no—
26C2×#13094017C2212yescomplemented
27C2×#13094015C2211yescharacteristic, complemented
28C2×#13094011C2211yescharacteristic
29C2×#13094011C2211yescharacteristic
30C2×#13094005C2212yescomplemented
31C2×#13094003C2211yescharacteristic
32C2×#13094003C2211yescharacteristic, complemented
33C2×#13093989C2211yescharacteristic, complemented
34C2×D4×Dic47—28no—
35C2×D4×Dic47C2211yescharacteristic
36C2×D4×Dic47C2212yes—
37C2×D4×Dic47C2211yescharacteristic
38C2×D4×Dic47C2212yes—
39C2×D4×Dic47C2211yescharacteristic
40C2×D4×Dic47C2211yescharacteristic
41C2×D4×Dic47C2211yescharacteristic
42C2×D4×Dic47C2211yescharacteristic
43C2×D4×Dic47C2212yescomplemented
44C2×D4×Dic47C2212yescomplemented
45C2×#13093980C2212yescomplemented
46C2×#13093980C2212yescomplemented
47C22×C4⋊Dic47C2211yescharacteristic
48C22×C22⋊Dic47C2212yes—
49C22×C4×Dic47C2211yescharacteristic
50C22×C4×Dic47C2211yescharacteristic, complemented
51#15689065C2212yescomplemented
52#15689059C2212yescomplemented
53#15689056C2212yescomplemented
54#15689055C2212yescomplemented
55#15689051C2212yescomplemented
56#15689051C2212yescomplemented
57#15689048C2212yescomplemented
58#15689048C2212yescomplemented
59#15689046C2212yescomplemented
60#15689046C2212yescomplemented
61#15689037C2212yes—
62#15689037C2212yes—
63#15689037C2212yescomplemented
64#15689037C2212yescomplemented
65#15689029C2211yescharacteristic, complemented
66#15689028C2211yescharacteristic, complemented
67#15689026C2211yescharacteristic
68#15689026C2211yescharacteristic
69#15689022C2211yescharacteristic, complemented
70#15689021C2211yescharacteristic, complemented
71#15689019C2211yescharacteristic, complemented
72#15689019C2211yescharacteristic, complemented
73#15689017C2212yescomplemented
74#15689016C2212yescomplemented
75#15689011C2212yescomplemented
76#15689011C2212yescomplemented
77#15689011C2212yescomplemented
78#15689005C2212yescomplemented
79#15689003C2212yes—
80#15689003C2212yescomplemented
81#15689003C2212yescomplemented
82#15689003C2212yescomplemented
83#15688998C2212yes—
84#15688998C2212yescomplemented
85#15688998C2212yescomplemented
86#15688995C2212yes—
87#15688988C2211yescharacteristic, complemented
88#15688984C2212yescomplemented
89#15688984C2212yescomplemented
90#15688983C2211yescharacteristic, complemented
91#15688981C2212yes—
92#15688981C2212yes—
93#15688981C2212yescomplemented
94#15688981C2212yescomplemented
95#15688979C2212yes—
96#15688979C2212yes—
97C4⋊C4×Dic47C2211yescharacteristic, complemented
98C4⋊C4×Dic47C2211yescharacteristic, complemented
99C4⋊C4×Dic47C2211yescharacteristic, complemented
100C4×C4⋊Dic47C2211yescharacteristic, complemented
101#15688974C2212yescomplemented
102C22⋊C4×Dic47C2211yescharacteristic
103C22⋊C4×Dic47C2212yes—
104C22⋊C4×Dic47C2211yescharacteristic
105C22⋊C4×Dic47C2212yescomplemented
106C22⋊C4×Dic47C2212yescomplemented
107C22⋊C4×Dic47C2212yescomplemented
108C22⋊C4×Dic47C2211yescharacteristic, complemented
109C22⋊C4×Dic47C2212yescomplemented
110C22⋊C4×Dic47C2211yescharacteristic, complemented
111C4×C22⋊Dic47C2211yescharacteristic
112C4×C22⋊Dic47C2211yescharacteristic, complemented
113C42×Dic47C2211yescharacteristic, complemented
114C23×D4×C47C2211yescharacteristic
115C2×#121×C47C2211yescharacteristic
116C2×#121×C47C2211yescharacteristic
117C2×#120×C47C2212yes—
118C2×C4×D4×C47C2211yescharacteristic
119C47×#394C2212yes—
120C47×#392C2212yes—
121C47×#390C2211yescharacteristic
122C47×#390C2211yescharacteristic
123C47×#380C2211yescharacteristic
124C47×#379C2212yes—
125C22×Dic94C2311yescharacteristic
126C23×Dic47—28no—
127C23×Dic47—28no—
128C23×Dic47—44no—
129C23×Dic47C2312yes—
130C23×Dic47C2311yescharacteristic
131C23×Dic47C2311yescharacteristic
132C23×Dic47C2311yescharacteristic
133C23×Dic47C2312yes—
134C23×Dic47C2312yes—
135C23×Dic47C2312yes—
136C23×Dic47C2312yes—
137C23×Dic47C2311yescharacteristic
138#13094017—28no—
139#13094015—24no—
140#13094011—24no—
141#13094011—24no—
142#13094005—28no—
143#13094003—24no—
144#13094003—24no—
145#13093989—24no—
146D4×Dic47—24no—
147D4×Dic47—24no—
148D4×Dic47—28no—
149D4×Dic47—28no—
150D4×Dic47—24no—
151D4×Dic47—28no—
152D4×Dic47—24no—
153D4×Dic47—24no—
154D4×Dic47—44no—
155D4×Dic47D418yescomplemented
156#13093980—28no—
157#13093980—44no—
158C2×C4⋊Dic47—24no—
159C2×C4⋊Dic47C2311yescharacteristic
160C2×C4⋊Dic47C2311yescharacteristic
161C2×C4⋊Dic47C2311yescharacteristic
162C2×C4⋊Dic47C2311yescharacteristic
163C2×C4⋊Dic47C2312yes—
164C2×C4⋊Dic47C2312yes—
165C2×C4⋊Dic47C2312yes—
166C2×C4⋊Dic47C2311yescharacteristic
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2312yes—
172C2×Dic47⋊C4C2312yes—
173C2×Dic47⋊C4C2312yes—
174C2×C22⋊Dic47—28no—
175C2×C22⋊Dic47C2311yescharacteristic
176C2×C22⋊Dic47C2311yescharacteristic
177C2×C22⋊Dic47C2311yescharacteristic
178C2×C22⋊Dic47C2311yescharacteristic
179C2×C22⋊Dic47C2312yes—
180C2×C22⋊Dic47C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2312yes—
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2312yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×C4×Dic47—24no—
195C2×C4×Dic47—24no—
196C2×C4×Dic47C2311yescharacteristic
197C2×C4×Dic47C2311yescharacteristic
198C2×C4×Dic47C2311yescharacteristic
199C2×C4×Dic47C2311yescharacteristic
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
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—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C25×C47C2312yes—
229C22×D4×C47—24no—
230C22×D4×C47—24no—
231C22×D4×C47—24no—
232C22×D4×C47C2312yes—
233C22×D4×C47C2312yes—
234C22×D4×C47C2312yes—
235C22×D4×C47C2311yescharacteristic
236C22×D4×C47C2311yescharacteristic
237C22×D4×C47C2311yescharacteristic
238C23×C4×C47C2311yescharacteristic
239C23×C4×C47C2311yescharacteristic
240#121×C47—24no—
241#121×C47—24no—
242#120×C47—28no—
243C4×D4×C47—24no—
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2311yescharacteristic
247C2×C22⋊C4×C47C2311yescharacteristic
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C22⋊C4×C47C2312yes—
253C2×C22⋊C4×C47C2312yes—
254C2×C22⋊C4×C47C2312yes—
255C2×C22⋊C4×C47C2312yes—
256C2×C42×C47C2311yescharacteristic
257#95×C47C2312yes—
258C24×C47—24no—
259C24×C47—24no—
260C24×C47—24no—
261C24×C47—24no—
262C24×C47—24no—
263C24×C47—42no—
264C24×C47—42no—
265C24×C47C2412yes—
266C24×C47C2412yes—
267C24×C47C2411yescharacteristic
268C24×C47C2411yescharacteristic
269C2×D4×C47—232no—
270C2×D4×C47—24no—
271C2×D4×C47—22no—
272C2×D4×C47—24no—
273C2×D4×C47—22no—
274C2×D4×C47—24no—
275C2×D4×C47—24no—
276C2×D4×C47—24no—
277C2×D4×C47—24no—
278C2×D4×C47—22no—
279C2×D4×C47—24no—
280C2×D4×C47—22no—
281C2×D4×C47—22no—
282C2×D4×C47—22no—
283C2×D4×C47—42no—
284C2×D4×C47—42no—
285C2×D4×C47C2×D414yes—
286C2×D4×C47#4114yes—
287C2×D4×C47#4114yes—
288C22×C4×C47—22no—
289C22×C4×C47—22no—
290C22×C4×C47—22no—
291C22×C4×C47—22no—
292C22×C4×C47—22no—
293C22×C4×C47#4114yes—
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C22×C4×C47C2412yes—
297C22×C4×C47C2412yes—
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C22×Dic47—22no—
302C22×Dic47—24no—
303C22×Dic47—24no—
304C22×Dic47—22no—
305C22×Dic47—24no—
306C22×Dic47—22no—
307C22×Dic47—22no—
308C22×Dic47—24no—
309C22×Dic47—22no—
310C22×Dic47—22no—
311C22×Dic47—22no—
312C22×Dic47—24no—
313C22×Dic47—24no—
314C22×Dic47—24no—
315C22×Dic47—22no—
316C22×Dic47—24no—
317C22×Dic47—24no—
318C22×Dic47—24no—
319C22×Dic47—22no—
320C22×Dic47—24no—
321C22×Dic47—42no—
322C22×Dic47—42no—
323C22×Dic47—42no—
324C22×Dic47—41no—
325C22×Dic47—41no—
326C22×Dic47—432no—
327C22×Dic47C2×D418yes—
328C22×Dic47#4114yes—
329C22×Dic47C2411yescharacteristic
330C22×Dic47C2412yes—
331C22×Dic47C2411yescharacteristic
332C22×Dic47C2411yescharacteristic
333C22×Dic47C2411yescharacteristic
334C22×Dic47C2412yes—
335C22×Dic47C2412yes—
336C22×Dic47C2411yescharacteristic
337C22×Dic47C2411yescharacteristic
338C22×Dic47C2412yes—
339C22×Dic47C2411yescharacteristic
340C22×Dic47C2411yescharacteristic
341C2×Dic94—22no—
342C2×Dic94—22no—
343C2×Dic94—22no—
344C4⋊C4×C47—22no—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
347C22⋊C4×C47—24no—
348C22⋊C4×C47—22no—
349C22⋊C4×C47—24no—
350C22⋊C4×C47—24no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—24no—
353C22⋊C4×C47—24no—
354C22⋊C4×C47—42no—
355C22⋊C4×C47—42no—
356C42×C47—22no—
357C22⋊Dic47—24no—
358C22⋊Dic47—24no—
359C22⋊Dic47—24no—
360C22⋊Dic47—22no—
361C22⋊Dic47—22no—
362C22⋊Dic47—22no—
363C22⋊Dic47—24no—
364C22⋊Dic47—24no—
365C22⋊Dic47—24no—
366C22⋊Dic47—24no—
367C22⋊Dic47—24no—
368C22⋊Dic47—24no—
369C22⋊Dic47—22no—
370C22⋊Dic47—42no—
371C22⋊Dic47—42no—
372C22⋊Dic47—42no—
373C22⋊Dic47—42no—
374C22⋊Dic47—42no—
375C22⋊Dic47C2×D418yes—
376C4⋊Dic47—22no—
377C4⋊Dic47—22no—
378C4⋊Dic47—22no—
379C4⋊Dic47—24no—
380C4⋊Dic47—24no—
381C4⋊Dic47—22no—
382C4⋊Dic47—42no—
383C4⋊Dic47C2×D414yes—
384Dic47⋊C4—24no—
385Dic47⋊C4—24no—
386Dic47⋊C4—24no—
387Dic47⋊C4—24no—
388Dic47⋊C4—42no—
389Dic47⋊C4—42no—
390Dic47⋊C4—42no—
391C4×Dic47—22no—
392C4×Dic47—22no—
393C4×Dic47—22no—
394C4×Dic47—22no—
395C4×Dic47—22no—
396C4×Dic47—22no—
397C4×Dic47—22no—
398C4×Dic47—22no—
399C4×Dic47—24no—
400C4×Dic47—22no—
401C4×Dic47—22no—
402C4×Dic47—24no—
403C4×Dic47—41no—
404C4×Dic47C2×D414yes—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47—21no—
409C23×C47—216no—
410C23×C47—21no—
411C23×C47—22no—
412C23×C47—21no—
413C23×C47—21no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—21no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—21no—
423C23×C47—22no—
424C23×C47—22no—
425C23×C47—22no—
426C23×C47—22no—
427C23×C47—21no—
428C23×C47—48no—
429C23×C47—48no—
430C23×C47—48no—
431C23×C47—48no—
432C23×C47—48no—
433C23×C47—48no—
434C23×C47C22×D414yes—
435C23×C47C2×#4112yes—
436C23×C47C2×#4114yes—
437C23×C47C2×#4112yes—
438C23×C47C2×#4112yes—
439C23×C47C2×#4112yes—
440C23×C47C2511yescharacteristic
441D4×C47—216no—
442D4×C47—28no—
443D4×C47—28no—
444D4×C47—28no—
445D4×C47—48no—
446D4×C47—48no—
447C2×C4×C47—21no—
448C2×C4×C47—21no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—28no—
452C2×C4×C47—21no—
453C2×C4×C47—22no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—22no—
457C2×C4×C47—22no—
458C2×C4×C47—21no—
459C2×C4×C47—22no—
460C2×C4×C47—21no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—22no—
464C2×C4×C47—44no—
465C2×C4×C47C22×D412yes—
466C2×C4×C47C2×#4112yes—
467C2×C4×C47C2×#4112yes—
468C2×C4×C47C2×#4112yes—
469C2×C4×C47C2×#4112yes—
470C2×Dic47—21no—
471C2×Dic47—21no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—21no—
475C2×Dic47—21no—
476C2×Dic47—28no—
477C2×Dic47—216no—
478C2×Dic47—21no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—22no—
488C2×Dic47—22no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—21no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—22no—
498C2×Dic47—21no—
499C2×Dic47—21no—
500C2×Dic47—22no—
501C2×Dic47—21no—
502C2×Dic47—48no—
503C2×Dic47—44no—
504C2×Dic47—44no—
505C2×Dic47—48no—
506C2×Dic47—48no—
507C2×Dic47—44no—
508C2×Dic47—48no—
509C2×Dic47C22×D412yes—
510C2×Dic47C22×D414yes—
511C2×Dic47C22×D412yes—
512C2×Dic47C2×#4112yes—
513C2×Dic47C2×#4112yes—
514C2×Dic47H(5,𝔽2)12yes—
515Dic94—44no—
516#34700—471nomaximal, Sylow
517C22×C47—22no—
518C22×C47—22no—
519C22×C47—22no—
520C22×C47—22no—
521C22×C47—22no—
522C22×C47—22no—
523C22×C47—24no—
524C22×C47—24no—
525C22×C47—22no—
526C22×C47—24no—
527C22×C47—22no—
528C22×C47—24no—
529C22×C47—24no—
530C22×C47—22no—
531C22×C47—24no—
532C22×C47—432no—
533C22×C47—41no—
534C22×C47—42no—
535C22×C47—42no—
536C22×C47—41no—
537C22×C47—42no—
538C22×C47—42no—
539C22×C47—42no—
540C22×C47—41no—
541C22×C47—42no—
542C22×C47—41no—
543C22×C47—42no—
544C22×C47—42no—
545C22×C47#52914yescomplemented
546C22×C47C23×D411yescharacteristic
547C22×C47C22×#4111yescharacteristic
548C22×C47C22×#4111yescharacteristic
549C22×C47C22×#4111yescharacteristic
550C22×C47C22×#4111yescharacteristic
551C22×C47C2×H(5,𝔽2)11yescharacteristic
552C22×C47#58511yescharacteristic
553C4×C47—22no—
554C4×C47—22no—
555C4×C47—41no—
556C4×C47—41no—
557C4×C47—42no—
558C4×C47—42no—
559C4×C47#52514yes—
560Dic47—22no—
561Dic47—24no—
562Dic47—22no—
563Dic47—42no—
564Dic47—42no—
565Dic47—41no—
566Dic47—42no—
567Dic47—41no—
568Dic47—41no—
569Dic47—41no—
570Dic47—41no—
571Dic47#54614yes—
572C2×#529—471no—
573C22×C4×D4—471no—
574#2480—472no—
575#2468—472no—
576#2457—472no—
577#2454—471no—
578#2447—471no—
579#2442—471no—
580#2435—471no—
581#2427—471no—
582#2420—471no—
583#2418—472no—
584#2417—471no—
585#2408D4711yescharacteristic
586#2395—472no—
587#2392—472no—
588C4×#124—471no—
589C4×C22⋊Q8—471no—
590C4×#121—471no—
591C4×#120—472no—
592#2293—471no—
593#2280—472no—
594C42×D4—471no—
595C2×C47—24no—
596C2×C47—42no—
597C2×C47—44no—
598C2×C47—44no—
599C2×C47C2×#52511yescharacteristic
600C2×C47C2×#52911yescharacteristic
601C2×C47#346011yescharacteristic
602C2×C47C2×#54611yescharacteristic
603C2×C47D4×#4111yescharacteristic
604C2×C47#347511yescharacteristic
605C2×C47#348111yescharacteristic
606C23×D4C2×D4711yescharacteristic
607C24×C4—472no—
608#529—948no—
609C2×#126—472no—
610C2×#125—471no—
611C2×#124—471no—
612C2×#124—471no—
613C2×#123—472no—
614C2×C22⋊Q8—471no—
615C2×C22⋊Q8—471no—
616C2×#121C2×D4711yescharacteristic
617C2×#121C2×D4711yescharacteristic
618C2×#120C2×D4712yes—
619C2×C4×Q8—471no—
620C2×C4×D4—471no—
621C2×C4×D4—472no—
622C2×C4×D4—472no—
623C2×C4×D4—471no—
624C2×C4×D4—471no—
625C2×C4×D4—472no—
626C2×C4×D4—471no—
627C2×C4×D4—471no—
628C2×C4×D4—471no—
629C2×C4×D4—472no—
630C2×C4×D4—948no—
631C2×C4×D4C2×D4711yescharacteristic
632C2×#117—472no—
633C2×#117—472no—
634C22×C4⋊C4—471no—
635C22×C22⋊C4—472no—
636C22×C42—471no—
637C22×C42—471no—
638#400—472no—
639#399—472no—
640#398—472no—
641#398—472no—
642#397—472no—
643#397—472no—
644#397—472no—
645#397—472no—
646#396—472no—
647#396—472no—
648#394—472no—
649#394—472no—
650#394—472no—
651#394—472no—
652#394C2×D4712yes—
653#392C2×D4712yes—
654#391—471no—
655#391—471no—
656#390—471no—
657#390—471no—
658#390C2×D4711yescharacteristic
659#390C2×D4711yescharacteristic
660#389—471no—
661#389—471no—
662#389—471no—
663#389—471no—
664#388—472no—
665#388—472no—
666#388—472no—
667#388—472no—
668#388—472no—
669#387—472no—
670#386—472no—
671#386—472no—
672#386—472no—
673#386—472no—
674#385—472no—
675#385—472no—
676#385—472no—
677#385—472no—
678#382—471no—
679#381—472no—
680#381—472no—
681#380—471no—
682#380—472no—
683#380—472no—
684#380—472no—
685#380—472no—
686#380C2×D4711yescharacteristic
687#379—472no—
688#379—472no—
689#379C2×D4712yes—
690C4×C4⋊C4—471no—
691C4×C4⋊C4—471no—
692C4×C4⋊C4—471no—
693C4×C4⋊C4—471no—
694C4×C4⋊C4—472no—
695C4×C22⋊C4—471no—
696C4×C22⋊C4—471no—
697C4×C22⋊C4—471no—
698C4×C22⋊C4—471no—
699C4×C22⋊C4—472no—
700C4×C22⋊C4—471no—
701C4×C22⋊C4—472no—
702C4×C22⋊C4—472no—
703C4×C22⋊C4—472no—
704C4×C22⋊C4—472no—
705C4×C22⋊C4—471no—
706C43—471no—
707C47#3470011yescharacteristic, complemented, Sylow
708C25C22×D4712yes—
709C22×Q8—471no—
710C22×D4—24no—
711C22×D4—24no—
712C22×D4—24no—
713C22×D4C22×D4712yes—
714C22×D4C22×D4712yes—
715C22×D4C22×D4712yes—
716C22×D4C22×D4711yescharacteristic
717C22×D4C22×D4711yescharacteristic
718C22×D4C22×D4711yescharacteristic
719C23×C4—472no—
720C23×C4—471no—
721C23×C4—471no—
722C23×C4—472no—
723C23×C4—471no—
724C23×C4—472no—
725C23×C4—472no—
726C23×C4—472no—
727C23×C4—471no—
728C23×C4—948no—
729C23×C4—948no—
730C23×C4—1884no—
731C23×C4C22×D4711yescharacteristic
732C23×C4C22×D4711yescharacteristic
733#126—948no—
734#125—944no—
735#124—944no—
736#124—944no—
737#123—948no—
738C22⋊Q8—944no—
739C22⋊Q8—944no—
740#121—24no—
741#121—24no—
742#120—28no—
743C4×Q8—944no—
744C4×D4—24no—
745C4×D4—478no—
746C4×D4—944no—
747C4×D4—948no—
748C4×D4—944no—
749C4×D4—948no—
750C4×D4—948no—
751C4×D4—944no—
752C4×D4—944no—
753C4×D4—944no—
754C4×D4—1884no—
755#117—948no—
756#117—1884no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—471no—
759C2×C4⋊C4—472no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—472no—
762C2×C4⋊C4—472no—
763C2×C4⋊C4—471no—
764C2×C4⋊C4—471no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—472no—
767C2×C4⋊C4—471no—
768C2×C4⋊C4—472no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—472no—
772C2×C4⋊C4—944no—
773C2×C4⋊C4C22×D4711yescharacteristic
774C2×C4⋊C4C22×D4711yescharacteristic
775C2×C4⋊C4C22×D4711yescharacteristic
776C2×C22⋊C4—472no—
777C2×C22⋊C4—472no—
778C2×C22⋊C4—472no—
779C2×C22⋊C4—472no—
780C2×C22⋊C4—472no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—471no—
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—472no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—948no—
796C2×C22⋊C4C22×D4712yes—
797C2×C22⋊C4C22×D4711yescharacteristic
798C2×C22⋊C4C22×D4711yescharacteristic
799C2×C22⋊C4C22×D4712yes—
800C2×C22⋊C4C22×D4712yes—
801C2×C22⋊C4C22×D4712yes—
802C2×C22⋊C4C22×D4712yes—
803C2×C22⋊C4C22×D4712yes—
804C2×C22⋊C4C22×D4712yes—
805C2×C42—471no—
806C2×C42—471no—
807C2×C42—471no—
808C2×C42—472no—
809C2×C42—472no—
810C2×C42—471no—
811C2×C42—471no—
812C2×C42—471no—
813C2×C42—471no—
814C2×C42—471no—
815C2×C42—471no—
816C2×C42—471no—
817C2×C42—471no—
818C2×C42—471no—
819C2×C42—944no—
820C2×C42—944no—
821C2×C42C22×D4711yescharacteristic
822#95—471no—
823#95—471no—
824#95—471no—
825#95—471no—
826#95—471no—
827#95—471no—
828#95—472no—
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#95C22×D4712yes—
841C24—24no—
842C24—24no—
843C24—24no—
844C24—24no—
845C24—24no—
846C24—42no—
847C24—42no—
848C24C23×D4712yes—
849C24C23×D4712yes—
850C24C23×D4711yescharacteristic
851C24C23×D4711yescharacteristic
852C2×Q8—942no—
853C2×Q8—942no—
854C2×Q8—942no—
855C2×D4—232no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—24no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4D4×D4714yes—
872C2×D4#1062535214yes—
873C2×D4#1062535214yes—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—471no—
880C22×C4—478no—
881C22×C4—474no—
882C22×C4—471no—
883C22×C4—471no—
884C22×C4—472no—
885C22×C4—471no—
886C22×C4—472no—
887C22×C4—471no—
888C22×C4—471no—
889C22×C4—471no—
890C22×C4—472no—
891C22×C4—472no—
892C22×C4—471no—
893C22×C4—942no—
894C22×C4—944no—
895C22×C4—944no—
896C22×C4—942no—
897C22×C4—942no—
898C22×C4—942no—
899C22×C4—942no—
900C22×C4—944no—
901C22×C4—944no—
902C22×C4—944no—
903C22×C4—942no—
904C22×C4—942no—
905C22×C4—944no—
906C22×C4—944no—
907C22×C4—944no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—944no—
911C22×C4—942no—
912C22×C4—942no—
913C22×C4—1881no—
914C22×C4—1881no—
915C22×C4—1882no—
916C22×C4—1882no—
917C22×C4—1882no—
918C22×C4—18832no—
919C22×C4#1062535214yes—
920C22×C4C23×D4712yes—
921C22×C4C23×D4711yescharacteristic
922C22×C4C23×D4711yescharacteristic
923C22×C4C23×D4712yes—
924C22×C4C23×D4711yescharacteristic
925C22×C4C23×D4711yescharacteristic
926C22×C4C23×D4711yescharacteristic
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—474no—
931C4⋊C4—944no—
932C4⋊C4—944no—
933C4⋊C4—944no—
934C4⋊C4—944no—
935C4⋊C4—942no—
936C4⋊C4—944no—
937C4⋊C4—942no—
938C4⋊C4—944no—
939C4⋊C4—942no—
940C4⋊C4—942no—
941C4⋊C4—1882no—
942C4⋊C4—1882no—
943C4⋊C4—1882no—
944C4⋊C4—1882no—
945C22⋊C4—24no—
946C22⋊C4—22no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—22no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—478no—
955C22⋊C4—944no—
956C22⋊C4—944no—
957C22⋊C4—942no—
958C22⋊C4—944no—
959C22⋊C4—944no—
960C22⋊C4—944no—
961C22⋊C4—944no—
962C22⋊C4—942no—
963C22⋊C4—942no—
964C22⋊C4—942no—
965C22⋊C4—944no—
966C22⋊C4—944no—
967C22⋊C4—944no—
968C22⋊C4—1882no—
969C22⋊C4—1882no—
970C22⋊C4—1882no—
971C22⋊C4—1882no—
972C22⋊C4—1882no—
973C42—22no—
974C42—474no—
975C42—942no—
976C42—942no—
977C42—942no—
978C42—942no—
979C42—944no—
980C42—942no—
981C42—944no—
982C42—942no—
983C42—942no—
984C42—942no—
985C42—942no—
986C42—942no—
987C42—1881no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—216no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—22no—
997C23—22no—
998C23—21no—
999C23—22no—
1000C23—22no—
1001C23—21no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—21no—
1011C23—48no—
1012C23—48no—
1013C23—48no—
1014C23—48no—
1015C23—48no—
1016C23—48no—
1017C23C2×D4×D4714yes—
1018C23#41×D4712yes—
1019C23C2×#1062535214yes—
1020C23C2×#1062535212yes—
1021C23C2×#1062535212yes—
1022C23C2×#1062535212yes—
1023C23C24×D4711yescharacteristic
1024Q8—1884no—
1025D4—216no—
1026D4—28no—
1027D4—28no—
1028D4—28no—
1029D4—48no—
1030D4—48no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—28no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—44no—
1049C2×C4—472no—
1050C2×C4—472no—
1051C2×C4—472no—
1052C2×C4—472no—
1053C2×C4—474no—
1054C2×C4—472no—
1055C2×C4—9416no—
1056C2×C4—948no—
1057C2×C4—941no—
1058C2×C4—942no—
1059C2×C4—941no—
1060C2×C4—942no—
1061C2×C4—941no—
1062C2×C4—941no—
1063C2×C4—941no—
1064C2×C4—941no—
1065C2×C4—941no—
1066C2×C4—942no—
1067C2×C4—942no—
1068C2×C4—941no—
1069C2×C4—941no—
1070C2×C4—942no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—941no—
1074C2×C4—942no—
1075C2×C4—942no—
1076C2×C4—941no—
1077C2×C4—941no—
1078C2×C4—942no—
1079C2×C4—942no—
1080C2×C4—941no—
1081C2×C4—941no—
1082C2×C4—942no—
1083C2×C4—941no—
1084C2×C4—942no—
1085C2×C4—941no—
1086C2×C4—941no—
1087C2×C4—1884no—
1088C2×C4—1888no—
1089C2×C4—1888no—
1090C2×C4—1884no—
1091C2×C4—1884no—
1092C2×C4—1888no—
1093C2×C4—1888no—
1094C2×C4C2×D4×D4712yes—
1095C2×C4C2×#1062535212yes—
1096C2×C4C2×#1062535212yes—
1097C2×C4C2×#1062535212yes—
1098C2×C4C2×#1062535212yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—24no—
1106C22—22no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—22no—
1111C22—24no—
1112C22—22no—
1113C22—24no—
1114C22—432no—
1115C22—42no—
1116C22—42no—
1117C22—41no—
1118C22—42no—
1119C22—41no—
1120C22—42no—
1121C22—41no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—41no—
1126C22—42no—
1127C22#1568965414yescomplemented
1128C22C22×D4×D4711yescharacteristic
1129C22C2×#41×D4711yescharacteristic
1130C22C22×#1062535211yescharacteristic
1131C22C22×#1062535211yescharacteristic
1132C22C22×#1062535211yescharacteristic
1133C22H(5,𝔽2)×D4711yescharacteristic
1134C22#1568995811yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—41no—
1138C4—42no—
1139C4—41no—
1140C4—42no—
1141C4—474no—
1142C4—942no—
1143C4—944no—
1144C4—942no—
1145C4—1882no—
1146C4—1882no—
1147C4—1881no—
1148C4—1881no—
1149C4—1881no—
1150C4—1882no—
1151C4—1881no—
1152C4—1881no—
1153C4#1568962914yes—
1154C2—24no—
1155C2—44no—
1156C2—44no—
1157C2—42no—
1158C2C2×#1568962911yescharacteristic
1159C2C2×#1568965411yescharacteristic
1160C2#2025680111yescharacteristic
1161C2#546×D4711yescharacteristic
1162C2D4×#1062535211yescharacteristic
1163C2#2025693911yescharacteristic
1164C2#2025698911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
Fitting, prime radicalC47×#2408C2
hypercenter#2408D47
hypocenterC47#34700
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#15689654C2semidirect
2. C22×D4×Dic47C2semidirect
3. #20247631C2semidirect
4. #20247447C2semidirect
5. #20247288C2semidirect
6. #20247263C2semidirect
7. #20247173C2semidirect
8. #20247113C2semidirect
9. #20247035C2semidirect
10. #20246967C2semidirect
11. #20246876C2semidirect
12. #20246846C2semidirect
13. #20246839C2semidirect
14. #20246644C2semidirect
15. #20246623C2semidirect
16. #20245935C2semidirect
17. #20245916C2semidirect
18. #121×Dic47C2semidirect
19. #120×Dic47C2semidirect
20. #20245850C2semidirect
21. #20245766C2semidirect
22. C4×D4×Dic47C2semidirect
26. C2×#13094017C22semidirect
27. C2×#13094015C22semidirect
30. C2×#13094005C22semidirect
32. C2×#13094003C22semidirect
33. C2×#13093989C22semidirect
43. C2×D4×Dic47C22semidirect
44. C2×D4×Dic47C22semidirect
45. C2×#13093980C22semidirect
46. C2×#13093980C22semidirect
50. C22×C4×Dic47C22semidirect
51. #15689065C22semidirect
52. #15689059C22semidirect
53. #15689056C22semidirect
54. #15689055C22semidirect
55. #15689051C22semidirect
56. #15689051C22semidirect
57. #15689048C22semidirect
58. #15689048C22semidirect
59. #15689046C22semidirect
60. #15689046C22semidirect
63. #15689037C22semidirect
64. #15689037C22semidirect
65. #15689029C22semidirect
66. #15689028C22semidirect
69. #15689022C22semidirect
70. #15689021C22semidirect
71. #15689019C22semidirect
72. #15689019C22semidirect
73. #15689017C22semidirect
74. #15689016C22semidirect
75. #15689011C22semidirect
76. #15689011C22semidirect
77. #15689011C22semidirect
78. #15689005C22semidirect
80. #15689003C22semidirect
81. #15689003C22semidirect
82. #15689003C22semidirect
84. #15688998C22semidirect
85. #15688998C22semidirect
87. #15688988C22semidirect
88. #15688984C22semidirect
89. #15688984C22semidirect
90. #15688983C22semidirect
93. #15688981C22semidirect
94. #15688981C22semidirect
97. C4⋊C4×Dic47C22semidirect
98. C4⋊C4×Dic47C22semidirect
99. C4⋊C4×Dic47C22semidirect
100. C4×C4⋊Dic47C22semidirect
101. #15688974C22semidirect
105. C22⋊C4×Dic47C22semidirect
106. C22⋊C4×Dic47C22semidirect
107. C22⋊C4×Dic47C22semidirect
108. C22⋊C4×Dic47C22semidirect
109. C22⋊C4×Dic47C22semidirect
110. C22⋊C4×Dic47C22semidirect
112. C4×C22⋊Dic47C22semidirect
113. C42×Dic47C22semidirect
155. D4×Dic47D4semidirect
545. C22×C47#529semidirect
707. C47#34700semidirect
1127. C22#15689654semidirect

Maximal subgroups

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

subgroupindex
C2×#156896542
C22×D4×Dic472
#202476312
#202474472
#202472882
#202472632
#202471732
#202471132
#202470352
#202469672
#202468762
#202468462
#202468392
#202466442
#202466232
#202459352
#202459162
#121×Dic472
#120×Dic472
#202458502
#202457662
C4×D4×Dic472
C47×#24082
#3470047