Finite Group Databasebeta

← #26384455

Subgroups — #26384455

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
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20247627C212yesmaximal, complemented
4#20247451C212yesmaximal, complemented
5#20247292C212yesmaximal, complemented
6#20247261C211yesmaximal, characteristic, complemented
7#20247169C211yesmaximal, characteristic, complemented
8#20247115C211yesmaximal, characteristic, complemented
9#20247038C211yesmaximal, characteristic, complemented
10#20246965C211yesmaximal, characteristic, complemented
11#20246843C212yesmaximal, complemented
12#20246841C211yesmaximal, characteristic, complemented
13#20246740C211yesmaximal, characteristic
14#20246646C212yesmaximal, complemented
15#20246631C212yesmaximal, complemented
16#20245927C211yesmaximal, characteristic, complemented
17#20245918C211yesmaximal, characteristic, complemented
18#20245894C211yesmaximal, characteristic, complemented
19#20245893C212yesmaximal, complemented
20#20245850C211yesmaximal, characteristic, complemented
21#20245768C212yesmaximal, complemented
22C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
23C47×#2420C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2212yes—
26#15689654—28no—
27C2×#13094017C2212yescomplemented
28C2×#13094015C2211yescharacteristic, complemented
29C2×#13094012C2211yescharacteristic
30C2×#13094011C2211yescharacteristic
31C2×#13094005C2212yescomplemented
32C2×#13094004C2211yescharacteristic
33C2×#13094003C2211yescharacteristic, complemented
34C2×#13093998C2211yescharacteristic
35C2×#13093992C2212yes—
36C2×#13093989C2211yescharacteristic, complemented
37C2×C4×D188C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×D4×Dic47C2212yescomplemented
40C2×#13093986C2211yescharacteristic
41C2×C4×C22⋊D47C2212yes—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×(C22⋊D47)⋊C4C2212yes—
44C2×(C22⋊D47)⋊C4C2211yescharacteristic
45C2×(C22⋊D47)⋊C4C2211yescharacteristic
46C2×(C22⋊D47)⋊C4C2212yescomplemented
47C4×D4×D47—28no—
48C2×#13093980C2212yescomplemented
49C2×#13093980C2212yescomplemented
50C2×C4⋊C4×D47C2211yescharacteristic
51C2×C22⋊C4×D47C2212yes—
52C22×C4×Dic47C2211yescharacteristic, complemented
53C2×C42×D47C2211yescharacteristic
54#15689064C2212yescomplemented
55#15689058C2212yescomplemented
56#15689057C2212yescomplemented
57#15689057C2212yescomplemented
58#15689052C2212yescomplemented
59#15689051C2212yescomplemented
60#15689051C2212yescomplemented
61#15689046C2212yescomplemented
62#15689045C2212yescomplemented
63#15689039C2212yes—
64#15689039C2212yes—
65#15689038C2212yes—
66#15689038C2212yescomplemented
67#15689031C2212yes—
68#15689029C2211yescharacteristic, complemented
69#15689028C2211yescharacteristic, complemented
70#15689026C2211yescharacteristic
71#15689024C2211yescharacteristic
72#15689024C2211yescharacteristic
73#15689021C2211yescharacteristic, complemented
74#15689019C2211yescharacteristic, complemented
75#15689019C2211yescharacteristic, complemented
76#15689017C2212yescomplemented
77#15689012C2212yescomplemented
78#15689012C2212yescomplemented
79#15689012C2212yescomplemented
80#15689011C2212yescomplemented
81#15689006C2212yescomplemented
82#15689000C2212yescomplemented
83#15688999C2212yes—
84#15688999C2212yescomplemented
85#15688997C2212yes—
86#15688997C2212yescomplemented
87#15688996C2212yescomplemented
88#15688994C2212yes—
89#15688986C2212yescomplemented
90#15688982C2212yes—
91#15688982C2212yes—
92#15688982C2212yescomplemented
93#15688982C2212yescomplemented
94#15688980C2211yescharacteristic
95#15688978C2212yes—
96#15688978C2212yes—
97#15688978C2212yes—
98C4⋊C4×Dic47C2211yescharacteristic, complemented
99C4⋊C4×Dic47C2212yescomplemented
100C4×Dic47⋊C4C2211yescharacteristic, complemented
101#15688974C2211yescharacteristic, complemented
102#15688974C2211yescharacteristic, complemented
103C22⋊C4×Dic47C2212yescomplemented
104C22⋊C4×Dic47C2211yescharacteristic, complemented
105C22⋊C4×Dic47C2211yescharacteristic, complemented
106C4×(C2×D47)⋊C4C2211yescharacteristic
107#15688970C2211yescharacteristic
108#15688970C2212yes—
109#15688970C2211yescharacteristic
110#15688970C2212yescomplemented
111#15688970C2212yescomplemented
112#15688970C2212yescomplemented
113C42×Dic47C2211yescharacteristic, complemented
114C2×#121×C47C2211yescharacteristic
115C2×C4×D4×C47C2211yescharacteristic
116C47×#397C2212yescomplemented
117C47×#394C2212yescomplemented
118C47×#390C2211yescharacteristic
119C47×#389C2211yescharacteristic, complemented
120C47×#386C2212yescomplemented
121C47×#382C2211yescharacteristic, complemented
122C47×#381C2212yescomplemented
123C47×#380C2211yescharacteristic, complemented
124C4×C22⋊C4×C47C2211yescharacteristic, complemented
125C24×D47C2312yes—
126C22×Dic94C2311yescharacteristic
127C22×D188C2311yescharacteristic
128C22×C22⋊D47C2312yes—
129C22×C22⋊D47C2312yes—
130C22×C22⋊D47C2311yescharacteristic
131C2×D4×D47—24no—
132C2×D4×D47—24no—
133C2×D4×D47—24no—
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C23×Dic47C2312yes—
137C22×C4×D47—28no—
138C22×C4×D47—28no—
139C22×C4×D47—44no—
140C22×C4×D47C2312yes—
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146#13094017—28no—
147#13094015—24no—
148#13094012—24no—
149#13094011—24no—
150#13094005—28no—
151#13094004—24no—
152#13094003—24no—
153#13093998—24no—
154#13093992—28no—
155#13093989—24no—
156C4×D188—24no—
157D4×Dic47—28no—
158D4×Dic47D418yescomplemented
159#13093986—24no—
160C4×C22⋊D47—24no—
161C4×C22⋊D47—28no—
162(C22⋊D47)⋊C4—24no—
163(C22⋊D47)⋊C4—28no—
164(C22⋊D47)⋊C4—24no—
165(C22⋊D47)⋊C4—44no—
166#13093980—28no—
167#13093980—44no—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2312yes—
170C2×C4⋊Dic47C2312yes—
171C2×C4⋊Dic47C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C4⋊C4×D47—24no—
183C2×C22⋊Dic47C2311yescharacteristic
184C2×C22⋊Dic47C2312yes—
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2312yes—
189C2×C22⋊Dic47C2312yes—
190C2×(C2×D47)⋊C4C2311yescharacteristic
191C2×(C2×D47)⋊C4C2311yescharacteristic
192C2×(C2×D47)⋊C4C2311yescharacteristic
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C22⋊C4×D47—28no—
205C2×C4×Dic47—24no—
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
210C2×C4×Dic47C2311yescharacteristic
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2311yescharacteristic
216C2×C4×Dic47C2311yescharacteristic
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C42×D47—24no—
220C47⋊#95C2311yescharacteristic
221C47⋊#95C2311yescharacteristic
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2311yescharacteristic
227C47⋊#95C2311yescharacteristic
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C22×D4×C47C2312yes—
234C22×D4×C47C2311yescharacteristic
235C23×C4×C47C2311yescharacteristic
236C23×C4×C47C2312yes—
237#121×C47—24no—
238C4×D4×C47—24no—
239C2×C4⋊C4×C47C2311yescharacteristic
240C2×C4⋊C4×C47C2311yescharacteristic
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2312yes—
243C2×C22⋊C4×C47C2311yescharacteristic
244C2×C22⋊C4×C47C2311yescharacteristic
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2312yes—
249C2×C22⋊C4×C47C2312yes—
250C2×C42×C47C2311yescharacteristic
251C2×C42×C47C2311yescharacteristic
252#95×C47C2311yescharacteristic
253#95×C47C2311yescharacteristic
254#95×C47C2312yes—
255#95×C47C2312yes—
256#95×C47C2312yes—
257#95×C47C2312yes—
258C24×C47C2412yes—
259C24×C47C2411yescharacteristic
260C23×D47—24no—
261C23×D47—24no—
262C23×D47—24no—
263C23×D47—24no—
264C23×D47—24no—
265C23×D47—42no—
266C23×D47—42no—
267C23×D47C2412yes—
268C23×D47C2411yescharacteristic
269C2×D4×C47—24no—
270C2×D4×C47—24no—
271C2×D4×C47—22no—
272C2×D4×C47—22no—
273C2×D4×C47—42no—
274C2×D4×C47C2×D414yes—
275C22×C4×C47—24no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—24no—
280C22×C4×C47—42no—
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C22×C4×C47C2412yes—
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2412yes—
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C2×C22⋊D47—24no—
291C2×C22⋊D47—22no—
292C2×C22⋊D47—22no—
293C2×C22⋊D47—24no—
294C2×C22⋊D47—24no—
295C2×C22⋊D47—24no—
296C2×C22⋊D47—24no—
297C2×C22⋊D47—42no—
298C2×C22⋊D47#4114yes—
299C22×Dic47—24no—
300C22×Dic47—24no—
301C22×Dic47—22no—
302C22×Dic47—22no—
303C22×Dic47—22no—
304C22×Dic47—22no—
305C22×Dic47—22no—
306C22×Dic47—41no—
307C22×Dic47C2×D418yes—
308C22×Dic47C2412yes—
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2412yes—
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C22×Dic47C2412yes—
315C22×Dic47C2411yescharacteristic
316C22×Dic47C2411yescharacteristic
317C22×Dic47C2411yescharacteristic
318D4×D47—232no—
319C2×D188—22no—
320C2×D188—22no—
321C2×D188#4114yes—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—22no—
325C2×C4×D47—22no—
326C2×C4×D47—22no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—22no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—24no—
333C2×C4×D47—24no—
334C2×C4×D47—24no—
335C2×C4×D47—432no—
336C2×C4×D47—42no—
337C2×C4×D47—42no—
338C2×C4×D47—41no—
339C2×C4×D47#4114yes—
340C2×C4×D47#4114yes—
341C2×Dic94—22no—
342C2×Dic94—22no—
343C2×Dic94—22no—
344C4⋊C4×C47—22no—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
347C4⋊C4×C47—42no—
348C22⋊C4×C47—24no—
349C22⋊C4×C47—24no—
350C22⋊C4×C47—22no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—42no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47—42no—
355C42×C47—22no—
356C42×C47—22no—
357C22⋊Dic47—24no—
358C22⋊Dic47—24no—
359C22⋊Dic47—24no—
360C22⋊Dic47—22no—
361C22⋊Dic47—24no—
362C22⋊Dic47—42no—
363C22⋊Dic47C2×D418yes—
364(C2×D47)⋊C4—22no—
365(C2×D47)⋊C4—22no—
366(C2×D47)⋊C4—22no—
367(C2×D47)⋊C4—24no—
368(C2×D47)⋊C4—24no—
369(C2×D47)⋊C4—24no—
370(C2×D47)⋊C4—24no—
371(C2×D47)⋊C4—24no—
372(C2×D47)⋊C4—24no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—24no—
375(C2×D47)⋊C4—42no—
376(C2×D47)⋊C4—42no—
377(C2×D47)⋊C4—42no—
378C4⋊Dic47—22no—
379C4⋊Dic47—24no—
380C4⋊Dic47—24no—
381C4⋊Dic47C2×D414yes—
382Dic47⋊C4—22no—
383Dic47⋊C4—24no—
384Dic47⋊C4—24no—
385Dic47⋊C4—24no—
386Dic47⋊C4—24no—
387Dic47⋊C4—22no—
388Dic47⋊C4—22no—
389Dic47⋊C4—42no—
390Dic47⋊C4—42no—
391Dic47⋊C4—42no—
392C4×Dic47—22no—
393C4×Dic47—22no—
394C4×Dic47—22no—
395C4×Dic47—22no—
396C4×Dic47—22no—
397C4×Dic47—22no—
398C4×Dic47—24no—
399C4×Dic47—22no—
400C4×Dic47—22no—
401C4×Dic47—22no—
402C4×Dic47—24no—
403C4×Dic47—41no—
404C4×Dic47C2×D414yes—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—22no—
408C23×C47—21no—
409C23×C47—22no—
410C23×C47—21no—
411C23×C47—22no—
412C23×C47—22no—
413C23×C47—22no—
414C23×C47—21no—
415C23×C47—22no—
416C23×C47—21no—
417C23×C47C22×D414yes—
418C23×C47C2×#4112yes—
419C23×C47C2511yescharacteristic
420C22×D47—21no—
421C22×D47—21no—
422C22×D47—21no—
423C22×D47—21no—
424C22×D47—216no—
425C22×D47—22no—
426C22×D47—22no—
427C22×D47—22no—
428C22×D47—22no—
429C22×D47—22no—
430C22×D47—22no—
431C22×D47—48no—
432C22×D47—48no—
433C22×D47—48no—
434C22×D47—48no—
435C22×D47—48no—
436C22×D47—48no—
437C22×D47C2×#4114yes—
438C22×D47C2×#4112yes—
439C22×D47C2×#4112yes—
440C22×D47C2×#4112yes—
441D4×C47—28no—
442D4×C47—48no—
443C2×C4×C47—21no—
444C2×C4×C47—21no—
445C2×C4×C47—21no—
446C2×C4×C47—22no—
447C2×C4×C47—21no—
448C2×C4×C47—22no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—22no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—21no—
457C2×C4×C47—22no—
458C2×C4×C47—22no—
459C2×C4×C47—21no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—21no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—21no—
466C2×C4×C47—48no—
467C2×C4×C47—44no—
468C2×C4×C47C22×D412yes—
469C2×C4×C47C2×#4112yes—
470C2×C4×C47C2×#4112yes—
471C2×C4×C47C2×#4112yes—
472C22⋊D47—216no—
473C22⋊D47—28no—
474C22⋊D47—48no—
475C2×Dic47—21no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—22no—
480C2×Dic47—21no—
481C2×Dic47—22no—
482C2×Dic47—21no—
483C2×Dic47—216no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—22no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—22no—
491C2×Dic47—22no—
492C2×Dic47—22no—
493C2×Dic47—22no—
494C2×Dic47—21no—
495C2×Dic47—22no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—21no—
499C2×Dic47—44no—
500C2×Dic47—44no—
501C2×Dic47C22×D412yes—
502C2×Dic47C22×D414yes—
503C2×Dic47C22×D412yes—
504C2×Dic47C2×#4112yes—
505C2×Dic47C2×#4112yes—
506C2×Dic47C2×#4112yes—
507C2×Dic47H(5,𝔽2)12yes—
508D188—28no—
509C4×D47—28no—
510C4×D47—28no—
511C4×D47—48no—
512C4×D47—44no—
513C4×D47—48no—
514C4×D47—48no—
515Dic94—44no—
516#34700—471nomaximal, Sylow
517C22×C47—24no—
518C22×C47—22no—
519C22×C47—24no—
520C22×C47—22no—
521C22×C47—24no—
522C22×C47—22no—
523C22×C47—41no—
524C22×C47—42no—
525C22×C47—42no—
526C22×C47—41no—
527C22×C47—41no—
528C22×C47—42no—
529C22×C47—41no—
530C22×C47—42no—
531C22×C47C23×D411yescharacteristic
532C22×C47C22×#4111yescharacteristic
533C22×C47C22×#4111yescharacteristic
534C22×C47C22×#4111yescharacteristic
535C22×C47C22×#4111yescharacteristic
536C22×C47C2×H(5,𝔽2)11yescharacteristic
537C22×C47#58511yescharacteristic
538C2×D47—22no—
539C2×D47—22no—
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—22no—
543C2×D47—22no—
544C2×D47—24no—
545C2×D47—24no—
546C2×D47—24no—
547C2×D47—432no—
548C2×D47—42no—
549C2×D47—42no—
550C2×D47—42no—
551C2×D47—42no—
552C2×D47#52914yescomplemented
553C4×C47—22no—
554C4×C47—41no—
555C4×C47—42no—
556C4×C47—42no—
557C4×C47—41no—
558C4×C47—42no—
559C4×C47—41no—
560C4×C47—41no—
561C4×C47#52514yes—
562Dic47—22no—
563Dic47—22no—
564Dic47—24no—
565Dic47—22no—
566Dic47—42no—
567Dic47—41no—
568Dic47—41no—
569Dic47—41no—
570Dic47—42no—
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#2420D4711yescharacteristic, complemented
583#2418—472no—
584#2417—471no—
585#2408—471no—
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—44no—
596C2×C47—42no—
597C2×C47C2×#52511yescharacteristic
598C2×C47C2×#52911yescharacteristic
599C2×C47#346011yescharacteristic
600C2×C47C2×#54611yescharacteristic
601C2×C47D4×#4111yescharacteristic
602C2×C47#347511yescharacteristic
603C2×C47#348111yescharacteristic
604D47—24no—
605D47—44no—
606C23×D4—471no—
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×#121—471no—
617C2×#121C2×D4711yescharacteristic
618C2×#120—472no—
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—472no—
629C2×C4×D4—471no—
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#397C2×D4712yescomplemented
646#396—472no—
647#396—472no—
648#394—472no—
649#394—472no—
650#394—472no—
651#394—472no—
652#394C2×D4712yescomplemented
653#392—472no—
654#391—471no—
655#391—471no—
656#390—471no—
657#390—471no—
658#390—471no—
659#390C2×D4711yescharacteristic
660#389—471no—
661#389—471no—
662#389—471no—
663#389C2×D4711yescharacteristic, complemented
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#386C2×D4712yescomplemented
674#385—472no—
675#385—472no—
676#385—472no—
677#385—472no—
678#382C2×D4711yescharacteristic, complemented
679#381—472no—
680#381C2×D4712yescomplemented
681#380—471no—
682#380—472no—
683#380—472no—
684#380—472no—
685#380—472no—
686#380C2×D4711yescharacteristic, complemented
687#379—472no—
688#379—472no—
689#379—472no—
690C4×C4⋊C4—472no—
691C4×C4⋊C4—471no—
692C4×C4⋊C4—471no—
693C4×C4⋊C4—471no—
694C4×C4⋊C4—471no—
695C4×C22⋊C4—471no—
696C4×C22⋊C4—472no—
697C4×C22⋊C4—471no—
698C4×C22⋊C4—471no—
699C4×C22⋊C4—471no—
700C4×C22⋊C4—471no—
701C4×C22⋊C4—472no—
702C4×C22⋊C4—472no—
703C4×C22⋊C4—472no—
704C4×C22⋊C4—472no—
705C4×C22⋊C4C2×D4711yescharacteristic, complemented
706C43—471no—
707C47#3470011yescharacteristic, complemented, Sylow
708C25—472no—
709C22×Q8—471no—
710C22×D4—471no—
711C22×D4—472no—
712C22×D4—472no—
713C22×D4—471no—
714C22×D4—944no—
715C22×D4—944no—
716C22×D4—944no—
717C22×D4C22×D4712yes—
718C22×D4C22×D4711yescharacteristic
719C23×C4—472no—
720C23×C4—471no—
721C23×C4—471no—
722C23×C4—471no—
723C23×C4—471no—
724C23×C4—472no—
725C23×C4—471no—
726C23×C4—472no—
727C23×C4—472no—
728C23×C4—948no—
729C23×C4—948no—
730C23×C4—1884no—
731C23×C4C22×D4711yescharacteristic
732C23×C4C22×D4712yes—
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—944no—
742#120—948no—
743C4×Q8—944no—
744C4×D4—24no—
745C4×D4—478no—
746C4×D4—944no—
747C4×D4—944no—
748C4×D4—948no—
749C4×D4—944no—
750C4×D4—944no—
751C4×D4—948no—
752C4×D4—944no—
753C4×D4—948no—
754C4×D4—1884no—
755#117—948no—
756#117—1884no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—472no—
759C2×C4⋊C4—472no—
760C2×C4⋊C4—472no—
761C2×C4⋊C4—472no—
762C2×C4⋊C4—471no—
763C2×C4⋊C4—471no—
764C2×C4⋊C4—471no—
765C2×C4⋊C4—472no—
766C2×C4⋊C4—471no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—472no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—944no—
772C2×C4⋊C4C22×D4711yescharacteristic
773C2×C4⋊C4C22×D4711yescharacteristic
774C2×C4⋊C4C22×D4711yescharacteristic
775C2×C4⋊C4C22×D4712yes—
776C2×C22⋊C4—472no—
777C2×C22⋊C4—472no—
778C2×C22⋊C4—472no—
779C2×C22⋊C4—472no—
780C2×C22⋊C4—471no—
781C2×C22⋊C4—472no—
782C2×C22⋊C4—472no—
783C2×C22⋊C4—472no—
784C2×C22⋊C4—471no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—472no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—472no—
791C2×C22⋊C4—472no—
792C2×C22⋊C4—472no—
793C2×C22⋊C4—472no—
794C2×C22⋊C4—472no—
795C2×C22⋊C4—472no—
796C2×C22⋊C4—472no—
797C2×C22⋊C4—948no—
798C2×C22⋊C4C22×D4712yes—
799C2×C22⋊C4C22×D4712yes—
800C2×C22⋊C4C22×D4711yescharacteristic
801C2×C22⋊C4C22×D4711yescharacteristic
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—944no—
819C2×C42—944no—
820C2×C42C22×D4711yescharacteristic
821C2×C42C22×D4711yescharacteristic
822#95—471no—
823#95—471no—
824#95—471no—
825#95—471no—
826#95—472no—
827#95—472no—
828#95—472no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95C22×D4711yescharacteristic
836#95C22×D4711yescharacteristic
837#95C22×D4712yes—
838#95C22×D4712yes—
839#95C22×D4712yes—
840#95C22×D4712yes—
841C24—471no—
842C24—472no—
843C24—944no—
844C24—944no—
845C24—944no—
846C24—944no—
847C24—944no—
848C24—1882no—
849C24—1882no—
850C24C23×D4712yes—
851C24C23×D4711yescharacteristic
852C2×Q8—942no—
853C2×Q8—942no—
854C2×Q8—942no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—42no—
860C2×D4—474no—
861C2×D4—474no—
862C2×D4—944no—
863C2×D4—9432no—
864C2×D4—942no—
865C2×D4—942no—
866C2×D4—944no—
867C2×D4—944no—
868C2×D4—944no—
869C2×D4—944no—
870C2×D4—942no—
871C2×D4—942no—
872C2×D4—1882no—
873C2×D4D4×D4714yes—
874C22×C4—24no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—24no—
879C22×C4—42no—
880C22×C4—471no—
881C22×C4—478no—
882C22×C4—471no—
883C22×C4—471no—
884C22×C4—471no—
885C22×C4—472no—
886C22×C4—474no—
887C22×C4—474no—
888C22×C4—472no—
889C22×C4—471no—
890C22×C4—471no—
891C22×C4—472no—
892C22×C4—471no—
893C22×C4—942no—
894C22×C4—942no—
895C22×C4—942no—
896C22×C4—944no—
897C22×C4—944no—
898C22×C4—944no—
899C22×C4—944no—
900C22×C4—944no—
901C22×C4—942no—
902C22×C4—944no—
903C22×C4—944no—
904C22×C4—944no—
905C22×C4—942no—
906C22×C4—942no—
907C22×C4—942no—
908C22×C4—942no—
909C22×C4—942no—
910C22×C4—942no—
911C22×C4—942no—
912C22×C4—944no—
913C22×C4—1881no—
914C22×C4—1882no—
915C22×C4—1882no—
916C22×C4—18832no—
917C22×C4—1881no—
918C22×C4C23×D4711yescharacteristic
919C22×C4C23×D4712yes—
920C22×C4C23×D4711yescharacteristic
921C22×C4C23×D4712yes—
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—42no—
931C4⋊C4—474no—
932C4⋊C4—944no—
933C4⋊C4—944no—
934C4⋊C4—944no—
935C4⋊C4—942no—
936C4⋊C4—942no—
937C4⋊C4—944no—
938C4⋊C4—944no—
939C4⋊C4—944no—
940C4⋊C4—942no—
941C4⋊C4—942no—
942C4⋊C4—1882no—
943C4⋊C4—1882no—
944C4⋊C4—1882no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—478no—
953C22⋊C4—944no—
954C22⋊C4—944no—
955C22⋊C4—944no—
956C22⋊C4—942no—
957C22⋊C4—942no—
958C22⋊C4—942no—
959C22⋊C4—944no—
960C22⋊C4—944no—
961C22⋊C4—944no—
962C22⋊C4—944no—
963C22⋊C4—944no—
964C22⋊C4—942no—
965C22⋊C4—944no—
966C22⋊C4—944no—
967C22⋊C4—944no—
968C22⋊C4—944no—
969C22⋊C4—1882no—
970C22⋊C4—1882no—
971C22⋊C4—1882no—
972C22⋊C4—1882no—
973C42—22no—
974C42—22no—
975C42—474no—
976C42—942no—
977C42—942no—
978C42—942no—
979C42—942no—
980C42—944no—
981C42—942no—
982C42—944no—
983C42—942no—
984C42—942no—
985C42—942no—
986C42—942no—
987C42—1881no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—21no—
1000C23—472no—
1001C23—472no—
1002C23—472no—
1003C23—474no—
1004C23—9416no—
1005C23—941no—
1006C23—941no—
1007C23—941no—
1008C23—941no—
1009C23—942no—
1010C23—942no—
1011C23—942no—
1012C23—942no—
1013C23—942no—
1014C23—942no—
1015C23—1888no—
1016C23—1888no—
1017C23—1888no—
1018C23—1888no—
1019C23—1888no—
1020C23—1888no—
1021C23C2×D4×D4714yes—
1022C23#41×D4712yes—
1023C23C24×D4711yescharacteristic
1024Q8—1884no—
1025D4—28no—
1026D4—48no—
1027D4—948no—
1028D4—9416no—
1029D4—948no—
1030D4—1888no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—472no—
1057C2×C4—472no—
1058C2×C4—472no—
1059C2×C4—472no—
1060C2×C4—474no—
1061C2×C4—472no—
1062C2×C4—472no—
1063C2×C4—948no—
1064C2×C4—9416no—
1065C2×C4—941no—
1066C2×C4—941no—
1067C2×C4—941no—
1068C2×C4—941no—
1069C2×C4—942no—
1070C2×C4—941no—
1071C2×C4—942no—
1072C2×C4—941no—
1073C2×C4—948no—
1074C2×C4—941no—
1075C2×C4—941no—
1076C2×C4—942no—
1077C2×C4—941no—
1078C2×C4—942no—
1079C2×C4—942no—
1080C2×C4—941no—
1081C2×C4—941no—
1082C2×C4—942no—
1083C2×C4—942no—
1084C2×C4—941no—
1085C2×C4—942no—
1086C2×C4—941no—
1087C2×C4—941no—
1088C2×C4—941no—
1089C2×C4—1888no—
1090C2×C4—1888no—
1091C2×C4—1884no—
1092C2×C4—1888no—
1093C2×C4—1884no—
1094C2×C4—1884no—
1095C2×C4C2×D4×D4712yes—
1096C2×C4#41×D4712yes—
1097C2×C4#41×D4712yes—
1098C2×C4#41×D4712yes—
1099C22—24no—
1100C22—22no—
1101C22—24no—
1102C22—24no—
1103C22—22no—
1104C22—22no—
1105C22—42no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—42no—
1110C22—42no—
1111C22—41no—
1112C22—42no—
1113C22—474no—
1114C22—942no—
1115C22—942no—
1116C22—942no—
1117C22—942no—
1118C22—942no—
1119C22—942no—
1120C22—944no—
1121C22—944no—
1122C22—944no—
1123C22—18832no—
1124C22—1882no—
1125C22—1882no—
1126C22—1882no—
1127C22—1882no—
1128C22C22×D4×D4711yescharacteristic
1129C22C2×#41×D4711yescharacteristic
1130C22C2×#41×D4711yescharacteristic
1131C22C2×#41×D4711yescharacteristic
1132C22C2×#41×D4711yescharacteristic
1133C22H(5,𝔽2)×D4711yescharacteristic
1134C22#1568995811yescharacteristic
1135C4—22no—
1136C4—42no—
1137C4—42no—
1138C4—41no—
1139C4—42no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—474no—
1144C4—944no—
1145C4—942no—
1146C4—942no—
1147C4—942no—
1148C4—1881no—
1149C4—1881no—
1150C4—1881no—
1151C4—1882no—
1152C4—1882no—
1153C4#1568963114yes—
1154C2—44no—
1155C2—42no—
1156C2—944no—
1157C2—1884no—
1158C2C2×#1568963111yescharacteristic
1159C2#529×D4711yescharacteristic
1160C2#2025680311yescharacteristic
1161C2#546×D4711yescharacteristic
1162C2#2025687211yescharacteristic
1163C2#2025694511yescharacteristic
1164C2#2025699511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2420C2
prime radical#20246740C2
hypercenter#2420D47
hypocenterC47#34700
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2420

Complements

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

NH ≅ G/Ntype
1. C2×#15689654C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20247627C2semidirect
4. #20247451C2semidirect
5. #20247292C2semidirect
6. #20247261C2semidirect
7. #20247169C2semidirect
8. #20247115C2semidirect
9. #20247038C2semidirect
10. #20246965C2semidirect
11. #20246843C2semidirect
12. #20246841C2semidirect
14. #20246646C2semidirect
15. #20246631C2semidirect
16. #20245927C2semidirect
17. #20245918C2semidirect
18. #20245894C2semidirect
19. #20245893C2semidirect
20. #20245850C2semidirect
21. #20245768C2semidirect
22. C4×(C22⋊D47)⋊C4C2semidirect
23. C47×#2420C2semidirect
27. C2×#13094017C22semidirect
28. C2×#13094015C22semidirect
31. C2×#13094005C22semidirect
33. C2×#13094003C22semidirect
36. C2×#13093989C22semidirect
39. C2×D4×Dic47C22semidirect
46. C2×(C22⋊D47)⋊C4C22semidirect
48. C2×#13093980C22semidirect
49. C2×#13093980C22semidirect
52. C22×C4×Dic47C22semidirect
54. #15689064C22semidirect
55. #15689058C22semidirect
56. #15689057C22semidirect
57. #15689057C22semidirect
58. #15689052C22semidirect
59. #15689051C22semidirect
60. #15689051C22semidirect
61. #15689046C22semidirect
62. #15689045C22semidirect
66. #15689038C22semidirect
68. #15689029C22semidirect
69. #15689028C22semidirect
73. #15689021C22semidirect
74. #15689019C22semidirect
75. #15689019C22semidirect
76. #15689017C22semidirect
77. #15689012C22semidirect
78. #15689012C22semidirect
79. #15689012C22semidirect
80. #15689011C22semidirect
81. #15689006C22semidirect
82. #15689000C22semidirect
84. #15688999C22semidirect
86. #15688997C22semidirect
87. #15688996C22semidirect
89. #15688986C22semidirect
92. #15688982C22semidirect
93. #15688982C22semidirect
98. C4⋊C4×Dic47C22semidirect
99. C4⋊C4×Dic47C22semidirect
100. C4×Dic47⋊C4C22semidirect
101. #15688974C22semidirect
102. #15688974C22semidirect
103. C22⋊C4×Dic47C22semidirect
104. C22⋊C4×Dic47C22semidirect
105. C22⋊C4×Dic47C22semidirect
110. #15688970C22semidirect
111. #15688970C22semidirect
112. #15688970C22semidirect
113. C42×Dic47C22semidirect
116. C47×#397C22semidirect
117. C47×#394C22semidirect
119. C47×#389C22semidirect
120. C47×#386C22semidirect
121. C47×#382C22semidirect
122. C47×#381C22semidirect
123. C47×#380C22semidirect
124. C4×C22⋊C4×C47C22semidirect
158. D4×Dic47D4semidirect
552. C2×D47#529semidirect
582. #2420D47semidirect
645. #397C2×D47semidirect
652. #394C2×D47semidirect
663. #389C2×D47semidirect
673. #386C2×D47semidirect
678. #382C2×D47semidirect
680. #381C2×D47semidirect
686. #380C2×D47semidirect
705. C4×C22⋊C4C2×D47semidirect
707. C47#34700semidirect

Maximal subgroups

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

subgroupindex
C2×#156896542
C2×C4×D4×D472
#202476272
#202474512
#202472922
#202472612
#202471692
#202471152
#202470382
#202469652
#202468432
#202468412
#202467402
#202466462
#202466312
#202459272
#202459182
#202458942
#202458932
#202458502
#202457682
C4×(C22⋊D47)⋊C42
C47×#24202
#3470047