Finite Group Databasebeta

← #26376571

Subgroups — #26376571

Order 12032.

3118 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689633C211yesmaximal, characteristic
2C2×#15689602C211yesmaximal, characteristic, complemented
3C2×#117×D47C211yesmaximal, characteristic, complemented
4#20246431C211yesmaximal, characteristic, complemented
5#20246430C211yesmaximal, characteristic, complemented
6#20246422C211yesmaximal, characteristic, complemented
7#20246417C211yesmaximal, characteristic, complemented
8#20246415C211yesmaximal, characteristic, complemented
9#20246414C211yesmaximal, characteristic, complemented
10#20246413C211yesmaximal, characteristic, complemented
11#20246336C212yesmaximal, complemented
12#20246334C212yesmaximal, complemented
13#20246315C212yesmaximal, complemented
14#20246311C212yesmaximal, complemented
15#20246047C212yesmaximal, complemented
16#20246044C212yesmaximal, complemented
17#20246010C211yesmaximal, characteristic, complemented
18#20245978C211yesmaximal, characteristic, complemented
19#20245915C212yesmaximal, complemented
20C4×#13094006C212yesmaximal, complemented
21#20245769C211yesmaximal, characteristic, complemented
22#20245742C211yesmaximal, characteristic, complemented
23C47×#2363C211yesmaximal, characteristic, complemented
24C22×#10625352C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689633C4116yescomplemented
27C2×#13094006C2212yes—
28C2×#13094004C2211yescharacteristic
29C2×#13094003C2211yescharacteristic
30C2×#13093995C2211yescharacteristic
31C2×#13093992C2212yes—
32#15689602—28no—
33C2×C4×Dic94C2211yescharacteristic, complemented
34C2×#13093989C2211yescharacteristic, complemented
35C2×D4×Dic47C2212yes—
36C2×D4×Dic47C2211yescharacteristic, complemented
37C2×C4×C22⋊D47C2212yes—
38C2×(C22⋊D47)⋊C4C2212yes—
39C2×(C22⋊D47)⋊C4C2212yes—
40C2×#13093983C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44C2×#13093981C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46C2×#13093981C2212yes—
47C2×#13093980C2212yes—
48C2×#13093980C2212yescomplemented
49#117×D47—28no—
50C22×Dic47⋊C4C2212yescomplemented
51C2×C4⋊C4×D47C2211yescharacteristic
52C2×C4⋊C4×D47C2211yescharacteristic
53C2×C22⋊C4×D47C2212yes—
54C2×C42×D47C2212yes—
55#15689029C2211yescharacteristic, complemented
56#15689028C2211yescharacteristic, complemented
57#15689026C2212yes—
58#15689026C2211yescharacteristic, complemented
59#15689023C2212yes—
60#15689023C2212yes—
61#15689022C2211yescharacteristic, complemented
62#15689021C2211yescharacteristic, complemented
63#15689019C2211yescharacteristic, complemented
64#15689017C2212yes—
65#15689017C2212yes—
66#15689017C2212yescomplemented
67#15689016C2212yescomplemented
68#15689015C2212yes—
69#15689014C2212yes—
70#15689013C2212yes—
71#15689012C2212yes—
72#15689011C2212yes—
73#15689011C2212yes—
74#15689011C2212yescomplemented
75#15689008C2212yescomplemented
76#15689007C2212yescomplemented
77#15689006C2212yescomplemented
78#15689005C2212yescomplemented
79#15689003C2212yes—
80#15689002C2212yes—
81#15689000C2212yes—
82#15688999C2212yes—
83#15688999C2212yes—
84#15688997C2212yes—
85#15688994C2212yes—
86#15688992C2212yescomplemented
87#15688987C2212yescomplemented
88#15688985C2211yescharacteristic
89#15688985C2211yescharacteristic
90#15688982C2211yescharacteristic
91#15688982C2211yescharacteristic
92#15688981C2211yescharacteristic
93#15688981C2211yescharacteristic
94#15688981C2212yescomplemented
95#15688981C2212yescomplemented
96#15688978C2211yescharacteristic
97#15688978C2211yescharacteristic
98C4⋊C4×Dic47C2212yescomplemented
99C4⋊C4×Dic47C2211yescharacteristic, complemented
100C4⋊C4×Dic47C2211yescharacteristic, complemented
101C4×Dic47⋊C4C2212yescomplemented
102C4×Dic47⋊C4C2212yescomplemented
103C4×C4⋊Dic47C2212yescomplemented
104C4×C4⋊Dic47C2211yescharacteristic, complemented
105#15688974C2212yescomplemented
106#15688974C2212yescomplemented
107C22⋊C4×Dic47C2212yescomplemented
108C22⋊C4×Dic47C2212yescomplemented
109C4×(C2×D47)⋊C4C2211yescharacteristic
110C4×(C2×D47)⋊C4C2211yescharacteristic
111C4×(C2×D47)⋊C4C2212yes—
112C4×C22⋊Dic47C2211yescharacteristic
113C4×C22⋊Dic47C2212yescomplemented
114#15688970C2212yes—
115C2×#121×C47C2211yescharacteristic
116C2×C4×D4×C47C2211yescharacteristic, complemented
117C2×#117×C47C2211yescharacteristic
118C47×#390C2212yes—
119C47×#390C2211yescharacteristic, complemented
120C47×#389C2211yescharacteristic, complemented
121C47×#388C2212yescomplemented
122C47×#386C2212yes—
123C4×C4⋊C4×C47C2211yescharacteristic, complemented
124C4×C22⋊C4×C47C2211yescharacteristic
125C4×C22⋊C4×C47C2212yescomplemented
126C24×D47C2311yescharacteristic
127C2×#10625352—24no—
128C2×#10625352—24no—
129C2×#10625352C2×C418yes—
130C22×Dic94C2311yescharacteristic
131C22×C22⋊D47C2312yes—
132C22×C22⋊D47C2312yes—
133C23×Dic47C2311yescharacteristic
134C23×Dic47C2312yes—
135C23×Dic47C2312yes—
136C22×C4×D47—24no—
137C22×C4×D47—24no—
138C22×C4×D47C2×C418yescomplemented
139C22×C4×D47C2311yescharacteristic
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145#13094006C2×C4116yescomplemented
146#13094004C2×C418yescomplemented
147#13094003C2×C418yescomplemented
148#13093995C2×C418yescomplemented
149#13093992C2×C4116yescomplemented
150C4×Dic94—24no—
151#13093989—24no—
152D4×Dic47—24no—
153D4×Dic47C2×C4116yescomplemented
154C4×C22⋊D47—28no—
155(C22⋊D47)⋊C4—28no—
156(C22⋊D47)⋊C4C2×C4116yescomplemented
157#13093983—24no—
158#13093982—24no—
159#13093982—24no—
160#13093982C2×C418yescomplemented
161#13093981—24no—
162#13093981—24no—
163#13093981—28no—
164#13093980—28no—
165#13093980—28no—
166C2×C4⋊Dic47C2311yescharacteristic
167C2×C4⋊Dic47C2312yes—
168C2×C4⋊Dic47C2312yes—
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2311yescharacteristic
171C2×Dic47⋊C4—28no—
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2311yescharacteristic
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C4⋊C4×D47—24no—
184C4⋊C4×D47D418yescomplemented
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2312yes—
187C2×C22⋊Dic47C2311yescharacteristic
188C2×C22⋊Dic47C2311yescharacteristic
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×(C2×D47)⋊C4C2311yescharacteristic
194C2×(C2×D47)⋊C4C2311yescharacteristic
195C2×(C2×D47)⋊C4C2311yescharacteristic
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C2×(C2×D47)⋊C4C2311yescharacteristic
201C2×(C2×D47)⋊C4C2311yescharacteristic
202C2×(C2×D47)⋊C4C2311yescharacteristic
203C2×(C2×D47)⋊C4C2312yes—
204C2×(C2×D47)⋊C4C2312yes—
205C22⋊C4×D47—28no—
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2312yes—
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2312yes—
213C2×C4×Dic47C2312yes—
214C2×C4×Dic47C2312yes—
215C2×C4×Dic47C2312yes—
216C2×C4×Dic47C2312yes—
217C42×D47—28no—
218C47⋊#95C2312yes—
219C47⋊#95C2311yescharacteristic
220C47⋊#95C2311yescharacteristic
221C47⋊#95C2311yescharacteristic
222C47⋊#95C2312yes—
223C47⋊#95C2311yescharacteristic
224C47⋊#95C2312yes—
225C47⋊#95C2311yescharacteristic
226C47⋊#95C2312yes—
227C47⋊#95C2311yescharacteristic
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C22×D4×C47C2311yescharacteristic
235C22×D4×C47C2312yes—
236C23×C4×C47C2311yescharacteristic
237C23×C4×C47C2312yes—
238#121×C47C2×C418yescomplemented
239C4×D4×C47—24no—
240#117×C47—24no—
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2312yes—
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2311yescharacteristic
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2312yes—
255C2×C42×C47C2312yes—
256#95×C47C2312yes—
257#95×C47C2311yescharacteristic
258#95×C47C2311yescharacteristic
259#95×C47C2312yes—
260C24×C47C2411yescharacteristic
261C24×C47C2412yes—
262C23×D47—22no—
263C23×D47—22no—
264C23×D47—41no—
265C23×D47—41no—
266C23×D47—41no—
267C23×D47—41no—
268C23×D47C22×C414yes—
269C23×D47C2411yescharacteristic
270C23×D47C2411yescharacteristic
271C2×D4×C47—22no—
272C2×D4×C47—22no—
273C2×D4×C47—42no—
274C2×D4×C47—42no—
275C2×D4×C47C22×C414yes—
276C2×D4×C47C22×C418yes—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—24no—
280C22×C4×C47—42no—
281C22×C4×C47—42no—
282C22×C4×C47C22×C414yes—
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2412yes—
290C22×C4×C47C2412yes—
291C22×C4×C47C2411yescharacteristic
292C2×C22⋊D47—24no—
293C2×C22⋊D47—24no—
294C2×C22⋊D47—42no—
295C2×C22⋊D47—42no—
296C2×C22⋊D47C22×C418yes—
297C2×C22⋊D47C22×C418yes—
298C22×Dic47—24no—
299C22×Dic47—22no—
300C22×Dic47—22no—
301C22×Dic47—24no—
302C22×Dic47—24no—
303C22×Dic47—42no—
304C22×Dic47—42no—
305C22×Dic47C22×C418yes—
306C22×Dic47C22×C414yes—
307C22×Dic47C2411yescharacteristic
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2412yes—
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2412yes—
314C22×Dic47C2412yes—
315C22×Dic47C2412yes—
316C22×Dic47C2411yescharacteristic
317#10625352—232no—
318C2×C4×D47—22no—
319C2×C4×D47—22no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—232no—
325C2×C4×D47—24no—
326C2×C4×D47—42no—
327C2×C4×D47—42no—
328C2×C4×D47—42no—
329C2×C4×D47—42no—
330C2×C4×D47C22×C414yes—
331C2×C4×D47C22×C414yes—
332C2×C4×D47C22×C414yes—
333C2×C4×D47C22×C414yes—
334C2×C4×D47C2×D418yes—
335C2×C4×D47C2×D414yes—
336C2×C4×D47#4114yes—
337C2×Dic94—22no—
338C2×Dic94—22no—
339C2×Dic94C22×C414yes—
340C4⋊C4×C47—22no—
341C4⋊C4×C47—42no—
342C4⋊C4×C47C22×C414yes—
343C4⋊C4×C47C2×D414yes—
344C22⋊C4×C47—24no—
345C22⋊C4×C47—24no—
346C22⋊C4×C47—41no—
347C22⋊C4×C47—41no—
348C22⋊C4×C47—42no—
349C22⋊C4×C47—42no—
350C22⋊C4×C47C22×C418yes—
351C42×C47—24no—
352C42×C47—22no—
353C42×C47—22no—
354C42×C47—42no—
355C22⋊Dic47—24no—
356C22⋊Dic47—24no—
357C22⋊Dic47—41no—
358C22⋊Dic47—41no—
359C22⋊Dic47—42no—
360C22⋊Dic47—42no—
361C22⋊Dic47C22×C418yes—
362C22⋊Dic47C22×C418yes—
363(C2×D47)⋊C4—22no—
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—41no—
370(C2×D47)⋊C4—41no—
371(C2×D47)⋊C4—41no—
372(C2×D47)⋊C4—41no—
373(C2×D47)⋊C4C22×C418yes—
374(C2×D47)⋊C4C22×C418yes—
375C4⋊Dic47—22no—
376C4⋊Dic47—42no—
377C4⋊Dic47C22×C414yes—
378C4⋊Dic47C22×C418yes—
379C4⋊Dic47C2×D414yes—
380Dic47⋊C4—24no—
381Dic47⋊C4—24no—
382Dic47⋊C4—22no—
383Dic47⋊C4—24no—
384Dic47⋊C4—22no—
385Dic47⋊C4—22no—
386Dic47⋊C4—22no—
387Dic47⋊C4—42no—
388Dic47⋊C4—42no—
389Dic47⋊C4C22×C418yes—
390Dic47⋊C4C2×D418yes—
391C4×Dic47—24no—
392C4×Dic47—24no—
393C4×Dic47—22no—
394C4×Dic47—22no—
395C4×Dic47—24no—
396C4×Dic47—24no—
397C4×Dic47—24no—
398C4×Dic47—42no—
399C4×Dic47—42no—
400C4×Dic47—42no—
401C4×Dic47C22×C418yes—
402C23×C47—21no—
403C23×C47—22no—
404C23×C47—22no—
405C23×C47—21no—
406C23×C47—22no—
407C23×C47—22no—
408C23×C47—21no—
409C23×C47—21no—
410C23×C47—22no—
411C23×C47—22no—
412C23×C47—21no—
413C23×C47—21no—
414C23×C47C23×C412yes—
415C23×C47C23×C414yes—
416C23×C47C2511yescharacteristic
417C22×D47—21no—
418C22×D47—21no—
419C22×D47—21no—
420C22×D47—21no—
421C22×D47—21no—
422C22×D47—21no—
423C22×D47—21no—
424C22×D47—21no—
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—28no—
428C22×D47—44no—
429C22×D47—44no—
430C22×D47—44no—
431C22×D47—44no—
432C22×D47—44no—
433C22×D47—44no—
434C22×D47C23×C412yes—
435C22×D47C23×C412yes—
436C22×D47C22×D412yes—
437C22×D47C2×#4112yes—
438D4×C47—28no—
439D4×C47—48no—
440C2×C4×C47—21no—
441C2×C4×C47—21no—
442C2×C4×C47—22no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—22no—
446C2×C4×C47—28no—
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—21no—
454C2×C4×C47—22no—
455C2×C4×C47—21no—
456C2×C4×C47—21no—
457C2×C4×C47—21no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—22no—
461C2×C4×C47—21no—
462C2×C4×C47—84no—
463C2×C4×C47C23×C414yes—
464C2×C4×C47C23×C412yes—
465C2×C4×C47C23×C412yes—
466C2×C4×C47C22×D414yes—
467C2×C4×C47C22×D412yes—
468C2×C4×C47C2×#4112yes—
469C22⋊D47—216no—
470C22⋊D47—48no—
471C2×Dic47—21no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—21no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—28no—
480C2×Dic47—216no—
481C2×Dic47—21no—
482C2×Dic47—22no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—22no—
490C2×Dic47—21no—
491C2×Dic47—22no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—21no—
495C2×Dic47—21no—
496C2×Dic47—84no—
497C2×Dic47C23×C414yes—
498C2×Dic47C23×C414yes—
499C2×Dic47C23×C412yes—
500C2×Dic47C23×C412yes—
501C2×Dic47C22×D414yes—
502C2×Dic47C22×D412yes—
503C2×Dic47C2×#4112yes—
504C4×D47—28no—
505C4×D47—28no—
506C4×D47—28no—
507C4×D47—48no—
508C4×D47—48no—
509C4×D47C4×D4116yes—
510Dic94—28no—
511#34201—471nomaximal, Sylow
512C22×C47—24no—
513C22×C47—22no—
514C22×C47—24no—
515C22×C47—22no—
516C22×C47—24no—
517C22×C47—22no—
518C22×C47—42no—
519C22×C47—41no—
520C22×C47—41no—
521C22×C47—42no—
522C22×C47—41no—
523C22×C47—41no—
524C22×C47—42no—
525C22×C47—42no—
526C22×C47C24×C411yescharacteristic
527C22×C47C23×D411yescharacteristic
528C22×C47C22×#4111yescharacteristic
529C22×C47#58511yescharacteristic
530C22×C47#58511yescharacteristic
531C22×C47#58511yescharacteristic
532C22×C47#58511yescharacteristic
533C2×D47—22no—
534C2×D47—22no—
535C2×D47—22no—
536C2×D47—22no—
537C2×D47—22no—
538C2×D47—22no—
539C2×D47—22no—
540C2×D47—22no—
541C2×D47—22no—
542C2×D47—416no—
543C2×D47—41no—
544C2×D47—41no—
545C2×D47—41no—
546C2×D47—41no—
547C2×D47C2×C4×D414yes—
548C4×C47—22no—
549C4×C47—24no—
550C4×C47—24no—
551C4×C47—41no—
552C4×C47—42no—
553C4×C47—41no—
554C4×C47—41no—
555C4×C47—41no—
556C4×C47C2×C4×D414yes—
557Dic47—24no—
558Dic47—22no—
559Dic47—24no—
560Dic47—24no—
561Dic47—41no—
562Dic47—42no—
563Dic47—41no—
564Dic47—41no—
565Dic47—41no—
566Dic47C2×C4×D414yes—
567C2×#525—471no—
568C2×#520—471no—
569C22×#117—471no—
570#2363—471no—
571#2363—471no—
572#2363—471no—
573#2363D4711yescharacteristic, complemented
574#2362—471no—
575#2362—471no—
576#2362—471no—
577#2362—471no—
578#2354—472no—
579#2354—472no—
580#2352—472no—
581#2352—472no—
582#2321—472no—
583#2321—472no—
584#2317—471no—
585#2311—471no—
586C4×#123—472no—
587C4×#123—472no—
588#2280—471no—
589#2274—471no—
590C2×C47—42no—
591C2×C47—44no—
592C2×C47C22×C4×D411yescharacteristic
593C2×C47#342811yescharacteristic
594C2×C47#342811yescharacteristic
595C2×C47#348511yescharacteristic
596C2×C47#348711yescharacteristic
597C2×C47#349311yescharacteristic
598C2×C47#349311yescharacteristic
599D47—24no—
600D47—42no—
601C22×#41—471no—
602C24×C4—471no—
603#525—4716no—
604C2×#123—472no—
605C2×C22⋊Q8—471no—
606C2×C22⋊Q8—471no—
607C2×#121—471no—
608C2×#121C2×D4711yescharacteristic
609C2×#120—472no—
610#520—948no—
611C2×C4×Q8—471no—
612C2×C4×Q8—471no—
613C2×C4×D4—472no—
614C2×C4×D4—471no—
615C2×C4×D4—472no—
616C2×C4×D4—472no—
617C2×C4×D4—472no—
618C2×C4×D4C2×D4711yescharacteristic, complemented
619C2×#117—471no—
620C2×#117—471no—
621C2×#117—471no—
622C2×#117—471no—
623C2×#117—472no—
624C2×#117—472no—
625C2×#117—471no—
626C2×#117—471no—
627C2×#117—472no—
628C2×#117—948no—
629C2×#117C2×D4711yescharacteristic
630C22×C4⋊C4—471no—
631C22×C4⋊C4—472no—
632C22×C4⋊C4—471no—
633C22×C22⋊C4—472no—
634C22×C42—472no—
635#391—471no—
636#391—471no—
637#390—471no—
638#390—472no—
639#390—472no—
640#390—472no—
641#390C2×D4712yes—
642#390C2×D4711yescharacteristic, complemented
643#389—471no—
644#389—471no—
645#389—471no—
646#389C2×D4711yescharacteristic, complemented
647#388—472no—
648#388—472no—
649#388—472no—
650#388—472no—
651#388—472no—
652#388—472no—
653#388—472no—
654#388—472no—
655#388—472no—
656#388—472no—
657#388—472no—
658#388C2×D4712yescomplemented
659#387—472no—
660#387—472no—
661#387—472no—
662#387—472no—
663#386—472no—
664#386—472no—
665#386—472no—
666#386—472no—
667#386—472no—
668#386C2×D4712yes—
669#385—472no—
670#385—472no—
671#384—472no—
672#382—472no—
673#381—471no—
674#381—471no—
675#380—472no—
676#380—472no—
677#380—471no—
678#380—471no—
679#380—471no—
680#380—471no—
681#379—471no—
682#379—471no—
683C4×C4⋊C4—472no—
684C4×C4⋊C4—471no—
685C4×C4⋊C4—471no—
686C4×C4⋊C4—472no—
687C4×C4⋊C4—471no—
688C4×C4⋊C4—472no—
689C4×C4⋊C4—472no—
690C4×C4⋊C4—472no—
691C4×C4⋊C4—472no—
692C4×C4⋊C4C2×D4711yescharacteristic, complemented
693C4×C22⋊C4—471no—
694C4×C22⋊C4—472no—
695C4×C22⋊C4—472no—
696C4×C22⋊C4—472no—
697C4×C22⋊C4—472no—
698C4×C22⋊C4—471no—
699C4×C22⋊C4—471no—
700C4×C22⋊C4—472no—
701C4×C22⋊C4C2×D4711yescharacteristic
702C4×C22⋊C4C2×D4712yescomplemented
703C47#3420111yescharacteristic, complemented, Sylow
704C25—471no—
705C2×#41—478no—
706C2×#41—944no—
707C2×#41—944no—
708C22×Q8—471no—
709C22×D4—472no—
710C22×D4—472no—
711C22×D4C22×D4711yescharacteristic
712C22×D4C22×D4712yes—
713C23×C4—471no—
714C23×C4—472no—
715C23×C4—471no—
716C23×C4—478no—
717C23×C4—471no—
718C23×C4—471no—
719C23×C4—471no—
720C23×C4—472no—
721C23×C4—472no—
722C23×C4—472no—
723C23×C4—944no—
724C23×C4—944no—
725C23×C4C22×D4711yescharacteristic
726C23×C4C22×D4712yes—
727#123—4716no—
728C22⋊Q8—478no—
729C22⋊Q8—478no—
730#121—478no—
731#121C4×D4718yescomplemented
732#120—4716no—
733C4×Q8—944no—
734C4×Q8—944no—
735C4×D4—24no—
736C4×D4—4716no—
737C4×D4—4716no—
738C4×D4—948no—
739C4×D4—944no—
740C4×D4—948no—
741#117—24no—
742#117—478no—
743#117—948no—
744#117—944no—
745#117—944no—
746#117—948no—
747#117—948no—
748#117—944no—
749#117—944no—
750#117—944no—
751C2×C4⋊C4—472no—
752C2×C4⋊C4—471no—
753C2×C4⋊C4—471no—
754C2×C4⋊C4—472no—
755C2×C4⋊C4—472no—
756C2×C4⋊C4—478no—
757C2×C4⋊C4—471no—
758C2×C4⋊C4—472no—
759C2×C4⋊C4—471no—
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—472no—
767C2×C4⋊C4—472no—
768C2×C4⋊C4—944no—
769C2×C4⋊C4—948no—
770C2×C4⋊C4C22×D4711yescharacteristic
771C2×C4⋊C4C22×D4712yes—
772C2×C4⋊C4C22×D4711yescharacteristic
773C2×C4⋊C4C22×D4711yescharacteristic
774C2×C22⋊C4—472no—
775C2×C22⋊C4—472no—
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—471no—
783C2×C22⋊C4—471no—
784C2×C22⋊C4—471no—
785C2×C22⋊C4—471no—
786C2×C22⋊C4—471no—
787C2×C22⋊C4—471no—
788C2×C22⋊C4—472no—
789C2×C22⋊C4—472no—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—471no—
794C2×C22⋊C4—948no—
795C2×C22⋊C4C22×D4712yes—
796C2×C22⋊C4C22×D4712yes—
797C2×C22⋊C4C22×D4712yes—
798C2×C22⋊C4C22×D4711yescharacteristic
799C2×C22⋊C4C22×D4711yescharacteristic
800C2×C22⋊C4C22×D4712yes—
801C2×C22⋊C4C22×D4712yes—
802C2×C42—472no—
803C2×C42—472no—
804C2×C42—472no—
805C2×C42—472no—
806C2×C42—471no—
807C2×C42—472no—
808C2×C42—472no—
809C2×C42—471no—
810C2×C42—472no—
811C2×C42—472no—
812C2×C42—472no—
813C2×C42—948no—
814C2×C42C22×D4712yes—
815C2×C42C22×D4711yescharacteristic
816C2×C42C22×D4711yescharacteristic
817C2×C42C22×D4712yes—
818#95—471no—
819#95—471no—
820#95—471no—
821#95—471no—
822#95—471no—
823#95—471no—
824#95—472no—
825#95—472no—
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#95C22×D4712yes—
835#95C22×D4711yescharacteristic
836#95C22×D4711yescharacteristic
837#95C22×D4712yes—
838C24—471no—
839C24—471no—
840C24—474no—
841C24—942no—
842C24—942no—
843C24—1881no—
844C24—1881no—
845C24—1881no—
846C24—1881no—
847C24C23×D4711yescharacteristic
848C24C23×D4712yes—
849#41—9432no—
850C2×Q8—474no—
851C2×Q8—942no—
852C2×Q8—942no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—478no—
858C2×D4—478no—
859C2×D4—944no—
860C2×D4—944no—
861C2×D4—1882no—
862C2×D4—1882no—
863C2×D4C2×C4×D4714yes—
864C2×D4C2×C4×D4718yes—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—471no—
871C22×C4—474no—
872C22×C4—474no—
873C22×C4—474no—
874C22×C4—474no—
875C22×C4—478no—
876C22×C4—471no—
877C22×C4—472no—
878C22×C4—472no—
879C22×C4—472no—
880C22×C4—474no—
881C22×C4—474no—
882C22×C4—474no—
883C22×C4—478no—
884C22×C4—471no—
885C22×C4—471no—
886C22×C4—471no—
887C22×C4—472no—
888C22×C4—471no—
889C22×C4—942no—
890C22×C4—942no—
891C22×C4—9432no—
892C22×C4—942no—
893C22×C4—942no—
894C22×C4—944no—
895C22×C4—944no—
896C22×C4—942no—
897C22×C4—942no—
898C22×C4—944no—
899C22×C4—944no—
900C22×C4—942no—
901C22×C4—942no—
902C22×C4—1882no—
903C22×C4—1882no—
904C22×C4—1882no—
905C22×C4—1882no—
906C22×C4—1882no—
907C22×C4—1882no—
908C22×C4C2×C4×D4714yes—
909C22×C4C23×D4711yescharacteristic
910C22×C4C23×D4711yescharacteristic
911C22×C4C23×D4711yescharacteristic
912C22×C4C23×D4712yes—
913C22×C4C23×D4711yescharacteristic
914C22×C4C23×D4711yescharacteristic
915C22×C4C23×D4712yes—
916C22×C4C23×D4712yes—
917C22×C4C23×D4711yescharacteristic
918C4⋊C4—22no—
919C4⋊C4—42no—
920C4⋊C4—478no—
921C4⋊C4—474no—
922C4⋊C4—478no—
923C4⋊C4—478no—
924C4⋊C4—474no—
925C4⋊C4—942no—
926C4⋊C4—944no—
927C4⋊C4—944no—
928C4⋊C4—942no—
929C4⋊C4—942no—
930C4⋊C4—942no—
931C4⋊C4—944no—
932C4⋊C4—942no—
933C4⋊C4—1882no—
934C4⋊C4—1882no—
935C4⋊C4—1882no—
936C4⋊C4C2×C4×D4714yes—
937C4⋊C4D4×D4714yes—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—42no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—42no—
944C22⋊C4—478no—
945C22⋊C4—478no—
946C22⋊C4—478no—
947C22⋊C4—478no—
948C22⋊C4—944no—
949C22⋊C4—942no—
950C22⋊C4—942no—
951C22⋊C4—942no—
952C22⋊C4—942no—
953C22⋊C4—944no—
954C22⋊C4—944no—
955C22⋊C4—944no—
956C22⋊C4—1881no—
957C22⋊C4—1881no—
958C22⋊C4—1881no—
959C22⋊C4—1881no—
960C22⋊C4—1882no—
961C22⋊C4—1881no—
962C22⋊C4—1881no—
963C22⋊C4—1882no—
964C22⋊C4C2×C4×D4718yes—
965C42—24no—
966C42—22no—
967C42—22no—
968C42—42no—
969C42—478no—
970C42—944no—
971C42—944no—
972C42—944no—
973C42—944no—
974C42—944no—
975C42—942no—
976C42—942no—
977C42—1882no—
978C42—1882no—
979C42—1882no—
980C23—21no—
981C23—22no—
982C23—21no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—21no—
987C23—21no—
988C23—22no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—472no—
993C23—472no—
994C23—472no—
995C23—472no—
996C23—948no—
997C23—941no—
998C23—941no—
999C23—941no—
1000C23—941no—
1001C23—941no—
1002C23—941no—
1003C23—941no—
1004C23—941no—
1005C23—941no—
1006C23—941no—
1007C23—1884no—
1008C23—1884no—
1009C23—1884no—
1010C23—1884no—
1011C23—1884no—
1012C23—1884no—
1013C23C22×C4×D4712yes—
1014C23C22×C4×D4714yes—
1015C23C24×D4711yescharacteristic
1016Q8—948no—
1017D4—28no—
1018D4—48no—
1019D4—9416no—
1020D4—1888no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—84no—
1044C2×C4—472no—
1045C2×C4—472no—
1046C2×C4—472no—
1047C2×C4—4716no—
1048C2×C4—474no—
1049C2×C4—472no—
1050C2×C4—474no—
1051C2×C4—474no—
1052C2×C4—948no—
1053C2×C4—948no—
1054C2×C4—948no—
1055C2×C4—9416no—
1056C2×C4—941no—
1057C2×C4—942no—
1058C2×C4—941no—
1059C2×C4—942no—
1060C2×C4—942no—
1061C2×C4—942no—
1062C2×C4—942no—
1063C2×C4—942no—
1064C2×C4—948no—
1065C2×C4—941no—
1066C2×C4—942no—
1067C2×C4—941no—
1068C2×C4—941no—
1069C2×C4—941no—
1070C2×C4—941no—
1071C2×C4—941no—
1072C2×C4—941no—
1073C2×C4—942no—
1074C2×C4—941no—
1075C2×C4—941no—
1076C2×C4—941no—
1077C2×C4—941no—
1078C2×C4—942no—
1079C2×C4—941no—
1080C2×C4—3764no—
1081C2×C4—1888no—
1082C2×C4—1888no—
1083C2×C4C22×C4×D4714yes—
1084C2×C4C22×C4×D4712yes—
1085C2×C4C22×C4×D4712yes—
1086C2×C4C2×D4×D4714yes—
1087C2×C4C2×D4×D4712yes—
1088C2×C4#41×D4712yes—
1089C22—22no—
1090C22—24no—
1091C22—22no—
1092C22—24no—
1093C22—24no—
1094C22—22no—
1095C22—42no—
1096C22—41no—
1097C22—41no—
1098C22—42no—
1099C22—41no—
1100C22—42no—
1101C22—41no—
1102C22—42no—
1103C22—474no—
1104C22—942no—
1105C22—942no—
1106C22—942no—
1107C22—942no—
1108C22—942no—
1109C22—942no—
1110C22—942no—
1111C22—942no—
1112C22—942no—
1113C22—18816no—
1114C22—1881no—
1115C22—1881no—
1116C22—1881no—
1117C22—1881no—
1118C22C23×C4×D4711yescharacteristic
1119C22C22×D4×D4711yescharacteristic
1120C22C2×#41×D4711yescharacteristic
1121C22#1568995811yescharacteristic
1122C22#1568995811yescharacteristic
1123C22#1568995911yescharacteristic
1124C22#1568995911yescharacteristic
1125C4—24no—
1126C4—22no—
1127C4—24no—
1128C4—41no—
1129C4—42no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—474no—
1134C4—944no—
1135C4—942no—
1136C4—944no—
1137C4—944no—
1138C4—1881no—
1139C4—1882no—
1140C4—1881no—
1141C4—1881no—
1142C4—1881no—
1143C4C4×D4×D4714yes—
1144C2—42no—
1145C2—44no—
1146C2—944no—
1147C2—1882no—
1148C2C2×C4×D4×D4711yescharacteristic
1149C2#2025658611yescharacteristic
1150C2#2025658711yescharacteristic
1151C2#2025702511yescharacteristic
1152C2#2025704111yescharacteristic
1153C2#2025709911yescharacteristic
1154C2#2025710411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2363C2
socle, cosocleC23×C47C25
prime radicalC2×#15689633C2
hypercenter#2363D47
hypocenterC47#34201
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#15689602C2semidirect
3. C2×#117×D47C2semidirect
4. #20246431C2semidirect
5. #20246430C2semidirect
6. #20246422C2semidirect
7. #20246417C2semidirect
8. #20246415C2semidirect
9. #20246414C2semidirect
10. #20246413C2semidirect
11. #20246336C2semidirect
12. #20246334C2semidirect
13. #20246315C2semidirect
14. #20246311C2semidirect
15. #20246047C2semidirect
16. #20246044C2semidirect
17. #20246010C2semidirect
18. #20245978C2semidirect
19. #20245915C2semidirect
20. C4×#13094006C2semidirect
21. #20245769C2semidirect
22. #20245742C2semidirect
23. C47×#2363C2semidirect
26. #15689633C4semidirect
33. C2×C4×Dic94C22semidirect
34. C2×#13093989C22semidirect
36. C2×D4×Dic47C22semidirect
48. C2×#13093980C22semidirect
50. C22×Dic47⋊C4C22semidirect
55. #15689029C22semidirect
56. #15689028C22semidirect
58. #15689026C22semidirect
61. #15689022C22semidirect
62. #15689021C22semidirect
63. #15689019C22semidirect
66. #15689017C22semidirect
67. #15689016C22semidirect
74. #15689011C22semidirect
75. #15689008C22semidirect
76. #15689007C22semidirect
77. #15689006C22semidirect
78. #15689005C22semidirect
86. #15688992C22semidirect
87. #15688987C22semidirect
94. #15688981C22semidirect
95. #15688981C22semidirect
98. C4⋊C4×Dic47C22semidirect
99. C4⋊C4×Dic47C22semidirect
100. C4⋊C4×Dic47C22semidirect
101. C4×Dic47⋊C4C22semidirect
102. C4×Dic47⋊C4C22semidirect
103. C4×C4⋊Dic47C22semidirect
104. C4×C4⋊Dic47C22semidirect
105. #15688974C22semidirect
106. #15688974C22semidirect
107. C22⋊C4×Dic47C22semidirect
108. C22⋊C4×Dic47C22semidirect
113. C4×C22⋊Dic47C22semidirect
116. C2×C4×D4×C47C22semidirect
119. C47×#390C22semidirect
120. C47×#389C22semidirect
121. C47×#388C22semidirect
123. C4×C4⋊C4×C47C22semidirect
125. C4×C22⋊C4×C47C22semidirect
138. C22×C4×D47C2×C4semidirect
145. #13094006C2×C4semidirect
146. #13094004C2×C4semidirect
147. #13094003C2×C4semidirect
148. #13093995C2×C4semidirect
149. #13093992C2×C4semidirect
153. D4×Dic47C2×C4semidirect
156. (C22⋊D47)⋊C4C2×C4semidirect
160. #13093982C2×C4semidirect
184. C4⋊C4×D47D4semidirect
238. #121×C47C2×C4semidirect
573. #2363D47semidirect
618. C2×C4×D4C2×D47semidirect
642. #390C2×D47semidirect
646. #389C2×D47semidirect
658. #388C2×D47semidirect
692. C4×C4⋊C4C2×D47semidirect
702. C4×C22⋊C4C2×D47semidirect
703. C47#34201semidirect
731. #121C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896332
C2×#156896022
C2×#117×D472
#202464312
#202464302
#202464222
#202464172
#202464152
#202464142
#202464132
#202463362
#202463342
#202463152
#202463112
#202460472
#202460442
#202460102
#202459782
#202459152
C4×#130940062
#202457692
#202457422
C47×#23632
#3420147