Finite Group Databasebeta

← #27086849

Subgroups — #27086849

Order 12032.

2394 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic, complemented
2#20254176C214yesmaximal, complemented
3#20254169C212yesmaximal, complemented
4#20254165C212yesmaximal, complemented
5#20254160C211yesmaximal, characteristic, complemented
6#20254153C212yesmaximal, complemented
7#20254149C212yesmaximal, complemented
8#20254145C211yesmaximal, characteristic, complemented
9#20254141C211yesmaximal, characteristic, complemented
10#20254136C211yesmaximal, characteristic, complemented
11#20253301C212yesmaximal, complemented
12#20253297C212yesmaximal, complemented
13#20252966C214yesmaximal, complemented
14#20252606C212yesmaximal, complemented
15#20252604C212yesmaximal, complemented
16C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
17C2×C47×#525C211yesmaximal, characteristic, complemented
18C22×#10625350C2211yescharacteristic, complemented
19C2×#13094044C2214yescomplemented
20C23×C47⋊C8C2212yescomplemented
21#15689634—21no—
22#15689634—21no—
23#15689634—21no—
24#15689634—21no—
25#15689634C2212yes—
26#15689634C2212yes—
27#15689634C2212yescomplemented
28#15689634C2212yescomplemented
29C2×#13094007—21no—
30C2×#13094003C2211yescharacteristic
31C2×#13094003C2211yescharacteristic, complemented
32C2×#13093998C2211yescharacteristic
33C2×#13093998C2211yescharacteristic, complemented
34C2×#13093993—21no—
35C2×C4×C22⋊D47—21no—
36C2×C4×C22⋊D47—21no—
37C2×#13093983C2211yescharacteristic, complemented
38#15689464C2214yescomplemented
39#15689461C2214yescomplemented
40#15689458C2212yescomplemented
41#15689456C2212yescomplemented
42#15689453C2212yescomplemented
43#15689451C2212yescomplemented
44#15689447C2214yescomplemented
45#15689444C2214yescomplemented
46#15689441C2212yescomplemented
47#15689439C2212yescomplemented
48#15689436C2212yescomplemented
49#15689434C2212yescomplemented
50#15689362C2214yescomplemented
51#15689362C2214yescomplemented
52#15689357C2214yescomplemented
53#15689357C2214yescomplemented
54#15689354C2214yescomplemented
55#15689354C2214yescomplemented
56#15689350C2214yescomplemented
57#15689350C2214yescomplemented
58#15689285C2214yescomplemented
59#15689283C2214yescomplemented
60#15689279C2212yescomplemented
61#15689278C2212yescomplemented
62#15689274C2212yescomplemented
63#15689273C2212yescomplemented
64#15689268C2214yescomplemented
65#15689266C2214yescomplemented
66#15689262C2212yescomplemented
67#15689261C2212yescomplemented
68#15689257C2212yescomplemented
69#15689256C2212yescomplemented
70#15689159C2214yescomplemented
71#15689119C2214yescomplemented
72#15689117C2214yescomplemented
73C2×C22⋊(C47⋊C8)C2211yescharacteristic
74C2×C22⋊(C47⋊C8)C2211yescharacteristic
75C2×C22⋊(C47⋊C8)C2212yescomplemented
76C2×C22⋊(C47⋊C8)C2212yescomplemented
77C2×C22⋊(C47⋊C8)C2212yescomplemented
78C2×C22⋊(C47⋊C8)C2212yescomplemented
79C2×C22⋊(C47⋊C8)C2212yescomplemented
80C22×#41×C47C2211yescharacteristic, complemented
81C24×C4×C47C2211yescharacteristic
82C47×#525—21no—
83C47×#525—21no—
84C47×#525—21no—
85C47×#525—21no—
86C47×#525C2212yes—
87C47×#525C2212yes—
88C47×#525C2212yescomplemented
89C47×#525C2212yescomplemented
90C2×#123×C47—21no—
91C2×C22⋊Q8×C47C2211yescharacteristic
92C2×C22⋊Q8×C47C2211yescharacteristic, complemented
93C2×#121×C47C2211yescharacteristic
94C2×#121×C47C2211yescharacteristic, complemented
95C2×#120×C47—21no—
96C2×C4×D4×C47—21no—
97C2×C4×D4×C47—21no—
98C2×#117×C47C2211yescharacteristic, complemented
99C2×#10625350—21no—
100C2×#10625350—21no—
101C2×#10625350—44no—
102C2×#10625350C2312yes—
103C2×#10625350C2312yes—
104C22×Dic94C2311yescharacteristic
105C22×D188C2311yescharacteristic
106C22×C22⋊D47—21no—
107C22×C22⋊D47—21no—
108C22×C22⋊D47—21no—
109C22×C4×D47—21no—
110#13094044—48no—
111C2×#10625337C2314yescomplemented
112C2×#10625335C2314yescomplemented
113C2×#10625336C2314yescomplemented
114C2×#10625334C2314yescomplemented
115C22×C47⋊C8—44no—
116C22×C47⋊C8C2314yes—
117C22×C47⋊C8C2312yes—
118C22×C47⋊C8C2312yes—
119C22×C47⋊C8C2314yes—
120#13094007—22no—
121#13094007—22no—
122#13094007—22no—
123#13094007—22no—
124#13094003—21no—
125#13094003—21no—
126#13094003—21no—
127#13094003—21no—
128#13094003C2312yes—
129#13094003C2312yes—
130#13094003C2312yes—
131#13094003C2312yes—
132#13093998—21no—
133#13093998—21no—
134#13093998—21no—
135#13093998—21no—
136#13093998C2312yes—
137#13093998C2312yes—
138#13093998C2312yes—
139#13093998C2312yes—
140#13093993—22no—
141#13093993—22no—
142#13093993—22no—
143#13093993—22no—
144C4×C22⋊D47—22no—
145C4×C22⋊D47—22no—
146C4×C22⋊D47—22no—
147C4×C22⋊D47—22no—
148C4×C22⋊D47—22no—
149C4×C22⋊D47—22no—
150C4×C22⋊D47—22no—
151C4×C22⋊D47—22no—
152#13093983—21no—
153#13093983—21no—
154#13093983C2312yes—
155#13093983C2312yes—
156C2×C4⋊Dic47C2311yescharacteristic
157C2×C4⋊Dic47C2311yescharacteristic
158C2×Dic47⋊C4—21no—
159C2×Dic47⋊C4—21no—
160C2×C22⋊Dic47—21no—
161C2×C22⋊Dic47—21no—
162C2×C22⋊Dic47—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×(C2×D47)⋊C4—21no—
165C2×C4×Dic47—21no—
166#13093957C2314yescomplemented
167#13093957C2314yescomplemented
168#13093955C2314yescomplemented
169#13093955C2314yescomplemented
170#13093948C2314yescomplemented
171#13093948C2314yescomplemented
172#13093947C2314yescomplemented
173#13093947C2314yescomplemented
174#13093945C2314yescomplemented
175#13093945C2314yescomplemented
176#13093944C2314yescomplemented
177#13093944C2314yescomplemented
178C22⋊(C47⋊C8)C2312yes—
179C22⋊(C47⋊C8)C2312yes—
180C22⋊(C47⋊C8)C2312yes—
181C22⋊(C47⋊C8)C2312yes—
182C22⋊(C47⋊C8)C2314yes—
183C22⋊(C47⋊C8)C2314yes—
184C25×C47D411yescharacteristic
185C2×#41×C47—21no—
186C2×#41×C47—21no—
187C2×#41×C47—44no—
188C2×#41×C47C2312yes—
189C2×#41×C47C2312yes—
190C22×Q8×C47C2311yescharacteristic
191C22×D4×C47—21no—
192C22×D4×C47—21no—
193C22×D4×C47—21no—
194C22×D4×C47C2311yescharacteristic
195C23×C4×C47—21no—
196C23×C4×C47—44no—
197C23×C4×C47D411yescharacteristic
198C23×C4×C47D411yescharacteristic
199C23×C4×C47D411yescharacteristic
200C23×C4×C47D411yescharacteristic
201C23×C4×C47D411yescharacteristic
202C23×C4×C47D411yescharacteristic
203C23×C4×C47D411yescharacteristic
204C23×C4×C47C2311yescharacteristic
205C23×C4×C47C2311yescharacteristic
206C23×C4×C47C2311yescharacteristic
207C23×C4×C47C2311yescharacteristic
208C23×C4×C47C2311yescharacteristic
209C23×C4×C47C2311yescharacteristic
210C23×C4×C47C2311yescharacteristic
211#123×C47—22no—
212#123×C47—22no—
213#123×C47—22no—
214#123×C47—22no—
215C22⋊Q8×C47—21no—
216C22⋊Q8×C47—21no—
217C22⋊Q8×C47—21no—
218C22⋊Q8×C47—21no—
219C22⋊Q8×C47C2312yes—
220C22⋊Q8×C47C2312yes—
221C22⋊Q8×C47C2312yes—
222C22⋊Q8×C47C2312yes—
223#121×C47—21no—
224#121×C47—21no—
225#121×C47—21no—
226#121×C47—21no—
227#121×C47C2312yes—
228#121×C47C2312yes—
229#121×C47C2312yes—
230#121×C47C2312yes—
231#120×C47—22no—
232#120×C47—22no—
233#120×C47—22no—
234#120×C47—22no—
235C4×D4×C47—22no—
236C4×D4×C47—22no—
237C4×D4×C47—22no—
238C4×D4×C47—22no—
239C4×D4×C47—22no—
240C4×D4×C47—22no—
241C4×D4×C47—22no—
242C4×D4×C47—22no—
243#117×C47—21no—
244#117×C47—21no—
245#117×C47C2312yes—
246#117×C47C2312yes—
247C2×C4⋊C4×C47—21no—
248C2×C4⋊C4×C47—21no—
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C4⋊C4×C47C2311yescharacteristic
251C2×C22⋊C4×C47—21no—
252C2×C22⋊C4×C47—21no—
253C2×C22⋊C4×C47—21no—
254C2×C22⋊C4×C47—21no—
255C2×C22⋊C4×C47—21no—
256C2×C42×C47—21no—
257C24×C47—24no—
258C24×C47—21no—
259C24×C47—42no—
260C24×C47—42no—
261C24×C47C2×D411yescharacteristic
262C24×C47C2×D411yescharacteristic
263C24×C47C2×D411yescharacteristic
264C24×C47C2×D411yescharacteristic
265C24×C47C2×D411yescharacteristic
266C24×C47C2×D411yescharacteristic
267C24×C47C2×D411yescharacteristic
268C23×D47—21no—
269#41×C47—28no—
270#41×C47—44no—
271#41×C47—44no—
272#41×C47—44no—
273C2×Q8×C47—21no—
274C2×Q8×C47—42no—
275C2×Q8×C47C2412yes—
276C2×D4×C47—22no—
277C2×D4×C47—22no—
278C2×D4×C47—22no—
279C2×D4×C47—22no—
280C2×D4×C47—22no—
281C2×D4×C47—22no—
282C2×D4×C47—21no—
283C2×D4×C47—42no—
284C2×D4×C47—44no—
285C2×D4×C47—44no—
286C2×D4×C47—44no—
287C2×D4×C47C2412yes—
288C22×C4×C47—24no—
289C22×C4×C47—24no—
290C22×C4×C47—24no—
291C22×C4×C47—21no—
292C22×C4×C47—21no—
293C22×C4×C47—21no—
294C22×C4×C47—22no—
295C22×C4×C47—22no—
296C22×C4×C47—42no—
297C22×C4×C47—42no—
298C22×C4×C47—42no—
299C22×C4×C47—42no—
300C22×C4×C47—42no—
301C22×C4×C47—42no—
302C22×C4×C47—42no—
303C22×C4×C47—42no—
304C22×C4×C47—42no—
305C22×C4×C47—42no—
306C22×C4×C47—42no—
307C22×C4×C47—44no—
308C22×C4×C47C2×D411yescharacteristic
309C22×C4×C47C2×D411yescharacteristic
310C22×C4×C47C2×D411yescharacteristic
311C22×C4×C47C2×D411yescharacteristic
312C22×C4×C47C2×D411yescharacteristic
313C22×C4×C47C2×D411yescharacteristic
314C22×C4×C47C2×D411yescharacteristic
315C22×C4×C47C2×D411yescharacteristic
316C22×C4×C47C2×D411yescharacteristic
317C22×C4×C47C2×D411yescharacteristic
318C22×C4×C47C2×D411yescharacteristic
319C22×C4×C47C2×D411yescharacteristic
320C22×C4×C47C2×D411yescharacteristic
321C22×C4×C47C2×D411yescharacteristic
322C22×C4×C47C2×D411yescharacteristic
323C22×C4×C47C2×D411yescharacteristic
324C22×C4×C47C2×D411yescharacteristic
325C22×C4×C47C2×D411yescharacteristic
326C22×C4×C47C2×D411yescharacteristic
327C22×C4×C47C2×D411yescharacteristic
328C22×C4×C47C2×D411yescharacteristic
329C22×C4×C47C2411yescharacteristic
330C22×C4×C47C2411yescharacteristic
331C22×C4×C47C2411yescharacteristic
332C22×C4×C47C2411yescharacteristic
333C22×C4×C47C2411yescharacteristic
334C22×C4×C47C2411yescharacteristic
335C22×C4×C47C2411yescharacteristic
336C2×C22⋊D47—22no—
337C2×C22⋊D47—22no—
338C2×C22⋊D47—22no—
339C2×C22⋊D47—22no—
340C2×C22⋊D47—22no—
341C2×C22⋊D47—22no—
342C2×C22⋊D47—44no—
343C2×C22⋊D47—44no—
344C2×C22⋊D47—44no—
345C22×Dic47—21no—
346C22×Dic47—21no—
347C22×Dic47—21no—
348#10625350—28no—
349#10625350—44no—
350#10625350—44no—
351#10625350—44no—
352C2×D188—21no—
353C2×D188—42no—
354C2×D188C2412yes—
355C2×C4×D47—22no—
356C2×C4×D47—22no—
357C2×C4×D47—44no—
358C2×Dic94—21no—
359C2×Dic94—42no—
360C2×Dic94C2412yes—
361C4⋊C4×C47—22no—
362C4⋊C4×C47—22no—
363C4⋊C4×C47—22no—
364C4⋊C4×C47—22no—
365C4⋊C4×C47—21no—
366C4⋊C4×C47—21no—
367C4⋊C4×C47C2412yes—
368C4⋊C4×C47C2412yes—
369C22⋊C4×C47—22no—
370C22⋊C4×C47—22no—
371C22⋊C4×C47—22no—
372C22⋊C4×C47—22no—
373C22⋊C4×C47—22no—
374C22⋊C4×C47—22no—
375C22⋊C4×C47—22no—
376C22⋊C4×C47—22no—
377C22⋊C4×C47—22no—
378C22⋊C4×C47—22no—
379C42×C47—22no—
380C42×C47—22no—
381C22⋊Dic47—22no—
382C22⋊Dic47—22no—
383C22⋊Dic47—22no—
384C22⋊Dic47—22no—
385C22⋊Dic47—22no—
386C22⋊Dic47—22no—
387#10625337—44no—
388#10625336—44no—
389#10625335—44no—
390#10625334—44no—
391(C2×D47)⋊C4—22no—
392(C2×D47)⋊C4—22no—
393(C2×D47)⋊C4—22no—
394(C2×D47)⋊C4—22no—
395C4⋊Dic47—21no—
396C4⋊Dic47—21no—
397C4⋊Dic47C2412yes—
398C4⋊Dic47C2412yes—
399Dic47⋊C4—22no—
400Dic47⋊C4—22no—
401Dic47⋊C4—22no—
402Dic47⋊C4—22no—
403C4×Dic47—22no—
404C4×Dic47—22no—
405C2×C47⋊C8—28no—
406C2×C47⋊C8—42no—
407C2×C47⋊C8—44no—
408C2×C47⋊C8—42no—
409C2×C47⋊C8C2414yes—
410C2×C47⋊C8C2414yes—
411C23×C47—22no—
412C23×C47—22no—
413C23×C47—22no—
414C23×C47—22no—
415C23×C47—22no—
416C23×C47—22no—
417C23×C47—22no—
418C23×C47—22no—
419C23×C47—22no—
420C23×C47—22no—
421C23×C47—22no—
422C23×C47—22no—
423C23×C47—22no—
424C23×C47—41no—
425C23×C47—41no—
426C23×C47—41no—
427C23×C47—41no—
428C23×C47—41no—
429C23×C47—41no—
430C23×C47—41no—
431C23×C47—41no—
432C23×C47—416no—
433C23×C47—42no—
434C23×C47—42no—
435C23×C47—42no—
436C23×C47#13514yescomplemented
437C23×C47C22×D411yescharacteristic
438C23×C47C22×D411yescharacteristic
439C23×C47C22×D411yescharacteristic
440C23×C47C22×D411yescharacteristic
441C23×C47C22×D411yescharacteristic
442C23×C47C22×D411yescharacteristic
443C23×C47C22×D411yescharacteristic
444C22×D47—22no—
445C22×D47—42no—
446C22×D47—42no—
447C22×D47—42no—
448Q8×C47—24no—
449Q8×C47—42no—
450D4×C47—24no—
451D4×C47—42no—
452D4×C47—44no—
453D4×C47—44no—
454D4×C47—44no—
455D4×C47—44no—
456D4×C47—44no—
457D4×C47—44no—
458C2×C4×C47—22no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
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—41no—
477C2×C4×C47—41no—
478C2×C4×C47—41no—
479C2×C4×C47—41no—
480C2×C4×C47—41no—
481C2×C4×C47—41no—
482C2×C4×C47—41no—
483C2×C4×C47—41no—
484C2×C4×C47—41no—
485C2×C4×C47—41no—
486C2×C4×C47—41no—
487C2×C4×C47—41no—
488C2×C4×C47—44no—
489C2×C4×C47—42no—
490C2×C4×C47—42no—
491C2×C4×C47—42no—
492C2×C4×C47—44no—
493C2×C4×C47C22×D411yescharacteristic
494C2×C4×C47C22×D411yescharacteristic
495C2×C4×C47C22×D411yescharacteristic
496C2×C4×C47C22×D411yescharacteristic
497C2×C4×C47C22×D411yescharacteristic
498C2×C4×C47C22×D411yescharacteristic
499C2×C4×C47C22×D411yescharacteristic
500C2×C4×C47H(5,𝔽2)14yes—
501C2×C4×C47C2511yescharacteristic
502C22⋊D47—44no—
503C22⋊D47—44no—
504C22⋊D47—44no—
505C22⋊D47—44no—
506C22⋊D47—44no—
507C22⋊D47—44no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—42no—
512C2×Dic47—42no—
513C2×Dic47—42no—
514D188—24no—
515D188—42no—
516C4×D47—44no—
517C4×D47—44no—
518Dic94—24no—
519Dic94—42no—
520C47⋊C8—24no—
521C47⋊C8—24no—
522#60734—471nomaximal, Sylow
523C22×C47—28no—
524C22×C47—21no—
525C22×C47—21no—
526C22×C47—21no—
527C22×C47—21no—
528C22×C47—21no—
529C22×C47—21no—
530C22×C47—21no—
531C22×C47—21no—
532C22×C47—21no—
533C22×C47—21no—
534C22×C47—21no—
535C22×C47—21no—
536C22×C47—21no—
537C22×C47—21no—
538C22×C47—21no—
539C22×C47—21no—
540C22×C47—44no—
541C22×C47—44no—
542C22×C47—44no—
543C22×C47—44no—
544C22×C47—44no—
545C22×C47—44no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—84no—
550C22×C47#53412yes—
551C22×C47C2×#13512yes—
552C22×C47C2×#13512yes—
553C22×C47C2×#13512yes—
554C22×C47#57512yes—
555C22×C47C23×D411yescharacteristic
556C2×D47—42no—
557C2×D47—42no—
558C2×D47—42no—
559C2×D47—84no—
560C4×C47—21no—
561C4×C47—21no—
562C4×C47—21no—
563C4×C47—21no—
564C4×C47—21no—
565C4×C47—21no—
566C4×C47—42no—
567C4×C47—42no—
568C4×C47—42no—
569C4×C47#53412yes—
570C4×C47C2×H(5,𝔽2)12yes—
571Dic47—42no—
572Dic47—42no—
573Dic47—42no—
574C2×#525—471no—
575C2×#525D4711yescharacteristic, complemented
576#3191—474no—
577#3190—472no—
578#3190—472no—
579#3189—471no—
580#3188—472no—
581#3188—472no—
582#3187—471no—
583#3187—471no—
584#3186—471no—
585#3091—472no—
586#3091—472no—
587#3050—474no—
588#3002—472no—
589#3002—472no—
590C22×C22⋊C8—471no—
591C2×C47—22no—
592C2×C47—22no—
593C2×C47—22no—
594C2×C47—22no—
595C2×C47—22no—
596C2×C47—41no—
597C2×C47—41no—
598C2×C47—82no—
599C2×C47C2×#53411yescharacteristic
600C2×C47C22×#13511yescharacteristic
601C2×C47C2×#57511yescharacteristic
602D47—82no—
603C22×#41—471no—
604C22×#41C2×D4711yescharacteristic, complemented
605C24×C4C2×D4711yescharacteristic
606C2×#135—474no—
607C23×C8—472no—
608#525—21no—
609#525—21no—
610#525—21no—
611#525—21no—
612#525—472no—
613#525—472no—
614#525—472no—
615#525—472no—
616#525—941no—
617#525—941no—
618#525—941no—
619#525—941no—
620#525C2×D4712yes—
621#525C2×D4712yes—
622#525C2×D4712yescomplemented
623#525C2×D4712yescomplemented
624C2×#123—21no—
625C2×#123—941no—
626C2×C22⋊Q8—471no—
627C2×C22⋊Q8—471no—
628C2×C22⋊Q8C2×D4711yescharacteristic
629C2×C22⋊Q8C2×D4711yescharacteristic, complemented
630C2×#121—471no—
631C2×#121—471no—
632C2×#121C2×D4711yescharacteristic
633C2×#121C2×D4711yescharacteristic, complemented
634C2×#120—21no—
635C2×#120—941no—
636C2×C4×D4—21no—
637C2×C4×D4—21no—
638C2×C4×D4—941no—
639C2×C4×D4—941no—
640C2×#117—471no—
641C2×#117C2×D4711yescharacteristic, complemented
642#485—474no—
643#485—474no—
644#484—472no—
645#484—472no—
646#483—472no—
647#483—472no—
648#482—474no—
649#482—474no—
650#481—472no—
651#481—472no—
652#480—472no—
653#480—472no—
654#467—474no—
655#467—474no—
656#466—474no—
657#466—474no—
658#465—474no—
659#465—474no—
660#465—474no—
661#465—474no—
662#452—474no—
663#452—474no—
664#451—472no—
665#451—472no—
666#450—472no—
667#450—472no—
668#449—474no—
669#449—474no—
670#448—472no—
671#448—472no—
672#447—472no—
673#447—472no—
674#427—474no—
675#416—474no—
676#416—474no—
677C2×C22⋊C8—472no—
678C2×C22⋊C8—472no—
679C2×C22⋊C8—471no—
680C2×C22⋊C8—471no—
681C2×C22⋊C8—472no—
682C2×C22⋊C8—472no—
683C2×C22⋊C8—472no—
684C47#6073411yescharacteristic, complemented, Sylow
685C25C22⋊D4711yescharacteristic
686C2×#41—21no—
687C2×#41—21no—
688C2×#41—44no—
689C2×#41—472no—
690C2×#41—472no—
691C2×#41—941no—
692C2×#41—941no—
693C2×#41—1884no—
694C2×#41C22×D4712yes—
695C2×#41C22×D4712yes—
696C22×Q8—471no—
697C22×Q8C22×D4711yescharacteristic
698C22×D4—21no—
699C22×D4—21no—
700C22×D4—21no—
701C22×D4—471no—
702C22×D4—941no—
703C22×D4—941no—
704C22×D4—941no—
705C22×D4C22×D4711yescharacteristic
706C23×C4—21no—
707C23×C4—44no—
708C23×C4—941no—
709C23×C4C22⋊D4711yescharacteristic
710C23×C4C22⋊D4711yescharacteristic
711C23×C4C22⋊D4711yescharacteristic
712C23×C4C22⋊D4711yescharacteristic
713C23×C4C22⋊D4711yescharacteristic
714C23×C4C22⋊D4711yescharacteristic
715C23×C4C22⋊D4711yescharacteristic
716C23×C4C22×D4711yescharacteristic
717C23×C4C22×D4711yescharacteristic
718C23×C4C22×D4711yescharacteristic
719C23×C4C22×D4711yescharacteristic
720C23×C4C22×D4711yescharacteristic
721C23×C4C22×D4711yescharacteristic
722C23×C4C22×D4711yescharacteristic
723#135—1888no—
724C2×Q16—474no—
725C2×SD16—474no—
726C2×SD16—474no—
727C2×D8—474no—
728C22×C8—474no—
729C22×C8—472no—
730C22×C8—474no—
731C22×C8—472no—
732C22×C8—1884no—
733#123—22no—
734#123—22no—
735#123—22no—
736#123—22no—
737#123—942no—
738#123—942no—
739#123—942no—
740#123—942no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—21no—
744C22⋊Q8—21no—
745C22⋊Q8—472no—
746C22⋊Q8—472no—
747C22⋊Q8—472no—
748C22⋊Q8—472no—
749C22⋊Q8—941no—
750C22⋊Q8—941no—
751C22⋊Q8—941no—
752C22⋊Q8—941no—
753C22⋊Q8C22×D4712yes—
754C22⋊Q8C22×D4712yes—
755C22⋊Q8C22×D4712yes—
756C22⋊Q8C22×D4712yes—
757#121—21no—
758#121—21no—
759#121—21no—
760#121—21no—
761#121—472no—
762#121—472no—
763#121—472no—
764#121—472no—
765#121—941no—
766#121—941no—
767#121—941no—
768#121—941no—
769#121C22×D4712yes—
770#121C22×D4712yes—
771#121C22×D4712yes—
772#121C22×D4712yes—
773#120—22no—
774#120—22no—
775#120—22no—
776#120—22no—
777#120—942no—
778#120—942no—
779#120—942no—
780#120—942no—
781C4×D4—22no—
782C4×D4—22no—
783C4×D4—22no—
784C4×D4—22no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—942no—
790C4×D4—942no—
791C4×D4—942no—
792C4×D4—942no—
793C4×D4—942no—
794C4×D4—942no—
795C4×D4—942no—
796C4×D4—942no—
797#117—21no—
798#117—21no—
799#117—472no—
800#117—472no—
801#117—941no—
802#117—941no—
803#117C22×D4712yes—
804#117C22×D4712yes—
805C2×C4⋊C4—21no—
806C2×C4⋊C4—21no—
807C2×C4⋊C4—471no—
808C2×C4⋊C4—471no—
809C2×C4⋊C4—941no—
810C2×C4⋊C4—941no—
811C2×C4⋊C4C22×D4711yescharacteristic
812C2×C4⋊C4C22×D4711yescharacteristic
813C2×C22⋊C4—21no—
814C2×C22⋊C4—21no—
815C2×C22⋊C4—21no—
816C2×C22⋊C4—21no—
817C2×C22⋊C4—21no—
818C2×C22⋊C4—941no—
819C2×C22⋊C4—941no—
820C2×C22⋊C4—941no—
821C2×C22⋊C4—941no—
822C2×C22⋊C4—941no—
823C2×C42—21no—
824C2×C42—941no—
825#107—474no—
826#107—474no—
827#106—474no—
828#106—474no—
829#103—474no—
830#103—474no—
831#103—474no—
832#103—474no—
833#102—474no—
834#102—474no—
835#102—474no—
836#102—474no—
837C22⋊C8—472no—
838C22⋊C8—472no—
839C22⋊C8—472no—
840C22⋊C8—472no—
841C22⋊C8—474no—
842C22⋊C8—474no—
843C24—24no—
844C24—21no—
845C24—42no—
846C24—42no—
847C24—941no—
848C24C2×C22⋊D4711yescharacteristic
849C24C2×C22⋊D4711yescharacteristic
850C24C2×C22⋊D4711yescharacteristic
851C24C2×C22⋊D4711yescharacteristic
852C24C2×C22⋊D4711yescharacteristic
853C24C2×C22⋊D4711yescharacteristic
854C24C2×C22⋊D4711yescharacteristic
855#41—28no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—948no—
860#41—1884no—
861#41—1884no—
862#41—1884no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—472no—
866C2×Q8—941no—
867C2×Q8—1882no—
868C2×Q8C23×D4712yes—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—21no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—472no—
881C2×D4—942no—
882C2×D4—942no—
883C2×D4—942no—
884C2×D4—942no—
885C2×D4—942no—
886C2×D4—942no—
887C2×D4—941no—
888C2×D4—1882no—
889C2×D4—1884no—
890C2×D4—1884no—
891C2×D4—1884no—
892C2×D4C23×D4712yes—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—941no—
914C22×C4—941no—
915C22×C4—941no—
916C22×C4—942no—
917C22×C4—942no—
918C22×C4—1884no—
919C22×C4C2×C22⋊D4711yescharacteristic
920C22×C4C2×C22⋊D4711yescharacteristic
921C22×C4C2×C22⋊D4711yescharacteristic
922C22×C4C2×C22⋊D4711yescharacteristic
923C22×C4C2×C22⋊D4711yescharacteristic
924C22×C4C2×C22⋊D4711yescharacteristic
925C22×C4C2×C22⋊D4711yescharacteristic
926C22×C4C2×C22⋊D4711yescharacteristic
927C22×C4C2×C22⋊D4711yescharacteristic
928C22×C4C2×C22⋊D4711yescharacteristic
929C22×C4C2×C22⋊D4711yescharacteristic
930C22×C4C2×C22⋊D4711yescharacteristic
931C22×C4C2×C22⋊D4711yescharacteristic
932C22×C4C2×C22⋊D4711yescharacteristic
933C22×C4C2×C22⋊D4711yescharacteristic
934C22×C4C2×C22⋊D4711yescharacteristic
935C22×C4C2×C22⋊D4711yescharacteristic
936C22×C4C2×C22⋊D4711yescharacteristic
937C22×C4C2×C22⋊D4711yescharacteristic
938C22×C4C2×C22⋊D4711yescharacteristic
939C22×C4C2×C22⋊D4711yescharacteristic
940C22×C4C23×D4711yescharacteristic
941C22×C4C23×D4711yescharacteristic
942C22×C4C23×D4711yescharacteristic
943C22×C4C23×D4711yescharacteristic
944C22×C4C23×D4711yescharacteristic
945C22×C4C23×D4711yescharacteristic
946C22×C4C23×D4711yescharacteristic
947Q16—1884no—
948SD16—1884no—
949SD16—1884no—
950D8—1884no—
951C2×C8—474no—
952C2×C8—474no—
953C2×C8—948no—
954C2×C8—1882no—
955C2×C8—1884no—
956C2×C8—1882no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—472no—
964C4⋊C4—472no—
965C4⋊C4—942no—
966C4⋊C4—942no—
967C4⋊C4—942no—
968C4⋊C4—942no—
969C4⋊C4—941no—
970C4⋊C4—941no—
971C4⋊C4C23×D4712yes—
972C4⋊C4C23×D4712yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—942no—
984C22⋊C4—942no—
985C22⋊C4—942no—
986C22⋊C4—942no—
987C22⋊C4—942no—
988C22⋊C4—942no—
989C22⋊C4—942no—
990C22⋊C4—942no—
991C22⋊C4—942no—
992C22⋊C4—942no—
993C42—22no—
994C42—22no—
995C42—942no—
996C42—942no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—416no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—942no—
1023C23—1882no—
1024C23—1882no—
1025C23—1882no—
1026C23#1309404414yescomplemented
1027C23C22×C22⋊D4711yescharacteristic
1028C23C22×C22⋊D4711yescharacteristic
1029C23C22×C22⋊D4711yescharacteristic
1030C23C22×C22⋊D4711yescharacteristic
1031C23C22×C22⋊D4711yescharacteristic
1032C23C22×C22⋊D4711yescharacteristic
1033C23C22×C22⋊D4711yescharacteristic
1034Q8—24no—
1035Q8—42no—
1036Q8—944no—
1037Q8—1882no—
1038D4—24no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—944no—
1047D4—1882no—
1048D4—1884no—
1049D4—1884no—
1050D4—1884no—
1051D4—1884no—
1052D4—1884no—
1053D4—1884no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—44no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—44no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—1884no—
1093C2×C4—1882no—
1094C2×C4—1882no—
1095C2×C4—1882no—
1096C2×C4—1884no—
1097C2×C4C22×C22⋊D4711yescharacteristic
1098C2×C4C22×C22⋊D4711yescharacteristic
1099C2×C4C22×C22⋊D4711yescharacteristic
1100C2×C4C22×C22⋊D4711yescharacteristic
1101C2×C4C22×C22⋊D4711yescharacteristic
1102C2×C4C22×C22⋊D4711yescharacteristic
1103C2×C4C22×C22⋊D4711yescharacteristic
1104C2×C4#1309406914yes—
1105C2×C4C24×D4711yescharacteristic
1106C8—944no—
1107C8—944no—
1108C22—28no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—84no—
1135C22—3764no—
1136C22—1882no—
1137C22—1882no—
1138C22—1882no—
1139C22#1568968212yes—
1140C22C2×#1309404412yes—
1141C22C2×#1309404412yes—
1142C22C2×#1309404412yes—
1143C22#1568992112yes—
1144C22C23×C22⋊D4711yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—1882no—
1155C4—1882no—
1156C4—1882no—
1157C4#1568968212yes—
1158C4C2×#1309406912yes—
1159C2—22no—
1160C2—22no—
1161C2—22no—
1162C2—22no—
1163C2—22no—
1164C2—41no—
1165C2—41no—
1166C2—82no—
1167C2—3762no—
1168C2C2×#1568968211yescharacteristic
1169C2C22×#1309404411yescharacteristic
1170C2C2×#1568992111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#525C2
socleC22×C47C23×D4
hypercenterC2×#525D47
hypocenterC47#60734
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#15689634C2semidirect
2. #20254176C2semidirect
3. #20254169C2semidirect
4. #20254165C2semidirect
5. #20254160C2semidirect
6. #20254153C2semidirect
7. #20254149C2semidirect
8. #20254145C2semidirect
9. #20254141C2semidirect
10. #20254136C2semidirect
11. #20253301C2semidirect
12. #20253297C2semidirect
13. #20252966C2semidirect
14. #20252606C2semidirect
15. #20252604C2semidirect
16. C22×C22⋊(C47⋊C8)C2semidirect
17. C2×C47×#525C2semidirect
18. C22×#10625350C22semidirect
19. C2×#13094044C22semidirect
20. C23×C47⋊C8C22semidirect
27. #15689634C22semidirect
28. #15689634C22semidirect
31. C2×#13094003C22semidirect
33. C2×#13093998C22semidirect
37. C2×#13093983C22semidirect
38. #15689464C22semidirect
39. #15689461C22semidirect
40. #15689458C22semidirect
41. #15689456C22semidirect
42. #15689453C22semidirect
43. #15689451C22semidirect
44. #15689447C22semidirect
45. #15689444C22semidirect
46. #15689441C22semidirect
47. #15689439C22semidirect
48. #15689436C22semidirect
49. #15689434C22semidirect
50. #15689362C22semidirect
51. #15689362C22semidirect
52. #15689357C22semidirect
53. #15689357C22semidirect
54. #15689354C22semidirect
55. #15689354C22semidirect
56. #15689350C22semidirect
57. #15689350C22semidirect
58. #15689285C22semidirect
59. #15689283C22semidirect
60. #15689279C22semidirect
61. #15689278C22semidirect
62. #15689274C22semidirect
63. #15689273C22semidirect
64. #15689268C22semidirect
65. #15689266C22semidirect
66. #15689262C22semidirect
67. #15689261C22semidirect
68. #15689257C22semidirect
69. #15689256C22semidirect
70. #15689159C22semidirect
71. #15689119C22semidirect
72. #15689117C22semidirect
75. C2×C22⋊(C47⋊C8)C22semidirect
76. C2×C22⋊(C47⋊C8)C22semidirect
77. C2×C22⋊(C47⋊C8)C22semidirect
78. C2×C22⋊(C47⋊C8)C22semidirect
79. C2×C22⋊(C47⋊C8)C22semidirect
80. C22×#41×C47C22semidirect
88. C47×#525C22semidirect
89. C47×#525C22semidirect
92. C2×C22⋊Q8×C47C22semidirect
94. C2×#121×C47C22semidirect
98. C2×#117×C47C22semidirect
111. C2×#10625337C23semidirect
112. C2×#10625335C23semidirect
113. C2×#10625336C23semidirect
114. C2×#10625334C23semidirect
166. #13093957C23semidirect
167. #13093957C23semidirect
168. #13093955C23semidirect
169. #13093955C23semidirect
170. #13093948C23semidirect
171. #13093948C23semidirect
172. #13093947C23semidirect
173. #13093947C23semidirect
174. #13093945C23semidirect
175. #13093945C23semidirect
176. #13093944C23semidirect
177. #13093944C23semidirect
436. C23×C47#135semidirect
575. C2×#525D47semidirect
604. C22×#41C2×D47semidirect
622. #525C2×D47semidirect
623. #525C2×D47semidirect
629. C2×C22⋊Q8C2×D47semidirect
633. C2×#121C2×D47semidirect
641. C2×#117C2×D47semidirect
684. C47#60734semidirect
1026. C23#13094044semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202541762
#202541692
#202541652
#202541602
#202541532
#202541492
#202541452
#202541412
#202541362
#202533012
#202532972
#202529662
#202526062
#202526042
C22×C22⋊(C47⋊C8)2
C2×C47×#5252
#6073447