Finite Group Databasebeta

← #27087043

Subgroups — #27087043

Order 12032.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic, complemented
2#20254225C214yesmaximal, complemented
3#20254218C212yesmaximal, complemented
4#20254202C212yesmaximal, complemented
5#20254176C214yesmaximal, complemented
6#20254169C212yesmaximal, complemented
7#20254153C212yesmaximal, complemented
8#20253336C211yesmaximal, characteristic, complemented
9#20253328C211yesmaximal, characteristic, complemented
10#20253317C212yesmaximal, complemented
11#20253020C212yesmaximal, complemented
12#20253009C212yesmaximal, complemented
13#20252648C211yesmaximal, characteristic, complemented
14#20252640C211yesmaximal, characteristic, complemented
15#20252628C212yesmaximal, complemented
16C2×#15689087C211yesmaximal, characteristic, complemented
17C2×C47×#525C211yesmaximal, characteristic, complemented
18C22×#10625350C2211yescharacteristic, complemented
19C2×#13094054C2212yescomplemented
20C2×#13094049C2212yescomplemented
21C22×#10625329C2212yescomplemented
22#15689634—21no—
23#15689634—21no—
24#15689634—21no—
25#15689634—21no—
26#15689634C2212yes—
27#15689634C2212yes—
28#15689634C2212yescomplemented
29#15689634C2212yescomplemented
30C2×#13094007—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094003C2211yescharacteristic, complemented
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic, complemented
35C2×#13093993—21no—
36C2×C4×C22⋊D47—21no—
37C2×C4×C22⋊D47—21no—
38C2×#13093983C2211yescharacteristic, complemented
39#15689464C2214yescomplemented
40#15689461C2214yescomplemented
41#15689461C2214yescomplemented
42#15689458C2212yescomplemented
43#15689453C2212yescomplemented
44#15689447C2214yescomplemented
45#15689444C2214yescomplemented
46#15689444C2214yescomplemented
47#15689441C2212yescomplemented
48#15689436C2212yescomplemented
49#15689379C2214yescomplemented
50#15689374C2214yescomplemented
51#15689371C2214yescomplemented
52#15689367C2214yescomplemented
53#15689362C2214yescomplemented
54#15689357C2214yescomplemented
55#15689354C2214yescomplemented
56#15689350C2214yescomplemented
57#15689285C2214yescomplemented
58#15689283C2214yescomplemented
59#15689283C2214yescomplemented
60#15689279C2212yescomplemented
61#15689274C2212yescomplemented
62#15689268C2214yescomplemented
63#15689266C2214yescomplemented
64#15689266C2214yescomplemented
65#15689262C2212yescomplemented
66#15689257C2212yescomplemented
67#15689166C2212yescomplemented
68#15689166C2212yescomplemented
69#15689131C2212yescomplemented
70#15689127C2212yescomplemented
71#15689124C2212yescomplemented
72#15689124C2212yescomplemented
73#15689087C2211yescharacteristic
74#15689087C2211yescharacteristic
75#15689087C2212yescomplemented
76#15689087C2212yescomplemented
77#15689087C2212yescomplemented
78C2×C22⋊(C47⋊C8)C2212yescomplemented
79C2×C22⋊(C47⋊C8)C2212yescomplemented
80C22×#41×C47C2211yescharacteristic
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, complemented
92C2×C22⋊Q8×C47C2211yescharacteristic, complemented
93C2×#121×C47C2211yescharacteristic, complemented
94C2×#121×C47C2211yescharacteristic, complemented
95C2×#120×C47—21no—
96C2×C4×D4×C47—21no—
97C2×C4×D4×C47—21no—
98C2×#117×C47C2211yescharacteristic
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#13094054—44no—
111#13094049—44no—
112C2×#10625337C2314yescomplemented
113C2×#10625335C2314yescomplemented
114C2×#10625336C2314yescomplemented
115C2×#10625334C2314yescomplemented
116C2×#10625329—44no—
117C2×#10625329C2312yes—
118C2×#10625329C2312yes—
119C2×#10625329C2314yes—
120C22×C47⋊C8C2314yes—
121#13094007—22no—
122#13094007—22no—
123#13094007—22no—
124#13094007—22no—
125#13094003—21no—
126#13094003—21no—
127#13094003—21no—
128#13094003—21no—
129#13094003C2312yes—
130#13094003C2312yes—
131#13094003C2312yes—
132#13094003C2312yes—
133#13093998—21no—
134#13093998—21no—
135#13093998—21no—
136#13093998—21no—
137#13093998C2312yes—
138#13093998C2312yes—
139#13093998C2312yes—
140#13093998C2312yes—
141#13093993—22no—
142#13093993—22no—
143#13093993—22no—
144#13093993—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—
152C4×C22⋊D47—22no—
153#13093983—21no—
154#13093983—21no—
155#13093983C2312yes—
156#13093983C2312yes—
157C2×C4⋊Dic47C2311yescharacteristic
158C2×C4⋊Dic47C2311yescharacteristic
159C2×Dic47⋊C4—21no—
160C2×Dic47⋊C4—21no—
161C2×C22⋊Dic47—21no—
162C2×C22⋊Dic47—21no—
163C2×C22⋊Dic47—21no—
164C2×(C2×D47)⋊C4—21no—
165C2×(C2×D47)⋊C4—21no—
166C2×C4×Dic47—21no—
167#13093957C2314yescomplemented
168#13093957C2314yescomplemented
169#13093955C2314yescomplemented
170#13093955C2314yescomplemented
171#13093948C2314yescomplemented
172#13093948C2314yescomplemented
173#13093947C2314yescomplemented
174#13093947C2314yescomplemented
175#13093945C2314yescomplemented
176#13093945C2314yescomplemented
177#13093944C2314yescomplemented
178#13093944C2314yescomplemented
179C22⋊(C47⋊C8)C2312yes—
180C22⋊(C47⋊C8)C2314yes—
181C22⋊(C47⋊C8)C2314yes—
182C22⋊(C47⋊C8)C2312yes—
183C22⋊(C47⋊C8)C2312yes—
184C22⋊(C47⋊C8)C2312yes—
185C25×C47D411yescharacteristic
186C2×#41×C47—21no—
187C2×#41×C47—21no—
188C2×#41×C47—44no—
189C2×#41×C47C2312yes—
190C2×#41×C47C2312yes—
191C22×Q8×C47C2311yescharacteristic
192C22×D4×C47—21no—
193C22×D4×C47—21no—
194C22×D4×C47—21no—
195C22×D4×C47C2311yescharacteristic
196C23×C4×C47—21no—
197C23×C4×C47—44no—
198C23×C4×C47D411yescharacteristic
199C23×C4×C47D411yescharacteristic
200C23×C4×C47D411yescharacteristic
201C23×C4×C47D411yescharacteristic
202C23×C4×C47D411yescharacteristic
203C23×C4×C47D411yescharacteristic
204C23×C4×C47D411yescharacteristic
205C23×C4×C47C2311yescharacteristic
206C23×C4×C47C2311yescharacteristic
207C23×C4×C47C2311yescharacteristic
208C23×C4×C47C2311yescharacteristic
209C23×C4×C47C2311yescharacteristic
210C23×C4×C47C2311yescharacteristic
211C23×C4×C47C2311yescharacteristic
212#123×C47—22no—
213#123×C47—22no—
214#123×C47—22no—
215#123×C47—22no—
216C22⋊Q8×C47—21no—
217C22⋊Q8×C47—21no—
218C22⋊Q8×C47—21no—
219C22⋊Q8×C47—21no—
220C22⋊Q8×C47C2312yes—
221C22⋊Q8×C47C2312yes—
222C22⋊Q8×C47C2312yes—
223C22⋊Q8×C47C2312yes—
224#121×C47—21no—
225#121×C47—21no—
226#121×C47—21no—
227#121×C47—21no—
228#121×C47C2312yes—
229#121×C47C2312yes—
230#121×C47C2312yes—
231#121×C47C2312yes—
232#120×C47—22no—
233#120×C47—22no—
234#120×C47—22no—
235#120×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—
243C4×D4×C47—22no—
244#117×C47—21no—
245#117×C47—21no—
246#117×C47C2312yes—
247#117×C47C2312yes—
248C2×C4⋊C4×C47—21no—
249C2×C4⋊C4×C47—21no—
250C2×C4⋊C4×C47C2311yescharacteristic
251C2×C4⋊C4×C47C2311yescharacteristic
252C2×C22⋊C4×C47—21no—
253C2×C22⋊C4×C47—21no—
254C2×C22⋊C4×C47—21no—
255C2×C22⋊C4×C47—21no—
256C2×C22⋊C4×C47—21no—
257C2×C42×C47—21no—
258C24×C47—21no—
259C24×C47—42no—
260C24×C47—42no—
261C24×C47—42no—
262C24×C47C2×D411yescharacteristic
263C24×C47C2×D411yescharacteristic
264C24×C47C2×D411yescharacteristic
265C24×C47C2×D411yescharacteristic
266C24×C47C2×D411yescharacteristic
267C24×C47C2×D411yescharacteristic
268C24×C47C2×D411yescharacteristic
269C23×D47—21no—
270#41×C47—24no—
271#41×C47—24no—
272#41×C47—42no—
273#41×C47—42no—
274#41×C47—44no—
275#41×C47—44no—
276C2×Q8×C47—21no—
277C2×Q8×C47—42no—
278C2×Q8×C47C2412yes—
279C2×D4×C47—22no—
280C2×D4×C47—22no—
281C2×D4×C47—22no—
282C2×D4×C47—22no—
283C2×D4×C47—22no—
284C2×D4×C47—22no—
285C2×D4×C47—21no—
286C2×D4×C47—42no—
287C2×D4×C47—44no—
288C2×D4×C47—44no—
289C2×D4×C47—44no—
290C2×D4×C47C2412yes—
291C22×C4×C47—24no—
292C22×C4×C47—24no—
293C22×C4×C47—24no—
294C22×C4×C47—21no—
295C22×C4×C47—21no—
296C22×C4×C47—21no—
297C22×C4×C47—22no—
298C22×C4×C47—22no—
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—42no—
308C22×C4×C47—42no—
309C22×C4×C47—42no—
310C22×C4×C47—44no—
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×C47C2×D411yescharacteristic
330C22×C4×C47C2×D411yescharacteristic
331C22×C4×C47C2×D411yescharacteristic
332C22×C4×C47C2411yescharacteristic
333C22×C4×C47C2411yescharacteristic
334C22×C4×C47C2411yescharacteristic
335C22×C4×C47C2411yescharacteristic
336C22×C4×C47C2411yescharacteristic
337C22×C4×C47C2411yescharacteristic
338C22×C4×C47C2411yescharacteristic
339C2×C22⋊D47—22no—
340C2×C22⋊D47—22no—
341C2×C22⋊D47—22no—
342C2×C22⋊D47—22no—
343C2×C22⋊D47—22no—
344C2×C22⋊D47—22no—
345C2×C22⋊D47—44no—
346C2×C22⋊D47—44no—
347C2×C22⋊D47—44no—
348C22×Dic47—21no—
349C22×Dic47—21no—
350C22×Dic47—21no—
351#10625350—44no—
352#10625350—44no—
353#10625350—44no—
354#10625350—44no—
355C2×D188—24no—
356C2×D188—21no—
357C2×D188C2412yes—
358C2×C4×D47—22no—
359C2×C4×D47—22no—
360C2×C4×D47—44no—
361C2×Dic94—24no—
362C2×Dic94—21no—
363C2×Dic94C2412yes—
364C4⋊C4×C47—22no—
365C4⋊C4×C47—22no—
366C4⋊C4×C47—22no—
367C4⋊C4×C47—22no—
368C4⋊C4×C47—21no—
369C4⋊C4×C47—21no—
370C4⋊C4×C47C2412yes—
371C4⋊C4×C47C2412yes—
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—
379C22⋊C4×C47—22no—
380C22⋊C4×C47—22no—
381C22⋊C4×C47—22no—
382C42×C47—22no—
383C42×C47—22no—
384C22⋊Dic47—22no—
385C22⋊Dic47—22no—
386C22⋊Dic47—22no—
387C22⋊Dic47—22no—
388C22⋊Dic47—22no—
389C22⋊Dic47—22no—
390#10625337—44no—
391#10625336—44no—
392#10625335—44no—
393#10625334—44no—
394(C2×D47)⋊C4—22no—
395(C2×D47)⋊C4—22no—
396(C2×D47)⋊C4—22no—
397(C2×D47)⋊C4—22no—
398C4⋊Dic47—21no—
399C4⋊Dic47—21no—
400C4⋊Dic47C2412yes—
401C4⋊Dic47C2412yes—
402Dic47⋊C4—22no—
403Dic47⋊C4—22no—
404Dic47⋊C4—22no—
405Dic47⋊C4—22no—
406C4×Dic47—22no—
407C4×Dic47—22no—
408#10625329—24no—
409#10625329—24no—
410#10625329—44no—
411C2×C47⋊C8—44no—
412C2×C47⋊C8C2414yes—
413C2×C47⋊C8C2414yes—
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—41no—
433C23×C47—41no—
434C23×C47—41no—
435C23×C47—41no—
436C23×C47—42no—
437C23×C47—42no—
438C23×C47—416no—
439C23×C47—42no—
440C23×C47C22×D411yescharacteristic
441C23×C47C22×D411yescharacteristic
442C23×C47C22×D411yescharacteristic
443C23×C47C22×D411yescharacteristic
444C23×C47C22×D411yescharacteristic
445C23×C47C22×D411yescharacteristic
446C23×C47C22×D411yescharacteristic
447C22×D47—22no—
448C22×D47—42no—
449C22×D47—42no—
450C22×D47—42no—
451Q8×C47—22no—
452Q8×C47—22no—
453Q8×C47—42no—
454D4×C47—22no—
455D4×C47—22no—
456D4×C47—42no—
457D4×C47—44no—
458D4×C47—44no—
459D4×C47—44no—
460D4×C47—44no—
461D4×C47—44no—
462D4×C47—44no—
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—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
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—41no—
489C2×C4×C47—41no—
490C2×C4×C47—41no—
491C2×C4×C47—41no—
492C2×C4×C47—41no—
493C2×C4×C47—44no—
494C2×C4×C47—42no—
495C2×C4×C47—42no—
496C2×C4×C47—42no—
497C2×C4×C47—44no—
498C2×C4×C47C22×D411yescharacteristic
499C2×C4×C47C22×D411yescharacteristic
500C2×C4×C47C22×D411yescharacteristic
501C2×C4×C47C22×D411yescharacteristic
502C2×C4×C47C22×D411yescharacteristic
503C2×C4×C47C22×D411yescharacteristic
504C2×C4×C47C22×D411yescharacteristic
505C2×C4×C47H(5,𝔽2)14yes—
506C2×C4×C47C2511yescharacteristic
507C22⋊D47—44no—
508C22⋊D47—44no—
509C22⋊D47—44no—
510C22⋊D47—44no—
511C22⋊D47—44no—
512C22⋊D47—44no—
513C2×Dic47—22no—
514C2×Dic47—22no—
515C2×Dic47—22no—
516C2×Dic47—42no—
517C2×Dic47—42no—
518C2×Dic47—42no—
519D188—24no—
520D188—42no—
521C4×D47—44no—
522C4×D47—44no—
523Dic94—24no—
524Dic94—42no—
525C47⋊C8—24no—
526C47⋊C8—24no—
527#60752—471nomaximal, Sylow
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—21no—
541C22×C47—21no—
542C22×C47—21no—
543C22×C47—21no—
544C22×C47—21no—
545C22×C47—21no—
546C22×C47—44no—
547C22×C47—44no—
548C22×C47—44no—
549C22×C47—44no—
550C22×C47—44no—
551C22×C47—44no—
552C22×C47—44no—
553C22×C47—42no—
554C22×C47—42no—
555C22×C47—42no—
556C22×C47—84no—
557C22×C47#53412yes—
558C22×C47#57512yes—
559C22×C47#57512yes—
560C22×C47C23×D411yescharacteristic
561C2×D47—42no—
562C2×D47—42no—
563C2×D47—42no—
564C2×D47—84no—
565C4×C47—21no—
566C4×C47—21no—
567C4×C47—21no—
568C4×C47—21no—
569C4×C47—21no—
570C4×C47—21no—
571C4×C47—42no—
572C4×C47—42no—
573C4×C47—42no—
574C4×C47#53412yes—
575C4×C47C2×H(5,𝔽2)12yes—
576Dic47—42no—
577Dic47—42no—
578Dic47—42no—
579C2×#525—471no—
580C2×#525D4711yescharacteristic, complemented
581#3197—474no—
582#3196—472no—
583#3194—472no—
584#3191—474no—
585#3190—472no—
586#3188—472no—
587#3095—471no—
588#3094—471no—
589#3093—472no—
590#3056—472no—
591#3055—472no—
592#3007—471no—
593#3006—471no—
594#3005—472no—
595C2×#407—471no—
596C2×C47—22no—
597C2×C47—22no—
598C2×C47—22no—
599C2×C47—41no—
600C2×C47—41no—
601C2×C47—41no—
602C2×C47—41no—
603C2×C47—82no—
604C2×C47C2×#53411yescharacteristic
605C2×C47C2×#57511yescharacteristic
606C2×C47C2×#57511yescharacteristic
607D47—82no—
608C22×#41—471no—
609C22×#41C2×D4711yescharacteristic
610C24×C4C2×D4711yescharacteristic
611C2×#137—472no—
612C2×AGL(1,ℤ/8)—472no—
613C22×M16—472no—
614#525—21no—
615#525—21no—
616#525—21no—
617#525—21no—
618#525—472no—
619#525—472no—
620#525—472no—
621#525—472no—
622#525—941no—
623#525—941no—
624#525—941no—
625#525—941no—
626#525C2×D4712yes—
627#525C2×D4712yes—
628#525C2×D4712yescomplemented
629#525C2×D4712yescomplemented
630C2×#123—21no—
631C2×#123—941no—
632C2×C22⋊Q8—471no—
633C2×C22⋊Q8—471no—
634C2×C22⋊Q8C2×D4711yescharacteristic, complemented
635C2×C22⋊Q8C2×D4711yescharacteristic, complemented
636C2×#121—471no—
637C2×#121—471no—
638C2×#121C2×D4711yescharacteristic, complemented
639C2×#121C2×D4711yescharacteristic, complemented
640C2×#120—21no—
641C2×#120—941no—
642C2×C4×D4—21no—
643C2×C4×D4—21no—
644C2×C4×D4—941no—
645C2×C4×D4—941no—
646C2×#117—471no—
647C2×#117C2×D4711yescharacteristic
648#485—474no—
649#485—474no—
650#485—474no—
651#484—472no—
652#483—472no—
653#482—474no—
654#482—474no—
655#482—474no—
656#481—472no—
657#480—472no—
658#470—474no—
659#469—474no—
660#468—474no—
661#468—474no—
662#467—474no—
663#466—474no—
664#465—474no—
665#465—474no—
666#452—474no—
667#452—474no—
668#452—474no—
669#451—472no—
670#450—472no—
671#449—474no—
672#449—474no—
673#449—474no—
674#448—472no—
675#447—472no—
676#428—472no—
677#428—472no—
678#419—472no—
679#418—472no—
680#417—472no—
681#417—472no—
682#407—472no—
683#407—471no—
684#407—471no—
685#407—472no—
686#407—472no—
687C2×C22⋊C8—472no—
688C2×C22⋊C8—472no—
689C47#6075211yescharacteristic, complemented, Sylow
690C25C22⋊D4711yescharacteristic
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—44no—
694C2×#41—472no—
695C2×#41—472no—
696C2×#41—941no—
697C2×#41—941no—
698C2×#41—1884no—
699C2×#41C22×D4712yes—
700C2×#41C22×D4712yes—
701C22×Q8—471no—
702C22×Q8C22×D4711yescharacteristic
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—21no—
706C22×D4—471no—
707C22×D4—941no—
708C22×D4—941no—
709C22×D4—941no—
710C22×D4C22×D4711yescharacteristic
711C23×C4—21no—
712C23×C4—44no—
713C23×C4—941no—
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
723C23×C4C22×D4711yescharacteristic
724C23×C4C22×D4711yescharacteristic
725C23×C4C22×D4711yescharacteristic
726C23×C4C22×D4711yescharacteristic
727C23×C4C22×D4711yescharacteristic
728#137—1884no—
729AGL(1,ℤ/8)—1884no—
730C2×Q16—474no—
731C2×SD16—474no—
732C2×SD16—474no—
733C2×D8—474no—
734C2×M16—472no—
735C2×M16—472no—
736C2×M16—474no—
737C2×M16—1884no—
738C22×C8—474no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743#123—942no—
744#123—942no—
745#123—942no—
746#123—942no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—472no—
752C22⋊Q8—472no—
753C22⋊Q8—472no—
754C22⋊Q8—472no—
755C22⋊Q8—941no—
756C22⋊Q8—941no—
757C22⋊Q8—941no—
758C22⋊Q8—941no—
759C22⋊Q8C22×D4712yes—
760C22⋊Q8C22×D4712yes—
761C22⋊Q8C22×D4712yes—
762C22⋊Q8C22×D4712yes—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—472no—
768#121—472no—
769#121—472no—
770#121—472no—
771#121—941no—
772#121—941no—
773#121—941no—
774#121—941no—
775#121C22×D4712yes—
776#121C22×D4712yes—
777#121C22×D4712yes—
778#121C22×D4712yes—
779#120—22no—
780#120—22no—
781#120—22no—
782#120—22no—
783#120—942no—
784#120—942no—
785#120—942no—
786#120—942no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4—942no—
796C4×D4—942no—
797C4×D4—942no—
798C4×D4—942no—
799C4×D4—942no—
800C4×D4—942no—
801C4×D4—942no—
802C4×D4—942no—
803#117—21no—
804#117—21no—
805#117—472no—
806#117—472no—
807#117—941no—
808#117—941no—
809#117C22×D4712yes—
810#117C22×D4712yes—
811C2×C4⋊C4—21no—
812C2×C4⋊C4—21no—
813C2×C4⋊C4—471no—
814C2×C4⋊C4—471no—
815C2×C4⋊C4—941no—
816C2×C4⋊C4—941no—
817C2×C4⋊C4C22×D4711yescharacteristic
818C2×C4⋊C4C22×D4711yescharacteristic
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—21no—
824C2×C22⋊C4—941no—
825C2×C22⋊C4—941no—
826C2×C22⋊C4—941no—
827C2×C22⋊C4—941no—
828C2×C22⋊C4—941no—
829C2×C42—21no—
830C2×C42—941no—
831#107—474no—
832#107—474no—
833#106—474no—
834#106—474no—
835#103—474no—
836#103—474no—
837#103—474no—
838#103—474no—
839#102—474no—
840#102—474no—
841#102—474no—
842#102—474no—
843C22⋊C8—472no—
844C22⋊C8—472no—
845C22⋊C8—474no—
846C22⋊C8—474no—
847C22⋊C8—472no—
848C22⋊C8—472no—
849C24—21no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—941no—
854C24C2×C22⋊D4711yescharacteristic
855C24C2×C22⋊D4711yescharacteristic
856C24C2×C22⋊D4711yescharacteristic
857C24C2×C22⋊D4711yescharacteristic
858C24C2×C22⋊D4711yescharacteristic
859C24C2×C22⋊D4711yescharacteristic
860C24C2×C22⋊D4711yescharacteristic
861#41—24no—
862#41—24no—
863#41—42no—
864#41—42no—
865#41—44no—
866#41—44no—
867#41—1884no—
868#41—1884no—
869#41—1884no—
870#41—1884no—
871C2×Q8—21no—
872C2×Q8—42no—
873C2×Q8—472no—
874C2×Q8—941no—
875C2×Q8—944no—
876C2×Q8C23×D4712yes—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—21no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—472no—
889C2×D4—942no—
890C2×D4—942no—
891C2×D4—942no—
892C2×D4—942no—
893C2×D4—942no—
894C2×D4—942no—
895C2×D4—941no—
896C2×D4—944no—
897C2×D4—1884no—
898C2×D4—1884no—
899C2×D4—1884no—
900C2×D4C23×D4712yes—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—941no—
922C22×C4—941no—
923C22×C4—941no—
924C22×C4—942no—
925C22×C4—942no—
926C22×C4—1884no—
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×C4C2×C22⋊D4711yescharacteristic
941C22×C4C2×C22⋊D4711yescharacteristic
942C22×C4C2×C22⋊D4711yescharacteristic
943C22×C4C2×C22⋊D4711yescharacteristic
944C22×C4C2×C22⋊D4711yescharacteristic
945C22×C4C2×C22⋊D4711yescharacteristic
946C22×C4C2×C22⋊D4711yescharacteristic
947C22×C4C2×C22⋊D4711yescharacteristic
948C22×C4C23×D4711yescharacteristic
949C22×C4C23×D4711yescharacteristic
950C22×C4C23×D4711yescharacteristic
951C22×C4C23×D4711yescharacteristic
952C22×C4C23×D4711yescharacteristic
953C22×C4C23×D4711yescharacteristic
954C22×C4C23×D4711yescharacteristic
955Q16—1884no—
956SD16—1884no—
957SD16—1884no—
958D8—1884no—
959M16—944no—
960M16—944no—
961M16—1884no—
962C2×C8—474no—
963C2×C8—474no—
964C2×C8—1884no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—472no—
972C4⋊C4—472no—
973C4⋊C4—942no—
974C4⋊C4—942no—
975C4⋊C4—942no—
976C4⋊C4—942no—
977C4⋊C4—941no—
978C4⋊C4—941no—
979C4⋊C4C23×D4712yes—
980C4⋊C4C23×D4712yes—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—942no—
992C22⋊C4—942no—
993C22⋊C4—942no—
994C22⋊C4—942no—
995C22⋊C4—942no—
996C22⋊C4—942no—
997C22⋊C4—942no—
998C22⋊C4—942no—
999C22⋊C4—942no—
1000C22⋊C4—942no—
1001C42—22no—
1002C42—22no—
1003C42—942no—
1004C42—942no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—416no—
1030C23—42no—
1031C23—942no—
1032C23—1882no—
1033C23—1882no—
1034C23—1882no—
1035C23C22×C22⋊D4711yescharacteristic
1036C23C22×C22⋊D4711yescharacteristic
1037C23C22×C22⋊D4711yescharacteristic
1038C23C22×C22⋊D4711yescharacteristic
1039C23C22×C22⋊D4711yescharacteristic
1040C23C22×C22⋊D4711yescharacteristic
1041C23C22×C22⋊D4711yescharacteristic
1042Q8—22no—
1043Q8—22no—
1044Q8—42no—
1045Q8—944no—
1046Q8—1882no—
1047D4—22no—
1048D4—22no—
1049D4—42no—
1050D4—44no—
1051D4—44no—
1052D4—44no—
1053D4—44no—
1054D4—44no—
1055D4—44no—
1056D4—944no—
1057D4—1884no—
1058D4—1884no—
1059D4—1884no—
1060D4—1884no—
1061D4—1884no—
1062D4—1884no—
1063D4—1882no—
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—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—44no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—44no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—1884no—
1103C2×C4—1884no—
1104C2×C4—1882no—
1105C2×C4—1882no—
1106C2×C4—1882no—
1107C2×C4C22×C22⋊D4711yescharacteristic
1108C2×C4C22×C22⋊D4711yescharacteristic
1109C2×C4C22×C22⋊D4711yescharacteristic
1110C2×C4C22×C22⋊D4711yescharacteristic
1111C2×C4C22×C22⋊D4711yescharacteristic
1112C2×C4C22×C22⋊D4711yescharacteristic
1113C2×C4C22×C22⋊D4711yescharacteristic
1114C2×C4#1309406914yes—
1115C2×C4C24×D4711yescharacteristic
1116C8—944no—
1117C8—944no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—84no—
1147C22—3764no—
1148C22—1882no—
1149C22—1882no—
1150C22—1882no—
1151C22#1568968212yes—
1152C22#1568992112yes—
1153C22#1568992112yes—
1154C22C23×C22⋊D4711yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—1882no—
1165C4—1882no—
1166C4—1882no—
1167C4#1568968212yes—
1168C4C2×#1309406912yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—82no—
1177C2—3762no—
1178C2C2×#1568968211yescharacteristic
1179C2C2×#1568992111yescharacteristic
1180C2C2×#1568992111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#525C2
socleC22×C47C23×D4
hypercenterC2×#525D47
hypocenterC47#60752
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#15689634C2semidirect
2. #20254225C2semidirect
3. #20254218C2semidirect
4. #20254202C2semidirect
5. #20254176C2semidirect
6. #20254169C2semidirect
7. #20254153C2semidirect
8. #20253336C2semidirect
9. #20253328C2semidirect
10. #20253317C2semidirect
11. #20253020C2semidirect
12. #20253009C2semidirect
13. #20252648C2semidirect
14. #20252640C2semidirect
15. #20252628C2semidirect
16. C2×#15689087C2semidirect
17. C2×C47×#525C2semidirect
18. C22×#10625350C22semidirect
19. C2×#13094054C22semidirect
20. C2×#13094049C22semidirect
21. C22×#10625329C22semidirect
28. #15689634C22semidirect
29. #15689634C22semidirect
32. C2×#13094003C22semidirect
34. C2×#13093998C22semidirect
38. C2×#13093983C22semidirect
39. #15689464C22semidirect
40. #15689461C22semidirect
41. #15689461C22semidirect
42. #15689458C22semidirect
43. #15689453C22semidirect
44. #15689447C22semidirect
45. #15689444C22semidirect
46. #15689444C22semidirect
47. #15689441C22semidirect
48. #15689436C22semidirect
49. #15689379C22semidirect
50. #15689374C22semidirect
51. #15689371C22semidirect
52. #15689367C22semidirect
53. #15689362C22semidirect
54. #15689357C22semidirect
55. #15689354C22semidirect
56. #15689350C22semidirect
57. #15689285C22semidirect
58. #15689283C22semidirect
59. #15689283C22semidirect
60. #15689279C22semidirect
61. #15689274C22semidirect
62. #15689268C22semidirect
63. #15689266C22semidirect
64. #15689266C22semidirect
65. #15689262C22semidirect
66. #15689257C22semidirect
67. #15689166C22semidirect
68. #15689166C22semidirect
69. #15689131C22semidirect
70. #15689127C22semidirect
71. #15689124C22semidirect
72. #15689124C22semidirect
75. #15689087C22semidirect
76. #15689087C22semidirect
77. #15689087C22semidirect
78. C2×C22⋊(C47⋊C8)C22semidirect
79. C2×C22⋊(C47⋊C8)C22semidirect
88. C47×#525C22semidirect
89. C47×#525C22semidirect
91. C2×C22⋊Q8×C47C22semidirect
92. C2×C22⋊Q8×C47C22semidirect
93. C2×#121×C47C22semidirect
94. C2×#121×C47C22semidirect
112. C2×#10625337C23semidirect
113. C2×#10625335C23semidirect
114. C2×#10625336C23semidirect
115. C2×#10625334C23semidirect
167. #13093957C23semidirect
168. #13093957C23semidirect
169. #13093955C23semidirect
170. #13093955C23semidirect
171. #13093948C23semidirect
172. #13093948C23semidirect
173. #13093947C23semidirect
174. #13093947C23semidirect
175. #13093945C23semidirect
176. #13093945C23semidirect
177. #13093944C23semidirect
178. #13093944C23semidirect
580. C2×#525D47semidirect
628. #525C2×D47semidirect
629. #525C2×D47semidirect
634. C2×C22⋊Q8C2×D47semidirect
635. C2×C22⋊Q8C2×D47semidirect
638. C2×#121C2×D47semidirect
639. C2×#121C2×D47semidirect
689. C47#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202542252
#202542182
#202542022
#202541762
#202541692
#202541532
#202533362
#202533282
#202533172
#202530202
#202530092
#202526482
#202526402
#202526282
C2×#156890872
C2×C47×#5252
#6075247