Finite Group Databasebeta

← C2×#20254252 #27086944

Subgroups — C2×#20254252 #27086944

Order 12032.

2506 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689692C211yesmaximal, characteristic, complemented
2C2×#15689689C211yesmaximal, characteristic, complemented
3#20254252C2116yesmaximal, direct product factor
4C2×#15689450C211yesmaximal, characteristic, complemented
5C2×#15689449C211yesmaximal, characteristic, complemented
6C2×#15689447C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689360C211yesmaximal, characteristic, complemented
10C2×#15689358C211yesmaximal, characteristic, complemented
11C2×#15689259C211yesmaximal, characteristic, complemented
12C2×#15689258C211yesmaximal, characteristic, complemented
13C2×#15689258C211yesmaximal, characteristic, complemented
14C2×#15689256C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×D188C2211yescharacteristic, complemented
19C22×D4×D47C2211yescharacteristic, complemented
20C22×D376C2211yescharacteristic
21C22×D376C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C22×#10625334C2211yescharacteristic
24C22×#10625324C2211yescharacteristic, complemented
25C22×C8×D47C2211yescharacteristic, complemented
26#15689692—24no—
27#15689692C2218yescomplemented
28#15689689—24no—
29#15689689C2218yescomplemented
30C2×#13094021—21no—
31C2×#13094020—21no—
32C2×#13094012—21no—
33C2×#13094010—21no—
34C2×#13093999C2211yescharacteristic
35C2×#13093999C2211yescharacteristic
36C2×#13093999C2211yescharacteristic, complemented
37C2×#13093999C2211yescharacteristic, complemented
38C2×#13093999C2211yescharacteristic, complemented
39C2×#13093998C2211yescharacteristic
40C2×#13093995C2211yescharacteristic, complemented
41C2×#13093994—21no—
42C2×#13093994—21no—
43C2×#13093994—21no—
44C2×#13093992—21no—
45C2×#13093982C2211yescharacteristic, complemented
46#15689450C2218yescomplemented
47#15689449C2218yescomplemented
48#15689447C2218yescomplemented
49#15689377C2218yescomplemented
50#15689375C2218yescomplemented
51#15689360C2218yescomplemented
52#15689358C2218yescomplemented
53#15689259C2218yescomplemented
54#15689258C2218yescomplemented
55#15689258C2218yescomplemented
56#15689256C2218yescomplemented
57C2×#13093957C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093946C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic, complemented
61C2×#13093944C2211yescharacteristic, complemented
62C2×#13093944C2211yescharacteristic, complemented
63C2×#13093944C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic, complemented
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C24×D47—21no—
79C2×#10625350—42no—
80C2×#10625350—42no—
81C2×#10625350D414yes—
82C2×#10625350C2314yes—
83C22×Dic94D411yescharacteristic
84C22×D188—21no—
85C22×D188—22no—
86C22×D188—21no—
87C22×D188—21no—
88C22×D188—21no—
89C22×D188—21no—
90C22×D188—21no—
91C22×D188—42no—
92C22×D188—42no—
93C22×D188D411yescharacteristic
94C22×D188C2311yescharacteristic
95C22×D188C2311yescharacteristic
96C22×D188C2311yescharacteristic
97C22×D188C2314yescomplemented
98C22×C22⋊D47—21no—
99C22×C22⋊D47—21no—
100C22×C22⋊D47—21no—
101C22×C22⋊D47D411yescharacteristic
102C22×C22⋊D47D411yescharacteristic
103C2×D4×D47—22no—
104C2×D4×D47—42no—
105C2×D4×D47—42no—
106C2×D4×D47C2314yescomplemented
107C22×C4×D47C2311yescharacteristic
108C22×C4×D47C2311yescharacteristic
109C2×D376—42no—
110C2×D376—42no—
111C2×D376C2314yes—
112C2×D376C2314yes—
113C2×#10625334—42no—
114C2×#10625334—42no—
115C2×#10625334C2314yes—
116C2×#10625334C2314yes—
117C2×#10625324—42no—
118C2×#10625324C2314yescomplemented
119C22×C47⋊C8C2311yescharacteristic
120C22×C47⋊C8C2311yescharacteristic
121C2×C8×D47—42no—
122C2×C8×D47C2314yescomplemented
123#13094021—28no—
124#13094020—28no—
125#13094012—28no—
126#13094010—28no—
127#13093999—22no—
128#13093999—22no—
129#13093999—22no—
130#13093999—22no—
131#13093999—22no—
132#13093999C2314yes—
133#13093999C2314yes—
134#13093999C2314yescomplemented
135#13093999C2314yescomplemented
136#13093999C2314yescomplemented
137#13093998—22no—
138#13093998C2314yes—
139#13093995—22no—
140#13093995C2314yescomplemented
141#13093994—28no—
142#13093994—28no—
143#13093994—28no—
144#13093992—28no—
145#13093982—22no—
146#13093982C2314yescomplemented
147C2×C4⋊Dic47C2311yescharacteristic
148C2×C22⋊Dic47—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×C4×Dic47—21no—
157#13093957C2314yescomplemented
158#13093955C2314yescomplemented
159#13093946C2314yescomplemented
160#13093946C2314yescomplemented
161#13093944C2314yescomplemented
162#13093944C2314yescomplemented
163#13093944C2314yescomplemented
164#13093944C2314yescomplemented
165C22⋊(C47⋊C8)C2314yescomplemented
166(C2×D47)⋊C8C2314yescomplemented
167(C2×D47)⋊C8C2314yescomplemented
168C22×D4×C47—21no—
169C22×D4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173#121×C47—22no—
174#121×C47C2314yes—
175#117×C47—22no—
176#117×C47C2314yescomplemented
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183#107×C47C2314yescomplemented
184#106×C47C2314yescomplemented
185#102×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187C22⋊C8×C47C2314yescomplemented
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—21no—
193C23×D47—24no—
194C23×D47—24no—
195C23×D47—44no—
196C23×D47—44no—
197C23×D47—82no—
198C23×D47—82no—
199C23×D47—82no—
200C23×D47—82no—
201C23×D47C2×D411yescharacteristic
202C23×D47C2×D411yescharacteristic
203C2×D4×C47—24no—
204C2×D4×C47—21no—
205C2×D4×C47—22no—
206C2×D4×C47—22no—
207C2×D4×C47—82no—
208C2×D4×C47C2412yes—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—42no—
222C2×C22⋊D47—42no—
223C2×C22⋊D47—44no—
224C2×C22⋊D47—82no—
225C2×C22⋊D47—82no—
226C2×C22⋊D47C2×D414yes—
227C2×C22⋊D47C2×D414yes—
228C22×Dic47—21no—
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231D4×D47—44no—
232D4×D47—44no—
233D4×D47—48no—
234#10625350—48no—
235#10625350—44no—
236#10625350—44no—
237C2×D188—22no—
238C2×D188—22no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—22no—
243C2×D188—21no—
244C2×D188—21no—
245C2×D188—21no—
246C2×D188—24no—
247C2×D188—24no—
248C2×D188—24no—
249C2×D188—24no—
250C2×D188—24no—
251C2×D188—24no—
252C2×D188—44no—
253C2×D188—44no—
254C2×D188—42no—
255C2×D188—44no—
256C2×D188—48no—
257C2×D188—82no—
258C2×D188—82no—
259C2×D188—82no—
260C2×D188—82no—
261C2×D188—82no—
262C2×D188C2×D414yes—
263C2×D188C2412yes—
264C2×D188C2412yes—
265C2×D188C2412yes—
266C2×C4×D47—22no—
267C2×C4×D47—22no—
268C2×C4×D47—22no—
269C2×C4×D47—22no—
270C2×C4×D47C2×D412yes—
271C2×C4×D47C2×D412yes—
272C2×C4×D47C2412yes—
273C2×C4×D47C2412yes—
274C2×Dic94—42no—
275C2×Dic94C2×D414yes—
276C2×C8×C47—22no—
277C2×C8×C47—22no—
278C2×C8×C47C2412yes—
279C2×C8×C47C2412yes—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47C2412yes—
284C4⋊C4×C47C2412yes—
285C4⋊C4×C47C2412yes—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—24no—
288C42×C47—24no—
289C22⋊Dic47—24no—
290#10625334—44no—
291#10625334—44no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297(C2×D47)⋊C4—24no—
298(C2×D47)⋊C4—24no—
299C4⋊Dic47—21no—
300C4⋊Dic47C2412yes—
301C4×Dic47—24no—
302C2×C47⋊C8—22no—
303C2×C47⋊C8—22no—
304C2×C47⋊C8C2412yes—
305C2×C47⋊C8C2412yes—
306D376—44no—
307D376—44no—
308#10625324—44no—
309C8×D47—44no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47C22×D412yes—
318C23×C47C22×D411yescharacteristic
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—48no—
329C22×D47—48no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47—42no—
335C22×D47—42no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—84no—
340C22×D47—84no—
341C22×D47—84no—
342C22×D47—84no—
343C22×D47—816no—
344C22×D47—816no—
345C22×D47C22×D412yes—
346C22×D47C22×D412yes—
347D4×C47—22no—
348D4×C47—22no—
349D4×C47—42no—
350D4×C47—84no—
351C2×C4×C47—22no—
352C2×C4×C47—24no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—42no—
359C2×C4×C47—42no—
360C2×C4×C47—42no—
361C2×C4×C47C22×D412yes—
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47H(5,𝔽2)12yes—
364C2×C4×C47H(5,𝔽2)12yes—
365C2×C4×C47C2511yescharacteristic
366C22⋊D47—44no—
367C22⋊D47—44no—
368C22⋊D47—48no—
369C22⋊D47—84no—
370C22⋊D47—84no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—42no—
375C2×Dic47C22×D412yes—
376C2×Dic47C22×D412yes—
377D188—22no—
378D188—22no—
379D188—22no—
380D188—22no—
381D188—22no—
382D188—22no—
383D188—44no—
384D188—48no—
385D188—42no—
386D188—42no—
387D188—42no—
388D188—84no—
389D188—84no—
390D188—84no—
391D188—84no—
392D188—84no—
393C4×D47—24no—
394C4×D47—24no—
395C4×D47—22no—
396C4×D47—22no—
397C4×D47—22no—
398C4×D47—22no—
399Dic94—44no—
400C8×C47—22no—
401C8×C47—22no—
402C47⋊C8—22no—
403C47⋊C8—22no—
404C2×#3199—471nomaximal, Sylow
405C22×C47—22no—
406C22×C47—22no—
407C22×C47—22no—
408C22×C47—44no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—84no—
413C22×C47#53412yes—
414C22×C47#57612yes—
415C22×C47#57612yes—
416C22×C47C23×D411yescharacteristic
417C2×D47—22no—
418C2×D47—22no—
419C2×D47—22no—
420C2×D47—22no—
421C2×D47—22no—
422C2×D47—22no—
423C2×D47—44no—
424C2×D47—44no—
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—42no—
428C2×D47—42no—
429C2×D47—42no—
430C2×D47—42no—
431C2×D47—42no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—816no—
435C2×D47—816no—
436C2×D47—84no—
437C2×D47—84no—
438C2×D47—84no—
439C4×C47—22no—
440C4×C47—42no—
441C4×C47—42no—
442C4×C47—42no—
443C4×C47#53412yes—
444C4×C47C2×H(5,𝔽2)11yescharacteristic
445C4×C47C2×H(5,𝔽2)11yescharacteristic
446Dic47—22no—
447Dic47—22no—
448Dic47—42no—
449C2×#535—471no—
450C2×#535—471no—
451#3199—4716no—
452C2×#482—471no—
453C2×#482—471no—
454C2×#482—471no—
455C2×#482D4711yescharacteristic, complemented
456C2×#469—471no—
457C2×#469—471no—
458C2×#466—471no—
459C2×#466—471no—
460C2×#447—471no—
461C2×#447—471no—
462C2×#447—471no—
463C2×#447—471no—
464C2×#408—471no—
465C2×C47—42no—
466C2×C47—82no—
467C2×C47#319914yescomplemented
468C2×C47C2×#53411yescharacteristic
469C2×C47C2×#57611yescharacteristic
470C2×C47C2×#57611yescharacteristic
471D47—42no—
472D47—42no—
473D47—82no—
474D47—82no—
475D47—82no—
476C22×#41—471no—
477C23×D4—471no—
478C23×D4—471no—
479C22×D8—471no—
480C22×D8—471no—
481C22×D8—471no—
482C22×D8—471no—
483C22×M16—471no—
484C23×C8—471no—
485#535—478no—
486#535—478no—
487#535—944no—
488#535—944no—
489C2×#127—941no—
490C2×#127—941no—
491C2×#124—941no—
492C2×#124—941no—
493C2×#121—471no—
494C2×#121—471no—
495C2×#121—471no—
496C2×#121—471no—
497C2×#121—471no—
498C2×#121—471no—
499C2×#121—471no—
500C2×#121C2×D4711yescharacteristic
501C2×#120—941no—
502C2×#120—941no—
503C2×#120—941no—
504C2×#120—941no—
505C2×#117—471no—
506C2×#117C2×D4711yescharacteristic, complemented
507#482—478no—
508#482—478no—
509#482—478no—
510#482C2×D4718yescomplemented
511#469—478no—
512#469—478no—
513#466—478no—
514#466—478no—
515#447—478no—
516#447—478no—
517#447—478no—
518#447—478no—
519C2×#107—471no—
520C2×#107C2×D4711yescharacteristic, complemented
521C2×#106—471no—
522C2×#106C2×D4711yescharacteristic, complemented
523C2×#102—471no—
524C2×#102—471no—
525C2×#102—471no—
526C2×#102—471no—
527C2×#102—471no—
528C2×#102—471no—
529C2×#102C2×D4711yescharacteristic, complemented
530C2×#102C2×D4711yescharacteristic, complemented
531#408—478no—
532C2×C22⋊C8—471no—
533C2×C22⋊C8—471no—
534C2×C22⋊C8—471no—
535C2×C22⋊C8C2×D4711yescharacteristic, complemented
536C47C2×#319911yescharacteristic, complemented, Sylow
537C25—941no—
538C25—941no—
539C2×#41—474no—
540C2×#41—474no—
541C2×#41—1882no—
542C2×#41—1882no—
543C22×Q8—471no—
544C22×D4—21no—
545C22×D4—471no—
546C22×D4—471no—
547C22×D4—474no—
548C22×D4—471no—
549C22×D4—471no—
550C22×D4—471no—
551C22×D4—471no—
552C22×D4—474no—
553C22×D4—941no—
554C22×D4—941no—
555C22×D4—941no—
556C22×D4—941no—
557C22×D4—941no—
558C22×D4—942no—
559C22×D4—941no—
560C22×D4—941no—
561C22×D4—941no—
562C22×D4—941no—
563C22×D4—942no—
564C22×D4—1882no—
565C22×D4—1882no—
566C22×D4—1882no—
567C22×D4—1882no—
568C22×D4C22×D4711yescharacteristic
569C23×C4—471no—
570C23×C4—471no—
571C23×C4C22×D4711yescharacteristic
572C2×D8—474no—
573C2×D8—474no—
574C2×D8—474no—
575C2×D8—474no—
576C2×D8—1882no—
577C2×D8—1882no—
578C2×D8—1882no—
579C2×D8—1882no—
580C2×M16—474no—
581C2×M16—1882no—
582C22×C8—471no—
583C22×C8—471no—
584C22×C8—474no—
585C22×C8—1882no—
586C22×C8C22×D4711yescharacteristic
587C22×C8C22×D4711yescharacteristic
588#127—948no—
589#127—948no—
590#124—948no—
591#124—948no—
592#121—22no—
593#121—474no—
594#121—474no—
595#121—474no—
596#121—474no—
597#121—474no—
598#121—474no—
599#121—474no—
600#121—942no—
601#121—942no—
602#121—942no—
603#121—942no—
604#121—942no—
605#121—942no—
606#121—942no—
607#121C22×D4714yes—
608#120—948no—
609#120—948no—
610#120—948no—
611#120—948no—
612#117—22no—
613#117—474no—
614#117—942no—
615#117C22×D4714yescomplemented
616C2×C4⋊C4—471no—
617C2×C4⋊C4C22×D4711yescharacteristic
618C2×C4⋊C4C22×D4711yescharacteristic
619C2×C4⋊C4C22×D4711yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—941no—
623C2×C22⋊C4—941no—
624C2×C22⋊C4—941no—
625C2×C22⋊C4—941no—
626C2×C22⋊C4—941no—
627C2×C22⋊C4—941no—
628C2×C22⋊C4—941no—
629C2×C22⋊C4—941no—
630C2×C42—21no—
631C2×C42—941no—
632#107—474no—
633#107C22×D4714yescomplemented
634#106—474no—
635#106C22×D4714yescomplemented
636#102—474no—
637#102—474no—
638#102—474no—
639#102—474no—
640#102—474no—
641#102—474no—
642#102C22×D4714yescomplemented
643#102C22×D4714yescomplemented
644C22⋊C8—474no—
645C22⋊C8—474no—
646C22⋊C8—474no—
647C22⋊C8C22×D4714yescomplemented
648C24—21no—
649C24—471no—
650C24—471no—
651C24—944no—
652C24—944no—
653C24—941no—
654C24—941no—
655C24—941no—
656C24—3762no—
657C24—3762no—
658C24—3762no—
659C24—3762no—
660C24—1884no—
661C24—1884no—
662C24D4×D4711yescharacteristic
663#41—1888no—
664#41—1884no—
665#41—1884no—
666C2×Q8—474no—
667C2×Q8—1882no—
668C2×D4—24no—
669C2×D4—21no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—82no—
673C2×D4—474no—
674C2×D4—474no—
675C2×D4—474no—
676C2×D4—472no—
677C2×D4—472no—
678C2×D4—472no—
679C2×D4—944no—
680C2×D4—944no—
681C2×D4—944no—
682C2×D4—944no—
683C2×D4—944no—
684C2×D4—944no—
685C2×D4—944no—
686C2×D4—944no—
687C2×D4—941no—
688C2×D4—941no—
689C2×D4—941no—
690C2×D4—944no—
691C2×D4—942no—
692C2×D4—942no—
693C2×D4—942no—
694C2×D4—942no—
695C2×D4—942no—
696C2×D4—942no—
697C2×D4—3762no—
698C2×D4—3762no—
699C2×D4—3762no—
700C2×D4—3762no—
701C2×D4—3762no—
702C2×D4—3762no—
703C2×D4—3762no—
704C2×D4—1884no—
705C2×D4—1884no—
706C2×D4—1882no—
707C2×D4—1884no—
708C2×D4—1888no—
709C2×D4—1884no—
710C2×D4—1884no—
711C2×D4—1888no—
712C2×D4—1882no—
713C2×D4—1882no—
714C2×D4—1884no—
715C2×D4C23×D4712yes—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—471no—
722C22×C4—471no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4—942no—
731C22×C4—941no—
732C22×C4D4×D4712yes—
733C22×C4D4×D4711yescharacteristic
734C22×C4C23×D4712yes—
735C22×C4C23×D4711yescharacteristic
736D8—1884no—
737D8—1884no—
738D8—1884no—
739D8—1884no—
740M16—1884no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—472no—
744C2×C8—472no—
745C2×C8—942no—
746C2×C8—942no—
747C2×C8—1884no—
748C2×C8C23×D4712yes—
749C2×C8C23×D4712yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—472no—
754C4⋊C4—941no—
755C4⋊C4C23×D4712yes—
756C4⋊C4C23×D4712yes—
757C4⋊C4C23×D4712yes—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—944no—
761C22⋊C4—944no—
762C22⋊C4—944no—
763C22⋊C4—944no—
764C22⋊C4—944no—
765C22⋊C4—944no—
766C22⋊C4—944no—
767C22⋊C4—944no—
768C42—24no—
769C42—944no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—472no—
778C23—472no—
779C23—942no—
780C23—942no—
781C23—942no—
782C23—942no—
783C23—942no—
784C23—942no—
785C23—942no—
786C23—942no—
787C23—942no—
788C23—3764no—
789C23—3764no—
790C23—3764no—
791C23—3764no—
792C23—37616no—
793C23—37616no—
794C23—1888no—
795C23—1888no—
796C23—1882no—
797C23—1882no—
798C23—1882no—
799C23—1882no—
800C23—1882no—
801C23—1882no—
802C23—1882no—
803C23—1882no—
804C23—1882no—
805C23C2×D4×D4712yes—
806C23C2×D4×D4711yescharacteristic
807Q8—1884no—
808D4—22no—
809D4—22no—
810D4—42no—
811D4—84no—
812D4—942no—
813D4—942no—
814D4—942no—
815D4—942no—
816D4—942no—
817D4—942no—
818D4—3764no—
819D4—3764no—
820D4—3764no—
821D4—3764no—
822D4—3764no—
823D4—3764no—
824D4—3764no—
825D4—1884no—
826D4—1888no—
827D4—1884no—
828D4—1884no—
829D4—1888no—
830D4—1882no—
831D4—1882no—
832D4—1882no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—472no—
844C2×C4—472no—
845C2×C4—942no—
846C2×C4—942no—
847C2×C4—944no—
848C2×C4—944no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—1882no—
855C2×C4C2×D4×D4712yes—
856C2×C4C2×D4×D4711yescharacteristic
857C2×C4#1309407012yes—
858C2×C4#1309407012yes—
859C2×C4C24×D4711yescharacteristic
860C8—22no—
861C8—22no—
862C8—942no—
863C8—942no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—44no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—84no—
872C22—942no—
873C22—942no—
874C22—942no—
875C22—942no—
876C22—942no—
877C22—942no—
878C22—37616no—
879C22—37616no—
880C22—3764no—
881C22—3764no—
882C22—3764no—
883C22—1882no—
884C22—1882no—
885C22—1882no—
886C22—1882no—
887C22—1882no—
888C22—1882no—
889C22—1882no—
890C22—1882no—
891C22—1882no—
892C22—1884no—
893C22—1884no—
894C22#1568968412yes—
895C22#1568992512yes—
896C22#1568992712yes—
897C22C22×D4×D4711yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—942no—
903C4—942no—
904C4—1882no—
905C4#1568968412yes—
906C4C2×#1309407011yescharacteristic
907C4C2×#1309407011yescharacteristic
908C2—42no—
909C2—82no—
910C2—3762no—
911C2—3762no—
912C2—3762no—
913C2—1882no—
914C2—1882no—
915C2#2025425214yesdirect product factor
916C2C2×#1568968411yescharacteristic
917C2C2×#1568992511yescharacteristic
918C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
hypercenterC2×#482D47
hypocenterC47C2×#3199
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#15689692C2semidirect
2. C2×#15689689C2semidirect
3. #20254252C2direct (N × H)
4. C2×#15689450C2semidirect
5. C2×#15689449C2semidirect
6. C2×#15689447C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689360C2semidirect
10. C2×#15689358C2semidirect
11. C2×#15689259C2semidirect
12. C2×#15689258C2semidirect
13. C2×#15689258C2semidirect
14. C2×#15689256C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#482C2semidirect
18. C23×D188C22semidirect
19. C22×D4×D47C22semidirect
24. C22×#10625324C22semidirect
25. C22×C8×D47C22semidirect
27. #15689692C22semidirect
29. #15689689C22semidirect
36. C2×#13093999C22semidirect
37. C2×#13093999C22semidirect
38. C2×#13093999C22semidirect
40. C2×#13093995C22semidirect
45. C2×#13093982C22semidirect
46. #15689450C22semidirect
47. #15689449C22semidirect
48. #15689447C22semidirect
49. #15689377C22semidirect
50. #15689375C22semidirect
51. #15689360C22semidirect
52. #15689358C22semidirect
53. #15689259C22semidirect
54. #15689258C22semidirect
55. #15689258C22semidirect
56. #15689256C22semidirect
57. C2×#13093957C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093946C22semidirect
60. C2×#13093946C22semidirect
61. C2×#13093944C22semidirect
62. C2×#13093944C22semidirect
63. C2×#13093944C22semidirect
64. C2×#13093944C22semidirect
65. #15689088C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C2×#117×C47C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
97. C22×D188C23semidirect
106. C2×D4×D47C23semidirect
118. C2×#10625324C23semidirect
122. C2×C8×D47C23semidirect
134. #13093999C23semidirect
135. #13093999C23semidirect
136. #13093999C23semidirect
140. #13093995C23semidirect
146. #13093982C23semidirect
157. #13093957C23semidirect
158. #13093955C23semidirect
159. #13093946C23semidirect
160. #13093946C23semidirect
161. #13093944C23semidirect
162. #13093944C23semidirect
163. #13093944C23semidirect
164. #13093944C23semidirect
165. C22⋊(C47⋊C8)C23semidirect
166. (C2×D47)⋊C8C23semidirect
167. (C2×D47)⋊C8C23semidirect
176. #117×C47C23semidirect
183. #107×C47C23semidirect
184. #106×C47C23semidirect
185. #102×C47C23semidirect
186. #102×C47C23semidirect
187. C22⋊C8×C47C23semidirect
455. C2×#482D47semidirect
467. C2×C47#3199semidirect
506. C2×#117C2×D47semidirect
510. #482C2×D47semidirect
520. C2×#107C2×D47semidirect
522. C2×#106C2×D47semidirect
529. C2×#102C2×D47semidirect
530. C2×#102C2×D47semidirect
535. C2×C22⋊C8C2×D47semidirect
536. C47C2×#3199semidirect
615. #117C22×D47semidirect
633. #107C22×D47semidirect
635. #106C22×D47semidirect
642. #102C22×D47semidirect
643. #102C22×D47semidirect
647. C22⋊C8C22×D47semidirect
915. C2#20254252direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896922
C2×#156896892
#202542522
C2×#156894502
C2×#156894492
C2×#156894472
C2×#156893772
C2×#156893752
C2×#156893602
C2×#156893582
C2×#156892592
C2×#156892582
C2×#156892562
C2×#156890882
C2×C47×#4822
C2×#319947