Finite Group Databasebeta

← C2×#20254354 #27087451

Subgroups — C2×#20254354 #27087451

Order 12032.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic, complemented
2C2×#124×D47C211yesmaximal, characteristic, complemented
3#20254354C2116yesmaximal, direct product factor
4C2×#15689507C211yesmaximal, characteristic, complemented
5C2×#15689505C211yesmaximal, characteristic, complemented
6C2×#15689480C211yesmaximal, characteristic, complemented
7C2×#15689348C211yesmaximal, characteristic, complemented
8C2×#15689344C211yesmaximal, characteristic, complemented
9C2×#15689341C211yesmaximal, characteristic, complemented
10C2×#15689337C211yesmaximal, characteristic, complemented
11C2×#15689280C211yesmaximal, characteristic, complemented
12C2×#15689263C211yesmaximal, characteristic, complemented
13C2×#15689275C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic
15C2×#15689174C211yesmaximal, characteristic, complemented
16C2×C47×#488C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×Dic188C2211yescharacteristic, complemented
20C22×#10625337C2211yescharacteristic, complemented
21C22×#10625325C2211yescharacteristic
22C22×#10625325C2211yescharacteristic, complemented
23C22×#10625335C2211yescharacteristic
24C22×#10625336C2211yescharacteristic, complemented
25C22×D376C2211yescharacteristic
26C22×#10625334C2211yescharacteristic
27#15689658—24no—
28#15689658C2218yescomplemented
29C2×#13094019—21no—
30C2×#13094013C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094012C2211yescharacteristic, complemented
33C2×#13094011C2211yescharacteristic
34C2×#13094010—21no—
35C2×#13094010—21no—
36#124×D47—24no—
37#124×D47C2218yescomplemented
38C2×#13094009—21no—
39C2×#13094004C2211yescharacteristic
40C2×#13093999C2211yescharacteristic
41C2×#13093989C2211yescharacteristic, complemented
42C2×#13093986—21no—
43C2×#13093986C2211yescharacteristic, complemented
44C2×#13093982—21no—
45C2×C22⋊C4×D47—21no—
46C2×C22⋊C4×D47—21no—
47C2×C42×D47C2211yescharacteristic
48#15689507C2218yescomplemented
49#15689505C2218yescomplemented
50#15689480C2218yescomplemented
51#15689348C2218yescomplemented
52#15689344C2218yescomplemented
53#15689341C2218yescomplemented
54#15689337C2218yescomplemented
55#15689280C2218yescomplemented
56#15689275C2218yescomplemented
57#15689263C2218yescomplemented
58#15689258C2218yes—
59#15689174C2218yescomplemented
60C2×Dic47⋊C8C2211yescharacteristic, complemented
61C2×Dic47⋊C8C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093947C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic, complemented
69C2×#125×C47C2211yescharacteristic, complemented
70C2×#124×C47C2211yescharacteristic
71C47×#488C2218yescomplemented
72C2×#103×C47C2211yescharacteristic, complemented
73C2×#103×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—22no—
82C2×Q8×D47—42no—
83C2×Q8×D47—42no—
84C2×Q8×D47C2314yes—
85C22×D188—21no—
86C22×D188C2311yescharacteristic
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C2×D4×D47—22no—
90C2×D4×D47—42no—
91C2×D4×D47—42no—
92C2×D4×D47C2314yes—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47D411yescharacteristic
96C22×C4×D47D411yescharacteristic
97C22×C4×D47C2311yescharacteristic
98C2×Dic188—42no—
99C2×Dic188C2314yescomplemented
100C2×#10625337—42no—
101C2×#10625337C2314yescomplemented
102C2×#10625325—42no—
103C2×#10625325—42no—
104C2×#10625325C2314yes—
105C2×#10625325C2314yescomplemented
106C2×#10625335—42no—
107C2×#10625335C2314yes—
108C2×#10625336—42no—
109C2×#10625336C2314yescomplemented
110C2×D376—42no—
111C2×D376C2314yes—
112C2×#10625334—42no—
113C2×#10625334C2314yes—
114C22×C47⋊C8C2311yescharacteristic
115C22×C47⋊C8C2311yescharacteristic
116#13094019—28no—
117#13094013—22no—
118#13094013C2314yes—
119#13094012—22no—
120#13094012—22no—
121#13094012C2314yes—
122#13094012C2314yescomplemented
123#13094011—22no—
124#13094011C2314yes—
125#13094010—28no—
126#13094010—28no—
127#13094009—28no—
128#13094004—22no—
129#13094004C2314yes—
130#13093999—22no—
131#13093999C2314yes—
132#13093989—22no—
133#13093989C2314yescomplemented
134#13093986—28no—
135#13093986—22no—
136#13093986C2314yescomplemented
137#13093982—28no—
138C2×C4⋊Dic47—21no—
139C2×Dic47⋊C4—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C22⋊C4×D47—28no—
152C22⋊C4×D47—28no—
153C2×C4×Dic47—21no—
154C2×C4×Dic47D411yescharacteristic
155C2×C4×Dic47D411yescharacteristic
156C2×C4×Dic47C2311yescharacteristic
157C42×D47D414yes—
158C42×D47C2314yes—
159Dic47⋊C8C2314yescomplemented
160Dic47⋊C8C2314yescomplemented
161#13093947C2314yescomplemented
162#13093947C2314yescomplemented
163#13093944C2314yes—
164#13093944C2314yes—
165(C2×D47)⋊C8C2314yes—
166(C2×D47)⋊C8C2314yes—
167C4×C47⋊C8C2314yescomplemented
168C22×Q8×C47C2311yescharacteristic
169C22×D4×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172#125×C47—22no—
173#125×C47C2314yescomplemented
174#124×C47—22no—
175#124×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C42×C47C2311yescharacteristic
183#103×C47C2314yescomplemented
184#103×C47C2314yescomplemented
185#102×C47C2314yes—
186#102×C47C2314yes—
187C4×C8×C47C2314yescomplemented
188C24×C47—21no—
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—24no—
192C23×D47—44no—
193C23×D47—44no—
194C23×D47—44no—
195C23×D47C2×D411yescharacteristic
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47C2412yes—
200C2×D4×C47—21no—
201C2×D4×C47—22no—
202C2×D4×C47—22no—
203C2×D4×C47C2412yes—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2411yescharacteristic
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217Q8×D47—44no—
218Q8×D47—44no—
219Q8×D47—48no—
220D4×D47—44no—
221D4×D47—44no—
222D4×D47—48no—
223C2×D188—22no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—24no—
228C2×D188—21no—
229C2×D188—21no—
230C2×D188—44no—
231C2×D188C2412yes—
232C2×D188C2412yes—
233C2×C4×D47—24no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—24no—
237C2×C4×D47—24no—
238C2×C4×D47—42no—
239C2×C4×D47—44no—
240C2×C4×D47—44no—
241C2×C4×D47C2×D412yes—
242C2×C4×D47C2×D414yes—
243C2×C4×D47C2×D414yes—
244C2×C4×D47C2412yes—
245C2×Dic94—22no—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—22no—
249C2×Dic94—21no—
250C2×Dic94—21no—
251C2×Dic94—24no—
252C2×Dic94—44no—
253C2×Dic94C2412yes—
254C2×Dic94C2412yes—
255C2×C8×C47—22no—
256C2×C8×C47—22no—
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C4⋊C4×C47—24no—
260C4⋊C4×C47—24no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47C2412yes—
264C4⋊C4×C47C2412yes—
265C22⋊C4×C47—24no—
266C22⋊C4×C47—24no—
267C42×C47C2×D412yes—
268C42×C47C2412yes—
269C22⋊Dic47—24no—
270C22⋊Dic47—24no—
271#10625337—44no—
272#10625336—44no—
273#10625335—44no—
274#10625334—44no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284C4⋊Dic47—24no—
285Dic47⋊C4—24no—
286C4×Dic47—24no—
287C4×Dic47C2×D412yes—
288C4×Dic47C2×D414yes—
289C4×Dic47C2×D414yes—
290C4×Dic47C2412yes—
291C2×C47⋊C8—22no—
292C2×C47⋊C8—22no—
293C2×C47⋊C8C2412yes—
294C2×C47⋊C8C2412yes—
295Dic188—44no—
296D376—44no—
297#10625325—44no—
298#10625325—44no—
299C23×C47—22no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47C22×D411yescharacteristic
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—48no—
309C22×D47—48no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—48no—
317C22×D47—816no—
318C22×D47#13514yes—
319C22×D47C22×D412yes—
320Q8×C47—22no—
321Q8×C47—22no—
322Q8×C47—42no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—42no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—42no—
332C2×C4×C47—42no—
333C2×C4×C47—42no—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47H(5,𝔽2)12yes—
338C2×C4×C47H(5,𝔽2)12yes—
339C2×C4×C47C2511yescharacteristic
340C22⋊D47—48no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47C22×D412yes—
349C2×Dic47C22×D412yes—
350C2×Dic47C22×D412yes—
351D188—22no—
352D188—22no—
353D188—22no—
354D188—22no—
355D188—48no—
356D188—42no—
357D188—42no—
358C4×D47—28no—
359C4×D47—24no—
360C4×D47—22no—
361C4×D47—22no—
362C4×D47—44no—
363C4×D47—48no—
364C4×D47—48no—
365Dic94—22no—
366Dic94—22no—
367Dic94—22no—
368Dic94—22no—
369Dic94—48no—
370Dic94—42no—
371Dic94—42no—
372C8×C47—22no—
373C8×C47—22no—
374C47⋊C8—22no—
375C47⋊C8—22no—
376C2×#3211—471nomaximal, Sylow
377C22×C47—42no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—84no—
381C22×C47#53512yes—
382C22×C47C2×#13512yes—
383C22×C47#57512yes—
384C22×C47C23×D411yescharacteristic
385C2×D47—22no—
386C2×D47—28no—
387C2×D47—22no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—816no—
395C2×D47—84no—
396C2×D47—84no—
397C2×D47C2×#13514yes—
398C4×C47—22no—
399C4×C47—22no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47#53512yes—
404C4×C47C2×H(5,𝔽2)11yescharacteristic
405C4×C47C2×H(5,𝔽2)11yescharacteristic
406Dic47—22no—
407Dic47—22no—
408Dic47—22no—
409Dic47—42no—
410Dic47—42no—
411C2×#529—471no—
412C22×#124—471no—
413#3211—4716no—
414C2×#495—471no—
415C2×#495—471no—
416C2×#488—471no—
417C2×#488D4711yescharacteristic, complemented
418C2×#464—471no—
419C2×#464—471no—
420C2×#463—471no—
421C2×#463—471no—
422C2×#451—471no—
423C2×#448—471no—
424C2×#450—471no—
425C2×#447—471no—
426C2×#431—471no—
427C2×C47—82no—
428C2×C47#321114yescomplemented
429C2×C47C2×#53511yescharacteristic
430C2×C47C22×#13511yescharacteristic
431C2×C47C2×#57511yescharacteristic
432D47—24no—
433D47—82no—
434D47—82no—
435C23×Q8—471no—
436C23×D4—471no—
437C22×Q16—471no—
438C22×Q16—471no—
439C22×SD16—471no—
440C22×SD16—471no—
441C22×SD16—471no—
442C22×SD16—471no—
443C22×D8—471no—
444C22×D8—471no—
445#529—478no—
446#529—944no—
447C2×#126—941no—
448C2×#125C2×D4711yescharacteristic, complemented
449C2×#124—471no—
450C2×#124—471no—
451C2×#124—478no—
452C2×#124—471no—
453C2×#124—471no—
454C2×#124—941no—
455C2×#124—941no—
456C2×#124—944no—
457C2×#124C2×D4711yescharacteristic
458C2×#123—941no—
459C2×C22⋊Q8—471no—
460C2×#121—471no—
461C2×C4×Q8—471no—
462C2×C4×D4—471no—
463C2×C4×D4—941no—
464C2×#117—941no—
465C22×C22⋊C4—941no—
466C22×C22⋊C4—941no—
467C22×C42—471no—
468#495—478no—
469#495—478no—
470#488—478no—
471#488C2×D4718yescomplemented
472#464—478no—
473#464—478no—
474#463—478no—
475#463—478no—
476#451—478no—
477#450—478no—
478#448—478no—
479#447—478no—
480#431—478no—
481C2×C4⋊C8—471no—
482C2×C4⋊C8—471no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103C2×D4711yescharacteristic, complemented
486C2×#103C2×D4711yescharacteristic, complemented
487C2×#102—471no—
488C2×#102—471no—
489C2×#102C2×D4711yescharacteristic
490C2×#102C2×D4711yescharacteristic
491C2×C22⋊C8—471no—
492C2×C22⋊C8—471no—
493C2×C4×C8—471no—
494C2×C4×C8C2×D4711yescharacteristic, complemented
495C47C2×#321111yescharacteristic, complemented, Sylow
496C25—941no—
497C22×Q8—474no—
498C22×Q8—471no—
499C22×Q8—471no—
500C22×Q8—941no—
501C22×Q8—942no—
502C22×Q8—1882no—
503C22×Q8—1882no—
504C22×Q8C22×D4711yescharacteristic
505C22×D4—474no—
506C22×D4—471no—
507C22×D4—471no—
508C22×D4—941no—
509C22×D4—942no—
510C22×D4—941no—
511C22×D4—1882no—
512C22×D4—1882no—
513C22×D4C22×D4711yescharacteristic
514C23×C4—471no—
515C23×C4—471no—
516C23×C4—471no—
517C23×C4—941no—
518C23×C4—941no—
519C2×Q16—474no—
520C2×Q16—474no—
521C2×Q16—1882no—
522C2×Q16—1882no—
523C2×SD16—474no—
524C2×SD16—474no—
525C2×SD16—474no—
526C2×SD16—474no—
527C2×SD16—1882no—
528C2×SD16—1882no—
529C2×SD16—1882no—
530C2×SD16—1882no—
531C2×D8—474no—
532C2×D8—474no—
533C2×D8—1882no—
534C2×D8—1882no—
535C22×C8—471no—
536C22×C8—471no—
537C22×C8C22×D4711yescharacteristic
538C22×C8C22×D4711yescharacteristic
539#126—948no—
540#125—22no—
541#125C22×D4714yescomplemented
542#124—22no—
543#124—474no—
544#124—474no—
545#124—474no—
546#124—474no—
547#124—948no—
548#124—948no—
549#124—942no—
550#124—942no—
551#124—942no—
552#124—942no—
553#124C22×D4714yes—
554#123—948no—
555C22⋊Q8—474no—
556C22⋊Q8—942no—
557#121—474no—
558#121—942no—
559C4×Q8—474no—
560C4×Q8—942no—
561C4×D4—474no—
562C4×D4—942no—
563C4×D4—948no—
564#117—948no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—941no—
568C2×C4⋊C4—941no—
569C2×C4⋊C4C22×D4711yescharacteristic
570C2×C4⋊C4C22×D4711yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—948no—
574C2×C22⋊C4—948no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—941no—
583C2×C22⋊C4—941no—
584C2×C22⋊C4—941no—
585C2×C22⋊C4—941no—
586C2×C42—471no—
587C2×C42—471no—
588C2×C42—471no—
589C2×C42—474no—
590C2×C42—474no—
591C2×C42—941no—
592C2×C42C22×D4711yescharacteristic
593C4⋊C8—474no—
594C4⋊C8—474no—
595#103—474no—
596#103—474no—
597#103C22×D4714yescomplemented
598#103C22×D4714yescomplemented
599#102—474no—
600#102—474no—
601#102C22×D4714yes—
602#102C22×D4714yes—
603C22⋊C8—474no—
604C22⋊C8—474no—
605C4×C8—474no—
606C4×C8C22×D4714yescomplemented
607C24—21no—
608C24—471no—
609C24—944no—
610C24—941no—
611C24—941no—
612C24—1884no—
613C24—1884no—
614C24—1884no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—472no—
619C2×Q8—472no—
620C2×Q8—944no—
621C2×Q8—941no—
622C2×Q8—941no—
623C2×Q8—942no—
624C2×Q8—942no—
625C2×Q8—942no—
626C2×Q8—942no—
627C2×Q8—1884no—
628C2×Q8—1884no—
629C2×Q8—1884no—
630C2×Q8—1888no—
631C2×Q8C23×D4712yes—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—472no—
636C2×D4—472no—
637C2×D4—944no—
638C2×D4—944no—
639C2×D4—941no—
640C2×D4—941no—
641C2×D4—942no—
642C2×D4—942no—
643C2×D4—942no—
644C2×D4—942no—
645C2×D4—1884no—
646C2×D4—1884no—
647C2×D4—1884no—
648C2×D4—1888no—
649C2×D4—1884no—
650C2×D4C23×D4712yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—471no—
655C22×C4—471no—
656C22×C4—471no—
657C22×C4—474no—
658C22×C4—472no—
659C22×C4—472no—
660C22×C4—474no—
661C22×C4—944no—
662C22×C4—944no—
663C22×C4—944no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—941no—
667C22×C4—941no—
668C22×C4—1882no—
669C22×C4—1884no—
670C22×C4—1884no—
671C22×C4D4×D4711yescharacteristic
672C22×C4D4×D4711yescharacteristic
673C22×C4C23×D4711yescharacteristic
674Q16—1884no—
675Q16—1884no—
676SD16—1884no—
677SD16—1884no—
678SD16—1884no—
679SD16—1884no—
680D8—1884no—
681D8—1884no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—472no—
685C2×C8—472no—
686C2×C8—942no—
687C2×C8—942no—
688C2×C8C23×D4712yes—
689C2×C8C23×D4712yes—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—944no—
695C4⋊C4—944no—
696C4⋊C4C23×D4712yes—
697C4⋊C4C23×D4712yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4—944no—
710C22⋊C4—944no—
711C42—474no—
712C42—472no—
713C42—474no—
714C42—472no—
715C42—944no—
716C42D4×D4712yes—
717C42C23×D4712yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—474no—
723C23—472no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—37616no—
729C23—1888no—
730C23—1888no—
731C23—1888no—
732C23—1882no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23—1882no—
737C23—1882no—
738C23C2×D4×D4711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—942no—
743Q8—942no—
744Q8—942no—
745Q8—942no—
746Q8—1888no—
747Q8—1882no—
748Q8—1882no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—942no—
753D4—942no—
754D4—942no—
755D4—942no—
756D4—1888no—
757D4—1888no—
758D4—1882no—
759D4—1882no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—472no—
769C2×C4—472no—
770C2×C4—472no—
771C2×C4—948no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—944no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—1884no—
781C2×C4—1888no—
782C2×C4—1888no—
783C2×C4—1882no—
784C2×C4—1882no—
785C2×C4C2×D4×D4712yes—
786C2×C4C2×D4×D4712yes—
787C2×C4C2×D4×D4711yescharacteristic
788C2×C4#1309407012yes—
789C2×C4#1309407012yes—
790C2×C4C24×D4711yescharacteristic
791C8—22no—
792C8—22no—
793C8—942no—
794C8—942no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—474no—
800C22—942no—
801C22—948no—
802C22—942no—
803C22—37616no—
804C22—3764no—
805C22—3764no—
806C22—1882no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—1882no—
812C22#1568969112yes—
813C22#135×D4712yes—
814C22#1568992012yes—
815C22C22×D4×D4711yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—942no—
822C4—942no—
823C4—942no—
824C4—1882no—
825C4—1882no—
826C4#1568969112yes—
827C4C2×#1309407011yescharacteristic
828C4C2×#1309407011yescharacteristic
829C2—82no—
830C2—944no—
831C2—3762no—
832C2—3762no—
833C2#2025435414yesdirect product factor
834C2C2×#1568969111yescharacteristic
835C2C2×#135×D4711yescharacteristic
836C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#488C2
socleC23×C47C22×D4
prime radicalC2×#15689258C2
hypercenterC2×#488D47
hypocenterC47C2×#3211
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#15689658C2semidirect
2. C2×#124×D47C2semidirect
3. #20254354C2direct (N × H)
4. C2×#15689507C2semidirect
5. C2×#15689505C2semidirect
6. C2×#15689480C2semidirect
7. C2×#15689348C2semidirect
8. C2×#15689344C2semidirect
9. C2×#15689341C2semidirect
10. C2×#15689337C2semidirect
11. C2×#15689280C2semidirect
12. C2×#15689263C2semidirect
13. C2×#15689275C2semidirect
15. C2×#15689174C2semidirect
16. C2×C47×#488C2semidirect
19. C22×Dic188C22semidirect
20. C22×#10625337C22semidirect
22. C22×#10625325C22semidirect
24. C22×#10625336C22semidirect
28. #15689658C22semidirect
32. C2×#13094012C22semidirect
37. #124×D47C22semidirect
41. C2×#13093989C22semidirect
43. C2×#13093986C22semidirect
48. #15689507C22semidirect
49. #15689505C22semidirect
50. #15689480C22semidirect
51. #15689348C22semidirect
52. #15689344C22semidirect
53. #15689341C22semidirect
54. #15689337C22semidirect
55. #15689280C22semidirect
56. #15689275C22semidirect
57. #15689263C22semidirect
59. #15689174C22semidirect
60. C2×Dic47⋊C8C22semidirect
61. C2×Dic47⋊C8C22semidirect
62. C2×#13093947C22semidirect
63. C2×#13093947C22semidirect
68. C2×C4×C47⋊C8C22semidirect
69. C2×#125×C47C22semidirect
71. C47×#488C22semidirect
72. C2×#103×C47C22semidirect
73. C2×#103×C47C22semidirect
76. C2×C4×C8×C47C22semidirect
99. C2×Dic188C23semidirect
101. C2×#10625337C23semidirect
105. C2×#10625325C23semidirect
109. C2×#10625336C23semidirect
122. #13094012C23semidirect
133. #13093989C23semidirect
136. #13093986C23semidirect
159. Dic47⋊C8C23semidirect
160. Dic47⋊C8C23semidirect
161. #13093947C23semidirect
162. #13093947C23semidirect
167. C4×C47⋊C8C23semidirect
173. #125×C47C23semidirect
183. #103×C47C23semidirect
184. #103×C47C23semidirect
187. C4×C8×C47C23semidirect
417. C2×#488D47semidirect
428. C2×C47#3211semidirect
448. C2×#125C2×D47semidirect
471. #488C2×D47semidirect
485. C2×#103C2×D47semidirect
486. C2×#103C2×D47semidirect
494. C2×C4×C8C2×D47semidirect
495. C47C2×#3211semidirect
541. #125C22×D47semidirect
597. #103C22×D47semidirect
598. #103C22×D47semidirect
606. C4×C8C22×D47semidirect
833. C2#20254354direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896582
C2×#124×D472
#202543542
C2×#156895072
C2×#156895052
C2×#156894802
C2×#156893482
C2×#156893442
C2×#156893412
C2×#156893372
C2×#156892802
C2×#156892632
C2×#156892752
C2×#156892582
C2×#156891742
C2×C47×#4882
C2×#321147