Finite Group Databasebeta

← C2×#20255422 #27092946

Subgroups — C2×#20255422 #27092946

Order 12032.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689841C211yesmaximal, characteristic, complemented
2C2×#15689770C211yesmaximal, characteristic
3#20255422C2116yesmaximal, direct product factor
4C2×#15689481C211yesmaximal, characteristic, complemented
5C2×#15689466C211yesmaximal, characteristic, complemented
6C2×#15689412C211yesmaximal, characteristic, complemented
7C2×#15689382C211yesmaximal, characteristic, complemented
8C2×#15689350C211yesmaximal, characteristic, complemented
9C2×#15689344C211yesmaximal, characteristic, complemented
10C2×#15689287C211yesmaximal, characteristic, complemented
11C2×#15689275C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689191C211yesmaximal, characteristic, complemented
14C2×#15689126C211yesmaximal, characteristic, complemented
15C2×#15689117C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×Dic188C2211yescharacteristic, complemented
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×#10625324C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic, complemented
24#15689841—24no—
25#15689841C2218yescomplemented
26#15689770—24no—
27#15689770C2218yes—
28C2×#13094023C2211yescharacteristic, complemented
29C2×#13094018—21no—
30C2×#13094017—21no—
31C2×#13094011C2211yescharacteristic
32C2×#13094010—21no—
33C2×#13094006—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094004C2211yescharacteristic
36C2×#13094003C2211yescharacteristic, complemented
37C2×#13093995—21no—
38C2×#13093992—21no—
39C2×C4×Dic94—21no—
40C2×#13093989C2211yescharacteristic, complemented
41C2×#13093986C2211yescharacteristic
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44C2×C22⋊C4×D47—21no—
45#15689481C2218yescomplemented
46#15689466C2218yescomplemented
47#15689412C2218yescomplemented
48#15689382C2218yescomplemented
49#15689350C2218yescomplemented
50#15689344C2218yescomplemented
51#15689287C2218yescomplemented
52#15689275C2218yescomplemented
53#15689222C2218yescomplemented
54#15689191C2218yescomplemented
55C2×#13093955C2211yescharacteristic, complemented
56C2×Dic47⋊C8C2211yescharacteristic, complemented
57#15689126C2218yescomplemented
58#15689117C2218yescomplemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic, complemented
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic, complemented
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—24no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47D411yescharacteristic
89C2×D4×D47—24no—
90C2×D4×D47—22no—
91C2×D4×D47—42no—
92C2×D4×D47C2314yes—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96C2×Dic188—42no—
97C2×Dic188C2314yescomplemented
98C2×#10625325—24no—
99C2×#10625325C2314yes—
100C2×#10625335—42no—
101C2×#10625335C2314yes—
102C2×#10625324—42no—
103C2×#10625324C2314yes—
104C22×C47⋊C8—42no—
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2314yescomplemented
108#13094023—22no—
109#13094023C2314yescomplemented
110#13094018—28no—
111#13094017—28no—
112#13094011—22no—
113#13094011C2314yes—
114#13094010—28no—
115#13094006—28no—
116#13094004—22no—
117#13094004—22no—
118#13094004C2314yes—
119#13094004C2314yes—
120#13094003—22no—
121#13094003C2314yescomplemented
122#13093995—28no—
123#13093992—28no—
124C4×Dic94—28no—
125#13093989—22no—
126#13093989C2314yescomplemented
127#13093986—22no—
128#13093986C2314yes—
129C4×C22⋊D47D414yes—
130C4×C22⋊D47C2314yes—
131#13093982—22no—
132#13093982C2314yes—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4D411yescharacteristic
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
142C2×C22⋊Dic47—21no—
143C2×C22⋊Dic47D411yescharacteristic
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4D411yescharacteristic
149C22⋊C4×D47—28no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47C2311yescharacteristic
153#13093955C2314yescomplemented
154Dic47⋊C8C2314yescomplemented
155#13093949C2314yescomplemented
156#13093947C2314yescomplemented
157#13093947C2314yescomplemented
158#13093947C2314yescomplemented
159#13093946C2314yes—
160#13093945C2314yes—
161#13093944C2314yes—
162#13093944C2314yes—
163(C2×D47)⋊C8C2314yes—
164#13093934C2314yescomplemented
165C22×D4×C47—21no—
166C22×D4×C47C2311yescharacteristic
167C23×C4×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170#121×C47—22no—
171#121×C47C2314yes—
172#117×C47—22no—
173#117×C47C2314yescomplemented
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C42×C47—21no—
180#107×C47C2314yescomplemented
181#106×C47C2314yescomplemented
182#102×C47C2314yes—
183#102×C47C2314yes—
184C22⋊C8×C47C2314yescomplemented
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—24no—
189C23×D47—44no—
190C23×D47—44no—
191C23×D47—82no—
192C23×D47C2×D411yescharacteristic
193C2×D4×C47—24no—
194C2×D4×C47—21no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—82no—
198C2×D4×C47C2412yes—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2411yescharacteristic
208C2×C22⋊D47—24no—
209C2×C22⋊D47—24no—
210C2×C22⋊D47—42no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—44no—
213C2×C22⋊D47C2×D414yes—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220D4×D47—28no—
221D4×D47—44no—
222D4×D47—48no—
223#10625350—28no—
224#10625350—44no—
225#10625350—48no—
226C2×D188—21no—
227C2×D188—22no—
228C2×D188#4114yes—
229C2×D188C2412yes—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—44no—
235C2×C4×D47—82no—
236C2×C4×D47C2×D412yes—
237C2×C4×D47C2412yes—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—22no—
241C2×Dic94—22no—
242C2×Dic94—21no—
243C2×Dic94—21no—
244C2×Dic94—24no—
245C2×Dic94—44no—
246C2×Dic94C2412yes—
247C2×Dic94C2412yes—
248C2×C8×C47—22no—
249C2×C8×C47—22no—
250C2×C8×C47C2412yes—
251C2×C8×C47C2412yes—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C42×C47—24no—
261C22⋊Dic47—24no—
262C22⋊Dic47—24no—
263C22⋊Dic47—24no—
264C22⋊Dic47C2×D414yes—
265#10625335—44no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4C2×D414yes—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47—24no—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4C2×D414yes—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47C2×D412yes—
282C4×Dic47C2412yes—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—44no—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288Dic188—44no—
289#10625325—28no—
290#10625324—44no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47C22×D412yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—22no—
301C22×D47—24no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—48no—
306C22×D47—48no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47—84no—
310C22×D47—816no—
311C22×D47C22×D412yes—
312D4×C47—22no—
313D4×C47—22no—
314D4×C47—42no—
315D4×C47—84no—
316C2×C4×C47—22no—
317C2×C4×C47—24no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47C22×D412yes—
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C2×#4112yes—
329C2×C4×C47H(5,𝔽2)12yes—
330C2×C4×C47C2511yescharacteristic
331C22⋊D47—44no—
332C22⋊D47—48no—
333C22⋊D47—48no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47C22×D412yes—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346D188—24no—
347D188—22no—
348D188C2×#4114yes—
349C4×D47—24no—
350C4×D47—22no—
351C4×D47—22no—
352C4×D47—48no—
353C4×D47—84no—
354Dic94—22no—
355Dic94—22no—
356Dic94—22no—
357Dic94—22no—
358Dic94—48no—
359Dic94—42no—
360Dic94—42no—
361C8×C47—22no—
362C8×C47—22no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C2×#3311—471nomaximal, Sylow
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—44no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—84no—
374C22×C47#54612yes—
375C22×C47#57512yes—
376C22×C47#57712yes—
377C22×C47C23×D411yescharacteristic
378C2×D47—22no—
379C2×D47—24no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—44no—
383C2×D47—48no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—816no—
387C4×C47—22no—
388C4×C47—42no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47#54612yes—
392C4×C47C22×#4111yescharacteristic
393C4×C47C2×H(5,𝔽2)11yescharacteristic
394Dic47—22no—
395Dic47—22no—
396Dic47—22no—
397Dic47—42no—
398Dic47—42no—
399Dic47—42no—
400C2×#556—471no—
401C2×#546—471no—
402#3311—4716no—
403C2×#489—471no—
404C2×#485—471no—
405C2×#482D4711yescharacteristic, complemented
406C2×#476—471no—
407C2×#470—471no—
408C2×#465—471no—
409C2×#464—471no—
410C2×#452—471no—
411C2×#450—471no—
412C2×#440—471no—
413C2×#435—471no—
414C2×#418—471no—
415C2×#416—471no—
416C2×C47—42no—
417C2×C47—82no—
418C2×C47#331114yescomplemented
419C2×C47C2×#54611yescharacteristic
420C2×C47C2×#57511yescharacteristic
421C2×C47C2×#57711yescharacteristic
422D47—42no—
423D47—44no—
424C22×#41—471no—
425C23×D4—471no—
426C22×Q16—471no—
427C22×SD16—471no—
428C22×SD16—471no—
429C22×M16—471no—
430C23×C8—471no—
431#556—478no—
432#556—944no—
433#546—478no—
434#546—944no—
435C2×C4⋊Q8—471no—
436C2×#126—941no—
437C2×#126—941no—
438C2×#124—471no—
439C2×#124—941no—
440C2×#123—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—471no—
443C2×C22⋊Q8—471no—
444C2×#121—941no—
445C2×#121C2×D4711yescharacteristic
446C2×#120—941no—
447C2×C4×Q8—471no—
448C2×C4×Q8—941no—
449C2×C4×D4—471no—
450C2×C4×D4—471no—
451C2×#117—471no—
452C2×#117C2×D4711yescharacteristic, complemented
453C22×C22⋊C4—941no—
454#489—478no—
455#485—478no—
456#482C2×D4718yescomplemented
457#476—478no—
458#470—478no—
459#465—478no—
460#464—478no—
461#452—478no—
462#450—478no—
463#440—478no—
464#435—478no—
465C2×#107C2×D4711yescharacteristic, complemented
466C2×#106—471no—
467C2×#106C2×D4711yescharacteristic, complemented
468C2×C4⋊C8—471no—
469#418—478no—
470#416—478no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102C2×D4711yescharacteristic
480C2×#102C2×D4711yescharacteristic
481C2×C22⋊C8—471no—
482C2×C22⋊C8C2×D4711yescharacteristic, complemented
483C2×#97—471no—
484C47C2×#331111yescharacteristic, complemented, Sylow
485C25—941no—
486C2×#41—474no—
487C2×#41—944no—
488C2×#41—942no—
489C2×#41—1882no—
490C22×Q8—471no—
491C22×Q8—471no—
492C22×Q8—941no—
493C22×D4—21no—
494C22×D4—471no—
495C22×D4—474no—
496C22×D4—471no—
497C22×D4—942no—
498C22×D4—941no—
499C22×D4—944no—
500C22×D4—941no—
501C22×D4—1882no—
502C22×D4C22×D4711yescharacteristic
503C23×C4—471no—
504C23×C4—941no—
505C23×C4—941no—
506C23×C4C22×D4711yescharacteristic
507C2×Q16—474no—
508C2×Q16—1882no—
509C2×SD16—474no—
510C2×SD16—474no—
511C2×SD16—944no—
512C2×SD16—1882no—
513C2×M16—474no—
514C2×M16—1882no—
515C22×C8—471no—
516C22×C8—471no—
517C22×C8—474no—
518C22×C8—1882no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521C4⋊Q8—474no—
522C4⋊Q8—942no—
523#126—948no—
524#126—948no—
525#124—474no—
526#124—942no—
527#124—948no—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—474no—
532C22⋊Q8—942no—
533C22⋊Q8—942no—
534C22⋊Q8—942no—
535#121—22no—
536#121—948no—
537#121C22×D4714yes—
538#120—948no—
539C4×Q8—474no—
540C4×Q8—948no—
541C4×Q8—942no—
542C4×D4—474no—
543C4×D4—474no—
544C4×D4—474no—
545C4×D4—942no—
546#117—22no—
547#117—474no—
548#117—942no—
549#117C22×D4714yescomplemented
550C2×C4⋊C4—471no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4—941no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4C22×D4711yescharacteristic
558C2×C4⋊C4C22×D4711yescharacteristic
559C2×C4⋊C4C22×D4711yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—471no—
563C2×C22⋊C4—471no—
564C2×C22⋊C4—948no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C42—21no—
573C2×C42—471no—
574C2×C42—941no—
575C2×C42—941no—
576#107C22×D4714yescomplemented
577#106—474no—
578#106C22×D4714yescomplemented
579C4⋊C8—474no—
580#103—474no—
581#103—474no—
582#103—474no—
583#103—474no—
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588#102C22×D4714yes—
589#102C22×D4714yes—
590C22⋊C8—474no—
591C22⋊C8C22×D4714yescomplemented
592#97—474no—
593C24—21no—
594C24—471no—
595C24—944no—
596C24—941no—
597C24—3762no—
598C24—1884no—
599C24—1884no—
600C24D4×D4711yescharacteristic
601#41—948no—
602#41—1884no—
603#41—1888no—
604C2×Q8—472no—
605C2×Q8—472no—
606C2×Q8—944no—
607C2×Q8—941no—
608C2×Q8—941no—
609C2×Q8—942no—
610C2×Q8—942no—
611C2×Q8—942no—
612C2×Q8—942no—
613C2×Q8—1884no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—82no—
619C2×D4—474no—
620C2×D4—474no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—948no—
624C2×D4—944no—
625C2×D4—941no—
626C2×D4—942no—
627C2×D4—1884no—
628C2×D4—1888no—
629C2×D4—1882no—
630C2×D4—1884no—
631C2×D4—1884no—
632C2×D4C23×D4712yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—471no—
639C22×C4—471no—
640C22×C4—471no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—944no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—941no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—944no—
650C22×C4—3762no—
651C22×C4—1884no—
652C22×C4D4×D4712yes—
653C22×C4D4×D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656Q16—1884no—
657SD16—948no—
658SD16—1884no—
659M16—1884no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8—1884no—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—474no—
673C4⋊C4—472no—
674C4⋊C4—944no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—941no—
680C4⋊C4C23×D4712yes—
681C4⋊C4C23×D4712yes—
682C4⋊C4C23×D4712yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—474no—
686C22⋊C4—474no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C42—24no—
695C42—472no—
696C42—472no—
697C42—944no—
698C42—944no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—472no—
707C23—942no—
708C23—944no—
709C23—942no—
710C23—942no—
711C23—942no—
712C23—3764no—
713C23—37616no—
714C23—1888no—
715C23—1888no—
716C23—1882no—
717C23—1882no—
718C23C2×D4×D4712yes—
719C23C2×D4×D4711yescharacteristic
720Q8—942no—
721Q8—942no—
722Q8—942no—
723Q8—942no—
724Q8—1888no—
725Q8—1882no—
726Q8—1882no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—474no—
732D4—944no—
733D4—942no—
734D4—1884no—
735D4—1888no—
736D4—1888no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—472no—
748C2×C4—472no—
749C2×C4—472no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—944no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—3764no—
760C2×C4—1888no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4C2×D4×D4712yes—
765C2×C4C2×D4×D4711yescharacteristic
766C2×C4#41×D4712yes—
767C2×C4#1309407012yes—
768C2×C4C24×D4711yescharacteristic
769C8—22no—
770C8—22no—
771C8—942no—
772C8—942no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—942no—
782C22—944no—
783C22—942no—
784C22—942no—
785C22—37616no—
786C22—1882no—
787C22—1882no—
788C22—1884no—
789C22—1888no—
790C22#1568976512yes—
791C22#1568992012yes—
792C22#1568993312yes—
793C22C22×D4×D4711yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—942no—
799C4—942no—
800C4—942no—
801C4—1882no—
802C4—1882no—
803C4—1882no—
804C4#1568976512yes—
805C4C2×#41×D4711yescharacteristic
806C4C2×#1309407011yescharacteristic
807C2—42no—
808C2—82no—
809C2—1882no—
810C2—1884no—
811C2#2025542214yesdirect product factor
812C2C2×#1568976511yescharacteristic
813C2C2×#1568992011yescharacteristic
814C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
prime radicalC2×#15689770C2
hypercenterC2×#482D47
hypocenterC47C2×#3311
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×#15689841C2semidirect
3. #20255422C2direct (N × H)
4. C2×#15689481C2semidirect
5. C2×#15689466C2semidirect
6. C2×#15689412C2semidirect
7. C2×#15689382C2semidirect
8. C2×#15689350C2semidirect
9. C2×#15689344C2semidirect
10. C2×#15689287C2semidirect
11. C2×#15689275C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689191C2semidirect
14. C2×#15689126C2semidirect
15. C2×#15689117C2semidirect
16. C2×C47×#482C2semidirect
19. C22×Dic188C22semidirect
23. C23×C47⋊C8C22semidirect
25. #15689841C22semidirect
28. C2×#13094023C22semidirect
36. C2×#13094003C22semidirect
40. C2×#13093989C22semidirect
45. #15689481C22semidirect
46. #15689466C22semidirect
47. #15689412C22semidirect
48. #15689382C22semidirect
49. #15689350C22semidirect
50. #15689344C22semidirect
51. #15689287C22semidirect
52. #15689275C22semidirect
53. #15689222C22semidirect
54. #15689191C22semidirect
55. C2×#13093955C22semidirect
56. C2×Dic47⋊C8C22semidirect
57. #15689126C22semidirect
58. #15689117C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093947C22semidirect
61. C2×#13093947C22semidirect
62. C2×#13093947C22semidirect
68. C2×#13093934C22semidirect
70. C2×#117×C47C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
97. C2×Dic188C23semidirect
107. C22×C47⋊C8C23semidirect
109. #13094023C23semidirect
121. #13094003C23semidirect
126. #13093989C23semidirect
153. #13093955C23semidirect
154. Dic47⋊C8C23semidirect
155. #13093949C23semidirect
156. #13093947C23semidirect
157. #13093947C23semidirect
158. #13093947C23semidirect
164. #13093934C23semidirect
173. #117×C47C23semidirect
180. #107×C47C23semidirect
181. #106×C47C23semidirect
184. C22⋊C8×C47C23semidirect
405. C2×#482D47semidirect
418. C2×C47#3311semidirect
452. C2×#117C2×D47semidirect
456. #482C2×D47semidirect
465. C2×#107C2×D47semidirect
467. C2×#106C2×D47semidirect
482. C2×C22⋊C8C2×D47semidirect
484. C47C2×#3311semidirect
549. #117C22×D47semidirect
576. #107C22×D47semidirect
578. #106C22×D47semidirect
591. C22⋊C8C22×D47semidirect
811. C2#20255422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898412
C2×#156897702
#202554222
C2×#156894812
C2×#156894662
C2×#156894122
C2×#156893822
C2×#156893502
C2×#156893442
C2×#156892872
C2×#156892752
C2×#156892222
C2×#156891912
C2×#156891262
C2×#156891172
C2×C47×#4822
C2×#331147