Finite Group Databasebeta

← C2×#20255609 #27093096

Subgroups — C2×#20255609 #27093096

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×#15689814C211yesmaximal, characteristic, complemented
2C2×#15689768C211yesmaximal, characteristic
3#20255609C2116yesmaximal, direct product factor
4C2×#15689478C211yesmaximal, characteristic, complemented
5C2×#15689443C211yesmaximal, characteristic, complemented
6C2×#15689467C211yesmaximal, characteristic, complemented
7C2×#15689423C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic, complemented
9C2×#15689372C211yesmaximal, characteristic, complemented
10C2×#15689345C211yesmaximal, characteristic, complemented
11C2×#15689282C211yesmaximal, characteristic, complemented
12C2×#15689272C211yesmaximal, characteristic, complemented
13C2×#15689202C211yesmaximal, characteristic, complemented
14C2×#15689121C211yesmaximal, characteristic, complemented
15C2×#15689126C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625337C2211yescharacteristic, complemented
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×#10625324C2211yescharacteristic, complemented
23#15689814—24no—
24#15689814C2218yescomplemented
25#15689768—24no—
26#15689768C2218yes—
27C2×#13094018—21no—
28C2×#13094016C2211yescharacteristic, complemented
29C2×#13094014—21no—
30C2×#13094012C2211yescharacteristic
31C2×#13094009—21no—
32C2×#13094008—21no—
33C2×#13094004C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×#13094000C2211yescharacteristic, complemented
36C2×#13093999C2211yescharacteristic
37C2×#13093998—21no—
38C2×#13093994—21no—
39C2×C4×D188C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093981—21no—
42C2×C4⋊C4×D47C2211yescharacteristic, complemented
43C22×(C2×D47)⋊C4—21no—
44#15689478C2218yescomplemented
45#15689467C2218yescomplemented
46#15689443C2218yescomplemented
47#15689423C2218yescomplemented
48#15689380C2218yescomplemented
49#15689372C2218yescomplemented
50#15689345C2218yescomplemented
51#15689282C2218yescomplemented
52#15689272C2218yescomplemented
53#15689202C2218yescomplemented
54C2×#13093957C2211yescharacteristic, complemented
55C2×#13093955C2211yescharacteristic, complemented
56C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
57#15689126C2218yescomplemented
58#15689121C2218yescomplemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic, complemented
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625352—24no—
79C2×#10625352—22no—
80C2×#10625352—42no—
81C2×#10625352C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×D188—21no—
84C22×D188D411yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C2×D4×D47—24no—
89C2×D4×D47—22no—
90C2×D4×D47—42no—
91C2×D4×D47C2314yes—
92C23×Dic47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C2×#10625337—42no—
97C2×#10625337C2314yescomplemented
98C2×#10625336—42no—
99C2×#10625336C2314yes—
100C2×#10625324—42no—
101C2×#10625324—42no—
102C2×#10625324C2314yes—
103C2×#10625324C2314yescomplemented
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106#13094018—28no—
107#13094016—22no—
108#13094016C2314yescomplemented
109#13094014—28no—
110#13094012—22no—
111#13094012C2314yes—
112#13094009—28no—
113#13094008—28no—
114#13094004—22no—
115#13094004C2314yes—
116#13094000—22no—
117#13094000—22no—
118#13094000C2314yes—
119#13094000C2314yescomplemented
120#13093999—22no—
121#13093999C2314yes—
122#13093998—28no—
123#13093994—28no—
124C4×D188D414yes—
125C4×D188C2314yes—
126#13093982—22no—
127#13093982C2314yes—
128#13093981—28no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47D411yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C4⋊C4×D47—22no—
139C4⋊C4×D47C2314yescomplemented
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—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—28no—
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×(C2×D47)⋊C4D411yescharacteristic
150C2×C4×Dic47—21no—
151#13093957C2314yescomplemented
152#13093955C2314yescomplemented
153C4⋊(C47⋊C8)C2314yescomplemented
154#13093949C2314yescomplemented
155#13093949C2314yescomplemented
156#13093947C2314yescomplemented
157#13093946C2314yes—
158#13093946C2314yes—
159#13093945C2314yes—
160#13093945C2314yes—
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yescomplemented
164C22×Q8×C47C2311yescharacteristic
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C2×SD16×C47—24no—
168C2×SD16×C47C2314yes—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yescomplemented
173C4×D4×C47—22no—
174C4×D4×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#106×C47C2314yescomplemented
182#103×C47C2314yescomplemented
183#102×C47C2314yes—
184C4×C8×C47C2314yescomplemented
185C24×C47—21no—
186C23×D47—21no—
187C23×D47—24no—
188C23×D47—44no—
189C23×D47—44no—
190C23×D47—82no—
191C23×D47C2×D411yescharacteristic
192C23×D47C2×D411yescharacteristic
193C2×Q8×C47—21no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47C2412yes—
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47#4114yes—
200C2×D4×C47C2412yes—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—82no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2411yescharacteristic
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—44no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—44no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220#10625352—28no—
221#10625352—44no—
222#10625352—48no—
223D4×D47—28no—
224D4×D47—44no—
225D4×D47—48no—
226C2×D188—22no—
227C2×D188—22no—
228C2×D188—21no—
229C2×D188—24no—
230C2×D188—42no—
231C2×D188—82no—
232C2×D188C2×D414yes—
233C2×D188C2412yes—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—24no—
239C2×C4×D47—44no—
240C2×C4×D47C2×D412yes—
241C2×C4×D47C2×D412yes—
242C2×C4×D47C2412yes—
243C2×C4×D47C2412yes—
244C2×Dic94—22no—
245C2×Dic94—22no—
246C2×Dic94—21no—
247C2×Dic94C2412yes—
248SD16×C47—28no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47C2412yes—
252C2×C8×C47C2412yes—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C42×C47—24no—
260C42×C47C2×D412yes—
261C42×C47C2412yes—
262#10625337—44no—
263#10625336—44no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4C2×D414yes—
272(C2×D47)⋊C4C2×D414yes—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—24no—
276C4⋊Dic47C2×D414yes—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284C4×Dic47—24no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625324—44no—
290#10625324—44no—
291C23×C47—24no—
292C23×C47—22no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D411yescharacteristic
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—48no—
304C22×D47—48no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—84no—
309C22×D47—816no—
310C22×D47C22×D412yes—
311C22×D47C22×D412yes—
312Q8×C47—22no—
313Q8×C47—22no—
314Q8×C47—42no—
315D4×C47—24no—
316D4×C47—22no—
317D4×C47C2×#4114yes—
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×C47—84no—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D412yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4112yes—
331C2×C4×C47H(5,𝔽2)12yes—
332C2×C4×C47C2511yescharacteristic
333C22⋊D47—48no—
334C22⋊D47—48no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—48no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346D188—22no—
347D188—22no—
348D188—44no—
349D188—42no—
350D188—84no—
351C4×D47—24no—
352C4×D47—24no—
353C4×D47—22no—
354C4×D47—22no—
355C4×D47—22no—
356C4×D47—22no—
357C4×D47—48no—
358Dic94—22no—
359Dic94—22no—
360Dic94—42no—
361C8×C47—22no—
362C8×C47—22no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C2×#3323—471nomaximal, Sylow
366C22×C47—24no—
367C22×C47—48no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47#54612yes—
371C22×C47#57512yes—
372C22×C47#57712yes—
373C22×C47C23×D411yescharacteristic
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—22no—
377C2×D47—22no—
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—44no—
381C2×D47—44no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—816no—
386C2×D47—84no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47#54612yes—
393C4×C47C22×#4111yescharacteristic
394C4×C47C2×H(5,𝔽2)11yescharacteristic
395Dic47—22no—
396Dic47—22no—
397Dic47—42no—
398Dic47—42no—
399Dic47—42no—
400C2×#552—471no—
401C2×#546—471no—
402#3323—4716no—
403C2×#488—471no—
404C2×#481—471no—
405C2×#485—471no—
406C2×#478—471no—
407C2×#470—471no—
408C2×#468—471no—
409C2×#464—471no—
410C2×#452—471no—
411C2×#450—471no—
412C2×C4×SD16D4711yescharacteristic, complemented
413C2×#436—471no—
414C2×#417—471no—
415C2×#418—471no—
416C2×C47—44no—
417C2×C47#332314yescomplemented
418C2×C47C2×#54611yescharacteristic
419C2×C47C2×#57511yescharacteristic
420C2×C47C2×#57711yescharacteristic
421D47—42no—
422D47—42no—
423D47—82no—
424C22×#41—471no—
425C23×D4—471no—
426C22×Q16—471no—
427C22×SD16—471no—
428C22×SD16C2×D4711yescharacteristic
429C22×M16—471no—
430C22×M16—471no—
431#552—478no—
432#552—944no—
433#546—478no—
434#546—944no—
435C2×#126—941no—
436C2×#125—471no—
437C2×#125—941no—
438C2×#124—471no—
439C2×#123—941no—
440C2×#123—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—471no—
443C2×C22⋊Q8—471no—
444C2×#121—471no—
445C2×#121—941no—
446C2×#120—941no—
447C2×C4×Q8C2×D4711yescharacteristic, complemented
448C2×C4×D4—471no—
449C2×C4×D4C2×D4711yescharacteristic
450C2×#117—471no—
451C2×#117—941no—
452C22×C4⋊C4—471no—
453C22×C22⋊C4—941no—
454#488—478no—
455#485—478no—
456#481—478no—
457#478—478no—
458#470—478no—
459#468—478no—
460#464—478no—
461#452—478no—
462#450—478no—
463C4×SD16C2×D4718yescomplemented
464#436—478no—
465C2×#107—471no—
466C2×#106—471no—
467C2×#106C2×D4711yescharacteristic, complemented
468C2×C4⋊C8—471no—
469#418—478no—
470#417—478no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103C2×D4711yescharacteristic, complemented
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102C2×D4711yescharacteristic
481C2×C22⋊C8—471no—
482C2×C22⋊C8—471no—
483C2×C4×C8C2×D4711yescharacteristic, complemented
484C47C2×#332311yescharacteristic, complemented, Sylow
485C25—941no—
486C2×#41—474no—
487C2×#41—942no—
488C2×#41—944no—
489C2×#41—1882no—
490C22×Q8—471no—
491C22×Q8C22×D4711yescharacteristic
492C22×D4—474no—
493C22×D4—471no—
494C22×D4—471no—
495C22×D4—941no—
496C22×D4—942no—
497C22×D4—941no—
498C22×D4—944no—
499C22×D4—941no—
500C22×D4—1882no—
501C22×D4C22×D4711yescharacteristic
502C23×C4—21no—
503C23×C4—471no—
504C23×C4—471no—
505C23×C4—941no—
506C23×C4—941no—
507C2×Q16—474no—
508C2×Q16—1882no—
509C2×SD16—24no—
510C2×SD16—474no—
511C2×SD16—1882no—
512C2×SD16C22×D4714yes—
513C2×M16—474no—
514C2×M16—474no—
515C2×M16—1882no—
516C2×M16—1882no—
517C22×C8—471no—
518C22×C8—471no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521#126—948no—
522#125—474no—
523#125—948no—
524#125—942no—
525#124—474no—
526#124—942no—
527#123—948no—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—474no—
532C22⋊Q8—942no—
533C22⋊Q8—942no—
534C22⋊Q8—942no—
535#121—474no—
536#121—948no—
537#121—942no—
538#120—948no—
539C4×Q8—22no—
540C4×Q8C22×D4714yescomplemented
541C4×D4—22no—
542C4×D4—474no—
543C4×D4—474no—
544C4×D4C22×D4714yes—
545#117—474no—
546#117—948no—
547#117—942no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—471no—
550C2×C4⋊C4—471no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—474no—
553C2×C4⋊C4—942no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C4⋊C4C22×D4711yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—471no—
564C2×C22⋊C4—471no—
565C2×C22⋊C4—948no—
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×C22⋊C4—941no—
573C2×C42—21no—
574C2×C42—941no—
575C2×C42C22×D4711yescharacteristic
576#107—474no—
577#106—474no—
578#106C22×D4714yescomplemented
579C4⋊C8—474no—
580#103—474no—
581#103—474no—
582#103—474no—
583#103C22×D4714yescomplemented
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588#102—474no—
589#102C22×D4714yes—
590C22⋊C8—474no—
591C22⋊C8—474no—
592C4×C8C22×D4714yescomplemented
593C24—21no—
594C24—471no—
595C24—471no—
596C24—944no—
597C24—941no—
598C24—3762no—
599C24—1884no—
600C24—1884no—
601#41—948no—
602#41—1884no—
603#41—1888no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—472no—
608C2×Q8—941no—
609C2×Q8—942no—
610C2×Q8—942no—
611C2×Q8C23×D4712yes—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—474no—
615C2×D4—472no—
616C2×D4—944no—
617C2×D4—944no—
618C2×D4—948no—
619C2×D4—944no—
620C2×D4—941no—
621C2×D4—942no—
622C2×D4—942no—
623C2×D4—3762no—
624C2×D4—1882no—
625C2×D4—1884no—
626C2×D4—1888no—
627C2×D4—1884no—
628C2×D4—1884no—
629C2×D4#1062535014yes—
630C2×D4C23×D4712yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—82no—
636C22×C4—471no—
637C22×C4—471no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—472no—
642C22×C4—944no—
643C22×C4—944no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—1884no—
652C22×C4—1884no—
653C22×C4D4×D4711yescharacteristic
654C22×C4D4×D4711yescharacteristic
655C22×C4C23×D4711yescharacteristic
656Q16—1884no—
657SD16—28no—
658SD16—1884no—
659M16—1884no—
660M16—1884no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—472no—
664C2×C8—472no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—474no—
673C4⋊C4—472no—
674C4⋊C4—472no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4—941no—
682C4⋊C4—941no—
683C4⋊C4C23×D4712yes—
684C4⋊C4C23×D4712yes—
685C22⋊C4—24no—
686C22⋊C4—474no—
687C22⋊C4—474no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C22⋊C4—944no—
695C42—24no—
696C42—944no—
697C42D4×D4712yes—
698C42C23×D4712yes—
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—472no—
704C23—472no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23—942no—
709C23—942no—
710C23—942no—
711C23—942no—
712C23—3764no—
713C23—37616no—
714C23—1888no—
715C23—1888no—
716C23—1882no—
717C23—1882no—
718C23—1882no—
719C23C2×D4×D4711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—942no—
724Q8—942no—
725Q8—1882no—
726D4—24no—
727D4—22no—
728D4—942no—
729D4—942no—
730D4—3764no—
731D4—1884no—
732D4—1888no—
733D4—1888no—
734D4—1882no—
735D4C2×#1062535014yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—472no—
746C2×C4—472no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—944no—
750C2×C4—944no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—1888no—
759C2×C4—1888no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4C2×D4×D4712yes—
764C2×C4C2×D4×D4712yes—
765C2×C4C2×D4×D4711yescharacteristic
766C2×C4C2×#1062535012yes—
767C2×C4#1309407012yes—
768C2×C4C24×D4711yescharacteristic
769C8—22no—
770C8—22no—
771C8—942no—
772C8—942no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—942no—
778C22—942no—
779C22—942no—
780C22—942no—
781C22—942no—
782C22—942no—
783C22—37616no—
784C22—3764no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1884no—
789C22—1884no—
790C22#1568976912yes—
791C22#1568992012yes—
792C22#1568992912yes—
793C22C22×D4×D4711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—942no—
800C4—942no—
801C4—1882no—
802C4—1882no—
803C4—1882no—
804C4#1568976912yes—
805C4C22×#1062535011yescharacteristic
806C4C2×#1309407011yescharacteristic
807C2—44no—
808C2—3762no—
809C2—1882no—
810C2—1882no—
811C2#2025560914yesdirect product factor
812C2C2×#1568976911yescharacteristic
813C2C2×#1568992011yescharacteristic
814C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689768C2
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15689814C2semidirect
3. #20255609C2direct (N × H)
4. C2×#15689478C2semidirect
5. C2×#15689443C2semidirect
6. C2×#15689467C2semidirect
7. C2×#15689423C2semidirect
8. C2×#15689380C2semidirect
9. C2×#15689372C2semidirect
10. C2×#15689345C2semidirect
11. C2×#15689282C2semidirect
12. C2×#15689272C2semidirect
13. C2×#15689202C2semidirect
14. C2×#15689121C2semidirect
15. C2×#15689126C2semidirect
16. C2×C4×SD16×C47C2semidirect
19. C22×#10625337C22semidirect
22. C22×#10625324C22semidirect
24. #15689814C22semidirect
28. C2×#13094016C22semidirect
35. C2×#13094000C22semidirect
42. C2×C4⋊C4×D47C22semidirect
44. #15689478C22semidirect
45. #15689467C22semidirect
46. #15689443C22semidirect
47. #15689423C22semidirect
48. #15689380C22semidirect
49. #15689372C22semidirect
50. #15689345C22semidirect
51. #15689282C22semidirect
52. #15689272C22semidirect
53. #15689202C22semidirect
54. C2×#13093957C22semidirect
55. C2×#13093955C22semidirect
56. C2×C4⋊(C47⋊C8)C22semidirect
57. #15689126C22semidirect
58. #15689121C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093947C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C2×C4×Q8×C47C22semidirect
72. C4×SD16×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#103×C47C22semidirect
76. C2×C4×C8×C47C22semidirect
97. C2×#10625337C23semidirect
103. C2×#10625324C23semidirect
108. #13094016C23semidirect
119. #13094000C23semidirect
139. C4⋊C4×D47C23semidirect
151. #13093957C23semidirect
152. #13093955C23semidirect
153. C4⋊(C47⋊C8)C23semidirect
154. #13093949C23semidirect
155. #13093949C23semidirect
156. #13093947C23semidirect
163. (C2×D47)⋊C8C23semidirect
172. C4×Q8×C47C23semidirect
181. #106×C47C23semidirect
182. #103×C47C23semidirect
184. C4×C8×C47C23semidirect
412. C2×C4×SD16D47semidirect
417. C2×C47#3323semidirect
447. C2×C4×Q8C2×D47semidirect
463. C4×SD16C2×D47semidirect
467. C2×#106C2×D47semidirect
474. C2×#103C2×D47semidirect
483. C2×C4×C8C2×D47semidirect
484. C47C2×#3323semidirect
540. C4×Q8C22×D47semidirect
578. #106C22×D47semidirect
583. #103C22×D47semidirect
592. C4×C8C22×D47semidirect
811. C2#20255609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898142
C2×#156897682
#202556092
C2×#156894782
C2×#156894432
C2×#156894672
C2×#156894232
C2×#156893802
C2×#156893722
C2×#156893452
C2×#156892822
C2×#156892722
C2×#156892022
C2×#156891212
C2×#156891262
C2×C4×SD16×C472
C2×#332347