Finite Group Databasebeta

← C2×#19144552 #25964423

Subgroups — C2×#19144552 #25964423

Order 11008.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583465C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic, complemented
3#19144552C2116yesmaximal, direct product factor
4C2×#14583219C211yesmaximal, characteristic, complemented
5C2×#14583225C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583222C211yesmaximal, characteristic, complemented
8C2×#14583220C211yesmaximal, characteristic, complemented
9C2×#14583212C211yesmaximal, characteristic, complemented
10C2×#14583211C211yesmaximal, characteristic, complemented
11C2×#14582938C211yesmaximal, characteristic, complemented
12C2×#14582934C211yesmaximal, characteristic, complemented
13C2×#14582902C211yesmaximal, characteristic, complemented
14C2×#102×D43C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#481C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583465—24no—
22#14583465C2218yes—
23C2×#13063321—21no—
24C2×#13063311—21no—
25C2×#13063300C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063296C2211yescharacteristic
28C2×#13063295—21no—
29C2×#13063293—21no—
30#14583380—24no—
31#14583380C2218yescomplemented
32C2×#13063290—21no—
33C2×#13063287—21no—
34C2×C4×C22⋊D43—21no—
35C2×C4×C22⋊D43—21no—
36C2×#13063284C2211yescharacteristic, complemented
37C2×#13063283C2211yescharacteristic
38C2×#13063283C2211yescharacteristic
39C2×#13063283C2211yescharacteristic, complemented
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic, complemented
42#14583225C2218yescomplemented
43#14583224C2218yescomplemented
44#14583222C2218yescomplemented
45#14583220C2218yescomplemented
46#14583219C2218yescomplemented
47#14583212C2218yescomplemented
48#14583211C2218yescomplemented
49#14582938C2218yescomplemented
50#14582934C2218yescomplemented
51C2×#13063259C2211yescharacteristic, complemented
52C2×#13063258C2211yescharacteristic, complemented
53C2×#13063258C2211yescharacteristic, complemented
54C2×#13063258C2211yescharacteristic, complemented
55C2×#13063257C2211yescharacteristic, complemented
56C2×#13063256C2211yescharacteristic, complemented
57#14582902C2218yescomplemented
58C2×#13063247C2211yescharacteristic
59C2×#13063247C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64#102×D43C2218yescomplemented
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic, complemented
71C43×#481C2218yescomplemented
72C2×#106×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898D414yes—
81C2×#10621898C2314yes—
82C22×Dic86D411yescharacteristic
83C22×D172—21no—
84C22×D172D411yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43D411yescharacteristic
90C22×C22⋊D43D411yescharacteristic
91C2×D4×D43—22no—
92C2×D4×D43—24no—
93C2×D4×D43—24no—
94C2×D4×D43C2314yes—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C2×#10621872—24no—
100C2×#10621872C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—24no—
104C2×C8×D43C2314yes—
105#13063321—28no—
106#13063311—28no—
107#13063300—22no—
108#13063300C2314yes—
109#13063299—22no—
110#13063299C2314yes—
111#13063296—22no—
112#13063296C2314yes—
113#13063295—28no—
114#13063293—28no—
115#13063290—28no—
116#13063287—28no—
117C4×C22⋊D43—28no—
118C4×C22⋊D43—28no—
119#13063284—22no—
120#13063284C2314yescomplemented
121#13063283—22no—
122#13063283—22no—
123#13063283—22no—
124#13063283C2314yes—
125#13063283C2314yes—
126#13063283C2314yescomplemented
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43—22no—
134C4⋊C4×D43C2314yes—
135C4⋊C4×D43C2314yescomplemented
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147#13063259C2314yescomplemented
148#13063258C2314yescomplemented
149#13063258C2314yescomplemented
150#13063258C2314yescomplemented
151#13063257C2314yescomplemented
152#13063256C2314yescomplemented
153#13063247C2314yes—
154#13063247C2314yes—
155#13063246C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yescomplemented
160(C2×D43)⋊C8C2314yescomplemented
161(C2×D43)⋊C8C2314yescomplemented
162C22×D4×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C23×C4×C43—21no—
165C23×C4×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#121×C43—22no—
169#121×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—22no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2314yescomplemented
176C2×C22⋊C4×C43—21no—
177#106×C43C2314yescomplemented
178#106×C43C2314yescomplemented
179#102×C43C2314yes—
180#102×C43C2314yes—
181C22⋊C8×C43C2314yescomplemented
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43—21no—
185C23×D43—24no—
186C23×D43—44no—
187C23×D43—82no—
188C23×D43—82no—
189C23×D43C2×D411yescharacteristic
190C23×D43C2×D411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43—24no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—82no—
196C2×D4×C43C2412yes—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—24no—
203C22×C4×C43—82no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—82no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43C2×D414yes—
217C2×C22⋊D43C2×D414yes—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223D4×D43—28no—
224D4×D43—28no—
225D4×D43—48no—
226#10621898—216no—
227#10621898—28no—
228#10621898—28no—
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—24no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172—82no—
235C2×D172C2×D414yes—
236C2×D172C2412yes—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—82no—
242C2×C4×D43—82no—
243C2×C4×D43C2×D412yes—
244C2×C4×D43C2×D412yes—
245C2×C4×D43#4114yes—
246C2×C4×D43#4114yes—
247C2×C4×D43C2412yes—
248C2×C4×D43C2412yes—
249C2×Dic86—24no—
250C2×Dic86C2×D414yes—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
253C2×C8×C43C2412yes—
254C2×C8×C43C2412yes—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—24no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—24no—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43C2412yes—
274C4⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43—24no—
281C4×Dic43—24no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286#10621872—28no—
287C8×D43—28no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—48no—
307C22×D43—84no—
308C22×D43—84no—
309C22×D43—816no—
310C22×D43#12314yes—
311C22×D43C22×D412yes—
312C22×D43C22×D412yes—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—42no—
316D4×C43—84no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—84no—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4112yes—
331C2×C4×C43C2×#4112yes—
332C2×C4×C43C2511yescharacteristic
333C22⋊D43—28no—
334C22⋊D43—28no—
335C22⋊D43—48no—
336C22⋊D43—84no—
337C22⋊D43—84no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43#12314yes—
346C2×Dic43C22×D412yes—
347C2×Dic43C22×D412yes—
348D172—28no—
349D172—22no—
350D172—22no—
351D172—42no—
352D172—84no—
353C4×D43—24no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—84no—
357C4×D43—84no—
358C4×D43#12318yes—
359C4×D43C2×#4114yes—
360C4×D43C2×#4114yes—
361Dic86—28no—
362C8×C43—22no—
363C8×C43—22no—
364C43⋊C8—22no—
365C43⋊C8—22no—
366C2×#3096—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—44no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—84no—
375C22×C43C2×#12312yes—
376C22×C43#57612yes—
377C22×C43#57712yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—28no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—44no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—816no—
390C2×D43—84no—
391C2×D43C2×#12314yes—
392C4×C43—22no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43C2×#12312yes—
397C4×C43C22×#4111yescharacteristic
398C4×C43C22×#4111yescharacteristic
399Dic43—22no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43C2×#12314yes—
404C2×#535—431no—
405C2×#520—431no—
406#3096—4316no—
407C2×#481—431no—
408C2×#481D4311yescharacteristic, complemented
409C2×#482—431no—
410C2×#482—431no—
411C2×#482—431no—
412C2×#482—431no—
413C2×#480—431no—
414C2×#480—431no—
415C2×#428—431no—
416C2×#427—431no—
417C2×#418—431no—
418C22×#102—431no—
419C2×#408—431no—
420C2×C43—42no—
421C2×C43—82no—
422C2×C43#309614yescomplemented
423C2×C43C22×#12311yescharacteristic
424C2×C43C2×#57611yescharacteristic
425C2×C43C2×#57711yescharacteristic
426D43—24no—
427D43—42no—
428D43—82no—
429C22×#41—431no—
430C23×D4—431no—
431C22×M16—431no—
432C23×C8—431no—
433#535—438no—
434#535—864no—
435C2×#127—861no—
436C2×#124—861no—
437C2×#121—431no—
438C2×#121—431no—
439C2×#121—431no—
440C2×#121C2×D4311yescharacteristic
441C2×#120—861no—
442C2×#120—861no—
443#520—438no—
444#520—864no—
445C2×C4×Q8—861no—
446C2×C4×D4—861no—
447C2×C4×D4—861no—
448C2×C4×D4—861no—
449C2×#117—431no—
450C2×#117—431no—
451C2×#117—431no—
452C2×#117—431no—
453C22×C4⋊C4—431no—
454C22×C4⋊C4—431no—
455C22×C4⋊C4C2×D4311yescharacteristic, complemented
456#482—438no—
457#482—438no—
458#482—438no—
459#482—438no—
460#481—438no—
461#481C2×D4318yescomplemented
462#480—438no—
463#480—438no—
464#428—438no—
465#427—438no—
466C2×#107—431no—
467C2×#107—431no—
468C2×#107—431no—
469C2×#107—431no—
470C2×#106—431no—
471C2×#106—431no—
472C2×#106C2×D4311yescharacteristic, complemented
473C2×#106C2×D4311yescharacteristic, complemented
474#418—438no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—438no—
482C2×#102C2×D4311yescharacteristic
483C2×#102C2×D4311yescharacteristic
484#408—438no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8C2×D4311yescharacteristic, complemented
489C43C2×#309611yescharacteristic, complemented, Sylow
490C25—861no—
491C2×#41—434no—
492C2×#41—434no—
493C2×#41—864no—
494C2×#41—864no—
495C22×Q8—431no—
496C22×D4—21no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—434no—
500C22×D4—431no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4—864no—
504C22×D4—864no—
505C22×D4—862no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4C22×D4311yescharacteristic
510C23×C4—21no—
511C23×C4—431no—
512C23×C4—431no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4C22×D4311yescharacteristic
516C2×M16—434no—
517C2×M16—864no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8—434no—
521C22×C8—864no—
522C22×C8C22×D4311yescharacteristic
523C22×C8C22×D4311yescharacteristic
524#127—868no—
525#124—868no—
526#121—22no—
527#121—434no—
528#121—434no—
529#121—434no—
530#121—862no—
531#121—862no—
532#121—862no—
533#121C22×D4314yes—
534#120—868no—
535#120—868no—
536C4×Q8—868no—
537C4×D4—868no—
538C4×D4—868no—
539C4×D4—868no—
540#117—434no—
541#117—434no—
542#117—434no—
543#117—434no—
544#117—862no—
545#117—862no—
546#117—862no—
547#117—862no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—434no—
554C2×C4⋊C4—434no—
555C2×C4⋊C4—862no—
556C2×C4⋊C4—862no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4314yescomplemented
563C2×C22⋊C4—21no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42—861no—
574C2×C42—861no—
575#107—434no—
576#107—434no—
577#107—434no—
578#107—434no—
579#106—434no—
580#106—434no—
581#106C22×D4314yescomplemented
582#106C22×D4314yescomplemented
583#102—434no—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102—434no—
589#102C22×D4314yes—
590#102C22×D4314yes—
591C22⋊C8—434no—
592C22⋊C8—434no—
593C22⋊C8—434no—
594C22⋊C8C22×D4314yescomplemented
595C24—21no—
596C24—431no—
597C24—431no—
598C24—864no—
599C24—861no—
600C24—3442no—
601C24—3442no—
602C24—1724no—
603C24D4×D4311yescharacteristic
604#41—8616no—
605#41—868no—
606#41—868no—
607C2×Q8—434no—
608C2×Q8—864no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—434no—
615C2×D4—434no—
616C2×D4—434no—
617C2×D4—432no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—868no—
621C2×D4—868no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—861no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—3442no—
631C2×D4—3442no—
632C2×D4—3442no—
633C2×D4—1728no—
634C2×D4—1724no—
635C2×D4C23×D4312yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—82no—
643C22×C4—431no—
644C22×C4—432no—
645C22×C4—434no—
646C22×C4—434no—
647C22×C4—432no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664M16—868no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—432no—
668C2×C8—432no—
669C2×C8—868no—
670C2×C8—862no—
671C2×C8—862no—
672C2×C8C23×D4312yes—
673C2×C8C23×D4312yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—432no—
679C4⋊C4—432no—
680C4⋊C4—432no—
681C4⋊C4—864no—
682C4⋊C4—864no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4C23×D4312yes—
687C4⋊C4C23×D4312yes—
688C4⋊C4C23×D4312yes—
689C22⋊C4—24no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C42—864no—
698C42—864no—
699C42—864no—
700C42—864no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—434no—
709C23—432no—
710C23—432no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—3444no—
718C23—3444no—
719C23—34416no—
720C23—1728no—
721C23—1722no—
722C23—1722no—
723C23—1722no—
724C23C2×D4×D4312yes—
725C23C2×D4×D4311yescharacteristic
726Q8—868no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—868no—
732D4—868no—
733D4—868no—
734D4—862no—
735D4—862no—
736D4—3444no—
737D4—3444no—
738D4—3444no—
739D4—1728no—
740D4—1722no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—434no—
753C2×C4—432no—
754C2×C4—438no—
755C2×C4—434no—
756C2×C4—434no—
757C2×C4—432no—
758C2×C4—862no—
759C2×C4—864no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—3444no—
766C2×C4—3444no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4C2×D4×D4312yes—
771C2×C4C2×D4×D4311yescharacteristic
772C2×C4#41×D4312yes—
773C2×C4#41×D4312yes—
774C2×C4C24×D4311yescharacteristic
775C8—22no—
776C8—22no—
777C8—862no—
778C8—862no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—434no—
788C22—862no—
789C22—862no—
790C22—868no—
791C22—862no—
792C22—862no—
793C22—862no—
794C22—34416no—
795C22—3444no—
796C22—1722no—
797C22—1722no—
798C22—1722no—
799C22—1724no—
800C22#123×D4312yes—
801C22#1458370312yes—
802C22#1458370512yes—
803C22C22×D4×D4311yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—434no—
809C4—862no—
810C4—1722no—
811C4—1722no—
812C4—1722no—
813C4#123×D4312yes—
814C4C2×#41×D4311yescharacteristic
815C4C2×#41×D4311yescharacteristic
816C2—42no—
817C2—82no—
818C2—864no—
819C2—3442no—
820C2—1722no—
821C2#1914455214yesdirect product factor
822C2C2×#123×D4311yescharacteristic
823C2C2×#1458370311yescharacteristic
824C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#481C2
socleC23×C43C22×D4
prime radicalC2×#14583465C2
hypercenterC2×#481D43
hypocenterC43C2×#3096
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#14583380C2semidirect
3. #19144552C2direct (N × H)
4. C2×#14583219C2semidirect
5. C2×#14583225C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583222C2semidirect
8. C2×#14583220C2semidirect
9. C2×#14583212C2semidirect
10. C2×#14583211C2semidirect
11. C2×#14582938C2semidirect
12. C2×#14582934C2semidirect
13. C2×#14582902C2semidirect
14. C2×#102×D43C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#481C2semidirect
31. #14583380C22semidirect
36. C2×#13063284C22semidirect
39. C2×#13063283C22semidirect
41. C2×C4⋊C4×D43C22semidirect
42. #14583225C22semidirect
43. #14583224C22semidirect
44. #14583222C22semidirect
45. #14583220C22semidirect
46. #14583219C22semidirect
47. #14583212C22semidirect
48. #14583211C22semidirect
49. #14582938C22semidirect
50. #14582934C22semidirect
51. C2×#13063259C22semidirect
52. C2×#13063258C22semidirect
53. C2×#13063258C22semidirect
54. C2×#13063258C22semidirect
55. C2×#13063257C22semidirect
56. C2×#13063256C22semidirect
57. #14582902C22semidirect
64. #102×D43C22semidirect
65. #14582864C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C22×C4⋊C4×C43C22semidirect
71. C43×#481C22semidirect
72. C2×#106×C43C22semidirect
73. C2×#106×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
120. #13063284C23semidirect
126. #13063283C23semidirect
135. C4⋊C4×D43C23semidirect
147. #13063259C23semidirect
148. #13063258C23semidirect
149. #13063258C23semidirect
150. #13063258C23semidirect
151. #13063257C23semidirect
152. #13063256C23semidirect
159. C22⋊(C43⋊C8)C23semidirect
160. (C2×D43)⋊C8C23semidirect
161. (C2×D43)⋊C8C23semidirect
175. C2×C4⋊C4×C43C23semidirect
177. #106×C43C23semidirect
178. #106×C43C23semidirect
181. C22⋊C8×C43C23semidirect
408. C2×#481D43semidirect
422. C2×C43#3096semidirect
455. C22×C4⋊C4C2×D43semidirect
461. #481C2×D43semidirect
472. C2×#106C2×D43semidirect
473. C2×#106C2×D43semidirect
488. C2×C22⋊C8C2×D43semidirect
489. C43C2×#3096semidirect
562. C2×C4⋊C4C22×D43semidirect
581. #106C22×D43semidirect
582. #106C22×D43semidirect
594. C22⋊C8C22×D43semidirect
821. C2#19144552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834652
C2×#145833802
#191445522
C2×#145832192
C2×#145832252
C2×#145832242
C2×#145832222
C2×#145832202
C2×#145832122
C2×#145832112
C2×#145829382
C2×#145829342
C2×#145829022
C2×#102×D432
C2×#145828642
C2×C43×#4812
C2×#309643