Finite Group Databasebeta

← C2×#19144944 #25965828

Subgroups — C2×#19144944 #25965828

Order 11008.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583526C211yesmaximal, characteristic, complemented
2C2×#14583462C211yesmaximal, characteristic
3#19144944C2116yesmaximal, direct product factor
4C2×#14583263C211yesmaximal, characteristic, complemented
5C2×#14583262C211yesmaximal, characteristic, complemented
6C2×#14583261C211yesmaximal, characteristic, complemented
7C2×#14583257C211yesmaximal, characteristic, complemented
8C2×#14583254C211yesmaximal, characteristic, complemented
9C2×#14583252C211yesmaximal, characteristic, complemented
10C2×#14583244C211yesmaximal, characteristic, complemented
11C2×#14582897C211yesmaximal, characteristic, complemented
12C2×#14582902C211yesmaximal, characteristic, complemented
13C2×#14582892C211yesmaximal, characteristic, complemented
14C2×#102×D43C211yesmaximal, characteristic, complemented
15C2×#14582853C211yesmaximal, characteristic, complemented
16C2×C43×#486C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583526—24no—
22#14583526C2218yescomplemented
23#14583462—24no—
24#14583462C2218yes—
25C2×#13063324C2211yescharacteristic, complemented
26C2×#13063323—21no—
27C2×#13063321C2211yescharacteristic
28C2×#13063317C2211yescharacteristic, complemented
29C2×#13063316C2211yescharacteristic, complemented
30C2×#13063315—21no—
31C2×#13063313C2211yescharacteristic
32C2×#13063312C2211yescharacteristic
33C2×#13063303—21no—
34C2×#13063301—21no—
35C2×#13063297—21no—
36C2×#13063297—21no—
37C2×#13063293—21no—
38C2×#13063293—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063282C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583263C2218yescomplemented
43#14583262C2218yescomplemented
44#14583261C2218yescomplemented
45#14583257C2218yescomplemented
46#14583254C2218yescomplemented
47#14583252C2218yescomplemented
48#14583244C2218yescomplemented
49#14582902C2218yescomplemented
50#14582897C2218yescomplemented
51#14582892C2218yescomplemented
52C2×#13063250C2211yescharacteristic, complemented
53C2×#13063250C2211yescharacteristic, complemented
54C2×#13063248C2211yescharacteristic, complemented
55C2×#13063248C2211yescharacteristic, complemented
56C2×#13063247C2211yescharacteristic
57C2×#13063247C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063246C2211yescharacteristic, complemented
61C2×#13063246C2211yescharacteristic, complemented
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64#102×D43C2218yescomplemented
65#14582853C2218yescomplemented
66C2×#13063236C2211yescharacteristic, complemented
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C2×C4⋊Q8×C43C2211yescharacteristic, complemented
70C2×#127×C43C2211yescharacteristic
71C43×#486C2218yescomplemented
72C2×#102×C43C2211yescharacteristic
73C2×#102×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C4×C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900—24no—
81C2×#10621900C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C2×D4×D43—22no—
90C2×D4×D43—24no—
91C2×D4×D43—24no—
92C2×D4×D43C2314yes—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96C2×#10621872—24no—
97C2×#10621872C2314yes—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—24no—
101C2×C8×D43C2314yes—
102#13063324—22no—
103#13063324C2314yescomplemented
104#13063323—28no—
105#13063321—22no—
106#13063321C2314yes—
107#13063317—22no—
108#13063317C2314yescomplemented
109#13063316—22no—
110#13063316C2314yescomplemented
111#13063315—28no—
112#13063313—22no—
113#13063313C2314yes—
114#13063312—22no—
115#13063312C2314yes—
116#13063303—28no—
117#13063301—28no—
118#13063297—28no—
119#13063297—28no—
120#13063293—28no—
121#13063293—28no—
122#13063283—22no—
123#13063283C2314yes—
124#13063282D414yes—
125#13063282C2314yes—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×Dic43⋊C4D411yescharacteristic
136C4⋊C4×D43—22no—
137C4⋊C4×D43C2314yes—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063250C2314yescomplemented
148#13063250C2314yescomplemented
149#13063248C2314yescomplemented
150#13063248C2314yescomplemented
151#13063247C2314yes—
152#13063247C2314yes—
153#13063246C2314yes—
154#13063246C2314yes—
155#13063246C2314yescomplemented
156#13063246C2314yescomplemented
157#13063245C2314yes—
158#13063245C2314yes—
159#13063236C2314yescomplemented
160#13063235C2314yescomplemented
161C8×Dic43C2314yescomplemented
162C22×Q8×C43—21no—
163C22×D4×C43—21no—
164C22×D4×C43—21no—
165C22×D4×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4⋊Q8×C43—22no—
170C4⋊Q8×C43C2314yescomplemented
171#127×C43—22no—
172#127×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177#102×C43C2314yes—
178#102×C43C2314yes—
179#102×C43C2314yescomplemented
180#102×C43C2314yescomplemented
181C4×C8×C43C2314yescomplemented
182C24×C43—21no—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43—24no—
186C23×D43—44no—
187C23×D43—82no—
188C23×D43—82no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—24no—
191C2×Q8×C43—82no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—24no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—82no—
201C2×D4×C43—82no—
202C2×D4×C43C2412yes—
203C2×D4×C43C2412yes—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43—82no—
217C22×Dic43—24no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—44no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225#10621900—28no—
226#10621900—28no—
227#10621900—48no—
228D4×D43—28no—
229D4×D43—28no—
230D4×D43—48no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172C2412yes—
235C2×C4×D43—24no—
236C2×C4×D43—82no—
237C2×C4×D43C2×D412yes—
238C2×C4×D43#4114yes—
239C2×C4×D43#4114yes—
240C2×C4×D43C2412yes—
241C2×Dic86—22no—
242C2×Dic86—22no—
243C2×Dic86—21no—
244C2×Dic86—24no—
245C2×Dic86—82no—
246C2×Dic86C2412yes—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43C2412yes—
255C4⋊C4×C43C2412yes—
256C42×C43C2×D412yes—
257C42×C43C2412yes—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4C2×D414yes—
264(C2×D43)⋊C4C2×D414yes—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4C2×D414yes—
276Dic43⋊C4C2×D414yes—
277C4×Dic43—24no—
278C4×Dic43C2×D412yes—
279C4×Dic43C2412yes—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8C2412yes—
283C2×C43⋊C8C2412yes—
284#10621872—28no—
285C8×D43—28no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—48no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—816no—
305C22×D43#12414yes—
306C22×D43C22×D412yes—
307Q8×C43—84no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—42no—
313D4×C43—42no—
314D4×C43—84no—
315D4×C43—84no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43C2×#4112yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43—48no—
329C22⋊D43—48no—
330C22⋊D43—84no—
331C22⋊D43—84no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—48no—
341C2×Dic43#12414yes—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—22no—
346D172—22no—
347D172—42no—
348C4×D43—84no—
349C4×D43#12418yes—
350C4×D43C2×#4114yes—
351C4×D43C2×#4114yes—
352Dic86—22no—
353Dic86—22no—
354Dic86—42no—
355Dic86—84no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3136—431nomaximal, Sylow
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—84no—
368C22×C43—84no—
369C22×C43C2×#12412yes—
370C22×C43#57612yes—
371C22×C43#57712yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—28no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—816no—
380C2×D43—84no—
381C2×D43C2×#12414yes—
382C4×C43—22no—
383C4×C43—22no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43C2×#12412yes—
387C4×C43C22×#4111yescharacteristic
388C4×C43C22×#4111yescharacteristic
389Dic43—22no—
390Dic43—22no—
391Dic43—42no—
392Dic43—42no—
393Dic43—42no—
394Dic43C2×#12414yes—
395C2×#544—431no—
396C2×#535—431no—
397#3136—4316no—
398C2×#490—431no—
399C2×#490—431no—
400C2×#489—431no—
401C2×#489—431no—
402C2×#488—431no—
403C2×#488—431no—
404C2×#486—431no—
405C2×#486D4311yescharacteristic, complemented
406C2×#417—431no—
407C2×#418—431no—
408C2×#416—431no—
409C22×#102—431no—
410C2×#405—431no—
411C2×C43—82no—
412C2×C43—82no—
413C2×C43#313614yescomplemented
414C2×C43C22×#12411yescharacteristic
415C2×C43C2×#57611yescharacteristic
416C2×C43C2×#57711yescharacteristic
417D43—24no—
418D43—82no—
419C22×#41—431no—
420C23×D4—431no—
421C22×M16—431no—
422C23×C8—431no—
423#544—438no—
424#544—864no—
425#535—438no—
426#535—864no—
427C2×C4⋊Q8—431no—
428C2×C4⋊Q8—861no—
429C2×C4⋊Q8C2×D4311yescharacteristic, complemented
430C2×#127—431no—
431C2×#127C2×D4311yescharacteristic
432C2×#125—431no—
433C2×#125—431no—
434C2×#125—861no—
435C2×#124—431no—
436C2×#124—431no—
437C2×C22⋊Q8—861no—
438C2×C22⋊Q8—861no—
439C2×#121—861no—
440C2×#121—861no—
441C2×#120—861no—
442C2×#120—861no—
443C2×#117—431no—
444C2×#117—431no—
445C22×C4⋊C4—431no—
446#490—438no—
447#490—438no—
448#489—438no—
449#489—438no—
450#488—438no—
451#488—438no—
452#486—438no—
453#486C2×D4318yescomplemented
454#418—438no—
455#417—438no—
456#416—438no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#102—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—438no—
470C2×#102C2×D4311yescharacteristic
471C2×#102C2×D4311yescharacteristic
472C2×#102C2×D4311yescharacteristic, complemented
473C2×#102C2×D4311yescharacteristic, complemented
474#405—438no—
475C2×#97—431no—
476C2×#97—431no—
477C2×C4×C8—431no—
478C2×C4×C8C2×D4311yescharacteristic, complemented
479C43C2×#313611yescharacteristic, complemented, Sylow
480C25—861no—
481C2×#41—434no—
482C2×#41—862no—
483C2×#41—864no—
484C2×#41—864no—
485C22×Q8—21no—
486C22×Q8—431no—
487C22×Q8—861no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—434no—
491C22×D4—431no—
492C22×D4—864no—
493C22×D4—864no—
494C22×D4—862no—
495C22×D4—861no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4C22×D4311yescharacteristic
500C22×D4C22×D4311yescharacteristic
501C23×C4—431no—
502C23×C4—861no—
503C23×C4—861no—
504C2×M16—434no—
505C2×M16—864no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—434no—
509C22×C8—864no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—434no—
514C4⋊Q8—862no—
515C4⋊Q8—868no—
516C4⋊Q8C22×D4314yescomplemented
517#127—22no—
518#127—434no—
519#127—862no—
520#127C22×D4314yes—
521#125—434no—
522#125—434no—
523#125—862no—
524#125—868no—
525#125—862no—
526#124—434no—
527#124—434no—
528#124—862no—
529#124—862no—
530C22⋊Q8—868no—
531C22⋊Q8—868no—
532#121—868no—
533#121—868no—
534#120—868no—
535#120—868no—
536#117—434no—
537#117—434no—
538#117—434no—
539#117—862no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—434no—
546C2×C4⋊C4—862no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4C22×D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—431no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—431no—
563C2×C42—861no—
564C2×C42C22×D4311yescharacteristic
565#103—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574#102—434no—
575#102—434no—
576#102—434no—
577#102C22×D4314yes—
578#102C22×D4314yes—
579#102C22×D4314yescomplemented
580#102C22×D4314yescomplemented
581#97—434no—
582#97—434no—
583C4×C8—434no—
584C4×C8C22×D4314yescomplemented
585C24—21no—
586C24—21no—
587C24—431no—
588C24—864no—
589C24—861no—
590C24—3442no—
591C24—3442no—
592C24—1724no—
593#41—868no—
594#41—868no—
595#41—1728no—
596C2×Q8—24no—
597C2×Q8—82no—
598C2×Q8—432no—
599C2×Q8—864no—
600C2×Q8—861no—
601C2×Q8—862no—
602C2×Q8—862no—
603C2×Q8—3442no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—432no—
615C2×D4—868no—
616C2×D4—868no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—861no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—1728no—
627C2×D4—1724no—
628C2×D4—1724no—
629C2×D4C23×D4312yes—
630C2×D4C23×D4312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—434no—
636C22×C4—434no—
637C22×C4—432no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—3442no—
646C22×C4—1724no—
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4C23×D4311yescharacteristic
650M16—868no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—432no—
654C2×C8—432no—
655C2×C8—868no—
656C2×C8—862no—
657C2×C8—862no—
658C2×C8C23×D4312yes—
659C2×C8C23×D4312yes—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—434no—
664C4⋊C4—434no—
665C4⋊C4—432no—
666C4⋊C4—432no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—864no—
674C4⋊C4—864no—
675C4⋊C4C23×D4312yes—
676C4⋊C4C23×D4312yes—
677C22⋊C4—434no—
678C22⋊C4—434no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C42—432no—
685C42—432no—
686C42—864no—
687C42D4×D4312yes—
688C42C23×D4312yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—434no—
698C23—432no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—3444no—
703C23—3444no—
704C23—34416no—
705C23—1728no—
706C23—1722no—
707C23—1722no—
708C23—1722no—
709C23C2×D4×D4311yescharacteristic
710Q8—84no—
711Q8—862no—
712Q8—862no—
713Q8—3444no—
714Q8—1722no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—862no—
724D4—862no—
725D4—3444no—
726D4—3444no—
727D4—1728no—
728D4—1728no—
729D4—1722no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—434no—
737C2×C4—432no—
738C2×C4—438no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—432no—
742C2×C4—432no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—3444no—
749C2×C4—1728no—
750C2×C4—1722no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4C2×D4×D4312yes—
754C2×C4C2×D4×D4312yes—
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4#41×D4312yes—
757C2×C4#41×D4312yes—
758C2×C4C24×D4311yescharacteristic
759C8—22no—
760C8—22no—
761C8—862no—
762C8—862no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—434no—
772C22—862no—
773C22—862no—
774C22—868no—
775C22—34416no—
776C22—3444no—
777C22—1722no—
778C22—1722no—
779C22—1722no—
780C22#124×D4312yes—
781C22#1458370012yes—
782C22#1458370512yes—
783C22C22×D4×D4311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—434no—
789C4—862no—
790C4—862no—
791C4—1722no—
792C4—1722no—
793C4—1722no—
794C4#124×D4312yes—
795C4C2×#41×D4311yescharacteristic
796C4C2×#41×D4311yescharacteristic
797C2—82no—
798C2—82no—
799C2—864no—
800C2—3442no—
801C2#1914494414yesdirect product factor
802C2C2×#124×D4311yescharacteristic
803C2C2×#1458370011yescharacteristic
804C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#486C2
socleC23×C43C22×D4
prime radicalC2×#14583462C2
hypercenterC2×#486D43
hypocenterC43C2×#3136
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#14583526C2semidirect
3. #19144944C2direct (N × H)
4. C2×#14583263C2semidirect
5. C2×#14583262C2semidirect
6. C2×#14583261C2semidirect
7. C2×#14583257C2semidirect
8. C2×#14583254C2semidirect
9. C2×#14583252C2semidirect
10. C2×#14583244C2semidirect
11. C2×#14582897C2semidirect
12. C2×#14582902C2semidirect
13. C2×#14582892C2semidirect
14. C2×#102×D43C2semidirect
15. C2×#14582853C2semidirect
16. C2×C43×#486C2semidirect
22. #14583526C22semidirect
25. C2×#13063324C22semidirect
28. C2×#13063317C22semidirect
29. C2×#13063316C22semidirect
42. #14583263C22semidirect
43. #14583262C22semidirect
44. #14583261C22semidirect
45. #14583257C22semidirect
46. #14583254C22semidirect
47. #14583252C22semidirect
48. #14583244C22semidirect
49. #14582902C22semidirect
50. #14582897C22semidirect
51. #14582892C22semidirect
52. C2×#13063250C22semidirect
53. C2×#13063250C22semidirect
54. C2×#13063248C22semidirect
55. C2×#13063248C22semidirect
60. C2×#13063246C22semidirect
61. C2×#13063246C22semidirect
64. #102×D43C22semidirect
65. #14582853C22semidirect
66. C2×#13063236C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
69. C2×C4⋊Q8×C43C22semidirect
71. C43×#486C22semidirect
74. C2×#102×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×C4×C8×C43C22semidirect
103. #13063324C23semidirect
108. #13063317C23semidirect
110. #13063316C23semidirect
147. #13063250C23semidirect
148. #13063250C23semidirect
149. #13063248C23semidirect
150. #13063248C23semidirect
155. #13063246C23semidirect
156. #13063246C23semidirect
159. #13063236C23semidirect
160. #13063235C23semidirect
161. C8×Dic43C23semidirect
170. C4⋊Q8×C43C23semidirect
179. #102×C43C23semidirect
180. #102×C43C23semidirect
181. C4×C8×C43C23semidirect
405. C2×#486D43semidirect
413. C2×C43#3136semidirect
429. C2×C4⋊Q8C2×D43semidirect
453. #486C2×D43semidirect
472. C2×#102C2×D43semidirect
473. C2×#102C2×D43semidirect
478. C2×C4×C8C2×D43semidirect
479. C43C2×#3136semidirect
516. C4⋊Q8C22×D43semidirect
579. #102C22×D43semidirect
580. #102C22×D43semidirect
584. C4×C8C22×D43semidirect
801. C2#19144944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835262
C2×#145834622
#191449442
C2×#145832632
C2×#145832622
C2×#145832612
C2×#145832572
C2×#145832542
C2×#145832522
C2×#145832442
C2×#145828972
C2×#145829022
C2×#145828922
C2×#102×D432
C2×#145828532
C2×C43×#4862
C2×#313643