Finite Group Databasebeta

← C2×#19144867 #25964923

Subgroups — C2×#19144867 #25964923

Order 11008.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583522C211yesmaximal, characteristic, complemented
2C2×#14583380C211yesmaximal, characteristic, complemented
3#19144867C2116yesmaximal, direct product factor
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583183C211yesmaximal, characteristic, complemented
6C2×#14583188C211yesmaximal, characteristic, complemented
7C2×#14583124C211yesmaximal, characteristic, complemented
8C2×#14583117C211yesmaximal, characteristic, complemented
9C2×#14583059C211yesmaximal, characteristic, complemented
10C2×#14583046C211yesmaximal, characteristic
11C2×#14583010C211yesmaximal, characteristic, complemented
12C2×#14583003C211yesmaximal, characteristic, complemented
13C2×#14582986C211yesmaximal, characteristic, complemented
14C2×#14582984C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#483C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583522—24no—
23#14583522C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063320—21no—
26C2×#13063314C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063307—21no—
29C2×#13063305—21no—
30C2×#13063299C2211yescharacteristic
31#14583380—24no—
32#14583380C2218yescomplemented
33C2×Q8×Dic43C2211yescharacteristic
34C2×#13063290C2211yescharacteristic
35C2×#13063290C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×C4×C22⋊D43—21no—
41C2×#13063284C2211yescharacteristic
42C2×#13063283—21no—
43C2×C4⋊C4×D43—21no—
44#14583217C2218yescomplemented
45#14583188C2218yescomplemented
46#14583183C2218yescomplemented
47#14583124C2218yescomplemented
48#14583117C2218yescomplemented
49#14583059C2218yescomplemented
50#14583046C2218yes—
51#14583010C2218yescomplemented
52#14583003C2218yescomplemented
53#14582986C2218yescomplemented
54#14582984C2218yescomplemented
55#14582957C2218yescomplemented
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#483C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C2×#10621885—24no—
92C2×#10621885C2314yes—
93C2×#10621873—24no—
94C2×#10621873C2314yes—
95C2×#10621884—24no—
96C2×#10621884C2314yes—
97C2×D344—24no—
98C2×D344C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063324—22no—
102#13063324C2314yes—
103#13063320—28no—
104#13063314—22no—
105#13063314C2314yes—
106#13063311—28no—
107#13063307—28no—
108#13063305—28no—
109#13063299—22no—
110#13063299C2314yes—
111Q8×Dic43—22no—
112Q8×Dic43C2314yes—
113#13063290—22no—
114#13063290—22no—
115#13063290C2314yes—
116#13063290C2314yes—
117#13063287—22no—
118#13063287—22no—
119#13063287—22no—
120#13063287C2314yes—
121#13063287C2314yes—
122#13063287C2314yes—
123C4×C22⋊D43—28no—
124C4×C22⋊D43—28no—
125#13063284D414yes—
126#13063284C2314yes—
127#13063283—28no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43D411yescharacteristic
130C2×C4⋊Dic43D411yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C4⋊C4×D43—28no—
136C2×C22⋊Dic43D411yescharacteristic
137C2×C22⋊Dic43D411yescharacteristic
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×(C2×D43)⋊C4—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149#13063256C2314yes—
150#13063256C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063247C2314yes—
156#13063245C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160#13063235C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—22no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2314yes—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C22⋊C4×C43—21no—
177#106×C43C2314yes—
178#106×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181C22⋊C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C23×D43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—24no—
196C22×C4×C43—82no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—28no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—82no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211#10621898—216no—
212#10621898—28no—
213#10621898—28no—
214C2×D172—21no—
215C2×D172—22no—
216C2×D172—21no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172#4114yes—
220C2×D172C2412yes—
221C2×D172C2412yes—
222C2×C4×D43—28no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—82no—
228C2×C4×D43—82no—
229C2×C4×D43—82no—
230C2×Dic86—21no—
231C2×Dic86—22no—
232C2×Dic86—24no—
233C2×Dic86—82no—
234C2×Dic86#4114yes—
235C2×Dic86C2412yes—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43C2412yes—
239C2×C8×C43C2412yes—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43C2412yes—
246C4⋊C4×C43C2412yes—
247C4⋊C4×C43C2412yes—
248C22⋊C4×C43—24no—
249C22⋊Dic43C2×D414yes—
250C22⋊Dic43C2×D414yes—
251#10621885—28no—
252#10621884—28no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259C4⋊Dic43—21no—
260C4⋊Dic43—24no—
261C4⋊Dic43C2×D414yes—
262C4⋊Dic43C2×D414yes—
263C4⋊Dic43C2412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43C2×D412yes—
271C4×Dic43C2×D412yes—
272C4×Dic43C2412yes—
273C4×Dic43C2412yes—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278D344—28no—
279#10621873—28no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—24no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293Q8×C43—22no—
294Q8×C43—22no—
295Q8×C43—42no—
296C2×C4×C43—22no—
297C2×C4×C43—24no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—84no—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4112yes—
312C2×C4×C43C2×#4112yes—
313C2×C4×C43C2511yescharacteristic
314C22⋊D43—216no—
315C22⋊D43—84no—
316C2×Dic43—24no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—42no—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328D172—24no—
329D172—22no—
330D172—22no—
331D172—22no—
332D172—42no—
333D172C2×#4114yes—
334C4×D43—216no—
335C4×D43—84no—
336C4×D43—84no—
337C4×D43—84no—
338Dic86—24no—
339Dic86—22no—
340Dic86—84no—
341Dic86C2×#4114yes—
342C8×C43—22no—
343C8×C43—22no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C2×#3125—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—44no—
351C22×C43#52512yes—
352C22×C43#57712yes—
353C22×C43#57712yes—
354C22×C43C23×D411yescharacteristic
355C2×D43—24no—
356C2×D43—48no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—84no—
363C4×C43—22no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43#52512yes—
369C4×C43C22×#4111yescharacteristic
370C4×C43C22×#4111yescharacteristic
371Dic43—24no—
372Dic43—22no—
373Dic43—22no—
374Dic43—22no—
375Dic43—22no—
376Dic43—42no—
377C2×#542—431no—
378C2×#520—431no—
379#3125—4316no—
380C2×#481—431no—
381C2×#483D4311yescharacteristic, complemented
382C2×#475—431no—
383C2×#476—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#452—431no—
387C2×#449—431no—
388C2×#442—431no—
389C2×#441—431no—
390C2×C4×SD16—431no—
391C2×C4×SD16—431no—
392C2×#433—431no—
393C2×C43—42no—
394C2×C43#312514yescomplemented
395C2×C43C2×#52511yescharacteristic
396C2×C43C2×#57711yescharacteristic
397C2×C43C2×#57711yescharacteristic
398D43—44no—
399D43—82no—
400C22×#41—431no—
401C22×Q16—431no—
402C22×SD16—431no—
403C22×SD16—431no—
404C22×D8—431no—
405#542—438no—
406#542—864no—
407C2×C4⋊Q8—431no—
408C2×#126—861no—
409C2×#124—431no—
410C2×#124—861no—
411C2×#123—861no—
412C2×C22⋊Q8—861no—
413C2×C22⋊Q8C2×D4311yescharacteristic
414C2×#121—431no—
415#520—438no—
416#520—864no—
417C2×C4×Q8—431no—
418C2×C4×Q8—431no—
419C2×C4×Q8—431no—
420C2×C4×D4—431no—
421C2×C4×D4—431no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C2×C4×D4—861no—
425C2×#117—431no—
426C2×#117—861no—
427C22×C4⋊C4—861no—
428C22×C4⋊C4C2×D4311yescharacteristic
429#483C2×D4318yescomplemented
430#481—438no—
431#476—438no—
432#475—438no—
433#464—438no—
434#463—438no—
435#452—438no—
436#449—438no—
437#442—438no—
438#441—438no—
439C4×SD16—438no—
440C4×SD16—438no—
441#433—438no—
442C2×#106—431no—
443C2×#106—431no—
444C2×#106C2×D4311yescharacteristic
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8—431no—
447C2×C4⋊C8—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103C2×D4311yescharacteristic
451C2×#103C2×D4311yescharacteristic
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8C2×D4311yescharacteristic
458C2×#97—431no—
459C2×C4×C8—431no—
460C43C2×#312511yescharacteristic, complemented, Sylow
461C2×#41—434no—
462C2×#41—864no—
463C2×#41—864no—
464C2×#41—862no—
465C22×Q8—431no—
466C22×Q8—861no—
467C22×Q8C22×D4311yescharacteristic
468C22×D4—431no—
469C22×D4—431no—
470C22×D4—861no—
471C22×D4—861no—
472C23×C4—21no—
473C23×C4—861no—
474C23×C4—861no—
475C23×C4—861no—
476C23×C4—861no—
477C23×C4C22×D4311yescharacteristic
478C2×Q16—434no—
479C2×Q16—864no—
480C2×SD16—434no—
481C2×SD16—434no—
482C2×SD16—864no—
483C2×SD16—864no—
484C2×D8—434no—
485C2×D8—864no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—434no—
491C4⋊Q8—862no—
492#126—868no—
493#124—434no—
494#124—862no—
495#124—868no—
496#123—868no—
497C22⋊Q8—22no—
498C22⋊Q8—868no—
499C22⋊Q8C22×D4314yes—
500#121—434no—
501#121—862no—
502C4×Q8—434no—
503C4×Q8—434no—
504C4×Q8—434no—
505C4×Q8—862no—
506C4×Q8—862no—
507C4×Q8—862no—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—434no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—868no—
515C4×D4—868no—
516#117—434no—
517#117—434no—
518#117—868no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—868no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4C22×D4311yescharacteristic
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C4⋊C4C22×D4314yes—
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C42—431no—
544C2×C42—431no—
545C2×C42—861no—
546C2×C42—861no—
547C2×C42—861no—
548#106—434no—
549#106—434no—
550#106C22×D4314yes—
551#106C22×D4314yes—
552C4⋊C8—434no—
553C4⋊C8—434no—
554#103—434no—
555#103—434no—
556#103C22×D4314yes—
557#103C22×D4314yes—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562C22⋊C8—434no—
563C22⋊C8C22×D4314yes—
564#97—434no—
565C4×C8—434no—
566C24—861no—
567C24—861no—
568C24D4×D4311yescharacteristic
569#41—868no—
570#41—868no—
571#41—8616no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—434no—
576C2×Q8—432no—
577C2×Q8—864no—
578C2×Q8—861no—
579C2×Q8—862no—
580C2×Q8—3442no—
581C2×Q8C23×D4312yes—
582C2×D4—434no—
583C2×D4—432no—
584C2×D4—432no—
585C2×D4—868no—
586C2×D4—864no—
587C2×D4—864no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—3442no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—82no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—868no—
610C22×C4—861no—
611C22×C4—864no—
612C22×C4—861no—
613C22×C4—3442no—
614C22×C4—3442no—
615C22×C4—3442no—
616C22×C4D4×D4312yes—
617C22×C4D4×D4311yescharacteristic
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620Q16—868no—
621SD16—868no—
622SD16—868no—
623D8—868no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8C23×D4312yes—
631C2×C8C23×D4312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—434no—
638C4⋊C4—434no—
639C4⋊C4—432no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—861no—
645C4⋊C4C23×D4312yes—
646C4⋊C4C23×D4312yes—
647C4⋊C4C23×D4312yes—
648C22⋊C4—24no—
649C22⋊C4—434no—
650C22⋊C4—434no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C42—432no—
658C42—432no—
659C42—432no—
660C42—432no—
661C42—864no—
662C42—864no—
663C42—864no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—864no—
668C23—862no—
669C23—862no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23C2×D4×D4312yes—
676C23C2×D4×D4311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—434no—
681Q8—864no—
682Q8—862no—
683Q8—3444no—
684D4—434no—
685D4—8616no—
686D4—864no—
687D4—862no—
688D4—862no—
689D4—862no—
690D4—3444no—
691D4—1722no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—432no—
708C2×C4—432no—
709C2×C4—8616no—
710C2×C4—864no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—3444no—
718C2×C4—3444no—
719C2×C4—3444no—
720C2×C4—1722no—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4#41×D4312yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—862no—
729C8—862no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—864no—
735C22—3444no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22—1728no—
742C22#1458340712yes—
743C22#1458370512yes—
744C22#1458370812yes—
745C22C22×D4×D4311yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—862no—
752C4—862no—
753C4—862no—
754C4—862no—
755C4—864no—
756C4—1722no—
757C4#1458340712yes—
758C4C2×#41×D4311yescharacteristic
759C4C2×#41×D4311yescharacteristic
760C2—42no—
761C2—3442no—
762C2—1724no—
763C2#1914486714yesdirect product factor
764C2C2×#1458340711yescharacteristic
765C2C2×#1458370511yescharacteristic
766C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
hypercenterC2×#483D43
hypocenterC43C2×#3125
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#14583522C2semidirect
2. C2×#14583380C2semidirect
3. #19144867C2direct (N × H)
4. C2×#14583217C2semidirect
5. C2×#14583183C2semidirect
6. C2×#14583188C2semidirect
7. C2×#14583124C2semidirect
8. C2×#14583117C2semidirect
9. C2×#14583059C2semidirect
11. C2×#14583010C2semidirect
12. C2×#14583003C2semidirect
13. C2×#14582986C2semidirect
14. C2×#14582984C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#483C2semidirect
23. #14583522C22semidirect
32. #14583380C22semidirect
44. #14583217C22semidirect
45. #14583188C22semidirect
46. #14583183C22semidirect
47. #14583124C22semidirect
48. #14583117C22semidirect
49. #14583059C22semidirect
51. #14583010C22semidirect
52. #14583003C22semidirect
53. #14582986C22semidirect
54. #14582984C22semidirect
55. #14582957C22semidirect
71. C43×#483C22semidirect
381. C2×#483D43semidirect
394. C2×C43#3125semidirect
429. #483C2×D43semidirect
460. C43C2×#3125semidirect
763. C2#19144867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835222
C2×#145833802
#191448672
C2×#145832172
C2×#145831832
C2×#145831882
C2×#145831242
C2×#145831172
C2×#145830592
C2×#145830462
C2×#145830102
C2×#145830032
C2×#145829862
C2×#145829842
C2×#145829572
C2×C43×#4832
C2×#312543