Finite Group Databasebeta

← C2×#19144859 #25964914

Subgroups — C2×#19144859 #25964914

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×#14583520C211yesmaximal, characteristic, complemented
2C2×#14583379C211yesmaximal, characteristic, complemented
3#19144859C2116yesmaximal, direct product factor
4C2×#14583235C211yesmaximal, characteristic, complemented
5C2×#14583213C211yesmaximal, characteristic, complemented
6C2×#14583195C211yesmaximal, characteristic, complemented
7C2×#14583180C211yesmaximal, characteristic, complemented
8C2×#14583122C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583063C211yesmaximal, characteristic, complemented
11C2×#14583046C211yesmaximal, characteristic
12C2×#14583001C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×C4×Dic172C211yesmaximal, characteristic, complemented
15C2×C4×D344C211yesmaximal, characteristic, complemented
16C2×C43×#433C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583520—24no—
23#14583520C2218yescomplemented
24C2×#13063325C2211yescharacteristic
25C2×#13063320—21no—
26C2×#13063313C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063307—21no—
29C2×#13063304C2211yescharacteristic
30C2×#13063303—21no—
31C2×#13063299C2211yescharacteristic
32#14583379—24no—
33#14583379C2218yescomplemented
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063283—21no—
43C22×C4⋊Dic43C2211yescharacteristic
44C2×C4⋊C4×D43—21no—
45#14583235C2218yescomplemented
46#14583213C2218yescomplemented
47#14583195C2218yescomplemented
48#14583180C2218yescomplemented
49#14583122C2218yescomplemented
50#14583115C2218yescomplemented
51#14583063C2218yescomplemented
52#14583046C2218yes—
53#14583001C2218yescomplemented
54#14583001C2218yescomplemented
55C4×Dic172C2218yescomplemented
56C4×D344C2218yescomplemented
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063259C2211yescharacteristic
60C2×#13063259C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×#117×C43C2211yescharacteristic
70C43×#433C2218yescomplemented
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×#97×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C23×Dic43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C2×Dic172—24no—
94C2×Dic172C2314yes—
95C2×#10621873—24no—
96C2×#10621873—24no—
97C2×#10621873C2314yes—
98C2×#10621873C2314yes—
99C2×D344—24no—
100C2×D344C2314yes—
101#13063325—22no—
102#13063325C2314yes—
103#13063320—28no—
104#13063313—22no—
105#13063313C2314yes—
106#13063311—28no—
107#13063307—28no—
108#13063304—22no—
109#13063304C2314yes—
110#13063303—28no—
111#13063299—22no—
112#13063299C2314yes—
113C4×Dic86—22no—
114C4×Dic86—22no—
115C4×Dic86—22no—
116C4×Dic86C2314yes—
117C4×Dic86C2314yes—
118C4×Dic86C2314yes—
119C4×D172—22no—
120C4×D172—22no—
121C4×D172—22no—
122C4×D172C2314yes—
123C4×D172C2314yes—
124C4×D172C2314yes—
125(C22⋊D43)⋊C4—28no—
126(C22⋊D43)⋊C4—28no—
127#13063283—28no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—22no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2314yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—28no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063259C2314yes—
154#13063259C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#117×C43D414yes—
169#117×C43C2314yes—
170C2×C4⋊C4×C43D411yescharacteristic
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177C4⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179C22⋊C8×C43C2314yes—
180#97×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C23×D43—21no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—28no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—82no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—24no—
206C22×Dic43—82no—
207#10621898—216no—
208#10621898—28no—
209#10621898—28no—
210C2×D172—21no—
211C2×D172—22no—
212C2×D172—21no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172#4114yes—
216C2×D172C2412yes—
217C2×D172C2412yes—
218C2×C4×D43—28no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—82no—
224C2×C4×D43—82no—
225C2×C4×D43—82no—
226C2×Dic86—21no—
227C2×Dic86—22no—
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—21no—
231C2×Dic86—24no—
232C2×Dic86—82no—
233C2×Dic86#4114yes—
234C2×Dic86C2412yes—
235C2×Dic86C2412yes—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—22no—
240C2×C8×C43C2412yes—
241C2×C8×C43C2412yes—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43C2×D414yes—
245C4⋊C4×C43C2×D414yes—
246C22⋊C4×C43C2×D414yes—
247C22⋊C4×C43C2×D414yes—
248C42×C43C2×D412yes—
249C42×C43C2×D412yes—
250C42×C43C2412yes—
251C42×C43C2412yes—
252C22⋊Dic43—24no—
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—24no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C2412yes—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268C4⋊Dic43C2412yes—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276Dic172—28no—
277D344—28no—
278#10621873—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—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—24no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4112yes—
308C2×C4×C43C2×#4112yes—
309C2×C4×C43C2511yescharacteristic
310C22⋊D43—216no—
311C22⋊D43—84no—
312C2×Dic43—24no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—84no—
325D172—24no—
326D172—22no—
327D172—22no—
328D172—22no—
329D172—42no—
330D172C2×#4114yes—
331C4×D43—216no—
332C4×D43—84no—
333C4×D43—84no—
334C4×D43—84no—
335Dic86—24no—
336Dic86—22no—
337Dic86—22no—
338Dic86—22no—
339Dic86—42no—
340Dic86—84no—
341Dic86C2×#4114yes—
342C8×C43—22no—
343C8×C43—22no—
344C8×C43—22no—
345C8×C43—22no—
346C2×#3124—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—44no—
351C22×C43#52512yes—
352C22×C43#57612yes—
353C22×C43#57812yes—
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—22no—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—22no—
368C4×C43#52512yes—
369C4×C43C22×#4111yescharacteristic
370C4×C43C22×#4111yescharacteristic
371Dic43—24no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377C2×#542—431no—
378C2×#520—431no—
379#3124—4316no—
380C2×#484—431no—
381C2×#480—431no—
382C2×#477—431no—
383C2×#474—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#452—431no—
387C2×#449—431no—
388C2×#440—431no—
389C2×#440—431no—
390C2×C4×Q16—431no—
391C2×C4×D8—431no—
392C2×#433D4311yescharacteristic, complemented
393C2×C43—42no—
394C2×C43#312414yescomplemented
395C2×C43C2×#52511yescharacteristic
396C2×C43C2×#57611yescharacteristic
397C2×C43C2×#57811yescharacteristic
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—431no—
413C2×C22⋊Q8—861no—
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—861no—
426C2×#117C2×D4311yescharacteristic
427C22×C4⋊C4—431no—
428C22×C4⋊C4—861no—
429#484—438no—
430#480—438no—
431#477—438no—
432#474—438no—
433#464—438no—
434#463—438no—
435#452—438no—
436#449—438no—
437#440—438no—
438#440—438no—
439C4×Q16—438no—
440C4×D8—438no—
441#433C2×D4318yescomplemented
442C2×#107—431no—
443C2×#107—431no—
444C2×#107—431no—
445C2×#107—431no—
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×C4⋊C8C2×D4311yescharacteristic
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8C2×D4311yescharacteristic
457C2×C22⋊C8C2×D4311yescharacteristic
458C2×#97C2×D4311yescharacteristic
459C2×C4×C8C2×D4311yescharacteristic
460C43C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—434no—
462C2×#41—864no—
463C2×#41—864no—
464C2×#41—862no—
465C22×Q8—431no—
466C22×Q8—431no—
467C22×Q8—861no—
468C22×D4—431no—
469C22×D4—431no—
470C22×D4—861no—
471C22×D4—861no—
472C23×C4—861no—
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×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—434no—
491C4⋊Q8—862no—
492#126—868no—
493#124—434no—
494#124—868no—
495#124—862no—
496#123—868no—
497C22⋊Q8—434no—
498C22⋊Q8—862no—
499C22⋊Q8—868no—
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—868no—
512C4×D4—868no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—862no—
516#117—868no—
517#117D17214yes—
518#117C22×D4314yes—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—862no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—868no—
532C2×C4⋊C4D17211yescharacteristic
533C2×C4⋊C4D17211yescharacteristic
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4D17211yescharacteristic
542C2×C22⋊C4D17211yescharacteristic
543C2×C42—861no—
544C2×C42—861no—
545C2×C42—861no—
546C2×C42C22×D4311yescharacteristic
547C2×C42C22×D4311yescharacteristic
548#107—434no—
549#107—434no—
550#107—434no—
551#107—434no—
552C4⋊C8C22×D4314yes—
553C4⋊C8C22×D4314yes—
554#103—434no—
555#103—434no—
556#103—434no—
557#103—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562C22⋊C8C22×D4314yes—
563C22⋊C8C22×D4314yes—
564#97C22×D4314yes—
565C4×C8C22×D4314yes—
566C24—861no—
567C24—861no—
568C24C2×D17211yescharacteristic
569#41—868no—
570#41—868no—
571#41—8616no—
572C2×Q8—434no—
573C2×Q8—432no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—864no—
577C2×Q8—861no—
578C2×Q8—862no—
579C2×Q8—862no—
580C2×Q8—862no—
581C2×Q8—3442no—
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—868no—
597C22×C4—861no—
598C22×C4—864no—
599C22×C4—864no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—3442no—
609C22×C4—3442no—
610C22×C4—3442no—
611C22×C4—3442no—
612C22×C4C2×D17212yes—
613C22×C4C2×D17211yescharacteristic
614C22×C4C2×D17211yescharacteristic
615C22×C4C2×D17211yescharacteristic
616C22×C4C2×D17211yescharacteristic
617C22×C4C2×D17211yescharacteristic
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620Q16—868no—
621SD16—868no—
622SD16—868no—
623D8—868no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D4312yes—
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C2×C8C23×D4312yes—
632C4⋊C4—432no—
633C4⋊C4—432no—
634C4⋊C4—432no—
635C4⋊C4—432no—
636C4⋊C4—864no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—864no—
645C4⋊C4—864no—
646C4⋊C4C2×D17214yes—
647C4⋊C4C2×D17214yes—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4C2×D17214yes—
656C22⋊C4C2×D17214yes—
657C42—864no—
658C42—864no—
659C42—864no—
660C42C2×D17212yes—
661C42C2×D17212yes—
662C42C23×D4312yes—
663C42C23×D4312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—864no—
668C23—862no—
669C23—862no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23C22×D17212yes—
676C23C22×D17211yescharacteristic
677Q8—434no—
678Q8—864no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8—3444no—
683Q8—1722no—
684D4—434no—
685D4—8616no—
686D4—864no—
687D4—862no—
688D4—862no—
689D4—862no—
690D4—3444no—
691D4—1722no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—8616no—
701C2×C4—864no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—3444no—
709C2×C4—3444no—
710C2×C4—3444no—
711C2×C4—3444no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4C22×D17212yes—
718C2×C4C22×D17212yes—
719C2×C4C22×D17212yes—
720C2×C4C22×D17212yes—
721C2×C4C22×D17212yes—
722C2×C4C22×D17211yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4#41×D4312yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
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#1458341112yes—
743C22#1458370412yes—
744C22#1458371612yes—
745C22C23×D17211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—864no—
752C4—1722no—
753C4—1722no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4#1458341112yes—
758C4C2×#41×D4311yescharacteristic
759C4C2×#41×D4311yescharacteristic
760C2—42no—
761C2—3442no—
762C2—1724no—
763C2#1914485914yesdirect product factor
764C2C2×#1458341111yescharacteristic
765C2C2×#1458370411yescharacteristic
766C2C2×#1458371611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
hypercenterC2×#433D43
hypocenterC43C2×#3124
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. C2×#14583379C2semidirect
3. #19144859C2direct (N × H)
4. C2×#14583235C2semidirect
5. C2×#14583213C2semidirect
6. C2×#14583195C2semidirect
7. C2×#14583180C2semidirect
8. C2×#14583122C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583063C2semidirect
12. C2×#14583001C2semidirect
13. C2×#14583001C2semidirect
14. C2×C4×Dic172C2semidirect
15. C2×C4×D344C2semidirect
16. C2×C43×#433C2semidirect
23. #14583520C22semidirect
33. #14583379C22semidirect
45. #14583235C22semidirect
46. #14583213C22semidirect
47. #14583195C22semidirect
48. #14583180C22semidirect
49. #14583122C22semidirect
50. #14583115C22semidirect
51. #14583063C22semidirect
53. #14583001C22semidirect
54. #14583001C22semidirect
55. C4×Dic172C22semidirect
56. C4×D344C22semidirect
70. C43×#433C22semidirect
392. C2×#433D43semidirect
394. C2×C43#3124semidirect
441. #433C2×D43semidirect
460. C43C2×#3124semidirect
763. C2#19144859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145833792
#191448592
C2×#145832352
C2×#145832132
C2×#145831952
C2×#145831802
C2×#145831222
C2×#145831152
C2×#145830632
C2×#145830462
C2×#145830012
C2×C4×Dic1722
C2×C4×D3442
C2×C43×#4332
C2×#312443