Finite Group Databasebeta

← C2×#19145945 #25969417

Subgroups — C2×#19145945 #25969417

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583436C211yesmaximal, characteristic, complemented
2C2×#14583428C211yesmaximal, characteristic, complemented
3#19145945C2116yesmaximal, direct product factor
4C2×#14583206C211yesmaximal, characteristic, complemented
5C2×#14583204C211yesmaximal, characteristic, complemented
6C2×#14583200C211yesmaximal, characteristic, complemented
7C2×#14583197C211yesmaximal, characteristic, complemented
8C2×#14583137C211yesmaximal, characteristic, complemented
9C2×#14583134C211yesmaximal, characteristic
10C2×#14583131C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14583123C211yesmaximal, characteristic, complemented
13C2×#14583116C211yesmaximal, characteristic, complemented
14C2×#14583111C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583436—24no—
22#14583436C2218yescomplemented
23#14583428—24no—
24#14583428C2218yescomplemented
25C2×#13063320—21no—
26C2×#13063318—21no—
27C2×#13063317C2211yescharacteristic
28C2×#13063316C2211yescharacteristic
29C2×#13063314C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063307—21no—
32C2×#13063301C2211yescharacteristic
33C2×#13063301C2211yescharacteristic
34C2×#13063300C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×C4×D172—21no—
38C2×C4×D172C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063282—21no—
42C2×#13063281—21no—
43C2×C42×D43C2211yescharacteristic
44#14583206C2218yescomplemented
45#14583204C2218yescomplemented
46#14583200C2218yescomplemented
47#14583197C2218yescomplemented
48#14583137C2218yescomplemented
49#14583134C2218yes—
50#14583131C2218yescomplemented
51#14583125C2218yescomplemented
52#14583123C2218yescomplemented
53#14583116C2218yescomplemented
54#14583111C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×C4⋊(C43⋊C8)C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C4⋊C8×D43C2218yescomplemented
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172C2311yescharacteristic
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C22×C4×D43D411yescharacteristic
83C22×C4×D43D411yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621884—42no—
86C2×#10621884C2314yes—
87C2×#10621882—42no—
88C2×#10621882C2314yes—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—42no—
92C2×C8×D43—42no—
93C2×C8×D43C2314yes—
94C2×C8×D43C2314yes—
95#13063320—28no—
96#13063318—28no—
97#13063317—22no—
98#13063317C2314yes—
99#13063316—22no—
100#13063316C2314yes—
101#13063314—22no—
102#13063314C2314yes—
103#13063310—28no—
104#13063307—28no—
105#13063301—22no—
106#13063301—22no—
107#13063301C2314yes—
108#13063301C2314yes—
109#13063300—22no—
110#13063300C2314yes—
111#13063296—22no—
112#13063296C2314yes—
113Q8×Dic43—22no—
114Q8×Dic43C2314yes—
115C4×D172—28no—
116C4×D172—22no—
117C4×D172C2314yes—
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120(C22⋊D43)⋊C4—28no—
121#13063282—28no—
122#13063281—28no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43D414yes—
146C42×D43C2314yes—
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063249C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C2×Q16×C43—42no—
164C2×Q16×C43C2314yes—
165C2×SD16×C43—42no—
166C2×SD16×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169#124×C43—22no—
170#124×C43C2314yes—
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C2×Q8×C43C2412yes—
193C2×D4×C43—21no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43C2412yes—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—44no—
205C22×Dic43—24no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—44no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×D172—21no—
214C2×D172—24no—
215C2×D172—22no—
216C2×D172—22no—
217C2×D172—44no—
218C2×D172C2412yes—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—42no—
224C2×C4×D43—44no—
225C2×C4×D43C2×D412yes—
226C2×C4×D43C2×D414yes—
227C2×C4×D43C2×D414yes—
228C2×C4×D43C2412yes—
229Q16×C43—44no—
230SD16×C43—44no—
231C2×C8×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43C2412yes—
234C2×C8×C43C2412yes—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C42×C43—24no—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245#10621884—44no—
246#10621882—44no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—24no—
257C4⋊Dic43—24no—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2×D414yes—
269C4×Dic43C2×D414yes—
270C4×Dic43C2412yes—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275C8×D43—44no—
276C8×D43—44no—
277C23×C43—22no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43#13514yes—
289C22×D43C22×D412yes—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—42no—
295Q8×C43—42no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—42no—
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×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43H(5,𝔽2)12yes—
311C2×C4×C432−1+412yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—48no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—48no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326C2×Dic43C22×D412yes—
327D172—22no—
328D172—22no—
329D172—48no—
330D172—42no—
331C4×D43—28no—
332C4×D43—24no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—44no—
336C4×D43—48no—
337C8×C43—22no—
338C8×C43—22no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C2×#3250—431nomaximal, Sylow
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—84no—
346C22×C43#53712yes—
347C22×C43C2×#13512yes—
348C22×C43#57512yes—
349C22×C43C23×D411yescharacteristic
350C2×D43—22no—
351C2×D43—28no—
352C2×D43—22no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—84no—
357C2×D43C2×#13514yes—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43#53712yes—
364C4×C43C2×H(5,𝔽2)11yescharacteristic
365C4×C43C2×2−1+411yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#529—431no—
373C2×#529—431no—
374#3250—4316no—
375C2×#479—431no—
376C2×#479—431no—
377C2×#478—431no—
378C2×#478—431no—
379C2×#467—431no—
380C2×#466—431no—
381C2×#465—431no—
382C2×#465—431no—
383C2×#464—431no—
384C2×#464D4311yescharacteristic, complemented
385C2×#463—431no—
386C2×#463—431no—
387C22×C4⋊C8—431no—
388C2×C43—82no—
389C2×C43#325014yescomplemented
390C2×C43C2×#53711yescharacteristic
391C2×C43C22×#13511yescharacteristic
392C2×C43C2×#57511yescharacteristic
393D43—24no—
394D43—82no—
395C22×Q16C2×D4311yescharacteristic
396C22×SD16—431no—
397C22×SD16C2×D4311yescharacteristic
398C22×D8—431no—
399C23×C8—431no—
400C23×C8—431no—
401#529—438no—
402#529—438no—
403#529—864no—
404#529—864no—
405C2×#126—861no—
406C2×#126—861no—
407C2×#125—431no—
408C2×#125—431no—
409C2×#124—431no—
410C2×#124C2×D4311yescharacteristic
411C2×#123—861no—
412C2×#123—861no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8—431no—
415C2×#121—431no—
416C2×#121—431no—
417C2×C4×Q8—431no—
418C2×C4×Q8C2×D4311yescharacteristic
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×C4×D4—861no—
422C2×C4×D4—861no—
423C2×#117—861no—
424C2×#117—861no—
425C22×C42—431no—
426#479—438no—
427#479—438no—
428#478—438no—
429#478—438no—
430#467—438no—
431#466—438no—
432#465—438no—
433#465—438no—
434#464—438no—
435#464C2×D4318yescomplemented
436#463—438no—
437#463—438no—
438C2×#107—431no—
439C2×#107—431no—
440C2×#106—431no—
441C2×#106—431no—
442C2×C4⋊C8—431no—
443C2×C4⋊C8—431no—
444C2×C4⋊C8—431no—
445C2×C4⋊C8—438no—
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103C2×D4311yescharacteristic
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102C2×D4311yescharacteristic
455C43C2×#325011yescharacteristic, complemented, Sylow
456C22×Q8C22×D4311yescharacteristic
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C22×D4—861no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C2×Q16—42no—
468C2×Q16C22×D4314yes—
469C2×SD16—42no—
470C2×SD16—434no—
471C2×SD16—1722no—
472C2×SD16C22×D4314yes—
473C2×D8—434no—
474C2×D8—1722no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—434no—
478C22×C8—434no—
479C22×C8—1722no—
480C22×C8—1722no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483#126—868no—
484#126—868no—
485#125—434no—
486#125—434no—
487#125—862no—
488#125—862no—
489#124—22no—
490#124—434no—
491#124—862no—
492#124C22×D4314yes—
493#123—868no—
494#123—868no—
495C22⋊Q8—434no—
496C22⋊Q8—434no—
497C22⋊Q8—862no—
498C22⋊Q8—862no—
499#121—434no—
500#121—434no—
501#121—862no—
502#121—862no—
503C4×Q8—22no—
504C4×Q8—434no—
505C4×Q8—862no—
506C4×Q8C22×D4314yes—
507C4×D4—434no—
508C4×D4—434no—
509C4×D4—868no—
510C4×D4—862no—
511C4×D4—868no—
512C4×D4—862no—
513#117—868no—
514#117—868no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—21no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—431no—
541C2×C42—434no—
542C2×C42—434no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—434no—
546#107—434no—
547#106—434no—
548#106—434no—
549C4⋊C8—434no—
550C4⋊C8—434no—
551C4⋊C8—434no—
552C4⋊C8C22×D4314yes—
553#103—434no—
554#103—434no—
555#103—434no—
556#103C22×D4314yes—
557#102—434no—
558#102—434no—
559#102—434no—
560#102C22×D4314yes—
561C24—21no—
562C24—431no—
563C24—861no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8C23×D4312yes—
571C2×Q8C23×D4312yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—861no—
579C2×D4—862no—
580C2×D4—862no—
581C2×D4—1724no—
582C2×D4—1724no—
583C2×D4C23×D4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—432no—
591C22×C4—434no—
592C22×C4—432no—
593C22×C4—434no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—864no—
602C22×C4—1722no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608Q16—44no—
609SD16—44no—
610SD16—1724no—
611D8—1724no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—432no—
615C2×C8—432no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—1724no—
619C2×C8—1724no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4C23×D4312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C42—24no—
649C42—434no—
650C42—434no—
651C42—432no—
652C42—432no—
653C42—864no—
654C42D4×D4312yes—
655C42C23×D4312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—434no—
661C23—432no—
662C23—862no—
663C23—862no—
664C23—862no—
665C23—1722no—
666C23—1722no—
667C23—1722no—
668C23C2×D4×D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—42no—
674Q8—42no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—862no—
679D4—862no—
680D4—1728no—
681D4—1728no—
682D4—1722no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—868no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—864no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—1724no—
705C2×C4—1728no—
706C2×C4—1728no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4C2×D4×D4312yes—
711C2×C4C2×D4×D4312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#1306337012yes—
714C2×C4#1306337212yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—862no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—434no—
725C22—862no—
726C22—862no—
727C22—868no—
728C22—3444no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22#1458347812yes—
733C22#135×D4312yes—
734C22#1458369812yes—
735C22C22×D4×D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—862no—
742C4—862no—
743C4—862no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4#1458347812yes—
748C4C2×#1306337011yescharacteristic
749C4C2×#1306337211yescharacteristic
750C2—82no—
751C2—864no—
752C2—3442no—
753C2#1914594514yesdirect product factor
754C2C2×#1458347811yescharacteristic
755C2C2×#135×D4311yescharacteristic
756C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583134C2
hypercenterC2×#464D43
hypocenterC43C2×#3250
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583436C2semidirect
2. C2×#14583428C2semidirect
3. #19145945C2direct (N × H)
4. C2×#14583206C2semidirect
5. C2×#14583204C2semidirect
6. C2×#14583200C2semidirect
7. C2×#14583197C2semidirect
8. C2×#14583137C2semidirect
10. C2×#14583131C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14583123C2semidirect
13. C2×#14583116C2semidirect
14. C2×#14583111C2semidirect
15. C2×C4⋊C8×D43C2semidirect
16. C2×C43×#464C2semidirect
22. #14583436C22semidirect
24. #14583428C22semidirect
44. #14583206C22semidirect
45. #14583204C22semidirect
46. #14583200C22semidirect
47. #14583197C22semidirect
48. #14583137C22semidirect
50. #14583131C22semidirect
51. #14583125C22semidirect
52. #14583123C22semidirect
53. #14583116C22semidirect
54. #14583111C22semidirect
62. C4⋊C8×D43C22semidirect
73. C43×#464C22semidirect
384. C2×#464D43semidirect
389. C2×C43#3250semidirect
435. #464C2×D43semidirect
455. C43C2×#3250semidirect
753. C2#19145945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834362
C2×#145834282
#191459452
C2×#145832062
C2×#145832042
C2×#145832002
C2×#145831972
C2×#145831372
C2×#145831342
C2×#145831312
C2×#145831252
C2×#145831232
C2×#145831162
C2×#145831112
C2×C4⋊C8×D432
C2×C43×#4642
C2×#325043