Finite Group Databasebeta

← C2×#19145164 #25966322

Subgroups — C2×#19145164 #25966322

Order 11008.

2070 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×#14583434C211yesmaximal, characteristic, complemented
2C2×#14583428C211yesmaximal, characteristic, complemented
3#19145164C2116yesmaximal, direct product factor
4C2×#14583298C211yesmaximal, characteristic, complemented
5C2×#14583281C211yesmaximal, characteristic, complemented
6C2×#14583254C211yesmaximal, characteristic, complemented
7C2×#14583139C211yesmaximal, characteristic, complemented
8C2×#14583134C211yesmaximal, characteristic
9C2×#14583131C211yesmaximal, characteristic, complemented
10C2×#14583127C211yesmaximal, characteristic, complemented
11C2×#14582991C211yesmaximal, characteristic, complemented
12C2×#14582990C211yesmaximal, characteristic, complemented
13C2×#14582984C211yesmaximal, characteristic, complemented
14C2×#14582979C211yesmaximal, characteristic, complemented
15C2×C4×C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#488C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583434—24no—
24#14583434C2218yescomplemented
25#14583428—24no—
26#14583428C2218yescomplemented
27C2×#13063320—21no—
28C2×#13063318—21no—
29C2×#13063317C2211yescharacteristic
30C2×#13063313C2211yescharacteristic
31C2×#13063310—21no—
32C2×#13063307—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063300C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×#13063290C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×#13063287—21no—
41C2×#13063287C2211yescharacteristic
42C2×(C22⋊D43)⋊C4—21no—
43C2×#13063283—21no—
44C2×#13063281—21no—
45C2×C42×D43C2211yescharacteristic
46#14583298C2218yescomplemented
47#14583281C2218yescomplemented
48#14583254C2218yescomplemented
49#14583139C2218yescomplemented
50#14583134C2218yes—
51#14583131C2218yescomplemented
52#14583127C2218yescomplemented
53#14582991C2218yescomplemented
54#14582990C2218yescomplemented
55#14582984C2218yescomplemented
56#14582979C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×C4×C43⋊C8C2211yescharacteristic
66C2×C8×Dic43C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C4×C8×D43C2218yescomplemented
69C2×#125×C43C2211yescharacteristic
70C2×#124×C43C2211yescharacteristic
71C43×#488C2218yescomplemented
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×#10621885—24no—
87C2×#10621885C2314yes—
88C2×#10621883—24no—
89C2×#10621883C2314yes—
90C2×#10621884—24no—
91C2×#10621884C2314yes—
92C2×#10621882—24no—
93C2×#10621882C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—24no—
97C2×C8×D43—24no—
98C2×C8×D43C2314yes—
99C2×C8×D43C2314yes—
100#13063320—28no—
101#13063318—28no—
102#13063317—22no—
103#13063317C2314yes—
104#13063313—22no—
105#13063313C2314yes—
106#13063310—28no—
107#13063307—28no—
108#13063305—22no—
109#13063305C2314yes—
110#13063301—22no—
111#13063301C2314yes—
112#13063300—22no—
113#13063300C2314yes—
114#13063296—22no—
115#13063296C2314yes—
116Q8×Dic43—22no—
117Q8×Dic43C2314yes—
118#13063290—22no—
119#13063290C2314yes—
120D4×Dic43—22no—
121D4×Dic43C2314yes—
122#13063287—28no—
123#13063287—22no—
124#13063287C2314yes—
125(C22⋊D43)⋊C4—28no—
126#13063283—28no—
127#13063281—28no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
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×(C2×D43)⋊C4—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C42×D43D414yes—
150C42×D43C2314yes—
151#13063258C2314yes—
152#13063258C2314yes—
153#13063256C2314yes—
154#13063256C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159C4×C43⋊C8C2314yes—
160C8×Dic43C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×D4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166#125×C43—22no—
167#125×C43C2314yes—
168#124×C43—22no—
169#124×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#103×C43C2314yes—
178#103×C43C2314yes—
179#102×C43C2314yes—
180#102×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43C2412yes—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—44no—
201C22×Dic43—24no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—44no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172—44no—
214C2×D172C2412yes—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—44no—
221C2×C4×D43C2×D412yes—
222C2×C4×D43C2×D414yes—
223C2×C4×D43C2×D414yes—
224C2×C4×D43C2412yes—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—21no—
228C2×Dic86C2412yes—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245#10621885—28no—
246#10621884—28no—
247#10621883—28no—
248#10621882—28no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—24no—
258C4⋊Dic43—24no—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2×D414yes—
269C4×Dic43C2×D414yes—
270C4×Dic43C2412yes—
271C2×C43⋊C8#4114yes—
272C2×C43⋊C8#4114yes—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275C8×D43—28no—
276C8×D43—28no—
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—42no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—42no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
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—48no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—48no—
320C2×Dic43#13514yes—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324D172—22no—
325D172—22no—
326D172—48no—
327D172—42no—
328C4×D43—28no—
329C4×D43—24no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—28no—
333C4×D43—48no—
334Dic86—22no—
335Dic86—22no—
336Dic86—42no—
337C8×C43—22no—
338C8×C43—22no—
339C43⋊C8C2×#4114yes—
340C43⋊C8C2×#4114yes—
341C2×#3168—431nomaximal, Sylow
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—84no—
346C22×C43#53212yes—
347C22×C43C2×#13512yes—
348C22×C43C2×#13512yes—
349C22×C43C23×D411yescharacteristic
350C2×D43—28no—
351C2×D43—22no—
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#53212yes—
364C4×C43C22×#4111yescharacteristic
365C4×C43C22×#4111yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43C2×#13514yes—
372C2×#529—431no—
373C2×#529—431no—
374#3168—4316no—
375C2×#499—431no—
376C2×#495—431no—
377C2×#488—431no—
378C2×#488D4311yescharacteristic, complemented
379C2×#467—431no—
380C2×#466—431no—
381C2×#465—431no—
382C2×#465—431no—
383C2×C4×Q16—431no—
384C2×C4×SD16—431no—
385C2×C4×SD16—431no—
386C2×C4×D8—431no—
387C22×C4×C8—431no—
388C2×C43—82no—
389C2×C43#316814yescomplemented
390C2×C43C2×#53211yescharacteristic
391C2×C43C22×#13511yescharacteristic
392C2×C43C22×#13511yescharacteristic
393D43—24no—
394D43—82no—
395C22×Q16—431no—
396C22×SD16—431no—
397C22×SD16—431no—
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×#125C2×D4311yescharacteristic
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×Q8—431no—
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#499—438no—
427#495—438no—
428#488—438no—
429#488C2×D4318yescomplemented
430#467—438no—
431#466—438no—
432#465—438no—
433#465—438no—
434C4×Q16—438no—
435C4×SD16—438no—
436C4×SD16—438no—
437C4×D8—438no—
438C2×#107—431no—
439C2×#107—431no—
440C2×#106—431no—
441C2×#106—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103C2×D4311yescharacteristic
445C2×#103C2×D4311yescharacteristic
446C2×#102—431no—
447C2×#102—431no—
448C2×#102C2×D4311yescharacteristic
449C2×#102C2×D4311yescharacteristic
450C2×C4×C8—431no—
451C2×C4×C8—431no—
452C2×C4×C8—431no—
453C2×C4×C8—438no—
454C2×C4×C8C2×D4311yescharacteristic
455C43C2×#316811yescharacteristic, complemented, Sylow
456C22×Q8—431no—
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—434no—
468C2×Q16—864no—
469C2×SD16—434no—
470C2×SD16—434no—
471C2×SD16—864no—
472C2×SD16—864no—
473C2×D8—434no—
474C2×D8—864no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—434no—
478C22×C8—434no—
479C22×C8—864no—
480C22×C8—864no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483#126—868no—
484#126—868no—
485#125—22no—
486#125—434no—
487#125—862no—
488#125C22×D4314yes—
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—434no—
504C4×Q8—434no—
505C4×Q8—862no—
506C4×Q8—862no—
507C4×D4—434no—
508C4×D4—434no—
509C4×D4—862no—
510C4×D4—862no—
511C4×D4—868no—
512C4×D4—868no—
513#117—868no—
514#117—868no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
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—431no—
538C2×C42—431no—
539C2×C42—431no—
540C2×C42—434no—
541C2×C42—434no—
542C2×C42—861no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—434no—
546#107—434no—
547#106—434no—
548#106—434no—
549#103—434no—
550#103—434no—
551#103C22×D4314yes—
552#103C22×D4314yes—
553#102—434no—
554#102—434no—
555#102C22×D4314yes—
556#102C22×D4314yes—
557C4×C8—434no—
558C4×C8—434no—
559C4×C8—434no—
560C4×C8C22×D4314yes—
561C24—21no—
562C24—431no—
563C24—861no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—862no—
570C2×Q8—862no—
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—434no—
591C22×C4—432no—
592C22×C4—434no—
593C22×C4—432no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—864no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608Q16—868no—
609SD16—868no—
610SD16—868no—
611D8—868no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—434no—
615C2×C8—434no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—868no—
619C2×C8—868no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—432no—
627C4⋊C4—432no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4C23×D4312yes—
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—434no—
649C42—432no—
650C42—434no—
651C42—432no—
652C42—864no—
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—42no—
672Q8—862no—
673Q8—862no—
674Q8—1722no—
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—434no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—868no—
696C2×C4—868no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
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#41×D4312yes—
714C2×C4#41×D4312yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—22no—
718C8—434no—
719C8—434no—
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#1458344812yes—
733C22#135×D4312yes—
734C22#135×D4312yes—
735C22C22×D4×D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—434no—
742C4—862no—
743C4—862no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4#1458344812yes—
748C4C2×#41×D4311yescharacteristic
749C4C2×#41×D4311yescharacteristic
750C2—82no—
751C2—864no—
752C2—3442no—
753C2#1914516414yesdirect product factor
754C2C2×#1458344811yescharacteristic
755C2C2×#135×D4311yescharacteristic
756C2C2×#135×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#488C2
socleC23×C43C22×D4
prime radicalC2×#14583134C2
hypercenterC2×#488D43
hypocenterC43C2×#3168
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#14583434C2semidirect
2. C2×#14583428C2semidirect
3. #19145164C2direct (N × H)
4. C2×#14583298C2semidirect
5. C2×#14583281C2semidirect
6. C2×#14583254C2semidirect
7. C2×#14583139C2semidirect
9. C2×#14583131C2semidirect
10. C2×#14583127C2semidirect
11. C2×#14582991C2semidirect
12. C2×#14582990C2semidirect
13. C2×#14582984C2semidirect
14. C2×#14582979C2semidirect
15. C2×C4×C8×D43C2semidirect
16. C2×C43×#488C2semidirect
24. #14583434C22semidirect
26. #14583428C22semidirect
46. #14583298C22semidirect
47. #14583281C22semidirect
48. #14583254C22semidirect
49. #14583139C22semidirect
51. #14583131C22semidirect
52. #14583127C22semidirect
53. #14582991C22semidirect
54. #14582990C22semidirect
55. #14582984C22semidirect
56. #14582979C22semidirect
68. C4×C8×D43C22semidirect
71. C43×#488C22semidirect
378. C2×#488D43semidirect
389. C2×C43#3168semidirect
429. #488C2×D43semidirect
455. C43C2×#3168semidirect
753. C2#19145164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×#145834282
#191451642
C2×#145832982
C2×#145832812
C2×#145832542
C2×#145831392
C2×#145831342
C2×#145831312
C2×#145831272
C2×#145829912
C2×#145829902
C2×#145829842
C2×#145829792
C2×C4×C8×D432
C2×C43×#4882
C2×#316843