Finite Group Databasebeta

← C2×#19147198 #25975322

Subgroups — C2×#19147198 #25975322

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic, complemented
2C2×#14583599C211yesmaximal, characteristic, complemented
3#19147198C2116yesmaximal, direct product factor
4C2×#14583298C211yesmaximal, characteristic, complemented
5C2×#14583225C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583214C211yesmaximal, characteristic, complemented
8C2×#14583211C211yesmaximal, characteristic, complemented
9C2×#14583200C211yesmaximal, characteristic, complemented
10C2×#14583151C211yesmaximal, characteristic, complemented
11C2×#14583151C211yesmaximal, characteristic, complemented
12C2×C4×#10621882C211yesmaximal, characteristic, complemented
13C2×#14582976C211yesmaximal, characteristic, complemented
14C2×#14582940C211yesmaximal, characteristic, complemented
15C2×#14582938C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×#10621882C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20#14583602—24no—
21#14583602C2218yescomplemented
22#14583599—24no—
23#14583599C2218yescomplemented
24C2×#13063320—21no—
25C2×#13063318—21no—
26C2×#13063317C2211yescharacteristic
27C2×#13063310—21no—
28C2×#13063308—21no—
29C2×#13063300—21no—
30C2×#13063300C2211yescharacteristic
31C2×#13063300C2211yescharacteristic
32C2×#13063298—21no—
33C2×#13063296C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×#13063287—21no—
38C2×C4×C22⋊D43—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583298C2218yescomplemented
44#14583225C2218yescomplemented
45#14583222C2218yescomplemented
46#14583214C2218yescomplemented
47#14583211C2218yescomplemented
48#14583200C2218yescomplemented
49#14583151C2218yescomplemented
50#14583151C2218yescomplemented
51C4×#10621882C2218yescomplemented
52#14582976C2218yescomplemented
53#14582940C2218yescomplemented
54#14582938C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×#13063256C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172—21no—
79C22×D172D411yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C2×#10621882—24no—
89C2×#10621882C2314yes—
90C2×#10621872—24no—
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C2×#10621872C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96#13063320—28no—
97#13063318—28no—
98#13063317—22no—
99#13063317C2314yes—
100#13063310—28no—
101#13063308—28no—
102#13063300—28no—
103#13063300—22no—
104#13063300—22no—
105#13063300C2314yes—
106#13063300C2314yes—
107#13063298—28no—
108#13063296—22no—
109#13063296—22no—
110#13063296C2314yes—
111#13063296C2314yes—
112C4×D172—22no—
113C4×D172D414yes—
114C4×D172C2314yes—
115C4×D172C2314yes—
116#13063287—28no—
117C4×C22⋊D43—28no—
118#13063283—22no—
119#13063283—22no—
120#13063283C2314yes—
121#13063283C2314yes—
122C2×C4⋊Dic43D411yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43C2314yes—
133C4⋊C4×D43C2314yes—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—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×(C2×D43)⋊C4D411yescharacteristic
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145#13063259C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152#13063247C2314yes—
153#13063247C2314yes—
154#13063246C2314yes—
155#13063245C2314yes—
156(C2×D43)⋊C8C2314yes—
157(C2×D43)⋊C8C2314yes—
158C4×C43⋊C8C2314yes—
159C22×D4×C43C2311yescharacteristic
160C23×C4×C43—21no—
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163#125×C43—22no—
164#125×C43C2314yes—
165C4×D4×C43—22no—
166C4×D4×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#107×C43C2314yes—
175#106×C43C2314yes—
176C4⋊C8×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C23×D43C2×D411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43—22no—
185C2×D4×C43—22no—
186C2×D4×C43C2412yes—
187C22×C4×C43—24no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—82no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—44no—
198C2×C22⋊D43—82no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C2×D172—21no—
205C2×D172—24no—
206C2×D172—24no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—42no—
210C2×D172—44no—
211C2×D172—82no—
212C2×D172C2×D414yes—
213C2×D172C2412yes—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—82no—
222C2×C4×D43—82no—
223C2×C4×D43—82no—
224C2×C4×D43C2×D412yes—
225C2×C4×D43C2×D412yes—
226C2×C4×D43C2412yes—
227C2×C4×D43C2412yes—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C22⋊C4×C43—24no—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245#10621882—28no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4C2×D414yes—
252(C2×D43)⋊C4C2×D414yes—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43C2×D414yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259C4⋊Dic43C2412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8#4114yes—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270#10621872—28no—
271#10621872—28no—
272C23×C43—22no—
273C23×C43—42no—
274C23×C43—42no—
275C23×C43—42no—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43C22×D412yes—
288C22×D43C22×D412yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—42no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—84no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4112yes—
305C2×C4×C432−1+412yes—
306C2×C4×C43C2511yescharacteristic
307C22⋊D43—48no—
308C22⋊D43—84no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319D172—22no—
320D172—22no—
321D172—44no—
322D172—48no—
323D172—42no—
324D172—84no—
325C4×D43—24no—
326C4×D43—24no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—84no—
332C4×D43—84no—
333C4×D43—84no—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—22no—
337C43⋊C8C2×#4114yes—
338C2×#3355—431nomaximal, Sylow
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—84no—
343C22×C43#54712yes—
344C22×C43#57512yes—
345C22×C43#57612yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—44no—
354C2×D43—44no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—84no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43#54712yes—
365C4×C43C22×#4111yescharacteristic
366C4×C43C2×2−1+411yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#553—431no—
373C2×#553—431no—
374#3355—4316no—
375C2×#499—431no—
376C2×#482—431no—
377C2×#482—431no—
378C2×#480—431no—
379C2×#480—431no—
380C2×#478—431no—
381C2×#478D4311yescharacteristic, complemented
382C2×#469—431no—
383C2×#469—431no—
384C2×C4×D8—431no—
385C2×#436—431no—
386C2×#428—431no—
387C2×#428—431no—
388C2×C43—82no—
389C2×C43#335514yescomplemented
390C2×C43C2×#54711yescharacteristic
391C2×C43C2×#57511yescharacteristic
392C2×C43C2×#57611yescharacteristic
393D43—42no—
394D43—42no—
395D43—82no—
396C22×D8—431no—
397C22×M16—431no—
398C22×M16—431no—
399#553—438no—
400#553—438no—
401#553—864no—
402#553—864no—
403C2×#126—861no—
404C2×#126—861no—
405C2×#125—431no—
406C2×#125C2×D4311yescharacteristic
407C2×#123—861no—
408C2×#123—861no—
409C2×#121—431no—
410C2×#121—431no—
411C2×#121—431no—
412C2×#121—431no—
413C2×#121—861no—
414C2×#121—861no—
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—861no—
418C2×C4×D4—861no—
419C2×C4×D4C2×D4311yescharacteristic
420C2×#117—431no—
421C2×#117—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—431no—
424#499—438no—
425#482—438no—
426#482—438no—
427#480—438no—
428#480—438no—
429#478—438no—
430#478C2×D4318yescomplemented
431#469—438no—
432#469—438no—
433C4×D8—438no—
434#436—438no—
435#428—438no—
436#428—438no—
437C2×#107—431no—
438C2×#107—431no—
439C2×#107—431no—
440C2×#107—431no—
441C2×#107C2×D4311yescharacteristic
442C2×#106—431no—
443C2×#106—431no—
444C2×#106—431no—
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102C2×D4311yescharacteristic
452C2×#102C2×D4311yescharacteristic
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×C4×C8—431no—
456C43C2×#335511yescharacteristic, complemented, Sylow
457C22×D4—431no—
458C22×D4—431no—
459C22×D4—861no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4C22×D4311yescharacteristic
464C23×C4—21no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4—861no—
470C2×D8—434no—
471C2×D8—864no—
472C2×M16—434no—
473C2×M16—434no—
474C2×M16—864no—
475C2×M16—864no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8C22×D4311yescharacteristic
479C22×C8C22×D4311yescharacteristic
480#126—868no—
481#126—868no—
482#125—22no—
483#125—434no—
484#125—862no—
485#125C22×D4314yes—
486#123—868no—
487#123—868no—
488#121—434no—
489#121—434no—
490#121—434no—
491#121—434no—
492#121—868no—
493#121—862no—
494#121—862no—
495#121—868no—
496#121—862no—
497#121—862no—
498C4×D4—22no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—434no—
502C4×D4—868no—
503C4×D4—868no—
504C4×D4—862no—
505C4×D4C22×D4314yes—
506#117—434no—
507#117—434no—
508#117—862no—
509#117—862no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—434no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
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—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540#107—434no—
541#107—434no—
542#107—434no—
543#107—434no—
544#107C22×D4314yes—
545#106—434no—
546#106—434no—
547#106—434no—
548#106C22×D4314yes—
549C4⋊C8C22×D4314yes—
550#102—434no—
551#102—434no—
552#102—434no—
553#102—434no—
554#102C22×D4314yes—
555#102C22×D4314yes—
556C22⋊C8—434no—
557C22⋊C8—434no—
558C4×C8—434no—
559C24—21no—
560C24—431no—
561C24—431no—
562C24—861no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—434no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—861no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—3442no—
576C2×D4—3442no—
577C2×D4—1722no—
578C2×D4—1724no—
579C2×D4—1724no—
580C2×D4C23×D4312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—864no—
593C22×C4—864no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—864no—
602C22×C4—3442no—
603C22×C4—3442no—
604C22×C4—3442no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608D8—868no—
609M16—868no—
610M16—868no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—434no—
614C2×C8—432no—
615C2×C8—432no—
616C2×C8—862no—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—434no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—432no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4C23×D4312yes—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C22⋊C4—24no—
639C22⋊C4—434no—
640C22⋊C4—434no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C42—864no—
649C42—864no—
650C42D4×D4312yes—
651C42C23×D4312yes—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—432no—
657C23—432no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—862no—
664C23—862no—
665C23—1722no—
666C23—1722no—
667C23—1722no—
668C23C2×D4×D4311yescharacteristic
669D4—22no—
670D4—22no—
671D4—42no—
672D4—862no—
673D4—862no—
674D4—3444no—
675D4—3444no—
676D4—1724no—
677D4—1728no—
678D4—1728no—
679D4—1722no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—864no—
698C2×C4—864no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—3444no—
703C2×C4—3444no—
704C2×C4—3444no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4C2×D4×D4312yes—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4#41×D4312yes—
712C2×C4#1306337312yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—22no—
716C8—434no—
717C8—862no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—3444no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1724no—
733C22—1724no—
734C22#1458355112yes—
735C22#1458369612yes—
736C22#1458370312yes—
737C22C22×D4×D4311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—862no—
744C4—862no—
745C4—1722no—
746C4—1722no—
747C4—1722no—
748C4#1458355112yes—
749C4C2×#41×D4311yescharacteristic
750C4C2×#1306337311yescharacteristic
751C2—82no—
752C2—3442no—
753C2—1722no—
754C2—1722no—
755C2#1914719814yesdirect product factor
756C2C2×#1458355111yescharacteristic
757C2C2×#1458369611yescharacteristic
758C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
hypercenterC2×#478D43
hypocenterC43C2×#3355
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583602C2semidirect
2. C2×#14583599C2semidirect
3. #19147198C2direct (N × H)
4. C2×#14583298C2semidirect
5. C2×#14583225C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583214C2semidirect
8. C2×#14583211C2semidirect
9. C2×#14583200C2semidirect
10. C2×#14583151C2semidirect
11. C2×#14583151C2semidirect
12. C2×C4×#10621882C2semidirect
13. C2×#14582976C2semidirect
14. C2×#14582940C2semidirect
15. C2×#14582938C2semidirect
16. C2×C43×#478C2semidirect
21. #14583602C22semidirect
23. #14583599C22semidirect
43. #14583298C22semidirect
44. #14583225C22semidirect
45. #14583222C22semidirect
46. #14583214C22semidirect
47. #14583211C22semidirect
48. #14583200C22semidirect
49. #14583151C22semidirect
50. #14583151C22semidirect
51. C4×#10621882C22semidirect
52. #14582976C22semidirect
53. #14582940C22semidirect
54. #14582938C22semidirect
71. C43×#478C22semidirect
381. C2×#478D43semidirect
389. C2×C43#3355semidirect
430. #478C2×D43semidirect
456. C43C2×#3355semidirect
755. C2#19147198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836022
C2×#145835992
#191471982
C2×#145832982
C2×#145832252
C2×#145832222
C2×#145832142
C2×#145832112
C2×#145832002
C2×#145831512
C2×C4×#106218822
C2×#145829762
C2×#145829402
C2×#145829382
C2×C43×#4782
C2×#335543