Finite Group Databasebeta

← C2×#19147196 #25975320

Subgroups — C2×#19147196 #25975320

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×#14583601C211yesmaximal, characteristic, complemented
2C2×#14583596C211yesmaximal, characteristic, complemented
3#19147196C2116yesmaximal, direct product factor
4C2×#14583299C211yesmaximal, characteristic, complemented
5C2×#14583222C211yesmaximal, characteristic, complemented
6C2×#14583220C211yesmaximal, characteristic, complemented
7C2×#14583211C211yesmaximal, characteristic, complemented
8C2×#14583210C211yesmaximal, characteristic, complemented
9C2×#14583201C211yesmaximal, characteristic, complemented
10C2×#14583197C211yesmaximal, characteristic, complemented
11C2×#14583149C211yesmaximal, characteristic, complemented
12C2×D8×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582975C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C2×#14582938C211yesmaximal, characteristic, complemented
16C2×C43×#469C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18#14583601—24no—
19#14583601C2218yescomplemented
20#14583596—24no—
21#14583596C2218yescomplemented
22C2×#13063318—21no—
23C2×#13063318—21no—
24C2×#13063316C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063309—21no—
27C2×#13063306—21no—
28C2×#13063297—21no—
29C2×#13063296—21no—
30C2×#13063296C2211yescharacteristic
31C2×#13063296C2211yescharacteristic
32C2×D4×Dic43—21no—
33C2×D4×Dic43C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic
35C2×C4×C22⋊D43C2211yescharacteristic
36C2×(C22⋊D43)⋊C4—21no—
37C2×#13063284C2211yescharacteristic
38C2×#13063283C2211yescharacteristic
39C22×C4⋊Dic43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41#14583299C2218yescomplemented
42#14583222C2218yescomplemented
43#14583220C2218yescomplemented
44#14583211C2218yescomplemented
45#14583210C2218yescomplemented
46#14583201C2218yescomplemented
47#14583197C2218yescomplemented
48#14583149C2218yescomplemented
49D8×Dic43C2218yescomplemented
50#14582975C2218yescomplemented
51#14582941C2218yescomplemented
52#14582938C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C2×#121×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#469C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×C22⋊D43—21no—
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C23×Dic43—21no—
81C23×Dic43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—24no—
86C2×#10621872C2314yes—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063318—28no—
90#13063318—28no—
91#13063316—22no—
92#13063316—22no—
93#13063316C2314yes—
94#13063316C2314yes—
95#13063309—28no—
96#13063306—28no—
97#13063297—28no—
98#13063296—28no—
99#13063296—22no—
100#13063296—22no—
101#13063296C2314yes—
102#13063296C2314yes—
103D4×Dic43—28no—
104D4×Dic43—22no—
105D4×Dic43—22no—
106D4×Dic43C2314yes—
107D4×Dic43C2314yes—
108C4×C22⋊D43D414yes—
109C4×C22⋊D43C2314yes—
110(C22⋊D43)⋊C4—28no—
111#13063284—22no—
112#13063284C2314yes—
113#13063283—22no—
114#13063283C2314yes—
115C2×C4⋊Dic43—22no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43C2314yes—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4D411yescharacteristic
128C4⋊C4×D43—22no—
129C4⋊C4×D43C2314yes—
130C2×C22⋊Dic43—21no—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43D411yescharacteristic
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4D411yescharacteristic
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43C2311yescharacteristic
141#13063259C2314yes—
142#13063259C2314yes—
143#13063258C2314yes—
144#13063258C2314yes—
145#13063258C2314yes—
146#13063257C2314yes—
147#13063257C2314yes—
148#13063256C2314yes—
149Dic43⋊C8C2314yes—
150#13063246C2314yes—
151#13063246C2314yes—
152#13063246C2314yes—
153#13063246C2314yes—
154C22⋊(C43⋊C8)C2314yes—
155(C2×D43)⋊C8C2314yes—
156C8×Dic43C2314yes—
157C22×D4×C43—21no—
158C22×D4×C43—21no—
159C22×D4×C43C2311yescharacteristic
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C2×D8×C43—24no—
163C2×D8×C43C2314yes—
164C2×M16×C43—24no—
165C2×M16×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#121×C43—22no—
169#121×C43—22no—
170#121×C43C2314yes—
171#121×C43C2314yes—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176#106×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43C2×D411yescharacteristic
182C23×D43C2×D411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—24no—
186C2×D4×C43—24no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—44no—
192C2×D4×C43—82no—
193C2×D4×C43C2412yes—
194C2×D4×C43C2412yes—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—82no—
208C2×C22⋊D43C2×D414yes—
209C22×Dic43—24no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—24no—
216C22×Dic43—82no—
217C22×Dic43—82no—
218C22×Dic43—82no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—24no—
225C2×C4×D43—82no—
226C2×C4×D43C2×D412yes—
227C2×C4×D43C2412yes—
228D8×C43—28no—
229M16×C43—28no—
230C2×C8×C43—22no—
231C2×C8×C43#4114yes—
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245C22⋊Dic43C2×D414yes—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4C2×D414yes—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4C2×D414yes—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C4×Dic43C2×D412yes—
266C4×Dic43C2412yes—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8C2412yes—
270C2×C43⋊C8C2412yes—
271#10621872—28no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43C22×D412yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—48no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—84no—
297C2×C4×C43—22no—
298C2×C4×C43—24no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4112yes—
308C2×C4×C432−1+412yes—
309C2×C4×C43C2511yescharacteristic
310C22⋊D43—44no—
311C22⋊D43—48no—
312C22⋊D43—84no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—84no—
325C2×Dic43—84no—
326C2×Dic43—84no—
327C2×Dic43C22×D412yes—
328C2×Dic43C22×D412yes—
329C2×Dic43C22×D412yes—
330C4×D43—24no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—84no—
334C8×C43—22no—
335C8×C43C2×#4114yes—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3355—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—44no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—84no—
350C22×C43—84no—
351C22×C43#54712yes—
352C22×C43#57512yes—
353C22×C43#57612yes—
354C22×C43C23×D411yescharacteristic
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—44no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43#54712yes—
363C4×C43C22×#4111yescharacteristic
364C4×C43C2×2−1+411yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—22no—
368Dic43—42no—
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×#478—431no—
382C2×#469—431no—
383C2×#469D4311yescharacteristic, complemented
384C2×C4×D8—431no—
385C2×#436—431no—
386C2×#428—431no—
387C2×#428—431no—
388C2×C43—42no—
389C2×C43—82no—
390C2×C43—82no—
391C2×C43#335514yescomplemented
392C2×C43C2×#54711yescharacteristic
393C2×C43C2×#57511yescharacteristic
394C2×C43C2×#57611yescharacteristic
395D43—42no—
396C22×D8C2×D4311yescharacteristic
397C22×M16—431no—
398C22×M16C2×D4311yescharacteristic
399#553—438no—
400#553—438no—
401#553—864no—
402#553—864no—
403C2×#126—861no—
404C2×#126—861no—
405C2×#125—431no—
406C2×#125—431no—
407C2×#123—861no—
408C2×#123—861no—
409C2×#121—431no—
410C2×#121—431no—
411C2×#121—861no—
412C2×#121—861no—
413C2×#121C2×D4311yescharacteristic
414C2×#121C2×D4311yescharacteristic
415C2×C4×D4—431no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×C4×D4—861no—
419C2×C4×D4—861no—
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#478—438no—
431#469—438no—
432#469C2×D4318yescomplemented
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×#107—431no—
442C2×#106—431no—
443C2×#106—431no—
444C2×#106—431no—
445C2×#106C2×D4311yescharacteristic
446C2×C4⋊C8—431no—
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—21no—
458C22×D4—21no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4C22×D4311yescharacteristic
463C22×D4C22×D4311yescharacteristic
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4C22×D4311yescharacteristic
470C2×D8—24no—
471C2×D8C22×D4314yes—
472C2×M16—24no—
473C2×M16—434no—
474C2×M16—864no—
475C2×M16C22×D4314yes—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8C22×D4311yescharacteristic
479C22×C8C22×D4311yescharacteristic
480#126—868no—
481#126—868no—
482#125—434no—
483#125—434no—
484#125—862no—
485#125—862no—
486#123—868no—
487#123—868no—
488#121—22no—
489#121—22no—
490#121—434no—
491#121—434no—
492#121—862no—
493#121—862no—
494#121—868no—
495#121—868no—
496#121C22×D4314yes—
497#121C22×D4314yes—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—434no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—868no—
505C4×D4—868no—
506#117—434no—
507#117—434no—
508#117—862no—
509#117—862no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—862no—
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
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—861no—
539C2×C42—861no—
540#107—434no—
541#107—434no—
542#107—434no—
543#107—434no—
544#107—434no—
545#106—434no—
546#106—434no—
547#106—434no—
548#106C22×D4314yes—
549C4⋊C8—434no—
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—21no—
561C24—431no—
562C24D4×D4311yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—434no—
574C2×D4—864no—
575C2×D4—864no—
576C2×D4—3442no—
577C2×D4—1722no—
578C2×D4—1724no—
579C2×D4C23×D4312yes—
580C2×D4C23×D4312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—864no—
591C22×C4—864no—
592C22×C4—864no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—864no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—3442no—
601C22×C4—3442no—
602C22×C4—3442no—
603C22×C4—3442no—
604C22×C4D4×D4312yes—
605C22×C4D4×D4311yescharacteristic
606C22×C4C23×D4312yes—
607C22×C4C23×D4311yescharacteristic
608D8—28no—
609M16—28no—
610M16—868no—
611C2×C8—22no—
612C2×C8—432no—
613C2×C8—432no—
614C2×C8—862no—
615C2×C8—862no—
616C2×C8#1062190014yes—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—434no—
622C4⋊C4—432no—
623C4⋊C4—432no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—864no—
635C4⋊C4—861no—
636C4⋊C4C23×D4312yes—
637C4⋊C4C23×D4312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—434no—
641C22⋊C4—434no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C42—432no—
649C42—432no—
650C42—864no—
651C42—864no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—432no—
664C23—862no—
665C23—862no—
666C23—862no—
667C23C2×D4×D4312yes—
668C23C2×D4×D4311yescharacteristic
669D4—22no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—84no—
677D4—3444no—
678D4—1724no—
679D4—1728no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—432no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—864no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—3444no—
702C2×C4—3444no—
703C2×C4—3444no—
704C2×C4—3444no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4C2×#1062190012yes—
712C2×C4#1306337212yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—862no—
716C8—862no—
717C8C2×#1062190014yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—1724no—
734C22#1458354912yes—
735C22#1458369512yes—
736C22#1458370312yes—
737C22C22×D4×D4311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—862no—
742C4—862no—
743C4—862no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4—1722no—
748C4#1458354912yes—
749C4C22×#1062190011yescharacteristic
750C4C2×#1306337211yescharacteristic
751C2—42no—
752C2—82no—
753C2—82no—
754C2—1722no—
755C2#1914719614yesdirect product factor
756C2C2×#1458354911yescharacteristic
757C2C2×#1458369511yescharacteristic
758C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#469C2
socleC23×C43C22×D4
hypercenterC2×#469D43
hypocenterC43C2×#3355
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#14583601C2semidirect
2. C2×#14583596C2semidirect
3. #19147196C2direct (N × H)
4. C2×#14583299C2semidirect
5. C2×#14583222C2semidirect
6. C2×#14583220C2semidirect
7. C2×#14583211C2semidirect
8. C2×#14583210C2semidirect
9. C2×#14583201C2semidirect
10. C2×#14583197C2semidirect
11. C2×#14583149C2semidirect
12. C2×D8×Dic43C2semidirect
13. C2×#14582975C2semidirect
14. C2×#14582941C2semidirect
15. C2×#14582938C2semidirect
16. C2×C43×#469C2semidirect
19. #14583601C22semidirect
21. #14583596C22semidirect
41. #14583299C22semidirect
42. #14583222C22semidirect
43. #14583220C22semidirect
44. #14583211C22semidirect
45. #14583210C22semidirect
46. #14583201C22semidirect
47. #14583197C22semidirect
48. #14583149C22semidirect
49. D8×Dic43C22semidirect
50. #14582975C22semidirect
51. #14582941C22semidirect
52. #14582938C22semidirect
73. C43×#469C22semidirect
383. C2×#469D43semidirect
391. C2×C43#3355semidirect
432. #469C2×D43semidirect
456. C43C2×#3355semidirect
755. C2#19147196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836012
C2×#145835962
#191471962
C2×#145832992
C2×#145832222
C2×#145832202
C2×#145832112
C2×#145832102
C2×#145832012
C2×#145831972
C2×#145831492
C2×D8×Dic432
C2×#145829752
C2×#145829412
C2×#145829382
C2×C43×#4692
C2×#335543