Finite Group Databasebeta

← C2×#19147070 #25975165

Subgroups — C2×#19147070 #25975165

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583599C211yesmaximal, characteristic, complemented
2C2×#14583554C211yesmaximal, characteristic, complemented
3#19147070C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583216C211yesmaximal, characteristic, complemented
6C2×#14583216C211yesmaximal, characteristic, complemented
7C2×#14583221C211yesmaximal, characteristic, complemented
8C2×#14583211C211yesmaximal, characteristic, complemented
9C2×#14583199C211yesmaximal, characteristic, complemented
10C2×#14583189C211yesmaximal, characteristic, complemented
11C2×#14583149C211yesmaximal, characteristic, complemented
12C2×#14583132C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582938C211yesmaximal, characteristic, complemented
15C2×#106×D43C211yesmaximal, characteristic, complemented
16C2×C43×#442C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583599—24no—
21#14583599C2218yescomplemented
22#14583554—24no—
23#14583554C2218yescomplemented
24C2×#13063325C2211yescharacteristic
25C2×#13063318—21no—
26C2×#13063317C2211yescharacteristic
27C2×#13063308—21no—
28C2×#13063307—21no—
29C2×#13063307—21no—
30C2×#13063304—21no—
31C2×#13063298—21no—
32C2×#13063296C2211yescharacteristic
33C2×#13063296C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×#13063283C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583221C2218yescomplemented
44#14583216C2218yescomplemented
45#14583216C2218yescomplemented
46#14583211C2218yescomplemented
47#14583199C2218yescomplemented
48#14583189C2218yescomplemented
49#14583149C2218yescomplemented
50#14583132C2218yescomplemented
51#14582972C2218yescomplemented
52#14582938C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61#106×D43C2218yescomplemented
62C2×C4⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#442C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×D172D411yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C2×#10621872—24no—
91C2×#10621872C2314yes—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C2×C8×D43—24no—
95C2×C8×D43C2314yes—
96#13063325—22no—
97#13063325C2314yes—
98#13063318—28no—
99#13063317—22no—
100#13063317C2314yes—
101#13063308—28no—
102#13063307—28no—
103#13063307—28no—
104#13063304—28no—
105#13063298—28no—
106#13063296—22no—
107#13063296—22no—
108#13063296—22no—
109#13063296—22no—
110#13063296C2314yes—
111#13063296C2314yes—
112#13063296C2314yes—
113#13063296C2314yes—
114C4×D172D414yes—
115C4×D172C2314yes—
116C4×C22⋊D43—28no—
117#13063283—22no—
118#13063283C2314yes—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43D411yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×Dic43⋊C4—21no—
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×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C4⋊C4×D43C2314yes—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144#13063259C2314yes—
145#13063259C2314yes—
146#13063258C2314yes—
147#13063257C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152C4⋊(C43⋊C8)C2314yes—
153#13063246C2314yes—
154#13063246C2314yes—
155#13063246C2314yes—
156#13063246C2314yes—
157(C2×D43)⋊C8C2314yes—
158(C2×D43)⋊C8C2314yes—
159C22×D4×C43C2311yescharacteristic
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43—21no—
162C23×C4×C43—21no—
163C2×D8×C43—24no—
164C2×D8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C4×D4×C43—22no—
168C4×D4×C43—22no—
169C4×D4×C43C2314yes—
170C4×D4×C43C2314yes—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C42×C43C2311yescharacteristic
176#106×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179#97×C43C2314yes—
180C24×C43—21no—
181C24×C43—21no—
182C23×D43C2×D411yescharacteristic
183C23×D43C2×D411yescharacteristic
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43C2412yes—
191C2×D4×C43C2412yes—
192C22×C4×C43—24no—
193C22×C4×C43—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—44no—
197C22×C4×C43—82no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—44no—
208C2×C22⋊D43—82no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215#10621898—432no—
216C2×D172—24no—
217C2×D172C2×D414yes—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—44no—
226C2×C4×D43—44no—
227C2×C4×D43—82no—
228C2×C4×D43C2×D412yes—
229C2×C4×D43C2×D412yes—
230C2×C4×D43C2412yes—
231C2×C4×D43C2412yes—
232C2×Dic86—24no—
233C2×Dic86—44no—
234D8×C43—28no—
235C2×C8×C43—22no—
236C2×C8×C43#4114yescomplemented
237C2×C8×C43C2412yes—
238C2×C8×C43C2412yes—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43C2412yes—
242C4⋊C4×C43C2412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C42×C43C2×D412yes—
246C42×C43C2412yes—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4C2×D414yes—
253(C2×D43)⋊C4C2×D414yes—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—24no—
258C4⋊Dic43—21no—
259C4⋊Dic43C2×D414yes—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269C4×Dic43—24no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274#10621872—28no—
275C8×D43—28no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43AGL(1,ℤ/8)14yes—
291C22×D43C22×D412yes—
292C22×D43C22×D412yes—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—42no—
298D4×C43—42no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—48no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—84no—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4112yes—
311C2×C4×C432−1+412yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—48no—
314C22⋊D43—48no—
315C22⋊D43—48no—
316C22⋊D43—84no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43C22×D412yes—
328C2×Dic43C22×D412yes—
329D172—28no—
330C4×D43—24no—
331C4×D43—24no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—48no—
337C4×D43—48no—
338C4×D43—84no—
339Dic86—48no—
340C8×C43—22no—
341C8×C43C2×#4114yescomplemented
342C43⋊C8—22no—
343C43⋊C8—22no—
344C2×#3345—431nomaximal, Sylow
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—84no—
352C22×C43—84no—
353C22×C43#54712yes—
354C22×C43C2×AGL(1,ℤ/8)12yes—
355C22×C43#57712yes—
356C22×C43C23×D411yescharacteristic
357C2×D43—28no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—44no—
364C2×D43C2×AGL(1,ℤ/8)14yes—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43#54712yes—
370C4×C43C22×#4111yescharacteristic
371C4×C43C2×2−1+411yescharacteristic
372Dic43—22no—
373Dic43—22no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378C2×#553—431no—
379C2×#547—431no—
380#3345—4316no—
381C2×#501—431no—
382C2×#481—431no—
383C2×#481—431no—
384C2×#482—431no—
385C2×#480—431no—
386C2×#478—431no—
387C2×#476—431no—
388C2×#469—431no—
389C2×#466—431no—
390C2×#442D4311yescharacteristic, complemented
391C2×#435—431no—
392C2×#428—431no—
393C22×#106—431no—
394C2×C43—82no—
395C2×C43—82no—
396C2×C43#334514yescomplemented
397C2×C43C2×#54711yescharacteristic
398C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C43C2×#57711yescharacteristic
400D43—24no—
401D43—42no—
402C22×#41—861no—
403C22×D8C2×D4311yescharacteristic
404C22×M16—431no—
405C23×C8—431no—
406#553—438no—
407#553—864no—
408#547—438no—
409#547—864no—
410C2×C4⋊Q8—431no—
411C2×#126—861no—
412C2×#125—431no—
413C2×#123—861no—
414C2×#123—861no—
415C2×#123—861no—
416C2×C22⋊Q8—861no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—861no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C2×C4×D4C2×D4311yescharacteristic
425C2×C4×D4C2×D4311yescharacteristic
426C2×#117—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4—431no—
430#501—438no—
431#482—438no—
432#481—438no—
433#481—438no—
434#480—438no—
435#478—438no—
436#476—438no—
437#469—438no—
438#466—438no—
439#442C2×D4318yescomplemented
440#435—438no—
441#428—438no—
442C2×#107—431no—
443C2×#107—431no—
444C2×#107—431no—
445C2×#106—431no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×#106—431no—
450C2×#106—438no—
451C2×#106C2×D4311yescharacteristic
452C2×C4⋊C8—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×#102C2×D4311yescharacteristic
458C2×#102C2×D4311yescharacteristic
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×#97C2×D4311yescharacteristic
462C43C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—868no—
464C2×#41—1728no—
465C22×Q8—861no—
466C22×D4—431no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4C22×D4311yescharacteristic
472C22×D4C22×D4311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—861no—
478C23×C4—861no—
479C23×C4—861no—
480C2×D8—24no—
481C2×D8C22×D4314yes—
482C2×M16—434no—
483C2×M16—864no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—434no—
487C22×C8—864no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—434no—
491C4⋊Q8—862no—
492#126—868no—
493#125—434no—
494#125—862no—
495#123—868no—
496#123—868no—
497#123—868no—
498C22⋊Q8—868no—
499#121—434no—
500#121—434no—
501#121—434no—
502#121—434no—
503#121—868no—
504#121—862no—
505#121—862no—
506#121—862no—
507#121—862no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—434no—
511C4×D4—434no—
512C4×D4—868no—
513C4×D4C22×D4314yes—
514C4×D4C22×D4314yes—
515#117—434no—
516#117—862no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—862no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—862no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—431no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—861no—
546C2×C42C22×D4311yescharacteristic
547#107—434no—
548#107—434no—
549#107—434no—
550#106—434no—
551#106—434no—
552#106—434no—
553#106—434no—
554#106—434no—
555#106C22×D4314yes—
556C4⋊C8—434no—
557#102—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102C22×D4314yes—
562#102C22×D4314yes—
563C22⋊C8—434no—
564C22⋊C8—434no—
565#97C22×D4314yes—
566C24—21no—
567C24—21no—
568C24—431no—
569C24—431no—
570#41—17232no—
571C2×Q8—864no—
572C2×Q8—1724no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—434no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—864no—
585C2×D4—3442no—
586C2×D4—1724no—
587C2×D4—1724no—
588C2×D4—1724no—
589C2×D4C23×D4312yes—
590C2×D4C23×D4312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—82no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—3442no—
615C22×C4—1724no—
616C22×C4—1724no—
617C22×C4D4×D4311yescharacteristic
618C22×C4D4×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620D8—28no—
621M16—868no—
622C2×C8—22no—
623C2×C8—432no—
624C2×C8—432no—
625C2×C8—862no—
626C2×C8—862no—
627C2×C8—868no—
628C2×C8#1062189814yescomplemented
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—434no—
634C4⋊C4—432no—
635C4⋊C4—432no—
636C4⋊C4—432no—
637C4⋊C4—432no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—864no—
646C4⋊C4—864no—
647C4⋊C4—864no—
648C4⋊C4C23×D4312yes—
649C4⋊C4C23×D4312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—434no—
653C22⋊C4—434no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C42—864no—
660C42D4×D4312yes—
661C42C23×D4312yes—
662C23—22no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—434no—
671C23—432no—
672C23—432no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23C2×D4×D4311yescharacteristic
679Q8—1728no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—42no—
686D4—868no—
687D4—3444no—
688D4—1728no—
689D4—1728no—
690D4—1728no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—84no—
699C2×C4—432no—
700C2×C4—432no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—864no—
704C2×C4—864no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—3444no—
714C2×C4—1728no—
715C2×C4—1728no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4C2×D4×D4312yes—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C2×#1062189812yes—
724C2×C4#1306337212yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—862no—
728C8—862no—
729C8C2×#1062189814yescomplemented
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—84no—
738C22—434no—
739C22—862no—
740C22—862no—
741C22—868no—
742C22—862no—
743C22—862no—
744C22—862no—
745C22—1724no—
746C22#1458355412yes—
747C22AGL(1,ℤ/8)×D4312yes—
748C22#1458370912yes—
749C22C22×D4×D4311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—862no—
755C4—862no—
756C4—1722no—
757C4—1722no—
758C4—1722no—
759C4—1722no—
760C4#1458355412yes—
761C4C22×#1062189811yescharacteristic
762C4C2×#1306337211yescharacteristic
763C2—82no—
764C2—82no—
765C2—864no—
766C2—1722no—
767C2#1914707014yesdirect product factor
768C2C2×#1458355411yescharacteristic
769C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
770C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
hypercenterC2×#442D43
hypocenterC43C2×#3345
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583599C2semidirect
2. C2×#14583554C2semidirect
3. #19147070C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583216C2semidirect
6. C2×#14583216C2semidirect
7. C2×#14583221C2semidirect
8. C2×#14583211C2semidirect
9. C2×#14583199C2semidirect
10. C2×#14583189C2semidirect
11. C2×#14583149C2semidirect
12. C2×#14583132C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582938C2semidirect
15. C2×#106×D43C2semidirect
16. C2×C43×#442C2semidirect
21. #14583599C22semidirect
23. #14583554C22semidirect
42. #14583308C22semidirect
43. #14583221C22semidirect
44. #14583216C22semidirect
45. #14583216C22semidirect
46. #14583211C22semidirect
47. #14583199C22semidirect
48. #14583189C22semidirect
49. #14583149C22semidirect
50. #14583132C22semidirect
51. #14582972C22semidirect
52. #14582938C22semidirect
61. #106×D43C22semidirect
72. C43×#442C22semidirect
236. C2×C8×C43#41semidirect
341. C8×C43C2×#41semidirect
390. C2×#442D43semidirect
396. C2×C43#3345semidirect
439. #442C2×D43semidirect
462. C43C2×#3345semidirect
628. C2×C8#10621898semidirect
729. C8C2×#10621898semidirect
767. C2#19147070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835992
C2×#145835542
#191470702
C2×#145833082
C2×#145832162
C2×#145832212
C2×#145832112
C2×#145831992
C2×#145831892
C2×#145831492
C2×#145831322
C2×#145829722
C2×#145829382
C2×#106×D432
C2×C43×#4422
C2×#334543