Finite Group Databasebeta

← C2×#19144674 #25964679

Subgroups — C2×#19144674 #25964679

Order 11008.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583428C211yesmaximal, characteristic
2C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
3#19144674C2116yesmaximal, direct product factor
4C2×#14583228C211yesmaximal, characteristic, complemented
5C2×#14583211C211yesmaximal, characteristic
6C2×#14583207C211yesmaximal, characteristic, complemented
7C2×#14583206C211yesmaximal, characteristic, complemented
8C2×#14583118C211yesmaximal, characteristic, complemented
9C2×#14583053C211yesmaximal, characteristic, complemented
10C2×#14583036C211yesmaximal, characteristic
11C2×Q16×Dic43C211yesmaximal, characteristic, complemented
12C2×#14582991C211yesmaximal, characteristic, complemented
13C2×#14582990C211yesmaximal, characteristic, complemented
14C2×SD16×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582951C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20#14583428—24no—
21#14583428C2218yes—
22C2×#13063318—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063307—21no—
25C2×#13063301C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×Dic86—21no—
30C2×C4×Dic86C2211yescharacteristic
31C2×#13063290—21no—
32C2×#13063290C2211yescharacteristic
33C4×Q8×D43—24no—
34C4×Q8×D43C2218yescomplemented
35C2×D4×Dic43C2211yescharacteristic
36C2×(C22⋊D43)⋊C4—21no—
37C2×#13063281—21no—
38C2×C4⋊C4×D43—21no—
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C42×D43—21no—
41C2×C42×D43C2211yescharacteristic
42#14583228C2218yescomplemented
43#14583211C2218yes—
44#14583207C2218yescomplemented
45#14583206C2218yescomplemented
46#14583118C2218yescomplemented
47#14583053C2218yescomplemented
48#14583036C2218yes—
49Q16×Dic43C2218yescomplemented
50#14582991C2218yescomplemented
51#14582990C2218yescomplemented
52SD16×Dic43C2218yescomplemented
53#14582951C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
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×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C2×Q8×D43—24no—
80C2×Q8×D43—22no—
81C2×Q8×D43—24no—
82C2×Q8×D43C2314yes—
83C22×C22⋊D43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43D411yescharacteristic
88C22×C4×D43D411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C2×#10621885—24no—
91C2×#10621885C2314yes—
92C2×#10621883—24no—
93C2×#10621883C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96#13063318—28no—
97#13063317—22no—
98#13063317C2314yes—
99#13063307—28no—
100#13063301—22no—
101#13063301C2314yes—
102#13063296—22no—
103#13063296C2314yes—
104Q8×Dic43—22no—
105Q8×Dic43—22no—
106Q8×Dic43C2314yes—
107Q8×Dic43C2314yes—
108C4×Dic86—22no—
109C4×Dic86—28no—
110C4×Dic86C2314yes—
111#13063290—22no—
112#13063290—28no—
113#13063290C2314yes—
114D4×Dic43—22no—
115D4×Dic43C2314yes—
116(C22⋊D43)⋊C4—28no—
117#13063281—28no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C4⋊C4×D43—28no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2314yes—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×C4×Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C42×D43—28no—
143C42×D43D414yes—
144C42×D43C2314yes—
145#13063259C2314yes—
146#13063258C2314yes—
147#13063257C2314yes—
148#13063256C2314yes—
149C4⋊(C43⋊C8)C2314yes—
150#13063250C2314yes—
151#13063250C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063246C2314yes—
156(C2×D43)⋊C8C2314yes—
157(C2×D43)⋊C8C2314yes—
158C8×Dic43C2314yes—
159C8×Dic43C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C2×SD16×C43—24no—
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×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43#4114yes—
190C2×Q8×C43C2412yes—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43C2412yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—44no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—44no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213Q8×D43—216no—
214Q8×D43—28no—
215Q8×D43—28no—
216C2×C4×D43—28no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—44no—
224C2×C4×D43C2×D414yes—
225C2×C4×D43C2×D412yes—
226C2×C4×D43C2×D414yes—
227C2×C4×D43C2412yes—
228C2×Dic86—28no—
229C2×Dic86—21no—
230C2×Dic86—22no—
231C2×Dic86—24no—
232C2×Dic86#4114yes—
233C2×Dic86C2412yes—
234Q16×C43—28no—
235SD16×C43—28no—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43C2412yes—
239C2×C8×C43C2412yes—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C42×C43—24no—
246C42×C43C2×D412yes—
247C42×C43C2412yes—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250#10621885—28no—
251#10621883—28no—
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—
266Dic43⋊C4—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43—24no—
271C4×Dic43C2×D412yes—
272C4×Dic43C2×D414yes—
273C4×Dic43C2×D414yes—
274C4×Dic43C2412yes—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279C23×C43—22no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43#13514yes—
287C22×D43C22×D412yes—
288Q8×C43—24no—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293Q8×C43C2×#4114yes—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—42no—
297C2×C4×C43—24no—
298C2×C4×C43—22no—
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×D412yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4112yes—
309C2×C4×C43C2×#4112yes—
310C2×C4×C43C2511yescharacteristic
311C22⋊D43—48no—
312C2×Dic43—22no—
313C2×Dic43—24no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—48no—
323C2×Dic43#13714yes—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326C2×Dic43C22×D412yes—
327C4×D43—216no—
328C4×D43—28no—
329C4×D43—24no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—28no—
333C4×D43—48no—
334Dic86—216no—
335Dic86—24no—
336Dic86—22no—
337Dic86C2×#4114yes—
338C8×C43—22no—
339C8×C43—22no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C2×#3108—431nomaximal, Sylow
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—84no—
347C22×C43#52512yes—
348C22×C43C2×#13512yes—
349C22×C43C2×#13712yes—
350C22×C43C23×D411yescharacteristic
351C2×D43—28no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43C2×#13514yes—
355C4×C43—24no—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43#52512yes—
361C4×C43C22×#4111yescharacteristic
362C4×C43C22×#4111yescharacteristic
363Dic43—22no—
364Dic43—24no—
365Dic43—22no—
366Dic43—42no—
367Dic43—42no—
368Dic43—42no—
369Dic43C2×#13714yes—
370C2×#529—431no—
371C22×C4×Q8—431no—
372#3108—4316no—
373C2×#483—431no—
374C2×#480—431no—
375C2×#479—431no—
376C2×#479—431no—
377C2×#464—431no—
378C2×#464D4311yescharacteristic, complemented
379C2×#451—431no—
380C2×#448—431no—
381C2×C4×Q16—431no—
382C2×C4×Q16—431no—
383C2×C4×SD16—431no—
384C2×C4×SD16—431no—
385C2×#431—431no—
386C2×C43—82no—
387C2×C43#310814yescomplemented
388C2×C43C2×#52511yescharacteristic
389C2×C43C22×#13511yescharacteristic
390C2×C43C22×#13711yescharacteristic
391D43—24no—
392C23×Q8—431no—
393C22×Q16—431no—
394C22×Q16C2×D4311yescharacteristic
395C22×SD16—431no—
396C22×SD16C2×D4311yescharacteristic
397#529—438no—
398#529—864no—
399C2×#126—861no—
400C2×#125—431no—
401C2×#124C2×D4311yescharacteristic
402C2×#123—861no—
403C2×C22⋊Q8—431no—
404C2×#121—431no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×Q8—438no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—861no—
411C2×C4×Q8—861no—
412C2×C4×Q8—864no—
413C2×C4×Q8C2×D4311yescharacteristic
414C2×C4×D4—431no—
415C2×C4×D4—861no—
416C2×#117—861no—
417C22×C4⋊C4—431no—
418C22×C4⋊C4—861no—
419C22×C42—431no—
420C22×C42—861no—
421#483—438no—
422#480—438no—
423#479—438no—
424#479—438no—
425#464—438no—
426#464C2×D4318yescomplemented
427#451—438no—
428#448—438no—
429C4×Q16—438no—
430C4×Q16—438no—
431C4×SD16—438no—
432C4×SD16—438no—
433#431—438no—
434C2×#107—431no—
435C2×#107—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×C4⋊C8—431no—
439C2×C4⋊C8C2×D4311yescharacteristic
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#103C2×D4311yescharacteristic
446C2×#102—431no—
447C2×#102C2×D4311yescharacteristic
448C2×C22⋊C8—431no—
449C2×C22⋊C8—431no—
450C2×C4×C8—431no—
451C2×C4×C8—431no—
452C43C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—434no—
454C22×Q8—431no—
455C22×Q8—861no—
456C22×Q8—862no—
457C22×Q8—864no—
458C22×Q8—864no—
459C22×Q8C22×D4311yescharacteristic
460C22×Q8C22×D4311yescharacteristic
461C22×D4—861no—
462C22×D4C22×D4311yescharacteristic
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C2×Q16—24no—
470C2×Q16—434no—
471C2×Q16—864no—
472C2×Q16C22×D4314yes—
473C2×SD16—24no—
474C2×SD16—434no—
475C2×SD16—864no—
476C2×SD16C22×D4314yes—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8C22×D4311yescharacteristic
480C22×C8C22×D4311yescharacteristic
481#126—868no—
482#125—434no—
483#125—862no—
484#124—22no—
485#124C22×D4314yes—
486#123—868no—
487C22⋊Q8—434no—
488C22⋊Q8—862no—
489#121—434no—
490#121—862no—
491C4×Q8—22no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—434no—
496C4×Q8—868no—
497C4×Q8—868no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8—862no—
502C4×Q8C22×D4314yes—
503C4×D4—434no—
504C4×D4—862no—
505C4×D4—868no—
506#117—868no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—434no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—868no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—868no—
535C2×C42—861no—
536C2×C42—861no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540#107—434no—
541#107—434no—
542#106—434no—
543#106—434no—
544C4⋊C8—434no—
545C4⋊C8C22×D4314yes—
546#103—434no—
547#103—434no—
548#103—434no—
549#103—434no—
550#103—434no—
551#103C22×D4314yes—
552#102—434no—
553#102C22×D4314yes—
554C22⋊C8—434no—
555C22⋊C8—434no—
556C4×C8—434no—
557C4×C8—434no—
558C24—21no—
559C24—431no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—434no—
566C2×Q8—432no—
567C2×Q8—864no—
568C2×Q8—868no—
569C2×Q8—868no—
570C2×Q8—8616no—
571C2×Q8—868no—
572C2×Q8—861no—
573C2×Q8—862no—
574C2×Q8#1062190014yes—
575C2×Q8C23×D4312yes—
576C2×Q8C23×D4312yes—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—864no—
581C2×D4—1724no—
582C2×D4C23×D4312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—434no—
590C22×C4—434no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—864no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—868no—
597C22×C4—864no—
598C22×C4—864no—
599C22×C4—861no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—1724no—
606C22×C4—1724no—
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610Q16—28no—
611Q16—868no—
612SD16—28no—
613SD16—868no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—432no—
617C2×C8—432no—
618C2×C8—862no—
619C2×C8—862no—
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⋊C4—864no—
638C4⋊C4C23×D4312yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C42—24no—
645C42—434no—
646C42—432no—
647C42—434no—
648C42—432no—
649C42—864no—
650C42—864no—
651C42—864no—
652C42—864no—
653C42D4×D4312yes—
654C42C23×D4312yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—434no—
660C23—432no—
661C23—862no—
662C23—862no—
663C23C2×D4×D4311yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—434no—
670Q8—8616no—
671Q8—864no—
672Q8—862no—
673Q8C2×#1062190014yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—1728no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—434no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—432no—
690C2×C4—868no—
691C2×C4—868no—
692C2×C4—8616no—
693C2×C4—862no—
694C2×C4—864no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—864no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—1728no—
704C2×C4—1728no—
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×C4C2×#1062190012yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—22no—
716C8—862no—
717C8—862no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—434no—
723C22—862no—
724C22—862no—
725C22—868no—
726C22#1458340912yes—
727C22#135×D4312yes—
728C22#137×D4312yes—
729C22C22×D4×D4311yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—434no—
736C4—862no—
737C4—862no—
738C4—864no—
739C4—1722no—
740C4—1722no—
741C4—1722no—
742C4#1458340912yes—
743C4C2×#41×D4311yescharacteristic
744C4C22×#1062190011yescharacteristic
745C2—82no—
746C2—864no—
747C2#1914467414yesdirect product factor
748C2C2×#1458340911yescharacteristic
749C2C2×#135×D4311yescharacteristic
750C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#464D43
hypocenterC43C2×#3108
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
2. C2×C4×Q8×D43C2semidirect
3. #19144674C2direct (N × H)
4. C2×#14583228C2semidirect
6. C2×#14583207C2semidirect
7. C2×#14583206C2semidirect
8. C2×#14583118C2semidirect
9. C2×#14583053C2semidirect
11. C2×Q16×Dic43C2semidirect
12. C2×#14582991C2semidirect
13. C2×#14582990C2semidirect
14. C2×SD16×Dic43C2semidirect
15. C2×#14582951C2semidirect
16. C2×C43×#464C2semidirect
34. C4×Q8×D43C22semidirect
42. #14583228C22semidirect
44. #14583207C22semidirect
45. #14583206C22semidirect
46. #14583118C22semidirect
47. #14583053C22semidirect
49. Q16×Dic43C22semidirect
50. #14582991C22semidirect
51. #14582990C22semidirect
52. SD16×Dic43C22semidirect
53. #14582951C22semidirect
73. C43×#464C22semidirect
378. C2×#464D43semidirect
387. C2×C43#3108semidirect
426. #464C2×D43semidirect
452. C43C2×#3108semidirect
747. C2#19144674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834282
C2×C4×Q8×D432
#191446742
C2×#145832282
C2×#145832112
C2×#145832072
C2×#145832062
C2×#145831182
C2×#145830532
C2×#145830362
C2×Q16×Dic432
C2×#145829912
C2×#145829902
C2×SD16×Dic432
C2×#145829512
C2×C43×#4642
C2×#310843