Finite Group Databasebeta

← C2×#19146995 #25975067

Subgroups — C2×#19146995 #25975067

Order 11008.

1994 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×#14583597C211yesmaximal, characteristic, complemented
3#19146995C2116yesmaximal, direct product factor
4C2×#14583299C211yesmaximal, characteristic, complemented
5C2×#14583218C211yesmaximal, characteristic, complemented
6C2×#14583225C211yesmaximal, characteristic, complemented
7C2×#14583222C211yesmaximal, characteristic, complemented
8C2×#14583201C211yesmaximal, characteristic, complemented
9C2×#14583198C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583133C211yesmaximal, characteristic, complemented
12C2×#14582979C211yesmaximal, characteristic, complemented
13C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
14C2×#14582934C211yesmaximal, characteristic, complemented
15C22×#13063258C211yesmaximal, characteristic, complemented
16C2×C43×#481C211yesmaximal, characteristic, complemented
17C22×#10621882C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583601—24no—
21#14583601C2218yescomplemented
22#14583597—24no—
23#14583597C2218yescomplemented
24C2×#13063320—21no—
25C2×#13063318—21no—
26C2×#13063316C2211yescharacteristic
27C2×#13063316C2211yescharacteristic
28C2×#13063310—21no—
29C2×#13063309—21no—
30C2×#13063300C2211yescharacteristic
31C2×#13063299—21no—
32C2×#13063299C2211yescharacteristic
33C2×#13063297—21no—
34C2×#13063296C2211yescharacteristic
35C2×D4×Dic43—21no—
36C2×D4×Dic43C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C22×C4⋊Dic43C2211yescharacteristic
43#14583299C2218yescomplemented
44#14583225C2218yescomplemented
45#14583222C2218yescomplemented
46#14583218C2218yescomplemented
47#14583201C2218yescomplemented
48#14583198C2218yescomplemented
49#14583134C2218yescomplemented
50#14583133C2218yescomplemented
51#14582979C2218yescomplemented
52(C22⋊D43)⋊C8C2218yescomplemented
53#14582934C2218yescomplemented
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063258C2218yescomplemented
60C2×#13063257C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#481C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172C2311yescharacteristic
79C22×C22⋊D43—21no—
80C22×C22⋊D43—21no—
81C22×C22⋊D43D411yescharacteristic
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621882—24no—
87C2×#10621882C2314yes—
88C22×C43⋊C8—24no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—24no—
93C2×C8×D43C2314yes—
94#13063320—28no—
95#13063318—28no—
96#13063316—22no—
97#13063316—22no—
98#13063316C2314yes—
99#13063316C2314yes—
100#13063310—28no—
101#13063309—28no—
102#13063300—22no—
103#13063300C2314yes—
104#13063299—22no—
105#13063299—28no—
106#13063299C2314yes—
107#13063297—28no—
108#13063296—22no—
109#13063296C2314yes—
110D4×Dic43—28no—
111D4×Dic43—22no—
112D4×Dic43C2314yes—
113#13063287—22no—
114#13063287C2314yes—
115C4×C22⋊D43—28no—
116C4×C22⋊D43D414yes—
117C4×C22⋊D43C2314yes—
118#13063283—22no—
119#13063283—22no—
120#13063283C2314yes—
121#13063283C2314yes—
122C2×C4⋊Dic43—22no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2314yes—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4D411yescharacteristic
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43D411yescharacteristic
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×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063258C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063258C2314yes—
150#13063257C2314yes—
151#13063257C2314yes—
152Dic43⋊C8C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063246C2314yes—
156#13063245C2314yes—
157(C2×D43)⋊C8C2314yes—
158C8×Dic43C2314yes—
159C22×D4×C43—21no—
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43—21no—
162C23×C4×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#121×C43—22no—
166#121×C43C2314yes—
167C2×C4⋊C4×C43—22no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2314yes—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C22⋊C4×C43—21no—
174#106×C43C2314yes—
175#106×C43C2314yes—
176#102×C43C2314yes—
177#102×C43C2314yes—
178C22⋊C8×C43C2314yes—
179C24×C43—21no—
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C23×D43C2×D411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43—24no—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43—44no—
188C2×D4×C43C2412yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—24no—
195C22×C4×C43—82no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—44no—
204C2×C22⋊D43—82no—
205C2×C22⋊D43C2×D414yes—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—24no—
211C22×Dic43—82no—
212C22×Dic43—82no—
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C2×D172—21no—
217C2×D172—24no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—82no—
221C2×D172C2412yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—24no—
225C2×C4×D43—82no—
226C2×C4×D43C2×D412yes—
227C2×C4×D43C2412yes—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43C2×D414yes—
243#10621882—28no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4C2×D414yes—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—24no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4C2×D414yes—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—28no—
268C2×C43⋊C8#4114yes—
269C2×C43⋊C8C2412yes—
270C2×C43⋊C8C2412yes—
271C8×D43—28no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43#13514yes—
279C23×C43C22×D412yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43C22×D412yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—48no—
292D4×C43—42no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—84no—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4112yes—
307C2×C4×C432−1+412yes—
308C2×C4×C43C2511yescharacteristic
309C22⋊D43—28no—
310C22⋊D43—48no—
311C22⋊D43—84no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—84no—
322C2×Dic43—84no—
323C2×Dic43C22×D412yes—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326D172—22no—
327D172—22no—
328D172—42no—
329D172—84no—
330C4×D43—24no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—84no—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—22no—
337C43⋊C8C2×#4114yes—
338C2×#3339—431nomaximal, Sylow
339C22×C43—28no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—84no—
346C22×C43#54712yes—
347C22×C43C2×#13514yes—
348C22×C43C2×#13512yes—
349C22×C43#57612yes—
350C22×C43C23×D411yescharacteristic
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—44no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—84no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43#54712yes—
364C4×C43C22×#4111yescharacteristic
365C4×C43C2×2−1+411yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#553—431no—
373C2×#553—431no—
374#3339—4316no—
375C2×#499—431no—
376C2×#481—431no—
377C2×#481D4311yescharacteristic, complemented
378C2×#482—431no—
379C2×#482—431no—
380C2×#478—431no—
381C2×#478—431no—
382C2×#466—431no—
383C2×#466—431no—
384C2×C4×D8—431no—
385C2×C8×D4—431no—
386C2×#427—431no—
387C22×#107—431no—
388C2×C43—24no—
389C2×C43—82no—
390C2×C43#333914yescomplemented
391C2×C43C2×#54711yescharacteristic
392C2×C43C22×#13511yescharacteristic
393C2×C43C2×#57611yescharacteristic
394D43—42no—
395D43—82no—
396C22×D8—431no—
397C23×C8—431no—
398C23×C8—431no—
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—431no—
412C2×#121—861no—
413C2×#121—861no—
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⋊C4C2×D4311yescharacteristic
424#499—438no—
425#482—438no—
426#482—438no—
427#481—438no—
428#481C2×D4318yescomplemented
429#478—438no—
430#478—438no—
431#466—438no—
432#466—438no—
433C4×D8—438no—
434C8×D4—438no—
435#427—438no—
436C2×#107—431no—
437C2×#107—431no—
438C2×#107—438no—
439C2×#107—431no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#106—431no—
443C2×#106—431no—
444C2×#106C2×D4311yescharacteristic
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⋊C8C2×D4311yescharacteristic
455C2×C4×C8—431no—
456C43C2×#333911yescharacteristic, complemented, Sylow
457C22×D4—21no—
458C22×D4—431no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4—861no—
463C22×D4C22×D4311yescharacteristic
464C23×C4—21no—
465C23×C4—431no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4C22×D4311yescharacteristic
470C2×D8—434no—
471C2×D8—864no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—434no—
475C22×C8—434no—
476C22×C8—864no—
477C22×C8—864no—
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—434no—
490#121—434no—
491#121—434no—
492#121—862no—
493#121—868no—
494#121—862no—
495#121—868no—
496#121—862no—
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—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4314yes—
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—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#106C22×D4314yes—
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⋊C8C22×D4314yes—
558C4×C8—434no—
559C24—21no—
560C24—431no—
561C24—861no—
562C24D4×D4311yescharacteristic
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—434no—
569C2×D4—432no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—864no—
573C2×D4—864no—
574C2×D4—861no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—3442no—
578C2×D4—3442no—
579C2×D4—1724no—
580C2×D4C23×D4312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—864no—
594C22×C4—864no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—864no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—3442no—
602C22×C4—3442no—
603C22×C4—3442no—
604C22×C4D4×D4312yes—
605C22×C4D4×D4311yescharacteristic
606C22×C4C23×D4312yes—
607C22×C4C23×D4311yescharacteristic
608D8—868no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—434no—
612C2×C8—432no—
613C2×C8—432no—
614C2×C8—868no—
615C2×C8—868no—
616C2×C8—862no—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—434no—
624C4⋊C4—432no—
625C4⋊C4—432no—
626C4⋊C4—432no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—864no—
634C4⋊C4—861no—
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—432no—
649C42—432no—
650C42—864no—
651C42—864no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—432no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23#1306334614yes—
667C23C2×D4×D4312yes—
668C23C2×D4×D4311yescharacteristic
669D4—22no—
670D4—22no—
671D4—48no—
672D4—42no—
673D4—868no—
674D4—862no—
675D4—862no—
676D4—3444no—
677D4—3444no—
678D4—1728no—
679D4—1722no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—3444no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4C2×D4×D4312yes—
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4#41×D4312yes—
712C2×C4#1306337212yes—
713C2×C4C24×D4311yescharacteristic
714C8—22no—
715C8—22no—
716C8—434no—
717C8—862no—
718C22—22no—
719C22—22no—
720C22—28no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—3444no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1724no—
733C22#1458354712yes—
734C22C2×#1306334614yes—
735C22C2×#1306334612yes—
736C22#1458370312yes—
737C22C22×D4×D4311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—862no—
743C4—862no—
744C4—862no—
745C4—1722no—
746C4—1722no—
747C4—1722no—
748C4#1458354712yes—
749C4C2×#41×D4311yescharacteristic
750C4C2×#1306337211yescharacteristic
751C2—24no—
752C2—82no—
753C2—3442no—
754C2—1722no—
755C2#1914699514yesdirect product factor
756C2C2×#1458354711yescharacteristic
757C2C22×#1306334611yescharacteristic
758C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#481C2
socleC23×C43C22×D4
hypercenterC2×#481D43
hypocenterC43C2×#3339
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#14583601C2semidirect
2. C2×#14583597C2semidirect
3. #19146995C2direct (N × H)
4. C2×#14583299C2semidirect
5. C2×#14583218C2semidirect
6. C2×#14583225C2semidirect
7. C2×#14583222C2semidirect
8. C2×#14583201C2semidirect
9. C2×#14583198C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583133C2semidirect
12. C2×#14582979C2semidirect
13. C2×(C22⋊D43)⋊C8C2semidirect
14. C2×#14582934C2semidirect
15. C22×#13063258C2semidirect
16. C2×C43×#481C2semidirect
21. #14583601C22semidirect
23. #14583597C22semidirect
43. #14583299C22semidirect
44. #14583225C22semidirect
45. #14583222C22semidirect
46. #14583218C22semidirect
47. #14583201C22semidirect
48. #14583198C22semidirect
49. #14583134C22semidirect
50. #14583133C22semidirect
51. #14582979C22semidirect
52. (C22⋊D43)⋊C8C22semidirect
53. #14582934C22semidirect
59. C2×#13063258C22semidirect
71. C43×#481C22semidirect
377. C2×#481D43semidirect
390. C2×C43#3339semidirect
428. #481C2×D43semidirect
456. C43C2×#3339semidirect
755. C2#19146995direct (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×#145835972
#191469952
C2×#145832992
C2×#145832182
C2×#145832252
C2×#145832222
C2×#145832012
C2×#145831982
C2×#145831342
C2×#145831332
C2×#145829792
C2×(C22⋊D43)⋊C82
C2×#145829342
C22×#130632582
C2×C43×#4812
C2×#333943