Finite Group Databasebeta

← #25002113

Subgroups — #25002113

Order 11008.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2C22×#13063251C211yesmaximal, characteristic
3C2×#14582901C211yesmaximal, characteristic
4#19134315C211yesmaximal, characteristic, complemented
5C2×#14582660C211yesmaximal, characteristic, complemented
6#19132824C211yesmaximal, characteristic, complemented
7C2×C43×#343C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583380—22no—
10#14583380—22no—
11#14583380—22no—
12#14583380C414yescomplemented
13C2×#13063290—21no—
14C2×#13063287—21no—
15C2×C4×C22⋊D43—22no—
16C2×#13063284C2211yescharacteristic
17C2×#13063283—21no—
18C22×C4⋊Dic43C2211yescharacteristic
19C2×C4⋊C4×D43—21no—
20C22×C4×Dic43C2211yescharacteristic
21C2×#13063251—22no—
22C2×#13063251—22no—
23C2×#13063251C414yescomplemented
24#14582901—22no—
25#14582901C414yescomplemented
26C2×#13063250—21no—
27C2×#13063247—21no—
28C2×C43⋊#95—22no—
29#14582662—21no—
30#14582662—21no—
31#14582660—22no—
32C22×M16×C43C2211yescharacteristic
33C22×M16×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#343—22no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898C2×C412yes—
43C2×#10621898C2×C412yes—
44C2×#10621898C2×C412yes—
45C2×#10621898D412yes—
46C2×#10621898D412yes—
47C2×#10621898Q812yes—
48C22×Dic86D411yescharacteristic
49C22×D172D411yescharacteristic
50C22×C22⋊D43—21no—
51C23×Dic43—21no—
52C23×Dic43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—22no—
55#13063290—24no—
56#13063290—24no—
57#13063287—24no—
58#13063287—24no—
59C4×C22⋊D43—28no—
60C4×C22⋊D43—28no—
61#13063284—21no—
62#13063284—21no—
63#13063284C2×C412yes—
64#13063284D412yes—
65#13063283—24no—
66#13063283—24no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2×C412yescomplemented
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43D411yescharacteristic
75C2×Dic43⋊C4—22no—
76C4⋊C4×D43—24no—
77C4⋊C4×D43—24no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—22no—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2×C412yescomplemented
88#13063251—28no—
89#13063250—24no—
90#13063247—24no—
91C43⋊#95—44no—
92C23×C4×C43D412yes—
93C23×C4×C43C2311yescharacteristic
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43—21no—
97C2×M16×C43—21no—
98C2×M16×C43—21no—
99C2×M16×C43—21no—
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43—21no—
103C2×M16×C43—21no—
104C2×M16×C43C2×C412yescomplemented
105C2×M16×C43C2×C412yescomplemented
106C22×C8×C43—21no—
107C22×C8×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2×C412yes—
113C2×C4⋊C4×C43D412yes—
114C24×C43C2×D411yescharacteristic
115C23×D43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—42no—
119C22×C4×C43—42no—
120C22×C4×C43C22⋊C414yes—
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×Q811yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156#10621898—22no—
157#10621898—22no—
158#10621898—22no—
159#10621898—22no—
160#10621898—22no—
161#10621898—22no—
162#10621898—22no—
163#10621898—22no—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898C4214yes—
169#10621898C22⋊C414yes—
170#10621898C4⋊C414yes—
171#10621898C4⋊C414yes—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22⋊C412yes—
176C2×D172C22⋊C412yes—
177C2×D172C4⋊C412yes—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—28no—
185C2×C4×D43—82no—
186C2×C4×D43—82no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86C22⋊C412yes—
191C2×Dic86C22⋊C412yes—
192C2×Dic86C4⋊C412yes—
193M16×C43—22no—
194M16×C43—22no—
195M16×C43—22no—
196M16×C43—22no—
197M16×C43—41no—
198M16×C43—41no—
199M16×C43—41no—
200M16×C43—41no—
201C2×C8×C43—22no—
202C2×C8×C43—22no—
203C2×C8×C43—41no—
204C2×C8×C43—41no—
205C2×C8×C43—41no—
206C2×C8×C43—41no—
207C4⋊C4×C43—22no—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—22no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213(C2×D43)⋊C4—28no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—22no—
217C4⋊Dic43—22no—
218C4⋊Dic43—41no—
219C4⋊Dic43—41no—
220C4⋊Dic43C22⋊C412yes—
221C4⋊Dic43C22⋊C412yes—
222Dic43⋊C4—28no—
223C4×Dic43—28no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43—22no—
227C4×Dic43—22no—
228C4×Dic43—41no—
229C4×Dic43—41no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43C2×C22⋊C411yescharacteristic
235C23×C43C4×D411yescharacteristic
236C23×C43C4×D411yescharacteristic
237C23×C43#12011yescharacteristic
238C23×C43#12011yescharacteristic
239C23×C43#12111yescharacteristic
240C23×C43C22⋊Q811yescharacteristic
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C2×C4×C43—24no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—44no—
252C2×C4×C43—82no—
253C2×C4×C43C2×C4211yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C4⋊C411yescharacteristic
259C2×C4×C43C2×C4⋊C411yescharacteristic
260C2×C4×C43C2×C4⋊C411yescharacteristic
261C2×C4×C43#11711yescharacteristic
262C2×C4×C43#11711yescharacteristic
263C2×C4×C43C4×D411yescharacteristic
264C2×C4×C43C4×D411yescharacteristic
265C2×C4×C43C4×D411yescharacteristic
266C2×C4×C43C4×D411yescharacteristic
267C2×C4×C43C4×D411yescharacteristic
268C2×C4×C43C4×D411yescharacteristic
269C2×C4×C43#12011yescharacteristic
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43#12111yescharacteristic
272C2×C4×C43#12111yescharacteristic
273C2×C4×C43#12111yescharacteristic
274C2×C4×C43C22⋊Q811yescharacteristic
275C2×C4×C43C22⋊Q811yescharacteristic
276C2×C4×C43C22⋊Q811yescharacteristic
277C2×C4×C43#12311yescharacteristic
278C2×C4×C43#12311yescharacteristic
279C2×C4×C43#12311yescharacteristic
280C2×C4×C43#12311yescharacteristic
281C22⋊D43—24no—
282C22⋊D43—24no—
283C22⋊D43—24no—
284C22⋊D43—24no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—24no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—44no—
302C2×Dic43—42no—
303C2×Dic43—82no—
304C2×Dic43—81no—
305C2×Dic43—81no—
306D172—22no—
307D172—22no—
308D172—22no—
309D172#9514yescomplemented
310C4×D43—24no—
311C4×D43—24no—
312C4×D43—24no—
313C4×D43—24no—
314C4×D43—88no—
315Dic86—22no—
316Dic86—22no—
317Dic86—22no—
318Dic86#9514yescomplemented
319C8×C43—42no—
320C8×C43—42no—
321#10781—431nomaximal, Sylow
322C22×C43—21no—
323C22×C43—21no—
324C22×C43—21no—
325C22×C43—21no—
326C22×C43—21no—
327C22×C43—21no—
328C22×C43—21no—
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—21no—
332C22×C43—21no—
333C22×C43—21no—
334C22×C43C4×C22⋊C411yescharacteristic
335C22×C43#37911yescharacteristic
336C22×C43#38011yescharacteristic
337C22×C43#38511yescharacteristic
338C22×C43#38511yescharacteristic
339C22×C43#38611yescharacteristic
340C22×C43#38611yescharacteristic
341C22×C43#45311yescharacteristic
342C22×C43#45411yescharacteristic
343C22×C43#45511yescharacteristic
344C22×C43#45611yescharacteristic
345C2×D43—24no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C4×C43—44no—
353C4×C43C2×#9511yescharacteristic
354C4×C43C4×C22⋊C411yescharacteristic
355C4×C43#38011yescharacteristic
356C4×C43#38111yescharacteristic
357C4×C43#38511yescharacteristic
358C4×C43#38511yescharacteristic
359C4×C43#38611yescharacteristic
360C4×C43#38611yescharacteristic
361Dic43—24no—
362Dic43—44no—
363Dic43—42no—
364Dic43—42no—
365Dic43—82no—
366C2×#520—431no—
367C22×#104—431no—
368C2×#417—431no—
369C2×#343D4311yescharacteristic, complemented
370#1736—431no—
371C2×#339—431no—
372C4⋊#95—431no—
373C2×C43—21no—
374C2×C43—21no—
375C2×C43—21no—
376C2×C43—21no—
377C2×C43C22⋊#9511yescharacteristic
378C2×C43#179211yescharacteristic
379C2×C43#179311yescharacteristic
380C2×C43#185911yescharacteristic
381C2×C43#186011yescharacteristic
382C2×C43#188211yescharacteristic
383C2×C43#188311yescharacteristic
384D43—44no—
385C22×#41—431no—
386C22×M16C2×D4311yescharacteristic
387C22×M16C2×D4311yescharacteristic
388#520—434no—
389#520—862no—
390#520—862no—
391#520—862no—
392C2×C4×Q8—861no—
393C2×C4×D4—861no—
394C2×C4×D4—862no—
395C2×#117—431no—
396C2×#117—861no—
397C22×C4⋊C4—431no—
398C22×C4⋊C4—861no—
399C22×C4⋊C4C2×D4311yescharacteristic
400C22×C42—431no—
401C2×#104—434no—
402C2×#104—862no—
403C2×#104—862no—
404#417—434no—
405#417—862no—
406C2×#103—861no—
407C2×#102—861no—
408C2×#95—862no—
409#343—22no—
410#340—861no—
411#340—861no—
412#339—862no—
413C43#1078111yescharacteristic, complemented, Sylow
414C2×#41—432no—
415C2×#41—432no—
416C2×#41—432no—
417C2×#41—432no—
418C2×#41—432no—
419C2×#41—432no—
420C2×#41—861no—
421C2×#41—861no—
422C2×#41—861no—
423C2×#41—861no—
424C2×#41—861no—
425C2×#41—861no—
426C22×Q8—431no—
427C22×D4—431no—
428C22×D4—861no—
429C23×C4—862no—
430C23×C4—861no—
431C23×C4—861no—
432C23×C4—861no—
433C23×C4D17212yes—
434C23×C4C22×D4311yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16C4×D4312yescomplemented
446C2×M16C4×D4312yescomplemented
447C22×C8—21no—
448C22×C8—21no—
449C4×Q8—864no—
450C4×Q8—864no—
451C4×D4—864no—
452C4×D4—864no—
453C4×D4—868no—
454C4×D4—868no—
455#117—432no—
456#117—432no—
457#117—864no—
458#117—864no—
459#117—861no—
460#117—861no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—432no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—864no—
470C2×C4⋊C4—862no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4C4×D4312yes—
477C2×C4⋊C4C22⋊D4312yes—
478C2×C22⋊C4—862no—
479C2×C22⋊C4—861no—
480C2×C42—432no—
481C2×C42—862no—
482C2×C42—861no—
483C2×C42—861no—
484C2×C42—861no—
485C2×C42—861no—
486C2×C42—861no—
487C2×C42—861no—
488#104—868no—
489#103—864no—
490#102—864no—
491#95—1724no—
492C24—861no—
493C24C2×D17211yescharacteristic
494#41—434no—
495#41—434no—
496#41—434no—
497#41—434no—
498#41—862no—
499#41—862no—
500#41—862no—
501#41—862no—
502#41—862no—
503#41—862no—
504#41—862no—
505#41—862no—
506#41—862no—
507#41—862no—
508#41—862no—
509#41—862no—
510C2×Q8—432no—
511C2×Q8—432no—
512C2×Q8—432no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×D4—432no—
517C2×D4—432no—
518C2×D4—432no—
519C2×D4—862no—
520C2×D4—862no—
521C2×D4—862no—
522C2×D4—862no—
523C2×D4—862no—
524C2×D4—862no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—868no—
533C22×C4—861no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—862no—
546C22×C4—3442no—
547C22×C4—3442no—
548C22×C4—1722no—
549C22×C4—1722no—
550C22×C4—1721no—
551C22×C4—1721no—
552C22×C4—1721no—
553C22×C4—1721no—
554C22×C4—1721no—
555C22×C4—1721no—
556C22×C4(C2×D43)⋊C414yes—
557C22×C4C2×C4×D4311yescharacteristic
558C22×C4C2×C4×D4311yescharacteristic
559C22×C4C2×C4×D4311yescharacteristic
560C22×C4#1062189811yescharacteristic
561C22×C4#1062189811yescharacteristic
562C22×C4D4×D4311yescharacteristic
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4#1062190011yescharacteristic
568C22×C4Q8×D4311yescharacteristic
569C22×C4#1062190211yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571M16—22no—
572M16—22no—
573M16—22no—
574M16—22no—
575M16—41no—
576M16—41no—
577M16—41no—
578M16—41no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—868no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—862no—
595C4⋊C4—862no—
596C4⋊C4—1721no—
597C4⋊C4—1721no—
598C22⋊C4—868no—
599C22⋊C4—862no—
600C22⋊C4—862no—
601C42—868no—
602C42—862no—
603C42—862no—
604C42—862no—
605C42—862no—
606C42—1721no—
607C42—1721no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—862no—
613C23—862no—
614C23—862no—
615C23—1721no—
616C23—1721no—
617C23—1721no—
618C23—1721no—
619C23C2×(C2×D43)⋊C411yescharacteristic
620C23C4×D17211yescharacteristic
621C23C4×D17211yescharacteristic
622C23#1306329511yescharacteristic
623C23#1306329511yescharacteristic
624C23#1306330011yescharacteristic
625C23#1306330511yescharacteristic
626Q8—434no—
627Q8—862no—
628Q8—862no—
629Q8—862no—
630D4—434no—
631D4—864no—
632D4—864no—
633D4—864no—
634D4—864no—
635D4—862no—
636D4—862no—
637D4—862no—
638C2×C4—24no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—82no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—864no—
647C2×C4—864no—
648C2×C4—864no—
649C2×C4—864no—
650C2×C4—864no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—3448no—
654C2×C4—3442no—
655C2×C4—3441no—
656C2×C4—3441no—
657C2×C4—1724no—
658C2×C4—1722no—
659C2×C4—1722no—
660C2×C4—1722no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1722no—
669C2×C4C42×D4311yescharacteristic
670C2×C4C22⋊C4×D4311yescharacteristic
671C2×C4C22⋊C4×D4311yescharacteristic
672C2×C4C22⋊C4×D4311yescharacteristic
673C2×C4C22⋊C4×D4311yescharacteristic
674C2×C4C4⋊C4×D4311yescharacteristic
675C2×C4C4⋊C4×D4311yescharacteristic
676C2×C4C4⋊C4×D4311yescharacteristic
677C2×C4#1306328211yescharacteristic
678C2×C4#1306328311yescharacteristic
679C2×C4(C22⋊D43)⋊C411yescharacteristic
680C2×C4(C22⋊D43)⋊C411yescharacteristic
681C2×C4C4×C22⋊D4311yescharacteristic
682C2×C4C4×C22⋊D4311yescharacteristic
683C2×C4#1306328711yescharacteristic
684C2×C4#1306328711yescharacteristic
685C2×C4#1306329311yescharacteristic
686C2×C4#1306329311yescharacteristic
687C2×C4#1306329611yescharacteristic
688C2×C4#1306329811yescharacteristic
689C2×C4#1306329811yescharacteristic
690C2×C4#1306330111yescharacteristic
691C2×C4#1306330311yescharacteristic
692C2×C4#1306330311yescharacteristic
693C2×C4#1306330711yescharacteristic
694C2×C4#1306330711yescharacteristic
695C2×C4#1306331011yescharacteristic
696C2×C4#1306331011yescharacteristic
697C8—42no—
698C8—42no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—864no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22C4×(C2×D43)⋊C411yescharacteristic
719C22#1458275411yescharacteristic
720C22#1458275611yescharacteristic
721C22#1458277311yescharacteristic
722C22#1458277311yescharacteristic
723C22#1458277711yescharacteristic
724C22#1458277711yescharacteristic
725C22#1458306911yescharacteristic
726C22#1458307411yescharacteristic
727C22#1458307911yescharacteristic
728C22#1458308411yescharacteristic
729C4—44no—
730C4—864no—
731C4—3442no—
732C4—1724no—
733C4—1722no—
734C4—1722no—
735C4#95×D4311yescharacteristic
736C4#1458274611yescharacteristic
737C4#1458275811yescharacteristic
738C4#1458276111yescharacteristic
739C4#1458277011yescharacteristic
740C4#1458277011yescharacteristic
741C4#1458277511yescharacteristic
742C4#1458277511yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—1724no—
748C2(C2×D43)⋊#9511yescharacteristic
749C2#1913455111yescharacteristic
750C2#1913455611yescharacteristic
751C2#1913482411yescharacteristic
752C2#1913483111yescharacteristic
753C2#1913496311yescharacteristic
754C2#1913497011yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#343C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#343D43
hypocenterC43#10781
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. #19134315C2semidirect
5. C2×#14582660C2semidirect
6. #19132824C2semidirect
7. C2×C43×#343C2semidirect
12. #14583380C4semidirect
23. C2×#13063251C4semidirect
25. #14582901C4semidirect
72. C2×C4⋊Dic43C2×C4semidirect
87. C2×C4×Dic43C2×C4semidirect
104. C2×M16×C43C2×C4semidirect
105. C2×M16×C43C2×C4semidirect
309. D172#95semidirect
318. Dic86#95semidirect
369. C2×#343D43semidirect
413. C43#10781semidirect
445. C2×M16C4×D43semidirect
446. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833802
C22×#130632512
C2×#145829012
#191343152
C2×#145826602
#191328242
C2×C43×#3432
#1078143