Finite Group Databasebeta

← #25149709

Subgroups — #25149709

Order 11008.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583604C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic, complemented
3C2×#14583157C211yesmaximal, characteristic, complemented
4#19138018C211yesmaximal, characteristic
5#19135927C211yesmaximal, characteristic, complemented
6#19135794C211yesmaximal, characteristic, complemented
7#19135735C211yesmaximal, characteristic, complemented
8#19135606C211yesmaximal, characteristic, complemented
9#19134937C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134892C211yesmaximal, characteristic
13#19134864C211yesmaximal, characteristic, complemented
14#19134789C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17#14583604—24no—
18#14583604—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063305C2211yescharacteristic
22C2×#13063305C2211yescharacteristic
23C2×#13063304—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063303—21no—
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31#14583229—24no—
32#14583157—24no—
33C2×#13063257C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45#14582824—21no—
46#14582815—21no—
47#14582804C2211yescharacteristic
48#14582798C2211yescharacteristic
49#14582797—21no—
50#14582790—21no—
51#14582756C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×Dic86C2311yescharacteristic
66C22×C22⋊D43D411yescharacteristic
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×Dic172—22no—
70C2×Dic172—22no—
71C2×Dic172—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063324—22no—
75#13063324—22no—
76#13063315—28no—
77#13063305—22no—
78#13063305—22no—
79#13063305—22no—
80#13063305—41no—
81#13063304—28no—
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304D414yes—
86#13063303—28no—
87#13063290—22no—
88#13063290—22no—
89C4×C22⋊D43—28no—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43D411yescharacteristic
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4D411yescharacteristic
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114#13063257—22no—
115#13063256—22no—
116#13063256—22no—
117#13063250—22no—
118#13063250—22no—
119#13063248—22no—
120#13063248—22no—
121#13063248—22no—
122#13063248—41no—
123C22⋊(C43⋊C8)—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—41no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C2×M16×C43—22no—
133C2×M16×C43—22no—
134C2×M16×C43—41no—
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#117×C43—22no—
138#117×C43—41no—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43D414yes—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—24no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—81no—
160C22×C4×C43—81no—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—24no—
182C2×C4×D43—81no—
183C2×C4×D43—81no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—24no—
196C2×Dic86—81no—
197C2×Dic86—81no—
198C2×Dic86C2×D412yes—
199M16×C43—44no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43#4112yes—
206C4⋊C4×C43—24no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43C2×D412yes—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43#4112yes—
215C22⋊C4×C43—42no—
216C42×C43—42no—
217C22⋊Dic43—24no—
218C22⋊Dic43—22no—
219C22⋊Dic43—42no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224C4⋊Dic43—24no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230C4⋊Dic43C2×D412yes—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—22no—
236Dic43⋊C4—42no—
237C4×Dic43—24no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246Dic172—44no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43#12012yes—
254C23×C43C22×D411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43#13712yes—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—84no—
281C2×C4×C43#12012yes—
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C22⋊D43—28no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43#13712yes—
310C4×D43—41no—
311C4×D43—41no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—84no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319Dic86—41no—
320Dic86—41no—
321Dic86—41no—
322Dic86—41no—
323Dic86—84no—
324C8×C43—22no—
325C8×C43—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#25561—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C2×#12011yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43#54711yescharacteristic
339C22×C43C2×#13711yescharacteristic
340C22×C43C2×#13711yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57711yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—81no—
355C4×C43#53211yescharacteristic
356C4×C43#53711yescharacteristic
357C4×C43#54611yescharacteristic
358C4×C43#54711yescharacteristic
359Dic43—22no—
360Dic43—42no—
361Dic43—41no—
362Dic43—41no—
363Dic43—42no—
364Dic43—81no—
365Dic43—81no—
366C2×#554—431no—
367C2×#483—431no—
368C2×#470—431no—
369#2415—431no—
370#2058—431no—
371#2035—431no—
372#2024—431no—
373#2001—431no—
374#1878—431no—
375#1873—431no—
376#1872—431no—
377#1870—431no—
378#1865—431no—
379#1853—431no—
380#1736D4311yescharacteristic, complemented
381C2×C43—42no—
382C2×C43#243011yescharacteristic
383C2×C43#300411yescharacteristic
384C2×C43#300911yescharacteristic
385C2×C43#331611yescharacteristic
386C2×C43#333111yescharacteristic
387C2×C43#334411yescharacteristic
388C2×C43#335611yescharacteristic
389D43—42no—
390C22×Q16—431no—
391C22×M16C2×D4311yescharacteristic
392#554—864no—
393#554—864no—
394C2×C4⋊Q8—431no—
395C2×#125—861no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8—431no—
398C2×C22⋊Q8—431no—
399C2×C22⋊Q8—431no—
400C2×C22⋊Q8—861no—
401C2×C22⋊Q8—861no—
402C2×C4×Q8—431no—
403C2×C4×D4—431no—
404C2×C4×D4—861no—
405C2×#117C2×D4311yescharacteristic
406C22×C4⋊C4—431no—
407C22×C4⋊C4C2×D4311yescharacteristic
408#483—864no—
409#470—864no—
410C2×#106—431no—
411C2×#106—431no—
412C2×#106—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422#397—861no—
423#394—861no—
424#391—431no—
425#389—431no—
426#389—861no—
427#388—861no—
428#380—431no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic
432#340C2×D4311yescharacteristic
433#340C2×D4311yescharacteristic
434#340C2×D4311yescharacteristic
435#336—431no—
436#336—431no—
437C43#2556111yescharacteristic, complemented, Sylow
438C22×Q8—431no—
439C22×Q8—431no—
440C22×Q8—861no—
441C22×D4—431no—
442C23×C4—21no—
443C23×C4—431no—
444C23×C4—861no—
445C23×C4C22×D4311yescharacteristic
446C2×Q16—862no—
447C2×Q16—862no—
448C2×Q16—1721no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458#125—868no—
459C22⋊Q8—434no—
460C22⋊Q8—862no—
461C22⋊Q8—868no—
462C22⋊Q8—868no—
463C22⋊Q8—862no—
464C22⋊Q8—862no—
465C22⋊Q8—862no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—1721no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—868no—
472C4×D4—862no—
473C4×D4—862no—
474#117—22no—
475#117—41no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—862no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4D17214yes—
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—431no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—21no—
505C2×C42—431no—
506C2×C42—861no—
507#106—862no—
508#106—862no—
509#106—862no—
510#103—862no—
511#103—862no—
512#103—862no—
513#103—862no—
514#103—862no—
515#103—1721no—
516C22⋊C8—862no—
517C22⋊C8—862no—
518C22⋊C8—1721no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523C24—431no—
524C24D4×D4311yescharacteristic
525C2×Q8—432no—
526C2×Q8—864no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—3441no—
539C2×Q8—3441no—
540C2×D4—862no—
541C2×D4—862no—
542C2×D4—862no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—864no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4C2×D17212yes—
571C22×C4D4×D4311yescharacteristic
572C22×C4D4×D4312yes—
573C22×C4C23×D4311yescharacteristic
574Q16—1724no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8#1062189812yes—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—432no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—862no—
600C4⋊C4—864no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—1722no—
605C4⋊C4—1722no—
606C4⋊C4—1722no—
607C4⋊C4C2×D17212yes—
608C4⋊C4C2×D17212yes—
609C4⋊C4#1062189812yes—
610C22⋊C4—42no—
611C22⋊C4—864no—
612C22⋊C4—862no—
613C22⋊C4—864no—
614C22⋊C4—862no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C42—42no—
619C42—864no—
620C42—861no—
621C42—861no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—432no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23#1306329512yes—
636C23C2×D4×D4311yescharacteristic
637Q8—862no—
638Q8—862no—
639Q8—3444no—
640Q8—1721no—
641Q8—1721no—
642Q8—1721no—
643Q8—1721no—
644Q8—1721no—
645Q8—1721no—
646D4—868no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4—432no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—862no—
670C2×C4—861no—
671C2×C4—862no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—3444no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4#1306329512yes—
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C22×D17211yescharacteristic
695C2×C4C2×#1062189811yescharacteristic
696C2×C4C2×#1062189811yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337311yescharacteristic
699C8—22no—
700C8—41no—
701C8—1721no—
702C8—1721no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—1721no—
714C22—1721no—
715C22—1721no—
716C22—1721no—
717C22C2×#1306329511yescharacteristic
718C22#1458353911yescharacteristic
719C22#1458355011yescharacteristic
720C22#137×D4311yescharacteristic
721C22#137×D4311yescharacteristic
722C22#1458370911yescharacteristic
723C22#1458370911yescharacteristic
724C4—22no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—81no—
729C4—862no—
730C4—3441no—
731C4—3441no—
732C4—1721no—
733C4—1722no—
734C4—1721no—
735C4—1722no—
736C4#1458344911yescharacteristic
737C4#1458348011yescharacteristic
738C4#1458353911yescharacteristic
739C4#1458355011yescharacteristic
740C2—42no—
741C2—1722no—
742C2#1913820511yescharacteristic
743C2#1914383111yescharacteristic
744C2#1914387311yescharacteristic
745C2#1914670711yescharacteristic
746C2#1914690711yescharacteristic
747C2#1914705111yescharacteristic
748C2#1914720611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1736D43
hypocenterC43#25561
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#14583229C2semidirect
3. C2×#14583157C2semidirect
5. #19135927C2semidirect
6. #19135794C2semidirect
7. #19135735C2semidirect
8. #19135606C2semidirect
9. #19134937C2semidirect
10. #19134907C2semidirect
11. #19134901C2semidirect
13. #19134864C2semidirect
14. #19134789C2semidirect
15. C43×#1736C2semidirect
380. #1736D43semidirect
437. C43#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145832292
C2×#145831572
#191380182
#191359272
#191357942
#191357352
#191356062
#191349372
#191349072
#191349012
#191348922
#191348642
#191347892
C43×#17362
#2556143