Finite Group Databasebeta

← #25149712

Subgroups — #25149712

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×#14583610C211yesmaximal, characteristic
2C2×#14583228C211yesmaximal, characteristic, complemented
3C2×#14583156C211yesmaximal, characteristic, complemented
4#19138027C211yesmaximal, characteristic
5#19135925C211yesmaximal, characteristic, complemented
6#19135794C211yesmaximal, characteristic, complemented
7#19135604C211yesmaximal, characteristic, complemented
8#19134939C211yesmaximal, characteristic, complemented
9#19134906C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134891C211yesmaximal, characteristic
12#19134866C211yesmaximal, characteristic, complemented
13#19134789C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#2024C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583610—24no—
19#14583610—24no—
20C2×#13063316—21no—
21C2×#13063305C2211yescharacteristic
22C2×#13063305C2211yescharacteristic
23C2×#13063301—21no—
24C2×#13063301—21no—
25C2×#13063301C2211yescharacteristic
26C2×#13063301C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×#13063287—21no—
30C2×#13063283C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14583228—24no—
34#14583156—24no—
35C2×#13063257C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063256C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45#14582828—21no—
46#14582817—21no—
47#14582797C2211yescharacteristic
48#14582796—21no—
49#14582788—21no—
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582654C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172D411yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—41no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063316—28no—
78#13063305—22no—
79#13063305—22no—
80#13063305—22no—
81#13063305D414yes—
82#13063301—28no—
83#13063301—28no—
84#13063301—22no—
85#13063301—22no—
86#13063301—22no—
87#13063301—41no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×D172—22no—
91C4×D172—22no—
92#13063287—28no—
93#13063283—22no—
94#13063283—41no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43D411yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C4⋊C4×D43D414yes—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121#13063257—22no—
122#13063256—22no—
123#13063256—22no—
124#13063250—22no—
125#13063250—22no—
126#13063249—22no—
127#13063248—41no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8—22no—
130(C2×D43)⋊C8—41no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C22×Q8×C43—21no—
134C22×Q8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C4⋊Q8×C43—22no—
138C4⋊Q8×C43—22no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144#103×C43—22no—
145#103×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148C23×D43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—24no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—81no—
158C2×Q8×C43—81no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×D172—22no—
173C2×D172—22no—
174C2×D172—22no—
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—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—24no—
186C2×C4×D43—24no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×C4×D43—81no—
191C2×C4×D43C2×D412yes—
192C2×C4×D43C2×D412yes—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86C2×D412yes—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C4⋊C4×C43—24no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43C2×D412yes—
211C4⋊C4×C43C2×D412yes—
212C42×C43—21no—
213C42×C43—21no—
214#10621885—44no—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223C4⋊Dic43—24no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—24no—
227C4⋊Dic43—22no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C2×D412yes—
231C4⋊Dic43#4112yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238C4×Dic43—24no—
239C4×Dic43—42no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8#4112yes—
246#10621872—44no—
247C23×C43C22×D411yescharacteristic
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43#12012yes—
261C22×D43#13712yes—
262Q8×C43—41no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43—84no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
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—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43#13712yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C432−1+411yescharacteristic
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—22no—
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#12012yes—
309D172—28no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—41no—
315C4×D43—41no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—84no—
319C4×D43—84no—
320Dic86—22no—
321Dic86—22no—
322Dic86—41no—
323Dic86—41no—
324C8×C43—41no—
325C8×C43—41no—
326C43⋊C8—22no—
327C43⋊C8—41no—
328#25561—431nomaximal, Sylow
329C22×C43C2×#12011yescharacteristic
330C22×C43#54611yescharacteristic
331C22×C43#54711yescharacteristic
332C22×C43C2×#13711yescharacteristic
333C22×C43C2×#13711yescharacteristic
334C22×C43#57711yescharacteristic
335C22×C43#57711yescharacteristic
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43#53211yescharacteristic
357C4×C43#53711yescharacteristic
358C4×C43#54611yescharacteristic
359C4×C43#54711yescharacteristic
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—41no—
364Dic43—42no—
365Dic43—81no—
366C2×#554—431no—
367C2×#483—431no—
368C2×#470—431no—
369#2415—431no—
370#2058—431no—
371#2035—431no—
372#2024D4311yescharacteristic, complemented
373#2001—431no—
374#1878—431no—
375#1873—431no—
376#1872—431no—
377#1870—431no—
378#1865—431no—
379#1853—431no—
380#1736—431no—
381C2×C43#243011yescharacteristic
382C2×C43#300411yescharacteristic
383C2×C43#300911yescharacteristic
384C2×C43#331611yescharacteristic
385C2×C43#333111yescharacteristic
386C2×C43#334411yescharacteristic
387C2×C43#335611yescharacteristic
388D43—42no—
389D43—42no—
390C22×Q16—431no—
391C22×M16—431no—
392#554—864no—
393#554—864no—
394C2×C4⋊Q8C2×D4311yescharacteristic
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×#117—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
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×#103C2×D4311yescharacteristic
418C2×#103C2×D4311yescharacteristic
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422#397—861no—
423#394—861no—
424#391C2×D4311yescharacteristic
425#389—431no—
426#389—861no—
427#388—861no—
428#380—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340C2×D4311yescharacteristic
434#340C2×D4311yescharacteristic
435#336—431no—
436#336C2×D4311yescharacteristic
437C43#2556111yescharacteristic, complemented, Sylow
438C22×Q8—21no—
439C22×Q8—431no—
440C22×Q8C22×D4311yescharacteristic
441C22×D4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—861no—
445C23×C4—861no—
446C2×Q16—862no—
447C2×Q16—862no—
448C2×Q16—1721no—
449C2×M16—862no—
450C2×M16—862no—
451C2×M16—1721no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458#125—868no—
459C22⋊Q8—434no—
460C22⋊Q8—862no—
461C22⋊Q8—862no—
462C22⋊Q8—868no—
463C22⋊Q8—868no—
464C22⋊Q8—862no—
465C22⋊Q8—862no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—1721no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—862no—
472C4×D4—862no—
473C4×D4—868no—
474#117—862no—
475#117—1721no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—434no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—862no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—431no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—861no—
505C2×C42—861no—
506C2×C42C22×D4311yescharacteristic
507#106—862no—
508#106—862no—
509#106—862no—
510#103—22no—
511#103—22no—
512#103—862no—
513#103—862no—
514#103—862no—
515#103—1721no—
516C22⋊C8—862no—
517C22⋊C8—862no—
518C22⋊C8—1721no—
519#95—21no—
520#95—21no—
521#95—861no—
522#95—861no—
523C24—431no—
524C24—431no—
525C2×Q8—24no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—81no—
533C2×Q8—81no—
534C2×Q8—432no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×D4—862no—
541C2×D4—862no—
542C2×D4—862no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—431no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—431no—
551C22×C4—864no—
552C22×C4—864no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
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—3441no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4—3441no—
571C22×C4D4×D4311yescharacteristic
572C22×C4D4×D4311yescharacteristic
573C22×C4C23×D4311yescharacteristic
574Q16—1724no—
575M16—1724no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—432no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—432no—
594C4⋊C4—432no—
595C4⋊C4—864no—
596C4⋊C4—862no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4—864no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—1722no—
606C4⋊C4—1722no—
607C4⋊C4—1722no—
608C4⋊C4D4×D4312yes—
609C4⋊C4D4×D4312yes—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—864no—
613C22⋊C4—864no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C42—21no—
619C42—21no—
620C42—864no—
621C42—1722no—
622C23—432no—
623C23—432no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23C2×D4×D4311yescharacteristic
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—84no—
642Q8—862no—
643Q8—862no—
644Q8—1721no—
645Q8—1721no—
646D4—868no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
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—432no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—861no—
674C2×C4—862no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—3444no—
678C2×C4—3444no—
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#1306335712yes—
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4#41×D4311yescharacteristic
697C2×C4#1306337111yescharacteristic
698C2×C4#1306337311yescharacteristic
699C8—41no—
700C8—41no—
701C8—862no—
702C8—1721no—
703C22—862no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—1721no—
710C22—1721no—
711C22—1721no—
712C22—1721no—
713C22—1721no—
714C22—1721no—
715C22—1721no—
716C22—1721no—
717C22#120×D4311yescharacteristic
718C22#1458354211yescharacteristic
719C22#1458355111yescharacteristic
720C22#137×D4311yescharacteristic
721C22C2×#1306335711yescharacteristic
722C22#1458370511yescharacteristic
723C22#1458370911yescharacteristic
724C4—22no—
725C4—41no—
726C4—42no—
727C4—42no—
728C4—81no—
729C4—81no—
730C4—862no—
731C4—3441no—
732C4—1722no—
733C4—1721no—
734C4—1722no—
735C4—1722no—
736C4#1458344811yescharacteristic
737C4#1458347911yescharacteristic
738C4#1458354211yescharacteristic
739C4#1458355111yescharacteristic
740C2—1722no—
741C2—1722no—
742C2#1913820811yescharacteristic
743C2#1914383011yescharacteristic
744C2#1914386711yescharacteristic
745C2#1914670511yescharacteristic
746C2#1914691011yescharacteristic
747C2#1914704711yescharacteristic
748C2#1914721311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2024C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenter#2024D43
hypocenterC43#25561
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. C2×#14583228C2semidirect
3. C2×#14583156C2semidirect
5. #19135925C2semidirect
6. #19135794C2semidirect
7. #19135604C2semidirect
8. #19134939C2semidirect
9. #19134906C2semidirect
10. #19134899C2semidirect
12. #19134866C2semidirect
13. #19134789C2semidirect
14. #19134313C2semidirect
15. C43×#2024C2semidirect
372. #2024D43semidirect
437. C43#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#145836102
C2×#145832282
C2×#145831562
#191380272
#191359252
#191357942
#191356042
#191349392
#191349062
#191348992
#191348912
#191348662
#191347892
#191343132
C43×#20242
#2556143