Finite Group Databasebeta

← #25131446

Subgroups — #25131446

Order 11008.

1138 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×#14583118C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19139961C211yesmaximal, characteristic, complemented
4#19135831C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic
6#19135689C211yesmaximal, characteristic, complemented
7#19135683C211yesmaximal, characteristic
8#19135532C211yesmaximal, characteristic, complemented
9#19135407C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134863C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134605C211yesmaximal, characteristic, complemented
15C2×C43×#559C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583118—24no—
21C4×#10621883—24no—
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582837—21no—
36#14582818—21no—
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582780—21no—
42#14582780—21no—
43#14582765C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#559—24no—
51C43×#559—24no—
52C2×#127×C43C2211yescharacteristic
53C2×#124×C43—21no—
54C2×#124×C43C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×#123×C43—21no—
57C2×#123×C43—21no—
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×Q8×C43C2211yescharacteristic
60C2×C4×D4×C43—21no—
61C2×C4×D4×C43C2211yescharacteristic
62C2×C4×D4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—41no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C4×Dic86—22no—
78C4×Dic86—22no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C4×Dic43—21no—
86#13063256—22no—
87C4⋊(C43⋊C8)—22no—
88#13063249—22no—
89#13063249—22no—
90#13063249—41no—
91#13063248—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96#13063246—41no—
97#13063246—41no—
98C4×C43⋊C8—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×Q8×C43D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43—21no—
110C22×D4×C43—21no—
111C22×D4×C43C2311yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C23×C4×C43—21no—
114C23×C4×C43—21no—
115#127×C43—22no—
116#127×C43—22no—
117#124×C43—28no—
118#124×C43—22no—
119#124×C43—22no—
120#124×C43—22no—
121#124×C43D414yes—
122#123×C43—28no—
123#123×C43—28no—
124C4×Q8×C43—22no—
125C4×Q8×C43—22no—
126C4×Q8×C43—22no—
127C4×Q8×C43—22no—
128C4×D4×C43—28no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43D414yes—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C24×C43—21no—
149C24×C43—21no—
150C2×Q8×C43—22no—
151C2×Q8×C43—22no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—41no—
158C2×Q8×C43C2×D412yes—
159C2×D4×C43—24no—
160C2×D4×C43—24no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43C2×D412yes—
176C2×D4×C43C2×D412yes—
177C22×C4×C43—24no—
178C22×C4×C43—24no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—81no—
182C22×C4×C43—81no—
183C22×C4×C43—81no—
184C22×C4×C43—81no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86#4112yes—
202C4⋊C4×C43—24no—
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—22no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43C2×D412yes—
208C22⋊C4×C43—24no—
209C22⋊C4×C43—24no—
210C22⋊C4×C43—24no—
211C22⋊C4×C43—24no—
212C22⋊C4×C43—24no—
213C22⋊C4×C43—24no—
214C42×C43—24no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43C2×D412yes—
220C42×C43C2×D412yes—
221#10621885—44no—
222#10621883—28no—
223#10621883—44no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230Dic43⋊C4—42no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233C4×Dic43—42no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8#4112yes—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43C22×D411yescharacteristic
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—44no—
264Q8×C43—41no—
265Q8×C43—41no—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—48no—
271D4×C43—41no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—84no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—22no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—84no—
298C2×C4×C43—84no—
299C2×C4×C43#12012yes—
300C2×C4×C43#12012yes—
301C2×C4×C43#13512yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C432−1+411yescharacteristic
308C2×Dic43—22no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320Dic86—22no—
321Dic86—22no—
322Dic86—41no—
323Dic86—41no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#24194—431nomaximal, Sylow
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43C2×#12011yescharacteristic
344C22×C43#54811yescharacteristic
345C22×C43#55011yescharacteristic
346C22×C43C2×#13511yescharacteristic
347C22×C43#57511yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—42no—
358C4×C43#52511yescharacteristic
359C4×C43#53711yescharacteristic
360C4×C43#54611yescharacteristic
361C4×C43#54711yescharacteristic
362Dic43—42no—
363Dic43—81no—
364Dic43—81no—
365Dic43—81no—
366C2×#559D4311yescharacteristic
367C2×#464—431no—
368C2×C4×SD16—431no—
369#2581—431no—
370#2042—431no—
371#2041—431no—
372#2015—431no—
373#2014—431no—
374#1984—431no—
375#1958—431no—
376#1878—431no—
377#1877—431no—
378#1865—431no—
379#1864—431no—
380#1804—431no—
381C2×C43—82no—
382C2×C43—82no—
383C2×C43#240711yescharacteristic
384C2×C43#300211yescharacteristic
385C2×C43#300911yescharacteristic
386C2×C43#336511yescharacteristic
387C2×C43#337111yescharacteristic
388C2×C43#339411yescharacteristic
389C2×C43#340111yescharacteristic
390C22×Q16—431no—
391C22×SD16—431no—
392C22×SD16—431no—
393#559—24no—
394#559—24no—
395C2×#127C2×D4311yescharacteristic
396C2×#124—21no—
397C2×#124C2×D4311yescharacteristic
398C2×#124C2×D4311yescharacteristic
399C2×#123—21no—
400C2×#123—21no—
401C2×C4×Q8—431no—
402C2×C4×Q8C2×D4311yescharacteristic
403C2×C4×Q8C2×D4311yescharacteristic
404C2×C4×D4—21no—
405C2×C4×D4C2×D4311yescharacteristic
406C2×C4×D4C2×D4311yescharacteristic
407#464—864no—
408C4×SD16—864no—
409C2×#106—431no—
410C2×C4⋊C8—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×C4×C8—431no—
422#400—861no—
423#395—861no—
424#391—431no—
425#391—431no—
426#389—431no—
427#389—431no—
428#387—861no—
429#387—861no—
430#382—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435#336—431no—
436#336—431no—
437C43#2419411yescharacteristic, complemented, Sylow
438C22×Q8—431no—
439C22×Q8C22⋊D4311yescharacteristic
440C22×Q8C22×D4311yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4C22×D4311yescharacteristic
444C22×D4C22×D4311yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C2×Q16—862no—
448C2×Q16—862no—
449C2×Q16—1721no—
450C2×SD16—862no—
451C2×SD16—862no—
452C2×SD16—862no—
453C2×SD16—862no—
454C2×SD16—862no—
455C2×SD16—1721no—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—431no—
460#127—22no—
461#127—22no—
462#124—28no—
463#124—22no—
464#124—22no—
465#124—22no—
466#124C22⋊D4314yes—
467#123—28no—
468#123—28no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—862no—
474C4×Q8—862no—
475C4×D4—28no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4C22⋊D4314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4C22⋊D4311yescharacteristic
488C2×C4⋊C4C22⋊D4311yescharacteristic
489C2×C4⋊C4C22⋊D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C42—21no—
498C2×C42—861no—
499C2×C42C22×D4311yescharacteristic
500C2×C42C22×D4311yescharacteristic
501C2×C42C22×D4311yescharacteristic
502#106—862no—
503C4⋊C8—862no—
504#103—862no—
505#103—862no—
506#103—862no—
507#103—1721no—
508#102—862no—
509#102—862no—
510#102—862no—
511#102—1721no—
512#102—1721no—
513#102—1721no—
514C4×C8—862no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523C24—21no—
524C24—21no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—41no—
533C2×Q8—432no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8C2×C22⋊D4312yes—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4C2×C22⋊D4312yes—
557C2×D4C2×C22⋊D4312yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C2×C22⋊D4311yescharacteristic
573C22×C4C2×C22⋊D4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C2×C22⋊D4311yescharacteristic
576C22×C4C23×D4311yescharacteristic
577Q16—1724no—
578SD16—868no—
579SD16—1724no—
580C2×C8—432no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—1722no—
604C4⋊C4—1722no—
605C4⋊C4—1722no—
606C4⋊C4C2×C22⋊D4312yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—1722no—
619C42C2×C22⋊D4312yes—
620C42C2×C22⋊D4312yes—
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×C22⋊D4311yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—44no—
639Q8—41no—
640Q8—41no—
641Q8—862no—
642Q8—862no—
643Q8—1721no—
644Q8—1721no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—862no—
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#1306329412yes—
691C2×C4#1306329412yes—
692C2×C4#1306334512yes—
693C2×C4C22×C22⋊D4311yescharacteristic
694C2×C4C22×C22⋊D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4#41×D4311yescharacteristic
697C2×C4#1306337111yescharacteristic
698C2×C4#1306337211yescharacteristic
699C8—862no—
700C8—1721no—
701C8—1721no—
702C8—1721no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×#1306329411yescharacteristic
718C22#1458355611yescharacteristic
719C22#1458356811yescharacteristic
720C22C2×#1306334511yescharacteristic
721C22#1458369711yescharacteristic
722C22#1458371011yescharacteristic
723C22#1458371011yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—3441no—
733C4—3441no—
734C4—3441no—
735C4—1722no—
736C4#1458340611yescharacteristic
737C4#1458347711yescharacteristic
738C4#1458353711yescharacteristic
739C4#1458354811yescharacteristic
740C2—82no—
741C2—82no—
742C2#1913793411yescharacteristic
743C2#1914381311yescharacteristic
744C2#1914387211yescharacteristic
745C2#1914728711yescharacteristic
746C2#1914735711yescharacteristic
747C2#1914758711yescharacteristic
748C2#1914765511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#559C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenterC2×#559D43
hypocenterC43#24194
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#14583118C2semidirect
2. C2×C4×#10621883C2semidirect
3. #19139961C2semidirect
4. #19135831C2semidirect
6. #19135689C2semidirect
8. #19135532C2semidirect
9. #19135407C2semidirect
10. #19134936C2semidirect
11. #19134929C2semidirect
12. #19134863C2semidirect
13. #19134856C2semidirect
14. #19134605C2semidirect
437. C43#24194semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
C2×C4×#106218832
#191399612
#191358312
#191358262
#191356892
#191356832
#191355322
#191354072
#191349362
#191349292
#191348632
#191348562
#191346052
C2×C43×#5592
#2419443