Finite Group Databasebeta

← #25116868

Subgroups — #25116868

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583036C211yesmaximal, characteristic
2C2×#14582996C211yesmaximal, characteristic, complemented
3C2×#103×D43C211yesmaximal, characteristic, complemented
4#19137616C211yesmaximal, characteristic
5#19137429C211yesmaximal, characteristic, complemented
6#19135282C211yesmaximal, characteristic, complemented
7#19135233C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic
9#19134953C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134846C211yesmaximal, characteristic, complemented
12#19134781C211yesmaximal, characteristic, complemented
13#19134426C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C43×#1973C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×(C22⋊D43)⋊C4—21no—
24C2×C4⋊C4×D43C2211yescharacteristic
25#14583036C418yescomplemented
26#14582996—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33#103×D43—24no—
34C2×#13063246C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582803—21no—
39#14582803—21no—
40#14582795C2211yescharacteristic
41#14582787—21no—
42#14582775—21no—
43#14582771—21no—
44#14582758—21no—
45#14582756C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47C4×(C2×D43)⋊C4C2211yescharacteristic
48#14582746—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C43×#391C2211yescharacteristic
61C43×#390C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—41no—
68C2×Q8×D43—41no—
69C2×Q8×D43C2×C414yescomplemented
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621883—22no—
76C2×#10621883—22no—
77C2×#10621883C2×C414yescomplemented
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—22no—
81C2×C8×D43—22no—
82C2×C8×D43—41no—
83#13063296—22no—
84#13063296C2×C414yes—
85C4×Dic86—22no—
86C4×Dic86—41no—
87#13063290—22no—
88#13063290—41no—
89D4×Dic43—22no—
90D4×Dic43—41no—
91(C22⋊D43)⋊C4—44no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—41no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110#13063258—22no—
111#13063250C2×C414yescomplemented
112#13063250D414yescomplemented
113#13063249—22no—
114#13063249C2×C414yescomplemented
115#13063248—22no—
116#13063246—41no—
117(C2×D43)⋊C8C2×C414yescomplemented
118#13063235—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95D411yescharacteristic
125C43⋊#95D411yescharacteristic
126C22×Q8×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C2×SD16×C43—41no—
129C2×SD16×C43—41no—
130C2×SD16×C43C2×C414yescomplemented
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#107×C43—41no—
139#103×C43—22no—
140#102×C43—22no—
141#97×C43—41no—
142#95×C43—21no—
143#95×C43—21no—
144C24×C43—21no—
145C23×D43C2×D411yescharacteristic
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C22×C412yes—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43C22×C412yes—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—81no—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177Q8×D43—28no—
178Q8×D43—44no—
179Q8×D43—44no—
180Q8×D43—44no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—24no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43C22×C412yes—
192C2×C4×D43#4112yes—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—24no—
197C2×Dic86—42no—
198C2×Dic86—42no—
199C2×Dic86C22×C412yes—
200C2×Dic86C2×D412yes—
201C2×Dic86#4112yes—
202SD16×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C22×C412yes—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—81no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—24no—
218C22⋊Dic43—42no—
219#10621883—28no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—42no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43C22×C412yes—
228C4⋊Dic43C2×D412yes—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—42no—
236C4×Dic43—42no—
237C4×Dic43—42no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244C8×D43—44no—
245C23×C43—22no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43C22×D411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43C4×D412yes—
258C22×D43AGL(1,ℤ/8)12yes—
259C22×D43#13712yes—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—41no—
267D4×C43—41no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C22⋊D43—48no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—22no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—84no—
311C2×Dic43C4×D412yes—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—48no—
317C4×D43—84no—
318Dic86—22no—
319Dic86—22no—
320Dic86—22no—
321Dic86—48no—
322Dic86C4×D414yescomplemented
323C8×C43—22no—
324C8×C43—22no—
325C43⋊C8—22no—
326C43⋊C8—41no—
327#22855—431nomaximal, Sylow
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43C2×C4×D411yescharacteristic
336C22×C43D4211yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C43C2×#13711yescharacteristic
340C22×C43#57711yescharacteristic
341C22×C43#57811yescharacteristic
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43#44014yescomplemented
349C4×C43—42no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43C2×C4×D411yescharacteristic
355C4×C43#51811yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#55111yescharacteristic
358Dic43—24no—
359Dic43—22no—
360Dic43—42no—
361Dic43—42no—
362Dic43—41no—
363Dic43—41no—
364Dic43—81no—
365C2×#448—431no—
366C2×#440—431no—
367C22×#103—431no—
368#2361—431no—
369Q8×C22⋊C4—431no—
370#1973D4311yescharacteristic, complemented
371#1935—431no—
372#1928—431no—
373#1893—431no—
374#1880—431no—
375#1877—431no—
376#1863—431no—
377#1852—431no—
378#1763—431no—
379#1752—431no—
380C2×C43—82no—
381C2×C43#235811yescharacteristic
382C2×C43C2×#44011yescharacteristic
383C2×C43#294711yescharacteristic
384C2×C43#326511yescharacteristic
385C2×C43#327011yescharacteristic
386C2×C43#330811yescharacteristic
387C2×C43#332011yescharacteristic
388D43—24no—
389C23×Q8—431no—
390C22×SD16—431no—
391C22×SD16C2×D4311yescharacteristic
392C23×C8—431no—
393C2×#121—431no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×D4—431no—
397C2×C4×D4—861no—
398C22×C4⋊C4—431no—
399#448—438no—
400#440—864no—
401C2×#107—431no—
402C2×#107C2×D4311yescharacteristic
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—864no—
409C2×#103C2×D4311yescharacteristic
410C2×#102—431no—
411C2×#102C2×D4311yescharacteristic
412C2×C22⋊C8—431no—
413C2×#97—431no—
414C2×#97C2×D4311yescharacteristic
415#391—431no—
416#391—861no—
417#391—861no—
418#391C2×D4311yescharacteristic
419#390C2×D4311yescharacteristic
420#389—431no—
421#388—861no—
422#386—861no—
423#385—861no—
424#380—431no—
425#380—861no—
426C4×C4⋊C4—431no—
427C4×C22⋊C4—431no—
428C4×C22⋊C4—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435C43#2285511yescharacteristic, complemented, Sylow
436C22×Q8—434no—
437C22×Q8—431no—
438C22×Q8—861no—
439C22×Q8—862no—
440C22×Q8—862no—
441C22×Q8—862no—
442C22×Q8—1721no—
443C22×Q8—1721no—
444C22×Q8C22×D4311yescharacteristic
445C22×D4—861no—
446C22×D4C22×D4311yescharacteristic
447C23×C4—431no—
448C23×C4—861no—
449C23×C4—861no—
450C23×C4—861no—
451C2×SD16—41no—
452C2×SD16—41no—
453C2×SD16—434no—
454C2×SD16—862no—
455C2×SD16—862no—
456C2×SD16C4×D4314yescomplemented
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8—1721no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#121—434no—
465#121—862no—
466C4×Q8—862no—
467C4×Q8—862no—
468C4×Q8—1721no—
469C4×Q8—1721no—
470C4×D4—862no—
471C4×D4—1721no—
472C4×D4—1724no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—862no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—1721no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—431no—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C42—431no—
492C2×C42—861no—
493C2×C42—861no—
494C2×C42—861no—
495C2×C42C22×D4311yescharacteristic
496#107—41no—
497#107—862no—
498#103—22no—
499#103—434no—
500#103—434no—
501#103—434no—
502#103—862no—
503#103—862no—
504#102—22no—
505#102—1721no—
506C22⋊C8—434no—
507#97—41no—
508#97—862no—
509#95—21no—
510#95—21no—
511#95—431no—
512#95—431no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518C24—21no—
519C24—431no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—432no—
526C2×Q8—432no—
527C2×Q8—432no—
528C2×Q8—864no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—868no—
533C2×Q8—1722no—
534C2×Q8—1722no—
535C2×Q8—1724no—
536C2×Q8—1724no—
537C2×Q8—1724no—
538C2×Q8C2×C4×D4312yes—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—864no—
545C2×D4—1722no—
546C2×D4—1722no—
547C2×D4C2×C4×D4312yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—431no—
552C22×C4—432no—
553C22×C4—432no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—864no—
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—3441no—
566C22×C4—3441no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4D4×D4311yescharacteristic
574C22×C4D4×D4311yescharacteristic
575C22×C4C23×D4311yescharacteristic
576SD16—44no—
577SD16—868no—
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—
588C2×C8—1724no—
589C2×C8C2×C4×D4312yes—
590C2×C8D4×D4312yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—432no—
596C4⋊C4—432no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C4⋊C4—1722no—
604C4⋊C4—1722no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—862no—
608C22⋊C4—862no—
609C22⋊C4—864no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C42—21no—
613C42—21no—
614C42—861no—
615C42—861no—
616C42—1722no—
617C42—1722no—
618C42—1722no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—432no—
627C23—432no—
628C23—432no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23C2×D4×D4311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—41no—
637Q8—41no—
638Q8—434no—
639Q8—862no—
640Q8—862no—
641Q8—862no—
642Q8—1728no—
643D4—22no—
644D4—22no—
645D4—41no—
646D4—41no—
647D4—1728no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
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—432no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—861no—
667C2×C4—862no—
668C2×C4—861no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—862no—
681C2×C4—3444no—
682C2×C4—3444no—
683C2×C4—1728no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4C22×C4×D4311yescharacteristic
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#41×D4311yescharacteristic
694C2×C4#41×D4311yescharacteristic
695C2×C4#1306337011yescharacteristic
696C2×C4#1306337011yescharacteristic
697C8—22no—
698C8—22no—
699C8—862no—
700C8—1721no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—434no—
709C22—862no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22C4×D4×D4311yescharacteristic
716C22#1458353411yescharacteristic
717C22#1458353811yescharacteristic
718C22AGL(1,ℤ/8)×D4311yescharacteristic
719C22#137×D4311yescharacteristic
720C22#1458370911yescharacteristic
721C22#1458371511yescharacteristic
722C4—41no—
723C4—42no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—862no—
728C4—864no—
729C4—3441no—
730C4—1721no—
731C4—1722no—
732C4—1721no—
733C4—1722no—
734C4C4×D4×D4311yescharacteristic
735C4#1458337211yescharacteristic
736C4#1458353811yescharacteristic
737C4#1458357911yescharacteristic
738C2—82no—
739C2—864no—
740C2#1913757611yescharacteristic
741C2#440×D4311yescharacteristic
742C2#1914343511yescharacteristic
743C2#1914608911yescharacteristic
744C2#1914616411yescharacteristic
745C2#1914658111yescharacteristic
746C2#1914676111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1973C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1973D43
hypocenterC43#22855
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. C2×#14582996C2semidirect
3. C2×#103×D43C2semidirect
5. #19137429C2semidirect
6. #19135282C2semidirect
7. #19135233C2semidirect
9. #19134953C2semidirect
10. #19134931C2semidirect
11. #19134846C2semidirect
12. #19134781C2semidirect
13. #19134426C2semidirect
14. #19134372C2semidirect
15. C43×#1973C2semidirect
25. #14583036C4semidirect
69. C2×Q8×D43C2×C4semidirect
77. C2×#10621883C2×C4semidirect
111. #13063250C2×C4semidirect
112. #13063250D4semidirect
114. #13063249C2×C4semidirect
117. (C2×D43)⋊C8C2×C4semidirect
130. C2×SD16×C43C2×C4semidirect
322. Dic86C4×D4semidirect
348. C2×D43#440semidirect
370. #1973D43semidirect
435. C43#22855semidirect
456. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830362
C2×#145829962
C2×#103×D432
#191376162
#191374292
#191352822
#191352332
#191350202
#191349532
#191349312
#191348462
#191347812
#191344262
#191343722
C43×#19732
#2285543