Finite Group Databasebeta

← #25132965

Subgroups — #25132965

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic, complemented
3C2×D8×Dic43C211yesmaximal, characteristic
4#19139515C211yesmaximal, characteristic, complemented
5#19135924C211yesmaximal, characteristic, complemented
6#19135922C211yesmaximal, characteristic, complemented
7#19135731C211yesmaximal, characteristic, complemented
8#19135729C211yesmaximal, characteristic, complemented
9#19135554C211yesmaximal, characteristic, complemented
10#19135529C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic
12#19134844C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134593C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic
16C23×Dic86—21no—
17D4×Dic86—24no—
18D4×Dic86—24no—
19C2×#13063325C2211yescharacteristic
20C2×#13063324C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063302—21no—
24C2×#13063302—21no—
25C2×#13063302—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×D4×Dic43C2211yescharacteristic
30#14583177—24no—
31D8×Dic43—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582822—21no—
42#14582822—21no—
43#14582802C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582768C2211yescharacteristic
47#14582757—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×D8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—28no—
64C22×Dic86—21no—
65C22×Dic86—21no—
66C22×Dic86—21no—
67C22×Dic86—44no—
68C22×Dic86—44no—
69C22×Dic86D411yescharacteristic
70C23×Dic43—21no—
71C23×Dic43—21no—
72C23×Dic43—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063325—22no—
76#13063325—22no—
77#13063324—22no—
78#13063324—22no—
79#13063324—22no—
80#13063324D414yes—
81#13063304—28no—
82#13063302—28no—
83#13063302—28no—
84#13063302—44no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90D4×Dic43—22no—
91D4×Dic43—22no—
92D4×Dic43D414yes—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43D411yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
106C2×Dic43⋊C4D411yescharacteristic
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114#13063259—22no—
115#13063259—22no—
116#13063258—22no—
117Dic43⋊C8—22no—
118#13063246—22no—
119#13063246—22no—
120#13063246—22no—
121#13063246—22no—
122C8×Dic43—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C2×D8×C43—22no—
129C2×D8×C43—22no—
130C2×D8×C43Q814yescomplemented
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C4×D4×C43—22no—
134C4×D4×C43—22no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#102×C43—22no—
142#102×C43—22no—
143C24×C43—21no—
144C24×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43C2×D412yes—
154C2×D4×C43C2×Q812yes—
155C2×D4×C43C2×Q812yescomplemented
156C2×D4×C43#4112yes—
157C22×C4×C43—24no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C22×Dic43—24no—
166C22×Dic43—24no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—42no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—24no—
185C2×Dic86—24no—
186C2×Dic86—24no—
187C2×Dic86—432no—
188C2×Dic86—42no—
189C2×Dic86—42no—
190C2×Dic86—42no—
191C2×Dic86—42no—
192C2×Dic86—42no—
193C2×Dic86—42no—
194C2×Dic86D814yescomplemented
195D8×C43—28no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C2×Q812yescomplemented
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C2×D412yes—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—81no—
209C42×C43—21no—
210C42×C43—21no—
211C22⋊Dic43—24no—
212C22⋊Dic43—24no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—81no—
216C4⋊Dic43—24no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—22no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—42no—
225C4⋊Dic43C2×D412yes—
226C4⋊Dic43C2×D412yes—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—22no—
230Dic43⋊C4—22no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233Dic43⋊C4—81no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43C2×D412yes—
237C4×Dic43C2×D412yes—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C23×C43—22no—
245C23×C43—22no—
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×C43C22×D411yescharacteristic
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43C22⋊Q814yescomplemented
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—48no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43C2×D812yes—
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C22×Q811yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C432−1+411yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—48no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—48no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—84no—
308C2×Dic43#12012yes—
309C2×Dic43#12012yes—
310C2×Dic43C2×D812yes—
311C2×Dic43C2×D812yes—
312C2×Dic43AGL(1,ℤ/8)12yes—
313Dic86—28no—
314Dic86—48no—
315Dic86—48no—
316Dic86—48no—
317C8×C43—22no—
318C8×C43—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#24326—431nomaximal, Sylow
322C22×C43—24no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43C2×#12011yescharacteristic
337C22×C43#54811yescharacteristic
338C22×C43D4×Q811yescharacteristic
339C22×C43C22×D811yescharacteristic
340C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57811yescharacteristic
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—41no—
346C4×C43—81no—
347C4×C43C2×C22⋊Q811yescharacteristic
348C4×C43#53611yescharacteristic
349C4×C43#54811yescharacteristic
350C4×C43D4×Q811yescharacteristic
351Dic43—22no—
352Dic43—22no—
353Dic43—42no—
354Dic43—42no—
355Dic43—41no—
356Dic43—81no—
357Dic43—81no—
358Dic43#44714yes—
359C2×D4×Q8—431no—
360C2×#474—431no—
361C2×C4×D8—431no—
362#2538—431no—
363#2057—431no—
364#2057—431no—
365#2023—431no—
366#2023—431no—
367#1990—431no—
368#1984—431no—
369#1879—431no—
370#1879D4311yescharacteristic
371#1862—431no—
372#1862—431no—
373#1802—431no—
374C2×C43—44no—
375C2×C43—82no—
376C2×C43#240911yescharacteristic
377C2×C43C2×#44711yescharacteristic
378C2×C43#301311yescharacteristic
379C2×C43#335811yescharacteristic
380C2×C43#336711yescharacteristic
381C2×C43Q8×D811yescharacteristic
382C2×C43#338411yescharacteristic
383C23×Q8—861no—
384C22×D8C2×D4311yescharacteristic
385D4×Q8—864no—
386D4×Q8—864no—
387C2×C4⋊Q8—431no—
388C2×C4⋊Q8—431no—
389C2×C4⋊Q8—431no—
390C2×C22⋊Q8—861no—
391C2×C22⋊Q8—861no—
392C2×C22⋊Q8—861no—
393C2×C22⋊Q8—861no—
394C2×C4×Q8—431no—
395C2×C4×D4—431no—
396C2×C4×D4—431no—
397C2×C4×D4—431no—
398C2×C4×D4C2×D4311yescharacteristic
399#474—864no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#107—431no—
404C2×C4⋊C8—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102C2×D4311yescharacteristic
410C2×#102C2×D4311yescharacteristic
411C2×C4×C8—431no—
412#396—861no—
413#396—861no—
414#390—431no—
415#390C2×D4311yescharacteristic
416#389—431no—
417#389—431no—
418#384—431no—
419#380—861no—
420#340—431no—
421#340—431no—
422#340—431no—
423#340—431no—
424#340—431no—
425#340C2×D4311yescharacteristic
426#336—431no—
427#336—431no—
428#336—431no—
429#336C2×D4311yescharacteristic
430C43#2432611yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×Q8—861no—
433C22×Q8—861no—
434C22×Q8—868no—
435C22×Q8—861no—
436C22×Q8—1724no—
437C22×Q8—1724no—
438C22×D4C22×D4311yescharacteristic
439C22×D4C22×D4311yescharacteristic
440C23×C4—21no—
441C23×C4—861no—
442C23×C4—861no—
443C23×C4—861no—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8Dic8614yescomplemented
447C22×C8—431no—
448C22×C8—431no—
449C22×C8C22×D4311yescharacteristic
450C22×C8C22×D4311yescharacteristic
451C4⋊Q8—434no—
452C4⋊Q8—862no—
453C4⋊Q8—862no—
454C4⋊Q8—862no—
455C4⋊Q8—862no—
456C4⋊Q8—862no—
457C22⋊Q8—868no—
458C22⋊Q8—868no—
459C22⋊Q8—868no—
460C22⋊Q8—1724no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—434no—
466C4×D4—862no—
467C4×D4—862no—
468C4×D4—862no—
469C4×D4—862no—
470C4×D4—862no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C42—431no—
496C2×C42—431no—
497C2×C42C22×D4311yescharacteristic
498#107—862no—
499#107—862no—
500#107—862no—
501C4⋊C8—862no—
502#102—22no—
503#102—22no—
504#102—862no—
505#102—862no—
506#102—862no—
507#102—862no—
508C4×C8—862no—
509#95—861no—
510#95—861no—
511C24—21no—
512C24—21no—
513C2×Q8—434no—
514C2×Q8—862no—
515C2×Q8—862no—
516C2×Q8—864no—
517C2×Q8—864no—
518C2×Q8—864no—
519C2×Q8—1722no—
520C2×Q8—1722no—
521C2×Q8—1722no—
522C2×Q8—1722no—
523C2×Q8—1722no—
524C2×Q8—17232no—
525C2×Q8—1722no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4C2×Dic8612yes—
535C2×D4C2×Dic8612yescomplemented
536C2×D4D4×D4312yes—
537C2×D4#1062190012yes—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—864no—
548C22×C4—864no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4D4×D4311yescharacteristic
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563D8—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8C2×Dic8612yescomplemented
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—432no—
580C4⋊C4—432no—
581C4⋊C4—862no—
582C4⋊C4—862no—
583C4⋊C4—862no—
584C4⋊C4—864no—
585C4⋊C4—864no—
586C4⋊C4—864no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—3441no—
594C4⋊C4—1722no—
595C4⋊C4—1722no—
596C4⋊C4—1722no—
597C4⋊C4D4×D4312yes—
598C22⋊C4—24no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—3441no—
604C22⋊C4—1722no—
605C22⋊C4—1722no—
606C42—21no—
607C42—21no—
608C42—432no—
609C42—432no—
610C42—861no—
611C42—861no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23C2×D4×D4311yescharacteristic
627Q8—868no—
628Q8—1728no—
629Q8—1728no—
630Q8—1728no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4#1306330214yescomplemented
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—48no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—432no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—3444no—
666C2×C4—1728no—
667C2×C4—1728no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4D8×D4312yes—
679C2×C4C2×D4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4C22×Dic8611yescharacteristic
682C2×C4C2×#1062190011yescharacteristic
683C2×C4#1306337211yescharacteristic
684C2×C4#1306337211yescharacteristic
685C8—22no—
686C8—41no—
687C8—1721no—
688C8—1721no—
689C22—24no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22#120×D4311yescharacteristic
704C22#1458355511yescharacteristic
705C22D4×Dic8611yescharacteristic
706C22C2×D8×D4311yescharacteristic
707C22AGL(1,ℤ/8)×D4311yescharacteristic
708C22#1458370911yescharacteristic
709C22#1458371311yescharacteristic
710C4—22no—
711C4—42no—
712C4—41no—
713C4—81no—
714C4—434no—
715C4—862no—
716C4—862no—
717C4—3441no—
718C4—3441no—
719C4—1722no—
720C4—1722no—
721C4—1721no—
722C4C2×#1306330211yescharacteristic
723C4#1458347111yescharacteristic
724C4#1458355511yescharacteristic
725C4D4×Dic8611yescharacteristic
726C2—44no—
727C2—82no—
728C2#1913795711yescharacteristic
729C2#447×D4311yescharacteristic
730C2#1914390811yescharacteristic
731C2#1914722511yescharacteristic
732C2#1914730811yescharacteristic
733C2D8×Dic8611yescharacteristic
734C2#1914749511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenter#1879D43
hypocenterC43#24326
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic86C2semidirect
2. C2×#14583177C2semidirect
4. #19139515C2semidirect
5. #19135924C2semidirect
6. #19135922C2semidirect
7. #19135731C2semidirect
8. #19135729C2semidirect
9. #19135554C2semidirect
10. #19135529C2semidirect
12. #19134844C2semidirect
13. #19134842C2semidirect
14. #19134593C2semidirect
130. C2×D8×C43Q8semidirect
155. C2×D4×C43C2×Q8semidirect
194. C2×Dic86D8semidirect
201. C2×C8×C43C2×Q8semidirect
266. D4×C43C22⋊Q8semidirect
430. C43#24326semidirect
446. C2×D8Dic86semidirect
535. C2×D4C2×Dic86semidirect
575. C2×C8C2×Dic86semidirect
638. D4#13063302semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145831772
C2×D8×Dic432
#191395152
#191359242
#191359222
#191357312
#191357292
#191355542
#191355292
#191349452
#191348442
#191348422
#191345932
C43×#18792
#2432643