Finite Group Databasebeta

← #25153656

Subgroups — #25153656

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583177C211yesmaximal, characteristic, complemented
2C22×#13063246C211yesmaximal, characteristic
3#19138298C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic
5#19136121C211yesmaximal, characteristic, complemented
6#19135981C211yesmaximal, characteristic, complemented
7#19135979C211yesmaximal, characteristic, complemented
8#19135729C211yesmaximal, characteristic, complemented
9#19134844C211yesmaximal, characteristic, complemented
10#19134840C211yesmaximal, characteristic, complemented
11#19134785C211yesmaximal, characteristic, complemented
12#19134772C211yesmaximal, characteristic, complemented
13#19134622C211yesmaximal, characteristic, complemented
14#19134593C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063324C2211yescharacteristic, complemented
18C2×#13063302—21no—
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43—21no—
23#14583177—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063259C2211yescharacteristic, complemented
26C2×#13063258C2211yescharacteristic, complemented
27C2×#13063258C2211yescharacteristic, complemented
28C2×Dic43⋊C8C2211yescharacteristic, complemented
29C2×Dic43⋊C8C2211yescharacteristic, complemented
30C2×#13063246—24no—
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35#14582833—21no—
36#14582820—21no—
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582798C2211yescharacteristic, complemented
40#14582795C2211yescharacteristic, complemented
41#14582779—21no—
42#14582779—21no—
43#14582771—21no—
44#14582768C2211yescharacteristic, complemented
45#14582759C2211yescharacteristic
46#14582755—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324—41no—
72#13063302—44no—
73D4×Dic43—22no—
74D4×Dic43—22no—
75D4×Dic43—41no—
76D4×Dic43—41no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—44no—
97C2×C22⋊Dic43D411yescharacteristic
98C2×C22⋊Dic43D411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063259—22no—
102#13063259—41no—
103#13063258—22no—
104#13063258—41no—
105Dic43⋊C8—22no—
106Dic43⋊C8—41no—
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246D414yes—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C25×C43—21no—
117C22×D4×C43—22no—
118C22×D4×C43—22no—
119C22×D4×C43—21no—
120C22×D4×C43—22no—
121C22×D4×C43—41no—
122C22×D4×C43—41no—
123C22×D4×C43Q814yescomplemented
124C22×D4×C43C2311yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132#102×C43—22no—
133#102×C43—22no—
134#102×C43—41no—
135#102×C43—41no—
136C22⋊C8×C43—22no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—81no—
146C24×C43—81no—
147C24×C43C2×D411yescharacteristic
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—28no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—44no—
163C2×D4×C43C2×D412yes—
164C2×D4×C43C2×Q812yes—
165C2×D4×C43C2×Q812yes—
166C2×D4×C43#4112yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×Q812yes—
175C22×C4×C43#4112yes—
176C22×C4×C43C2411yescharacteristic
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43—42no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C22×Dic43—81no—
188C22×Dic43—81no—
189C22×Dic43—81no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C2×Dic86—42no—
195C2×Dic86—42no—
196C2×Dic86—81no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C22⋊C4×C43—42no—
208C22⋊Dic43—22no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—42no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C22⋊Dic43D814yes—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—42no—
225C4⋊Dic43—42no—
226C4⋊Dic43C2×D412yes—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229Dic43⋊C4—42no—
230Dic43⋊C4—81no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—44no—
241C2×C43⋊C8C2×D412yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—48no—
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×C43—41no—
261C23×C43—48no—
262C23×C43—84no—
263C23×C43—84no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43C22⋊Q812yes—
268C23×C43C2×D812yes—
269C23×C43#13712yes—
270C23×C43C22×D411yescharacteristic
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—48no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43C22⋊Q814yescomplemented
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43C22⋊Q812yes—
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×Q811yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
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—
320C2×Dic43—41no—
321C2×Dic43—84no—
322C2×Dic43—84no—
323C2×Dic43—84no—
324C2×Dic43C2×D812yes—
325C2×Dic43C2×D812yes—
326Dic86—84no—
327C8×C43—41no—
328C8×C43—41no—
329C43⋊C8—22no—
330C43⋊C8—41no—
331#25950—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—24no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—816no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43#47414yescomplemented
354C22×C43C2×C22⋊Q811yescharacteristic
355C22×C43D4211yescharacteristic
356C22×C43#54611yescharacteristic
357C22×C43C22×D811yescharacteristic
358C22×C43C2×#13711yescharacteristic
359C22×C43#57611yescharacteristic
360C22×C43#57711yescharacteristic
361C4×C43—22no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43C2×C22⋊Q811yescharacteristic
365C4×C43#54311yescharacteristic
366C4×C43#54611yescharacteristic
367C4×C43#55111yescharacteristic
368Dic43—22no—
369Dic43—22no—
370Dic43—41no—
371Dic43—42no—
372Dic43—41no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376C2×#474—431no—
377C22×#102—431no—
378#2440—431no—
379D4×C22⋊C4—431no—
380#2093—431no—
381#2067—431no—
382#2067—431no—
383#2023—431no—
384#1862—431no—
385#1862—431no—
386#1852—431no—
387#1850—431no—
388#1808—431no—
389#1802—431no—
390#1786D4311yescharacteristic
391C2×C43—24no—
392C2×C43—44no—
393C2×C43—82no—
394C2×C43#243711yescharacteristic
395C2×C43C2×#47411yescharacteristic
396C2×C43#308111yescharacteristic
397C2×C43#326611yescharacteristic
398C2×C43D4×D811yescharacteristic
399C2×C43#329411yescharacteristic
400C2×C43#331411yescharacteristic
401C23×D4C2×D4311yescharacteristic
402C23×C8—431no—
403C2×C4⋊Q8—431no—
404C2×C22⋊Q8—861no—
405C2×C4×D4—431no—
406C2×C4×D4—431no—
407C22×C4⋊C4—431no—
408C22×C22⋊C4—861no—
409#474—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—864no—
421C2×#102C2×D4311yescharacteristic
422C2×#102C2×D4311yescharacteristic
423C2×#102C2×D4311yescharacteristic
424C2×#102C2×D4311yescharacteristic
425C2×C22⋊C8C2×D4311yescharacteristic
426#398—861no—
427#395—861no—
428#390—431no—
429#390—431no—
430#389—431no—
431#389—431no—
432#386—861no—
433#386—861no—
434#385—861no—
435#384—431no—
436#380—431no—
437#380C2×D4311yescharacteristic
438#379—861no—
439C4×C22⋊C4—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#336—431no—
445#336—431no—
446C43#2595011yescharacteristic, complemented, Sylow
447C25—21no—
448C22×Q8—861no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—21no—
452C22×D4—22no—
453C22×D4—41no—
454C22×D4—41no—
455C22×D4Dic8614yescomplemented
456C22×D4C22×D4311yescharacteristic
457C22×D4C22×D4311yescharacteristic
458C23×C4—861no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—862no—
465C22×C8—862no—
466C22×C8—1721no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4⋊Q8—862no—
470C4⋊Q8—1721no—
471C22⋊Q8—1724no—
472C4×D4—862no—
473C4×D4—862no—
474C4×D4—1721no—
475C4×D4—1721no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—1721no—
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—1724no—
501C2×C42—431no—
502C2×C42—431no—
503#107—862no—
504#107—862no—
505#107—1721no—
506#107—1721no—
507C4⋊C8—862no—
508C4⋊C8—1721no—
509#102—22no—
510#102—22no—
511#102—41no—
512#102—41no—
513#102—434no—
514#102—862no—
515#102—862no—
516#102—862no—
517C22⋊C8—22no—
518#95—21no—
519#95—431no—
520#95—431no—
521#95—861no—
522#95—861no—
523#95—861no—
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24D4×D4311yescharacteristic
534C2×Q8—3441no—
535C2×Q8—1722no—
536C2×Q8—1722no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×Dic8612yes—
553C2×D4C2×Dic8612yes—
554C2×D4D4×D4312yes—
555C2×D4#1062190012yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—3441no—
571C22×C4—3441no—
572C22×C4—3441no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4C2×Dic8612yes—
580C22×C4D4×D4311yescharacteristic
581C22×C4#1062190012yes—
582C22×C4C23×D4311yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—1724no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—432no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—3441no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C22⋊C4—42no—
615C22⋊C4—434no—
616C22⋊C4—862no—
617C22⋊C4—3441no—
618C22⋊C4—3441no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C42—861no—
625C42—861no—
626C42—861no—
627C42—861no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—48no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#1306330212yes—
654C23D8×D4312yes—
655C23#1306335412yes—
656C23C2×D4×D4311yescharacteristic
657Q8—3444no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1306330214yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—862no—
691C2×C4—861no—
692C2×C4—3444no—
693C2×C4—3444no—
694C2×C4—3444no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4#1306330212yes—
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C22×Dic8611yescharacteristic
709C2×C4C2×#1062190011yescharacteristic
710C2×C4C2×#1062190011yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337011yescharacteristic
713C8—41no—
714C8—41no—
715C8—862no—
716C8—1721no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1458317714yescomplemented
739C22C2×#1306330211yescharacteristic
740C22#1458353111yescharacteristic
741C22#1458353611yescharacteristic
742C22C2×D8×D4311yescharacteristic
743C22C2×#1306335411yescharacteristic
744C22#1458370311yescharacteristic
745C22#1458370911yescharacteristic
746C4—22no—
747C4—81no—
748C4—81no—
749C4—862no—
750C4—862no—
751C4—3441no—
752C4—3441no—
753C4—3441no—
754C4—1722no—
755C4—1721no—
756C4—1721no—
757C4C2×#1306330211yescharacteristic
758C4#1458352511yescharacteristic
759C4#1458353611yescharacteristic
760C4#1458358011yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1913826111yescharacteristic
765C2C2×#1458317711yescharacteristic
766C2#1914442811yescharacteristic
767C2#1914610911yescharacteristic
768C2#1914626511yescharacteristic
769C2#1914640111yescharacteristic
770C2#1914668011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenter#1786D43
hypocenterC43#25950
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#14583177C2semidirect
3. #19138298C2semidirect
5. #19136121C2semidirect
6. #19135981C2semidirect
7. #19135979C2semidirect
8. #19135729C2semidirect
9. #19134844C2semidirect
10. #19134840C2semidirect
11. #19134785C2semidirect
12. #19134772C2semidirect
13. #19134622C2semidirect
14. #19134593C2semidirect
17. C2×#13063324C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063259C22semidirect
26. C2×#13063258C22semidirect
27. C2×#13063258C22semidirect
28. C2×Dic43⋊C8C22semidirect
29. C2×Dic43⋊C8C22semidirect
39. #14582798C22semidirect
40. #14582795C22semidirect
44. #14582768C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
123. C22×D4×C43Q8semidirect
279. D4×C43C22⋊Q8semidirect
353. C22×C43#474semidirect
446. C43#25950semidirect
455. C22×D4Dic86semidirect
666. D4#13063302semidirect
738. C22#14583177semidirect

Maximal subgroups

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

subgroupindex
C2×#145831772
C22×#130632462
#191382982
D4×C22⋊Dic432
#191361212
#191359812
#191359792
#191357292
#191348442
#191348402
#191347852
#191347722
#191346222
#191345932
C43×#17862
#2595043