Finite Group Databasebeta

← #25153652

Subgroups — #25153652

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
2C2×#102×D43C211yesmaximal, characteristic
3#19138295C211yesmaximal, characteristic, complemented
4D4×(C2×D43)⋊C4C211yesmaximal, characteristic
5#19136122C211yesmaximal, characteristic, complemented
6#19135980C211yesmaximal, characteristic, complemented
7#19135978C211yesmaximal, characteristic, complemented
8#19135730C211yesmaximal, characteristic, complemented
9#19134844C211yesmaximal, characteristic, complemented
10#19134784C211yesmaximal, characteristic, complemented
11#19134774C211yesmaximal, characteristic, complemented
12#19134621C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic
15C43×#1862C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063324C2211yescharacteristic, complemented
19C2×#13063305—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C22×(C2×D43)⋊C4—21no—
23#14583177—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063259C2211yescharacteristic, complemented
26C2×#13063258C2211yescharacteristic, complemented
27C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
28C2×Dic43⋊C8C2211yescharacteristic, complemented
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35#102×D43—24no—
36C2×(C2×D43)⋊C8C2211yescharacteristic
37#14582829—21no—
38#14582820—21no—
39#14582801C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582798C2211yescharacteristic, complemented
42#14582778—21no—
43#14582776—21no—
44#14582773—21no—
45#14582769C2211yescharacteristic, complemented
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582754—21no—
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C2×C4×D4×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic, complemented
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C24×D43—21no—
62C22×Dic86—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C2×D4×D43—22no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—41no—
69C2×D4×D43—41no—
70C2×D4×D43Q814yescomplemented
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—22no—
77C2×C8×D43—22no—
78C2×C8×D43—41no—
79#13063324—22no—
80#13063324—41no—
81#13063305—44no—
82D4×Dic43—22no—
83D4×Dic43—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—41no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—44no—
102C2×(C2×D43)⋊C4D411yescharacteristic
103C2×(C2×D43)⋊C4D411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063259—22no—
106#13063259—41no—
107#13063258—22no—
108C4⋊(C43⋊C8)—41no—
109Dic43⋊C8—22no—
110#13063247—22no—
111#13063247—41no—
112#13063246—22no—
113#13063246—22no—
114#13063245—22no—
115#13063245—41no—
116(C2×D43)⋊C8—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×D4×C43—22no—
127C4×D4×C43—41no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—41no—
135#102×C43—22no—
136#102×C43D414yes—
137#95×C43—21no—
138C24×C43—21no—
139C23×D43—21no—
140C23×D43—24no—
141C23×D43—42no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C2×D412yes—
152C2×D4×C43C2×Q812yes—
153C2×D4×C43#4112yes—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—81no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—24no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—42no—
170C22×Dic43—42no—
171C22×Dic43—81no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175D4×D43—28no—
176D4×D43—44no—
177D4×D43—44no—
178D4×D43—44no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172C2×Q812yes—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—81no—
192C2×C4×D43C2×Q812yes—
193C2×C4×D43#4112yes—
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×C43C2×D412yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43C2×D412yes—
210C22⋊C4×C43—42no—
211C42×C43—21no—
212C42×C43—21no—
213C22⋊Dic43—42no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—81no—
220(C2×D43)⋊C4—81no—
221(C2×D43)⋊C4D814yes—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230C4⋊Dic43—81no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
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—21no—
241C8×D43—44no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—22no—
255C22×D43—48no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—48no—
263C22×D43—84no—
264C22×D43—84no—
265C22×D43—84no—
266C22×D43—84no—
267C22×D43—84no—
268C22×D43C22⋊Q812yes—
269C22×D43C2×D812yes—
270C22×D43#13712yes—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43C22⋊Q814yescomplemented
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—84no—
290C2×C4×C43C2×D812yes—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×Q811yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C22⋊D43—48no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—84no—
315C2×Dic43C22⋊Q812yes—
316C2×Dic43C2×D812yes—
317D172—22no—
318D172—22no—
319D172—41no—
320D172—41no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—84no—
326Dic86—84no—
327C8×C43—22no—
328C8×C43—41no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331#25950—431nomaximal, Sylow
332C22×C43—24no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43C2×C22⋊Q811yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43C22×D811yescharacteristic
343C22×C43C2×#13711yescharacteristic
344C22×C43#57611yescharacteristic
345C22×C43#57711yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—816no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43#47414yescomplemented
361C4×C43—22no—
362C4×C43—42no—
363C4×C43—41no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43C2×C22⋊Q811yescharacteristic
367C4×C43#54311yescharacteristic
368C4×C43#54611yescharacteristic
369C4×C43#55111yescharacteristic
370Dic43—22no—
371Dic43—22no—
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#1862D4311yescharacteristic, complemented
386#1852—431no—
387#1850—431no—
388#1808—431no—
389#1802—431no—
390#1786—431no—
391C2×C43—44no—
392C2×C43#243711yescharacteristic
393C2×C43C2×#47411yescharacteristic
394C2×C43#308111yescharacteristic
395C2×C43#326611yescharacteristic
396C2×C43D4×D811yescharacteristic
397C2×C43#329411yescharacteristic
398C2×C43#331411yescharacteristic
399D43—24no—
400D43—82no—
401C23×D4—431no—
402C23×C8—431no—
403C2×C4⋊Q8—431no—
404C2×C22⋊Q8—861no—
405C2×C4×D4—431no—
406C2×C4×D4C2×D4311yescharacteristic
407C22×C4⋊C4—431no—
408C22×C22⋊C4—861no—
409#474—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107C2×D4311yescharacteristic, complemented
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—864no—
423C2×#102C2×D4311yescharacteristic
424C2×#102C2×D4311yescharacteristic
425C2×C22⋊C8—431no—
426#398—861no—
427#395—861no—
428#390—431no—
429#390—431no—
430#389—431no—
431#389C2×D4311yescharacteristic, complemented
432#386—861no—
433#386—861no—
434#385—861no—
435#384—431no—
436#380—431no—
437#380—431no—
438#379—861no—
439C4×C22⋊C4—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340C2×D4311yescharacteristic, complemented
444#336—431no—
445#336C2×D4311yescharacteristic, complemented
446C43#2595011yescharacteristic, complemented, Sylow
447C25—861no—
448C22×Q8—861no—
449C22×D4—434no—
450C22×D4—431no—
451C22×D4—862no—
452C22×D4—861no—
453C22×D4—862no—
454C22×D4—862no—
455C22×D4—1721no—
456C22×D4—1721no—
457C22×D4C22×D4311yescharacteristic
458C23×C4—21no—
459C23×C4—431no—
460C23×C4—861no—
461C23×C4—861no—
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—22no—
473C4×D4—41no—
474C4×D4—862no—
475C4×D4—1721no—
476C2×C4⋊C4—21no—
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—1721no—
487C2×C4⋊C4C22×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
503#107—41no—
504#107—862no—
505#107—862no—
506#107—1721no—
507C4⋊C8—862no—
508C4⋊C8—1721no—
509#102—22no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—862no—
514#102—1721no—
515#102—1721no—
516#102D17214yes—
517C22⋊C8—862no—
518#95—21no—
519#95—431no—
520#95—431no—
521#95—861no—
522#95—861no—
523#95—861no—
524C24—21no—
525C24—431no—
526C24—864no—
527C24—861no—
528C24—3441no—
529C24—3441no—
530C24—1722no—
531C24—1722no—
532C24—1722no—
533C24—1722no—
534C2×Q8—3441no—
535C2×Q8—1722no—
536C2×Q8—1722no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—432no—
541C2×D4—864no—
542C2×D4—868no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—1724no—
549C2×D4—1724no—
550C2×D4—1724no—
551C2×D4—1722no—
552C2×D4—1722no—
553C2×D4C2×D17212yes—
554C2×D4#1062190012yes—
555C2×D4Q8×D4312yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—431no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—3441no—
575C22×C4—3441no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4D4×D4311yescharacteristic
581C22×C4D4×D4311yescharacteristic
582C22×C4C23×D4311yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—1724no—
595C2×C8C2×D17212yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
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⋊C4C2×D17212yes—
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—21no—
625C42—21no—
626C42—861no—
627C42—861no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—432no—
636C23—432no—
637C23—432no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—862no—
643C23—3444no—
644C23—3444no—
645C23—3444no—
646C23—3444no—
647C23—3444no—
648C23—1728no—
649C23—1728no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23C2×D4×D4311yescharacteristic
657Q8—3444no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—862no—
662D4—862no—
663D4—1728no—
664D4—1721no—
665D4—1721no—
666D4#1306330514yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—3444no—
696C2×C4—3444no—
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×C4D8×D4312yes—
707C2×C4C22×D17211yescharacteristic
708C2×C4C2×Q8×D4311yescharacteristic
709C2×C4#41×D4311yescharacteristic
710C2×C4C2×#1062190011yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337111yescharacteristic
713C8—22no—
714C8—41no—
715C8—1721no—
716C8—1721no—
717C22—24no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—434no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—34416no—
732C22—3441no—
733C22—3441no—
734C22—3441no—
735C22—3441no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22C22⋊Q8×D4311yescharacteristic
740C22D4×D17211yescharacteristic
741C22#1458353611yescharacteristic
742C22C2×D8×D4311yescharacteristic
743C22#137×D4311yescharacteristic
744C22#1458370111yescharacteristic
745C22#1458370911yescharacteristic
746C4—22no—
747C4—42no—
748C4—41no—
749C4—81no—
750C4—81no—
751C4—862no—
752C4—862no—
753C4—3441no—
754C4—3441no—
755C4—3441no—
756C4—1721no—
757C4C2×#1306330511yescharacteristic
758C4#1458352411yescharacteristic
759C4#1458354411yescharacteristic
760C4#1458357211yescharacteristic
761C2—44no—
762C2—864no—
763C2—3442no—
764C2#1913825911yescharacteristic
765C2#474×D4311yescharacteristic
766C2#1914442311yescharacteristic
767C2#1914610711yescharacteristic
768C2D8×D17211yescharacteristic
769C2#1914640111yescharacteristic
770C2#1914666911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenter#1862D43
hypocenterC43#25950
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. C2×#14583177C2semidirect
3. #19138295C2semidirect
5. #19136122C2semidirect
6. #19135980C2semidirect
7. #19135978C2semidirect
8. #19135730C2semidirect
9. #19134844C2semidirect
10. #19134784C2semidirect
11. #19134774C2semidirect
12. #19134621C2semidirect
13. #19134595C2semidirect
15. C43×#1862C2semidirect
18. C2×#13063324C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063259C22semidirect
26. C2×#13063258C22semidirect
27. C2×C4⋊(C43⋊C8)C22semidirect
28. C2×Dic43⋊C8C22semidirect
41. #14582798C22semidirect
45. #14582769C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582653C22semidirect
55. C2×#107×C43C22semidirect
58. C43×#389C22semidirect
59. C43×#340C22semidirect
60. C43×#336C22semidirect
70. C2×D4×D43Q8semidirect
274. D4×C43C22⋊Q8semidirect
360. C2×D43#474semidirect
385. #1862D43semidirect
413. C2×#107C2×D43semidirect
431. #389C2×D43semidirect
443. #340C2×D43semidirect
445. #336C2×D43semidirect
446. C43#25950semidirect
666. D4#13063305semidirect

Maximal subgroups

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

subgroupindex
C2×#145831772
C2×#102×D432
#191382952
D4×(C2×D43)⋊C42
#191361222
#191359802
#191359782
#191357302
#191348442
#191347842
#191347742
#191346212
#191345952
#191345242
C43×#18622
#2595043