Finite Group Databasebeta

← #25134964

Subgroups — #25134964

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583233C211yesmaximal, characteristic, complemented
2C2×#102×D43C211yesmaximal, characteristic
3#19138243C211yesmaximal, characteristic
4#19137471C211yesmaximal, characteristic, complemented
5#19135980C211yesmaximal, characteristic, complemented
6#19135979C211yesmaximal, characteristic, complemented
7#19135833C211yesmaximal, characteristic, complemented
8#19135528C211yesmaximal, characteristic, complemented
9#19135524C211yesmaximal, characteristic, complemented
10#19135217C211yesmaximal, characteristic, complemented
11#19135216C211yesmaximal, characteristic, complemented
12#19135015C211yesmaximal, characteristic, complemented
13#19134774C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic
15C43×#2042C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21#14583233—24no—
22C2×#13063259C2211yescharacteristic, complemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
25C2×Dic43⋊C8C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34#102×D43—24no—
35C2×(C2×D43)⋊C8C2211yescharacteristic
36#14582814—21no—
37#14582814—21no—
38#14582802C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582798C2211yescharacteristic, complemented
41#14582786—21no—
42#14582780—21no—
43#14582756—21no—
44#14582756C2211yescharacteristic
45#14582754—21no—
46#14582754—21no—
47C4⋊C4×Dic43C2211yescharacteristic, complemented
48C4×C4⋊Dic43C2211yescharacteristic, complemented
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582746—21no—
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C2×#124×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic, complemented
56C2×#103×C43C2211yescharacteristic, complemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#389C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C24×D43—21no—
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C2×D4×D43—22no—
65C2×D4×D43—22no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—41no—
69C2×D4×D43—41no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—41no—
76C2×C8×D43—41no—
77#13063314—22no—
78#13063314—41no—
79#13063301—22no—
80#13063301—22no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43D414yes—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063259—22no—
103#13063258—22no—
104C4⋊(C43⋊C8)—41no—
105Dic43⋊C8—41no—
106#13063249—22no—
107#13063249—41no—
108#13063247—22no—
109#13063247—22no—
110#13063246—22no—
111#13063246—41no—
112#13063245—22no—
113#13063245—41no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95D411yescharacteristic
120C43⋊#95D411yescharacteristic
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#124×C43—22no—
126#124×C43—41no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#103×C43—22no—
134#103×C43—41no—
135#102×C43—22no—
136#102×C43—22no—
137#95×C43—21no—
138C24×C43—21no—
139C23×D43—21no—
140C23×D43—42no—
141C23×D43—42no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43C2×D411yescharacteristic
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43#4112yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
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×D172#4112yes—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—24no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C4×D43C2×D412yes—
193C2×C4×D43#4112yes—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—81no—
204C4⋊C4×C43C2×D412yes—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C42×C43—21no—
208C42×C43—21no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211(C2×D43)⋊C4—22no—
212(C2×D43)⋊C4—22no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—81no—
225C4⋊Dic43C2×D412yes—
226Dic43⋊C4—24no—
227Dic43⋊C4—42no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—81no—
231C4×Dic43—81no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C8×D43—44no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43C22×D411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—22no—
252C22×D43—48no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—84no—
260C22×D43—84no—
261C22×D43—84no—
262C22×D43—84no—
263C22×D43—84no—
264C22×D43—84no—
265C22×D43#12112yes—
266C22×D43#13512yes—
267C22×D43#13712yes—
268Q8×C43—41no—
269Q8×C43—41no—
270Q8×C43—41no—
271Q8×C43—41no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—41no—
275D4×C43—41no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
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—41no—
290C2×C4×C43—41no—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
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—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43#12112yes—
316D172—22no—
317D172—22no—
318D172—41no—
319D172—41no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—84no—
325C8×C43—41no—
326C8×C43—41no—
327C43⋊C8—41no—
328C43⋊C8—41no—
329#24479—431nomaximal, Sylow
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43C2×#12111yescharacteristic
338C22×C43#54611yescharacteristic
339C22×C43#54611yescharacteristic
340C22×C43C2×#13511yescharacteristic
341C22×C43C2×#13711yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57611yescharacteristic
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—816no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43#46414yes—
359C4×C43—42no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43#52511yescharacteristic
365C4×C43#53511yescharacteristic
366C4×C43#55111yescharacteristic
367C4×C43#55111yescharacteristic
368Dic43—22no—
369Dic43—42no—
370Dic43—41no—
371Dic43—41no—
372Dic43—81no—
373Dic43—81no—
374C2×#484—431no—
375C22×#102—431no—
376#2435—431no—
377#2345—431no—
378#2067—431no—
379#2067—431no—
380#2042—431no—
381#2042D4311yescharacteristic, complemented
382#1983—431no—
383#1983—431no—
384#1925—431no—
385#1925—431no—
386#1892—431no—
387#1850—431no—
388#1786—431no—
389C2×C43—82no—
390C2×C43#241111yescharacteristic
391C2×C43C2×#46411yescharacteristic
392C2×C43#304111yescharacteristic
393C2×C43#329711yescharacteristic
394C2×C43#329711yescharacteristic
395C2×C43#331411yescharacteristic
396C2×C43#331411yescharacteristic
397D43—24no—
398D43—82no—
399C23×D4—431no—
400C23×C8—431no—
401C2×#124—431no—
402C2×#124C2×D4311yescharacteristic
403C2×C22⋊Q8—431no—
404C22×C4⋊C4—431no—
405#484—864no—
406C2×#107—431no—
407C2×#107—431no—
408C2×C4⋊C8—431no—
409C2×C4⋊C8—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103C2×D4311yescharacteristic, complemented
413C2×#103C2×D4311yescharacteristic, complemented
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—864no—
421C2×#102C2×D4311yescharacteristic
422C2×#102C2×D4311yescharacteristic
423C2×C22⋊C8—431no—
424#394—861no—
425#394—861no—
426#390—431no—
427#390—431no—
428#389—431no—
429#389C2×D4311yescharacteristic, complemented
430#387—861no—
431#387—861no—
432#380—431no—
433#380—861no—
434#379—861no—
435#379—861no—
436C4×C4⋊C4—431no—
437C4×C4⋊C4—431no—
438C4×C22⋊C4—431no—
439C4×C22⋊C4—861no—
440#340—431no—
441#340—431no—
442#336—431no—
443#336C2×D4311yescharacteristic, complemented
444C43#2447911yescharacteristic, complemented, Sylow
445C25—861no—
446C22×Q8C22×D4311yescharacteristic
447C22×D4—431no—
448C22×D4—862no—
449C22×D4—862no—
450C22×D4—861no—
451C22×D4—862no—
452C22×D4—862no—
453C22×D4—1721no—
454C22×D4—1721no—
455C22×D4C22×D4311yescharacteristic
456C23×C4—431no—
457C23×C4—861no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—862no—
461C22×C8—1721no—
462C22×C8—1721no—
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465#124—22no—
466#124—41no—
467#124—862no—
468#124—1721no—
469C22⋊Q8—862no—
470C22⋊Q8—862no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—434no—
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⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C42—431no—
495C2×C42—861no—
496C2×C42—861no—
497C2×C42C22×D4311yescharacteristic
498#107—862no—
499#107—862no—
500C4⋊C8—1721no—
501C4⋊C8—1721no—
502#103—22no—
503#103—41no—
504#103—862no—
505#103—1721no—
506#102—22no—
507#102—22no—
508#102—862no—
509#102—862no—
510#102—862no—
511#102—862no—
512#102—1721no—
513#102—1721no—
514C22⋊C8—862no—
515#95—21no—
516#95—431no—
517#95—431no—
518#95—861no—
519#95—861no—
520#95—861no—
521#95—861no—
522C24—21no—
523C24—431no—
524C24—861no—
525C24—3441no—
526C24—3441no—
527C24—1722no—
528C24—1722no—
529C24—1722no—
530C24—1722no—
531C24—1722no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—432no—
544C2×D4—868no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—861no—
550C2×D4—1722no—
551C2×D4—1724no—
552C2×D4—1724no—
553C2×D4—1724no—
554C2×D4—1722no—
555C2×D4—1722no—
556C2×D4#1062190012yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—431no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—864no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—3441no—
574C22×C4—3441no—
575C22×C4D4×D4311yescharacteristic
576C22×C4D4×D4311yescharacteristic
577C22×C4C23×D4311yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—1724no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—81no—
595C4⋊C4—432no—
596C4⋊C4—864no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—3441no—
603C4⋊C4—1722no—
604C4⋊C4D4×D4312yes—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—862no—
608C22⋊C4—862no—
609C22⋊C4—3441no—
610C22⋊C4—3441no—
611C22⋊C4—3441no—
612C22⋊C4—3441no—
613C22⋊C4—1722no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C42—21no—
618C42—21no—
619C42—861no—
620C42—861no—
621C42—3441no—
622C42—3441no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—432no—
631C23—432no—
632C23—432no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—862no—
638C23—3444no—
639C23—3444no—
640C23—3444no—
641C23—3444no—
642C23—3444no—
643C23—3444no—
644C23—1728no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23C2×D4×D4311yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—862no—
661D4—862no—
662D4—1728no—
663D4—1721no—
664D4—1721no—
665C2×C4—22no—
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—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—432no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
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×C4C2×D4×D4311yescharacteristic
704C2×C4#41×D4311yescharacteristic
705C2×C4#41×D4311yescharacteristic
706C2×C4C2×#1062190011yescharacteristic
707C2×C4#1306337011yescharacteristic
708C2×C4#1306337111yescharacteristic
709C8—41no—
710C8—41no—
711C8—1721no—
712C8—1721no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—434no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—34416no—
728C22—3441no—
729C22—3441no—
730C22—3441no—
731C22—3441no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22#121×D4311yescharacteristic
736C22#1458353611yescharacteristic
737C22#1458354211yescharacteristic
738C22#135×D4311yescharacteristic
739C22#137×D4311yescharacteristic
740C22#1458370111yescharacteristic
741C22#1458370311yescharacteristic
742C4—42no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—862no—
748C4—3441no—
749C4—3441no—
750C4—1722no—
751C4—1721no—
752C4—1721no—
753C4#1458340911yescharacteristic
754C4#1458346511yescharacteristic
755C4#1458357211yescharacteristic
756C4#1458357711yescharacteristic
757C2—82no—
758C2—864no—
759C2—3442no—
760C2#1913797311yescharacteristic
761C2#464×D4311yescharacteristic
762C2#1914409611yescharacteristic
763C2#1914643811yescharacteristic
764C2#1914644411yescharacteristic
765C2#1914666911yescharacteristic
766C2#1914667511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2042C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
hypercenter#2042D43
hypocenterC43#24479
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2042

Complements

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

NH ≅ G/Ntype
1. C2×#14583233C2semidirect
4. #19137471C2semidirect
5. #19135980C2semidirect
6. #19135979C2semidirect
7. #19135833C2semidirect
8. #19135528C2semidirect
9. #19135524C2semidirect
10. #19135217C2semidirect
11. #19135216C2semidirect
12. #19135015C2semidirect
13. #19134774C2semidirect
15. C43×#2042C2semidirect
22. C2×#13063259C22semidirect
23. C2×#13063258C22semidirect
24. C2×C4⋊(C43⋊C8)C22semidirect
25. C2×Dic43⋊C8C22semidirect
26. C2×#13063249C22semidirect
27. C2×#13063249C22semidirect
40. #14582798C22semidirect
47. C4⋊C4×Dic43C22semidirect
48. C4×C4⋊Dic43C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582653C22semidirect
55. C2×#103×C43C22semidirect
56. C2×#103×C43C22semidirect
59. C43×#389C22semidirect
60. C43×#336C22semidirect
381. #2042D43semidirect
412. C2×#103C2×D43semidirect
413. C2×#103C2×D43semidirect
429. #389C2×D43semidirect
443. #336C2×D43semidirect
444. C43#24479semidirect

Maximal subgroups

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

subgroupindex
C2×#145832332
C2×#102×D432
#191382432
#191374712
#191359802
#191359792
#191358332
#191355282
#191355242
#191352172
#191352162
#191350152
#191347742
#191345242
C43×#20422
#2447943