Finite Group Databasebeta

← #25130597

Subgroups — #25130597

Order 11008.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583587C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19139492C211yesmaximal, characteristic
4#19135800C211yesmaximal, characteristic, complemented
5#19135793C211yesmaximal, characteristic, complemented
6#19135599C211yesmaximal, characteristic, complemented
7#19135599C211yesmaximal, characteristic, complemented
8#19135561C211yesmaximal, characteristic, complemented
9#19135388C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134791C211yesmaximal, characteristic, complemented
13#19134786C211yesmaximal, characteristic, complemented
14#19134611C211yesmaximal, characteristic, complemented
15C2×C43×#478C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17#14583587—24no—
18#14583587—24no—
19C2×#13063320—21no—
20C2×#13063316—21no—
21C2×#13063310—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063305C2211yescharacteristic
24C2×#13063296C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063283—21no—
29C2×#13063283C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C4×#10621883—24no—
32C2×#13063256C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582824—21no—
43#14582808—21no—
44#14582778—21no—
45#14582778—21no—
46#14582765C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#478—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172D411yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C22×C4×D43C2311yescharacteristic
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063320—28no—
76#13063316—28no—
77#13063310—28no—
78#13063305—22no—
79#13063305—22no—
80#13063305—22no—
81#13063305—22no—
82#13063296—22no—
83#13063296—22no—
84#13063296—41no—
85#13063296—41no—
86C4×Dic86—22no—
87C4×Dic86D414yescomplemented
88C4×D172—22no—
89C4×D172—22no—
90#13063283—28no—
91#13063283—22no—
92#13063283—22no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43D411yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43—22no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4D411yescharacteristic
111C2×(C2×D43)⋊C4D411yescharacteristic
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114#13063256—22no—
115#13063250—41no—
116#13063250—41no—
117#13063248—22no—
118#13063246—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—41no—
122(C2×D43)⋊C8—41no—
123C4×C43⋊C8—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43—21no—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132#125×C43—22no—
133#125×C43D414yescomplemented
134C4×D4×C43—22no—
135C4×D4×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C42×C43C2311yescharacteristic
143#107×C43—22no—
144#106×C43—22no—
145C4⋊C8×C43—22no—
146#102×C43—22no—
147#102×C43—22no—
148C24×C43—21no—
149C23×D43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43#4112yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—42no—
161C22×C4×C43—81no—
162C22×C4×C43—81no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C2×D172—22no—
179C2×D172—22no—
180C2×D172—41no—
181C2×C4×D43—24no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86C2×D412yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—24no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43C2×D412yes—
215C4⋊C4×C43C2×D412yes—
216C22⋊C4×C43—42no—
217C42×C43C2×D412yes—
218C42×C43C2×D412yes—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221#10621883—28no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—81no—
228(C2×D43)⋊C4—81no—
229C4⋊Dic43—24no—
230C4⋊Dic43—24no—
231C4⋊Dic43—22no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43C2×D412yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240C4×Dic43—24no—
241C4×Dic43—24no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8#4112yes—
248C23×C43—22no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C22×D411yescharacteristic
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43#13512yes—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—41no—
273D4×C43—41no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—41no—
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—84no—
288C2×C4×C43#12012yes—
289C2×C4×C43#12012yes—
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C432−1+411yescharacteristic
296C22⋊D43—84no—
297C22⋊D43—84no—
298C2×Dic43—22no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
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—41no—
315C2×Dic43—41no—
316D172—44no—
317C4×D43—48no—
318C4×D43—41no—
319C4×D43—41no—
320C4×D43—41no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—41no—
324C4×D43—41no—
325C4×D43—41no—
326Dic86—22no—
327Dic86—22no—
328Dic86—41no—
329Dic86—41no—
330C8×C43—41no—
331C8×C43—41no—
332C43⋊C8—22no—
333C43⋊C8—41no—
334#24125—431nomaximal, Sylow
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43C2×#12011yescharacteristic
343C22×C43#54611yescharacteristic
344C22×C43#54711yescharacteristic
345C22×C43C2×#13511yescharacteristic
346C22×C43#57511yescharacteristic
347C22×C43#57711yescharacteristic
348C22×C43#57711yescharacteristic
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—41no—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43—81no—
368C4×C43#52511yescharacteristic
369C4×C43#53711yescharacteristic
370C4×C43#54811yescharacteristic
371C4×C43#55011yescharacteristic
372Dic43—42no—
373Dic43—41no—
374Dic43—41no—
375Dic43—42no—
376Dic43—81no—
377Dic43—81no—
378C2×#552—431no—
379C2×#478D4311yescharacteristic, complemented
380C2×C4×SD16—431no—
381#2535—431no—
382#2036—431no—
383#2035—431no—
384#2000—431no—
385#2000—431no—
386#1991—431no—
387#1954—431no—
388#1875—431no—
389#1874—431no—
390#1854—431no—
391#1853—431no—
392#1805—431no—
393C2×C43—82no—
394C2×C43#240711yescharacteristic
395C2×C43#300211yescharacteristic
396C2×C43#301011yescharacteristic
397C2×C43#329611yescharacteristic
398C2×C43#332311yescharacteristic
399C2×C43#333711yescharacteristic
400C2×C43#335111yescharacteristic
401D43—42no—
402D43—81no—
403C22×SD16—431no—
404#552—864no—
405#552—864no—
406C2×#126—861no—
407C2×#125—861no—
408C2×#125C2×D4311yescharacteristic
409C2×#123—861no—
410C2×C22⋊Q8—431no—
411C2×C22⋊Q8—431no—
412C2×#121—431no—
413C2×#121—431no—
414C2×C4×Q8—431no—
415C2×C4×D4—431no—
416C2×C4×D4C2×D4311yescharacteristic
417C2×#117—431no—
418C2×#117—861no—
419C22×C4⋊C4—431no—
420#478—24no—
421C4×SD16—864no—
422C2×#107C2×D4311yescharacteristic
423C2×#106—431no—
424C2×#106C2×D4311yescharacteristic
425C2×C4⋊C8C2×D4311yescharacteristic
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102C2×D4311yescharacteristic
431C2×#102C2×D4311yescharacteristic
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C4×C8—431no—
437#397—861no—
438#392—861no—
439#386—861no—
440#386—861no—
441#382—431no—
442#380—431no—
443#380—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450C43#2412511yescharacteristic, complemented, Sylow
451C22×Q8—431no—
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4C22×D4311yescharacteristic
456C23×C4—21no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—861no—
460C2×SD16—862no—
461C2×SD16—862no—
462C2×SD16—862no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467#126—868no—
468#125—22no—
469#125—868no—
470#125C22⋊D4314yescomplemented
471#123—868no—
472C22⋊Q8—862no—
473C22⋊Q8—862no—
474C22⋊Q8—862no—
475C22⋊Q8—862no—
476#121—862no—
477#121—862no—
478#121—1721no—
479#121—1721no—
480C4×Q8—434no—
481C4×Q8—862no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—862no—
485C4×D4—862no—
486#117—862no—
487#117—868no—
488#117—862no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—862no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—861no—
515C2×C42—861no—
516C2×C42C22×D4311yescharacteristic
517#107—22no—
518#106—22no—
519#106—862no—
520C4⋊C8—22no—
521#103—862no—
522#103—1721no—
523#103—1721no—
524#102—22no—
525#102—22no—
526#102—862no—
527C22⋊C8—862no—
528C22⋊C8—862no—
529C22⋊C8—1721no—
530C22⋊C8—1721no—
531C4×C8—862no—
532#95—861no—
533#95—861no—
534#95—861no—
535#95—861no—
536C24—21no—
537C24—431no—
538C24—431no—
539C2×Q8—432no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—862no—
551C2×D4—862no—
552C2×D4—3441no—
553C2×D4—3441no—
554C2×D4—1721no—
555C2×D4—1722no—
556C2×D4—1722no—
557C2×D4—1722no—
558C2×D4—1722no—
559C2×D4#1062190212yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—864no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—432no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—432no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—862no—
614C4⋊C4—864no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4C2×C22⋊D4312yes—
621C4⋊C4C2×C22⋊D4312yes—
622C22⋊C4—42no—
623C22⋊C4—864no—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—862no—
627C22⋊C4—862no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C42—864no—
633C42—864no—
634C42D4×D4312yes—
635C42C2×C22⋊D4312yes—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—432no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23C2×D4×D4311yescharacteristic
658Q8—862no—
659Q8—862no—
660Q8—1721no—
661Q8—1721no—
662D4—22no—
663D4—22no—
664D4—41no—
665D4—41no—
666D4—3444no—
667D4—3444no—
668D4—1724no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4—862no—
684C2×C4—861no—
685C2×C4—862no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—1728no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
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—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4#1306329312yes—
711C2×C4#1306329312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4C22×C22⋊D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C2×C4C2×#1062190211yescharacteristic
716C2×C4#1306337111yescharacteristic
717C2×C4#1306337311yescharacteristic
718C8—41no—
719C8—41no—
720C8—862no—
721C8—1721no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—1721no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22C2×#1306329311yescharacteristic
744C22#1458354011yescharacteristic
745C22#1458355111yescharacteristic
746C22#135×D4311yescharacteristic
747C22#1458369611yescharacteristic
748C22#1458370911yescharacteristic
749C22#1458370911yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—81no—
755C4—3441no—
756C4—3441no—
757C4—1722no—
758C4—1721no—
759C4—1721no—
760C4—1722no—
761C4#1458341211yescharacteristic
762C4#1458347911yescharacteristic
763C4#1458356011yescharacteristic
764C4#1458356811yescharacteristic
765C2—82no—
766C2—3441no—
767C2—1722no—
768C2#1913794211yescharacteristic
769C2#1914380911yescharacteristic
770C2#1914388011yescharacteristic
771C2#1914642711yescharacteristic
772C2#1914680811yescharacteristic
773C2#1914698111yescharacteristic
774C2#1914716211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radical#19139492C2
hypercenterC2×#478D43
hypocenterC43#24125
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583587C2semidirect
2. C2×C4×#10621883C2semidirect
4. #19135800C2semidirect
5. #19135793C2semidirect
6. #19135599C2semidirect
7. #19135599C2semidirect
8. #19135561C2semidirect
9. #19135388C2semidirect
10. #19134914C2semidirect
11. #19134909C2semidirect
12. #19134791C2semidirect
13. #19134786C2semidirect
14. #19134611C2semidirect
15. C2×C43×#478C2semidirect
87. C4×Dic86D4semidirect
133. #125×C43D4semidirect
379. C2×#478D43semidirect
450. C43#24125semidirect
470. #125C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835872
C2×C4×#106218832
#191394922
#191358002
#191357932
#191355992
#191355612
#191353882
#191349142
#191349092
#191347912
#191347862
#191346112
C2×C43×#4782
#2412543