Finite Group Databasebeta

← #25140125

Subgroups — #25140125

Order 11008.

1064 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×#14583230C211yesmaximal, characteristic, complemented
2C2×#14582901C211yesmaximal, characteristic, complemented
3#19137940C211yesmaximal, characteristic
4D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
5#19136127C211yesmaximal, characteristic, complemented
6#19136005C211yesmaximal, characteristic, complemented
7#19135792C211yesmaximal, characteristic, complemented
8#19135778C211yesmaximal, characteristic, complemented
9#19135237C211yesmaximal, characteristic, complemented
10#19135223C211yesmaximal, characteristic, complemented
11#19134910C211yesmaximal, characteristic, complemented
12#19134790C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×D4×Dic43—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22#14583230—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27#14582901—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582814—21no—
37#14582807—21no—
38#14582805C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582798—21no—
41#14582775—21no—
42#14582774—21no—
43#14582774—21no—
44#14582770—21no—
45#14582769C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48#14582759C2211yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C23×Dic43—21no—
73C22×C4×D43—21no—
74#13063304—22no—
75#13063304—41no—
76#13063299—22no—
77#13063299—41no—
78D4×Dic43—44no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—41no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102#13063259—41no—
103#13063257—22no—
104#13063257—22no—
105#13063257—41no—
106#13063250—22no—
107#13063250—22no—
108#13063250—41no—
109#13063250D414yescomplemented
110#13063247—22no—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×D4×C43D411yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×M16×C43—22no—
124C2×M16×C43—22no—
125C2×M16×C43—41no—
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C22⋊C8×C43—22no—
137C22⋊C8×C43—22no—
138C22⋊C8×C43—41no—
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C2×D4×C43—22no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43#4112yes—
160C22×C4×C43#4112yes—
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—81no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181#10621898—28no—
182#10621898—44no—
183#10621898—44no—
184#10621898—44no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172#4112yes—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86C2×D412yes—
200M16×C43—44no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43C2×D412yes—
213C4⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C42×C43—21no—
217C42×C43—21no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—81no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—81no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—42no—
237C4⋊Dic43—42no—
238C4⋊Dic43—42no—
239C4⋊Dic43—81no—
240C4⋊Dic43C2×D412yes—
241Dic43⋊C4—42no—
242C4×Dic43—42no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43#12312yes—
256C23×C43AGL(1,ℤ/8)12yes—
257C23×C43C22×D411yescharacteristic
258C22×D43—22no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265D4×C43—28no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43#12312yes—
285C2×C4×C43#13712yes—
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C22⋊D43—48no—
293C22⋊D43—84no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
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—41no—
315C2×Dic43—84no—
316C2×Dic43—84no—
317D172—22no—
318D172—22no—
319D172—41no—
320D172—41no—
321C4×D43—48no—
322Dic86—22no—
323Dic86—22no—
324Dic86—41no—
325Dic86—41no—
326C8×C43—22no—
327C8×C43—41no—
328C8×C43—41no—
329C8×C43—41no—
330#24879—431nomaximal, Sylow
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43C2×#12311yescharacteristic
346C22×C43D4211yescharacteristic
347C22×C43#54611yescharacteristic
348C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C43C2×#13711yescharacteristic
350C22×C43#57711yescharacteristic
351C22×C43#57711yescharacteristic
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—41no—
362C4×C43—41no—
363C4×C43#52511yescharacteristic
364C4×C43#53811yescharacteristic
365C4×C43#54611yescharacteristic
366C4×C43#55111yescharacteristic
367Dic43—42no—
368Dic43—42no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372Dic43—81no—
373Dic43—81no—
374C2×#483—431no—
375C2×#417—431no—
376#2407—431no—
377D4×C4⋊C4—431no—
378#2094—431no—
379#2072—431no—
380#2035—431no—
381#2033—431no—
382#1928—431no—
383#1926—431no—
384#1874—431no—
385#1870D4311yescharacteristic, complemented
386#1853—431no—
387#1809—431no—
388#1788—431no—
389C2×C43—42no—
390C2×C43—42no—
391C2×C43#241811yescharacteristic
392C2×C43#309211yescharacteristic
393C2×C43#309911yescharacteristic
394C2×C43#326511yescharacteristic
395C2×C43#327811yescharacteristic
396C2×C43#330611yescharacteristic
397C2×C43#333111yescharacteristic
398D43—82no—
399C22×#41—431no—
400C22×M16C2×D4311yescharacteristic
401C2×C22⋊Q8—431no—
402C2×#121—431no—
403C2×C4×D4—861no—
404C2×C4×D4C2×D4311yescharacteristic
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407#483—864no—
408C2×#107—431no—
409C2×#106—431no—
410C2×#106—431no—
411C2×#106—431no—
412#417—864no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×C22⋊C8C2×D4311yescharacteristic
422C2×C22⋊C8C2×D4311yescharacteristic
423C2×C22⋊C8C2×D4311yescharacteristic
424#394—861no—
425#392—861no—
426#391—431no—
427#390—431no—
428#389—861no—
429#386—861no—
430#385—861no—
431#385—861no—
432#385—861no—
433#384—431no—
434#380—431no—
435#380—431no—
436#380—431no—
437C4×C4⋊C4—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442#336C2×D4311yescharacteristic
443#336C2×D4311yescharacteristic
444C43#2487911yescharacteristic, complemented, Sylow
445C2×#41—862no—
446C2×#41—862no—
447C2×#41—862no—
448C2×#41—862no—
449C2×#41—1721no—
450C2×#41—1721no—
451C22×Q8—431no—
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4D17211yescharacteristic
456C23×C4—861no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4C22×D4311yescharacteristic
460C23×C4C22×D4311yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C22⋊Q8—862no—
469C22⋊Q8—1721no—
470#121—862no—
471#121—1721no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—1724no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—1721no—
489C2×C4⋊C4—1721no—
490C2×C4⋊C4D17211yescharacteristic
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4D17211yescharacteristic
499C2×C22⋊C4D17211yescharacteristic
500C2×C42—861no—
501C2×C42C22×D4311yescharacteristic
502#107—1721no—
503#106—862no—
504#106—862no—
505#106—1721no—
506#103—434no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—1721no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—41no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95—861no—
523C24—861no—
524C24C2×D17211yescharacteristic
525C24C2×D17211yescharacteristic
526#41—868no—
527#41—1724no—
528#41—1724no—
529#41—1724no—
530C2×Q8—432no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—432no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—3441no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C2×D4—1722no—
550C2×D4—1722no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4C2×D17211yescharacteristic
578C22×C4C2×D17211yescharacteristic
579C22×C4C2×D17211yescharacteristic
580C22×C4C2×D17211yescharacteristic
581C22×C4#1062190012yes—
582C22×C4#1062190012yes—
583C22×C4C23×D4311yescharacteristic
584M16—44no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8D4×D4312yes—
597C4⋊C4—22no—
598C4⋊C4—432no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—3441no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C4⋊C4—1722no—
615C22⋊C4—22no—
616C22⋊C4—22no—
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—1722no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—862no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23#1306330912yes—
647C23#1306335312yes—
648C23C22×D17211yescharacteristic
649Q8—862no—
650Q8—862no—
651Q8—1721no—
652Q8—1721no—
653D4—28no—
654D4—862no—
655D4—862no—
656D4—3444no—
657D4—1728no—
658D4—1721no—
659D4—1721no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—3444no—
681C2×C4—3444no—
682C2×C4—1728no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
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#1306330912yes—
703C2×C4#1306335812yes—
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4#41×D4311yescharacteristic
706C2×C4C2×#1062190011yescharacteristic
707C2×C4C2×#1062190011yescharacteristic
708C2×C4#1306337011yescharacteristic
709C2×C4#1306337111yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—3441no—
729C22—3441no—
730C22—3441no—
731C22—3441no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22C2×#1306330911yescharacteristic
736C22D4×D17211yescharacteristic
737C22#1458354411yescharacteristic
738C22C2×#1306335311yescharacteristic
739C22C2×#1306335811yescharacteristic
740C22#1458371111yescharacteristic
741C22#1458371111yescharacteristic
742C4—22no—
743C4—22no—
744C4—41no—
745C4—41no—
746C4—3441no—
747C4—3441no—
748C4—3441no—
749C4—3441no—
750C4—3441no—
751C4—1722no—
752C4—1722no—
753C4#1458340911yescharacteristic
754C4#1458348611yescharacteristic
755C4#1458353611yescharacteristic
756C4#1458357211yescharacteristic
757C2—42no—
758C2—42no—
759C2—3442no—
760C2#1913805511yescharacteristic
761C2#1914452011yescharacteristic
762C2#1914458611yescharacteristic
763C2#1914609511yescharacteristic
764C2#1914626311yescharacteristic
765C2#1914655811yescharacteristic
766C2#1914691211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1870C2
socleC23×C43C22×D4
prime radical#19137940C2
hypercenter#1870D43
hypocenterC43#24879
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#14583230C2semidirect
2. C2×#14582901C2semidirect
4. D4×C4⋊Dic43C2semidirect
5. #19136127C2semidirect
6. #19136005C2semidirect
7. #19135792C2semidirect
8. #19135778C2semidirect
9. #19135237C2semidirect
10. #19135223C2semidirect
11. #19134910C2semidirect
12. #19134790C2semidirect
13. #19134628C2semidirect
14. #19134536C2semidirect
15. C43×#1870C2semidirect
109. #13063250D4semidirect
385. #1870D43semidirect
444. C43#24879semidirect

Maximal subgroups

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

subgroupindex
C2×#145832302
C2×#145829012
#191379402
D4×C4⋊Dic432
#191361272
#191360052
#191357922
#191357782
#191352372
#191352232
#191349102
#191347902
#191346282
#191345362
C43×#18702
#2487943