Finite Group Databasebeta

← #25138998

Subgroups — #25138998

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583146C211yesmaximal, characteristic, complemented
2C2×#14583145C211yesmaximal, characteristic, complemented
3C2×#14582975C211yesmaximal, characteristic, complemented
4#19138029C211yesmaximal, characteristic
5#19138018C211yesmaximal, characteristic, complemented
6#19135978C211yesmaximal, characteristic, complemented
7#19135971C211yesmaximal, characteristic, complemented
8#19135800C211yesmaximal, characteristic, complemented
9#19135786C211yesmaximal, characteristic, complemented
10#19135447C211yesmaximal, characteristic, complemented
11#19135329C211yesmaximal, characteristic, complemented
12#19134917C211yesmaximal, characteristic, complemented
13#19134902C211yesmaximal, characteristic, complemented
14#19134625C211yesmaximal, characteristic, complemented
15C2×C43×#428C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063300C2211yescharacteristic
21C2×#13063299—21no—
22C2×#13063299C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24#14583146—24no—
25#14583145—24no—
26#14582975—24no—
27C2×#13063259C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582824—21no—
39#14582821—21no—
40#14582816—21no—
41#14582815—21no—
42#14582804C2211yescharacteristic
43#14582800C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582797—21no—
47#14582790—21no—
48#14582778—21no—
49#14582756C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C43×#428—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#107×C43C2211yescharacteristic
61C2×#106×C43C2211yescharacteristic
62C2×#106×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43D411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873—22no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—22no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063305—22no—
78#13063305—41no—
79#13063304—22no—
80#13063304—22no—
81#13063300—22no—
82#13063300—41no—
83#13063299—22no—
84#13063299—22no—
85#13063299—44no—
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4D411yescharacteristic
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43D411yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106#13063259—22no—
107Dic43⋊C8—22no—
108#13063250—22no—
109#13063248—22no—
110#13063248—41no—
111#13063247—22no—
112#13063245—22no—
113#13063245—41no—
114C22⋊(C43⋊C8)—22no—
115(C2×D43)⋊C8—22no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—22no—
126C2×M16×C43—22no—
127C2×M16×C43D414yescomplemented
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#117×C43—22no—
131#117×C43—41no—
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—41no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C42×C43—21no—
141#107×C43—22no—
142#107×C43D414yescomplemented
143#106×C43—22no—
144#106×C43—22no—
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C23×D43C2×D411yescharacteristic
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×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—81no—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4112yes—
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—41no—
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
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—42no—
182C2×D172—42no—
183C2×D172—81no—
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×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196M16×C43—28no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43C2×D412yes—
200C2×C8×C43C2×D412yes—
201C2×C8×C43C2×D412yes—
202C2×C8×C43#4112yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—42no—
210C4⋊C4×C43C2×D412yes—
211C4⋊C4×C43C2×D412yes—
212C22⋊C4×C43—42no—
213C42×C43—42no—
214C22⋊Dic43—22no—
215C22⋊Dic43—42no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230C4⋊Dic43—42no—
231Dic43⋊C4—22no—
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—
241#10621873—44no—
242#10621872—44no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43#12112yes—
250C23×C43C22×D411yescharacteristic
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—84no—
284C2×C4×C43#12112yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C432−1+411yescharacteristic
291C22⋊D43—44no—
292C22⋊D43—84no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
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×Dic43AGL(1,ℤ/8)12yes—
311D172—41no—
312D172—41no—
313D172—41no—
314D172—41no—
315D172—84no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320Dic86—41no—
321Dic86—41no—
322Dic86—41no—
323Dic86—41no—
324C8×C43—22no—
325C8×C43#12114yescomplemented
326C43⋊C8—41no—
327C43⋊C8—41no—
328#24794—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C2×#12111yescharacteristic
337C22×C43D4211yescharacteristic
338C22×C43#54711yescharacteristic
339C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57811yescharacteristic
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C4×C43—22no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43C2×#12111yescharacteristic
363C4×C43#53711yescharacteristic
364C4×C43#54811yescharacteristic
365C4×C43#55311yescharacteristic
366Dic43—22no—
367Dic43—41no—
368Dic43—41no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372C2×#468—431no—
373C2×#468—431no—
374C2×#436—431no—
375C2×#428D4311yescharacteristic, complemented
376#2416—431no—
377#2415—431no—
378#2067—431no—
379#2066—431no—
380#2036—431no—
381#2034—431no—
382#1968—431no—
383#1942—431no—
384#1875—431no—
385#1872—431no—
386#1809—431no—
387C2×C43—42no—
388C2×C43#241611yescharacteristic
389C2×C43#305511yescharacteristic
390C2×C43#306311yescharacteristic
391C2×C43#327211yescharacteristic
392C2×C43#327711yescharacteristic
393C2×C43#335111yescharacteristic
394C2×C43#335311yescharacteristic
395D43—81no—
396D43—161no—
397C22×SD16—431no—
398C22×M16—431no—
399C22×M16C2×D4311yescharacteristic
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—431no—
402C2×#121—431no—
403C2×#121—431no—
404C2×#121—861no—
405C2×C4×D4—431no—
406C2×#117C2×D4311yescharacteristic
407C22×C4⋊C4C2×D4311yescharacteristic
408#468—864no—
409#468—864no—
410#436—864no—
411#428—24no—
412C2×#107—431no—
413C2×#107C2×D4311yescharacteristic
414C2×#107C2×D4311yescharacteristic
415C2×#106C2×D4311yescharacteristic
416C2×#106C2×D4311yescharacteristic
417C2×C4⋊C8—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×C22⋊C8—431no—
425C2×C22⋊C8—431no—
426C2×C4×C8—431no—
427#397—861no—
428#396—861no—
429#394—861no—
430#394—861no—
431#391—431no—
432#390—431no—
433#389—431no—
434#389—431no—
435#389—861no—
436#388—861no—
437#386—861no—
438#380—431no—
439#380—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444C43#2479411yescharacteristic, complemented, Sylow
445C22×Q8—431no—
446C22×D4—431no—
447C22×D4—431no—
448C22×D4—861no—
449C22×D4—861no—
450C23×C4—21no—
451C23×C4—431no—
452C23×C4C22×D4311yescharacteristic
453C2×SD16—862no—
454C2×SD16—862no—
455C2×SD16—862no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16D17214yescomplemented
462C22×C8—431no—
463C22×C8—431no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—862no—
469C22⋊Q8—1721no—
470#121—862no—
471#121—862no—
472#121—862no—
473#121—1721no—
474#121—1724no—
475C4×D4—862no—
476C4×D4—862no—
477#117—22no—
478#117—41no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—21no—
505C2×C42—431no—
506#107—22no—
507#107—862no—
508#107C22⋊D4314yescomplemented
509#106—22no—
510#106—22no—
511C4⋊C8—862no—
512#103—862no—
513#103—862no—
514#103—1721no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—862no—
520C4×C8—862no—
521#95—861no—
522#95—861no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527C24—431no—
528C24—861no—
529C24D4×D4311yescharacteristic
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—862no—
537C2×D4—862no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—3441no—
545C2×D4—1722no—
546C2×D4—1722no—
547C2×D4—1721no—
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—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4C2×D17212yes—
575C22×C4D4×D4311yescharacteristic
576C22×C4#1062190212yes—
577C22×C4C23×D4311yescharacteristic
578SD16—1724no—
579M16—28no—
580M16—1724no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8C2×D17212yes—
590C2×C8C2×D17212yes—
591C2×C8#1062189812yes—
592C2×C8C2×C22⋊D4312yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—862no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—1722no—
606C4⋊C4—1722no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C4⋊C4C2×C22⋊D4312yes—
610C4⋊C4C2×C22⋊D4312yes—
611C22⋊C4—42no—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C22⋊C4—3441no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C42—42no—
623C42—861no—
624C42—861no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23#1306330012yes—
646C23C2×D4×D4311yescharacteristic
647Q8—1721no—
648Q8—1721no—
649Q8—1721no—
650Q8—1721no—
651D4—3444no—
652D4—3444no—
653D4—1724no—
654D4—1721no—
655D4—1721no—
656D4—1721no—
657D4—1721no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—432no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
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#1306330012yes—
700C2×C4C22×C22⋊D4311yescharacteristic
701C2×C4C22×D17211yescharacteristic
702C2×C4C2×#1062189811yescharacteristic
703C2×C4C2×#1062190211yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337311yescharacteristic
706C8—22no—
707C8—1721no—
708C8—1721no—
709C8#1306329914yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—3441no—
718C22—3441no—
719C22—3441no—
720C22—3441no—
721C22—3441no—
722C22—3441no—
723C22—3441no—
724C22—1721no—
725C22—1721no—
726C22—1721no—
727C22—1721no—
728C22—1721no—
729C22—1721no—
730C22—1721no—
731C22C2×#1306330011yescharacteristic
732C22D4×C22⋊D4311yescharacteristic
733C22#1458355011yescharacteristic
734C22AGL(1,ℤ/8)×D4311yescharacteristic
735C22#1458369811yescharacteristic
736C22#1458370911yescharacteristic
737C22#1458371511yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—81no—
742C4—81no—
743C4—862no—
744C4—3441no—
745C4—3441no—
746C4—3441no—
747C4—1721no—
748C4—1721no—
749C4C2×#1306329911yescharacteristic
750C4#1458348011yescharacteristic
751C4#1458356011yescharacteristic
752C4#1458359711yescharacteristic
753C2—42no—
754C2—3441no—
755C2—6881no—
756C2#1913802911yescharacteristic
757C2#1914421511yescharacteristic
758C2#1914428711yescharacteristic
759C2#1914618911yescharacteristic
760C2#1914624611yescharacteristic
761C2#1914715611yescharacteristic
762C2#1914717511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radical#19138029C2
hypercenterC2×#428D43
hypocenterC43#24794
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#14583146C2semidirect
2. C2×#14583145C2semidirect
3. C2×#14582975C2semidirect
5. #19138018C2semidirect
6. #19135978C2semidirect
7. #19135971C2semidirect
8. #19135800C2semidirect
9. #19135786C2semidirect
10. #19135447C2semidirect
11. #19135329C2semidirect
12. #19134917C2semidirect
13. #19134902C2semidirect
14. #19134625C2semidirect
15. C2×C43×#428C2semidirect
127. C2×M16×C43D4semidirect
142. #107×C43D4semidirect
325. C8×C43#121semidirect
375. C2×#428D43semidirect
444. C43#24794semidirect
461. C2×M16D172semidirect
508. #107C22⋊D43semidirect
709. C8#13063299semidirect

Maximal subgroups

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

subgroupindex
C2×#145831462
C2×#145831452
C2×#145829752
#191380292
#191380182
#191359782
#191359712
#191358002
#191357862
#191354472
#191353292
#191349172
#191349022
#191346252
C2×C43×#4282
#2479443