Finite Group Databasebeta

← #25117304

Subgroups — #25117304

Order 11008.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583050C211yesmaximal, characteristic
2C2×#14582990C211yesmaximal, characteristic, complemented
3#19137622C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic
5#19135477C211yesmaximal, characteristic, complemented
6#19135275C211yesmaximal, characteristic, complemented
7#19135225C211yesmaximal, characteristic, complemented
8#19135028C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063290C2211yescharacteristic, complemented
20C2×D4×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C22×C22⋊Dic43—21no—
23#14583050C418yescomplemented
24#14582990—24no—
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063250C2211yescharacteristic, complemented
28C2×#13063250C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic, complemented
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582804C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582795C2211yescharacteristic, complemented
38#14582793—21no—
39#14582787—21no—
40#14582783—21no—
41#14582779—21no—
42#14582779—21no—
43#14582759C2211yescharacteristic
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C4×Dic43⋊C4—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C43×#418—24no—
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—41no—
68C2×#10621883—41no—
69C2×#10621883C2×C414yes—
70C2×#10621883C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063304—22no—
74#13063304C2×C414yescomplemented
75#13063290—22no—
76#13063290—41no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—41no—
80D4×Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—44no—
96C2×C22⋊Dic43D411yescharacteristic
97C2×C22⋊Dic43D411yescharacteristic
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063258—41no—
103#13063256—22no—
104#13063250—22no—
105#13063250—41no—
106#13063246C2×C414yes—
107#13063246C2×C414yescomplemented
108C22⋊(C43⋊C8)C2×C414yescomplemented
109#13063235—41no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C25×C43—21no—
119C22×D4×C43—22no—
120C22×D4×C43—22no—
121C22×D4×C43—21no—
122C22×D4×C43—22no—
123C22×D4×C43—41no—
124C22×D4×C43—41no—
125C22×D4×C43C2×C414yes—
126C22×D4×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C2×M16×C43—22no—
130C2×M16×C43—22no—
131C2×M16×C43—41no—
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134#117×C43—22no—
135#117×C43—41no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—21no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43D414yes—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—24no—
147C24×C43—42no—
148C24×C43—42no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—81no—
152C24×C43—81no—
153C24×C43C2×D411yescharacteristic
154C2×D4×C43—24no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—28no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43C22×C412yes—
170C2×D4×C43C22×C412yes—
171C2×D4×C43C2×D412yes—
172C2×D4×C43#4112yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43C22×C412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43#4112yes—
182C22×C4×C43C2411yescharacteristic
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—81no—
192C22×Dic43—81no—
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86C22×C412yes—
203M16×C43—44no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43C2×D412yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—42no—
215C42×C43—42no—
216C22⋊Dic43—22no—
217C22⋊Dic43—24no—
218C22⋊Dic43—41no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—42no—
224C22⋊Dic43—81no—
225C22⋊Dic43—81no—
226#10621883—28no—
227#10621883—44no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C22×C412yes—
234Dic43⋊C4—24no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—42no—
242C4×Dic43—42no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C22×C412yes—
248C2×C43⋊C8C22×C412yes—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—21no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—22no—
259C23×C43—48no—
260C23×C43—48no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—84no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43C4×D412yes—
277C23×C43C22×D411yescharacteristic
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—48no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43C4×D414yes—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43C4×D412yes—
300C2×C4×C43C23×C411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—84no—
330C2×Dic43—84no—
331C2×Dic43AGL(1,ℤ/8)12yes—
332Dic86—22no—
333Dic86—22no—
334Dic86—41no—
335Dic86—41no—
336C8×C43—22no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—22no—
340#22884—431nomaximal, Sylow
341C22×C43—24no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—41no—
350C22×C43—42no—
351C22×C43—41no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—816no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43C2×C4×D411yescharacteristic
364C22×C43D4211yescharacteristic
365C22×C43#54611yescharacteristic
366C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57711yescharacteristic
369C22×C43#57711yescharacteristic
370C4×C43—22no—
371C4×C43—42no—
372C4×C43—81no—
373C4×C43C2×C4×D411yescharacteristic
374C4×C43#51811yescharacteristic
375C4×C43#54611yescharacteristic
376C4×C43#55111yescharacteristic
377Dic43—22no—
378Dic43—42no—
379Dic43—42no—
380Dic43—41no—
381Dic43—41no—
382Dic43—41no—
383Dic43—81no—
384Dic43—81no—
385C2×#450—431no—
386C2×C4×SD16—431no—
387C2×#418D4311yescharacteristic
388#2362—431no—
389D4×C22⋊C4—431no—
390#1973—431no—
391#1934—431no—
392#1926—431no—
393#1894—431no—
394#1880—431no—
395#1877—431no—
396#1862—431no—
397#1854—431no—
398#1762—431no—
399#1753—431no—
400C2×C43—42no—
401C2×C43—44no—
402C2×C43—82no—
403C2×C43#235811yescharacteristic
404C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
405C2×C43#294911yescharacteristic
406C2×C43#326511yescharacteristic
407C2×C43#326711yescharacteristic
408C2×C43#332311yescharacteristic
409C2×C43#332411yescharacteristic
410C23×D4C2×D4311yescharacteristic
411C22×SD16—431no—
412C22×SD16—431no—
413C22×M16C2×D4311yescharacteristic
414C2×C22⋊Q8—431no—
415C2×C4×Q8—431no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×#117C2×D4311yescharacteristic
419C22×C22⋊C4—861no—
420#450—438no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424#418—24no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102C2×D4311yescharacteristic
430C2×#102C2×D4311yescharacteristic
431C2×#102C2×D4311yescharacteristic
432C2×#102C2×D4311yescharacteristic
433C2×C22⋊C8—431no—
434C2×#97—431no—
435C2×C4×C8—431no—
436#391—431no—
437#390—431no—
438#390—431no—
439#389—431no—
440#388—861no—
441#388—861no—
442#387—861no—
443#386—861no—
444#386—861no—
445#380—431no—
446#379—861no—
447C4×C4⋊C4—431no—
448C4×C4⋊C4—861no—
449C4×C22⋊C4—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340—431no—
454#336—431no—
455#336—431no—
456C43#2288411yescharacteristic, complemented, Sylow
457C25—21no—
458C22×Q8—431no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—41no—
464C22×D4—41no—
465C22×D4C4×D4314yes—
466C22×D4C22×D4311yescharacteristic
467C22×D4C22×D4311yescharacteristic
468C23×C4—861no—
469C23×C4—861no—
470C23×C4C22×D4311yescharacteristic
471C2×SD16—434no—
472C2×SD16—434no—
473C2×SD16—862no—
474C2×SD16—862no—
475C2×SD16—1721no—
476C2×SD16—1721no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—41no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C22⋊Q8—434no—
485C22⋊Q8—862no—
486C4×Q8—862no—
487C4×Q8—1721no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—1721no—
491C4×D4—1721no—
492#117—22no—
493#117—41no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
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—1724no—
514C2×C42—21no—
515C2×C42—431no—
516C2×C42—431no—
517C2×C42—861no—
518C2×C42—861no—
519#107—1721no—
520#106—862no—
521#103—862no—
522#103—1721no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—434no—
527#102—434no—
528#102C22⋊D4314yes—
529C22⋊C8—434no—
530#97—1721no—
531C4×C8—862no—
532#95—431no—
533#95—431no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—81no—
547C24—81no—
548C24D4×D4311yescharacteristic
549C2×Q8—432no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×D4—28no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4C2×C4×D4312yes—
571C2×D4C2×C4×D4312yes—
572C2×D4#1062189812yes—
573C2×D4C2×C22⋊D4312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—3441no—
589C22×C4—3441no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4C2×C4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4#1062190012yes—
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599SD16—1724no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8C2×C22⋊D4312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—1722no—
624C4⋊C4—1722no—
625C4⋊C4C2×C22⋊D4312yes—
626C22⋊C4—42no—
627C22⋊C4—862no—
628C22⋊C4—864no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—1722no—
632C22⋊C4—1721no—
633C22⋊C4—1722no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—42no—
638C42—861no—
639C42—861no—
640C42—861no—
641C42—861no—
642C42—1722no—
643C42—1722no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23(C22⋊D43)⋊C412yes—
672C23C2×D4×D4311yescharacteristic
673Q8—862no—
674Q8—862no—
675Q8—1721no—
676Q8—1721no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4C4×C22⋊D4314yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—432no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—3444no—
713C2×C4—3444no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4(C22⋊D43)⋊C412yes—
725C2×C4C22×C4×D4311yescharacteristic
726C2×C4C22×C22⋊D4311yescharacteristic
727C2×C4C2×#1062190011yescharacteristic
728C2×C4C2×#1062189811yescharacteristic
729C2×C4#1306337011yescharacteristic
730C2×C4#1306337011yescharacteristic
731C8—22no—
732C8—41no—
733C8—862no—
734C8—862no—
735C22—22no—
736C22—22no—
737C22—24no—
738C22—22no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×(C22⋊D43)⋊C411yescharacteristic
758C22D4×C22⋊D4311yescharacteristic
759C22#1458353911yescharacteristic
760C22AGL(1,ℤ/8)×D4311yescharacteristic
761C22#1458369511yescharacteristic
762C22#1458370911yescharacteristic
763C22#1458370911yescharacteristic
764C4—22no—
765C4—42no—
766C4—81no—
767C4—862no—
768C4—3441no—
769C4—3441no—
770C4—1722no—
771C4—1721no—
772C4—1721no—
773C4—1721no—
774C4—1722no—
775C4C2×C4×C22⋊D4311yescharacteristic
776C4#1458337211yescharacteristic
777C4#1458354311yescharacteristic
778C4#1458357511yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#1913757411yescharacteristic
783C2#1914339911yescharacteristic
784C2#1914345711yescharacteristic
785C2#1914608411yescharacteristic
786C2#1914611411yescharacteristic
787C2#1914680711yescharacteristic
788C2#1914682211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#418D43
hypocenterC43#22884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#14582990C2semidirect
3. #19137622C2semidirect
5. #19135477C2semidirect
6. #19135275C2semidirect
7. #19135225C2semidirect
8. #19135028C2semidirect
9. #19134947C2semidirect
10. #19134927C2semidirect
11. #19134840C2semidirect
12. #19134794C2semidirect
13. #19134422C2semidirect
14. #19134376C2semidirect
19. C2×#13063290C22semidirect
23. #14583050C4semidirect
25. C2×#13063258C22semidirect
26. C2×#13063256C22semidirect
27. C2×#13063250C22semidirect
28. C2×#13063250C22semidirect
32. C2×#13063235C22semidirect
33. C2×C8×Dic43C22semidirect
34. #14582804C22semidirect
37. #14582795C22semidirect
45. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
70. C2×#10621883C2×C4semidirect
74. #13063304C2×C4semidirect
107. #13063246C2×C4semidirect
108. C22⋊(C43⋊C8)C2×C4semidirect
456. C43#22884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
C2×#145829902
#191376222
D4×C22⋊Dic432
#191354772
#191352752
#191352252
#191350282
#191349472
#191349272
#191348402
#191347942
#191344222
#191343762
C2×C43×#4182
#2288443