Finite Group Databasebeta

← #25117244

Subgroups — #25117244

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic, complemented
3#19137633C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19135468C211yesmaximal, characteristic, complemented
6#19135275C211yesmaximal, characteristic, complemented
7#19135218C211yesmaximal, characteristic, complemented
8#19135033C211yesmaximal, characteristic, complemented
9#19134941C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134854C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic, complemented
22C22×C22⋊Dic43—21no—
23#14583033C418yescomplemented
24#14582979—24no—
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063247C2211yescharacteristic, complemented
28C2×#13063247C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic, complemented
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582800C2211yescharacteristic, complemented
37#14582799—21no—
38#14582795C2211yescharacteristic, complemented
39#14582790—21no—
40#14582779—21no—
41#14582779—21no—
42#14582775—21no—
43#14582759C2211yescharacteristic
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C4×(C2×D43)⋊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×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—41no—
70C2×#10621882—41no—
71C2×#10621882C2×C414yes—
72C2×#10621882C2×C414yescomplemented
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063299—22no—
76#13063299C2×C414yescomplemented
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—41no—
80D4×Dic43—41no—
81#13063287—22no—
82#13063287—41no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
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—44no—
95C2×C22⋊Dic43D411yescharacteristic
96C2×C22⋊Dic43D411yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063258—22no—
105#13063256—41no—
106#13063247—22no—
107#13063247—41no—
108#13063246C2×C414yescomplemented
109#13063246C2×C414yescomplemented
110C22⋊(C43⋊C8)C2×C414yescomplemented
111#13063235—41no—
112C8×Dic43—22no—
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×C414yescomplemented
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×C43D414yescomplemented
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
154C23×D43—21no—
155C2×D4×C43—24no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—28no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43C22×C412yes—
171C2×D4×C43C22×C412yes—
172C2×D4×C43C2×D412yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43#4112yes—
183C22×C4×C43C2411yescharacteristic
184C2×C22⋊D43—24no—
185C2×C22⋊D43—81no—
186C2×C22⋊D43—81no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—81no—
195C22×Dic43—81no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172C22×C412yes—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—81no—
209M16×C43—44no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43C2×D412yes—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—42no—
221C42×C43—42no—
222C22⋊Dic43—22no—
223C22⋊Dic43—41no—
224C22⋊Dic43—42no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228C22⋊Dic43—42no—
229C22⋊Dic43—81no—
230C22⋊Dic43—81no—
231#10621882—28no—
232#10621882—44no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—81no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43C22×C412yes—
243Dic43⋊C4—81no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—81no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8C22×C412yes—
254C2×C43⋊C8C22×C412yes—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—21no—
258C23×C43—22no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—22no—
265C23×C43—48no—
266C23×C43—48no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43—84no—
282C23×C43C4×D412yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—48no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43C4×D414yes—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43C4×D412yes—
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C22⋊D43—84no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—22no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—84no—
341C2×Dic43—84no—
342C2×Dic43AGL(1,ℤ/8)12yes—
343D172—22no—
344D172—22no—
345D172—41no—
346D172—41no—
347C4×D43—84no—
348C8×C43—22no—
349C8×C43—41no—
350C43⋊C8—22no—
351C43⋊C8—22no—
352#22880—431nomaximal, Sylow
353C22×C43—24no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—41no—
360C22×C43—42no—
361C22×C43—41no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—816no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43C2×C4×D411yescharacteristic
376C22×C43D4211yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C43#57511yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57611yescharacteristic
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43—81no—
389C4×C43—22no—
390C4×C43—42no—
391C4×C43—81no—
392C4×C43C2×C4×D411yescharacteristic
393C4×C43#51811yescharacteristic
394C4×C43#54611yescharacteristic
395C4×C43#55111yescharacteristic
396Dic43—22no—
397Dic43—42no—
398Dic43—41no—
399Dic43—41no—
400Dic43—41no—
401Dic43—81no—
402Dic43—81no—
403C2×#447—431no—
404C2×C4×D8—431no—
405C2×#418D4311yescharacteristic, complemented
406#2363—431no—
407D4×C22⋊C4—431no—
408#1972—431no—
409#1934—431no—
410#1925—431no—
411#1895—431no—
412#1879—431no—
413#1879—431no—
414#1864—431no—
415#1854—431no—
416#1762—431no—
417#1753—431no—
418C2×C43—42no—
419C2×C43—44no—
420C2×C43—82no—
421C2×C43#235811yescharacteristic
422C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C43#294811yescharacteristic
424C2×C43#326411yescharacteristic
425C2×C43#326811yescharacteristic
426C2×C43#332211yescharacteristic
427C2×C43#332511yescharacteristic
428D43—82no—
429C23×D4C2×D4311yescharacteristic
430C22×D8—431no—
431C22×D8—431no—
432C22×M16C2×D4311yescharacteristic
433C2×#121—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×#117C2×D4311yescharacteristic
438C22×C22⋊C4—861no—
439#447—438no—
440C4×D8—864no—
441C2×#107—431no—
442C2×#106—431no—
443#418—24no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102C2×D4311yescharacteristic
449C2×#102C2×D4311yescharacteristic
450C2×#102C2×D4311yescharacteristic
451C2×#102C2×D4311yescharacteristic
452C2×C22⋊C8—431no—
453C2×#97—431no—
454C2×C4×C8—431no—
455#390—431no—
456#390—431no—
457#390—431no—
458#390—861no—
459#389—431no—
460#388—861no—
461#386—861no—
462#386—861no—
463#386—861no—
464#380—431no—
465#379—861no—
466C4×C4⋊C4—431no—
467C4×C22⋊C4—431no—
468C4×C22⋊C4—861no—
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473#336—431no—
474#336—431no—
475C43#2288011yescharacteristic, complemented, Sylow
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4—431no—
484C22×D4—861no—
485C22×D4C4×D4314yescomplemented
486C22×D4C22×D4311yescharacteristic
487C22×D4C22×D4311yescharacteristic
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×D8—434no—
493C2×D8—434no—
494C2×D8—862no—
495C2×D8—862no—
496C2×D8—1721no—
497C2×D8—1721no—
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#121—434no—
506#121—862no—
507C4×D4—862no—
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—1724no—
536C2×C42—21no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—861no—
540#107—862no—
541#106—1721no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—434no—
546#102—434no—
547#102—862no—
548#102—1721no—
549#102C22⋊D4314yescomplemented
550C22⋊C8—434no—
551#97—1721no—
552C4×C8—862no—
553#95—431no—
554#95—431no—
555#95—861no—
556#95—861no—
557#95—861no—
558C24—21no—
559C24—21no—
560C24—24no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24—861no—
568C24D4×D4311yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—432no—
585C2×D4—864no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—3441no—
592C2×D4—3441no—
593C2×D4C2×C4×D4312yes—
594C2×D4C2×C4×D4312yes—
595C2×D4#1062189812yes—
596C2×D4C2×C22⋊D4312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—3441no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4C2×C4×D4312yes—
620C22×C4D4×D4311yescharacteristic
621C22×C4#1062190012yes—
622C22×C4C23×D4311yescharacteristic
623D8—868no—
624D8—1724no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—432no—
632C2×C8—432no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8C2×C22⋊D4312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—432no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—3441no—
648C4⋊C4C2×C22⋊D4312yes—
649C22⋊C4—42no—
650C22⋊C4—862no—
651C22⋊C4—864no—
652C22⋊C4—3441no—
653C22⋊C4—3441no—
654C22⋊C4—3441no—
655C22⋊C4—1722no—
656C22⋊C4—1722no—
657C22⋊C4—1722no—
658C22⋊C4—1721no—
659C22⋊C4—1722no—
660C22⋊C4—1722no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C42—42no—
664C42—861no—
665C42—861no—
666C42—861no—
667C42—861no—
668C42—3441no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—48no—
680C23—48no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—862no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23(C22⋊D43)⋊C412yes—
704C23C2×D4×D4311yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—862no—
714D4—862no—
715D4—3444no—
716D4—1721no—
717D4—1721no—
718D4C4×C22⋊D4314yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—432no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—3444no—
745C2×C4—3444no—
746C2×C4—3444no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4(C22⋊D43)⋊C412yes—
756C2×C4C22×C4×D4311yescharacteristic
757C2×C4C22×C22⋊D4311yescharacteristic
758C2×C4C2×#1062190011yescharacteristic
759C2×C4C2×#1062189811yescharacteristic
760C2×C4#1306337011yescharacteristic
761C2×C4#1306337011yescharacteristic
762C8—22no—
763C8—41no—
764C8—862no—
765C8—862no—
766C22—22no—
767C22—22no—
768C22—24no—
769C22—22no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—3441no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22C2×(C22⋊D43)⋊C411yescharacteristic
796C22D4×C22⋊D4311yescharacteristic
797C22#1458353911yescharacteristic
798C22AGL(1,ℤ/8)×D4311yescharacteristic
799C22#1458369511yescharacteristic
800C22#1458370311yescharacteristic
801C22#1458370311yescharacteristic
802C4—22no—
803C4—42no—
804C4—81no—
805C4—862no—
806C4—3441no—
807C4—3441no—
808C4—1722no—
809C4—1721no—
810C4—1721no—
811C4—1721no—
812C4C2×C4×C22⋊D4311yescharacteristic
813C4#1458337211yescharacteristic
814C4#1458354311yescharacteristic
815C4#1458357511yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—3442no—
820C2#1913757411yescharacteristic
821C2#1914339911yescharacteristic
822C2#1914344311yescharacteristic
823C2#1914606911yescharacteristic
824C2#1914612911yescharacteristic
825C2#1914679211yescharacteristic
826C2#1914683311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenterC2×#418D43
hypocenterC43#22880
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×#14582979C2semidirect
3. #19137633C2semidirect
4. D4×C22⋊Dic43C2semidirect
5. #19135468C2semidirect
6. #19135275C2semidirect
7. #19135218C2semidirect
8. #19135033C2semidirect
9. #19134941C2semidirect
10. #19134940C2semidirect
11. #19134854C2semidirect
12. #19134794C2semidirect
13. #19134422C2semidirect
14. #19134376C2semidirect
15. C2×C43×#418C2semidirect
21. C2×#13063287C22semidirect
23. #14583033C4semidirect
25. C2×#13063258C22semidirect
26. C2×#13063256C22semidirect
27. C2×#13063247C22semidirect
28. C2×#13063247C22semidirect
32. C2×#13063235C22semidirect
33. C2×C8×Dic43C22semidirect
36. #14582800C22semidirect
38. #14582795C22semidirect
45. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
72. C2×#10621882C2×C4semidirect
76. #13063299C2×C4semidirect
108. #13063246C2×C4semidirect
109. #13063246C2×C4semidirect
110. C22⋊(C43⋊C8)C2×C4semidirect
125. C22×D4×C43C2×C4semidirect
143. #102×C43D4semidirect
405. C2×#418D43semidirect
475. C43#22880semidirect
485. C22×D4C4×D43semidirect
549. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
C2×#145829792
#191376332
D4×C22⋊Dic432
#191354682
#191352752
#191352182
#191350332
#191349412
#191349402
#191348542
#191347942
#191344222
#191343762
C2×C43×#4182
#2288043