Finite Group Databasebeta

← #25117248

Subgroups — #25117248

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×D8×Dic43C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3#19137637C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19135472C211yesmaximal, characteristic, complemented
6#19135280C211yesmaximal, characteristic, complemented
7#19135217C211yesmaximal, characteristic, complemented
8#19135034C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C2×C43×#447C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic, complemented
20C2×#13063284C2211yescharacteristic
21C22×C22⋊Dic43—21no—
22D8×Dic43—24no—
23C2×#13063259C2211yescharacteristic, complemented
24C2×#13063257C2211yescharacteristic, complemented
25#14582904—24no—
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic, complemented
31C2×#13063246C2211yescharacteristic, complemented
32C2×#13063235C2211yescharacteristic, complemented
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582802—21no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic, complemented
38#14582798C2211yescharacteristic, complemented
39#14582792—21no—
40#14582779—21no—
41#14582779—21no—
42#14582779—21no—
43#14582759C2211yescharacteristic
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C22⋊C4×Dic43—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×D8×C43C2211yescharacteristic
56C22×D8×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C43×#447C418yescomplemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70D4×Dic43—22no—
71D4×Dic43—22no—
72D4×Dic43—22no—
73D4×Dic43—41no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76#13063284—22no—
77#13063284—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—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×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063259—22no—
102#13063257—41no—
103#13063246—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—41no—
108#13063246D414yescomplemented
109#13063235—41no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C25×C43—21no—
117C22×D4×C43—22no—
118C22×D4×C43—22no—
119C22×D4×C43—21no—
120C22×D4×C43—21no—
121C22×D4×C43—22no—
122C22×D4×C43—41no—
123C22×D4×C43—41no—
124C22×D4×C43C2×C414yescomplemented
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C2×D8×C43—22no—
130C2×D8×C43—22no—
131C2×D8×C43—41no—
132C2×D8×C43—41no—
133C2×D8×C43C2×C414yes—
134C2×D8×C43C2×C414yescomplemented
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#121×C43—22no—
138#121×C43C2×C414yescomplemented
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141#102×C43C2×C414yescomplemented
142#102×C43C2×C414yescomplemented
143C22⋊C8×C43C2×C414yescomplemented
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—24no—
148C24×C43—42no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—42no—
152C24×C43—81no—
153C24×C43—81no—
154C24×C43C2×D411yescharacteristic
155C2×D4×C43—24no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—24no—
162C2×D4×C43—28no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—44no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C22×C412yes—
180C2×D4×C43C22×C412yes—
181C2×D4×C43C2×D412yes—
182C2×D4×C43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43C22×C412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43#4112yes—
191C22×C4×C43C2411yescharacteristic
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C22×Dic43—81no—
203C22×Dic43—81no—
204C22×Dic43—81no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209D8×C43—28no—
210D8×C43—44no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43C22×C412yes—
216C2×C8×C43C22×C412yes—
217C4⋊C4×C43—21no—
218C4⋊C4×C43C22×C412yes—
219C22⋊C4×C43—24no—
220C22⋊Dic43—22no—
221C22⋊Dic43—41no—
222C22⋊Dic43—42no—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228C22⋊Dic43—42no—
229C22⋊Dic43—42no—
230C22⋊Dic43—81no—
231C22⋊Dic43—81no—
232C22⋊Dic43—81no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—81no—
241C4⋊Dic43C2×D412yes—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—42no—
247C4×Dic43—81no—
248#10621877—44no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8C2×D412yes—
255C23×C43—22no—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—48no—
267C23×C43—48no—
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—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—84no—
285C23×C43—84no—
286C23×C43—84no—
287C23×C43—84no—
288C23×C43—84no—
289C23×C43C4×D412yes—
290C23×C43C22×D411yescharacteristic
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—48no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—84no—
304D4×C43C4×D414yes—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43C4×D412yes—
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—22no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—84no—
345C2×Dic43—84no—
346C2×Dic43—84no—
347C2×Dic43AGL(1,ℤ/8)12yes—
348C8×C43—22no—
349C8×C43—22no—
350C43⋊C8—22no—
351C43⋊C8—41no—
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—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—816no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43C2×C4×D411yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C43#57511yescharacteristic
387C22×C43#57611yescharacteristic
388C22×C43#57611yescharacteristic
389C4×C43—22no—
390C4×C43—42no—
391C4×C43C2×C4×D411yescharacteristic
392C4×C43#51811yescharacteristic
393C4×C43#54611yescharacteristic
394C4×C43#55111yescharacteristic
395Dic43—22no—
396Dic43—42no—
397Dic43—41no—
398Dic43—41no—
399Dic43—41no—
400Dic43—81no—
401Dic43—81no—
402Dic43—81no—
403C2×#447D4311yescharacteristic
404C2×C4×D8—431no—
405C2×#418—431no—
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—82no—
422C2×C43#235811yescharacteristic
423C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C43#294811yescharacteristic
425C2×C43#326411yescharacteristic
426C2×C43#326811yescharacteristic
427C2×C43#332211yescharacteristic
428C2×C43#332511yescharacteristic
429C23×D4C2×D4311yescharacteristic
430C22×D8C2×D4311yescharacteristic
431C22×D8C2×D4311yescharacteristic
432C22×M16—431no—
433C2×#121C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×#117—431no—
438C22×C22⋊C4—861no—
439#447Dic4318yescomplemented
440C4×D8—864no—
441C2×#107—431no—
442C2×#106—431no—
443#418—864no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102C2×D4311yescharacteristic
451C2×#102C2×D4311yescharacteristic
452C2×C22⋊C8C2×D4311yescharacteristic
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—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×Dic4314yescomplemented
485C22×D4C22×D4311yescharacteristic
486C22×D4C22×D4311yescharacteristic
487C22×D4C22×D4311yescharacteristic
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×Dic4314yes—
497C2×D8C2×Dic4314yescomplemented
498C2×M16—862no—
499C2×M16—862no—
500C2×M16—1721no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#121—22no—
506#121C2×Dic4314yescomplemented
507C4×D4—862no—
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513#117—862no—
514#117—1721no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—861no—
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—431no—
537C2×C42—431no—
538C2×C42—861no—
539C2×C42—861no—
540#107—862no—
541#106—1721no—
542#102—434no—
543#102—862no—
544#102—862no—
545#102—862no—
546#102—862no—
547#102—1721no—
548#102C2×Dic4314yescomplemented
549#102C2×Dic4314yescomplemented
550C22⋊C8C2×Dic4314yescomplemented
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—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24D4×D4311yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4D4×D4312yes—
593C2×D4#1062190012yes—
594C2×D4C22×Dic4312yes—
595C2×D4C22×Dic4312yes—
596C2×D4C22×Dic4312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—861no—
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×C4D4×D4311yescharacteristic
620C22×C4#1062190012yes—
621C22×C4C22×Dic4312yes—
622C22×C4C23×D4311yescharacteristic
623D8—28no—
624D8—44no—
625M16—1724no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—432no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8C22×Dic4312yes—
637C2×C8C22×Dic4312yes—
638C4⋊C4—21no—
639C4⋊C4—432no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—3441no—
648C4⋊C4C22×Dic4312yes—
649C22⋊C4—24no—
650C22⋊C4—862no—
651C22⋊C4—3441no—
652C22⋊C4—3441no—
653C22⋊C4—3441no—
654C22⋊C4—1722no—
655C22⋊C4—1721no—
656C22⋊C4—1722no—
657C22⋊C4—1722no—
658C22⋊C4—1722no—
659C22⋊C4—1722no—
660C22⋊C4—1722no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C42—861no—
664C42—861no—
665C42—861no—
666C42—861no—
667C42—3441no—
668C42—1722no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23D4×Dic4312yes—
704C23C2×D4×D4311yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4D4×Dic4314yes—
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—432no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—862no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—3444no—
742C2×C4—3444no—
743C2×C4—3444no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
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×C4D4×Dic4312yes—
756C2×C4C23×Dic4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×#1062190011yescharacteristic
759C2×C4C2×#1062190011yescharacteristic
760C2×C4#1306337011yescharacteristic
761C2×C4#1306337011yescharacteristic
762C8—22no—
763C8—22no—
764C8—862no—
765C8—1721no—
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—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×D4×Dic4311yescharacteristic
796C22#1458353111yescharacteristic
797C22#1458353611yescharacteristic
798C22AGL(1,ℤ/8)×D4311yescharacteristic
799C22#1458369511yescharacteristic
800C22#1458370011yescharacteristic
801C22#1458370011yescharacteristic
802C4—22no—
803C4—42no—
804C4—862no—
805C4—3441no—
806C4—3441no—
807C4—3441no—
808C4—1721no—
809C4—1721no—
810C4—1722no—
811C4—1721no—
812C4C2×D4×Dic4311yescharacteristic
813C4#1458337411yescharacteristic
814C4#1458353611yescharacteristic
815C4#1458358011yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2#1913757911yescharacteristic
821C2AGL(1,ℤ/8)×Dic4311yescharacteristic
822C2#1914344711yescharacteristic
823C2#1914607311yescharacteristic
824C2#1914613311yescharacteristic
825C2#1914680011yescharacteristic
826C2#1914683011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#447D43
hypocenterC43#22880
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic43C2semidirect
2. C2×#14582904C2semidirect
3. #19137637C2semidirect
4. D4×C22⋊Dic43C2semidirect
5. #19135472C2semidirect
6. #19135280C2semidirect
7. #19135217C2semidirect
8. #19135034C2semidirect
9. #19134945C2semidirect
10. #19134945C2semidirect
11. #19134858C2semidirect
12. #19134796C2semidirect
13. #19134422C2semidirect
14. #19134381C2semidirect
19. C2×D4×Dic43C22semidirect
23. C2×#13063259C22semidirect
24. C2×#13063257C22semidirect
30. C2×#13063246C22semidirect
31. C2×#13063246C22semidirect
32. C2×#13063235C22semidirect
33. C2×C8×Dic43C22semidirect
37. #14582802C22semidirect
38. #14582798C22semidirect
45. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
58. C43×#447C4semidirect
108. #13063246D4semidirect
124. C22×D4×C43C2×C4semidirect
134. C2×D8×C43C2×C4semidirect
138. #121×C43C2×C4semidirect
141. #102×C43C2×C4semidirect
142. #102×C43C2×C4semidirect
143. C22⋊C8×C43C2×C4semidirect
439. #447Dic43semidirect
475. C43#22880semidirect
484. C22×D4C2×Dic43semidirect
497. C2×D8C2×Dic43semidirect
506. #121C2×Dic43semidirect
548. #102C2×Dic43semidirect
549. #102C2×Dic43semidirect
550. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic432
C2×#145829042
#191376372
D4×C22⋊Dic432
#191354722
#191352802
#191352172
#191350342
#191349452
#191348582
#191347962
#191344222
#191343812
C2×C43×#4472
#2288043