Finite Group Databasebeta

← #25107726

Subgroups — #25107726

Order 11008.

1308 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×#14583031C211yesmaximal, characteristic
2C4×#13063296C211yesmaximal, characteristic, complemented
3#390×D43C211yesmaximal, characteristic, complemented
4#19135462C211yesmaximal, characteristic, complemented
5#19135458C211yesmaximal, characteristic, complemented
6#19135276C211yesmaximal, characteristic, complemented
7#19135275C211yesmaximal, characteristic, complemented
8#19135216C211yesmaximal, characteristic, complemented
9#19135212C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134784C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22C2×C22⋊C4×D43—21no—
23C2×C42×D43C2211yescharacteristic
24#14583031C418yescomplemented
25C2×#13063259C2211yescharacteristic, complemented
26C2×#13063258C2211yescharacteristic, complemented
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic, complemented
32C2×#13063245C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic, complemented
36C2×C8×Dic43C2211yescharacteristic, complemented
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582799—21no—
42#14582799—21no—
43#14582795C2211yescharacteristic, complemented
44#14582787—21no—
45#14582775—21no—
46#14582756C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic, complemented
48C4×C22⋊Dic43—21no—
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C22×D8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic, complemented
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic, complemented
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C2×D4×D43—22no—
65C2×D4×D43—41no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43—41no—
69C2×D4×D43C2×C414yescomplemented
70C22×C4×D43—21no—
71C22×C4×D43D411yescharacteristic
72C22×C4×D43D411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621882—41no—
75C2×#10621882—41no—
76C2×#10621882C2×C414yescomplemented
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063296—22no—
80#13063296C2×C414yes—
81C4×C22⋊D43—44no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—41no—
88C4⋊C4×D43—41no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C22⋊C4×D43—44no—
100C22⋊C4×D43—44no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43D411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C42×D43—41no—
106C42×D43—41no—
107#13063259—41no—
108#13063258—41no—
109#13063247—41no—
110#13063247C2×C414yescomplemented
111#13063246—41no—
112#13063246—41no—
113#13063246C2×C414yescomplemented
114#13063245—41no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8C2×C414yescomplemented
117C8×Dic43—41no—
118C8×Dic43—41no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C22×D4×C43C2311yescharacteristic
123C22×D4×C43C2311yescharacteristic
124C23×C4×C43—21no—
125C2×D8×C43—41no—
126C2×D8×C43—41no—
127C2×D8×C43C2×C414yescomplemented
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4×D4×C43—41no—
131C4×D4×C43—41no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#102×C43—41no—
139#102×C43—41no—
140C24×C43—21no—
141C24×C43—21no—
142C23×D43—21no—
143C23×D43—24no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43C22×C412yes—
162C2×D4×C43C22×C412yes—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—42no—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—24no—
173C2×C22⋊D43—42no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183D4×D43—44no—
184D4×D43—44no—
185D4×D43—44no—
186D4×D43—44no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C22×C412yes—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—22no—
198C2×C4×D43—22no—
199C2×C4×D43—41no—
200C2×C4×D43—41no—
201C2×C4×D43—41no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43D814yescomplemented
206C2×C4×D43C22×C412yes—
207C2×C4×D43#4112yes—
208D8×C43—44no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43C22×C412yes—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C42×C43—21no—
223C42×C43—21no—
224C22⋊Dic43—24no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228C22⋊Dic43—42no—
229#10621882—44no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—42no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43C22×C412yes—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—41no—
246C4×Dic43—41no—
247C4×Dic43—42no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8C22×C412yes—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43C22×D411yescharacteristic
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—22no—
274C22×D43—48no—
275C22×D43—48no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—48no—
283C22×D43—84no—
284C22×D43—84no—
285C22×D43—84no—
286C22×D43—84no—
287C22×D43C4×D412yes—
288C22×D43C2×D812yes—
289C22×D43#13512yes—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—84no—
310C2×C4×C43C2×D812yes—
311C2×C4×C43C23×C411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C2×C4×C43H(5,𝔽2)11yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C22⋊D43—48no—
318C22⋊D43—48no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—22no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43C4×D412yes—
335C2×Dic43C2×D812yes—
336C2×Dic43AGL(1,ℤ/8)12yes—
337D172—22no—
338D172—22no—
339D172—41no—
340D172—41no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—44no—
346C4×D43—44no—
347C4×D43—84no—
348C8×C43—22no—
349C8×C43—41no—
350C43⋊C8—22no—
351C43⋊C8—41no—
352#22040—431nomaximal, Sylow
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43C2×C4×D411yescharacteristic
368C22×C43#53411yescharacteristic
369C22×C43#53511yescharacteristic
370C22×C43C22×D811yescharacteristic
371C22×C43C2×#13511yescharacteristic
372C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C43#57511yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—816no—
384C2×D43—81no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—81no—
388C2×D43C4×D814yes—
389C4×C43—22no—
390C4×C43—41no—
391C4×C43—81no—
392C4×C43—81no—
393C4×C43#51811yescharacteristic
394C4×C43#51811yescharacteristic
395C4×C43#53811yescharacteristic
396C4×C43#53811yescharacteristic
397Dic43—22no—
398Dic43—22no—
399Dic43—22no—
400Dic43—42no—
401Dic43—81no—
402Dic43—81no—
403C2×#447—431no—
404C4×#121—431no—
405C2×#390—431no—
406#1970—431no—
407#1970—431no—
408#1934—431no—
409#1934—431no—
410#1925—431no—
411#1925—431no—
412#1879—431no—
413#1879D4311yescharacteristic, complemented
414#1874—431no—
415#1852—431no—
416#1786—431no—
417C4×C22⋊C8—431no—
418C2×C43—82no—
419C2×C43—82no—
420C2×C43#232111yescharacteristic
421C2×C43C2×C4×D811yescharacteristic
422C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C43#318611yescharacteristic
424C2×C43#318811yescharacteristic
425C2×C43#320511yescharacteristic
426C2×C43#321111yescharacteristic
427D43—24no—
428D43—82no—
429C23×D4—431no—
430C22×D8—431no—
431C22×D8C2×D4311yescharacteristic
432C2×#121—431no—
433C2×C4×D4—861no—
434C2×C4×D4C2×D4311yescharacteristic, complemented
435C22×C4⋊C4—431no—
436C22×C22⋊C4—861no—
437C22×C22⋊C4—861no—
438C22×C42—431no—
439#447—438no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102C2×D4311yescharacteristic
449C2×#102C2×D4311yescharacteristic, complemented
450C2×C22⋊C8—431no—
451C2×C22⋊C8—431no—
452C2×C4×C8—431no—
453C2×C4×C8—431no—
454#390—431no—
455#390—431no—
456#390—431no—
457#390—431no—
458#390—861no—
459#390—861no—
460#390C2×D4311yescharacteristic
461#389—431no—
462#388—861no—
463#386—861no—
464#380—431no—
465C4×C4⋊C4—431no—
466C4×C22⋊C4—861no—
467#340—431no—
468#340—431no—
469#340—431no—
470#340C2×D4311yescharacteristic, complemented
471#336—431no—
472#336C2×D4311yescharacteristic, complemented
473C43#2204011yescharacteristic, complemented, Sylow
474C25—861no—
475C22×D4—434no—
476C22×D4—431no—
477C22×D4—862no—
478C22×D4—861no—
479C22×D4—861no—
480C22×D4—1721no—
481C22×D4—1721no—
482C22×D4—1721no—
483C22×D4—1721no—
484C22×D4C22×D4311yescharacteristic
485C22×D4C22×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—861no—
491C2×D8—41no—
492C2×D8—41no—
493C2×D8—434no—
494C2×D8—1721no—
495C2×D8—1721no—
496C2×D8C4×D4314yescomplemented
497C22×C8—431no—
498C22×C8—431no—
499C22×C8C22×D4311yescharacteristic
500C22×C8C22×D4311yescharacteristic
501#121—434no—
502#121—862no—
503C4×D4—41no—
504C4×D4—41no—
505C4×D4—1724no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—1721no—
512C2×C4⋊C4—1721no—
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—1724no—
529C2×C22⋊C4—1724no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—431no—
533C2×C42—861no—
534C2×C42—1721no—
535C2×C42—1721no—
536C2×C42C22×D4311yescharacteristic
537#107—1721no—
538#107—1721no—
539#102—41no—
540#102—41no—
541#102—434no—
542#102—434no—
543#102—1721no—
544#102—1721no—
545#102—1721no—
546#102—1721no—
547C22⋊C8—434no—
548C22⋊C8—862no—
549C4×C8—1721no—
550C4×C8—1721no—
551#95—861no—
552#95—861no—
553#95—861no—
554C24—21no—
555C24—21no—
556C24—431no—
557C24—864no—
558C24—861no—
559C24—1722no—
560C24—1722no—
561C24—1722no—
562C24—1722no—
563C24—1722no—
564C24—1722no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—861no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—1724no—
584C2×D4—1724no—
585C2×D4—1724no—
586C2×D4—1724no—
587C2×D4—1722no—
588C2×D4—1722no—
589C2×D4—1722no—
590C2×D4—1722no—
591C2×D4C2×C4×D4312yes—
592C2×D4C2×C4×D4312yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—434no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—1721no—
614C22×C4—1721no—
615C22×C4—1721no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4D4×D4311yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4C23×D4311yescharacteristic
622D8—44no—
623D8—1724no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—432no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8C2×C4×D4312yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—432no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—1722no—
647C4⋊C4—1722no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—864no—
652C22⋊C4—1722no—
653C22⋊C4—1722no—
654C22⋊C4—1722no—
655C22⋊C4—1722no—
656C22⋊C4—1722no—
657C22⋊C4—1722no—
658C22⋊C4—1722no—
659C22⋊C4—1722no—
660C22⋊C4—1722no—
661C42—21no—
662C42—21no—
663C42—861no—
664C42—861no—
665C42—1721no—
666C42—1721no—
667C42—1722no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—432no—
683C23—432no—
684C23—432no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—862no—
690C23—3444no—
691C23—3444no—
692C23—3444no—
693C23—3444no—
694C23—1728no—
695C23—1728no—
696C23—1728no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23C2×D4×D4311yescharacteristic
704D4—22no—
705D4—22no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—862no—
713D4—862no—
714D4—1728no—
715D4—1728no—
716D4—1721no—
717D4—1721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—3444no—
745C2×C4—1724no—
746C2×C4—1724no—
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×C4D8×D4312yes—
756C2×C4C22×C4×D4311yescharacteristic
757C2×C4#41×D4311yescharacteristic
758C2×C4#1306337011yescharacteristic
759C2×C4#1306337011yescharacteristic
760C2×C4#1306337011yescharacteristic
761C2×C4#1306337111yescharacteristic
762C8—22no—
763C8—41no—
764C8—862no—
765C8—1721no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—434no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—34416no—
788C22—3441no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22C4×D4×D4311yescharacteristic
796C22#1458345911yescharacteristic
797C22#1458346511yescharacteristic
798C22C2×D8×D4311yescharacteristic
799C22#135×D4311yescharacteristic
800C22AGL(1,ℤ/8)×D4311yescharacteristic
801C22#1458369511yescharacteristic
802C4—22no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—862no—
807C4—862no—
808C4—862no—
809C4—3441no—
810C4—3441no—
811C4—1722no—
812C4#1458337111yescharacteristic
813C4#1458337211yescharacteristic
814C4#1458348111yescharacteristic
815C4#1458348511yescharacteristic
816C2—82no—
817C2—82no—
818C2—864no—
819C2—3442no—
820C2#1913725111yescharacteristic
821C2C4×D8×D4311yescharacteristic
822C2#1914340611yescharacteristic
823C2#1914534411yescharacteristic
824C2#1914535811yescharacteristic
825C2#1914551211yescharacteristic
826C2#1914555811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#22040
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C4×#13063296C2semidirect
3. #390×D43C2semidirect
4. #19135462C2semidirect
5. #19135458C2semidirect
6. #19135276C2semidirect
7. #19135275C2semidirect
8. #19135216C2semidirect
9. #19135212C2semidirect
10. #19134943C2semidirect
11. #19134909C2semidirect
12. #19134784C2semidirect
13. #19134524C2semidirect
14. #19134352C2semidirect
15. C43×#1879C2semidirect
24. #14583031C4semidirect
25. C2×#13063259C22semidirect
26. C2×#13063258C22semidirect
31. C2×#13063246C22semidirect
35. C2×C8×Dic43C22semidirect
36. C2×C8×Dic43C22semidirect
38. #14582802C22semidirect
43. #14582795C22semidirect
47. C4×C4⋊Dic43C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582654C22semidirect
54. C2×C4×D4×C43C22semidirect
56. C2×#102×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
69. C2×D4×D43C2×C4semidirect
76. C2×#10621882C2×C4semidirect
110. #13063247C2×C4semidirect
113. #13063246C2×C4semidirect
116. (C2×D43)⋊C8C2×C4semidirect
127. C2×D8×C43C2×C4semidirect
205. C2×C4×D43D8semidirect
413. #1879D43semidirect
434. C2×C4×D4C2×D43semidirect
449. C2×#102C2×D43semidirect
470. #340C2×D43semidirect
472. #336C2×D43semidirect
473. C43#22040semidirect
496. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830312
C4×#130632962
#390×D432
#191354622
#191354582
#191352762
#191352752
#191352162
#191352122
#191349432
#191349092
#191347842
#191345242
#191343522
C43×#18792
#2204043