Finite Group Databasebeta

← #25116908

Subgroups — #25116908

Order 11008.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583031C211yesmaximal, characteristic
2C2×#102×D43C211yesmaximal, characteristic, complemented
3#19137607C211yesmaximal, characteristic, complemented
4D4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5#19135468C211yesmaximal, characteristic, complemented
6#19135292C211yesmaximal, characteristic, complemented
7#19135221C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134786C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C2×C43×#442C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22C2×C4⋊C4×D43C2211yescharacteristic
23C22×(C2×D43)⋊C4—21no—
24#14583031C418yescomplemented
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic, complemented
31C2×#13063245C2211yescharacteristic
32#102×D43—24no—
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063235C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic, complemented
36#14582801C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582797C2211yescharacteristic, complemented
39#14582793—21no—
40#14582778—21no—
41#14582776—21no—
42#14582775—21no—
43#14582772—21no—
44#14582756C2211yescharacteristic
45#14582754—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47C4×(C2×D43)⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C22×D8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic, complemented
57C43×#442—24no—
58C2×#106×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic, complemented
61C2×#97×C43C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—41no—
70C2×D4×D43—41no—
71C2×D4×D43C2×C414yescomplemented
72C23×Dic43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621882—41no—
76C2×#10621882—41no—
77C2×#10621882C2×C414yescomplemented
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—22no—
81C2×C8×D43—22no—
82C2×C8×D43—41no—
83#13063296—22no—
84#13063296C2×C414yescomplemented
85D4×Dic43—22no—
86D4×Dic43—41no—
87C4×C22⋊D43—44no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43—41no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—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)⋊C4—44no—
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109#13063256—41no—
110#13063247—22no—
111#13063247C2×C414yescomplemented
112#13063246—22no—
113#13063246—41no—
114#13063246C2×C414yescomplemented
115#13063245—22no—
116(C2×D43)⋊C8C2×C414yescomplemented
117#13063235—41no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95D411yescharacteristic
122C43⋊#95D411yescharacteristic
123C22×D4×C43C2311yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43—21no—
126C23×C4×C43—21no—
127C2×D8×C43—22no—
128C2×D8×C43—22no—
129C2×D8×C43C2×C414yescomplemented
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C4×D4×C43—41no—
135C4×D4×C43—41no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#106×C43—22no—
142#102×C43—22no—
143#102×C43D414yescomplemented
144#97×C43—22no—
145C24×C43—21no—
146C24×C43—21no—
147C23×D43—21no—
148C23×D43—24no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43—81no—
154C23×D43—81no—
155C23×D43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43C22×C412yes—
165C2×D4×C43C22×C412yes—
166C2×D4×C43C2×D412yes—
167C2×D4×C43#4112yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—42no—
171C22×C4×C43—42no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43—81no—
175C22×C4×C43—81no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—81no—
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194D4×D43—28no—
195D4×D43—44no—
196D4×D43—44no—
197D4×D43—44no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172C22×C412yes—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—81no—
211C2×C4×D43C22×C412yes—
212C2×C4×D43#4112yes—
213D8×C43—28no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43C22×C412yes—
219C2×C8×C43C2×D412yes—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43C2×D412yes—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C42×C43—21no—
227C42×C43—21no—
228C22⋊Dic43—24no—
229C22⋊Dic43—42no—
230C22⋊Dic43—42no—
231C22⋊Dic43—81no—
232#10621882—44no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—22no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—81no—
239(C2×D43)⋊C4—81no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43C22×C412yes—
246Dic43⋊C4—42no—
247Dic43⋊C4—42no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—42no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C22×C412yes—
257C8×D43—44no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
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—41no—
272C23×C43C22×D411yescharacteristic
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—22no—
278C22×D43—48no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—48no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43—84no—
291C22×D43C4×D412yes—
292C22×D43AGL(1,ℤ/8)12yes—
293C22×D43AGL(1,ℤ/8)12yes—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43C4×D414yescomplemented
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—84no—
315C2×C4×C43—84no—
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C22⋊D43—48no—
323C22⋊D43—48no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—22no—
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—84no—
342C2×Dic43C4×D412yes—
343D172—22no—
344D172—22no—
345D172—41no—
346D172—41no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—84no—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#22858—431nomaximal, Sylow
357C22×C43—24no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43C2×C4×D411yescharacteristic
372C22×C43D4211yescharacteristic
373C22×C43#54611yescharacteristic
374C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C43#57611yescharacteristic
377C22×C43#57711yescharacteristic
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—816no—
388C2×D43—81no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C2×D43#44214yescomplemented
393C4×C43—42no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—81no—
397C4×C43C2×C4×D411yescharacteristic
398C4×C43#51811yescharacteristic
399C4×C43#54611yescharacteristic
400C4×C43#55111yescharacteristic
401Dic43—22no—
402Dic43—42no—
403Dic43—41no—
404Dic43—41no—
405Dic43—81no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442D4311yescharacteristic, complemented
409C22×#102—431no—
410#2361—431no—
411D4×C22⋊C4—431no—
412#1972—431no—
413#1936—431no—
414#1926—431no—
415#1893—431no—
416#1879—431no—
417#1879—431no—
418#1864—431no—
419#1853—431no—
420#1762—431no—
421#1752—431no—
422C2×C43—44no—
423C2×C43—82no—
424C2×C43#235811yescharacteristic
425C2×C43C2×#44211yescharacteristic
426C2×C43#294611yescharacteristic
427C2×C43#326411yescharacteristic
428C2×C43#326511yescharacteristic
429C2×C43#330611yescharacteristic
430C2×C43#331811yescharacteristic
431D43—24no—
432D43—82no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8C2×D4311yescharacteristic
436C23×C8—431no—
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—861no—
440C2×C4×D4C2×D4311yescharacteristic
441C2×C4×D4C2×D4311yescharacteristic, complemented
442C22×C4⋊C4—431no—
443C22×C22⋊C4—861no—
444#447—438no—
445#442—24no—
446C2×#106—431no—
447C2×#106C2×D4311yescharacteristic, complemented
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—864no—
455C2×#102C2×D4311yescharacteristic
456C2×#102C2×D4311yescharacteristic, complemented
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97C2×D4311yescharacteristic, complemented
460#390—431no—
461#390—431no—
462#390—431no—
463#389—431no—
464#388—861no—
465#386—861no—
466#386—861no—
467#386—861no—
468#385—861no—
469#380—431no—
470#379—861no—
471C4×C4⋊C4—431no—
472C4×C22⋊C4—431no—
473#340—431no—
474#340—431no—
475#340—431no—
476#340—431no—
477#336—431no—
478#336—431no—
479C43#2285811yescharacteristic, complemented, Sylow
480C25—861no—
481C22×D4—434no—
482C22×D4—431no—
483C22×D4—862no—
484C22×D4—861no—
485C22×D4—862no—
486C22×D4—862no—
487C22×D4—861no—
488C22×D4—1721no—
489C22×D4—1721no—
490C22×D4C22×D4311yescharacteristic
491C22×D4C22×D4311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—431no—
495C23×C4—861no—
496C23×C4—861no—
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—434no—
500C2×D8—1721no—
501C2×D8—1721no—
502C2×D8C4×D4314yescomplemented
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—862no—
506C22×C8—862no—
507C22×C8—1721no—
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510#121—434no—
511#121—862no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—862no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—1721no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—1724no—
542C2×C42—431no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#106—22no—
546#106—1721no—
547#102—22no—
548#102—434no—
549#102—434no—
550#102—862no—
551#102—862no—
552#102—862no—
553#102—1721no—
554#102C22⋊D4314yescomplemented
555C22⋊C8—434no—
556#97—22no—
557#97—1721no—
558#95—431no—
559#95—431no—
560#95—861no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—21no—
565C24—431no—
566C24—864no—
567C24—861no—
568C24—3441no—
569C24—3441no—
570C24—1722no—
571C24—1722no—
572C24—1722no—
573C24—1722no—
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—432no—
583C2×D4—864no—
584C2×D4—868no—
585C2×D4—864no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—1724no—
592C2×D4—1724no—
593C2×D4—1724no—
594C2×D4—1722no—
595C2×D4—1722no—
596C2×D4—1722no—
597C2×D4—1722no—
598C2×D4C2×C4×D4312yes—
599C2×D4C2×C4×D4312yes—
600C2×D4#1062189812yes—
601C2×D4C2×C22⋊D4312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—431no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—3441no—
623C22×C4—3441no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4D4×D4311yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4C23×D4311yescharacteristic
631D8—28no—
632D8—1724no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—432no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—1724no—
644C2×C8C2×C4×D4312yes—
645C2×C8C2×C22⋊D4312yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—432no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—1722no—
656C4⋊C4—1722no—
657C4⋊C4C2×C22⋊D4312yes—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—862no—
661C22⋊C4—862no—
662C22⋊C4—864no—
663C22⋊C4—3441no—
664C22⋊C4—3441no—
665C22⋊C4—3441no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—21no—
672C42—21no—
673C42—861no—
674C42—861no—
675C42—1722no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—432no—
691C23—432no—
692C23—432no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—862no—
698C23—3444no—
699C23—3444no—
700C23—3444no—
701C23—3444no—
702C23—3444no—
703C23—1728no—
704C23—1728no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23—1721no—
709C23—1721no—
710C23—1721no—
711C23C2×D4×D4311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—41no—
718D4—41no—
719D4—862no—
720D4—862no—
721D4—1728no—
722D4—1728no—
723D4—1721no—
724D4—1721no—
725D4C4×C22⋊D4314yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—432no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—3444no—
755C2×C4—3444no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C22×C22⋊D4311yescharacteristic
766C2×C4#41×D4311yescharacteristic
767C2×C4C2×#1062189811yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337111yescharacteristic
770C8—22no—
771C8—22no—
772C8—862no—
773C8—1721no—
774C22—24no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—434no—
789C22—862no—
790C22—862no—
791C22—862no—
792C22—862no—
793C22—862no—
794C22—862no—
795C22—34416no—
796C22—3441no—
797C22—3441no—
798C22—3441no—
799C22—3441no—
800C22—1722no—
801C22—1722no—
802C22—1722no—
803C22C4×D4×D4311yescharacteristic
804C22D4×C22⋊D4311yescharacteristic
805C22#1458354511yescharacteristic
806C22AGL(1,ℤ/8)×D4311yescharacteristic
807C22AGL(1,ℤ/8)×D4311yescharacteristic
808C22#1458370311yescharacteristic
809C22#1458370911yescharacteristic
810C4—41no—
811C4—42no—
812C4—41no—
813C4—81no—
814C4—862no—
815C4—3441no—
816C4—3441no—
817C4—1721no—
818C4—1722no—
819C4—1721no—
820C4C2×C4×C22⋊D4311yescharacteristic
821C4#1458337111yescharacteristic
822C4#1458353711yescharacteristic
823C4#1458357811yescharacteristic
824C2—44no—
825C2—82no—
826C2—864no—
827C2—3442no—
828C2#1913757211yescharacteristic
829C2#442×D4311yescharacteristic
830C2#1914342411yescharacteristic
831C2#1914606911yescharacteristic
832C2#1914608411yescharacteristic
833C2#1914656111yescharacteristic
834C2#1914674111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenterC2×#442D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#102×D43C2semidirect
3. #19137607C2semidirect
4. D4×(C2×D43)⋊C4C2semidirect
5. #19135468C2semidirect
6. #19135292C2semidirect
7. #19135221C2semidirect
8. #19135020C2semidirect
9. #19134945C2semidirect
10. #19134943C2semidirect
11. #19134856C2semidirect
12. #19134786C2semidirect
13. #19134422C2semidirect
14. #19134372C2semidirect
15. C2×C43×#442C2semidirect
24. #14583031C4semidirect
25. C2×#13063256C22semidirect
30. C2×#13063246C22semidirect
34. C2×#13063235C22semidirect
35. #14582802C22semidirect
38. #14582797C22semidirect
46. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582654C22semidirect
53. #14582653C22semidirect
56. C2×C4×D4×C43C22semidirect
58. C2×#106×C43C22semidirect
60. C2×#102×C43C22semidirect
61. C2×#97×C43C22semidirect
71. C2×D4×D43C2×C4semidirect
77. C2×#10621882C2×C4semidirect
84. #13063296C2×C4semidirect
111. #13063247C2×C4semidirect
114. #13063246C2×C4semidirect
116. (C2×D43)⋊C8C2×C4semidirect
129. C2×D8×C43C2×C4semidirect
143. #102×C43D4semidirect
301. D4×C43C4×D4semidirect
392. C2×D43#442semidirect
408. C2×#442D43semidirect
441. C2×C4×D4C2×D43semidirect
447. C2×#106C2×D43semidirect
456. C2×#102C2×D43semidirect
459. C2×#97C2×D43semidirect
479. C43#22858semidirect
502. C2×D8C4×D43semidirect
554. #102C22⋊D43semidirect
725. D4C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830312
C2×#102×D432
#191376072
D4×(C2×D43)⋊C42
#191354682
#191352922
#191352212
#191350202
#191349452
#191349432
#191348562
#191347862
#191344222
#191343722
C2×C43×#4422
#2285843