Finite Group Databasebeta

← #25116916

Subgroups — #25116916

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×#14583034C211yesmaximal, characteristic
2C2×#14583008C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic, complemented
4#19137613C211yesmaximal, characteristic, complemented
5D4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6#19135471C211yesmaximal, characteristic, complemented
7#19135293C211yesmaximal, characteristic, complemented
8#19135222C211yesmaximal, characteristic, complemented
9#19135022C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134858C211yesmaximal, characteristic, complemented
13#19134789C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063300C2211yescharacteristic
21C2×C4×D172—21no—
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063287C2211yescharacteristic, complemented
24C2×C4⋊C4×D43C2211yescharacteristic
25C22×(C2×D43)⋊C4—21no—
26#14583034C418yescomplemented
27#14583008—24no—
28C2×#13063257C2211yescharacteristic, complemented
29C2×#13063256C2211yescharacteristic, complemented
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic, complemented
36#102×D43—24no—
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic, complemented
41#14582800C2211yescharacteristic
42#14582798C2211yescharacteristic, complemented
43#14582790—21no—
44#14582778—21no—
45#14582777—21no—
46#14582776—21no—
47#14582773—21no—
48#14582756C2211yescharacteristic
49#14582754—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582654C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic, complemented
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172—21no—
64C22×D172C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—41no—
71C2×D4×D43—41no—
72C2×D4×D43C2×C414yescomplemented
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×D344—41no—
78C2×D344—41no—
79C2×D344C2×C414yescomplemented
80C2×#10621882—22no—
81C2×#10621882—22no—
82C2×#10621882C2×C414yescomplemented
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—22no—
86C2×C8×D43—22no—
87C2×C8×D43—41no—
88#13063300—22no—
89#13063300C2×C414yescomplemented
90C4×D172—44no—
91D4×Dic43—22no—
92D4×Dic43—41no—
93#13063287—22no—
94#13063287—41no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—41no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—44no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115#13063257—41no—
116#13063256—22no—
117#13063247—22no—
118#13063247—22no—
119#13063246—22no—
120#13063245—22no—
121#13063245—41no—
122#13063245C2×C414yescomplemented
123(C2×D43)⋊C8C2×C414yescomplemented
124#13063235—22no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95D411yescharacteristic
128C43⋊#95D411yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C4×D4×C43—22no—
134C4×D4×C43—41no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#102×C43C2×C414yescomplemented
142#102×C43D414yescomplemented
143#97×C43—41no—
144#95×C43—21no—
145C24×C43—21no—
146C23×D43—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×C43C22×C412yes—
160C2×D4×C43C2×D412yes—
161C2×D4×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—81no—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—42no—
173C2×C22⋊D43—42no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—81no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182D4×D43—28no—
183D4×D43—44no—
184D4×D43—44no—
185D4×D43—44no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—24no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—42no—
198C2×D172—42no—
199C2×D172C22×C412yes—
200C2×D172C22×C412yes—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—81no—
210C2×C4×D43—81no—
211C2×C4×D43C22×C412yes—
212C2×C4×D43#4112yes—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C22×C412yes—
218C2×C8×C43C2×D412yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43C22×C412yes—
224C4⋊C4×C43C2×D412yes—
225C22⋊C4×C43—42no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—42no—
229C22⋊Dic43—42no—
230#10621882—28no—
231(C2×D43)⋊C4—24no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—81no—
240(C2×D43)⋊C4—81no—
241(C2×D43)⋊C4—81no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—42no—
247Dic43⋊C4—42no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256D344—44no—
257C8×D43—44no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43C22×D411yescharacteristic
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—48no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
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×C43C4×D414yescomplemented
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—84no—
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C22⋊D43—48no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—84no—
336C2×Dic43C4×D412yes—
337D172—22no—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—48no—
342D172—41no—
343D172—41no—
344D172—41no—
345D172—41no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—84no—
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×C43C2×C4×D411yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43#54611yescharacteristic
367C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C43#57611yescharacteristic
370C22×C43#57711yescharacteristic
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
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×D43—81no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C2×D43#44214yescomplemented
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43—81no—
398C4×C43C2×C4×D411yescharacteristic
399C4×C43#51811yescharacteristic
400C4×C43#54611yescharacteristic
401C4×C43#55111yescharacteristic
402Dic43—22no—
403Dic43—41no—
404Dic43—41no—
405Dic43—81no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
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#1762D4311yescharacteristic, complemented
421#1752—431no—
422C2×C43—44no—
423C2×C43#235811yescharacteristic
424C2×C43C2×#44211yescharacteristic
425C2×C43#294611yescharacteristic
426C2×C43#326411yescharacteristic
427C2×C43#326511yescharacteristic
428C2×C43#330611yescharacteristic
429C2×C43#331811yescharacteristic
430D43—24no—
431D43—82no—
432D43—82no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8—431no—
436C23×C8—431no—
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×C4×D4C2×D4311yescharacteristic
442C22×C4⋊C4—431no—
443C22×C22⋊C4—861no—
444#447—438no—
445#442—864no—
446C2×#106—431no—
447C2×#106—431no—
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
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⋊C4C2×D4311yescharacteristic, complemented
472C4×C22⋊C4—431no—
473#340—431no—
474#340—431no—
475#340C2×D4311yescharacteristic, complemented
476#340C2×D4311yescharacteristic, complemented
477#336—431no—
478#336—431no—
479C43#2285811yescharacteristic, complemented, Sylow
480C25—861no—
481C22×D4—434no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4—861no—
485C22×D4—862no—
486C22×D4—861no—
487C22×D4—862no—
488C22×D4—862no—
489C22×D4—1721no—
490C22×D4—1721no—
491C22×D4C22×D4311yescharacteristic
492C23×C4—21no—
493C23×C4—431no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—862no—
500C2×D8—862no—
501C2×D8—1721no—
502C2×D8—1721no—
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—41no—
514C4×D4—862no—
515C4×D4—862no—
516C4×D4—1724no—
517C4×D4—1721no—
518C4×D4—1721no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—862no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—1721no—
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—861no—
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—21no—
543C2×C42—431no—
544C2×C42C22×D4311yescharacteristic
545#106—862no—
546#106—1721no—
547#102—434no—
548#102—862no—
549#102—862no—
550#102—862no—
551#102—862no—
552#102—1721no—
553#102C4×D4314yescomplemented
554#102D17214yescomplemented
555C22⋊C8—434no—
556#97—41no—
557#97—862no—
558#95—21no—
559#95—431no—
560#95—431no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—431no—
565C24—864no—
566C24—861no—
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—432no—
578C2×D4—432no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—868no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—1722no—
593C2×D4—1722no—
594C2×D4—1724no—
595C2×D4—1724no—
596C2×D4—1724no—
597C2×D4—1722no—
598C2×D4—1722no—
599C2×D4C2×C4×D4312yes—
600C2×D4C2×D17212yes—
601C2×D4#1062189812yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—431no—
609C22×C4—432no—
610C22×C4—432no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—3441no—
620C22×C4—3441no—
621C22×C4—3441no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4D4×D4311yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4C23×D4311yescharacteristic
631D8—868no—
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×D17212yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—1722no—
655C4⋊C4—1722no—
656C4⋊C4C2×C4×D4312yes—
657C4⋊C4C2×D17212yes—
658C22⋊C4—42no—
659C22⋊C4—864no—
660C22⋊C4—862no—
661C22⋊C4—862no—
662C22⋊C4—3441no—
663C22⋊C4—3441no—
664C22⋊C4—3441no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—21no—
672C42—21no—
673C42—42no—
674C42—861no—
675C42—861no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—432no—
684C23—432no—
685C23—432no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—862no—
691C23—862no—
692C23—3444no—
693C23—3444no—
694C23—3444no—
695C23—3444no—
696C23—3444no—
697C23—1728no—
698C23—1728no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23—1721no—
709C23—1721no—
710C23—1721no—
711C23C2×D4×D4311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—862no—
716D4—862no—
717D4—862no—
718D4—862no—
719D4—1728no—
720D4—1728no—
721D4—1721no—
722D4—1721no—
723D4—1721no—
724D4—1721no—
725D4C4×D17214yescomplemented
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4—432no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—3444no—
756C2×C4—3444no—
757C2×C4—3444no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C22×D17211yescharacteristic
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—434no—
782C22—862no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—34416no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—3441no—
793C22—3441no—
794C22—3441no—
795C22—3441no—
796C22—3441no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22—1722no—
803C22C4×D4×D4311yescharacteristic
804C22D4×D17211yescharacteristic
805C22#1458353911yescharacteristic
806C22AGL(1,ℤ/8)×D4311yescharacteristic
807C22AGL(1,ℤ/8)×D4311yescharacteristic
808C22#1458370311yescharacteristic
809C22#1458370811yescharacteristic
810C4—41no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—81no—
815C4—862no—
816C4—3441no—
817C4—3441no—
818C4—1721no—
819C4—1721no—
820C4C2×C4×D17211yescharacteristic
821C4#1458337111yescharacteristic
822C4#1458354411yescharacteristic
823C4#1458357311yescharacteristic
824C2—44no—
825C2—864no—
826C2—3442no—
827C2—3442no—
828C2#1913757711yescharacteristic
829C2#442×D4311yescharacteristic
830C2#1914342611yescharacteristic
831C2#1914607711yescharacteristic
832C2#1914609211yescharacteristic
833C2#1914655711yescharacteristic
834C2#1914673711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583034C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. C2×#102×D43C2semidirect
4. #19137613C2semidirect
5. D4×(C2×D43)⋊C4C2semidirect
6. #19135471C2semidirect
7. #19135293C2semidirect
8. #19135222C2semidirect
9. #19135022C2semidirect
10. #19134944C2semidirect
11. #19134943C2semidirect
12. #19134858C2semidirect
13. #19134789C2semidirect
14. #19134372C2semidirect
15. C43×#1762C2semidirect
23. C2×#13063287C22semidirect
26. #14583034C4semidirect
28. C2×#13063257C22semidirect
29. C2×#13063256C22semidirect
31. C2×#13063247C22semidirect
35. C2×#13063245C22semidirect
38. C2×#13063235C22semidirect
40. #14582801C22semidirect
42. #14582798C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582654C22semidirect
54. #14582653C22semidirect
58. C2×#97×C43C22semidirect
59. C4×C4⋊C4×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
72. C2×D4×D43C2×C4semidirect
79. C2×D344C2×C4semidirect
82. C2×#10621882C2×C4semidirect
89. #13063300C2×C4semidirect
122. #13063245C2×C4semidirect
123. (C2×D43)⋊C8C2×C4semidirect
141. #102×C43C2×C4semidirect
142. #102×C43D4semidirect
297. D4×C43C4×D4semidirect
392. C2×D43#442semidirect
420. #1762D43semidirect
459. C2×#97C2×D43semidirect
471. C4×C4⋊C4C2×D43semidirect
475. #340C2×D43semidirect
476. #340C2×D43semidirect
479. C43#22858semidirect
553. #102C4×D43semidirect
554. #102D172semidirect
725. D4C4×D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145830342
C2×#145830082
C2×#102×D432
#191376132
D4×(C2×D43)⋊C42
#191354712
#191352932
#191352222
#191350222
#191349442
#191349432
#191348582
#191347892
#191343722
C43×#17622
#2285843