Finite Group Databasebeta

← #25116918

Subgroups — #25116918

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×#14583011C211yesmaximal, characteristic, complemented
2C22×#13063246C211yesmaximal, characteristic, complemented
3#19137615C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19135472C211yesmaximal, characteristic, complemented
6#19135294C211yesmaximal, characteristic, complemented
7#19135224C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134790C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134374C211yesmaximal, characteristic, complemented
15C2×C43×#447C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×D4×Dic43—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic, complemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43—21no—
23#14583011—24no—
24C2×#13063257C2211yescharacteristic, complemented
25C2×#13063257C2211yescharacteristic, complemented
26C2×#13063246—24no—
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic, complemented
33C2×#13063235C2211yescharacteristic, complemented
34C2×#13063235C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic, complemented
38#14582798C2211yescharacteristic, complemented
39#14582792—21no—
40#14582779—21no—
41#14582779—21no—
42#14582779—21no—
43#14582774—21no—
44#14582759C2211yescharacteristic
45#14582755—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
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—
65C23×Dic43—21no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—22no—
68C22×C43⋊C8—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71D4×Dic43—22no—
72D4×Dic43—22no—
73D4×Dic43—22no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76D4×Dic43—41no—
77D4×Dic43—44no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
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—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—44no—
97C2×C22⋊Dic43D411yescharacteristic
98C2×C22⋊Dic43D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063257—22no—
103#13063257—41no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—41no—
109#13063246D414yescomplemented
110#13063235—22no—
111#13063235—41no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C25×C43—21no—
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—21no—
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
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C2×D8×C43—22no—
131C2×D8×C43—22no—
132C2×D8×C43—41no—
133C2×D8×C43—41no—
134C2×D8×C43C2×C414yescomplemented
135C2×D8×C43C2×C414yescomplemented
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#121×C43—22no—
139#121×C43C2×C414yescomplemented
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142#102×C43C2×C414yescomplemented
143#102×C43C2×C414yescomplemented
144C22⋊C8×C43C2×C414yescomplemented
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—21no—
148C24×C43—24no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—42no—
152C24×C43—42no—
153C24×C43—81no—
154C24×C43—81no—
155C24×C43C2×D411yescharacteristic
156C2×D4×C43—24no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—24no—
163C2×D4×C43—28no—
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—21no—
172C2×D4×C43—42no—
173C2×D4×C43—42no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43—44no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43C22×C412yes—
180C2×D4×C43C22×C412yes—
181C2×D4×C43C22×C412yes—
182C2×D4×C43C2×D412yes—
183C2×D4×C43#4112yes—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43#4112yes—
192C22×C4×C43C2411yescharacteristic
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—81no—
206C22×Dic43—81no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213D8×C43—28no—
214D8×C43—44no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43C22×C412yes—
220C2×C8×C43C22×C412yes—
221C4⋊C4×C43—21no—
222C4⋊C4×C43C22×C412yes—
223C22⋊C4×C43—24no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228C22⋊Dic43—42no—
229C22⋊Dic43—42no—
230C22⋊Dic43—42no—
231C22⋊Dic43—42no—
232C22⋊Dic43—42no—
233C22⋊Dic43—81no—
234C22⋊Dic43—81no—
235C22⋊Dic43—81no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—42no—
244C4⋊Dic43—42no—
245C4⋊Dic43C2×D412yes—
246C4×Dic43—21no—
247C4×Dic43—21no—
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⋊C8—44no—
257C2×C43⋊C8C2×D412yes—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—22no—
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—48no—
285C23×C43—84no—
286C23×C43—84no—
287C23×C43—84no—
288C23×C43—84no—
289C23×C43—84no—
290C23×C43C4×D412yes—
291C23×C43AGL(1,ℤ/8)12yes—
292C23×C43AGL(1,ℤ/8)12yes—
293C23×C43C22×D411yescharacteristic
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—48no—
302D4×C43—48no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43C4×D414yescomplemented
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43C4×D412yes—
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
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—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—84no—
349C2×Dic43—84no—
350C2×Dic43—84no—
351C2×Dic43—84no—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#22858—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—24no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—816no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43#44214yescomplemented
386C22×C43C2×C4×D411yescharacteristic
387C22×C43D4211yescharacteristic
388C22×C43#54611yescharacteristic
389C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
391C22×C43#57611yescharacteristic
392C22×C43#57711yescharacteristic
393C4×C43—22no—
394C4×C43—42no—
395C4×C43C2×C4×D411yescharacteristic
396C4×C43#51811yescharacteristic
397C4×C43#54611yescharacteristic
398C4×C43#55111yescharacteristic
399Dic43—41no—
400Dic43—42no—
401Dic43—41no—
402Dic43—41no—
403Dic43—41no—
404Dic43—81no—
405Dic43—81no—
406Dic43—81no—
407C2×#447D4311yescharacteristic
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#1762—431no—
421#1752—431no—
422C2×C43—24no—
423C2×C43—44no—
424C2×C43—82no—
425C2×C43—82no—
426C2×C43#235811yescharacteristic
427C2×C43C2×#44211yescharacteristic
428C2×C43#294611yescharacteristic
429C2×C43#326411yescharacteristic
430C2×C43#326511yescharacteristic
431C2×C43#330611yescharacteristic
432C2×C43#331811yescharacteristic
433C23×D4C2×D4311yescharacteristic
434C22×D8C2×D4311yescharacteristic
435C22×D8C2×D4311yescharacteristic
436C23×C8—431no—
437C2×#121C2×D4311yescharacteristic
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C22⋊C4—861no—
444#447Dic4318yescomplemented
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⋊C8C2×D4311yescharacteristic
458C2×#97—431no—
459C2×#97—431no—
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—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—22no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C2×Dic4314yescomplemented
489C22×D4C22×D4311yescharacteristic
490C22×D4C22×D4311yescharacteristic
491C22×D4C22×D4311yescharacteristic
492C23×C4—861no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×Dic4314yescomplemented
502C2×D8C2×Dic4314yescomplemented
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—862no—
506C22×C8—862no—
507C22×C8—1721no—
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510#121—22no—
511#121C2×Dic4314yescomplemented
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1721no—
516C4×D4—1721no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—862no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—1721no—
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—431no—
543C2×C42—431no—
544C2×C42—861no—
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#102C2×Dic4314yescomplemented
554#102C2×Dic4314yescomplemented
555C22⋊C8C2×Dic4314yescomplemented
556#97—862no—
557#97—1721no—
558#95—431no—
559#95—431no—
560#95—861no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24D4×D4311yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
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—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4D4×D4312yes—
598C2×D4#1062190012yes—
599C2×D4C22×Dic4312yes—
600C2×D4C22×Dic4312yes—
601C2×D4C22×Dic4312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—3441no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4—3441no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4D4×D4311yescharacteristic
628C22×C4#1062190012yes—
629C22×C4C22×Dic4312yes—
630C22×C4C23×D4311yescharacteristic
631D8—28no—
632D8—44no—
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×C8C22×Dic4312yes—
645C2×C8C22×Dic4312yes—
646C4⋊C4—21no—
647C4⋊C4—432no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—1722no—
656C4⋊C4—1722no—
657C4⋊C4C22×Dic4312yes—
658C22⋊C4—24no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—3441no—
662C22⋊C4—3441no—
663C22⋊C4—3441no—
664C22⋊C4—1722no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—861no—
672C42—861no—
673C42—861no—
674C42—861no—
675C42—1722no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—48no—
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—48no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23D4×Dic4312yes—
709C23#1306334912yes—
710C23#1306334912yes—
711C23C2×D4×D4311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4D4×Dic4314yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
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—861no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—3444no—
749C2×C4—3444no—
750C2×C4—3444no—
751C2×C4—3444no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4D4×Dic4312yes—
764C2×C4C23×Dic4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4C2×#1062190011yescharacteristic
767C2×C4C2×#1062190011yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337011yescharacteristic
770C8—22no—
771C8—22no—
772C8—862no—
773C8—1721no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22#1458301114yescomplemented
803C22C2×D4×Dic4311yescharacteristic
804C22#1458353111yescharacteristic
805C22#1458353611yescharacteristic
806C22C2×#1306334911yescharacteristic
807C22C2×#1306334911yescharacteristic
808C22#1458370311yescharacteristic
809C22#1458370911yescharacteristic
810C4—22no—
811C4—42no—
812C4—3441no—
813C4—3441no—
814C4—3441no—
815C4—1721no—
816C4—1721no—
817C4—1722no—
818C4—1721no—
819C4—1721no—
820C4C2×D4×Dic4311yescharacteristic
821C4#1458337411yescharacteristic
822C4#1458353611yescharacteristic
823C4#1458358011yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2#1913757911yescharacteristic
829C2C2×#1458301111yescharacteristic
830C2#1914342811yescharacteristic
831C2#1914606811yescharacteristic
832C2#1914609411yescharacteristic
833C2#1914656011yescharacteristic
834C2#1914674011yescharacteristic
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#22858
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×#14583011C2semidirect
2. C22×#13063246C2semidirect
3. #19137615C2semidirect
4. D4×C22⋊Dic43C2semidirect
5. #19135472C2semidirect
6. #19135294C2semidirect
7. #19135224C2semidirect
8. #19135024C2semidirect
9. #19134945C2semidirect
10. #19134945C2semidirect
11. #19134858C2semidirect
12. #19134790C2semidirect
13. #19134422C2semidirect
14. #19134374C2semidirect
20. C2×D4×Dic43C22semidirect
24. C2×#13063257C22semidirect
25. C2×#13063257C22semidirect
31. C2×#13063246C22semidirect
32. C2×#13063246C22semidirect
33. C2×#13063235C22semidirect
34. C2×#13063235C22semidirect
37. #14582802C22semidirect
38. #14582798C22semidirect
46. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
58. C43×#447C4semidirect
109. #13063246D4semidirect
125. C22×D4×C43C2×C4semidirect
134. C2×D8×C43C2×C4semidirect
135. C2×D8×C43C2×C4semidirect
139. #121×C43C2×C4semidirect
142. #102×C43C2×C4semidirect
143. #102×C43C2×C4semidirect
144. C22⋊C8×C43C2×C4semidirect
307. D4×C43C4×D4semidirect
385. C22×C43#442semidirect
444. #447Dic43semidirect
479. C43#22858semidirect
488. C22×D4C2×Dic43semidirect
501. C2×D8C2×Dic43semidirect
502. C2×D8C2×Dic43semidirect
511. #121C2×Dic43semidirect
553. #102C2×Dic43semidirect
554. #102C2×Dic43semidirect
555. C22⋊C8C2×Dic43semidirect
725. D4D4×Dic43semidirect
802. C22#14583011semidirect

Maximal subgroups

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

subgroupindex
C2×#145830112
C22×#130632462
#191376152
D4×C22⋊Dic432
#191354722
#191352942
#191352242
#191350242
#191349452
#191348582
#191347902
#191344222
#191343742
C2×C43×#4472
#2285843