Finite Group Databasebeta

← #25112138

Subgroups — #25112138

Order 11008.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic, complemented
4#19137525C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135417C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134526C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic, complemented
16C23×C22⋊D43—21no—
17C22×D4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic, complemented
19D4×C22⋊D43—24no—
20D4×C22⋊D43C418yescomplemented
21C2×#13063321C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×#13063294—21no—
26C2×#13063293—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic, complemented
30#14582968—24no—
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32C2×#13063247C2211yescharacteristic, complemented
33C2×#13063247C2211yescharacteristic, complemented
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic, complemented
38C2×#13063245C2211yescharacteristic, complemented
39C2×#13063245C2211yescharacteristic, complemented
40#102×D43—24no—
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
43C2×#13063235C2211yescharacteristic, complemented
44#14582793—21no—
45#14582783—21no—
46#14582775—21no—
47#14582764C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic, complemented
49#14582756C2211yescharacteristic, complemented
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×(C2×D43)⋊C4—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C23×D4×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic, complemented
58C2×#117×C43C2211yescharacteristic, complemented
59C43×#418—24no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C2×#102×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43—28no—
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—44no—
73C22×C22⋊D43—44no—
74C22×C22⋊D43D411yescharacteristic
75C2×D4×D43—22no—
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—41no—
79C2×D4×D43—41no—
80C2×D4×D43C2×C414yes—
81C23×Dic43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C2×C8×D43—22no—
87C2×C8×D43—22no—
88C2×C8×D43—41no—
89#13063321—22no—
90#13063321C2×C414yescomplemented
91#13063299—22no—
92#13063299C2×C414yescomplemented
93#13063297—28no—
94#13063296—22no—
95#13063296C2×C414yes—
96#13063294—28no—
97#13063293—28no—
98D4×Dic43—22no—
99D4×Dic43C2×C414yescomplemented
100C4×C22⋊D43C2×C414yes—
101C4×C22⋊D43D414yes—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C4⋊C4×D43—22no—
108C4⋊C4×D43—41no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43D411yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4D411yescharacteristic
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119#13063247—22no—
120#13063247—41no—
121#13063246—22no—
122#13063246—22no—
123#13063246—41no—
124#13063246—41no—
125#13063245—22no—
126#13063245—41no—
127C22⋊(C43⋊C8)—22no—
128(C2×D43)⋊C8—22no—
129#13063235—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C25×C43—21no—
136C22×D4×C43—22no—
137C22×D4×C43—22no—
138C22×D4×C43—21no—
139C22×D4×C43—22no—
140C22×D4×C43—41no—
141C22×D4×C43—41no—
142C22×D4×C43C2×C414yescomplemented
143C22×D4×C43C2311yescharacteristic
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×M16×C43—22no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151#117×C43—22no—
152#117×C43—41no—
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156C2×C42×C43—21no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—22no—
160#102×C43D414yescomplemented
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—24no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43—42no—
168C24×C43—81no—
169C24×C43—81no—
170C24×C43C2×D411yescharacteristic
171C23×D43—21no—
172C23×D43—24no—
173C23×D43—42no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—42no—
177C23×D43—81no—
178C23×D43—81no—
179C23×D43C2×D411yescharacteristic
180C2×D4×C43—24no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—28no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—42no—
191C2×D4×C43—42no—
192C2×D4×C43—44no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43C22×C412yes—
196C2×D4×C43C22×C412yes—
197C2×D4×C43C2×D412yes—
198C2×D4×C43#4112yes—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43C22×C412yes—
206C22×C4×C43C2×D412yes—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—22no—
215C2×C22⋊D43—22no—
216C2×C22⋊D43—42no—
217C2×C22⋊D43—42no—
218C2×C22⋊D43—42no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—42no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—432no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—81no—
226C2×C22⋊D43—81no—
227C2×C22⋊D43C22⋊C414yes—
228C22×Dic43—24no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—42no—
233C22×Dic43—42no—
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236C22×Dic43C2×D411yescharacteristic
237D4×D43—28no—
238D4×D43—44no—
239D4×D43—44no—
240D4×D43—44no—
241C2×D172—21no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172C22×C412yes—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—42no—
252C2×C4×D43—42no—
253C2×C4×D43—81no—
254C2×C4×D43C22×C412yes—
255C2×C4×D43C2×D412yes—
256M16×C43—44no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43C2×D412yescomplemented
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C2×D412yescomplemented
267C22⋊C4×C43—42no—
268C42×C43—42no—
269C22⋊Dic43—24no—
270C22⋊Dic43—24no—
271C22⋊Dic43—81no—
272C22⋊Dic43C22⋊C414yes—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—42no—
275(C2×D43)⋊C4C22⋊C414yes—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43C22×C412yes—
282Dic43⋊C4—42no—
283Dic43⋊C4C22⋊C414yes—
284C4×Dic43—81no—
285C4×Dic43C22×C412yes—
286C4×Dic43C2×D412yes—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C8×D43—44no—
294C23×C43—22no—
295C23×C43—21no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—48no—
305C23×C43—48no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—84no—
317C23×C43—84no—
318C23×C43—84no—
319C23×C43—84no—
320C23×C43—84no—
321C23×C43C2×C22⋊C412yes—
322C23×C43C22×D411yescharacteristic
323C22×D43—21no—
324C22×D43—21no—
325C22×D43—21no—
326C22×D43—21no—
327C22×D43—22no—
328C22×D43—48no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—48no—
336C22×D43—84no—
337C22×D43—84no—
338C22×D43—84no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43C2×C22⋊C412yes—
342C22×D43AGL(1,ℤ/8)12yes—
343C22×D43AGL(1,ℤ/8)12yes—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—22no—
348D4×C43—22no—
349D4×C43—48no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43C4×D414yes—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43C2×C22⋊C412yes—
366C2×C4×C43C23×C411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43H(5,𝔽2)11yescharacteristic
371C2×C4×C43H(5,𝔽2)11yescharacteristic
372C22⋊D43—28no—
373C22⋊D43—48no—
374C22⋊D43—48no—
375C22⋊D43—48no—
376C22⋊D43—48no—
377C22⋊D43—84no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—22no—
385C2×Dic43—48no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43C2×C22⋊C412yes—
395C2×Dic43C2×C22⋊C412yes—
396C2×Dic43C2×C22⋊C412yes—
397D172—22no—
398D172—22no—
399D172—41no—
400D172—41no—
401C4×D43—22no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—84no—
406C8×C43—22no—
407C8×C43—41no—
408C43⋊C8—41no—
409C43⋊C8—41no—
410#22423—431nomaximal, Sylow
411C22×C43—24no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—41no—
419C22×C43—42no—
420C22×C43—41no—
421C22×C43—42no—
422C22×C43—41no—
423C22×C43—42no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—816no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43—81no—
432C22×C43—81no—
433C22×C43C22×C22⋊C411yescharacteristic
434C22×C43D4211yescharacteristic
435C22×C43#54611yescharacteristic
436C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
438C22×C43#57611yescharacteristic
439C22×C43#57711yescharacteristic
440C2×D43—22no—
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—22no—
445C2×D43—22no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—816no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43#41814yescomplemented
455C4×C43—22no—
456C4×C43—42no—
457C4×C43—81no—
458C4×C43C2×C4×D411yescharacteristic
459C4×C43#51811yescharacteristic
460C4×C43D4211yescharacteristic
461C4×C43#54611yescharacteristic
462Dic43—22no—
463Dic43—22no—
464Dic43—22no—
465Dic43—42no—
466Dic43—81no—
467Dic43—81no—
468C2×D42—431no—
469C2×#435—431no—
470C2×#418D4311yescharacteristic, complemented
471C22×#102—431no—
472#2352—431no—
473#1982—431no—
474#1961—431no—
475#1895—431no—
476#1893—431no—
477#1875—431no—
478#1874—431no—
479#1804—431no—
480#1786—431no—
481#1786—431no—
482#1762—431no—
483C2×C43—44no—
484C2×C43—42no—
485C2×C43—82no—
486C2×C43D4×C22⋊C411yescharacteristic
487C2×C43C2×#41811yescharacteristic
488C2×C43#289711yescharacteristic
489C2×C43#326411yescharacteristic
490C2×C43#326511yescharacteristic
491C2×C43#331011yescharacteristic
492C2×C43#331811yescharacteristic
493D43—24no—
494D43—82no—
495C23×D4—431no—
496C23×D4—861no—
497C23×D4C2×D4311yescharacteristic
498C22×M16C2×D4311yescharacteristic, complemented
499C23×C8—431no—
500D42—438no—
501D42—864no—
502C2×#127—431no—
503C2×#121—431no—
504C2×#121—431no—
505C2×#121—861no—
506C2×#120—861no—
507C2×#120—861no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×#117C2×D4311yescharacteristic, complemented
511C22×C4⋊C4—431no—
512#435—864no—
513C2×C4⋊C8—431no—
514#418—24no—
515C2×#102—431no—
516C2×#102—431no—
517C2×#102—431no—
518C2×#102—431no—
519C2×#102—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—864no—
524C2×#102C2×D4311yescharacteristic
525C2×#102C2×D4311yescharacteristic
526C2×#102C2×D4311yescharacteristic, complemented
527C2×#102C2×D4311yescharacteristic, complemented
528C2×C22⋊C8—431no—
529C2×C22⋊C8—431no—
530C2×#97—431no—
531#388—861no—
532#387—861no—
533#386—861no—
534#382—431no—
535#380—431no—
536#380—431no—
537C4×C4⋊C4—431no—
538C4×C22⋊C4—861no—
539#340—431no—
540#340—431no—
541#340—431no—
542#340—431no—
543C43#2242311yescharacteristic, complemented, Sylow
544C25—21no—
545C25—861no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—21no—
549C22×D4—22no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—431no—
553C22×D4—434no—
554C22×D4—431no—
555C22×D4—862no—
556C22×D4—861no—
557C22×D4—861no—
558C22×D4—861no—
559C22×D4—868no—
560C22×D4—862no—
561C22×D4—862no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—1721no—
565C22×D4—1721no—
566C22×D4—1724no—
567C22×D4—1724no—
568C22×D4C4×D4314yescomplemented
569C22×D4C22×D4311yescharacteristic
570C22×D4C22×D4311yescharacteristic
571C23×C4—431no—
572C23×C4—861no—
573C23×C4—861no—
574C23×C4C22×D4311yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—431no—
579C22×C8—431no—
580C22×C8—862no—
581C22×C8—862no—
582C22×C8—1721no—
583C22×C8C22×D4311yescharacteristic
584C22×C8C22×D4311yescharacteristic
585#127—434no—
586#127—862no—
587#121—434no—
588#121—434no—
589#121—868no—
590#121—862no—
591#121—862no—
592#120—868no—
593#120—868no—
594C4×D4—434no—
595C4×D4—434no—
596C4×D4—434no—
597C4×D4—862no—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—862no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—1721no—
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C4⋊C4C22×D4311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—431no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—21no—
618C2×C42—431no—
619C2×C42—861no—
620C4⋊C8—862no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—862no—
625#102—862no—
626#102—862no—
627#102—862no—
628#102—1721no—
629#102—1721no—
630#102—1721no—
631#102—1721no—
632#102C22⋊D4314yescomplemented
633C22⋊C8—862no—
634C22⋊C8—862no—
635#97—862no—
636#95—861no—
637#95—861no—
638#95—861no—
639#95—861no—
640#95—861no—
641C24—21no—
642C24—21no—
643C24—24no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—42no—
648C24—81no—
649C24—81no—
650C24—431no—
651C24—864no—
652C24—861no—
653C24—3441no—
654C24—3441no—
655C24—1722no—
656C24—1722no—
657C24—1722no—
658C24—1722no—
659C24D4×D4311yescharacteristic
660C2×D4—28no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—434no—
676C2×D4—432no—
677C2×D4—864no—
678C2×D4—864no—
679C2×D4—864no—
680C2×D4—862no—
681C2×D4—862no—
682C2×D4—868no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—3441no—
691C2×D4—3441no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4—1724no—
695C2×D4—1722no—
696C2×D4—1722no—
697C2×D4—1722no—
698C2×D4—1722no—
699C2×D4—17232no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4—1722no—
703C2×D4—1722no—
704C2×D4C2×C4×D4312yes—
705C2×D4C2×C4×D4312yes—
706C2×D4#1062189812yes—
707C2×D4C2×C22⋊D4312yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—432no—
718C22×C4—432no—
719C22×C4—864no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—3441no—
728C22×C4—1722no—
729C22×C4—1722no—
730C22×C4—1722no—
731C22×C4—1722no—
732C22×C4C2×C4×D4312yes—
733C22×C4D4×D4311yescharacteristic
734C22×C4D4×D4312yes—
735C22×C4C23×D4311yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—861no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—1724no—
749C2×C8C2×C22⋊D4312yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—434no—
754C4⋊C4—432no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—1722no—
761C4⋊C4C2×C22⋊D4312yescomplemented
762C22⋊C4—42no—
763C22⋊C4—434no—
764C22⋊C4—434no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C22⋊C4—3441no—
769C22⋊C4—1722no—
770C42—42no—
771C42—432no—
772C42—432no—
773C42—3441no—
774C23—22no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—48no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—432no—
802C23—432no—
803C23—432no—
804C23—861no—
805C23—861no—
806C23—861no—
807C23—861no—
808C23—862no—
809C23—3444no—
810C23—3444no—
811C23—3444no—
812C23—3444no—
813C23—3444no—
814C23—1728no—
815C23—1728no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23—1721no—
820C23—1721no—
821C23—1721no—
822C23C22⋊C4×D4312yes—
823C23C2×D4×D4311yescharacteristic
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—41no—
831D4—41no—
832D4—868no—
833D4—862no—
834D4—862no—
835D4—3444no—
836D4—1728no—
837D4—1728no—
838D4—1728no—
839D4—1728no—
840D4—1721no—
841D4—1721no—
842D4C4×C22⋊D4314yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—432no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—3444no—
870C2×C4—1728no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4C22⋊C4×D4312yes—
880C2×C4C22×C4×D4311yescharacteristic
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C22×C22⋊D4311yescharacteristic
883C2×C4C2×#1062189811yescharacteristic
884C2×C4#1306337011yescharacteristic
885C2×C4#1306337011yescharacteristic
886C8—22no—
887C8—41no—
888C8—1721no—
889C8—1721no—
890C22—22no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—434no—
913C22—862no—
914C22—862no—
915C22—862no—
916C22—862no—
917C22—862no—
918C22—862no—
919C22—34416no—
920C22—3441no—
921C22—3441no—
922C22—3441no—
923C22—3441no—
924C22—1722no—
925C22—1722no—
926C22—1722no—
927C22C2×C22⋊C4×D4311yescharacteristic
928C22D4×C22⋊D4311yescharacteristic
929C22#1458353911yescharacteristic
930C22AGL(1,ℤ/8)×D4311yescharacteristic
931C22AGL(1,ℤ/8)×D4311yescharacteristic
932C22#1458370311yescharacteristic
933C22#1458370911yescharacteristic
934C4—22no—
935C4—42no—
936C4—81no—
937C4—862no—
938C4—862no—
939C4—862no—
940C4—3441no—
941C4—3441no—
942C4—1722no—
943C4C2×C4×C22⋊D4311yescharacteristic
944C4#1458337211yescharacteristic
945C4D4×C22⋊D4311yescharacteristic
946C4#1458353911yescharacteristic
947C2—42no—
948C2—44no—
949C2—82no—
950C2—864no—
951C2—3442no—
952C2C22⋊C4×C22⋊D4311yescharacteristic
953C2#418×D4311yescharacteristic
954C2#1914312011yescharacteristic
955C2#1914606911yescharacteristic
956C2#1914608411yescharacteristic
957C2#1914661711yescharacteristic
958C2#1914673711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC2×D4×C22⋊D43C2
cosocleC22×C4×C43C24
hypercenterC2×#418D43
hypocenterC43#22423
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. C2×#102×D43C2semidirect
4. #19137525C2semidirect
5. #19135520C2semidirect
6. #19135417C2semidirect
7. #19135033C2semidirect
8. #19135020C2semidirect
9. #19134917C2semidirect
10. #19134909C2semidirect
11. #19134603C2semidirect
12. #19134526C2semidirect
13. #19134524C2semidirect
14. #19134422C2semidirect
15. C2×C43×#418C2semidirect
18. C22×C8×D43C22semidirect
20. D4×C22⋊D43C4semidirect
29. C2×C4⋊C4×D43C22semidirect
31. C2×Dic43⋊C8C22semidirect
32. C2×#13063247C22semidirect
33. C2×#13063247C22semidirect
36. C2×#13063246C22semidirect
37. C2×#13063246C22semidirect
38. C2×#13063245C22semidirect
39. C2×#13063245C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
42. C2×(C2×D43)⋊C8C22semidirect
43. C2×#13063235C22semidirect
47. #14582764C22semidirect
48. #14582759C22semidirect
49. #14582756C22semidirect
50. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C22×M16×C43C22semidirect
58. C2×#117×C43C22semidirect
62. C2×#102×C43C22semidirect
63. C2×#102×C43C22semidirect
90. #13063321C2×C4semidirect
92. #13063299C2×C4semidirect
99. D4×Dic43C2×C4semidirect
142. C22×D4×C43C2×C4semidirect
160. #102×C43D4semidirect
262. C2×C8×C43C2×D4semidirect
266. C4⋊C4×C43C2×D4semidirect
454. C2×D43#418semidirect
470. C2×#418D43semidirect
498. C22×M16C2×D43semidirect
510. C2×#117C2×D43semidirect
526. C2×#102C2×D43semidirect
527. C2×#102C2×D43semidirect
543. C43#22423semidirect
568. C22×D4C4×D43semidirect
632. #102C22⋊D43semidirect
749. C2×C8C2×C22⋊D43semidirect
761. C4⋊C4C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D432
C2×#145829682
C2×#102×D432
#191375252
#191355202
#191354172
#191350332
#191350202
#191349172
#191349092
#191346032
#191345262
#191345242
#191344222
C2×C43×#4182
#2242343