Finite Group Databasebeta

← #25112131

Subgroups — #25112131

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×D172C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3C2×#14582903C211yesmaximal, characteristic, complemented
4C22×#13063245C211yesmaximal, characteristic, complemented
5#19135522C211yesmaximal, characteristic, complemented
6#19135418C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134912C211yesmaximal, characteristic, complemented
11#19134602C211yesmaximal, characteristic, complemented
12#19134525C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134423C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×D4×D43—21no—
19C22×#10621877C2211yescharacteristic, complemented
20C23×C43⋊C8C2211yescharacteristic, complemented
21D4×D172—24no—
22D4×D172C418yescomplemented
23C2×#13063322C2211yescharacteristic
24C2×#13063300—21no—
25C2×#13063299C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063295—21no—
28C2×#13063295—21no—
29C2×C4×D172C2211yescharacteristic
30#14582971—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
32#14582903—24no—
33C2×#13063245—24no—
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic, complemented
39C2×#13063245C2211yescharacteristic, complemented
40C2×#13063245C2211yescharacteristic, complemented
41C2×#13063245C2211yescharacteristic, complemented
42C2×#13063245C2211yescharacteristic, complemented
43C2×#13063245C2211yescharacteristic, complemented
44C2×#13063245C2211yescharacteristic, complemented
45C2×#13063245C2211yescharacteristic, complemented
46C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
48C2×#13063236C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic, complemented
55C22×C4⋊C4×C43C2211yescharacteristic, complemented
56C43×#388—21no—
57C43×#387—21no—
58C43×#386—21no—
59C43×#382C2211yescharacteristic, complemented
60C43×#380C2211yescharacteristic, complemented
61C43×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C43C2211yescharacteristic, complemented
63C4×C22⋊C4×C43—21no—
64C24×D43—21no—
65C24×D43—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—22no—
70C22×D172—21no—
71C22×D172—21no—
72C22×D172—21no—
73C22×D172—22no—
74C22×D172—22no—
75C22×D172—21no—
76C22×D172—41no—
77C22×D172—41no—
78C22×D172—41no—
79C22×D172—41no—
80C22×D172C2×C414yes—
81C22×D172C2×C414yescomplemented
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C2×D4×D43—28no—
88C2×D4×D43—44no—
89C2×D4×D43—44no—
90C22×C4×D43—21no—
91C2×#10621877—22no—
92C2×#10621877—22no—
93C2×#10621877—41no—
94C22×C43⋊C8—22no—
95C22×C43⋊C8—22no—
96C22×C43⋊C8—41no—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063322—22no—
102#13063322C2×C414yescomplemented
103#13063300—28no—
104#13063299—22no—
105#13063299—22no—
106#13063299C2×C414yes—
107#13063299C2×C414yescomplemented
108#13063295—28no—
109#13063295—28no—
110C4×D172—22no—
111C4×D172C2×C414yescomplemented
112C2×C4⋊Dic43C2311yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C4⋊(C43⋊C8)—22no—
117#13063245—22no—
118#13063245—22no—
119#13063245—22no—
120#13063245—22no—
121#13063245—22no—
122#13063245—22no—
123#13063245—22no—
124#13063245—41no—
125#13063245—41no—
126#13063245—41no—
127#13063245—41no—
128#13063245D414yescomplemented
129C22⋊(C43⋊C8)—22no—
130C22⋊(C43⋊C8)—22no—
131#13063236—22no—
132C22×D4×C43D411yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C4×D4×C43C2×C414yes—
137C4×D4×C43D414yes—
138#117×C43—22no—
139#117×C43—41no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—41no—
143C2×C4⋊C4×C43D411yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43D411yescharacteristic
153C2×C42×C43—21no—
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156#95×C43—21no—
157#95×C43—21no—
158#95×C43—21no—
159#95×C43—21no—
160#95×C43—21no—
161C24×C43C2×D411yescharacteristic
162C24×C43C2×D411yescharacteristic
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—24no—
167C23×D43—24no—
168C23×D43—42no—
169C23×D43—42no—
170C23×D43—42no—
171C23×D43—42no—
172C23×D43—42no—
173C23×D43—42no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—81no—
177C23×D43—81no—
178C23×D43—81no—
179C23×D43—81no—
180C2×D4×C43—22no—
181C2×D4×C43—22no—
182C2×D4×C43C22⋊C414yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—81no—
198C22×C4×C43C22×C412yes—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—42no—
211C2×C22⋊D43—42no—
212C2×C22⋊D43—42no—
213C22×Dic43—21no—
214D4×D43—432no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—24no—
219C2×D172—24no—
220C2×D172—24no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—24no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—28no—
233C2×D172—28no—
234C2×D172—42no—
235C2×D172—42no—
236C2×D172—42no—
237C2×D172—42no—
238C2×D172—44no—
239C2×D172—44no—
240C2×D172—44no—
241C2×D172—44no—
242C2×D172—44no—
243C2×D172—44no—
244C2×D172—42no—
245C2×D172—42no—
246C2×D172—81no—
247C2×D172—81no—
248C2×D172C22×C412yes—
249C2×D172C22×C412yes—
250C2×D172C22×C412yes—
251C2×D172C2×D412yes—
252C2×D172#4112yes—
253C2×C4×D43—24no—
254C2×C4×D43—42no—
255C2×C4×D43—42no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—42no—
264C4⋊C4×C43C22⋊C414yes—
265C4⋊C4×C43C2×D412yescomplemented
266C22⋊C4×C43—42no—
267C22⋊C4×C43—42no—
268C22⋊C4×C43—81no—
269C22⋊C4×C43C22⋊C414yes—
270C22⋊C4×C43C22⋊C414yes—
271C42×C43—42no—
272C42×C43—81no—
273C42×C43C22×C412yes—
274C42×C43C2×D412yes—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278C4⋊Dic43—21no—
279C4⋊Dic43C22×C412yes—
280#10621877—44no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—44no—
293C2×C43⋊C8C2×D412yescomplemented
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43C2×C22⋊C412yes—
305C23×C43C2×C22⋊C412yes—
306C23×C43AGL(1,ℤ/8)12yes—
307C23×C43AGL(1,ℤ/8)12yes—
308C23×C43C22×D411yescharacteristic
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—48no—
315C22×D43—48no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—48no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—48no—
334C22×D43—84no—
335C22×D43—84no—
336C22×D43—84no—
337C22×D43—84no—
338C22×D43—84no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43—84no—
342C22×D43—84no—
343C22×D43—84no—
344D4×C43—28no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—84no—
374C2×C4×C43C2×C22⋊C412yes—
375C2×C4×C43C2×C22⋊C412yes—
376C2×C4×C43C2×C22⋊C412yes—
377C2×C4×C43C2×C22⋊C412yes—
378C2×C4×C43C23×C411yescharacteristic
379C2×C4×C43C22×D411yescharacteristic
380C2×C4×C43C22×D411yescharacteristic
381C2×C4×C43C2×#4111yescharacteristic
382C2×C4×C43H(5,𝔽2)11yescharacteristic
383C2×C4×C43H(5,𝔽2)11yescharacteristic
384C22⋊D43—48no—
385C22⋊D43—48no—
386C2×Dic43—22no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389D172—22no—
390D172—22no—
391D172—22no—
392D172—22no—
393D172—22no—
394D172—22no—
395D172—22no—
396D172—48no—
397D172—48no—
398D172—48no—
399D172—41no—
400D172—41no—
401D172—41no—
402D172—41no—
403D172—84no—
404D172C4×D414yes—
405C4×D43—48no—
406C43⋊C8—22no—
407C43⋊C8—41no—
408C43⋊C8—41no—
409C43⋊C8—41no—
410#22423—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43#41814yescomplemented
425C22×C43C22×C22⋊C411yescharacteristic
426C22×C43D4211yescharacteristic
427C22×C43#54611yescharacteristic
428C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C43#57611yescharacteristic
431C22×C43#57711yescharacteristic
432C2×D43—24no—
433C2×D43—42no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—816no—
446C2×D43—816no—
447C2×D43—81no—
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43—81no—
455C4×C43—22no—
456C4×C43—22no—
457C4×C43—22no—
458C4×C43—22no—
459C4×C43—42no—
460C4×C43—81no—
461C4×C43—81no—
462C4×C43—81no—
463C4×C43C2×C4×D411yescharacteristic
464C4×C43#51811yescharacteristic
465C4×C43D4211yescharacteristic
466C4×C43#54611yescharacteristic
467Dic43—42no—
468C2×D42—431no—
469C2×#435—431no—
470C2×#418—431no—
471C22×#102—431no—
472#2352D4311yescharacteristic, complemented
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—24no—
484C2×C43—42no—
485C2×C43D4×C22⋊C411yescharacteristic
486C2×C43C2×#41811yescharacteristic
487C2×C43#289711yescharacteristic
488C2×C43#326411yescharacteristic
489C2×C43#326511yescharacteristic
490C2×C43#331011yescharacteristic
491C2×C43#331811yescharacteristic
492D43—44no—
493D43—82no—
494D43—82no—
495C23×D4—431no—
496C23×D4—431no—
497C23×D4—861no—
498C22×M16—431no—
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×D4C2×D4311yescharacteristic
510C2×#117C2×D4311yescharacteristic, complemented
511C22×C4⋊C4C2×D4311yescharacteristic, complemented
512#435—864no—
513C2×C4⋊C8—431no—
514#418—864no—
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—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—864no—
528C2×C22⋊C8—431no—
529C2×C22⋊C8—431no—
530C2×#97—431no—
531#388—21no—
532#387—21no—
533#386—21no—
534#382C2×D4311yescharacteristic, complemented
535#380C2×D4311yescharacteristic, complemented
536#380C2×D4311yescharacteristic, complemented
537C4×C4⋊C4C2×D4311yescharacteristic, complemented
538C4×C22⋊C4—21no—
539#340—431no—
540#340—431no—
541#340—431no—
542#340—431no—
543C43#2242311yescharacteristic, complemented, Sylow
544C25—861no—
545C25—861no—
546C22×D4—434no—
547C22×D4—434no—
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—431no—
551C22×D4—862no—
552C22×D4—862no—
553C22×D4—862no—
554C22×D4—862no—
555C22×D4—861no—
556C22×D4—861no—
557C22×D4—868no—
558C22×D4—862no—
559C22×D4—862no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—1721no—
565C22×D4—1721no—
566C22×D4—1721no—
567C22×D4—1721no—
568C22×D4—1724no—
569C22×D4—1724no—
570C22×D4C22⋊D4311yescharacteristic
571C23×C4—21no—
572C23×C4—861no—
573C23×C4C22×D4311yescharacteristic
574C23×C4C22×D4311yescharacteristic
575C2×M16—862no—
576C2×M16—862no—
577C2×M16—1721no—
578C22×C8—431no—
579C22×C8—431no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—862no—
583C22×C8—862no—
584C22×C8—1721no—
585#127—434no—
586#127—862no—
587#121—434no—
588#121—434no—
589#121—862no—
590#121—862no—
591#121—868no—
592#120—868no—
593#120—868no—
594C4×D4—434no—
595C4×D4—862no—
596C4×D4C4×D4314yes—
597C4×D4D17214yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4C22⋊D4311yescharacteristic
605C2×C4⋊C4C22×D4311yescharacteristic
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C4⋊C4C22×D4311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4C22⋊D4311yescharacteristic
616C2×C22⋊C4C22⋊D4311yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C22×D4311yescharacteristic
620C4⋊C8—862no—
621#102—434no—
622#102—862no—
623#102—862no—
624#102—862no—
625#102—862no—
626#102—862no—
627#102—862no—
628#102—862no—
629#102—1721no—
630#102—1721no—
631#102—1721no—
632#102—1721no—
633C22⋊C8—862no—
634C22⋊C8—862no—
635#97—862no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—861no—
642C24—864no—
643C24—864no—
644C24—861no—
645C24—861no—
646C24—3441no—
647C24—3441no—
648C24—3441no—
649C24—3441no—
650C24—1722no—
651C24—1722no—
652C24—1722no—
653C24—1722no—
654C24—1722no—
655C24—1722no—
656C24—1722no—
657C24—1722no—
658C24C2×C22⋊D4311yescharacteristic
659C24C2×C22⋊D4311yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—432no—
663C2×D4—432no—
664C2×D4—432no—
665C2×D4—432no—
666C2×D4—432no—
667C2×D4—868no—
668C2×D4—868no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—3441no—
689C2×D4—3441no—
690C2×D4—1724no—
691C2×D4—1724no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4—1724no—
695C2×D4—1724no—
696C2×D4—1722no—
697C2×D4—1722no—
698C2×D4—1722no—
699C2×D4—1722no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4—17232no—
703C2×D4—1722no—
704C2×D4—1722no—
705C2×D4—1722no—
706C2×D4—1722no—
707C2×D4(C2×D43)⋊C414yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—861no—
724C22×C4—864no—
725C22×C4—1722no—
726C22×C4—1722no—
727C22×C4C2×C4×D4312yes—
728C22×C4C2×C4×D4312yes—
729C22×C4C2×D17212yes—
730C22×C4C2×D17212yes—
731C22×C4C2×C22⋊D4311yescharacteristic
732C22×C4C2×C22⋊D4311yescharacteristic
733C22×C4C2×C22⋊D4311yescharacteristic
734C22×C4C2×C22⋊D4311yescharacteristic
735C22×C4C23×D4311yescharacteristic
736M16—1724no—
737C2×C8—432no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—861no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—1724no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—42no—
758C4⋊C4—432no—
759C4⋊C4—861no—
760C4⋊C4(C2×D43)⋊C414yes—
761C4⋊C4D4×D4312yescomplemented
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C22⋊C4(C2×D43)⋊C414yes—
769C22⋊C4(C2×D43)⋊C414yes—
770C42—42no—
771C42—81no—
772C42C2×C4×D4312yes—
773C42C2×D17212yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—3444no—
790C23—3444no—
791C23—3444no—
792C23—3444no—
793C23—3444no—
794C23—3444no—
795C23—3444no—
796C23—3444no—
797C23—3444no—
798C23—3444no—
799C23—1728no—
800C23—1728no—
801C23—1728no—
802C23—1728no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23—1721no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23—1721no—
811C23—1721no—
812C23—1721no—
813C23—1721no—
814C23—1721no—
815C23—1721no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23C2×(C2×D43)⋊C412yes—
820C23C2×(C2×D43)⋊C412yes—
821C23#1306335012yes—
822C23#1306335012yes—
823C23C22×C22⋊D4311yescharacteristic
824D4—28no—
825D4—434no—
826D4—862no—
827D4—862no—
828D4—862no—
829D4—862no—
830D4—862no—
831D4—862no—
832D4—862no—
833D4—3444no—
834D4—1728no—
835D4—1728no—
836D4—1728no—
837D4—1728no—
838D4—1728no—
839D4—1721no—
840D4—1721no—
841D4—1721no—
842D4—1721no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—84no—
872C2×C4—862no—
873C2×C4—1728no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4C2×(C2×D43)⋊C412yes—
877C2×C4C2×(C2×D43)⋊C412yes—
878C2×C4C2×(C2×D43)⋊C412yes—
879C2×C4C2×(C2×D43)⋊C412yes—
880C2×C4C22×C4×D4311yescharacteristic
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C22×D17211yescharacteristic
883C2×C4#41×D4311yescharacteristic
884C2×C4#1306337011yescharacteristic
885C2×C4#1306337111yescharacteristic
886C8—862no—
887C8—1721no—
888C8—1721no—
889C8—1721no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—864no—
904C22—34416no—
905C22—34416no—
906C22—3441no—
907C22—3441no—
908C22—3441no—
909C22—3441no—
910C22—3441no—
911C22—3441no—
912C22—3441no—
913C22—3441no—
914C22—1722no—
915C22—1722no—
916C22—1722no—
917C22—1722no—
918C22—1722no—
919C22—1722no—
920C22—1722no—
921C22—1722no—
922C22—1722no—
923C22—1722no—
924C22—1722no—
925C22—1722no—
926C22#1458290314yescomplemented
927C22C22×(C2×D43)⋊C411yescharacteristic
928C22D4×C22⋊D4311yescharacteristic
929C22#1458353711yescharacteristic
930C22C2×#1306335011yescharacteristic
931C22C2×#1306335011yescharacteristic
932C22#1458370211yescharacteristic
933C22#1458370711yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—1722no—
943C4C4×D4×D4311yescharacteristic
944C4#1458337111yescharacteristic
945C4D4×D17211yescharacteristic
946C4#1458354411yescharacteristic
947C2—24no—
948C2—42no—
949C2—3442no—
950C2—3442no—
951C2—1724no—
952C2D4×(C2×D43)⋊C411yescharacteristic
953C2C2×#1458290311yescharacteristic
954C2#1914311811yescharacteristic
955C2#1914607611yescharacteristic
956C2#1914609111yescharacteristic
957C2#1914661011yescharacteristic
958C2#1914673011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC2×D4×D172C2
cosocleC22×C4×C43C24
hypercenter#2352D43
hypocenterC43#22423
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. C2×#14582903C2semidirect
4. C22×#13063245C2semidirect
5. #19135522C2semidirect
6. #19135418C2semidirect
7. #19135031C2semidirect
8. #19135021C2semidirect
9. #19134917C2semidirect
10. #19134912C2semidirect
11. #19134602C2semidirect
12. #19134525C2semidirect
13. #19134525C2semidirect
14. #19134423C2semidirect
15. C43×#2352C2semidirect
19. C22×#10621877C22semidirect
20. C23×C43⋊C8C22semidirect
22. D4×D172C4semidirect
31. C2×C4⋊(C43⋊C8)C22semidirect
38. C2×#13063245C22semidirect
39. C2×#13063245C22semidirect
40. C2×#13063245C22semidirect
41. C2×#13063245C22semidirect
42. C2×#13063245C22semidirect
43. C2×#13063245C22semidirect
44. C2×#13063245C22semidirect
45. C2×#13063245C22semidirect
46. C2×C22⋊(C43⋊C8)C22semidirect
47. C2×C22⋊(C43⋊C8)C22semidirect
48. C2×#13063236C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
54. C2×#117×C43C22semidirect
55. C22×C4⋊C4×C43C22semidirect
59. C43×#382C22semidirect
60. C43×#380C22semidirect
61. C43×#380C22semidirect
62. C4×C4⋊C4×C43C22semidirect
81. C22×D172C2×C4semidirect
102. #13063322C2×C4semidirect
107. #13063299C2×C4semidirect
111. C4×D172C2×C4semidirect
128. #13063245D4semidirect
265. C4⋊C4×C43C2×D4semidirect
293. C2×C43⋊C8C2×D4semidirect
424. C22×C43#418semidirect
472. #2352D43semidirect
510. C2×#117C2×D43semidirect
511. C22×C4⋊C4C2×D43semidirect
534. #382C2×D43semidirect
535. #380C2×D43semidirect
536. #380C2×D43semidirect
537. C4×C4⋊C4C2×D43semidirect
543. C43#22423semidirect
761. C4⋊C4D4×D43semidirect
926. C22#14582903semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D1722
C2×#145829712
C2×#145829032
C22×#130632452
#191355222
#191354182
#191350312
#191350212
#191349172
#191349122
#191346022
#191345252
#191344232
C43×#23522
#2242343