Finite Group Databasebeta

← #25112253

Subgroups — #25112253

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583568C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#14582899C211yesmaximal, characteristic, complemented
5#19137491C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135399C211yesmaximal, characteristic, complemented
8#19135031C211yesmaximal, characteristic, complemented
9#19135030C211yesmaximal, characteristic, complemented
10#19134910C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134598C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583568—24no—
20#14583568C418yescomplemented
21C2×#13063321—21no—
22C2×#13063321C2211yescharacteristic
23C2×#13063299—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063296—21no—
26C2×#13063296C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×(C22⋊D43)⋊C4—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14582974—24no—
34C2×Dic43⋊C8C2211yescharacteristic
35#14582900—24no—
36#14582899—24no—
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×C8×Dic43C2211yescharacteristic
47#14582796—21no—
48#14582773—21no—
49#14582771—21no—
50#14582768C2211yescharacteristic
51#14582756C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yescomplemented
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C22×C22⋊D43D411yescharacteristic
77C23×Dic43—21no—
78C22×C4×D43—21no—
79C22×C4×D43—21no—
80C22×C4×D43C2311yescharacteristic
81C2×#10621877—22no—
82C2×#10621877—22no—
83C2×#10621877—41no—
84C2×#10621872—22no—
85C2×#10621872—22no—
86C2×#10621872—41no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063321—28no—
90#13063321—22no—
91#13063321C2×C414yescomplemented
92#13063299—22no—
93#13063299—28no—
94#13063299C2×C414yescomplemented
95#13063296—22no—
96#13063296—28no—
97#13063296C2×C414yescomplemented
98Q8×Dic43—22no—
99Q8×Dic43C2×C414yescomplemented
100C4×C22⋊D43—28no—
101C4×C22⋊D43C2×C414yes—
102C4×C22⋊D43D414yes—
103(C22⋊D43)⋊C4—44no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—41no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4D411yescharacteristic
115C4⋊C4×D43—22no—
116C4⋊C4×D43—41no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43D411yescharacteristic
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4D411yescharacteristic
122C2×C4×Dic43—21no—
123C2×C4×Dic43—21no—
124C2×C4×Dic43C2311yescharacteristic
125Dic43⋊C8—22no—
126#13063249—22no—
127#13063249D414yescomplemented
128#13063247—22no—
129#13063247—41no—
130#13063246—22no—
131#13063246—22no—
132#13063245—22no—
133#13063245—41no—
134(C2×D43)⋊C8—22no—
135C8×Dic43—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C2×#41×C43—22no—
139C2×#41×C43—22no—
140C2×#41×C43—22no—
141C2×#41×C43—41no—
142C2×#41×C43—41no—
143C2×#41×C43C2×C414yescomplemented
144C22×Q8×C43C2311yescharacteristic
145C22×D4×C43—21no—
146C22×D4×C43C2311yescharacteristic
147C23×C4×C43—21no—
148C23×C4×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154#103×C43—22no—
155#103×C43—22no—
156#102×C43—41no—
157#102×C43—41no—
158C22⋊C8×C43—22no—
159#95×C43—21no—
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C23×D43—21no—
163C23×D43C2×D411yescharacteristic
164#41×C43—28no—
165#41×C43—44no—
166#41×C43—44no—
167#41×C43—44no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43C22×C412yes—
172C2×Q8×C43C2×D412yes—
173C2×Q8×C43#4112yes—
174C2×D4×C43—21no—
175C2×D4×C43—24no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43C22×C412yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—24no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43C22⋊C414yes—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43—81no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221#10621902—28no—
222#10621902—44no—
223#10621902—44no—
224#10621902—44no—
225C2×D172—21no—
226C2×D172—24no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—42no—
232C2×D172—42no—
233C2×D172C22×C412yes—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—24no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×C4×D43—42no—
242C2×C4×D43—42no—
243C2×C4×D43—81no—
244C2×C4×D43C22×C412yes—
245C2×C4×D43C2×D412yes—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C22⋊C4×C43—42no—
257C22⋊Dic43—24no—
258C22⋊Dic43C22⋊C414yes—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4C22⋊C414yes—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—42no—
268C4⋊Dic43C22×C412yes—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—42no—
271Dic43⋊C4—42no—
272Dic43⋊C4—81no—
273Dic43⋊C4C22⋊C414yes—
274C4×Dic43—24no—
275C4×Dic43—42no—
276C4×Dic43C22×C412yes—
277C4×Dic43C2×D412yes—
278#10621877—44no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8C2×D412yes—
285#10621872—44no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—22no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43C2×C22⋊C412yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—22no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43C2×C22⋊C412yes—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43C4×D414yescomplemented
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—48no—
322D4×C43—41no—
323D4×C43—41no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—48no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43C2×C22⋊C412yes—
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C22⋊D43—28no—
348C22⋊D43—48no—
349C22⋊D43—84no—
350C22⋊D43—84no—
351C22⋊D43—84no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—84no—
366C2×Dic43C2×C22⋊C412yes—
367C2×Dic43C2×C22⋊C412yes—
368C2×Dic43C2×C22⋊C412yes—
369C2×Dic43AGL(1,ℤ/8)12yes—
370C2×Dic43#13712yes—
371D172—22no—
372D172—22no—
373D172—48no—
374D172—41no—
375D172—41no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—48no—
381C4×D43—84no—
382C8×C43—41no—
383C8×C43—41no—
384C43⋊C8—22no—
385C43⋊C8—41no—
386#22432—431nomaximal, Sylow
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43C22×C22⋊C411yescharacteristic
402C22×C43D4211yescharacteristic
403C22×C43#54611yescharacteristic
404C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C43C2×#13711yescharacteristic
406C22×C43#57611yescharacteristic
407C22×C43#57711yescharacteristic
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—41no—
414C2×D43—41no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43—81no—
421C2×D43—81no—
422C4×C43—24no—
423C4×C43—22no—
424C4×C43—81no—
425C4×C43—81no—
426C4×C43C2×C4×D411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43D4211yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—42no—
434Dic43—81no—
435Dic43#41714yescomplemented
436C2×#550—431no—
437C2×#436—431no—
438C2×#417—431no—
439C2×#417—431no—
440D4×C4⋊C4—431no—
441#1982—431no—
442#1957—431no—
443#1895—431no—
444#1895—431no—
445#1874—431no—
446#1874—431no—
447#1803—431no—
448#1788—431no—
449#1788D4311yescharacteristic, complemented
450C4×#103—431no—
451C2×C43—42no—
452C2×C43—82no—
453C2×C43D4×C22⋊C411yescharacteristic
454C2×C43C2×#41711yescharacteristic
455C2×C43#289711yescharacteristic
456C2×C43#327411yescharacteristic
457C2×C43#327811yescharacteristic
458C2×C43#333211yescharacteristic
459C2×C43#333311yescharacteristic
460D43—42no—
461D43—82no—
462C22×#41—431no—
463C22×#41C2×D4311yescharacteristic
464C22×M16—431no—
465C22×M16—431no—
466#550—438no—
467#550—864no—
468C2×#127—431no—
469C2×#127—861no—
470C2×#121—431no—
471C2×#121—431no—
472C2×#121—861no—
473C2×#121—861no—
474C2×C4×Q8—431no—
475C2×C4×D4—431no—
476C2×C4×D4—861no—
477C2×C4×D4—861no—
478C22×C4⋊C4—431no—
479C22×C4⋊C4—431no—
480#436—864no—
481C2×C4⋊C8—431no—
482#417—864no—
483#417—864no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#103C2×D4311yescharacteristic
487C2×#103C2×D4311yescharacteristic
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102C2×D4311yescharacteristic
495C2×#102C2×D4311yescharacteristic
496C2×C22⋊C8—431no—
497C2×C22⋊C8C2×D4311yescharacteristic
498C2×C4×C8—431no—
499#389—861no—
500#385—861no—
501#385—861no—
502#384—431no—
503#380—431no—
504#380C2×D4311yescharacteristic
505C4×C4⋊C4—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509#340—431no—
510C43#2243211yescharacteristic, complemented, Sylow
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—434no—
517C2×#41—862no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—1721no—
521C2×#41—1721no—
522C2×#41C4×D4314yescomplemented
523C22×Q8C22×D4311yescharacteristic
524C22×D4—21no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—861no—
528C22×D4—861no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4C22×D4311yescharacteristic
533C23×C4—21no—
534C23×C4—431no—
535C23×C4—861no—
536C23×C4—861no—
537C23×C4—861no—
538C23×C4C22×D4311yescharacteristic
539C2×M16—862no—
540C2×M16—862no—
541C2×M16—862no—
542C2×M16—862no—
543C2×M16—1721no—
544C2×M16—1721no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8C22×D4311yescharacteristic
548C22×C8C22×D4311yescharacteristic
549#127—434no—
550#127—862no—
551#127—868no—
552#121—434no—
553#121—434no—
554#121—868no—
555#121—868no—
556#121—862no—
557#121—862no—
558C4×Q8—434no—
559C4×Q8—862no—
560C4×D4—434no—
561C4×D4—434no—
562C4×D4—868no—
563C4×D4—1724no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—862no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—1721no—
576C2×C4⋊C4—1721no—
577C2×C4⋊C4C22×D4311yescharacteristic
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—431no—
581C2×C22⋊C4—431no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C42—431no—
586C2×C42—861no—
587C2×C42—861no—
588C4⋊C8—862no—
589#103—22no—
590#103—22no—
591#103—434no—
592#103—862no—
593#102—41no—
594#102—41no—
595#102—862no—
596#102—862no—
597#102—862no—
598#102—862no—
599#102—1721no—
600#102—1721no—
601C22⋊C8—22no—
602C22⋊C8—862no—
603C4×C8—862no—
604#95—21no—
605#95—861no—
606#95—861no—
607C24—21no—
608C24—431no—
609C24—861no—
610C24D4×D4311yescharacteristic
611#41—28no—
612#41—44no—
613#41—44no—
614#41—44no—
615#41—868no—
616#41—1724no—
617#41—1724no—
618#41—1724no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×C4×D4312yes—
623C2×Q8D4×D4312yes—
624C2×Q8#1062190012yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—434no—
634C2×D4—432no—
635C2×D4—864no—
636C2×D4—862no—
637C2×D4—862no—
638C2×D4—864no—
639C2×D4—864no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—3441no—
648C2×D4—3441no—
649C2×D4—3441no—
650C2×D4—3441no—
651C2×D4—3441no—
652C2×D4—3441no—
653C2×D4—1722no—
654C2×D4—1722no—
655C2×D4—1722no—
656C2×D4—1722no—
657C2×D4C2×C4×D4312yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—432no—
672C22×C4—432no—
673C22×C4—864no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—3441no—
682C22×C4—3441no—
683C22×C4—1722no—
684C22×C4—1722no—
685C22×C4—1722no—
686C22×C4—1722no—
687C22×C4—1722no—
688C22×C4—1722no—
689C22×C4C2×C4×D4312yes—
690C22×C4D4×D4311yescharacteristic
691C22×C4D4×D4312yes—
692C22×C4C23×D4311yescharacteristic
693M16—1724no—
694M16—1724no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—432no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—434no—
712C4⋊C4—432no—
713C4⋊C4—432no—
714C4⋊C4—864no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—3441no—
720C4⋊C4—1722no—
721C4⋊C4—1722no—
722C4⋊C4—1722no—
723C22⋊C4—42no—
724C22⋊C4—434no—
725C22⋊C4—434no—
726C22⋊C4—864no—
727C22⋊C4—864no—
728C22⋊C4—1722no—
729C42—432no—
730C42—432no—
731C42—864no—
732C42—1722no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—432no—
747C23—861no—
748C23—861no—
749C23—861no—
750C23—861no—
751C23—861no—
752C23—861no—
753C23—862no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23C22⋊C4×D4312yes—
761C23C2×D4×D4311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8(C22⋊D43)⋊C414yescomplemented
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—868no—
772D4—862no—
773D4—862no—
774D4—3444no—
775D4—3444no—
776D4—3444no—
777D4—1728no—
778D4—1728no—
779D4—1721no—
780D4—1721no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—432no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—3444no—
813C2×C4—3444no—
814C2×C4—1728no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4C22⋊C4×D4312yes—
823C2×C4C22×C4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4C2×#1062190011yescharacteristic
827C2×C4#1306337011yescharacteristic
828C2×C4#1306337011yescharacteristic
829C8—41no—
830C8—41no—
831C8—862no—
832C8—1721no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—862no—
848C22—862no—
849C22—862no—
850C22—3441no—
851C22—3441no—
852C22—3441no—
853C22—3441no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1721no—
858C22—1721no—
859C22—1721no—
860C22—1721no—
861C22C2×C22⋊C4×D4311yescharacteristic
862C22#1458353111yescharacteristic
863C22#1458353611yescharacteristic
864C22AGL(1,ℤ/8)×D4311yescharacteristic
865C22#137×D4311yescharacteristic
866C22#1458370111yescharacteristic
867C22#1458370611yescharacteristic
868C4—22no—
869C4—24no—
870C4—81no—
871C4—81no—
872C4—434no—
873C4—862no—
874C4—862no—
875C4—3441no—
876C4—1722no—
877C4—1722no—
878C4C2×(C22⋊D43)⋊C411yescharacteristic
879C4#1458337211yescharacteristic
880C4#1458353111yescharacteristic
881C4#1458353611yescharacteristic
882C2—42no—
883C2—82no—
884C2—3442no—
885C2—1722no—
886C2#1913741111yescharacteristic
887C2#417×D4311yescharacteristic
888C2#1914311711yescharacteristic
889C2#1914620811yescharacteristic
890C2#1914625411yescharacteristic
891C2#1914691511yescharacteristic
892C2#1914692611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22432
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. C2×#14582900C2semidirect
4. C2×#14582899C2semidirect
5. #19137491C2semidirect
6. #19135520C2semidirect
7. #19135399C2semidirect
8. #19135031C2semidirect
9. #19135030C2semidirect
10. #19134910C2semidirect
11. #19134909C2semidirect
12. #19134598C2semidirect
13. #19134534C2semidirect
14. #103×Dic43C2semidirect
15. C43×#1788C2semidirect
20. #14583568C4semidirect
69. C2×#10621902C2×C4semidirect
91. #13063321C2×C4semidirect
94. #13063299C2×C4semidirect
97. #13063296C2×C4semidirect
99. Q8×Dic43C2×C4semidirect
127. #13063249D4semidirect
143. C2×#41×C43C2×C4semidirect
318. Q8×C43C4×D4semidirect
435. Dic43#417semidirect
449. #1788D43semidirect
510. C43#22432semidirect
522. C2×#41C4×D43semidirect
765. Q8(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145835682
C2×#145829742
C2×#145829002
C2×#145828992
#191374912
#191355202
#191353992
#191350312
#191350302
#191349102
#191349092
#191345982
#191345342
#103×Dic432
C43×#17882
#2243243