Finite Group Databasebeta

← #25112256

Subgroups — #25112256

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×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135399C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583568—24no—
19#14583568C418yescomplemented
20C2×#13063321—21no—
21C2×#13063321C2211yescharacteristic
22C2×#13063299—21no—
23C2×#13063299C2211yescharacteristic
24C2×#13063296—21no—
25C2×#13063296C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31#14582975—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33#14582899—24no—
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582794—21no—
46#14582772—21no—
47#14582770—21no—
48#14582768C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C43×#417—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
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
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43C2311yescharacteristic
80C2×#10621872—22no—
81C2×#10621872—22no—
82C2×#10621872—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063321—28no—
86#13063321—22no—
87#13063321C2×C414yescomplemented
88#13063299—22no—
89#13063299—28no—
90#13063299C2×C414yescomplemented
91#13063296—22no—
92#13063296—28no—
93#13063296C2×C414yescomplemented
94Q8×Dic43—22no—
95Q8×Dic43C2×C414yescomplemented
96C4×C22⋊D43—28no—
97C4×C22⋊D43—44no—
98C4×C22⋊D43C2×C414yes—
99C4×C22⋊D43D414yes—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4D411yescharacteristic
108C4⋊C4×D43—22no—
109C4⋊C4×D43—41no—
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×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119Dic43⋊C8—22no—
120#13063249—22no—
121#13063249—22no—
122#13063247—22no—
123#13063247—41no—
124#13063246—41no—
125#13063246—41no—
126#13063245—22no—
127#13063245—41no—
128C22⋊(C43⋊C8)—22no—
129(C2×D43)⋊C8—22no—
130C8×Dic43—22no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43—41no—
138C2×#41×C43—41no—
139C2×#41×C43C2×C414yescomplemented
140C22×Q8×C43C2311yescharacteristic
141C22×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C23×C4×C43—21no—
145C23×C4×C43C2311yescharacteristic
146C2×M16×C43—22no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43—41no—
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156#103×C43—22no—
157#103×C43D414yescomplemented
158#102×C43—22no—
159#102×C43—22no—
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×C43—42no—
194C22×C4×C43—42no—
195C22×C4×C43—81no—
196C22×C4×C43C22×C412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43—81no—
212C2×C22⋊D43—81no—
213C2×C22⋊D43—81no—
214C2×C22⋊D43C22⋊C414yes—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
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—
246M16×C43—44no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43C2×D412yes—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—42no—
257C4⋊C4×C43C2×D412yes—
258C22⋊Dic43—24no—
259C22⋊Dic43—42no—
260C22⋊Dic43C22⋊C414yes—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—42no—
263(C2×D43)⋊C4C22⋊C414yes—
264C4⋊Dic43—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C22×C412yes—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273Dic43⋊C4—81no—
274Dic43⋊C4C22⋊C414yes—
275C4×Dic43—24no—
276C4×Dic43—42no—
277C4×Dic43C22×C412yes—
278C4×Dic43C2×D412yes—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
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—22no—
334C2×C4×C43—48no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—84no—
341C2×C4×C43C2×C22⋊C412yes—
342C2×C4×C43C23×C411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C22⋊D43—28no—
349C22⋊D43—48no—
350C22⋊D43—84no—
351C22⋊D43—84no—
352C22⋊D43—84no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
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—41no—
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—22no—
383C8×C43—41no—
384C43⋊C8—41no—
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—42no—
425C4×C43—81no—
426C4×C43C2×C4×D411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43D4211yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—81no—
434Dic43—81no—
435Dic43#41714yescomplemented
436C2×#550—431no—
437C2×#436—431no—
438C2×#417—431no—
439C2×#417D4311yescharacteristic, complemented
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#1788—431no—
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×M16C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic
480#436—864no—
481C2×C4⋊C8—431no—
482#417—24no—
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⋊C8—431no—
498C2×C4×C8—431no—
499#389—861no—
500#385—861no—
501#385—861no—
502#384—431no—
503#380—431no—
504#380—431no—
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—21no—
535C23×C4—431no—
536C23×C4—861no—
537C23×C4—861no—
538C23×C4C22×D4311yescharacteristic
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—862no—
543C2×M16—862no—
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—22no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—862no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—1721no—
577C2×C4⋊C4C22×D4311yescharacteristic
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C22⋊C4—431no—
580C2×C22⋊C4—431no—
581C2×C22⋊C4—861no—
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—862no—
591#103—862no—
592#103C22⋊D4314yescomplemented
593#102—22no—
594#102—22no—
595#102—862no—
596#102—862no—
597#102—1721no—
598#102—1721no—
599#102—1721no—
600#102—1721no—
601C22⋊C8—862no—
602C22⋊C8—862no—
603C4×C8—862no—
604#95—861no—
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×Q8#1062189812yes—
624C2×Q8C2×C22⋊D4312yes—
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—21no—
664C22×C4—24no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—81no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—432no—
675C22×C4—432no—
676C22×C4—864no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—3441no—
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—44no—
694M16—1724no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8C2×C22⋊D4312yes—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—42no—
711C4⋊C4—434no—
712C4⋊C4—432no—
713C4⋊C4—864no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—3441no—
720C4⋊C4—1722no—
721C4⋊C4—1722no—
722C4⋊C4C2×C22⋊D4312yes—
723C22⋊C4—434no—
724C22⋊C4—434no—
725C22⋊C4—864no—
726C22⋊C4—864no—
727C22⋊C4—1722no—
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—
765Q8C4×C22⋊D4314yescomplemented
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—22no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—432no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—3444no—
813C2×C4—1728no—
814C2×C4—1721no—
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×C4C22×C22⋊D4311yescharacteristic
826C2×C4C2×#1062189811yescharacteristic
827C2×C4#1306337011yescharacteristic
828C2×C4#1306337011yescharacteristic
829C8—22no—
830C8—41no—
831C8—1721no—
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
862C22D4×C22⋊D4311yescharacteristic
863C22#1458353911yescharacteristic
864C22AGL(1,ℤ/8)×D4311yescharacteristic
865C22#137×D4311yescharacteristic
866C22#1458370311yescharacteristic
867C22#1458370811yescharacteristic
868C4—22no—
869C4—24no—
870C4—42no—
871C4—81no—
872C4—434no—
873C4—862no—
874C4—862no—
875C4—3441no—
876C4—3441no—
877C4—1722no—
878C4C2×C4×C22⋊D4311yescharacteristic
879C4#1458337211yescharacteristic
880C4D4×C22⋊D4311yescharacteristic
881C4#1458353911yescharacteristic
882C2—42no—
883C2—82no—
884C2—3442no—
885C2—1722no—
886C2C22⋊C4×C22⋊D4311yescharacteristic
887C2#417×D4311yescharacteristic
888C2#1914311911yescharacteristic
889C2#1914620911yescharacteristic
890C2#1914625511yescharacteristic
891C2#1914691811yescharacteristic
892C2#1914692911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22432
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582899C2semidirect
4. C4⋊C4×C22⋊D43C2semidirect
5. #19135520C2semidirect
6. #19135399C2semidirect
7. #19135033C2semidirect
8. #19135030C2semidirect
9. #19134912C2semidirect
10. #19134909C2semidirect
11. #19134598C2semidirect
12. #19134535C2semidirect
13. #19134534C2semidirect
14. #103×Dic43C2semidirect
15. C2×C43×#417C2semidirect
19. #14583568C4semidirect
69. C2×#10621902C2×C4semidirect
87. #13063321C2×C4semidirect
90. #13063299C2×C4semidirect
93. #13063296C2×C4semidirect
95. Q8×Dic43C2×C4semidirect
139. C2×#41×C43C2×C4semidirect
157. #103×C43D4semidirect
318. Q8×C43C4×D4semidirect
435. Dic43#417semidirect
439. C2×#417D43semidirect
510. C43#22432semidirect
522. C2×#41C4×D43semidirect
592. #103C22⋊D43semidirect
765. Q8C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835682
C2×#145829752
C2×#145828992
C4⋊C4×C22⋊D432
#191355202
#191353992
#191350332
#191350302
#191349122
#191349092
#191345982
#191345352
#191345342
#103×Dic432
C2×C43×#4172
#2243243