Finite Group Databasebeta

← #25112204

Subgroups — #25112204

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583542C211yesmaximal, characteristic
2C2×#14582976C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#14582902C211yesmaximal, characteristic, complemented
5#19137527C211yesmaximal, characteristic, complemented
6#19135407C211yesmaximal, characteristic, complemented
7#19135030C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#1983C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic, complemented
20#14583542—24no—
21#14583542C418yescomplemented
22C2×#13063307—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063298—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063295—21no—
27C2×C4×D172C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic, complemented
31C2×C22⋊C4×D43—21no—
32#14582976—24no—
33#14582902—24no—
34#14582899—24no—
35C2×#13063249C2211yescharacteristic, complemented
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
45C2×C4×C43⋊C8C2211yescharacteristic, complemented
46#14582790—21no—
47#14582784—21no—
48#14582777—21no—
49#14582765C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic
51#14582756C2211yescharacteristic, complemented
52C4×(C2×D43)⋊C4—21no—
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×#124×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic, complemented
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C4×C4⋊C4×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—41no—
69C2×#10621902—41no—
70C2×#10621902C2×C414yes—
71C22×D172—21no—
72C22×D172D411yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—41no—
80C2×D4×D43—41no—
81C2×D4×D43C2×C414yescomplemented
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C2×#10621872—22no—
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—22no—
91C2×#10621872—41no—
92C2×#10621872—41no—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063307—28no—
96#13063301—22no—
97#13063301C2×C414yescomplemented
98#13063298—28no—
99#13063296—22no—
100#13063296C2×C414yes—
101#13063295—28no—
102C4×D172—22no—
103C4×D172C2×C414yes—
104C4×D172C2×C414yescomplemented
105C4×D172D414yes—
106#13063283—22no—
107#13063283—41no—
108C2×C4⋊Dic43D411yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C4⋊C4×D43—22no—
115C4⋊C4×D43—41no—
116C2×C22⋊Dic43—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4D411yescharacteristic
123C2×(C2×D43)⋊C4D411yescharacteristic
124C22⋊C4×D43—28no—
125C2×C4×Dic43—21no—
126#13063249—22no—
127#13063249—41no—
128#13063247—22no—
129#13063247—22no—
130#13063246—22no—
131#13063246—41no—
132#13063245—22no—
133#13063245D414yescomplemented
134(C2×D43)⋊C8—22no—
135(C2×D43)⋊C8—22no—
136C4×C43⋊C8—22no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43C2311yescharacteristic
142C22×D4×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145#124×C43—22no—
146#124×C43C2×C414yescomplemented
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151C2×C42×C43—21no—
152C2×C42×C43C2311yescharacteristic
153C4⋊C8×C43—22no—
154#103×C43—22no—
155#103×C43—41no—
156#102×C43—22no—
157#102×C43—41no—
158#95×C43—21no—
159C24×C43—21no—
160C23×D43—21no—
161C23×D43—24no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—81no—
167C23×D43—81no—
168C23×D43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43C22×C412yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—24no—
189C2×C22⋊D43—24no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—81no—
193C2×C22⋊D43—81no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621902—28no—
200#10621902—44no—
201#10621902—44no—
202#10621902—44no—
203D4×D43—28no—
204D4×D43—44no—
205D4×D43—44no—
206D4×D43—44no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—41no—
212C2×D172—41no—
213C2×D172—42no—
214C2×D172—42no—
215C2×D172C22⋊C414yes—
216C2×D172C22×C412yes—
217C2×D172C2×D412yes—
218C2×D172#4112yes—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—81no—
234C2×C4×D43—81no—
235C2×C4×D43—81no—
236C2×C4×D43C22×C412yes—
237C2×C4×D43C22×C412yes—
238C2×C4×D43C2×D412yes—
239C2×C4×D43C2×D412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2×D412yes—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C42×C43—81no—
253C42×C43C22×C412yes—
254C42×C43C2×D412yes—
255C22⋊Dic43—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—81no—
261(C2×D43)⋊C4C22⋊C414yes—
262(C2×D43)⋊C4C22⋊C414yes—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43C22⋊C414yes—
269C4⋊Dic43C22×C412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—42no—
272C4×Dic43—42no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8C2×D412yes—
279#10621872—44no—
280#10621872—44no—
281C23×C43—22no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—22no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—22no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—48no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43C2×C22⋊C412yes—
316C22×D43C2×C22⋊C412yes—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—41no—
324D4×C43—41no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43C2×C22⋊C412yes—
339C2×C4×C43C2×C22⋊C412yes—
340C2×C4×C43C23×C411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C22⋊D43—48no—
347C22⋊D43—84no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—22no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43C2×C22⋊C412yes—
362C2×Dic43C2×C22⋊C412yes—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—44no—
367D172—48no—
368D172C4×D414yes—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—48no—
378C4×D43—84no—
379C4×D43—84no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#22427—431nomaximal, Sylow
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43#57511yescharacteristic
396C22×C43#57511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C2×D43—24no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—42no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—42no—
414C2×D43—41no—
415C2×D43—41no—
416C2×D43—42no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—42no—
420C2×D43—816no—
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—42no—
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—
435C2×#546—431no—
436C2×#436—431no—
437C2×#417—431no—
438C2×#418—431no—
439#2352—431no—
440#1983D4311yescharacteristic, complemented
441#1958—431no—
442#1895—431no—
443#1894—431no—
444#1874—431no—
445#1873—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—82no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43#289611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#327311yescharacteristic
455C2×C43#327511yescharacteristic
456C2×C43#332211yescharacteristic
457C2×C43#332311yescharacteristic
458D43—42no—
459D43—42no—
460D43—44no—
461C22×#41—431no—
462C23×D4—431no—
463C22×M16—431no—
464C22×M16—431no—
465#546—438no—
466#546—864no—
467C2×#124C2×D4311yescharacteristic
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478#436—864no—
479C2×C4⋊C8C2×D4311yescharacteristic, complemented
480#418—864no—
481#417—864no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#103C2×D4311yescharacteristic, complemented
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380—431no—
503C4×C4⋊C4C2×D4311yescharacteristic, complemented
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509C43#2242711yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8C22×D4311yescharacteristic
518C22×D4—434no—
519C22×D4—431no—
520C22×D4—431no—
521C22×D4—861no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—431no—
531C23×C4—431no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4—861no—
535C2×M16—862no—
536C2×M16—862no—
537C2×M16—862no—
538C2×M16—862no—
539C2×M16—1721no—
540C2×M16—1721no—
541C22×C8—431no—
542C22×C8—431no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—22no—
546#124C4×D4314yescomplemented
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—862no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—1721no—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—431no—
574C2×C22⋊C4—868no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—21no—
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—41no—
587#103—862no—
588#103—1721no—
589#102—22no—
590#102—41no—
591#102—434no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—21no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—431no—
607C24—431no—
608C24—864no—
609C24—861no—
610C24—3441no—
611C24—3441no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24—1722no—
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C2×C4×D4312yes—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—434no—
632C2×D4—432no—
633C2×D4—432no—
634C2×D4—432no—
635C2×D4—864no—
636C2×D4—864no—
637C2×D4—868no—
638C2×D4—864no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1721no—
645C2×D4—1721no—
646C2×D4—1722no—
647C2×D4—1722no—
648C2×D4—1724no—
649C2×D4—1724no—
650C2×D4—1724no—
651C2×D4—1722no—
652C2×D4—1722no—
653C2×D4C2×C4×D4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—864no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—864no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—3441no—
677C22×C4—3441no—
678C22×C4—3441no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686M16—1724no—
687M16—1724no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—432no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—434no—
704C4⋊C4—432no—
705C4⋊C4—864no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—1722no—
712C4⋊C4D4×D4312yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—434no—
716C22⋊C4—434no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—3441no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—81no—
724C42—1722no—
725C42C2×C4×D4312yes—
726C42D4×D4312yes—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—432no—
735C23—432no—
736C23—862no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—862no—
748C23—861no—
749C23—861no—
750C23—862no—
751C23—3444no—
752C23—3444no—
753C23—3444no—
754C23—3444no—
755C23—3444no—
756C23—1728no—
757C23—1728no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23—1721no—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—434no—
772D4—862no—
773D4—862no—
774D4—862no—
775D4—3444no—
776D4—1724no—
777D4—1728no—
778D4—1728no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—3444no—
808C2×C4—3444no—
809C2×C4—1728no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4C22⋊C4×D4312yes—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4#41×D4311yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—862no—
838C22—862no—
839C22—864no—
840C22—862no—
841C22—862no—
842C22—862no—
843C22—862no—
844C22—34416no—
845C22—1721no—
846C22—1721no—
847C22—1722no—
848C22—1721no—
849C22—1721no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1721no—
854C22—1721no—
855C22—1722no—
856C22—1721no—
857C22—1721no—
858C22—1722no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353311yescharacteristic
861C22#1458354611yescharacteristic
862C22#1458369611yescharacteristic
863C22#1458369611yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370811yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—3441no—
875C4—1722no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4#1458353411yescharacteristic
879C4#1458354211yescharacteristic
880C2—82no—
881C2—1722no—
882C2—1722no—
883C2—1724no—
884C2#1913741611yescharacteristic
885C2#1914311011yescharacteristic
886C2#1914311911yescharacteristic
887C2#1914620111yescharacteristic
888C2#1914622111yescharacteristic
889C2#1914680311yescharacteristic
890C2#1914681811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC2×#14583542C2
cosocleC22×C4×C43C24
hypercenter#1983D43
hypocenterC43#22427
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#14582976C2semidirect
3. C2×#14582899C2semidirect
4. C2×#14582902C2semidirect
5. #19137527C2semidirect
6. #19135407C2semidirect
7. #19135030C2semidirect
8. #19135025C2semidirect
9. #19134909C2semidirect
10. #19134904C2semidirect
11. #19134606C2semidirect
12. #19134534C2semidirect
13. #19134524C2semidirect
14. C4×#13063245C2semidirect
15. C43×#1983C2semidirect
19. C22×#10621872C22semidirect
21. #14583542C4semidirect
30. C2×C4⋊C4×D43C22semidirect
35. C2×#13063249C22semidirect
36. C2×#13063249C22semidirect
44. C2×(C2×D43)⋊C8C22semidirect
45. C2×C4×C43⋊C8C22semidirect
49. #14582765C22semidirect
51. #14582756C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×C4⋊C8×C43C22semidirect
59. C2×#103×C43C22semidirect
60. C2×#103×C43C22semidirect
63. C4×C4⋊C4×C43C22semidirect
81. C2×D4×D43C2×C4semidirect
97. #13063301C2×C4semidirect
104. C4×D172C2×C4semidirect
133. #13063245D4semidirect
146. #124×C43C2×C4semidirect
440. #1983D43semidirect
479. C2×C4⋊C8C2×D43semidirect
484. C2×#103C2×D43semidirect
485. C2×#103C2×D43semidirect
503. C4×C4⋊C4C2×D43semidirect
509. C43#22427semidirect
546. #124C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835422
C2×#145829762
C2×#145828992
C2×#145829022
#191375272
#191354072
#191350302
#191350252
#191349092
#191349042
#191346062
#191345342
#191345242
C4×#130632452
C43×#19832
#2242743