Finite Group Databasebeta

← #25098048

Subgroups — #25098048

Order 11008.

1850 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D43C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3C2×#14582906C211yesmaximal, characteristic, complemented
4C2×#14582902C211yesmaximal, characteristic
5#19137174C211yesmaximal, characteristic
6#19134953C211yesmaximal, characteristic, complemented
7#19134952C211yesmaximal, characteristic, complemented
8#19134951C211yesmaximal, characteristic, complemented
9#19134950C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic, complemented
11#19134948C211yesmaximal, characteristic, complemented
12#19134947C211yesmaximal, characteristic, complemented
13#19134310C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C2×SD16×D43—24no—
22C2×SD16×D43—24no—
23C2×SD16×D43C418yescomplemented
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583375—24no—
27#14583375—24no—
28C2×Q8×Dic43C2211yescharacteristic, complemented
29C2×C4×Dic86—21no—
30C2×C4×Dic86C2211yescharacteristic, complemented
31C2×#13063290—21no—
32C2×#13063290C2211yescharacteristic, complemented
33C2×#13063283—21no—
34C2×#13063283C2211yescharacteristic
35C2×#13063283C2211yescharacteristic
36C2×#13063282—21no—
37C2×#13063282C2211yescharacteristic
38#14582906—24no—
39#14582902—24no—
40C2×#13063250C2211yescharacteristic, complemented
41C2×#13063249C2211yescharacteristic, complemented
42C2×#13063248C2211yescharacteristic, complemented
43C2×#13063247C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46#14582802C2211yescharacteristic
47#14582801C2211yescharacteristic
48#14582800C2211yescharacteristic
49#14582799—21no—
50#14582799—21no—
51#14582754—21no—
52#14582754—21no—
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582654C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58#14582653C2211yescharacteristic, complemented
59C22×SD16×C43C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×#102×C43C2211yescharacteristic
63C43×#390C2211yescharacteristic
64C43×#340C2211yescharacteristic, complemented
65C43×#336C2211yescharacteristic, complemented
66C24×D43—21no—
67C22×Dic86—21no—
68C22×Dic86C2311yescharacteristic
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43C2×C414yes—
73C2×Q8×D43D414yes—
74C2×Q8×D43D414yes—
75C22×D172C2311yescharacteristic
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43—22no—
81C2×D4×D43—22no—
82C2×D4×D43C2×C414yes—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621873—22no—
86C2×#10621873—22no—
87C2×#10621873C2×C414yes—
88C2×#10621883—22no—
89C2×#10621883—22no—
90C2×#10621883C2×C414yes—
91C2×#10621884—22no—
92C2×#10621884—22no—
93C2×#10621884C2×C414yes—
94SD16×D43—232no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872—22no—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—22no—
101C2×C8×D43—22no—
102C2×C8×D43C2×C414yes—
103Q8×Dic43—22no—
104Q8×Dic43—22no—
105C4×Dic86—28no—
106C4×Dic86—22no—
107C4×Dic86—22no—
108#13063290—28no—
109#13063290—22no—
110#13063290—22no—
111#13063283—28no—
112#13063283—22no—
113#13063283—22no—
114#13063283—22no—
115#13063283D414yes—
116#13063282—28no—
117#13063282—22no—
118#13063282—22no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4D411yescharacteristic
125C2×Dic43⋊C4D411yescharacteristic
126C2×C22⋊Dic43—21no—
127C2×C22⋊Dic43—21no—
128C2×(C2×D43)⋊C4—21no—
129C2×(C2×D43)⋊C4—21no—
130C2×(C2×D43)⋊C4—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4D411yescharacteristic
135C2×(C2×D43)⋊C4D411yescharacteristic
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43C2311yescharacteristic
142#13063250—22no—
143#13063249—22no—
144#13063248—22no—
145#13063247—22no—
146#13063246—22no—
147#13063245—22no—
148C22×Q8×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C2×SD16×C43—22no—
151C2×SD16×C43—22no—
152C2×SD16×C43C2×C414yes—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C4×Q8×C43—22no—
156C4×Q8×C43—22no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C42×C43—21no—
163C2×C42×C43C2311yescharacteristic
164#103×C43—22no—
165#102×C43—22no—
166C24×C43—21no—
167C23×D43—21no—
168C23×D43—24no—
169C23×D43—42no—
170C23×D43—42no—
171C23×D43—81no—
172C23×D43—81no—
173C23×D43—81no—
174C23×D43—81no—
175C23×D43C2×D411yescharacteristic
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43C22×C412yes—
180C2×Q8×C43C2×D412yes—
181C2×Q8×C43C2×D412yes—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43C22×C412yes—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203Q8×D43—28no—
204Q8×D43—28no—
205Q8×D43—28no—
206Q8×D43C22⋊C4116yescomplemented
207D4×D43—28no—
208D4×D43—28no—
209D4×D43—44no—
210D4×D43—44no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172C22×C412yes—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43C22×C412yes—
221C2×C4×D43C2×D412yes—
222C2×C4×D43C2×D412yes—
223C2×C4×D43C2×D412yes—
224C2×C4×D43#4112yes—
225C2×C4×D43#4112yes—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—24no—
230C2×Dic86—24no—
231C2×Dic86—24no—
232C2×Dic86C22×C412yes—
233C2×Dic86C2×D412yes—
234C2×Dic86C2×D412yes—
235SD16×C43—28no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43C22×C412yes—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43C2×D412yes—
247C22⋊C4×C43—81no—
248C22⋊C4×C43—81no—
249C42×C43—24no—
250C42×C43—21no—
251C42×C43—21no—
252C22⋊Dic43—81no—
253C22⋊Dic43—81no—
254#10621884—28no—
255#10621883—28no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—22no—
258(C2×D43)⋊C4—22no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—81no—
261(C2×D43)⋊C4—81no—
262(C2×D43)⋊C4—81no—
263(C2×D43)⋊C4—81no—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43C2×D412yes—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—22no—
272Dic43⋊C4—22no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—24no—
279C4×Dic43—42no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8C22×C412yes—
286#10621873—28no—
287#10621872—44no—
288C8×D43—28no—
289C23×C43—22no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43C22×D411yescharacteristic
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—22no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—48no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43C4×D412yes—
316C22×D43#12012yes—
317C22×D43#12112yes—
318Q8×C43—22no—
319Q8×C43—22no—
320Q8×C43—22no—
321Q8×C43C2×C22⋊C414yes—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—41no—
325D4×C43—41no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C22⋊D43—48no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43C4×D412yes—
364C2×Dic43#12012yes—
365C2×Dic43#12112yes—
366D172—22no—
367D172—22no—
368D172—41no—
369D172—41no—
370C4×D43—216no—
371C4×D43C2×C22⋊C414yes—
372C4×D43C4×D414yes—
373C4×D43#12114yes—
374C4×D43#12314yes—
375Dic86—22no—
376Dic86—22no—
377Dic86—22no—
378Dic86—216no—
379Dic86C2×C22⋊C414yes—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#20936—431nomaximal, Sylow
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43C2×C4×D411yescharacteristic
393C22×C43C2×#12011yescharacteristic
394C22×C43C2×#12111yescharacteristic
395C22×C43#57711yescharacteristic
396C22×C43#57711yescharacteristic
397C22×C43#57711yescharacteristic
398C22×C43#57711yescharacteristic
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—816no—
409C2×D43—81no—
410C2×D43—81no—
411C2×D43—81no—
412C2×D43—81no—
413C2×D43#38614yes—
414C4×C43—24no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43—42no—
418C4×C43—81no—
419C4×C43C22×C22⋊C411yescharacteristic
420C4×C43C2×C4×D411yescharacteristic
421C4×C43C2×#12111yescharacteristic
422C4×C43C2×#12311yescharacteristic
423Dic43—24no—
424Dic43—41no—
425Dic43—41no—
426Dic43—42no—
427Dic43—81no—
428Dic43#38614yes—
429C23×SD16—431no—
430C2×#519—431no—
431C2×#419—431no—
432C2×#418—431no—
433#2309—431no—
434#1880—431no—
435#1880—431no—
436#1880—431no—
437#1880—431no—
438#1880—431no—
439#1880—431no—
440#1880—431no—
441#1880D4311yescharacteristic, complemented
442#1735—431no—
443#1729—431no—
444C2×C43—82no—
445C2×C43C2×#38611yescharacteristic
446C2×C43#294911yescharacteristic
447C2×C43#294911yescharacteristic
448C2×C43#301011yescharacteristic
449C2×C43#301011yescharacteristic
450C2×C43#304311yescharacteristic
451C2×C43#304311yescharacteristic
452D43—24no—
453D43—82no—
454C23×Q8—431no—
455C23×D4—431no—
456C22×SD16—431no—
457C22×SD16—431no—
458C22×SD16—438no—
459C22×SD16—431no—
460C22×SD16—864no—
461C22×SD16—864no—
462C22×SD16C2×D4311yescharacteristic
463C22×M16—431no—
464C23×C8—431no—
465#519—864no—
466#519—864no—
467C2×C4×Q8—431no—
468C2×C4×Q8—431no—
469C2×C4×Q8—431no—
470C2×C4×Q8—861no—
471C2×C4×Q8—861no—
472C2×C4×Q8C2×D4311yescharacteristic, complemented
473C2×#117—431no—
474C2×#117—431no—
475C2×#117—431no—
476C2×#117—861no—
477C2×#117—861no—
478#419—864no—
479#418—864no—
480C2×#103—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic, complemented
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102C2×D4311yescharacteristic
488#390—431no—
489#390—431no—
490#390—431no—
491#390—861no—
492#390—861no—
493#390C2×D4311yescharacteristic
494#379—861no—
495#379—861no—
496#340—431no—
497#340—431no—
498#340—431no—
499#340C2×D4311yescharacteristic, complemented
500#336—431no—
501#336—431no—
502#336—431no—
503#336C2×D4311yescharacteristic, complemented
504C43#2093611yescharacteristic, complemented, Sylow
505C25—861no—
506C22×Q8—434no—
507C22×Q8—434no—
508C22×Q8—434no—
509C22×Q8—431no—
510C22×Q8—861no—
511C22×Q8—862no—
512C22×Q8—862no—
513C22×Q8—862no—
514C22×Q8C22×D4311yescharacteristic
515C22×D4—434no—
516C22×D4—431no—
517C22×D4—862no—
518C22×D4—862no—
519C22×D4—862no—
520C22×D4—862no—
521C22×D4—862no—
522C22×D4—861no—
523C22×D4C22×D4311yescharacteristic
524C23×C4—431no—
525C23×C4—861no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—434no—
529C2×SD16—434no—
530C2×SD16—434no—
531C2×SD16—862no—
532C2×SD16—862no—
533C2×SD16—8632no—
534C2×SD16—862no—
535C2×SD16—862no—
536C2×SD16—862no—
537C2×SD16—862no—
538C2×SD16C4×D4314yes—
539C2×M16—862no—
540C2×M16—862no—
541C2×M16—862no—
542C22×C8—431no—
543C22×C8—434no—
544C22×C8—431no—
545C22×C8—862no—
546C22×C8—862no—
547C22×C8C22×D4311yescharacteristic
548C22×C8C22×D4311yescharacteristic
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—862no—
552C4×Q8—862no—
553C4×Q8—868no—
554C4×Q8—862no—
555C4×Q8—868no—
556C4×Q8—862no—
557C4×Q8—862no—
558C4×Q8—862no—
559#117—434no—
560#117—862no—
561#117—862no—
562#117—868no—
563#117—862no—
564#117—868no—
565#117—862no—
566#117—862no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4C22×D4311yescharacteristic
576C2×C4⋊C4C22×D4311yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
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×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C42—21no—
590C2×C42—431no—
591C2×C42—861no—
592C2×C42—861no—
593C2×C42—861no—
594C2×C42—861no—
595C2×C42—861no—
596C2×C42C22×D4311yescharacteristic
597#103—22no—
598#103—862no—
599#103—862no—
600#103—862no—
601#102—22no—
602#102—862no—
603#102—862no—
604#102—862no—
605C24—21no—
606C24—431no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—3441no—
612C24—3441no—
613C24—1722no—
614C24—1722no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—4316no—
619C2×Q8—432no—
620C2×Q8—432no—
621C2×Q8—432no—
622C2×Q8—864no—
623C2×Q8—864no—
624C2×Q8—864no—
625C2×Q8—868no—
626C2×Q8—868no—
627C2×Q8—868no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8C2×C4×D4312yes—
632C2×Q8D4×D4312yes—
633C2×Q8D4×D4312yes—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—432no—
640C2×D4—868no—
641C2×D4—868no—
642C2×D4—864no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—1724no—
649C2×D4—1724no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4C2×C4×D4312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—431no—
657C22×C4—432no—
658C22×C4—432no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—864no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—28no—
675SD16—868no—
676SD16—868no—
677SD16—868no—
678M16—1724no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—432no—
685C2×C8—868no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8C2×C4×D4312yes—
692C4⋊C4—24no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—432no—
697C4⋊C4—862no—
698C4⋊C4—862no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—864no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4D4×D4312yes—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—862no—
709C22⋊C4—862no—
710C22⋊C4—864no—
711C22⋊C4—3441no—
712C22⋊C4—3441no—
713C22⋊C4—3441no—
714C22⋊C4—3441no—
715C22⋊C4—3441no—
716C22⋊C4—3441no—
717C22⋊C4—1722no—
718C42—24no—
719C42—21no—
720C42—21no—
721C42—864no—
722C42—864no—
723C42—864no—
724C42—864no—
725C42—861no—
726C42—861no—
727C42—1722no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—432no—
736C23—432no—
737C23—432no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—862no—
743C23—3444no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—3444no—
748C23—3444no—
749C23—1728no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23C2×D4×D4311yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8—434no—
761Q8—8616no—
762Q8—862no—
763Q8—862no—
764Q8—862no—
765Q8C22⋊C4×D4314yes—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—862no—
771D4—862no—
772D4—1728no—
773D4—1721no—
774D4—1721no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—432no—
791C2×C4—432no—
792C2×C4—432no—
793C2×C4—434no—
794C2×C4—434no—
795C2×C4—434no—
796C2×C4—434no—
797C2×C4—8616no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4C22×C4×D4311yescharacteristic
814C2×C4C2×D4×D4311yescharacteristic
815C2×C4C2×D4×D4311yescharacteristic
816C2×C4C2×D4×D4311yescharacteristic
817C2×C4#41×D4311yescharacteristic
818C2×C4#41×D4311yescharacteristic
819C8—22no—
820C8—41no—
821C8—862no—
822C8—1721no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—434no—
831C22—862no—
832C22—862no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—862no—
837C22—34416no—
838C22—3441no—
839C22—3441no—
840C22—3441no—
841C22—3441no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22C4×D4×D4311yescharacteristic
846C22#120×D4311yescharacteristic
847C22#121×D4311yescharacteristic
848C22#1458370511yescharacteristic
849C22#1458370611yescharacteristic
850C22#1458370811yescharacteristic
851C22#1458370911yescharacteristic
852C4—24no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—81no—
857C4—434no—
858C4—864no—
859C4—3441no—
860C4—1721no—
861C4—1722no—
862C4—1721no—
863C4C2×C22⋊C4×D4311yescharacteristic
864C4C4×D4×D4311yescharacteristic
865C4#121×D4311yescharacteristic
866C4#123×D4311yescharacteristic
867C2—82no—
868C2—864no—
869C2—3442no—
870C2#386×D4311yescharacteristic
871C2#1914344911yescharacteristic
872C2#1914345111yescharacteristic
873C2#1914387611yescharacteristic
874C2#1914387811yescharacteristic
875C2#1914411111yescharacteristic
876C2#1914411411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#20936
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#14583375C2semidirect
3. C2×#14582906C2semidirect
6. #19134953C2semidirect
7. #19134952C2semidirect
8. #19134951C2semidirect
9. #19134950C2semidirect
10. #19134949C2semidirect
11. #19134948C2semidirect
12. #19134947C2semidirect
13. #19134310C2semidirect
14. #19134290C2semidirect
15. C43×#1880C2semidirect
23. C2×SD16×D43C4semidirect
28. C2×Q8×Dic43C22semidirect
30. C2×C4×Dic86C22semidirect
32. C2×#13063290C22semidirect
40. C2×#13063250C22semidirect
41. C2×#13063249C22semidirect
42. C2×#13063248C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. #14582654C22semidirect
57. #14582653C22semidirect
58. #14582653C22semidirect
60. C2×C4×Q8×C43C22semidirect
61. C2×#103×C43C22semidirect
64. C43×#340C22semidirect
65. C43×#336C22semidirect
206. Q8×D43C22⋊C4semidirect
441. #1880D43semidirect
472. C2×C4×Q8C2×D43semidirect
483. C2×#103C2×D43semidirect
499. #340C2×D43semidirect
503. #336C2×D43semidirect
504. C43#20936semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D432
C2×#145833752
C2×#145829062
C2×#145829022
#191371742
#191349532
#191349522
#191349512
#191349502
#191349492
#191349482
#191349472
#191343102
#191342902
C43×#18802
#2093643