Finite Group Databasebeta

← #25098320

Subgroups — #25098320

Order 11008.

1754 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063333C211yesmaximal, characteristic
2C2×#14583472C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic, complemented
4C2×#103×D43C211yesmaximal, characteristic, complemented
5#19137184C211yesmaximal, characteristic
6#19135028C211yesmaximal, characteristic, complemented
7#19135027C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19135019C211yesmaximal, characteristic, complemented
10#19135017C211yesmaximal, characteristic, complemented
11#19135016C211yesmaximal, characteristic, complemented
12#19135015C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#1894C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C2×#13063333—24no—
19C2×#13063333—24no—
20C2×#13063333—24no—
21C22×#10621872C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583472—24no—
27#14583472C418yescomplemented
28C2×#13063324—21no—
29C2×#13063311—21no—
30C2×#13063310—21no—
31C2×#13063307—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063304C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063283C2211yescharacteristic
36C2×#13063283C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582906—24no—
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45#103×D43—24no—
46#14582803—21no—
47#14582799—21no—
48#14582777—21no—
49#14582775—21no—
50#14582759C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582756C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57#14582661C2211yescharacteristic
58#14582661C2211yescharacteristic
59C22×M16×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#340C2211yescharacteristic
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898C2×C414yes—
71C2×#10621898D414yes—
72C22×Dic86—21no—
73C22×Dic86D411yescharacteristic
74C22×Dic86C2311yescharacteristic
75C2×Q8×D43—22no—
76C2×Q8×D43—22no—
77C2×Q8×D43—22no—
78C2×Q8×D43—22no—
79C2×Q8×D43—22no—
80C2×Q8×D43C2×C414yes—
81C22×D172D411yescharacteristic
82C22×C22⋊D43D411yescharacteristic
83C22×C22⋊D43D411yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2311yescharacteristic
88#13063333—232no—
89C2×#10621872—22no—
90C2×#10621872—22no—
91C2×#10621872—22no—
92C2×#10621872—22no—
93C2×#10621872—22no—
94C2×#10621872D414yes—
95C22×C43⋊C8—22no—
96C22×C43⋊C8—22no—
97C22×C43⋊C8—22no—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—22no—
101C2×C8×D43—22no—
102C2×C8×D43—22no—
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C2×C8×D43D414yes—
106#13063324—28no—
107#13063311—28no—
108#13063310—28no—
109#13063307—28no—
110#13063305—22no—
111#13063305C2×C414yescomplemented
112#13063304—22no—
113#13063304C2×C414yescomplemented
114#13063301—22no—
115#13063301C2×C414yescomplemented
116#13063283—22no—
117#13063283—22no—
118#13063283—22no—
119#13063283C2×C414yes—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C4⋊C4×D43—22no—
128C4⋊C4×D43—22no—
129C2×C22⋊Dic43—21no—
130C2×C22⋊Dic43—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139#13063250—22no—
140#13063250—22no—
141#13063249—22no—
142#13063249—22no—
143#13063248—22no—
144#13063248—22no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×Q8×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×M16×C43—22no—
151C2×M16×C43—22no—
152C2×M16×C43—22no—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22⋊Q8×C43—22no—
156C22⋊Q8×C43C2×C414yescomplemented
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163#103×C43—22no—
164#103×C43—22no—
165#95×C43—21no—
166C24×C43C2×D411yescharacteristic
167C23×D43C2×D411yescharacteristic
168C23×D43C2×D411yescharacteristic
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43C22×C412yes—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43C22×C412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43C22⋊C414yes—
192C2×C22⋊D43C22⋊C414yes—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199Q8×D43—28no—
200Q8×D43—28no—
201Q8×D43—44no—
202Q8×D43—44no—
203#10621898—28no—
204#10621898—28no—
205#10621898—28no—
206#10621898—28no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172C22⋊C414yes—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—24no—
215C2×C4×D43—42no—
216C2×C4×D43—42no—
217C2×C4×D43—42no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43C22×C412yes—
221C2×C4×D43C22×C412yes—
222C2×C4×D43C2×D412yes—
223C2×C4×D43C2×D412yes—
224C2×C4×D43C2×D412yes—
225C2×C4×D43C2×D412yes—
226C2×C4×D43#4112yes—
227C2×C4×D43#4112yes—
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—24no—
236C2×Dic86—42no—
237C2×Dic86—42no—
238C2×Dic86C22⋊C414yes—
239C2×Dic86C22×C412yes—
240M16×C43—28no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43C2×D412yes—
246C2×C8×C43C2×D412yes—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C22×C412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—81no—
256C22⋊Dic43—24no—
257C22⋊Dic43—81no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4—81no—
263(C2×D43)⋊C4—81no—
264C4⋊Dic43—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C22×C412yes—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—42no—
274C4×Dic43—24no—
275C4×Dic43—42no—
276C2×C43⋊C8—28no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8C2×D412yes—
282C2×C43⋊C8C2×D412yes—
283#10621872—28no—
284#10621872—28no—
285C8×D43—28no—
286C8×D43—28no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43C2×C22⋊C412yes—
294C23×C43C22×D411yescharacteristic
295C22×D43—21no—
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—21no—
305C22×D43C2×C22⋊C412yes—
306C22×D43C2×C22⋊C412yes—
307C22×D43#12112yes—
308C22×D43#12112yes—
309Q8×C43—22no—
310Q8×C43—22no—
311Q8×C43—41no—
312Q8×C43—41no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43C2×C22⋊C412yes—
332C2×C4×C43C23×C411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C22⋊D43—28no—
339C22⋊D43—28no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43C2×C22⋊C412yes—
355C2×Dic43C2×C22⋊C412yes—
356C2×Dic43#12112yes—
357C2×Dic43#12112yes—
358D172—28no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—48no—
364C4×D43—84no—
365C4×D43C4×D414yes—
366C4×D43C4×D414yes—
367C4×D43#12014yes—
368C4×D43#12314yes—
369Dic86—28no—
370Dic86—22no—
371Dic86—22no—
372Dic86—41no—
373Dic86—41no—
374Dic86—48no—
375C8×C43—22no—
376C8×C43—22no—
377C43⋊C8—22no—
378C43⋊C8—22no—
379#20974—431nomaximal, Sylow
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43C22×C22⋊C411yescharacteristic
388C22×C43C2×#12111yescharacteristic
389C22×C43C2×#12111yescharacteristic
390C22×C43#57711yescharacteristic
391C22×C43#57711yescharacteristic
392C22×C43#57811yescharacteristic
393C22×C43#57811yescharacteristic
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43#38614yes—
408C4×C43—22no—
409C4×C43—42no—
410C4×C43—42no—
411C4×C43—81no—
412C4×C43—81no—
413C4×C43C2×C4×D411yescharacteristic
414C4×C43C2×C4×D411yescharacteristic
415C4×C43C2×#12011yescharacteristic
416C4×C43C2×#12311yescharacteristic
417Dic43—22no—
418Dic43—42no—
419Dic43—42no—
420Dic43—81no—
421Dic43—81no—
422Dic43#38614yes—
423C22×#131—431no—
424C2×#536—431no—
425C2×#419—431no—
426C22×#103—431no—
427#2311—431no—
428#1894—431no—
429#1894—431no—
430#1894—431no—
431#1894D4311yescharacteristic, complemented
432#1892—431no—
433#1892—431no—
434#1892—431no—
435#1892—431no—
436#1736—431no—
437#1735—431no—
438C2×C43—42no—
439C2×C43C2×#38611yescharacteristic
440C2×C43#289811yescharacteristic
441C2×C43#289811yescharacteristic
442C2×C43#305711yescharacteristic
443C2×C43#305911yescharacteristic
444C2×C43#306311yescharacteristic
445C2×C43#306311yescharacteristic
446D43—24no—
447D43—42no—
448C22×#41—431no—
449C23×Q8—431no—
450C2×#131—864no—
451C2×#131—864no—
452C2×#131—864no—
453C22×M16—431no—
454C22×M16—431no—
455C22×M16C2×D4311yescharacteristic
456C23×C8—431no—
457C23×C8—431no—
458C23×C8—431no—
459#536—438no—
460#536—864no—
461C2×C4⋊Q8—861no—
462C2×#124—861no—
463C2×#123—861no—
464C2×#123—861no—
465C2×C22⋊Q8—431no—
466C2×C22⋊Q8—431no—
467C2×C22⋊Q8—431no—
468C2×C22⋊Q8C2×D4311yescharacteristic
469C2×#117—431no—
470C2×#117—431no—
471C22×C4⋊C4—431no—
472#419—864no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—864no—
480C2×#103C2×D4311yescharacteristic
481C2×#103C2×D4311yescharacteristic
482#391—861no—
483#390—861no—
484#386—861no—
485#386—861no—
486#380—431no—
487#380—431no—
488#380—431no—
489#380C2×D4311yescharacteristic
490#340—431no—
491#340—431no—
492#340—431no—
493#340—431no—
494#340—431no—
495#340—431no—
496#340C2×D4311yescharacteristic
497#340C2×D4311yescharacteristic
498C43#2097411yescharacteristic, complemented, Sylow
499C2×#41—434no—
500C2×#41—434no—
501C2×#41—862no—
502C2×#41—862no—
503C2×#41—862no—
504C2×#41—862no—
505C22×Q8—431no—
506C22×Q8—434no—
507C22×Q8—431no—
508C22×Q8—861no—
509C22×Q8—862no—
510C22×Q8—862no—
511C22×Q8—862no—
512C22×Q8—862no—
513C22×Q8—862no—
514C22×Q8C22×D4311yescharacteristic
515C22×D4—431no—
516C22×D4—431no—
517C22×D4—431no—
518C23×C4—431no—
519C23×C4—431no—
520C23×C4—861no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523#131—8632no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—434no—
528C2×M16—862no—
529C2×M16—862no—
530C2×M16—862no—
531C2×M16—862no—
532C2×M16—862no—
533C22×C8—431no—
534C22×C8—431no—
535C22×C8—434no—
536C22×C8—862no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—862no—
542C22×C8—862no—
543C22×C8—862no—
544C22×C8C22×D4311yescharacteristic
545C22×C8C22×D4311yescharacteristic
546C4⋊Q8—868no—
547#124—868no—
548#123—868no—
549#123—868no—
550C22⋊Q8—22no—
551C22⋊Q8—434no—
552C22⋊Q8—434no—
553C22⋊Q8—434no—
554C22⋊Q8—862no—
555C22⋊Q8—862no—
556C22⋊Q8—862no—
557C22⋊Q8C4×D4314yescomplemented
558#117—434no—
559#117—862no—
560#117—862no—
561#117—862no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4—862no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C42—861no—
586C2×C42—861no—
587#103—22no—
588#103—22no—
589#103—862no—
590#103—862no—
591#103—862no—
592#103—862no—
593#103—862no—
594#103—862no—
595#95—21no—
596#95—861no—
597#95—861no—
598#95—861no—
599C24—431no—
600C24—431no—
601C24D4×D4311yescharacteristic
602#41—868no—
603#41—868no—
604#41—868no—
605#41—868no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—434no—
612C2×Q8—432no—
613C2×Q8—862no—
614C2×Q8—862no—
615C2×Q8—864no—
616C2×Q8—868no—
617C2×Q8—868no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—1722no—
624C2×Q8—1722no—
625C2×Q8—1724no—
626C2×Q8—1724no—
627C2×Q8C2×C4×D4312yes—
628C2×D4—434no—
629C2×D4—434no—
630C2×D4—434no—
631C2×D4—862no—
632C2×D4—862no—
633C2×D4—862no—
634C2×D4—862no—
635C2×D4—862no—
636C2×D4—862no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—431no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—432no—
652C22×C4—431no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—864no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—3441no—
665C22×C4—3441no—
666C22×C4—1722no—
667C22×C4—1722no—
668C22×C4—1722no—
669C22×C4C2×C4×D4312yes—
670C22×C4D4×D4311yescharacteristic
671C22×C4D4×D4312yes—
672C22×C4C23×D4311yescharacteristic
673M16—28no—
674M16—868no—
675M16—868no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—432no—
681C2×C8—432no—
682C2×C8—868no—
683C2×C8—868no—
684C2×C8—868no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8D4×D4312yes—
690C2×C8D4×D4312yes—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—432no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—1722no—
707C4⋊C4C2×C4×D4312yes—
708C22⋊C4—24no—
709C22⋊C4—81no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C22⋊C4—864no—
713C22⋊C4—864no—
714C22⋊C4—3441no—
715C22⋊C4—3441no—
716C22⋊C4—3441no—
717C22⋊C4—1722no—
718C42—864no—
719C42—1722no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—432no—
727C23—432no—
728C23—432no—
729C23—432no—
730C23—861no—
731C23—861no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23C22⋊C4×D4312yes—
741C23C2×D4×D4311yescharacteristic
742Q8—22no—
743Q8—22no—
744Q8—41no—
745Q8—41no—
746Q8—868no—
747Q8—862no—
748Q8—862no—
749Q8—1728no—
750Q8—1721no—
751Q8—1721no—
752D4—868no—
753D4—868no—
754D4—868no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—432no—
774C2×C4—432no—
775C2×C4—432no—
776C2×C4—434no—
777C2×C4—434no—
778C2×C4—434no—
779C2×C4—434no—
780C2×C4—432no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—3444no—
790C2×C4—1728no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4C22⋊C4×D4312yes—
802C2×C4C22×C4×D4311yescharacteristic
803C2×C4C2×D4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4#41×D4311yescharacteristic
807C2×C4#41×D4311yescharacteristic
808C8—22no—
809C8—22no—
810C8—862no—
811C8—862no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—434no—
820C22—862no—
821C22—862no—
822C22—862no—
823C22—862no—
824C22—862no—
825C22—862no—
826C22—862no—
827C22—862no—
828C22—862no—
829C22—1721no—
830C22—1721no—
831C22—1721no—
832C22—1721no—
833C22C2×C22⋊C4×D4311yescharacteristic
834C22#121×D4311yescharacteristic
835C22#121×D4311yescharacteristic
836C22#1458370811yescharacteristic
837C22#1458370911yescharacteristic
838C22#1458371511yescharacteristic
839C22#1458371511yescharacteristic
840C4—22no—
841C4—42no—
842C4—42no—
843C4—81no—
844C4—81no—
845C4—434no—
846C4—862no—
847C4—3441no—
848C4—3441no—
849C4—1722no—
850C4—1722no—
851C4C4×D4×D4311yescharacteristic
852C4C4×D4×D4311yescharacteristic
853C4#120×D4311yescharacteristic
854C4#123×D4311yescharacteristic
855C2—42no—
856C2—864no—
857C2—1722no—
858C2#386×D4311yescharacteristic
859C2#1914312611yescharacteristic
860C2#1914312711yescharacteristic
861C2#1914423211yescharacteristic
862C2#1914424811yescharacteristic
863C2#1914428111yescharacteristic
864C2#1914428311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#20974
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
3. C2×#14582906C2semidirect
4. C2×#103×D43C2semidirect
6. #19135028C2semidirect
7. #19135027C2semidirect
8. #19135025C2semidirect
9. #19135019C2semidirect
10. #19135017C2semidirect
11. #19135016C2semidirect
12. #19135015C2semidirect
13. #19134313C2semidirect
14. #19134310C2semidirect
15. C43×#1894C2semidirect
27. #14583472C4semidirect
111. #13063305C2×C4semidirect
113. #13063304C2×C4semidirect
115. #13063301C2×C4semidirect
156. C22⋊Q8×C43C2×C4semidirect
431. #1894D43semidirect
498. C43#20974semidirect
557. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633332
C2×#145834722
C2×#145829062
C2×#103×D432
#191371842
#191350282
#191350272
#191350252
#191350192
#191350172
#191350162
#191350152
#191343132
#191343102
C43×#18942
#2097443