Finite Group Databasebeta

← #25098329

Subgroups — #25098329

Order 11008.

1946 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063333C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic
3C2×#14582902C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137184C211yesmaximal, characteristic, complemented
6#19135033C211yesmaximal, characteristic, complemented
7#19135032C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19135024C211yesmaximal, characteristic, complemented
10#19135022C211yesmaximal, characteristic, complemented
11#19135021C211yesmaximal, characteristic, complemented
12#19135020C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#1895C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C2×#13063333—24no—
19C2×#13063333—24no—
20C2×#13063333—24no—
21C22×#10621872C2211yescharacteristic
22C22×#10621872C2211yescharacteristic, complemented
23C23×C43⋊C8C2211yescharacteristic, complemented
24C22×C8×D43C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic, complemented
26#14583465—24no—
27#14583465C418yescomplemented
28C2×#13063321—21no—
29C2×#13063311—21no—
30C2×#13063300C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063296C2211yescharacteristic
33C2×#13063295—21no—
34C2×#13063293—21no—
35C2×#13063283C2211yescharacteristic
36C2×#13063283C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582902—24no—
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45#102×D43—24no—
46#14582803—21no—
47#14582799—21no—
48#14582777—21no—
49#14582775—21no—
50#14582759C2211yescharacteristic, complemented
51#14582756C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57#14582661C2211yescharacteristic, complemented
58#14582661C2211yescharacteristic, complemented
59C22×M16×C43C2211yescharacteristic, complemented
60C2×#121×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic, complemented
64C43×#340C2211yescharacteristic, complemented
65C43×#340C2211yescharacteristic, complemented
66C24×D43—21no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—22no—
71C2×#10621898C2×C414yes—
72C2×#10621898D414yes—
73C22×Dic86D411yescharacteristic
74C22×D172—21no—
75C22×D172D411yescharacteristic
76C22×D172C2311yescharacteristic
77C22×C22⋊D43—21no—
78C22×C22⋊D43—21no—
79C22×C22⋊D43—21no—
80C22×C22⋊D43D411yescharacteristic
81C22×C22⋊D43D411yescharacteristic
82C2×D4×D43—22no—
83C2×D4×D43—22no—
84C2×D4×D43—22no—
85C2×D4×D43—22no—
86C2×D4×D43—22no—
87C2×D4×D43C2×C414yes—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91#13063333—232no—
92C2×#10621872—22no—
93C2×#10621872—22no—
94C2×#10621872—22no—
95C2×#10621872—22no—
96C2×#10621872—22no—
97C2×#10621872D414yescomplemented
98C22×C43⋊C8—22no—
99C22×C43⋊C8—22no—
100C22×C43⋊C8—22no—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—22no—
104C2×C8×D43—22no—
105C2×C8×D43—22no—
106C2×C8×D43—22no—
107C2×C8×D43—22no—
108C2×C8×D43D414yescomplemented
109#13063321—28no—
110#13063311—28no—
111#13063300—22no—
112#13063300C2×C414yescomplemented
113#13063299—22no—
114#13063299C2×C414yescomplemented
115#13063296—22no—
116#13063296C2×C414yescomplemented
117#13063295—28no—
118#13063293—28no—
119#13063283—22no—
120#13063283—22no—
121#13063283—22no—
122#13063283C2×C414yes—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
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#13063247—22no—
140#13063247—22no—
141#13063246—22no—
142#13063246—22no—
143#13063245—22no—
144#13063245—22no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C43⋊#95—21no—
148C22×D4×C43—21no—
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C2×M16×C43—22no—
152C2×M16×C43—22no—
153C2×M16×C43—22no—
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#121×C43—22no—
157#121×C43C2×C414yescomplemented
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163#102×C43—22no—
164#102×C43—22no—
165#95×C43—21no—
166C24×C43—21no—
167C24×C43C2×D411yescharacteristic
168C23×D43—21no—
169C23×D43—24no—
170C23×D43—42no—
171C23×D43—42no—
172C23×D43—81no—
173C23×D43—81no—
174C23×D43—81no—
175C23×D43—81no—
176C23×D43C2×D411yescharacteristic
177C23×D43C2×D411yescharacteristic
178C2×D4×C43—21no—
179C2×D4×C43—24no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—81no—
185C2×D4×C43—81no—
186C2×D4×C43C22×C412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43C22×C412yes—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43C22⋊C414yes—
212C2×C22⋊D43C22⋊C414yes—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218D4×D43—28no—
219D4×D43—28no—
220D4×D43—44no—
221D4×D43—44no—
222#10621898—28no—
223#10621898—28no—
224#10621898—28no—
225#10621898—28no—
226C2×D172—21no—
227C2×D172—24no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—81no—
235C2×D172—81no—
236C2×D172C22⋊C414yes—
237C2×D172C22×C412yes—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—42no—
243C2×C4×D43—81no—
244C2×C4×D43—81no—
245C2×C4×D43C22×C412yes—
246C2×C4×D43C22×C412yes—
247C2×C4×D43C2×D412yes—
248C2×C4×D43C2×D412yes—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2×D412yes—
251C2×C4×D43#4112yes—
252C2×C4×D43#4112yes—
253C2×Dic86—22no—
254C2×Dic86—22no—
255C2×Dic86C22⋊C414yes—
256M16×C43—28no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43C2×D412yes—
262C2×C8×C43C2×D412yes—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43C22×C412yes—
269C22⋊C4×C43—24no—
270C22⋊C4×C43—81no—
271C22⋊Dic43—24no—
272C22⋊Dic43—81no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—42no—
277(C2×D43)⋊C4—81no—
278(C2×D43)⋊C4—81no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43C22×C412yes—
285Dic43⋊C4—42no—
286C4×Dic43—24no—
287C4×Dic43—42no—
288C2×C43⋊C8—28no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8C2×D412yes—
294C2×C43⋊C8C2×D412yes—
295#10621872—28no—
296#10621872—28no—
297C8×D43—28no—
298C8×D43—28no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—22no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43C2×C22⋊C412yes—
313C23×C43C22×D411yescharacteristic
314C22×D43—21no—
315C22×D43—21no—
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—21no—
324C22×D43—22no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—48no—
332C22×D43—84no—
333C22×D43—84no—
334C22×D43—84no—
335C22×D43—84no—
336C22×D43—84no—
337C22×D43—84no—
338C22×D43C2×C22⋊C412yes—
339C22×D43C2×C22⋊C412yes—
340C22×D43#12112yes—
341C22×D43#12112yes—
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—41no—
345D4×C43—41no—
346D4×C43—84no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43C2×C22⋊C412yes—
363C2×C4×C43C23×C411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C2×#4111yescharacteristic
368C2×C4×C43C2×#4111yescharacteristic
369C22⋊D43—28no—
370C22⋊D43—28no—
371C22⋊D43—48no—
372C22⋊D43—84no—
373C22⋊D43—84no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—22no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43C2×C22⋊C412yes—
386C2×Dic43C2×C22⋊C412yes—
387C2×Dic43#12112yes—
388C2×Dic43#12112yes—
389D172—28no—
390D172—22no—
391D172—22no—
392D172—41no—
393D172—41no—
394D172—84no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—22no—
398C4×D43—22no—
399C4×D43—84no—
400C4×D43C4×D414yes—
401C4×D43C4×D414yes—
402C4×D43#12014yes—
403C4×D43#12314yes—
404Dic86—28no—
405C8×C43—22no—
406C8×C43—22no—
407C43⋊C8—22no—
408C43⋊C8—22no—
409#20975—431nomaximal, Sylow
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—41no—
417C22×C43—42no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—81no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43—81no—
424C22×C43C22×C22⋊C411yescharacteristic
425C22×C43C2×#12111yescharacteristic
426C22×C43C2×#12111yescharacteristic
427C22×C43#57611yescharacteristic
428C22×C43#57611yescharacteristic
429C22×C43#57711yescharacteristic
430C22×C43#57711yescharacteristic
431C2×D43—22no—
432C2×D43—22no—
433C2×D43—22no—
434C2×D43—22no—
435C2×D43—22no—
436C2×D43—22no—
437C2×D43—22no—
438C2×D43—22no—
439C2×D43—22no—
440C2×D43—41no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—42no—
447C2×D43—816no—
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43#38614yes—
453C4×C43—22no—
454C4×C43—42no—
455C4×C43—81no—
456C4×C43—81no—
457C4×C43C2×C4×D411yescharacteristic
458C4×C43C2×C4×D411yescharacteristic
459C4×C43C2×#12011yescharacteristic
460C4×C43C2×#12311yescharacteristic
461Dic43—22no—
462Dic43—42no—
463Dic43—81no—
464Dic43—81no—
465Dic43#38614yes—
466C22×#131—431no—
467C2×#535—431no—
468C2×#418—431no—
469C22×#102—431no—
470#2311—431no—
471#1895—431no—
472#1895—431no—
473#1895—431no—
474#1895D4311yescharacteristic, complemented
475#1893—431no—
476#1893—431no—
477#1893—431no—
478#1893—431no—
479#1736—431no—
480#1735—431no—
481C2×C43—42no—
482C2×C43—82no—
483C2×C43C2×#38611yescharacteristic
484C2×C43#289711yescharacteristic
485C2×C43#289711yescharacteristic
486C2×C43#305711yescharacteristic
487C2×C43#305811yescharacteristic
488C2×C43#306211yescharacteristic
489C2×C43#306211yescharacteristic
490D43—24no—
491D43—42no—
492D43—82no—
493C22×#41—431no—
494C23×D4—431no—
495C2×#131—864no—
496C2×#131—864no—
497C2×#131—864no—
498C22×M16—431no—
499C22×M16—431no—
500C22×M16C2×D4311yescharacteristic, complemented
501C23×C8—431no—
502C23×C8—431no—
503C23×C8—431no—
504#535—438no—
505#535—864no—
506C2×#127—861no—
507C2×#124—861no—
508C2×#121—431no—
509C2×#121—431no—
510C2×#121—431no—
511C2×#121C2×D4311yescharacteristic
512C2×#120—861no—
513C2×#120—861no—
514C2×#117—431no—
515C2×#117—431no—
516C22×C4⋊C4—431no—
517#418—864no—
518C2×#102—431no—
519C2×#102—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—431no—
524C2×#102—864no—
525C2×#102C2×D4311yescharacteristic
526C2×#102C2×D4311yescharacteristic
527#391—861no—
528#390—861no—
529#386—861no—
530#386—861no—
531#380—431no—
532#380—431no—
533#380—431no—
534#380C2×D4311yescharacteristic, complemented
535#340—431no—
536#340—431no—
537#340—431no—
538#340—431no—
539#340—431no—
540#340—431no—
541#340C2×D4311yescharacteristic, complemented
542#340C2×D4311yescharacteristic, complemented
543C43#2097511yescharacteristic, complemented, Sylow
544C25—861no—
545C2×#41—434no—
546C2×#41—434no—
547C2×#41—862no—
548C2×#41—862no—
549C2×#41—862no—
550C2×#41—862no—
551C22×Q8—431no—
552C22×D4—21no—
553C22×D4—431no—
554C22×D4—431no—
555C22×D4—434no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—861no—
559C22×D4—862no—
560C22×D4—862no—
561C22×D4—862no—
562C22×D4—862no—
563C22×D4—862no—
564C22×D4—861no—
565C22×D4—861no—
566C22×D4—861no—
567C22×D4C22×D4311yescharacteristic
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—861no—
571C23×C4C22×D4311yescharacteristic
572#131—8632no—
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—434no—
577C2×M16—862no—
578C2×M16—862no—
579C2×M16—862no—
580C2×M16—862no—
581C2×M16—862no—
582C22×C8—431no—
583C22×C8—431no—
584C22×C8—434no—
585C22×C8—862no—
586C22×C8—862no—
587C22×C8—862no—
588C22×C8—862no—
589C22×C8—862no—
590C22×C8—862no—
591C22×C8—862no—
592C22×C8—862no—
593C22×C8C22×D4311yescharacteristic
594C22×C8C22×D4311yescharacteristic
595#127—868no—
596#124—868no—
597#121—22no—
598#121—434no—
599#121—434no—
600#121—434no—
601#121—862no—
602#121—862no—
603#121—862no—
604#121C4×D4314yescomplemented
605#120—868no—
606#120—868no—
607#117—434no—
608#117—862no—
609#117—862no—
610#117—862no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—862no—
615C2×C4⋊C4—862no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C4⋊C4C22×D4311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C42—861no—
631C2×C42—861no—
632#102—22no—
633#102—22no—
634#102—862no—
635#102—862no—
636#102—862no—
637#102—862no—
638#102—862no—
639#102—862no—
640#95—21no—
641#95—861no—
642#95—861no—
643#95—861no—
644C24—21no—
645C24—431no—
646C24—431no—
647C24—864no—
648C24—861no—
649C24—3441no—
650C24—3441no—
651C24—3441no—
652C24—3441no—
653C24—1722no—
654C24—1722no—
655C24D4×D4311yescharacteristic
656#41—868no—
657#41—868no—
658#41—868no—
659#41—868no—
660C2×Q8—434no—
661C2×Q8—862no—
662C2×Q8—862no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—434no—
672C2×D4—434no—
673C2×D4—434no—
674C2×D4—432no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—864no—
678C2×D4—868no—
679C2×D4—868no—
680C2×D4—862no—
681C2×D4—862no—
682C2×D4—864no—
683C2×D4—862no—
684C2×D4—862no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—861no—
691C2×D4—861no—
692C2×D4—3441no—
693C2×D4—3441no—
694C2×D4—3441no—
695C2×D4—3441no—
696C2×D4—3441no—
697C2×D4—3441no—
698C2×D4—1724no—
699C2×D4—1724no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4C2×C4×D4312yes—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—431no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—432no—
715C22×C4—432no—
716C22×C4—432no—
717C22×C4—431no—
718C22×C4—432no—
719C22×C4—432no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—3441no—
728C22×C4—3441no—
729C22×C4—1722no—
730C22×C4C2×C4×D4312yes—
731C22×C4D4×D4311yescharacteristic
732C22×C4D4×D4312yes—
733C22×C4C23×D4311yescharacteristic
734M16—28no—
735M16—868no—
736M16—868no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—432no—
742C2×C8—432no—
743C2×C8—868no—
744C2×C8—868no—
745C2×C8—868no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8D4×D4312yes—
751C2×C8D4×D4312yes—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—432no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—1722no—
764C4⋊C4C2×C4×D4312yes—
765C22⋊C4—24no—
766C22⋊C4—81no—
767C22⋊C4—864no—
768C22⋊C4—864no—
769C22⋊C4—864no—
770C22⋊C4—864no—
771C22⋊C4—3441no—
772C22⋊C4—3441no—
773C22⋊C4—3441no—
774C22⋊C4—1722no—
775C42—864no—
776C42—1722no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—432no—
791C23—432no—
792C23—432no—
793C23—432no—
794C23—861no—
795C23—861no—
796C23—861no—
797C23—861no—
798C23—861no—
799C23—861no—
800C23—861no—
801C23—861no—
802C23—861no—
803C23—861no—
804C23—862no—
805C23—3444no—
806C23—3444no—
807C23—3444no—
808C23—3444no—
809C23—3444no—
810C23—3444no—
811C23—1728no—
812C23—1721no—
813C23—1721no—
814C23—1721no—
815C23—1721no—
816C23—1721no—
817C23—1721no—
818C23C22⋊C4×D4312yes—
819C23C2×D4×D4311yescharacteristic
820Q8—868no—
821D4—22no—
822D4—22no—
823D4—41no—
824D4—41no—
825D4—84no—
826D4—868no—
827D4—868no—
828D4—868no—
829D4—862no—
830D4—862no—
831D4—3444no—
832D4—3444no—
833D4—3444no—
834D4—1728no—
835D4—1721no—
836D4—1721no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—432no—
853C2×C4—432no—
854C2×C4—432no—
855C2×C4—434no—
856C2×C4—434no—
857C2×C4—434no—
858C2×C4—434no—
859C2×C4—432no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—3444no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4C22⋊C4×D4312yes—
877C2×C4C22×C4×D4311yescharacteristic
878C2×C4C2×D4×D4311yescharacteristic
879C2×C4C2×D4×D4311yescharacteristic
880C2×C4C2×D4×D4311yescharacteristic
881C2×C4#41×D4311yescharacteristic
882C2×C4#41×D4311yescharacteristic
883C8—22no—
884C8—22no—
885C8—862no—
886C8—862no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—434no—
902C22—862no—
903C22—862no—
904C22—862no—
905C22—862no—
906C22—862no—
907C22—862no—
908C22—862no—
909C22—862no—
910C22—862no—
911C22—34416no—
912C22—3441no—
913C22—3441no—
914C22—3441no—
915C22—3441no—
916C22—1722no—
917C22—1722no—
918C22—1722no—
919C22—1721no—
920C22—1721no—
921C22—1721no—
922C22—1721no—
923C22C2×C22⋊C4×D4311yescharacteristic
924C22#121×D4311yescharacteristic
925C22#121×D4311yescharacteristic
926C22#1458370311yescharacteristic
927C22#1458370311yescharacteristic
928C22#1458370811yescharacteristic
929C22#1458370911yescharacteristic
930C4—22no—
931C4—42no—
932C4—81no—
933C4—81no—
934C4—434no—
935C4—862no—
936C4—3441no—
937C4—3441no—
938C4—1722no—
939C4C4×D4×D4311yescharacteristic
940C4C4×D4×D4311yescharacteristic
941C4#120×D4311yescharacteristic
942C4#123×D4311yescharacteristic
943C2—42no—
944C2—82no—
945C2—864no—
946C2—3442no—
947C2—1722no—
948C2#386×D4311yescharacteristic
949C2#1914311911yescharacteristic
950C2#1914312011yescharacteristic
951C2#1914423211yescharacteristic
952C2#1914424111yescharacteristic
953C2#1914427011yescharacteristic
954C2#1914427211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#14583465C2
cosocleC22×C4×C43C24
hypercenter#1895D43
hypocenterC43#20975
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C22×#13063333C2semidirect
3. C2×#14582902C2semidirect
4. C2×#102×D43C2semidirect
5. #19137184C2semidirect
6. #19135033C2semidirect
7. #19135032C2semidirect
8. #19135030C2semidirect
9. #19135024C2semidirect
10. #19135022C2semidirect
11. #19135021C2semidirect
12. #19135020C2semidirect
13. #19134313C2semidirect
14. #19134310C2semidirect
15. C43×#1895C2semidirect
22. C22×#10621872C22semidirect
23. C23×C43⋊C8C22semidirect
25. C22×C8×D43C22semidirect
27. #14583465C4semidirect
50. #14582759C22semidirect
51. #14582756C22semidirect
52. #14582756C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
57. #14582661C22semidirect
58. #14582661C22semidirect
59. C22×M16×C43C22semidirect
63. C43×#380C22semidirect
64. C43×#340C22semidirect
65. C43×#340C22semidirect
97. C2×#10621872D4semidirect
108. C2×C8×D43D4semidirect
112. #13063300C2×C4semidirect
114. #13063299C2×C4semidirect
116. #13063296C2×C4semidirect
157. #121×C43C2×C4semidirect
474. #1895D43semidirect
500. C22×M16C2×D43semidirect
534. #380C2×D43semidirect
541. #340C2×D43semidirect
542. #340C2×D43semidirect
543. C43#20975semidirect
604. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633332
C2×#145834652
C2×#145829022
C2×#102×D432
#191371842
#191350332
#191350322
#191350302
#191350242
#191350222
#191350212
#191350202
#191343132
#191343102
C43×#18952
#2097543