Finite Group Databasebeta

← #25100696

Subgroups — #25100696

Order 11008.

1726 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583462C211yesmaximal, characteristic
2C2×#14582924C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582902C211yesmaximal, characteristic, complemented
5C2×#14582892C211yesmaximal, characteristic, complemented
6C2×#102×D43C211yesmaximal, characteristic, complemented
7#19136949C211yesmaximal, characteristic, complemented
8#19135527C211yesmaximal, characteristic, complemented
9#19135526C211yesmaximal, characteristic, complemented
10#19135526C211yesmaximal, characteristic, complemented
11#19135525C211yesmaximal, characteristic, complemented
12#19135523C211yesmaximal, characteristic, complemented
13#19135520C211yesmaximal, characteristic, complemented
14#19135520C211yesmaximal, characteristic, complemented
15C43×#1982C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583462—24no—
21#14583462C418yescomplemented
22C2×#13063321C2211yescharacteristic
23C2×#13063313C2211yescharacteristic
24C2×#13063312C2211yescharacteristic
25C2×#13063297—21no—
26C2×#13063297—21no—
27C2×#13063293—21no—
28C2×#13063293—21no—
29C2×#13063283C2211yescharacteristic
30C2×#13063282C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582924—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
34C2×Dic43⋊C8C2211yescharacteristic, complemented
35C2×Dic43⋊C8C2211yescharacteristic, complemented
36#14582902—24no—
37#14582897—24no—
38#14582892—24no—
39C2×#13063250C2211yescharacteristic, complemented
40C2×#13063250C2211yescharacteristic, complemented
41C2×#13063248C2211yescharacteristic, complemented
42C2×#13063248C2211yescharacteristic, complemented
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063246C2211yescharacteristic
46C2×#13063246C2211yescharacteristic
47C2×#13063246C2211yescharacteristic, complemented
48C2×#13063246C2211yescharacteristic, complemented
49C2×#13063245C2211yescharacteristic
50C2×#13063245C2211yescharacteristic
51#102×D43—24no—
52C4⋊C4×Dic43C2211yescharacteristic, complemented
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54C4×Dic43⋊C4—21no—
55C4×C4⋊Dic43C2211yescharacteristic, complemented
56#14582750—21no—
57C4×(C2×D43)⋊C4—21no—
58#14582746—21no—
59C2×#127×C43C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic, complemented
64C2×#102×C43C2211yescharacteristic, complemented
65C4×C4⋊C4×C43C2211yescharacteristic, complemented
66C24×D43—21no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900—22no—
71C2×#10621900—22no—
72C2×#10621900C2×C414yes—
73C22×Dic86C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C22×C22⋊D43—21no—
78C22×C22⋊D43—21no—
79C2×D4×D43—22no—
80C2×D4×D43—22no—
81C2×D4×D43—22no—
82C2×D4×D43—22no—
83C2×D4×D43—22no—
84C2×D4×D43C2×C414yes—
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—22no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—22no—
94C2×C8×D43—22no—
95C2×C8×D43—22no—
96#13063321—22no—
97#13063321C2×C414yescomplemented
98#13063313—22no—
99#13063313C2×C414yescomplemented
100#13063312—22no—
101#13063312C2×C414yescomplemented
102#13063297—28no—
103#13063297—28no—
104#13063293—28no—
105#13063293—28no—
106#13063283—22no—
107#13063283D414yescomplemented
108#13063282C2×C414yes—
109#13063282D414yes—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4D411yescharacteristic
114C2×Dic43⋊C4D411yescharacteristic
115C4⋊C4×D43—22no—
116C4⋊C4×D43D414yescomplemented
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4D411yescharacteristic
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×C4×Dic43—21no—
125C2×C4×Dic43—21no—
126C2×C4×Dic43—21no—
127C2×C4×Dic43—21no—
128C2×C4×Dic43C2311yescharacteristic
129C4⋊(C43⋊C8)—22no—
130Dic43⋊C8—22no—
131Dic43⋊C8—22no—
132#13063250—22no—
133#13063250—22no—
134#13063248—22no—
135#13063248—22no—
136#13063247—22no—
137#13063247—22no—
138#13063246—22no—
139#13063246—22no—
140#13063246—22no—
141#13063246—22no—
142#13063245—22no—
143#13063245—22no—
144C43⋊#95—21no—
145C43⋊#95—21no—
146C43⋊#95—21no—
147C22×D4×C43—21no—
148C22×D4×C43—21no—
149C22×D4×C43C2311yescharacteristic
150C22×D4×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C22×C8×C43C2311yescharacteristic
153#127×C43—22no—
154#127×C43C2×C414yescomplemented
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C42×C43—21no—
158C2×C42×C43C2311yescharacteristic
159C4⋊C8×C43—22no—
160#102×C43—22no—
161#102×C43—22no—
162#102×C43—22no—
163#102×C43—22no—
164#95×C43—21no—
165C24×C43—21no—
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×D4×C43—24no—
177C2×D4×C43—24no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—81no—
189C2×D4×C43—81no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43C22×C412yes—
193C2×D4×C43C22×C412yes—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220#10621900—28no—
221#10621900—28no—
222#10621900—44no—
223#10621900—44no—
224D4×D43—28no—
225D4×D43—28no—
226D4×D43—44no—
227D4×D43—44no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172C22×C412yes—
234C2×C4×D43—24no—
235C2×C4×D43—81no—
236C2×C4×D43—81no—
237C2×C4×D43C22×C412yes—
238C2×C4×D43C2×D412yes—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2×D412yes—
241C2×C4×D43#4112yes—
242C2×C4×D43#4112yes—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86C22×C412yes—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2×D412yes—
258C4⋊C4×C43C2×D412yes—
259C42×C43—81no—
260C42×C43C22×C412yes—
261C42×C43C2×D412yes—
262C22⋊Dic43—24no—
263C22⋊Dic43—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4C22⋊C414yes—
268(C2×D43)⋊C4C22⋊C414yes—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43C2×D412yes—
272C4⋊Dic43C2×D412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4C22⋊C414yes—
275Dic43⋊C4C22⋊C414yes—
276C4×Dic43—24no—
277C4×Dic43—81no—
278C4×Dic43—81no—
279C4×Dic43—81no—
280C4×Dic43C22×C412yes—
281C4×Dic43C2×D412yes—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288#10621872—44no—
289C8×D43—44no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43C22×D411yescharacteristic
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—21no—
308C22×D43—21no—
309C22×D43—22no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—48no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43—84no—
320C22×D43—84no—
321C22×D43—84no—
322C22×D43—84no—
323C22×D43C2×C22⋊C412yes—
324C22×D43#12112yes—
325C22×D43#12112yes—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—22no—
329D4×C43—22no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—41no—
334D4×C43—84no—
335D4×C43—84no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43C2×C22⋊C412yes—
347C2×C4×C43C2×C22⋊C412yes—
348C2×C4×C43C23×C411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C22⋊D43—48no—
355C22⋊D43—48no—
356C22⋊D43—84no—
357C22⋊D43—84no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—48no—
372C2×Dic43C2×C22⋊C412yes—
373C2×Dic43C2×C22⋊C412yes—
374C2×Dic43C2×C22⋊C412yes—
375C2×Dic43#12112yes—
376C2×Dic43#12112yes—
377D172—22no—
378D172—22no—
379D172—41no—
380D172—41no—
381C4×D43—84no—
382C4×D43C4×D414yes—
383C4×D43C4×D414yes—
384C4×D43#12414yes—
385C4×D43#12714yes—
386Dic86—22no—
387Dic86—22no—
388Dic86—41no—
389Dic86—41no—
390C8×C43—41no—
391C8×C43—41no—
392C43⋊C8—41no—
393C43⋊C8—41no—
394#21263—431nomaximal, Sylow
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43C22×C22⋊C411yescharacteristic
410C22×C43C2×#12111yescharacteristic
411C22×C43C2×#12111yescharacteristic
412C22×C43#57611yescharacteristic
413C22×C43#57611yescharacteristic
414C22×C43#57711yescharacteristic
415C22×C43#57711yescharacteristic
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—816no—
426C2×D43—81no—
427C2×D43—81no—
428C2×D43—81no—
429C2×D43—81no—
430C2×D43#39014yes—
431C4×C43—22no—
432C4×C43—22no—
433C4×C43—42no—
434C4×C43—42no—
435C4×C43C2×C4×D411yescharacteristic
436C4×C43C2×C4×D411yescharacteristic
437C4×C43C2×#12411yescharacteristic
438C4×C43C2×#12711yescharacteristic
439Dic43—22no—
440Dic43—22no—
441Dic43—42no—
442Dic43—42no—
443Dic43—42no—
444Dic43#39014yes—
445C2×#535—431no—
446C2×#424—431no—
447C2×#417—431no—
448C2×#418—431no—
449C2×#416—431no—
450C22×#102—431no—
451#2274—431no—
452#1983—431no—
453#1983—431no—
454#1983—431no—
455#1983—431no—
456#1982—431no—
457#1982—431no—
458#1982—431no—
459#1982D4311yescharacteristic, complemented
460C2×C43—82no—
461C2×C43—82no—
462C2×C43C2×#39011yescharacteristic
463C2×C43#289711yescharacteristic
464C2×C43#289711yescharacteristic
465C2×C43#304111yescharacteristic
466C2×C43#304311yescharacteristic
467C2×C43#304511yescharacteristic
468C2×C43#304511yescharacteristic
469D43—24no—
470D43—82no—
471C22×#41—431no—
472C23×D4—431no—
473C22×M16—431no—
474C23×C8—431no—
475#535—438no—
476#535—864no—
477C2×#127—431no—
478C2×#127C2×D4311yescharacteristic
479C2×#124—431no—
480C2×#124—431no—
481C2×#121—861no—
482C2×#121—861no—
483C2×#120—861no—
484C2×#120—861no—
485C2×#117—431no—
486C2×#117—431no—
487C22×C4⋊C4—431no—
488#424—864no—
489C2×C4⋊C8—431no—
490C2×C4⋊C8—431no—
491C2×C4⋊C8—431no—
492C2×C4⋊C8C2×D4311yescharacteristic, complemented
493#418—864no—
494#417—864no—
495#416—864no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#103—431no—
499C2×#103—431no—
500C2×#102—431no—
501C2×#102—431no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—864no—
509C2×#102C2×D4311yescharacteristic
510C2×#102C2×D4311yescharacteristic
511C2×#102C2×D4311yescharacteristic, complemented
512C2×#102C2×D4311yescharacteristic, complemented
513C4×C4⋊C4—431no—
514C4×C4⋊C4—431no—
515C4×C4⋊C4—431no—
516C4×C4⋊C4—861no—
517C4×C4⋊C4—861no—
518C4×C4⋊C4C2×D4311yescharacteristic, complemented
519C4×C22⋊C4—861no—
520C4×C22⋊C4—861no—
521C43#2126311yescharacteristic, complemented, Sylow
522C25—861no—
523C2×#41—434no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—862no—
529C22×Q8—431no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—434no—
533C22×D4—431no—
534C22×D4—862no—
535C22×D4—862no—
536C22×D4—862no—
537C22×D4—862no—
538C22×D4—862no—
539C22×D4—861no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4C22×D4311yescharacteristic
544C22×D4C22×D4311yescharacteristic
545C23×C4—431no—
546C23×C4—861no—
547C23×C4—861no—
548C2×M16—862no—
549C2×M16—862no—
550C2×M16—862no—
551C22×C8—431no—
552C22×C8—431no—
553C22×C8—862no—
554C22×C8—862no—
555C22×C8—862no—
556C22×C8C22×D4311yescharacteristic
557C22×C8C22×D4311yescharacteristic
558#127—22no—
559#127—434no—
560#127—862no—
561#127C4×D4314yescomplemented
562#124—434no—
563#124—434no—
564#124—862no—
565#124—862no—
566#121—868no—
567#121—868no—
568#120—868no—
569#120—868no—
570#117—434no—
571#117—434no—
572#117—434no—
573#117—862no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—434no—
579C2×C4⋊C4—862no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C4⋊C4C22×D4311yescharacteristic
583C2×C22⋊C4—431no—
584C2×C22⋊C4—431no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C42—21no—
591C2×C42—431no—
592C2×C42—861no—
593C2×C42—861no—
594C2×C42—861no—
595C2×C42—861no—
596C2×C42C22×D4311yescharacteristic
597C4⋊C8—22no—
598C4⋊C8—862no—
599C4⋊C8—862no—
600C4⋊C8—862no—
601#103—862no—
602#103—862no—
603#103—862no—
604#103—862no—
605#102—22no—
606#102—22no—
607#102—22no—
608#102—22no—
609#102—862no—
610#102—862no—
611#102—862no—
612#102—862no—
613#102—862no—
614#102—862no—
615#102—862no—
616#102—862no—
617#95—21no—
618#95—861no—
619#95—861no—
620#95—861no—
621C24—21no—
622C24—21no—
623C24—431no—
624C24—864no—
625C24—861no—
626C24—3441no—
627C24—3441no—
628C24—3441no—
629C24—3441no—
630C24—1722no—
631C24—1722no—
632#41—868no—
633#41—868no—
634#41—1724no—
635#41—1724no—
636C2×Q8—432no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×Q8—861no—
641C2×Q8—861no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—432no—
659C2×D4—868no—
660C2×D4—868no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—3441no—
671C2×D4—3441no—
672C2×D4—3441no—
673C2×D4—3441no—
674C2×D4—1724no—
675C2×D4—1724no—
676C2×D4—1722no—
677C2×D4—1722no—
678C2×D4—1722no—
679C2×D4—1722no—
680C2×D4C2×C4×D4312yes—
681C2×D4C2×C4×D4312yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—431no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4—432no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—431no—
692C22×C4—431no—
693C22×C4—864no—
694C22×C4—864no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—3441no—
699C22×C4—3441no—
700C22×C4—1722no—
701C22×C4—1722no—
702C22×C4D4×D4311yescharacteristic
703C22×C4D4×D4311yescharacteristic
704C22×C4C23×D4311yescharacteristic
705M16—1724no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—861no—
713C2×C8—861no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—861no—
718C2×C8—1724no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—434no—
722C4⋊C4—434no—
723C4⋊C4—432no—
724C4⋊C4—432no—
725C4⋊C4—864no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4D4×D4312yes—
729C4⋊C4D4×D4312yes—
730C22⋊C4—434no—
731C22⋊C4—434no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C42—81no—
738C42—432no—
739C42—432no—
740C42—864no—
741C42—3441no—
742C42—3441no—
743C42—3441no—
744C42C2×C4×D4312yes—
745C42D4×D4312yes—
746C23—22no—
747C23—22no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—432no—
761C23—432no—
762C23—432no—
763C23—861no—
764C23—861no—
765C23—861no—
766C23—861no—
767C23—862no—
768C23—3444no—
769C23—3444no—
770C23—3444no—
771C23—3444no—
772C23—3444no—
773C23—3444no—
774C23—1728no—
775C23—1721no—
776C23—1721no—
777C23—1721no—
778C23—1721no—
779C23—1721no—
780C23—1721no—
781C23C2×D4×D4311yescharacteristic
782Q8—862no—
783Q8—862no—
784Q8—1721no—
785Q8—1721no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—84no—
795D4—84no—
796D4—862no—
797D4—862no—
798D4—3444no—
799D4—3444no—
800D4—1728no—
801D4—1728no—
802D4—1721no—
803D4—1721no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—432no—
815C2×C4—432no—
816C2×C4—432no—
817C2×C4—434no—
818C2×C4—434no—
819C2×C4—434no—
820C2×C4—434no—
821C2×C4—432no—
822C2×C4—432no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—3444no—
831C2×C4—1728no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4C22⋊C4×D4312yes—
839C2×C4C22⋊C4×D4312yes—
840C2×C4C22×C4×D4311yescharacteristic
841C2×C4C2×D4×D4311yescharacteristic
842C2×C4C2×D4×D4311yescharacteristic
843C2×C4C2×D4×D4311yescharacteristic
844C2×C4#41×D4311yescharacteristic
845C2×C4#41×D4311yescharacteristic
846C8—41no—
847C8—41no—
848C8—1721no—
849C8—1721no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—434no—
865C22—862no—
866C22—862no—
867C22—862no—
868C22—862no—
869C22—862no—
870C22—862no—
871C22—34416no—
872C22—3441no—
873C22—3441no—
874C22—3441no—
875C22—3441no—
876C22—1722no—
877C22—1722no—
878C22—1722no—
879C22C2×C22⋊C4×D4311yescharacteristic
880C22#121×D4311yescharacteristic
881C22#121×D4311yescharacteristic
882C22#1458370011yescharacteristic
883C22#1458370311yescharacteristic
884C22#1458370511yescharacteristic
885C22#1458370911yescharacteristic
886C4—22no—
887C4—22no—
888C4—42no—
889C4—42no—
890C4—434no—
891C4—862no—
892C4—862no—
893C4—1722no—
894C4—1722no—
895C4—1722no—
896C4C4×D4×D4311yescharacteristic
897C4C4×D4×D4311yescharacteristic
898C4#124×D4311yescharacteristic
899C4#127×D4311yescharacteristic
900C2—82no—
901C2—82no—
902C2—864no—
903C2—3442no—
904C2#390×D4311yescharacteristic
905C2#1914311611yescharacteristic
906C2#1914312011yescharacteristic
907C2#1914409311yescharacteristic
908C2#1914411111yescharacteristic
909C2#1914412911yescharacteristic
910C2#1914413111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1982C2
socleC23×C43C22×D4
prime radicalC2×#14583462C2
cosocleC22×C4×C43C24
hypercenter#1982D43
hypocenterC43#21263
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#14582924C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582902C2semidirect
5. C2×#14582892C2semidirect
6. C2×#102×D43C2semidirect
7. #19136949C2semidirect
8. #19135527C2semidirect
9. #19135526C2semidirect
10. #19135526C2semidirect
11. #19135525C2semidirect
12. #19135523C2semidirect
13. #19135520C2semidirect
14. #19135520C2semidirect
15. C43×#1982C2semidirect
21. #14583462C4semidirect
33. C2×C4⋊(C43⋊C8)C22semidirect
34. C2×Dic43⋊C8C22semidirect
35. C2×Dic43⋊C8C22semidirect
39. C2×#13063250C22semidirect
40. C2×#13063250C22semidirect
41. C2×#13063248C22semidirect
42. C2×#13063248C22semidirect
47. C2×#13063246C22semidirect
48. C2×#13063246C22semidirect
52. C4⋊C4×Dic43C22semidirect
53. C4⋊C4×Dic43C22semidirect
55. C4×C4⋊Dic43C22semidirect
60. C2×C4⋊C8×C43C22semidirect
63. C2×#102×C43C22semidirect
64. C2×#102×C43C22semidirect
65. C4×C4⋊C4×C43C22semidirect
97. #13063321C2×C4semidirect
99. #13063313C2×C4semidirect
101. #13063312C2×C4semidirect
107. #13063283D4semidirect
116. C4⋊C4×D43D4semidirect
154. #127×C43C2×C4semidirect
459. #1982D43semidirect
492. C2×C4⋊C8C2×D43semidirect
511. C2×#102C2×D43semidirect
512. C2×#102C2×D43semidirect
518. C4×C4⋊C4C2×D43semidirect
521. C43#21263semidirect
561. #127C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834622
C2×#145829242
C2×#145828972
C2×#145829022
C2×#145828922
C2×#102×D432
#191369492
#191355272
#191355262
#191355252
#191355232
#191355202
C43×#19822
#2126343