Finite Group Databasebeta

← #25097866

Subgroups — #25097866

Order 11008.

1842 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583479C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#14582894C211yesmaximal, characteristic, complemented
5C2×#14582864C211yesmaximal, characteristic, complemented
6#19134916C211yesmaximal, characteristic, complemented
7#19134915C211yesmaximal, characteristic, complemented
8#19134912C211yesmaximal, characteristic, complemented
9#19134911C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic, complemented
11#19134904C211yesmaximal, characteristic, complemented
12#19134899C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621898C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583479—24no—
21#14583479C418yescomplemented
22C2×#13063303—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063300—21no—
25C2×#13063300C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063298—21no—
28C2×#13063298—21no—
29#14583380—24no—
30#14583380—24no—
31C2×#13063290—21no—
32C2×#13063287—21no—
33C2×C4×C22⋊D43—21no—
34C2×C4×C22⋊D43—21no—
35C2×#13063284C2211yescharacteristic
36C2×#13063283C2211yescharacteristic
37C2×#13063283C2211yescharacteristic
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41#14582899—24no—
42#14582894—24no—
43C2×#13063249C2211yescharacteristic
44C2×#13063249C2211yescharacteristic
45C2×#13063247C2211yescharacteristic
46C2×#13063247C2211yescharacteristic
47C2×#13063245C2211yescharacteristic
48C2×#13063245C2211yescharacteristic
49#14582864—24no—
50C2×C22⋊(C43⋊C8)C2211yescharacteristic
51C2×(C2×D43)⋊C8C2211yescharacteristic
52C2×(C2×D43)⋊C8C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57#14582661C2211yescharacteristic
58#14582661C2211yescharacteristic
59C2×C22⋊Q8×C43C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#340C2211yescharacteristic
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902—22no—
70C2×#10621902—22no—
71C2×#10621902C2×C414yescomplemented
72C2×#10621898—22no—
73C2×#10621898—22no—
74C2×#10621898—22no—
75C2×#10621898—22no—
76C2×#10621898C2×C414yes—
77C2×#10621898D414yes—
78C22×Dic86D411yescharacteristic
79C22×D172—21no—
80C22×D172—21no—
81C22×D172D411yescharacteristic
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43D411yescharacteristic
85C22×C22⋊D43D411yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C22×C4×D43C2311yescharacteristic
92C2×#10621872—22no—
93C2×#10621872—22no—
94C2×#10621872—22no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C2×C8×D43—22no—
98C2×C8×D43—22no—
99C2×C8×D43—22no—
100#13063303—28no—
101#13063301—22no—
102#13063301C2×C414yescomplemented
103#13063300—28no—
104#13063300—22no—
105#13063300C2×C414yescomplemented
106#13063299—22no—
107#13063299C2×C414yescomplemented
108#13063298—28no—
109#13063298—28no—
110#13063290—28no—
111#13063287—28no—
112C4×C22⋊D43—28no—
113C4×C22⋊D43—28no—
114#13063284—22no—
115#13063284—22no—
116#13063283—22no—
117#13063283—22no—
118#13063283—22no—
119#13063283D414yescomplemented
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C4⋊C4×D43—22no—
128C4⋊C4×D43—22no—
129C4⋊C4×D43—22no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2×C414yescomplemented
132C4⋊C4×D43D414yescomplemented
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142#13063249—22no—
143#13063249—22no—
144#13063247—22no—
145#13063247—22no—
146#13063245—22no—
147#13063245—22no—
148C22⋊(C43⋊C8)—22no—
149(C2×D43)⋊C8—22no—
150(C2×D43)⋊C8—22no—
151C22×Q8×C43C2311yescharacteristic
152C23×C4×C43—21no—
153C23×C4×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C22⋊Q8×C43—22no—
157C22⋊Q8×C43C2×C414yescomplemented
158C2×C4⋊C4×C43—21no—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43C2311yescharacteristic
163C2×C4⋊C4×C43C2311yescharacteristic
164C2×C4⋊C4×C43C2311yescharacteristic
165C2×C22⋊C4×C43—21no—
166#103×C43—22no—
167#103×C43—22no—
168C22⋊C8×C43—22no—
169C24×C43C2×D411yescharacteristic
170C23×D43—21no—
171C23×D43C2×D411yescharacteristic
172C23×D43C2×D411yescharacteristic
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43C22×C412yes—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—24no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—81no—
189C22×C4×C43—81no—
190C22×C4×C43C22×C412yes—
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—22no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—81no—
200C2×C22⋊D43—81no—
201C2×C22⋊D43C22⋊C414yes—
202C2×C22⋊D43C22⋊C414yes—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208#10621902—28no—
209#10621902—28no—
210#10621902—44no—
211#10621902—44no—
212#10621898—28no—
213#10621898—28no—
214#10621898—28no—
215#10621898—28no—
216C2×D172—21no—
217C2×D172—24no—
218C2×D172—24no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—42no—
226C2×D172—42no—
227C2×D172—81no—
228C2×D172—81no—
229C2×D172C22⋊C414yes—
230C2×D172C22×C412yes—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×C4×D43—81no—
242C2×C4×D43—81no—
243C2×C4×D43—81no—
244C2×C4×D43—81no—
245C2×C4×D43—81no—
246C2×C4×D43—81no—
247C2×C4×D43C22×C412yes—
248C2×C4×D43C22×C412yes—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2×D412yes—
251C2×C4×D43C2×D412yes—
252C2×C4×D43C2×D412yes—
253C2×C4×D43#4112yes—
254C2×C4×D43#4112yes—
255C2×Dic86—22no—
256C2×Dic86—22no—
257C2×Dic86C22⋊C414yes—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C4⋊C4×C43—24no—
265C4⋊C4×C43—24no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C22×C412yes—
270C4⋊C4×C43C2×D412yes—
271C4⋊C4×C43C2×D412yes—
272C22⋊C4×C43—24no—
273C22⋊Dic43—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43C22×C412yes—
283C4⋊Dic43C2×D412yes—
284C4⋊Dic43C2×D412yes—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289C4×Dic43—24no—
290C4×Dic43—24no—
291C4×Dic43—24no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298#10621872—44no—
299C8×D43—44no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43C2×C22⋊C412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—21no—
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43—21no—
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—22no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43C2×C22⋊C412yes—
326C22×D43C2×C22⋊C412yes—
327C22×D43#12012yes—
328C22×D43#12312yes—
329Q8×C43—22no—
330Q8×C43—22no—
331Q8×C43—41no—
332Q8×C43—41no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—84no—
352C2×C4×C43C2×C22⋊C412yes—
353C2×C4×C43C23×C411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C2×C4×C43C2×#4111yescharacteristic
359C22⋊D43—28no—
360C22⋊D43—28no—
361C22⋊D43—84no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43C2×C22⋊C412yes—
374C2×Dic43C2×C22⋊C412yes—
375C2×Dic43#12012yes—
376C2×Dic43#12312yes—
377D172—28no—
378D172—22no—
379D172—22no—
380D172—48no—
381D172—41no—
382D172—41no—
383D172—84no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—48no—
389C4×D43—84no—
390C4×D43—84no—
391C4×D43—84no—
392C4×D43C4×D414yes—
393C4×D43C4×D414yes—
394C4×D43#12114yes—
395C4×D43#12114yes—
396Dic86—28no—
397C8×C43—41no—
398C8×C43—41no—
399C43⋊C8—41no—
400C43⋊C8—41no—
401#20915—431nomaximal, Sylow
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43C22×C22⋊C411yescharacteristic
410C22×C43C2×#12011yescharacteristic
411C22×C43C2×#12311yescharacteristic
412C22×C43#57611yescharacteristic
413C22×C43#57711yescharacteristic
414C22×C43#57711yescharacteristic
415C22×C43#57811yescharacteristic
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43—41no—
428C2×D43—41no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—81no—
433C2×D43—81no—
434C2×D43—81no—
435C2×D43—81no—
436C2×D43#38614yes—
437C4×C43—22no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43—42no—
442C4×C43C2×C4×D411yescharacteristic
443C4×C43C2×C4×D411yescharacteristic
444C4×C43C2×#12111yescharacteristic
445C4×C43C2×#12111yescharacteristic
446Dic43—22no—
447Dic43—42no—
448Dic43—42no—
449Dic43—42no—
450Dic43#38614yes—
451C2×#537—431no—
452C2×#520—431no—
453C2×#417—431no—
454C2×#416—431no—
455C2×#408—431no—
456#1875—431no—
457#1875—431no—
458#1874—431no—
459#1874—431no—
460#1873—431no—
461#1873—431no—
462#1872—431no—
463#1872D4311yescharacteristic, complemented
464#1736—431no—
465C2×#340—431no—
466C2×C43—42no—
467C2×C43C2×#38611yescharacteristic
468C2×C43#289711yescharacteristic
469C2×C43#289811yescharacteristic
470C2×C43#301211yescharacteristic
471C2×C43#301311yescharacteristic
472C2×C43#309811yescharacteristic
473C2×C43#309911yescharacteristic
474D43—24no—
475D43—42no—
476D43—82no—
477C22×#41—431no—
478C22×#41—431no—
479C22×M16—431no—
480C23×C8—431no—
481#537—438no—
482#537—864no—
483C2×C22⋊Q8—431no—
484C2×C22⋊Q8—861no—
485C2×C22⋊Q8C2×D4311yescharacteristic
486C2×#121—431no—
487C2×#121—431no—
488C2×#121—861no—
489C2×#121—861no—
490C2×#121—861no—
491#520—864no—
492#520—864no—
493C2×C4×Q8—861no—
494C2×C4×D4—861no—
495C2×C4×D4—861no—
496C2×C4×D4—861no—
497C2×#117—431no—
498C2×#117—431no—
499C2×#117—431no—
500C22×C4⋊C4—431no—
501C22×C4⋊C4—431no—
502C22×C4⋊C4—431no—
503C22×C4⋊C4C2×D4311yescharacteristic
504#417—864no—
505#416—864no—
506C2×#103—431no—
507C2×#103—431no—
508C2×#103C2×D4311yescharacteristic
509C2×#103C2×D4311yescharacteristic
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514#408—864no—
515C2×C22⋊C8—431no—
516C2×C22⋊C8—431no—
517C2×C22⋊C8—431no—
518C2×C22⋊C8C2×D4311yescharacteristic
519#340—431no—
520#340—431no—
521#340—431no—
522#340—431no—
523#340—431no—
524#340—431no—
525#340C2×D4311yescharacteristic
526#340C2×D4311yescharacteristic
527C43#2091511yescharacteristic, complemented, Sylow
528C2×#41—434no—
529C2×#41—434no—
530C2×#41—434no—
531C2×#41—862no—
532C2×#41—862no—
533C2×#41—862no—
534C2×#41—862no—
535C2×#41—862no—
536C2×#41—862no—
537C2×#41—862no—
538C2×#41—862no—
539C2×#41—862no—
540C22×Q8—431no—
541C22×Q8C22×D4311yescharacteristic
542C22×D4—431no—
543C22×D4—431no—
544C22×D4—431no—
545C22×D4—431no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—861no—
549C23×C4—21no—
550C23×C4—431no—
551C23×C4—431no—
552C23×C4—861no—
553C23×C4—861no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×M16—862no—
558C2×M16—862no—
559C2×M16—862no—
560C22×C8—431no—
561C22×C8—431no—
562C22×C8—862no—
563C22×C8—862no—
564C22×C8—862no—
565C22×C8C22×D4311yescharacteristic
566C22×C8C22×D4311yescharacteristic
567C22⋊Q8—22no—
568C22⋊Q8—434no—
569C22⋊Q8—868no—
570C22⋊Q8—862no—
571C22⋊Q8C4×D4314yescomplemented
572#121—434no—
573#121—434no—
574#121—868no—
575#121—868no—
576#121—862no—
577#121—868no—
578#121—862no—
579C4×Q8—868no—
580C4×D4—868no—
581C4×D4—868no—
582C4×D4—868no—
583#117—434no—
584#117—862no—
585#117—862no—
586#117—862no—
587#117—862no—
588#117—862no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—434no—
597C2×C4⋊C4—434no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—862no—
600C2×C4⋊C4—862no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C4⋊C4C22×D4311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C42—861no—
617C2×C42—861no—
618C2×C42—861no—
619#103—22no—
620#103—22no—
621#103—862no—
622#103—862no—
623#102—862no—
624#102—862no—
625#102—862no—
626#102—862no—
627C22⋊C8—22no—
628C22⋊C8—862no—
629C22⋊C8—862no—
630C22⋊C8—862no—
631C24—431no—
632C24—431no—
633C24—861no—
634C24D4×D4311yescharacteristic
635#41—868no—
636#41—868no—
637#41—868no—
638#41—868no—
639#41—868no—
640#41—868no—
641#41—1724no—
642#41—1724no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—434no—
649C2×Q8—862no—
650C2×Q8—862no—
651C2×Q8C2×C4×D4312yes—
652C2×D4—434no—
653C2×D4—434no—
654C2×D4—434no—
655C2×D4—432no—
656C2×D4—862no—
657C2×D4—862no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—862no—
661C2×D4—862no—
662C2×D4—862no—
663C2×D4—862no—
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—1722no—
675C2×D4—1722no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4—431no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—431no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—864no—
700C22×C4—864no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—3441no—
709C22×C4—3441no—
710C22×C4—3441no—
711C22×C4—3441no—
712C22×C4—3441no—
713C22×C4—3441no—
714C22×C4—1722no—
715C22×C4—1722no—
716C22×C4C2×C4×D4312yes—
717C22×C4D4×D4311yescharacteristic
718C22×C4D4×D4312yes—
719C22×C4C23×D4311yescharacteristic
720M16—1724no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—861no—
728C2×C8—861no—
729C2×C8—861no—
730C2×C8—861no—
731C2×C8—861no—
732C2×C8—861no—
733C2×C8—1724no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—432no—
740C4⋊C4—432no—
741C4⋊C4—432no—
742C4⋊C4—864no—
743C4⋊C4—864no—
744C4⋊C4—864no—
745C4⋊C4—864no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4C2×C4×D4312yes—
750C4⋊C4D4×D4312yes—
751C4⋊C4D4×D4312yes—
752C22⋊C4—24no—
753C22⋊C4—864no—
754C22⋊C4—864no—
755C22⋊C4—864no—
756C22⋊C4—864no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C42—864no—
760C42—864no—
761C42—864no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—432no—
769C23—432no—
770C23—432no—
771C23—432no—
772C23—861no—
773C23—861no—
774C23—861no—
775C23—861no—
776C23—861no—
777C23—861no—
778C23—861no—
779C23—861no—
780C23—861no—
781C23—861no—
782C23—862no—
783C23—1721no—
784C23—1721no—
785C23—1721no—
786C23—1721no—
787C23—1721no—
788C23—1721no—
789C23C22⋊C4×D4312yes—
790C23C2×D4×D4311yescharacteristic
791Q8—22no—
792Q8—22no—
793Q8—41no—
794Q8—41no—
795Q8—868no—
796D4—868no—
797D4—868no—
798D4—868no—
799D4—862no—
800D4—862no—
801D4—3444no—
802D4—3444no—
803D4—1728no—
804D4—1721no—
805D4—1721no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—84no—
825C2×C4—432no—
826C2×C4—432no—
827C2×C4—432no—
828C2×C4—434no—
829C2×C4—434no—
830C2×C4—434no—
831C2×C4—434no—
832C2×C4—432no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—862no—
836C2×C4—862no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—3444no—
843C2×C4—3444no—
844C2×C4—3444no—
845C2×C4—1728no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4—1721no—
850C2×C4—1721no—
851C2×C4—1721no—
852C2×C4C22⋊C4×D4312yes—
853C2×C4C22×C4×D4311yescharacteristic
854C2×C4C2×D4×D4311yescharacteristic
855C2×C4C2×D4×D4311yescharacteristic
856C2×C4C2×D4×D4311yescharacteristic
857C2×C4#41×D4311yescharacteristic
858C2×C4#41×D4311yescharacteristic
859C8—41no—
860C8—41no—
861C8—1721no—
862C8—1721no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—434no—
871C22—862no—
872C22—862no—
873C22—862no—
874C22—862no—
875C22—862no—
876C22—862no—
877C22—862no—
878C22—862no—
879C22—862no—
880C22—3441no—
881C22—3441no—
882C22—3441no—
883C22—3441no—
884C22—1722no—
885C22—1722no—
886C22—1722no—
887C22—1721no—
888C22—1721no—
889C22—1721no—
890C22—1721no—
891C22C2×C22⋊C4×D4311yescharacteristic
892C22#120×D4311yescharacteristic
893C22#123×D4311yescharacteristic
894C22#1458370311yescharacteristic
895C22#1458370511yescharacteristic
896C22#1458370811yescharacteristic
897C22#1458371211yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4—434no—
904C4—862no—
905C4—1722no—
906C4—1722no—
907C4—1722no—
908C4C4×D4×D4311yescharacteristic
909C4C4×D4×D4311yescharacteristic
910C4#121×D4311yescharacteristic
911C4#121×D4311yescharacteristic
912C2—42no—
913C2—864no—
914C2—3442no—
915C2—1722no—
916C2#386×D4311yescharacteristic
917C2#1914311911yescharacteristic
918C2#1914312311yescharacteristic
919C2#1914390011yescharacteristic
920C2#1914391111yescharacteristic
921C2#1914457411yescharacteristic
922C2#1914457911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC2×#14583479C2
cosocleC22×C4×C43C24
hypercenter#1872D43
hypocenterC43#20915
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#14583380C2semidirect
3. C2×#14582899C2semidirect
4. C2×#14582894C2semidirect
5. C2×#14582864C2semidirect
6. #19134916C2semidirect
7. #19134915C2semidirect
8. #19134912C2semidirect
9. #19134911C2semidirect
10. #19134908C2semidirect
11. #19134904C2semidirect
12. #19134899C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C43×#1872C2semidirect
21. #14583479C4semidirect
71. C2×#10621902C2×C4semidirect
102. #13063301C2×C4semidirect
105. #13063300C2×C4semidirect
107. #13063299C2×C4semidirect
119. #13063283D4semidirect
131. C4⋊C4×D43C2×C4semidirect
132. C4⋊C4×D43D4semidirect
157. C22⋊Q8×C43C2×C4semidirect
463. #1872D43semidirect
527. C43#20915semidirect
571. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834792
C2×#145833802
C2×#145828992
C2×#145828942
C2×#145828642
#191349162
#191349152
#191349122
#191349112
#191349082
#191349042
#191348992
#191343132
#340×D432
C43×#18722
#2091543