Finite Group Databasebeta

← #25097872

Subgroups — #25097872

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×#14583478C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582892C211yesmaximal, characteristic, complemented
5C2×#14582864C211yesmaximal, characteristic, complemented
6#19134918C211yesmaximal, characteristic, complemented
7#19134914C211yesmaximal, characteristic, complemented
8#19134909C211yesmaximal, characteristic, complemented
9#19134906C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134901C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621900C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583478—24no—
21#14583478C418yescomplemented
22C2×#13063305C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063302—21no—
25C2×#13063298—21no—
26C2×#13063297—21no—
27C2×#13063296—21no—
28C2×#13063296C2211yescharacteristic
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#14582897—24no—
42#14582892—24no—
43C2×#13063250C2211yescharacteristic
44C2×#13063250C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×#13063248C2211yescharacteristic
47C2×#13063246C2211yescharacteristic
48C2×#13063246C2211yescharacteristic
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×#121×C43C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C43×#340C2211yescharacteristic
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898C2×C414yes—
71C2×#10621898D414yes—
72C2×#10621900—22no—
73C2×#10621900—22no—
74C2×#10621900—22no—
75C2×#10621900—22no—
76C2×#10621900—22no—
77C2×#10621900C2×C414yescomplemented
78C22×Dic86D411yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172D411yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43D411yescharacteristic
84C22×C22⋊D43D411yescharacteristic
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621872—22no—
92C2×#10621872—22no—
93C2×#10621872—22no—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—22no—
97C2×C8×D43—22no—
98C2×C8×D43—22no—
99#13063305—22no—
100#13063305C2×C414yescomplemented
101#13063304—22no—
102#13063304C2×C414yescomplemented
103#13063302—28no—
104#13063298—28no—
105#13063297—28no—
106#13063296—28no—
107#13063296—22no—
108#13063296C2×C414yescomplemented
109#13063290—28no—
110#13063287—28no—
111C4×C22⋊D43—28no—
112C4×C22⋊D43—28no—
113#13063284—22no—
114#13063284—22no—
115#13063283—22no—
116#13063283—22no—
117#13063283—22no—
118#13063283D414yescomplemented
119C2×C4⋊Dic43—21no—
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×C22⋊Dic43—21no—
135C2×C22⋊Dic43—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#13063250—22no—
143#13063250—22no—
144#13063248—22no—
145#13063248—22no—
146#13063246—22no—
147#13063246—22no—
148C22⋊(C43⋊C8)—22no—
149(C2×D43)⋊C8—22no—
150(C2×D43)⋊C8—22no—
151C22×D4×C43—21no—
152C22×D4×C43C2311yescharacteristic
153C23×C4×C43—21no—
154C23×C4×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157#121×C43—22no—
158#121×C43C2×C414yescomplemented
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#102×C43—22no—
167#102×C43—22no—
168C22⋊C8×C43—22no—
169C24×C43—21no—
170C24×C43C2×D411yescharacteristic
171C23×D43C2×D411yescharacteristic
172C23×D43C2×D411yescharacteristic
173C2×D4×C43—21no—
174C2×D4×C43—24no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—81no—
180C2×D4×C43—81no—
181C2×D4×C43C22×C412yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—81no—
191C22×C4×C43—81no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—81no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43C22⋊C414yes—
207C2×C22⋊D43C22⋊C414yes—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—42no—
214C22×Dic43—42no—
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621900—28no—
218#10621900—28no—
219#10621900—44no—
220#10621900—44no—
221#10621898—28no—
222#10621898—28no—
223#10621898—28no—
224#10621898—28no—
225C2×D172—22no—
226C2×D172—22no—
227C2×D172C22⋊C414yes—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—81no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×C4×D43—81no—
239C2×C4×D43—81no—
240C2×C4×D43—81no—
241C2×C4×D43C22×C412yes—
242C2×C4×D43C22×C412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2×D412yes—
246C2×C4×D43C2×D412yes—
247C2×C4×D43#4112yes—
248C2×C4×D43#4112yes—
249C2×Dic86—22no—
250C2×Dic86—22no—
251C2×Dic86—21no—
252C2×Dic86—21no—
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86—21no—
256C2×Dic86C22⋊C414yes—
257C2×Dic86C22×C412yes—
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—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43C22×C412yes—
269C4⋊C4×C43C2×D412yes—
270C4⋊C4×C43C2×D412yes—
271C22⋊C4×C43—24no—
272C22⋊Dic43—24no—
273C22⋊Dic43—24no—
274C22⋊Dic43—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—24no—
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×C43—22no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43C2×C22⋊C412yes—
314C23×C43C22×D411yescharacteristic
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—21no—
325C22×D43C2×C22⋊C412yes—
326C22×D43C2×C22⋊C412yes—
327C22×D43#12012yes—
328C22×D43#12312yes—
329D4×C43—22no—
330D4×C43—22no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—84no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
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—84no—
350C2×C4×C43C2×C22⋊C412yes—
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C2×#4111yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C22⋊D43—28no—
358C22⋊D43—28no—
359C22⋊D43—48no—
360C22⋊D43—84no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—22no—
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×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—48no—
376C2×Dic43C2×C22⋊C412yes—
377C2×Dic43C2×C22⋊C412yes—
378C2×Dic43#12012yes—
379C2×Dic43#12312yes—
380D172—28no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—84no—
386C4×D43—84no—
387C4×D43—84no—
388C4×D43C4×D414yes—
389C4×D43C4×D414yes—
390C4×D43#12114yes—
391C4×D43#12114yes—
392Dic86—28no—
393Dic86—22no—
394Dic86—22no—
395Dic86—41no—
396Dic86—41no—
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×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43—81no—
416C22×C43C22×C22⋊C411yescharacteristic
417C22×C43C2×#12011yescharacteristic
418C22×C43C2×#12311yescharacteristic
419C22×C43#57611yescharacteristic
420C22×C43#57711yescharacteristic
421C22×C43#57711yescharacteristic
422C22×C43#57811yescharacteristic
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—22no—
428C2×D43—22no—
429C2×D43—22no—
430C2×D43—22no—
431C2×D43—22no—
432C2×D43—41no—
433C2×D43—41no—
434C2×D43—41no—
435C2×D43—41no—
436C2×D43#38614yes—
437C4×C43—22no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43C2×C4×D411yescharacteristic
442C4×C43C2×C4×D411yescharacteristic
443C4×C43C2×#12111yescharacteristic
444C4×C43C2×#12111yescharacteristic
445Dic43—22no—
446Dic43—42no—
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#1874D4311yescharacteristic, complemented
460#1873—431no—
461#1873—431no—
462#1872—431no—
463#1872—431no—
464#1736—431no—
465C2×#340—431no—
466C2×C43—42no—
467C2×C43—82no—
468C2×C43C2×#38611yescharacteristic
469C2×C43#289711yescharacteristic
470C2×C43#289811yescharacteristic
471C2×C43#301211yescharacteristic
472C2×C43#301311yescharacteristic
473C2×C43#309811yescharacteristic
474C2×C43#309911yescharacteristic
475D43—24no—
476D43—42no—
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—431no—
485C2×C22⋊Q8—861no—
486C2×#121—431no—
487C2×#121—861no—
488C2×#121—861no—
489C2×#121—861no—
490C2×#121C2×D4311yescharacteristic
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×#103—431no—
509C2×#103—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×#102C2×D4311yescharacteristic
513C2×#102C2×D4311yescharacteristic
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×Q8—431no—
542C22×D4—21no—
543C22×D4—431no—
544C22×D4—431no—
545C22×D4—431no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4C22×D4311yescharacteristic
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—434no—
568C22⋊Q8—434no—
569C22⋊Q8—868no—
570C22⋊Q8—862no—
571C22⋊Q8—862no—
572#121—22no—
573#121—434no—
574#121—868no—
575#121—862no—
576#121—868no—
577#121—868no—
578#121C4×D4314yescomplemented
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—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—434no—
596C2×C4⋊C4—434no—
597C2×C4⋊C4—862no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—862no—
600C2×C4⋊C4—861no—
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—862no—
620#103—862no—
621#103—862no—
622#103—862no—
623#102—22no—
624#102—22no—
625#102—862no—
626#102—862no—
627C22⋊C8—22no—
628C22⋊C8—862no—
629C22⋊C8—862no—
630C22⋊C8—862no—
631C24—21no—
632C24—431no—
633C24—431no—
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—434no—
644C2×Q8—432no—
645C2×Q8—862no—
646C2×Q8—862no—
647C2×Q8—861no—
648C2×Q8—861no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—861no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—434no—
661C2×D4—434no—
662C2×D4—434no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—862no—
666C2×D4—862no—
667C2×D4—862no—
668C2×D4—862no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—3441no—
672C2×D4—3441no—
673C2×D4—1722no—
674C2×D4—1722no—
675C2×D4C2×C4×D4312yes—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—24no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—431no—
687C22×C4—432no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—431no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—864no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—864no—
700C22×C4—861no—
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—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—432no—
739C4⋊C4—432no—
740C4⋊C4—432no—
741C4⋊C4—864no—
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—22no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—432no—
776C23—432no—
777C23—432no—
778C23—432no—
779C23—861no—
780C23—861no—
781C23—861no—
782C23—861no—
783C23—861no—
784C23—861no—
785C23—861no—
786C23—861no—
787C23—861no—
788C23—861no—
789C23C22⋊C4×D4312yes—
790C23C2×D4×D4311yescharacteristic
791Q8—868no—
792Q8—862no—
793Q8—862no—
794Q8—1721no—
795Q8—1721no—
796D4—22no—
797D4—22no—
798D4—41no—
799D4—41no—
800D4—84no—
801D4—868no—
802D4—868no—
803D4—868no—
804D4—3444no—
805D4—1728no—
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—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4—432no—
823C2×C4—432no—
824C2×C4—432no—
825C2×C4—434no—
826C2×C4—434no—
827C2×C4—434no—
828C2×C4—434no—
829C2×C4—432no—
830C2×C4—861no—
831C2×C4—861no—
832C2×C4—862no—
833C2×C4—862no—
834C2×C4—862no—
835C2×C4—862no—
836C2×C4—862no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—3444no—
841C2×C4—3444no—
842C2×C4—3444no—
843C2×C4—1728no—
844C2×C4—1721no—
845C2×C4—1721no—
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—42no—
871C22—42no—
872C22—42no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—434no—
878C22—862no—
879C22—862no—
880C22—862no—
881C22—862no—
882C22—862no—
883C22—862no—
884C22—862no—
885C22—862no—
886C22—862no—
887C22—1721no—
888C22—1721no—
889C22—1721no—
890C22—1721no—
891C22C2×C22⋊C4×D4311yescharacteristic
892C22#120×D4311yescharacteristic
893C22#123×D4311yescharacteristic
894C22#1458370011yescharacteristic
895C22#1458370511yescharacteristic
896C22#1458370911yescharacteristic
897C22#1458371511yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—434no—
903C4—862no—
904C4—1722no—
905C4—1722no—
906C4—1722no—
907C4—1722no—
908C4C4×D4×D4311yescharacteristic
909C4C4×D4×D4311yescharacteristic
910C4#121×D4311yescharacteristic
911C4#121×D4311yescharacteristic
912C2—42no—
913C2—82no—
914C2—864no—
915C2—1722no—
916C2#386×D4311yescharacteristic
917C2#1914311611yescharacteristic
918C2#1914312611yescharacteristic
919C2#1914389411yescharacteristic
920C2#1914390511yescharacteristic
921C2#1914456811yescharacteristic
922C2#1914458511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583478C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#20915
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#14583380C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582892C2semidirect
5. C2×#14582864C2semidirect
6. #19134918C2semidirect
7. #19134914C2semidirect
8. #19134909C2semidirect
9. #19134906C2semidirect
10. #19134905C2semidirect
11. #19134902C2semidirect
12. #19134901C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C43×#1874C2semidirect
21. #14583478C4semidirect
77. C2×#10621900C2×C4semidirect
100. #13063305C2×C4semidirect
102. #13063304C2×C4semidirect
108. #13063296C2×C4semidirect
118. #13063283D4semidirect
131. C4⋊C4×D43C2×C4semidirect
132. C4⋊C4×D43D4semidirect
158. #121×C43C2×C4semidirect
459. #1874D43semidirect
527. C43#20915semidirect
578. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834782
C2×#145833802
C2×#145828972
C2×#145828922
C2×#145828642
#191349182
#191349142
#191349092
#191349062
#191349052
#191349022
#191349012
#191343132
#340×D432
C43×#18742
#2091543