Finite Group Databasebeta

← #25097979

Subgroups — #25097979

Order 11008.

2046 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063349C211yesmaximal, characteristic
2C2×C4×#10621900C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582902C211yesmaximal, characteristic, complemented
5#390×D43C211yesmaximal, characteristic, complemented
6#19134953C211yesmaximal, characteristic, complemented
7#19134951C211yesmaximal, characteristic, complemented
8#19134949C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134941C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C2×#13063349—24no—
19C2×#13063349—24no—
20C2×#13063349C418yescomplemented
21C22×#10621873C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×#10621872C2211yescharacteristic
26C4×#10621900—24no—
27C4×#10621900—24no—
28C2×C4×Dic86C2211yescharacteristic, complemented
29C2×#13063290C2211yescharacteristic, complemented
30C2×D4×Dic43C2211yescharacteristic, complemented
31C2×C4×C22⋊D43—21no—
32C2×(C22⋊D43)⋊C4—21no—
33C2×#13063283C2211yescharacteristic
34C2×#13063281—21no—
35C2×C4⋊C4×D43C2211yescharacteristic
36C2×C22⋊C4×D43—21no—
37C2×C22⋊C4×D43—21no—
38C22×C4×Dic43—21no—
39C2×C42×D43C2211yescharacteristic
40#14582902—24no—
41#14582897—24no—
42C2×#13063250C2211yescharacteristic, complemented
43C2×#13063248C2211yescharacteristic, complemented
44C2×#13063247C2211yescharacteristic
45C2×#13063246C2211yescharacteristic
46C2×#13063246C2211yescharacteristic, complemented
47C2×#13063245C2211yescharacteristic
48#14582802C2211yescharacteristic
49#14582801C2211yescharacteristic
50#14582800C2211yescharacteristic
51#14582799—21no—
52#14582799—21no—
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582654C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58#14582653C2211yescharacteristic, complemented
59C22×D8×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic, complemented
63C43×#390C2211yescharacteristic
64C43×#340C2211yescharacteristic, complemented
65C43×#336C2211yescharacteristic, complemented
66C24×D43—21no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900C2×C414yes—
71C2×#10621900D414yes—
72C2×#10621900D414yes—
73C22×Dic86C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43—22no—
81C2×D4×D43—22no—
82C2×D4×D43C2×C414yescomplemented
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43D411yescharacteristic
87C22×C4×D43D411yescharacteristic
88C22×C4×D43C2311yescharacteristic
89#13063349—232no—
90C2×#10621873—22no—
91C2×#10621873—22no—
92C2×#10621873C2×C414yescomplemented
93C2×#10621883—22no—
94C2×#10621883—22no—
95C2×#10621883C2×C414yescomplemented
96C2×#10621882—22no—
97C2×#10621882—22no—
98C2×#10621882C2×C414yescomplemented
99C2×#10621872—22no—
100C2×#10621872—22no—
101C2×#10621872—22no—
102C2×#10621872—22no—
103C2×#10621872—22no—
104C2×#10621872C2×C414yescomplemented
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C4×Dic86—22no—
108C4×Dic86—22no—
109#13063290—22no—
110#13063290—22no—
111D4×Dic43—22no—
112D4×Dic43—22no—
113C4×C22⋊D43—28no—
114(C22⋊D43)⋊C4—28no—
115#13063283—22no—
116#13063283D414yes—
117#13063281—28no—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C4⋊C4×D43—22no—
124C4⋊C4×D43—22no—
125C2×C22⋊Dic43—21no—
126C2×C22⋊Dic43—21no—
127C2×C22⋊Dic43—21no—
128C2×(C2×D43)⋊C4—21no—
129C2×(C2×D43)⋊C4—21no—
130C2×(C2×D43)⋊C4—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C22⋊C4×D43—44no—
134C22⋊C4×D43—44no—
135C2×C4×Dic43—28no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C42×D43—22no—
143C42×D43—22no—
144#13063250—22no—
145#13063248—22no—
146#13063247—22no—
147#13063246—22no—
148#13063246—22no—
149#13063245—22no—
150C22×D4×C43C2311yescharacteristic
151C22×D4×C43C2311yescharacteristic
152C23×C4×C43—21no—
153C2×D8×C43—22no—
154C2×D8×C43—22no—
155C2×D8×C43C2×C414yescomplemented
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C4×D4×C43—22no—
159C4×D4×C43—22no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C4⋊C4×C43C2311yescharacteristic
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43—21no—
165C2×C42×C43C2311yescharacteristic
166#102×C43—22no—
167#102×C43—22no—
168C24×C43—21no—
169C24×C43—21no—
170C23×D43—21no—
171C23×D43—24no—
172C23×D43—42no—
173C23×D43—42no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—42no—
177C23×D43—42no—
178C23×D43C2×D411yescharacteristic
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×C43C22×C412yes—
188C2×D4×C43C22×C412yes—
189C2×D4×C43C2×D412yes—
190C2×D4×C43C2×D412yes—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
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—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—24no—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—42no—
213C22×Dic43—42no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621900—28no—
218#10621900—28no—
219#10621900—28no—
220#10621900C22⋊C4116yescomplemented
221D4×D43—28no—
222D4×D43—28no—
223D4×D43—44no—
224D4×D43—44no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172C22×C412yes—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—41no—
236C2×C4×D43—41no—
237C2×C4×D43—42no—
238C2×C4×D43—42no—
239C2×C4×D43—42no—
240C2×C4×D43C22×C412yes—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43#4112yes—
245C2×C4×D43#4112yes—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86C22×C412yes—
250C2×Dic86C2×D412yes—
251C2×Dic86C2×D412yes—
252D8×C43—28no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43C22×C412yes—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C2×D412yes—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—42no—
265C22⋊C4×C43—42no—
266C42×C43—21no—
267C42×C43—21no—
268C22⋊Dic43—24no—
269C22⋊Dic43—42no—
270C22⋊Dic43—42no—
271#10621883—28no—
272#10621882—28no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—42no—
275(C2×D43)⋊C4—42no—
276(C2×D43)⋊C4—42no—
277(C2×D43)⋊C4—42no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43C2×D412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—42no—
285C4×Dic43—24no—
286C4×Dic43—24no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—22no—
290C4×Dic43—22no—
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⋊C8C22×C412yes—
298#10621873—28no—
299#10621872—28no—
300#10621872—44no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43C22×D411yescharacteristic
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—22no—
321C22×D43—48no—
322C22×D43—48no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—48no—
330C22×D43—84no—
331C22×D43—84no—
332C22×D43—84no—
333C22×D43—84no—
334C22×D43C4×D412yes—
335C22×D43#12012yes—
336C22×D43#12112yes—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—22no—
342D4×C43—41no—
343D4×C43—41no—
344D4×C43C2×C22⋊C414yescomplemented
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—48no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43AGL(1,ℤ/8)12yescomplemented
358C2×C4×C43C23×C411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C2×#4111yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C22⋊D43—216no—
365C22⋊D43—48no—
366C2×Dic43—22no—
367C2×Dic43—21no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—21no—
371C2×Dic43—216no—
372C2×Dic43—21no—
373C2×Dic43—22no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—48no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43C4×D412yes—
383C2×Dic43#12012yes—
384C2×Dic43#12112yes—
385C2×Dic43AGL(1,ℤ/8)12yescomplemented
386D172—22no—
387D172—22no—
388D172—41no—
389D172—41no—
390C4×D43—44no—
391C4×D43—44no—
392C4×D43—84no—
393C4×D43C2×C22⋊C414yes—
394C4×D43C4×D414yes—
395C4×D43#12114yes—
396C4×D43#12314yes—
397Dic86—22no—
398Dic86—22no—
399Dic86—22no—
400Dic86C2×C22⋊C414yescomplemented
401C8×C43—22no—
402C8×C43—41no—
403C43⋊C8—22no—
404C43⋊C8—41no—
405#20928—431nomaximal, Sylow
406C22×C43—24no—
407C22×C43—42no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—42no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43—81no—
420C22×C43C2×C4×D411yescharacteristic
421C22×C43C2×#12011yescharacteristic
422C22×C43C2×#12111yescharacteristic
423C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C43#57511yescharacteristic
426C22×C43#57511yescharacteristic
427C2×D43—22no—
428C2×D43—22no—
429C2×D43—22no—
430C2×D43—22no—
431C2×D43—22no—
432C2×D43—22no—
433C2×D43—42no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—816no—
437C2×D43—81no—
438C2×D43—81no—
439C2×D43—81no—
440C2×D43—81no—
441C2×D43#38614yes—
442C4×C43—22no—
443C4×C43—41no—
444C4×C43—42no—
445C4×C43—81no—
446C4×C43C22×C22⋊C411yescharacteristic
447C4×C43C2×C4×D411yescharacteristic
448C4×C43C2×#12111yescharacteristic
449C4×C43C2×#12311yescharacteristic
450Dic43—22no—
451Dic43—24no—
452Dic43—41no—
453Dic43—42no—
454Dic43—81no—
455Dic43#38614yes—
456C22×AGL(1,ℤ/8)—431no—
457C2×C4×#41—431no—
458C2×#417—431no—
459C2×#418—431no—
460C2×#390—431no—
461#1880—431no—
462#1880—431no—
463#1880—431no—
464#1880—431no—
465#1879—431no—
466#1879—431no—
467#1879—431no—
468#1879D4311yescharacteristic, complemented
469#1736—431no—
470#1728—431no—
471C2×C43—44no—
472C2×C43—82no—
473C2×C43C2×#38611yescharacteristic
474C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
475C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
476C2×C43#300611yescharacteristic
477C2×C43#300611yescharacteristic
478C2×C43#303811yescharacteristic
479C2×C43#304011yescharacteristic
480D43—24no—
481D43—82no—
482C22×#41—431no—
483C23×D4—431no—
484C2×AGL(1,ℤ/8)—438no—
485C2×AGL(1,ℤ/8)—864no—
486C2×AGL(1,ℤ/8)—864no—
487C22×SD16—431no—
488C22×SD16—431no—
489C22×D8—431no—
490C22×D8C2×D4311yescharacteristic
491C22×M16—431no—
492C22×M16—431no—
493C4×#41—864no—
494C4×#41—864no—
495C2×C4×Q8—431no—
496C2×C4×Q8—431no—
497C2×C4×D4—431no—
498C2×C4×D4—861no—
499C2×C4×D4—861no—
500C2×C4×D4C2×D4311yescharacteristic, complemented
501C2×#117—431no—
502C2×#117—861no—
503C22×C4⋊C4—431no—
504C22×C22⋊C4—861no—
505C22×C22⋊C4—861no—
506C22×C42—431no—
507C22×C42—861no—
508#418—864no—
509#417—864no—
510C2×#103—431no—
511C2×#103—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102—431no—
516C2×#102C2×D4311yescharacteristic
517C2×#102C2×D4311yescharacteristic, complemented
518#390—431no—
519#390—431no—
520#390—431no—
521#390—861no—
522#390—861no—
523#390C2×D4311yescharacteristic
524#340—431no—
525#340—431no—
526#340—431no—
527#340C2×D4311yescharacteristic, complemented
528#336—431no—
529#336—431no—
530#336—431no—
531#336C2×D4311yescharacteristic, complemented
532C43#2092811yescharacteristic, complemented, Sylow
533C25—861no—
534C2×#41—434no—
535C2×#41—434no—
536C2×#41—434no—
537C2×#41—862no—
538C2×#41—862no—
539C2×#41—862no—
540C22×Q8—431no—
541C22×D4—434no—
542C22×D4—431no—
543C22×D4—862no—
544C22×D4—862no—
545C22×D4—862no—
546C22×D4—862no—
547C22×D4—862no—
548C22×D4—861no—
549C22×D4—861no—
550C22×D4C22×D4311yescharacteristic
551C22×D4C22×D4311yescharacteristic
552C23×C4—21no—
553C23×C4—431no—
554C23×C4—431no—
555C23×C4—431no—
556C23×C4—861no—
557C23×C4—861no—
558C23×C4—861no—
559AGL(1,ℤ/8)—8632no—
560C2×SD16—434no—
561C2×SD16—434no—
562C2×SD16—862no—
563C2×SD16—862no—
564C2×SD16—862no—
565C2×SD16—862no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—434no—
569C2×D8—862no—
570C2×D8—862no—
571C2×D8C4×D4314yescomplemented
572C2×M16—434no—
573C2×M16—862no—
574C2×M16—862no—
575C2×M16—862no—
576C2×M16—862no—
577C2×M16—862no—
578C22×C8—431no—
579C22×C8—431no—
580C22×C8C22×D4311yescharacteristic
581C22×C8C22×D4311yescharacteristic
582C4×Q8—862no—
583C4×Q8—862no—
584C4×Q8—862no—
585C4×Q8—862no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—868no—
589C4×D4—862no—
590C4×D4—868no—
591C4×D4—862no—
592#117—434no—
593#117—868no—
594#117—862no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—862no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4C22×D4311yescharacteristic
603C2×C4⋊C4C22×D4311yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—1724no—
616C2×C22⋊C4—1724no—
617C2×C42—431no—
618C2×C42—431no—
619C2×C42—431no—
620C2×C42—862no—
621C2×C42—862no—
622C2×C42—861no—
623C2×C42—861no—
624C2×C42—868no—
625C2×C42—861no—
626C2×C42C22×D4311yescharacteristic
627#103—862no—
628#103—862no—
629#102—22no—
630#102—22no—
631#102—862no—
632#102—862no—
633#102—862no—
634#102—862no—
635C24—21no—
636C24—21no—
637C24—431no—
638C24—864no—
639C24—861no—
640C24—1722no—
641C24—1722no—
642C24—1722no—
643C24—1722no—
644C24—1722no—
645C24—1722no—
646#41—4316no—
647#41—868no—
648#41—868no—
649#41—868no—
650C2×Q8—432no—
651C2×Q8—432no—
652C2×Q8—432no—
653C2×Q8—861no—
654C2×Q8—861no—
655C2×Q8—861no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—432no—
665C2×D4—868no—
666C2×D4—868no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—1724no—
677C2×D4—1724no—
678C2×D4—1722no—
679C2×D4—1722no—
680C2×D4C2×C4×D4312yes—
681C2×D4C2×C4×D4312yes—
682C2×D4D4×D4312yes—
683C2×D4D4×D4312yes—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—431no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—862no—
699C22×C4—862no—
700C22×C4—862no—
701C22×C4—864no—
702C22×C4—864no—
703C22×C4—864no—
704C22×C4—861no—
705C22×C4—864no—
706C22×C4—861no—
707C22×C4—862no—
708C22×C4—861no—
709C22×C4—1721no—
710C22×C4—1721no—
711C22×C4—1722no—
712C22×C4—1722no—
713C22×C4—1722no—
714C22×C4—1722no—
715C22×C4—1722no—
716C22×C4D4×D4311yescharacteristic
717C22×C4D4×D4311yescharacteristic
718C22×C4C23×D4311yescharacteristic
719SD16—868no—
720SD16—868no—
721D8—28no—
722D8—868no—
723M16—868no—
724M16—1724no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—432no—
731C2×C8—861no—
732C2×C8—861no—
733C2×C8—861no—
734C2×C8—861no—
735C2×C8—861no—
736C2×C8C2×C4×D4312yes—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—432no—
741C4⋊C4—864no—
742C4⋊C4—864no—
743C4⋊C4—861no—
744C4⋊C4—861no—
745C4⋊C4—861no—
746C4⋊C4—1722no—
747C4⋊C4D4×D4312yes—
748C22⋊C4—24no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—864no—
752C22⋊C4—864no—
753C22⋊C4—1722no—
754C22⋊C4—1722no—
755C22⋊C4—1722no—
756C22⋊C4—1722no—
757C22⋊C4—1722no—
758C22⋊C4—1722no—
759C42—21no—
760C42—21no—
761C42—862no—
762C42—862no—
763C42—864no—
764C42—864no—
765C42—864no—
766C42—861no—
767C42—861no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—432no—
783C23—432no—
784C23—432no—
785C23—861no—
786C23—861no—
787C23—861no—
788C23—861no—
789C23—862no—
790C23—3444no—
791C23—3444no—
792C23—3444no—
793C23—3444no—
794C23—1728no—
795C23—1728no—
796C23—1728no—
797C23—1721no—
798C23—1721no—
799C23—1721no—
800C23—1721no—
801C23—1721no—
802C23—1721no—
803C23C2×D4×D4311yescharacteristic
804Q8—434no—
805Q8—862no—
806Q8—862no—
807Q8—862no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—41no—
814D4—41no—
815D4—8616no—
816D4—862no—
817D4—862no—
818D4—1728no—
819D4—1721no—
820D4—1721no—
821D4C22⋊C4×D4314yescomplemented
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—432no—
835C2×C4—432no—
836C2×C4—432no—
837C2×C4—434no—
838C2×C4—434no—
839C2×C4—434no—
840C2×C4—434no—
841C2×C4—432no—
842C2×C4—8616no—
843C2×C4—862no—
844C2×C4—861no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—861no—
848C2×C4—862no—
849C2×C4—861no—
850C2×C4—861no—
851C2×C4—861no—
852C2×C4—3444no—
853C2×C4—1724no—
854C2×C4—1724no—
855C2×C4—1728no—
856C2×C4—1721no—
857C2×C4—1721no—
858C2×C4—1721no—
859C2×C4—1721no—
860C2×C4—1721no—
861C2×C4#1306334912yescomplemented
862C2×C4C22×C4×D4311yescharacteristic
863C2×C4C2×D4×D4311yescharacteristic
864C2×C4C2×D4×D4311yescharacteristic
865C2×C4C2×D4×D4311yescharacteristic
866C2×C4#41×D4311yescharacteristic
867C2×C4#41×D4311yescharacteristic
868C8—22no—
869C8—41no—
870C8—862no—
871C8—1721no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—434no—
887C22—862no—
888C22—862no—
889C22—862no—
890C22—862no—
891C22—862no—
892C22—862no—
893C22—34416no—
894C22—3441no—
895C22—3441no—
896C22—3441no—
897C22—3441no—
898C22—1722no—
899C22—1722no—
900C22—1722no—
901C22C4×D4×D4311yescharacteristic
902C22#120×D4311yescharacteristic
903C22#121×D4311yescharacteristic
904C22AGL(1,ℤ/8)×D4311yescharacteristic
905C22C2×#1306334911yescharacteristic
906C22#1458369511yescharacteristic
907C22#1458369611yescharacteristic
908C4—22no—
909C4—42no—
910C4—41no—
911C4—81no—
912C4—434no—
913C4—862no—
914C4—864no—
915C4—3441no—
916C4—1721no—
917C4—1722no—
918C4C2×C22⋊C4×D4311yescharacteristic
919C4C4×D4×D4311yescharacteristic
920C4#121×D4311yescharacteristic
921C4#123×D4311yescharacteristic
922C2—44no—
923C2—82no—
924C2—864no—
925C2—3442no—
926C2#386×D4311yescharacteristic
927C2C4×#1306334911yescharacteristic
928C2#1914340611yescharacteristic
929C2#1914384211yescharacteristic
930C2#1914384411yescharacteristic
931C2#1914407011yescharacteristic
932C2#1914408411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC22×#13063349C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#20928
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621900C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582902C2semidirect
5. #390×D43C2semidirect
6. #19134953C2semidirect
7. #19134951C2semidirect
8. #19134949C2semidirect
9. #19134947C2semidirect
10. #19134945C2semidirect
11. #19134943C2semidirect
12. #19134941C2semidirect
13. #19134313C2semidirect
14. #19134287C2semidirect
15. C43×#1879C2semidirect
20. C2×#13063349C4semidirect
28. C2×C4×Dic86C22semidirect
29. C2×#13063290C22semidirect
30. C2×D4×Dic43C22semidirect
42. C2×#13063250C22semidirect
43. C2×#13063248C22semidirect
46. C2×#13063246C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. #14582654C22semidirect
57. #14582653C22semidirect
58. #14582653C22semidirect
60. C2×C4×D4×C43C22semidirect
62. C2×#102×C43C22semidirect
64. C43×#340C22semidirect
65. C43×#336C22semidirect
82. C2×D4×D43C2×C4semidirect
92. C2×#10621873C2×C4semidirect
95. C2×#10621883C2×C4semidirect
98. C2×#10621882C2×C4semidirect
104. C2×#10621872C2×C4semidirect
155. C2×D8×C43C2×C4semidirect
220. #10621900C22⋊C4semidirect
344. D4×C43C2×C22⋊C4semidirect
357. C2×C4×C43AGL(1,ℤ/8)semidirect
385. C2×Dic43AGL(1,ℤ/8)semidirect
400. Dic86C2×C22⋊C4semidirect
468. #1879D43semidirect
500. C2×C4×D4C2×D43semidirect
517. C2×#102C2×D43semidirect
527. #340C2×D43semidirect
531. #336C2×D43semidirect
532. C43#20928semidirect
571. C2×D8C4×D43semidirect
821. D4C22⋊C4×D43semidirect
861. C2×C4#13063349semidirect

Maximal subgroups

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

subgroupindex
C22×#130633492
C2×C4×#106219002
C2×#145828972
C2×#145829022
#390×D432
#191349532
#191349512
#191349492
#191349472
#191349452
#191349432
#191349412
#191343132
#191342872
C43×#18792
#2092843