Finite Group Databasebeta

← #25097342

Subgroups — #25097342

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2C2×#14582940C211yesmaximal, characteristic, complemented
3C2×#14582938C211yesmaximal, characteristic, complemented
4C2×#14582861C211yesmaximal, characteristic
5#380×D43C211yesmaximal, characteristic
6#19134796C211yesmaximal, characteristic, complemented
7#19134794C211yesmaximal, characteristic, complemented
8#19134792C211yesmaximal, characteristic, complemented
9#19134789C211yesmaximal, characteristic, complemented
10#19134786C211yesmaximal, characteristic, complemented
11#19134784C211yesmaximal, characteristic, complemented
12#19134781C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063282—21no—
23C2×#13063281—21no—
24#117×D43—24no—
25#117×D43—24no—
26C2×C4⋊C4×D43C2211yescharacteristic
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31C2×C22⋊C4×D43—21no—
32C2×C42×D43—21no—
33#14582940—24no—
34#14582938—24no—
35C2×#13063259C2211yescharacteristic, complemented
36C2×#13063258C2211yescharacteristic, complemented
37C2×#13063258C2211yescharacteristic, complemented
38C2×#13063257C2211yescharacteristic, complemented
39C2×#13063256C2211yescharacteristic, complemented
40C2×#13063256C2211yescharacteristic, complemented
41#14582861C418yescomplemented
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582758—21no—
47#14582757—21no—
48#14582756C2211yescharacteristic
49#14582756C2211yescharacteristic
50#95×D43—21no—
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×#117×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic, complemented
59C2×#106×C43C2211yescharacteristic, complemented
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43D411yescharacteristic
65C23×Dic43D411yescharacteristic
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2×C414yes—
75C22×C4×D43D411yescharacteristic
76C22×C4×D43D411yescharacteristic
77C22×C4×D43Q814yes—
78C22×C4×D43C2311yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C2×#10621872—22no—
81C2×#10621872—22no—
82C2×#10621872—22no—
83C2×#10621872—22no—
84C2×#10621872C2×C414yescomplemented
85C2×#10621872C2×C414yescomplemented
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063284—22no—
89#13063284—22no—
90#13063283—22no—
91#13063283—22no—
92#13063283D414yes—
93#13063283D414yes—
94#13063282—28no—
95#13063281—28no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43—22no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C22⋊C4×D43—28no—
119C22⋊C4×D43—44no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C42×D43—28no—
124#13063259—22no—
125#13063258—22no—
126#13063258—22no—
127#13063257—22no—
128#13063256—22no—
129#13063256—22no—
130C22⋊(C43⋊C8)C2×C414yescomplemented
131(C2×D43)⋊C8C2×C414yescomplemented
132(C2×D43)⋊C8C2×C414yescomplemented
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C23×C4×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#117×C43—22no—
140#117×C43—22no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148#107×C43—22no—
149#106×C43—22no—
150C22⋊C8×C43C2×C414yescomplemented
151#95×C43—21no—
152C24×C43C2×D411yescharacteristic
153C23×D43—22no—
154C23×D43—22no—
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—41no—
158C23×D43—41no—
159C23×D43C4⋊C414yes—
160C23×D43C2×D411yescharacteristic
161C23×D43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C22×C412yes—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×Q812yes—
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43C4⋊C414yes—
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—28no—
190C2×C4×D43—28no—
191C2×C4×D43—28no—
192C2×C4×D43—28no—
193C2×C4×D43—24no—
194C2×C4×D43—24no—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43C4⋊C414yes—
208C2×C4×D43C4⋊C414yes—
209C2×C4×D43C22×C412yes—
210C2×C4×D43C22×C412yes—
211C2×C4×D43C2×D412yes—
212C2×C4×D43C2×D412yes—
213C2×C4×D43C2×Q812yes—
214C2×C4×D43C2×Q812yes—
215C2×C4×D43#4112yes—
216C2×C4×D43#4112yes—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43C22×C412yes—
222C2×C8×C43C22×C412yes—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43C2×D412yes—
230C4⋊C4×C43C2×D412yes—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—42no—
233C42×C43—24no—
234C22⋊Dic43—24no—
235C22⋊Dic43—42no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—42no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43C2×D412yes—
247C4⋊Dic43C2×D412yes—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250Dic43⋊C4—42no—
251Dic43⋊C4—42no—
252C4×Dic43—24no—
253C4×Dic43—24no—
254C4×Dic43—24no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8C22×C412yes—
260C2×C43⋊C8C22×C412yes—
261#10621872—28no—
262#10621872—28no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43C2×C4⋊C412yes—
270C23×C43C22×D411yescharacteristic
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—28no—
280C22×D43—28no—
281C22×D43—44no—
282C22×D43—44no—
283C22×D43—44no—
284C22×D43—44no—
285C22×D43—44no—
286C22×D43C2×C4⋊C412yes—
287C22×D43C2×C4⋊C412yes—
288C22×D43#12012yes—
289C22×D43#12312yes—
290C22×D43AGL(1,ℤ/8)12yes—
291C22×D43#13712yes—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43C2×C4⋊C412yes—
311C2×C4×C43C23×C411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×Q811yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—28no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43C2×C4⋊C412yes—
333C2×Dic43C2×C4⋊C412yes—
334C2×Dic43#12012yes—
335C2×Dic43#12312yes—
336C4×D43—28no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—28no—
342C4×D43—48no—
343C4×D43—48no—
344C4×D43—84no—
345C4×D43—84no—
346C4×D43C4×D414yes—
347C4×D43C4×D414yes—
348C4×D43C22⋊Q814yes—
349C4×D43C22⋊Q814yes—
350C8×C43—22no—
351C8×C43—22no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354#20846—431nomaximal, Sylow
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43C22×C4⋊C411yescharacteristic
363C22×C43C2×#12011yescharacteristic
364C22×C43C2×#12311yescharacteristic
365C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C43C2×#13711yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57511yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—416no—
382C2×D43#38514yes—
383C2×D43#42814yescomplemented
384C4×C43—22no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43C2×C4×D411yescharacteristic
390C4×C43C2×C4×D411yescharacteristic
391C4×C43C2×C22⋊Q811yescharacteristic
392C4×C43C2×C22⋊Q811yescharacteristic
393Dic43—22no—
394Dic43—42no—
395Dic43—42no—
396Dic43—81no—
397Dic43—81no—
398Dic43#38514yes—
399C22×#117—431no—
400C2×#428—431no—
401C2×#428—431no—
402C2×#407—431no—
403C2×#380—431no—
404#1854—431no—
405#1854—431no—
406#1854—431no—
407#1854D4311yescharacteristic, complemented
408#1853—431no—
409#1853—431no—
410#1852—431no—
411#1852—431no—
412#1736—431no—
413#1736—431no—
414C2×C43—42no—
415C2×C43C2×#38511yescharacteristic
416C2×C43C2×#42811yescharacteristic
417C2×C43#291111yescharacteristic
418C2×C43#300611yescharacteristic
419C2×C43#300711yescharacteristic
420C2×C43#309411yescharacteristic
421C2×C43#309511yescharacteristic
422D43—24no—
423D43—24no—
424C24×C4—431no—
425C22×M16—431no—
426C22×M16—431no—
427C2×#117—431no—
428C2×#117—431no—
429C2×#117—431no—
430C2×#117—861no—
431C2×#117—861no—
432C2×#117—864no—
433C2×#117—864no—
434C2×#117C2×D4311yescharacteristic
435C22×C4⋊C4—431no—
436C22×C4⋊C4—431no—
437C22×C4⋊C4—431no—
438C22×C4⋊C4—431no—
439C22×C22⋊C4—861no—
440C22×C22⋊C4—861no—
441C22×C42—861no—
442#428—864no—
443#428—864no—
444C2×#107—431no—
445C2×#107—431no—
446C2×#107—431no—
447C2×#107C2×D4311yescharacteristic, complemented
448C2×#106—431no—
449C2×#106—431no—
450C2×#106—431no—
451C2×#106C2×D4311yescharacteristic, complemented
452#407—438no—
453C2×C22⋊C8—431no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C22⋊C8C2×D4311yescharacteristic
457#380—431no—
458#380—431no—
459#380—431no—
460#380—861no—
461#380—861no—
462#380C2×D4311yescharacteristic
463C2×#95—861no—
464#340—431no—
465#340—431no—
466#340—431no—
467#340—431no—
468#340—431no—
469#340—431no—
470#340C2×D4311yescharacteristic, complemented
471#340C2×D4311yescharacteristic, complemented
472C43#2084611yescharacteristic, complemented, Sylow
473C25—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—434no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—434no—
480C23×C4—431no—
481C23×C4—862no—
482C23×C4—862no—
483C23×C4—862no—
484C23×C4—862no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4C22×D4311yescharacteristic
490C2×M16—434no—
491C2×M16—434no—
492C2×M16—862no—
493C2×M16—862no—
494C2×M16—862no—
495C2×M16—862no—
496C22×C8—431no—
497C22×C8—431no—
498C22×C8C22×D4311yescharacteristic
499C22×C8C22×D4311yescharacteristic
500#117—22no—
501#117—22no—
502#117—434no—
503#117—434no—
504#117—868no—
505#117—868no—
506#117—862no—
507#117—862no—
508#117—862no—
509#117—862no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—862no—
515C2×C4⋊C4—862no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—862no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—868no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—1724no—
540C2×C42—21no—
541C2×C42—868no—
542C2×C42—861no—
543C2×C42—861no—
544C2×C42—861no—
545#107—22no—
546#107—862no—
547#107—862no—
548#107—862no—
549#106—22no—
550#106—862no—
551#106—862no—
552#106—862no—
553C22⋊C8—434no—
554C22⋊C8—434no—
555C22⋊C8—434no—
556C22⋊C8C4×D4314yescomplemented
557#95—21no—
558#95—861no—
559#95—861no—
560#95—861no—
561C24—431no—
562C24—431no—
563C24—434no—
564C24—862no—
565C24—862no—
566C24—862no—
567C24—862no—
568C24—1721no—
569C24—1721no—
570C24D4×D4311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—431no—
580C22×C4—432no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—434no—
587C22×C4—431no—
588C22×C4—434no—
589C22×C4—434no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—868no—
595C22×C4—868no—
596C22×C4—868no—
597C22×C4—868no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4C2×C4×D4312yes—
623C22×C4D4×D4311yescharacteristic
624C22×C4Q8×D4312yes—
625C22×C4C23×D4311yescharacteristic
626M16—868no—
627M16—868no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—432no—
633C2×C8—432no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8C2×C4×D4312yes—
639C2×C8C2×C4×D4312yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—432no—
647C4⋊C4—432no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—1722no—
657C4⋊C4—1722no—
658C4⋊C4D4×D4312yes—
659C4⋊C4D4×D4312yes—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C42—24no—
669C42—864no—
670C42—864no—
671C42—864no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—432no—
679C23—432no—
680C23—432no—
681C23—432no—
682C23—432no—
683C23—432no—
684C23—868no—
685C23—868no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—1724no—
695C23—1724no—
696C23—1724no—
697C23—1724no—
698C23—1724no—
699C23C4⋊C4×D4312yes—
700C23C2×D4×D4311yescharacteristic
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—434no—
723C2×C4—434no—
724C2×C4—434no—
725C2×C4—434no—
726C2×C4—432no—
727C2×C4—868no—
728C2×C4—868no—
729C2×C4—868no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—3444no—
739C2×C4—3444no—
740C2×C4—1728no—
741C2×C4—1728no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4C4⋊C4×D4312yes—
753C2×C4C22×C4×D4311yescharacteristic
754C2×C4C2×D4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C2×C4C2×Q8×D4311yescharacteristic
757C2×C4#41×D4311yescharacteristic
758C2×C4#41×D4311yescharacteristic
759C8—22no—
760C8—22no—
761C8—862no—
762C8—862no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—434no—
771C22—434no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—862no—
776C22—862no—
777C22—862no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—862no—
782C22—862no—
783C22—862no—
784C22—17216no—
785C22C2×C4⋊C4×D4311yescharacteristic
786C22#120×D4311yescharacteristic
787C22#123×D4311yescharacteristic
788C22AGL(1,ℤ/8)×D4311yescharacteristic
789C22#137×D4311yescharacteristic
790C22#1458369611yescharacteristic
791C22#1458369611yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—81no—
796C4—81no—
797C4—434no—
798C4—862no—
799C4—3441no—
800C4—3441no—
801C4—1722no—
802C4—1722no—
803C4C4×D4×D4311yescharacteristic
804C4C4×D4×D4311yescharacteristic
805C4C22⋊Q8×D4311yescharacteristic
806C4C22⋊Q8×D4311yescharacteristic
807C2—42no—
808C2—864no—
809C2—864no—
810C2#385×D4311yescharacteristic
811C2#428×D4311yescharacteristic
812C2#1914318311yescharacteristic
813C2#1914384411yescharacteristic
814C2#1914385211yescharacteristic
815C2#1914453411yescharacteristic
816C2#1914454211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#20846
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#14582940C2semidirect
3. C2×#14582938C2semidirect
6. #19134796C2semidirect
7. #19134794C2semidirect
8. #19134792C2semidirect
9. #19134789C2semidirect
10. #19134786C2semidirect
11. #19134784C2semidirect
12. #19134781C2semidirect
13. #19134313C2semidirect
14. #19134313C2semidirect
15. C43×#1854C2semidirect
35. C2×#13063259C22semidirect
36. C2×#13063258C22semidirect
37. C2×#13063258C22semidirect
38. C2×#13063257C22semidirect
39. C2×#13063256C22semidirect
40. C2×#13063256C22semidirect
41. #14582861C4semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×#107×C43C22semidirect
59. C2×#106×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
84. C2×#10621872C2×C4semidirect
85. C2×#10621872C2×C4semidirect
130. C22⋊(C43⋊C8)C2×C4semidirect
131. (C2×D43)⋊C8C2×C4semidirect
132. (C2×D43)⋊C8C2×C4semidirect
150. C22⋊C8×C43C2×C4semidirect
383. C2×D43#428semidirect
407. #1854D43semidirect
447. C2×#107C2×D43semidirect
451. C2×#106C2×D43semidirect
470. #340C2×D43semidirect
471. #340C2×D43semidirect
472. C43#20846semidirect
556. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
C2×#145829402
C2×#145829382
C2×#145828612
#380×D432
#191347962
#191347942
#191347922
#191347892
#191347862
#191347842
#191347812
#191343132
C43×#18542
#2084643