Finite Group Databasebeta

← #25112081

Subgroups — #25112081

Order 11008.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583543C211yesmaximal, characteristic
2C2×#14582967C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C22×#13063246C211yesmaximal, characteristic, complemented
5#19137491C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135410C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19135016C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134900C211yesmaximal, characteristic, complemented
12#19134593C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic, complemented
18C23×C43⋊C8C2211yescharacteristic
19#14583543—24no—
20#14583543C418yescomplemented
21C2×#13063312C2211yescharacteristic
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063294—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C22×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic, complemented
32C22×C22⋊Dic43—21no—
33#14582967—24no—
34C2×Dic43⋊C8C2211yescharacteristic, complemented
35#14582897—24no—
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063248C2211yescharacteristic, complemented
40C2×#13063246—24no—
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
46C2×#13063235C2211yescharacteristic, complemented
47#14582796—21no—
48#14582773—21no—
49#14582771—21no—
50#14582768C2211yescharacteristic, complemented
51#14582756C2211yescharacteristic, complemented
52C4⋊C4×Dic43C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C23×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43D411yescharacteristic
74C23×Dic43—21no—
75C23×Dic43—21no—
76C23×Dic43—21no—
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872—41no—
82C22×C43⋊C8—22no—
83C22×C43⋊C8—22no—
84C22×C43⋊C8—41no—
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063312—22no—
88#13063312C2×C414yescomplemented
89#13063306—28no—
90#13063304—22no—
91#13063304C2×C414yescomplemented
92#13063297—28no—
93#13063296—22no—
94#13063296C2×C414yescomplemented
95#13063294—28no—
96D4×Dic43—22no—
97D4×Dic43C2×C414yescomplemented
98C4×C22⋊D43C2×C414yes—
99C4×C22⋊D43D414yes—
100(C22⋊D43)⋊C4—44no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—41no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C4⋊C4×D43—22no—
113C4⋊C4×D43—41no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43—28no—
120C2×C22⋊Dic43D411yescharacteristic
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4D411yescharacteristic
123C2×C4×Dic43—21no—
124C2×C4×Dic43C2311yescharacteristic
125Dic43⋊C8—22no—
126#13063250—22no—
127#13063250—41no—
128#13063248—22no—
129#13063248—41no—
130#13063246—22no—
131#13063246—22no—
132#13063246—22no—
133#13063246D414yescomplemented
134(C2×D43)⋊C8—22no—
135#13063235—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C25×C43—21no—
139C22×D4×C43—22no—
140C22×D4×C43—22no—
141C22×D4×C43—21no—
142C22×D4×C43—22no—
143C22×D4×C43—41no—
144C22×D4×C43—41no—
145C22×D4×C43C2×C414yescomplemented
146C22×D4×C43C2311yescharacteristic
147C22×D4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154#102×C43—22no—
155#102×C43—22no—
156#102×C43—41no—
157#102×C43—41no—
158C22⋊C8×C43—22no—
159#95×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—24no—
163C24×C43—42no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43—81no—
168C24×C43—81no—
169C24×C43C2×D411yescharacteristic
170C23×D43C2×D411yescharacteristic
171C2×D4×C43—24no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—28no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—44no—
184C2×D4×C43—44no—
185C2×D4×C43—44no—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C22×C412yes—
188C2×D4×C43C2×D412yes—
189C2×D4×C43#4112yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C22×C412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—22no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—42no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43C22⋊C414yes—
209C22×Dic43—24no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43—42no—
218C22×Dic43—42no—
219C22×Dic43—81no—
220C22×Dic43—81no—
221C22×Dic43—81no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225#10621900—28no—
226#10621900—44no—
227#10621900—44no—
228#10621900—44no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—81no—
236C2×C4×D43C22×C412yes—
237C2×C4×D43C2×D412yes—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22×C412yes—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C22⋊C4×C43—42no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43C22⋊C414yes—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4C22⋊C414yes—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—42no—
268C4⋊Dic43C22×C412yes—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273Dic43⋊C4—81no—
274Dic43⋊C4C22⋊C414yes—
275C4×Dic43—42no—
276C4×Dic43C22×C412yes—
277C4×Dic43C2×D412yes—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—44no—
284C2×C43⋊C8C2×D412yes—
285#10621872—44no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—48no—
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×C43—41no—
305C23×C43—48no—
306C23×C43—84no—
307C23×C43—84no—
308C23×C43—84no—
309C23×C43—84no—
310C23×C43—84no—
311C23×C43C2×C22⋊C412yes—
312C23×C43AGL(1,ℤ/8)12yes—
313C23×C43#13712yes—
314C23×C43C22×D411yescharacteristic
315C22×D43—21no—
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43C2×C22⋊C412yes—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—22no—
327D4×C43—48no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43C4×D414yescomplemented
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43C2×C22⋊C412yes—
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C22⋊D43—28no—
351C22⋊D43—48no—
352C22⋊D43—84no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—48no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—84no—
373C2×Dic43—84no—
374C2×Dic43C2×C22⋊C412yes—
375C2×Dic43C2×C22⋊C412yes—
376C2×Dic43C2×C22⋊C412yes—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—84no—
382Dic86—22no—
383Dic86—22no—
384Dic86—41no—
385Dic86—41no—
386C8×C43—41no—
387C8×C43—41no—
388C43⋊C8—22no—
389C43⋊C8—41no—
390#22419—431nomaximal, Sylow
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—24no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—816no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43#41714yescomplemented
413C22×C43C22×C22⋊C411yescharacteristic
414C22×C43D4211yescharacteristic
415C22×C43#54611yescharacteristic
416C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C43C2×#13711yescharacteristic
418C22×C43#57611yescharacteristic
419C22×C43#57711yescharacteristic
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—41no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43—41no—
427C4×C43—22no—
428C4×C43—81no—
429C4×C43—81no—
430C4×C43C2×C4×D411yescharacteristic
431C4×C43#51811yescharacteristic
432C4×C43D4211yescharacteristic
433C4×C43#54611yescharacteristic
434Dic43—22no—
435Dic43—22no—
436Dic43—22no—
437Dic43—42no—
438Dic43—42no—
439Dic43—42no—
440Dic43—81no—
441C2×#546—431no—
442C2×#435—431no—
443C2×#417—431no—
444C22×#102—431no—
445D4×C4⋊C4—431no—
446#1983—431no—
447#1959—431no—
448#1895—431no—
449#1892—431no—
450#1874—431no—
451#1872—431no—
452#1802—431no—
453#1788—431no—
454#1786D4311yescharacteristic, complemented
455#1762—431no—
456C2×C43—24no—
457C2×C43—44no—
458C2×C43—82no—
459C2×C43D4×C22⋊C411yescharacteristic
460C2×C43C2×#41711yescharacteristic
461C2×C43#289711yescharacteristic
462C2×C43#326411yescharacteristic
463C2×C43#326611yescharacteristic
464C2×C43#330611yescharacteristic
465C2×C43#331411yescharacteristic
466D43—42no—
467C22×#41—431no—
468C23×D4C2×D4311yescharacteristic
469C22×M16—431no—
470C23×C8—431no—
471#546—438no—
472#546—864no—
473C2×#124—431no—
474C2×#123—861no—
475C2×C22⋊Q8—431no—
476C2×#121—431no—
477C2×#121—861no—
478C2×#120—861no—
479C2×C4×D4—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8—431no—
487#417—864no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—864no—
497C2×#102C2×D4311yescharacteristic
498C2×#102C2×D4311yescharacteristic
499C2×#102C2×D4311yescharacteristic
500C2×#102C2×D4311yescharacteristic
501C2×C22⋊C8—431no—
502C2×C22⋊C8C2×D4311yescharacteristic
503C2×#97—431no—
504#389—861no—
505#385—861no—
506#385—861no—
507#384—431no—
508#380—431no—
509#380C2×D4311yescharacteristic
510C4×C4⋊C4—431no—
511#340—431no—
512#340—431no—
513#340—431no—
514#340—431no—
515C43#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—434no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—862no—
521C2×#41—1721no—
522C2×#41—1721no—
523C22×Q8—431no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—22no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—431no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4C4×D4314yescomplemented
534C22×D4C22×D4311yescharacteristic
535C22×D4C22×D4311yescharacteristic
536C23×C4—431no—
537C23×C4—861no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×M16—862no—
543C2×M16—862no—
544C2×M16—1721no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—862no—
548C22×C8—862no—
549C22×C8—1721no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#124—434no—
553#124—862no—
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—434no—
558#121—868no—
559#121—862no—
560#120—868no—
561C4×D4—434no—
562C4×D4—434no—
563C4×D4—434no—
564C4×D4—862no—
565C4×D4—1724no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—862no—
571C2×C4⋊C4—862no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—1721no—
578C2×C4⋊C4—1721no—
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—431no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—868no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—431no—
592C2×C42—861no—
593C4⋊C8—862no—
594#103—862no—
595#103—862no—
596#103—1721no—
597#103—1721no—
598#102—22no—
599#102—22no—
600#102—41no—
601#102—41no—
602#102—434no—
603#102—862no—
604#102—862no—
605#102—862no—
606C22⋊C8—22no—
607C22⋊C8—862no—
608#97—862no—
609#95—21no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24—431no—
622C24D4×D4311yescharacteristic
623#41—868no—
624#41—1724no—
625#41—1724no—
626#41—1724no—
627C2×Q8—432no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8—861no—
632C2×Q8—861no—
633C2×D4—28no—
634C2×D4—24no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—434no—
649C2×D4—862no—
650C2×D4—862no—
651C2×D4—864no—
652C2×D4—864no—
653C2×D4—3441no—
654C2×D4—3441no—
655C2×D4—1722no—
656C2×D4—1722no—
657C2×D4C2×C4×D4312yes—
658C2×D4C2×C4×D4312yes—
659C2×D4D4×D4312yes—
660C2×D4#1062190012yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—432no—
671C22×C4—432no—
672C22×C4—864no—
673C22×C4—864no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—3441no—
683C22×C4—3441no—
684C22×C4—3441no—
685C22×C4—3441no—
686C22×C4—1722no—
687C22×C4—1722no—
688C22×C4—1722no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4C2×C4×D4312yes—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4312yes—
695C22×C4C23×D4311yescharacteristic
696M16—1724no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—432no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—1724no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—434no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—864no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—3441no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4—1722no—
726C22⋊C4—42no—
727C22⋊C4—434no—
728C22⋊C4—434no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—1722no—
735C42—432no—
736C42—432no—
737C42—1722no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23—432no—
764C23—861no—
765C23—861no—
766C23—861no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23C22⋊C4×D4312yes—
771C23#1306334912yes—
772C23#1306335412yes—
773C23C2×D4×D4311yescharacteristic
774Q8—862no—
775Q8—862no—
776Q8—1721no—
777Q8—1721no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—41no—
785D4—41no—
786D4—868no—
787D4—3444no—
788D4—1728no—
789D4(C22⋊D43)⋊C414yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—432no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—3444no—
819C2×C4—3444no—
820C2×C4—3444no—
821C2×C4—1728no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4C22⋊C4×D4312yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4C2×#1062190011yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337011yescharacteristic
838C8—41no—
839C8—41no—
840C8—862no—
841C8—1721no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—862no—
864C22—862no—
865C22—862no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22—1721no—
870C22#1458289714yescomplemented
871C22C2×C22⋊C4×D4311yescharacteristic
872C22#1458353111yescharacteristic
873C22#1458353611yescharacteristic
874C22C2×#1306334911yescharacteristic
875C22C2×#1306335411yescharacteristic
876C22#1458370311yescharacteristic
877C22#1458370911yescharacteristic
878C4—22no—
879C4—81no—
880C4—81no—
881C4—862no—
882C4—862no—
883C4—862no—
884C4—3441no—
885C4—1722no—
886C4—1722no—
887C4—1722no—
888C4C2×(C22⋊D43)⋊C411yescharacteristic
889C4#1458337211yescharacteristic
890C4#1458353111yescharacteristic
891C4#1458353611yescharacteristic
892C2—24no—
893C2—44no—
894C2—82no—
895C2—1722no—
896C2#1913741111yescharacteristic
897C2C2×#1458289711yescharacteristic
898C2#1914312011yescharacteristic
899C2#1914606811yescharacteristic
900C2#1914610911yescharacteristic
901C2#1914656011yescharacteristic
902C2#1914668011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14582967C2semidirect
3. C2×#14582897C2semidirect
4. C22×#13063246C2semidirect
5. #19137491C2semidirect
6. #19135526C2semidirect
7. #19135410C2semidirect
8. #19135030C2semidirect
9. #19135016C2semidirect
10. #19134909C2semidirect
11. #19134900C2semidirect
12. #19134593C2semidirect
13. #19134532C2semidirect
14. #19134422C2semidirect
15. C43×#1786C2semidirect
17. C22×#10621872C22semidirect
20. #14583543C4semidirect
31. C2×C4⋊C4×D43C22semidirect
34. C2×Dic43⋊C8C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063248C22semidirect
39. C2×#13063248C22semidirect
45. C2×(C2×D43)⋊C8C22semidirect
46. C2×#13063235C22semidirect
50. #14582768C22semidirect
51. #14582756C22semidirect
52. C4⋊C4×Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
69. C2×#10621900C2×C4semidirect
88. #13063312C2×C4semidirect
91. #13063304C2×C4semidirect
94. #13063296C2×C4semidirect
97. D4×Dic43C2×C4semidirect
133. #13063246D4semidirect
145. C22×D4×C43C2×C4semidirect
330. D4×C43C4×D4semidirect
412. C22×C43#417semidirect
454. #1786D43semidirect
515. C43#22419semidirect
533. C22×D4C4×D43semidirect
789. D4(C22⋊D43)⋊C4semidirect
870. C22#14582897semidirect

Maximal subgroups

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

subgroupindex
C2×#145835432
C2×#145829672
C2×#145828972
C22×#130632462
#191374912
#191355262
#191354102
#191350302
#191350162
#191349092
#191349002
#191345932
#191345322
#191344222
C43×#17862
#2241943