Finite Group Databasebeta

← #25134188

Subgroups — #25134188

Order 11008.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583138C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583050C211yesmaximal, characteristic, complemented
4C22×#13063246C211yesmaximal, characteristic, complemented
5#19138046C211yesmaximal, characteristic, complemented
6#19135831C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135689C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic, complemented
22C22×C4⋊Dic43C2211yescharacteristic
23#14583138—24no—
24#14583061—24no—
25#14583050—24no—
26C2×#13063258C2211yescharacteristic, complemented
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063249C2211yescharacteristic, complemented
30C2×#13063248C2211yescharacteristic, complemented
31C2×#13063246—24no—
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41#14582832—21no—
42#14582822—21no—
43#14582805C2211yescharacteristic, complemented
44#14582797C2211yescharacteristic, complemented
45#14582779—21no—
46#14582759C2211yescharacteristic, complemented
47#14582757—21no—
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C23×D4×C43C2211yescharacteristic
54C43×#546—24no—
55C43×#546—24no—
56C2×#124×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C22⋊C4×C43—21no—
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—41no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—41no—
75C2×#10621883—41no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86#13063304—41no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99#13063258—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—41no—
103#13063248—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246D414yescomplemented
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—41no—
123C2×#41×C43—41no—
124C22×Q8×C43C2311yescharacteristic
125C22×D4×C43—22no—
126C22×D4×C43—22no—
127C22×D4×C43—21no—
128C22×D4×C43—21no—
129C22×D4×C43—21no—
130C22×D4×C43—22no—
131C22×D4×C43—41no—
132C22×D4×C43—41no—
133C22×D4×C43D411yescharacteristic
134C22×D4×C43D414yes—
135C22×D4×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C23×C4×C43—21no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141#124×C43—22no—
142#124×C43—22no—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43D414yes—
146#121×C43—28no—
147#121×C43—22no—
148#121×C43—22no—
149#120×C43—28no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C4×D4×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43D411yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43—28no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—24no—
169C24×C43—42no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—42no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C24×C43C2×D411yescharacteristic
177#41×C43—44no—
178#41×C43—44no—
179#41×C43—44no—
180#41×C43—44no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43C2×D412yes—
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—28no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—44no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—81no—
210C2×D4×C43—81no—
211C2×D4×C43C2×D412yes—
212C2×D4×C43C2×D412yes—
213C2×D4×C43C2×D412yes—
214C2×D4×C43#4112yes—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—24no—
220C22×C4×C43—24no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—42no—
230C22×C4×C43—42no—
231C22×C4×C43—81no—
232C22×C4×C43—81no—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2411yescharacteristic
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—42no—
245C22×Dic43—42no—
246C22×Dic43—81no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—21no—
252C2×Dic86—21no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—22no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2×D412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—24no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—22no—
262C22⋊C4×C43—22no—
263C22⋊C4×C43—24no—
264C42×C43—21no—
265C42×C43—21no—
266C22⋊Dic43—42no—
267C22⋊Dic43—42no—
268C22⋊Dic43—81no—
269#10621885—44no—
270#10621883—44no—
271#10621883—44no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—42no—
278C4⋊Dic43C2×D412yes—
279Dic43⋊C4—42no—
280Dic43⋊C4—42no—
281Dic43⋊C4—81no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—44no—
294C2×C43⋊C8C2×D412yes—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—48no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—48no—
322C23×C43—84no—
323C23×C43—84no—
324C23×C43—84no—
325C23×C43—84no—
326C23×C43—84no—
327C23×C43#12012yes—
328C23×C43#13512yes—
329C23×C43#13712yes—
330C23×C43C22×D411yescharacteristic
331Q8×C43—22no—
332Q8×C43—22no—
333Q8×C43—41no—
334Q8×C43—41no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—22no—
340D4×C43—48no—
341D4×C43—48no—
342D4×C43—44no—
343D4×C43—41no—
344D4×C43—41no—
345D4×C43—84no—
346D4×C43#12114yes—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—22no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—48no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—84no—
374C2×C4×C43#12012yes—
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C2×#4111yescharacteristic
379C2×C4×C43H(5,𝔽2)11yescharacteristic
380C2×C4×C43H(5,𝔽2)11yescharacteristic
381C2×Dic43—22no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—84no—
394Dic86—41no—
395Dic86—41no—
396Dic86—41no—
397Dic86—41no—
398C43⋊C8—22no—
399C43⋊C8—41no—
400C43⋊C8—41no—
401C43⋊C8—41no—
402#24426—431nomaximal, Sylow
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—24no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—42no—
416C22×C43—41no—
417C22×C43—42no—
418C22×C43—41no—
419C22×C43—42no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—42no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—816no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43—81no—
431C22×C43#45214yescomplemented
432C22×C43C2×#12011yescharacteristic
433C22×C43D4211yescharacteristic
434C22×C43#54611yescharacteristic
435C22×C43C2×#13511yescharacteristic
436C22×C43C2×#13711yescharacteristic
437C22×C43#57611yescharacteristic
438C22×C43#57711yescharacteristic
439C4×C43—22no—
440C4×C43—41no—
441C4×C43—42no—
442C4×C43—41no—
443C4×C43—41no—
444C4×C43—42no—
445C4×C43C2×#12111yescharacteristic
446C4×C43#53411yescharacteristic
447C4×C43D4211yescharacteristic
448C4×C43#54611yescharacteristic
449Dic43—42no—
450Dic43—81no—
451Dic43—81no—
452Dic43—81no—
453C2×#546D4311yescharacteristic
454C2×#467—431no—
455C2×#452—431no—
456C2×#450—431no—
457C22×#102—431no—
458#2417—431no—
459#2042—431no—
460#2033—431no—
461#2015—431no—
462#2000—431no—
463#1877—431no—
464#1872—431no—
465#1869—431no—
466#1862—431no—
467#1788—431no—
468C2×C43—24no—
469C2×C43—44no—
470C2×C43—81no—
471C2×C43—82no—
472C2×C43#241011yescharacteristic
473C2×C43C2×#45211yescharacteristic
474C2×C43#301211yescharacteristic
475C2×C43#326611yescharacteristic
476C2×C43#328011yescharacteristic
477C2×C43#329611yescharacteristic
478C2×C43#331411yescharacteristic
479C22×#41C2×D4311yescharacteristic
480C23×D4C2×D4311yescharacteristic
481C22×Q16—431no—
482C22×SD16—431no—
483C22×SD16—431no—
484C23×C8—431no—
485#546—24no—
486#546—24no—
487C2×#124C2×D4311yescharacteristic
488C2×#123—21no—
489C2×C22⋊Q8—431no—
490C2×C22⋊Q8—431no—
491C2×C22⋊Q8C2×D4311yescharacteristic
492C2×#121—21no—
493C2×#121C2×D4311yescharacteristic
494C2×#120—21no—
495C2×C4×D4C2×D4311yescharacteristic
496C2×C4×D4C2×D4311yescharacteristic
497C22×C4⋊C4—431no—
498C22×C22⋊C4—21no—
499#467—864no—
500#452—864no—
501#450—864no—
502C2×#107—431no—
503C2×#103—431no—
504C2×#103—431no—
505C2×#103—431no—
506C2×#103—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—864no—
514C2×C22⋊C8—431no—
515C2×C22⋊C8—431no—
516C2×C22⋊C8—431no—
517#398—861no—
518#396—861no—
519#391—431no—
520#389—431no—
521#386—861no—
522#380—431no—
523#380—861no—
524#340—431no—
525#340—431no—
526#336—431no—
527#336—431no—
528C43#2442611yescharacteristic, complemented, Sylow
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—41no—
535C2×#41—41no—
536C22×Q8—431no—
537C22×Q8C22×D4311yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4C22⋊D4311yescharacteristic
547C22×D4C22⋊D4314yes—
548C22×D4C22×D4311yescharacteristic
549C22×D4C22×D4311yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—861no—
553C23×C4C22×D4311yescharacteristic
554C23×C4C22×D4311yescharacteristic
555C2×Q16—862no—
556C2×Q16—862no—
557C2×Q16—1721no—
558C2×SD16—862no—
559C2×SD16—862no—
560C2×SD16—862no—
561C2×SD16—862no—
562C2×SD16—1721no—
563C2×SD16—1721no—
564C22×C8—431no—
565C22×C8—431no—
566C22×C8—431no—
567C22×C8—431no—
568C22×C8—862no—
569C22×C8—862no—
570C22×C8—1721no—
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—862no—
576C22⋊Q8—862no—
577C22⋊Q8—862no—
578C22⋊Q8—1721no—
579C22⋊Q8C22⋊D4314yes—
580#121—28no—
581#121—22no—
582#121—22no—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—862no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—1721no—
598C2×C4⋊C4C22⋊D4311yescharacteristic
599C2×C4⋊C4C22×D4311yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4C22⋊D4311yescharacteristic
610C2×C22⋊C4C22⋊D4311yescharacteristic
611C2×C42C22×D4311yescharacteristic
612#107—862no—
613#103—862no—
614#103—862no—
615#103—862no—
616#103—1721no—
617#102—434no—
618#102—862no—
619#102—862no—
620#102—862no—
621#102—862no—
622#102—862no—
623C22⋊C8—862no—
624C22⋊C8—862no—
625C22⋊C8—1721no—
626#95—861no—
627#95—861no—
628#95—861no—
629#95—861no—
630C24—21no—
631C24—21no—
632C24—24no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×C22⋊D4311yescharacteristic
640C24C2×C22⋊D4311yescharacteristic
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—861no—
651C2×Q8—861no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8—861no—
655C2×Q8—861no—
656C2×Q8C2×C22⋊D4312yes—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4D4×D4312yes—
682C2×D4#1062190012yes—
683C2×D4C2×C22⋊D4312yes—
684C2×D4C2×C22⋊D4312yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—3441no—
708C22×C4—1722no—
709C22×C4—1722no—
710C22×C4C2×C22⋊D4311yescharacteristic
711C22×C4C2×C22⋊D4311yescharacteristic
712C22×C4C2×C22⋊D4311yescharacteristic
713C22×C4C2×C22⋊D4311yescharacteristic
714C22×C4C2×C22⋊D4312yes—
715C22×C4C2×C22⋊D4312yes—
716C22×C4C23×D4311yescharacteristic
717Q16—1724no—
718SD16—1724no—
719SD16—1724no—
720C2×C8—432no—
721C2×C8—861no—
722C2×C8—861no—
723C2×C8—861no—
724C2×C8—861no—
725C2×C8—861no—
726C2×C8—861no—
727C2×C8—861no—
728C2×C8—861no—
729C2×C8—861no—
730C2×C8—861no—
731C2×C8—861no—
732C2×C8—1724no—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—432no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—3441no—
743C4⋊C4—1722no—
744C4⋊C4—1722no—
745C4⋊C4—1722no—
746C4⋊C4C2×C22⋊D4312yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—22no—
754C22⋊C4—3441no—
755C22⋊C4—1722no—
756C22⋊C4—1722no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—48no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#1306329412yes—
792C23#1306334512yes—
793C23#1306335512yes—
794C23C22×C22⋊D4311yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—1721no—
800Q8—1721no—
801Q8—1721no—
802Q8—1721no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—48no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#1306329714yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—48no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—84no—
842C2×C4—862no—
843C2×C4—3444no—
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×C4—1721no—
853C2×C4—1721no—
854C2×C4—1721no—
855C2×C4#1306329412yes—
856C2×C4C2×D4×D4311yescharacteristic
857C2×C4C22×C22⋊D4311yescharacteristic
858C2×C4C22×C22⋊D4311yescharacteristic
859C2×C4C2×#1062190011yescharacteristic
860C2×C4#1306337011yescharacteristic
861C2×C4#1306337011yescharacteristic
862C8—862no—
863C8—1721no—
864C8—1721no—
865C8—1721no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—816no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22#1458306114yescomplemented
895C22C2×#1306329411yescharacteristic
896C22D4×C22⋊D4311yescharacteristic
897C22#1458354311yescharacteristic
898C22C2×#1306334511yescharacteristic
899C22C2×#1306335511yescharacteristic
900C22#1458370211yescharacteristic
901C22#1458371011yescharacteristic
902C4—22no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—41no—
907C4—42no—
908C4—3441no—
909C4—3441no—
910C4—3441no—
911C4—1722no—
912C4C2×#1306329711yescharacteristic
913C4#1458345811yescharacteristic
914C4D4×C22⋊D4311yescharacteristic
915C4#1458354311yescharacteristic
916C2—24no—
917C2—44no—
918C2—81no—
919C2—82no—
920C2#1913796911yescharacteristic
921C2C2×#1458306111yescharacteristic
922C2#1914389911yescharacteristic
923C2#1914610111yescharacteristic
924C2#1914627611yescharacteristic
925C2#1914643011yescharacteristic
926C2#1914667611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#24426
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583138C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14583050C2semidirect
4. C22×#13063246C2semidirect
5. #19138046C2semidirect
6. #19135831C2semidirect
7. #19135774C2semidirect
8. #19135689C2semidirect
9. #19135598C2semidirect
10. #19134929C2semidirect
11. #19134903C2semidirect
12. #19134888C2semidirect
13. #19134842C2semidirect
14. #19134535C2semidirect
16. C22×#10621885C22semidirect
21. C2×#13063304C22semidirect
26. C2×#13063258C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063249C22semidirect
30. C2×#13063248C22semidirect
39. C2×C22⋊(C43⋊C8)C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
43. #14582805C22semidirect
44. #14582797C22semidirect
46. #14582759C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
109. #13063246D4semidirect
431. C22×C43#452semidirect
528. C43#24426semidirect
894. C22#14583061semidirect

Maximal subgroups

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

subgroupindex
C2×#145831382
C2×#145830612
C2×#145830502
C22×#130632462
#191380462
#191358312
#191357742
#191356892
#191355982
#191349292
#191349032
#191348882
#191348422
#191345352
C2×C43×#5462
#2442643