Finite Group Databasebeta

← #25144026

Subgroups — #25144026

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583112C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic, complemented
3C2×#14582990C211yesmaximal, characteristic, complemented
4#19138157C211yesmaximal, characteristic, complemented
5D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
6#19135965C211yesmaximal, characteristic, complemented
7#19135799C211yesmaximal, characteristic, complemented
8#19135781C211yesmaximal, characteristic, complemented
9#19135670C211yesmaximal, characteristic, complemented
10#19135462C211yesmaximal, characteristic, complemented
11#19135198C211yesmaximal, characteristic, complemented
12#19134947C211yesmaximal, characteristic, complemented
13#19134945C211yesmaximal, characteristic, complemented
14#19134844C211yesmaximal, characteristic, complemented
15C2×C43×#447C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063312C2211yescharacteristic, complemented
19C2×#13063304C2211yescharacteristic
20C2×#13063290C2211yescharacteristic, complemented
21C2×D4×Dic43C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C22×C22⋊Dic43—21no—
24#14583112—24no—
25#14583050—24no—
26#14582990—24no—
27C2×#13063259C2211yescharacteristic, complemented
28C2×#13063256C2211yescharacteristic, complemented
29C2×Dic43⋊C8C2211yescharacteristic, complemented
30C2×#13063250C2211yescharacteristic, complemented
31C2×#13063250C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic, complemented
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic, complemented
38#14582822—21no—
39#14582813—21no—
40#14582802—21no—
41#14582802C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582802C2211yescharacteristic, complemented
44#14582798C2211yescharacteristic, complemented
45#14582787—21no—
46#14582779—21no—
47#14582779—21no—
48#14582759C2211yescharacteristic
49#14582755—21no—
50C4×C22⋊Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C23×D4×C43C2211yescharacteristic
56C22×D8×C43C2211yescharacteristic
57C22×D8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C43×#447—24no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—41no—
71C2×#10621883D414yescomplemented
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063312—22no—
75#13063312—41no—
76#13063304—22no—
77#13063304—41no—
78#13063290—22no—
79#13063290—41no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—41no—
83D4×Dic43—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—44no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×C22⋊Dic43D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108#13063259—41no—
109#13063256—22no—
110Dic43⋊C8—22no—
111#13063250—22no—
112#13063250—22no—
113#13063246—22no—
114#13063246—22no—
115#13063246—22no—
116#13063246—41no—
117C22⋊(C43⋊C8)—22no—
118C8×Dic43—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95D411yescharacteristic
122C43⋊#95D411yescharacteristic
123C25×C43—21no—
124C22×D4×C43—22no—
125C22×D4×C43—22no—
126C22×D4×C43—22no—
127C22×D4×C43—22no—
128C22×D4×C43—21no—
129C22×D4×C43—21no—
130C22×D4×C43—41no—
131C22×D4×C43—41no—
132C22×D4×C43C2311yescharacteristic
133C22×D4×C43C2311yescharacteristic
134C22×D4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×D8×C43—22no—
137C2×D8×C43—22no—
138C2×D8×C43—22no—
139C2×D8×C43—22no—
140C2×D8×C43—22no—
141C2×D8×C43—41no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#121×C43—22no—
145#121×C43—41no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148#102×C43—22no—
149#102×C43D414yes—
150C22⋊C8×C43—22no—
151C24×C43—21no—
152C24×C43—24no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43C2×D411yescharacteristic
162C2×D4×C43—24no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—44no—
181C2×D4×C43—44no—
182C2×D4×C43—44no—
183C2×D4×C43—44no—
184C2×D4×C43—42no—
185C2×D4×C43—81no—
186C2×D4×C43C2×D412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43#4112yes—
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×C43—21no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86C2×D412yes—
219D8×C43—44no—
220D8×C43—44no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43C2×D412yes—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C2×D412yes—
229C22⋊C4×C43—42no—
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43—42no—
233C22⋊Dic43—42no—
234C22⋊Dic43—42no—
235C22⋊Dic43—42no—
236C22⋊Dic43—42no—
237C22⋊Dic43—42no—
238C22⋊Dic43—42no—
239C22⋊Dic43—42no—
240C22⋊Dic43—42no—
241C22⋊Dic43—81no—
242C22⋊Dic43—81no—
243C22⋊Dic43—81no—
244#10621883—28no—
245#10621883—44no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—81no—
253Dic43⋊C4—42no—
254Dic43⋊C4—42no—
255C4×Dic43—21no—
256C4×Dic43—21no—
257C4×Dic43—21no—
258C4×Dic43—21no—
259C4×Dic43—42no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8C2×D412yes—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—48no—
277C23×C43—48no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—84no—
296C23×C43—84no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43—84no—
300C23×C43#13512yes—
301C23×C43C22×D411yescharacteristic
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—48no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—41no—
313D4×C43—41no—
314D4×C43—84no—
315D4×C43#12114yes—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—22no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—84no—
356C2×Dic43—84no—
357C2×Dic43AGL(1,ℤ/8)12yes—
358Dic86—22no—
359Dic86—22no—
360Dic86—41no—
361Dic86—41no—
362C8×C43—22no—
363C8×C43—41no—
364C43⋊C8—22no—
365C43⋊C8—41no—
366#25152—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—24no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—42no—
372C22×C43—41no—
373C22×C43—42no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—816no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43#52511yescharacteristic
397C22×C43D4211yescharacteristic
398C22×C43D4211yescharacteristic
399C22×C43C2×#13511yescharacteristic
400C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C43#57611yescharacteristic
402C22×C43#57711yescharacteristic
403C4×C43—41no—
404C4×C43—42no—
405C4×C43C2×#12111yescharacteristic
406C4×C43#53811yescharacteristic
407C4×C43#54611yescharacteristic
408C4×C43#54611yescharacteristic
409Dic43—22no—
410Dic43—42no—
411Dic43—41no—
412Dic43—41no—
413Dic43—41no—
414Dic43—81no—
415Dic43—81no—
416Dic43—81no—
417C2×#463—431no—
418C2×#450—431no—
419C2×#447D4311yescharacteristic
420C2×C4×SD16—431no—
421#2426—431no—
422D4×C22⋊C4—431no—
423#2065—431no—
424#2036—431no—
425#2034—431no—
426#2012—431no—
427#1970—431no—
428#1923—431no—
429#1880—431no—
430#1879—431no—
431#1862—431no—
432C2×C43—42no—
433C2×C43—44no—
434C2×C43—82no—
435C2×C43—161no—
436C2×C43#242411yescharacteristic
437C2×C43#310511yescharacteristic
438C2×C43#311811yescharacteristic
439C2×C43#326511yescharacteristic
440C2×C43#327411yescharacteristic
441C2×C43#328011yescharacteristic
442C2×C43#328211yescharacteristic
443C23×D4C2×D4311yescharacteristic
444C22×SD16—431no—
445C22×SD16—431no—
446C22×D8C2×D4311yescharacteristic
447C22×D8C2×D4311yescharacteristic
448C2×#124—431no—
449C2×C22⋊Q8—431no—
450C2×#121C2×D4311yescharacteristic
451C2×C4×Q8—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C22×C22⋊C4—861no—
455#463—864no—
456#450—864no—
457#447—24no—
458C4×SD16—864no—
459C2×#107—431no—
460C2×#106—431no—
461C2×C4⋊C8—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102C2×D4311yescharacteristic
469C2×#102C2×D4311yescharacteristic
470C2×C22⋊C8—431no—
471C2×C22⋊C8C2×D4311yescharacteristic
472C2×C4×C8—431no—
473#396—861no—
474#394—861no—
475#390—431no—
476#390—431no—
477#390—431no—
478#390—861no—
479#389—431no—
480#388—861no—
481#386—861no—
482#386—861no—
483#380—431no—
484#379—861no—
485C4×C22⋊C4—431no—
486#340—431no—
487#340—431no—
488#336—431no—
489#336—431no—
490C43#2515211yescharacteristic, complemented, Sylow
491C25—21no—
492C22×Q8—431no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C22×D4311yescharacteristic
502C22×D4C22×D4311yescharacteristic
503C22×D4C22×D4311yescharacteristic
504C23×C4—861no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×SD16—434no—
508C2×SD16—862no—
509C2×SD16—862no—
510C2×SD16—862no—
511C2×SD16—862no—
512C2×SD16—1721no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8C22×D4311yescharacteristic
522C22×C8C22×D4311yescharacteristic
523#124—862no—
524#124—1721no—
525C22⋊Q8—862no—
526C22⋊Q8—1721no—
527#121—22no—
528#121—41no—
529C4×Q8—862no—
530C4×Q8—1721no—
531C4×D4—862no—
532C4×D4—862no—
533C4×D4—1721no—
534C4×D4—1721no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—431no—
544C2×C22⋊C4—431no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—1724no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—861no—
561#107—1721no—
562#106—862no—
563C4⋊C8—862no—
564#103—862no—
565#103—862no—
566#102—22no—
567#102—862no—
568#102—862no—
569#102—862no—
570#102—1721no—
571#102C22⋊D4314yes—
572C22⋊C8—22no—
573C22⋊C8—862no—
574C4×C8—862no—
575#95—431no—
576#95—431no—
577#95—861no—
578#95—861no—
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24D4×D4311yescharacteristic
590C2×Q8—432no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4D4×D4312yes—
621C2×D4#1062190012yes—
622C2×D4#1062190012yes—
623C2×D4C2×C22⋊D4312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—1722no—
642C22×C4—1722no—
643C22×C4—1722no—
644C22×C4—1722no—
645C22×C4D4×D4311yescharacteristic
646C22×C4C23×D4311yescharacteristic
647SD16—868no—
648SD16—1724no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—432no—
657C2×C8—861no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8C2×C22⋊D4312yes—
663C4⋊C4—21no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—3441no—
671C4⋊C4—1722no—
672C4⋊C4—1722no—
673C4⋊C4C2×C22⋊D4312yes—
674C22⋊C4—42no—
675C22⋊C4—862no—
676C22⋊C4—862no—
677C22⋊C4—3441no—
678C22⋊C4—3441no—
679C22⋊C4—3441no—
680C22⋊C4—1722no—
681C22⋊C4—1722no—
682C22⋊C4—1722no—
683C22⋊C4—1722no—
684C22⋊C4—1722no—
685C22⋊C4—1722no—
686C22⋊C4—1722no—
687C22⋊C4—1722no—
688C22⋊C4—1722no—
689C42—861no—
690C42—861no—
691C42—861no—
692C42—861no—
693C42—1722no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#1306334412yes—
729C23C2×D4×D4311yescharacteristic
730Q8—862no—
731Q8—862no—
732Q8—1721no—
733Q8—1721no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#1306329614yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—432no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—862no—
770C2×C4—861no—
771C2×C4—3444no—
772C2×C4—3444no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4C22×C22⋊D4311yescharacteristic
786C2×C4C2×#1062190011yescharacteristic
787C2×C4C2×#1062190011yescharacteristic
788C2×C4#1306337011yescharacteristic
789C2×C4#1306337011yescharacteristic
790C8—22no—
791C8—41no—
792C8—862no—
793C8—1721no—
794C22—22no—
795C22—22no—
796C22—24no—
797C22—22no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22#1458340511yescharacteristic
824C22#1458353111yescharacteristic
825C22D4×C22⋊D4311yescharacteristic
826C22C2×#1306334411yescharacteristic
827C22AGL(1,ℤ/8)×D4311yescharacteristic
828C22#1458370011yescharacteristic
829C22#1458370911yescharacteristic
830C4—42no—
831C4—41no—
832C4—862no—
833C4—3441no—
834C4—3441no—
835C4—3441no—
836C4—1721no—
837C4—1721no—
838C4—1722no—
839C4—1721no—
840C4C2×#1306329611yescharacteristic
841C4#1458348411yescharacteristic
842C4#1458353611yescharacteristic
843C4#1458354311yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2#1913812711yescharacteristic
849C2#1914463711yescharacteristic
850C2#1914477211yescharacteristic
851C2#1914608411yescharacteristic
852C2#1914621311yescharacteristic
853C2#1914628011yescharacteristic
854C2#1914630611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#25152
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#14583112C2semidirect
2. C2×#14583050C2semidirect
3. C2×#14582990C2semidirect
4. #19138157C2semidirect
5. D4×C22⋊Dic43C2semidirect
6. #19135965C2semidirect
7. #19135799C2semidirect
8. #19135781C2semidirect
9. #19135670C2semidirect
10. #19135462C2semidirect
11. #19135198C2semidirect
12. #19134947C2semidirect
13. #19134945C2semidirect
14. #19134844C2semidirect
18. C2×#13063312C22semidirect
20. C2×#13063290C22semidirect
27. C2×#13063259C22semidirect
28. C2×#13063256C22semidirect
29. C2×Dic43⋊C8C22semidirect
30. C2×#13063250C22semidirect
31. C2×#13063250C22semidirect
34. C2×#13063246C22semidirect
35. C2×#13063246C22semidirect
37. C2×C8×Dic43C22semidirect
43. #14582802C22semidirect
44. #14582798C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582653C22semidirect
54. #14582653C22semidirect
71. C2×#10621883D4semidirect
490. C43#25152semidirect

Maximal subgroups

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

subgroupindex
C2×#145831122
C2×#145830502
C2×#145829902
#191381572
D4×C22⋊Dic432
#191359652
#191357992
#191357812
#191356702
#191354622
#191351982
#191349472
#191349452
#191348442
C2×C43×#4472
#2515243