Finite Group Databasebeta

← #25113434

Subgroups — #25113434

Order 11008.

1366 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583570C211yesmaximal, characteristic
2C2×#14583027C211yesmaximal, characteristic, complemented
3#19137553C211yesmaximal, characteristic, complemented
4#19135522C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135419C211yesmaximal, characteristic, complemented
8#19135417C211yesmaximal, characteristic, complemented
9#19135399C211yesmaximal, characteristic, complemented
10#19134605C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134594C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#10621898—21no—
17#14583570—24no—
18#14583570C418yescomplemented
19C2×#13063322C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×#13063321C2211yescharacteristic
22C2×#13063299—21no—
23C2×#13063298—21no—
24C2×#13063298—21no—
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28#14583027—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582803—21no—
45#14582783—21no—
46#14582782—21no—
47#14582768C2211yescharacteristic
48#14582765C2211yescharacteristic
49#14582764C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52C4×Dic43⋊C4—21no—
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—28no—
63C2×#10621898—44no—
64C2×#10621898—44no—
65C22×Dic86D411yescharacteristic
66C22×D172—21no—
67C22×D172—21no—
68C22×D172C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063322—22no—
79#13063322C2×C414yes—
80#13063321—22no—
81#13063321—22no—
82#13063321C2×C414yes—
83#13063321C2×C414yes—
84#13063299—28no—
85#13063298—28no—
86#13063298—28no—
87C4×Dic86C2×C414yes—
88C4×Dic86D414yes—
89#13063287—22no—
90#13063287—22no—
91#13063287C2×C414yes—
92#13063287C2×C414yes—
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4D411yescharacteristic
99C2×Dic43⋊C4D411yescharacteristic
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C4⋊(C43⋊C8)—22no—
107Dic43⋊C8—22no—
108Dic43⋊C8—22no—
109#13063247—22no—
110#13063247—22no—
111#13063247—41no—
112#13063247—41no—
113#13063246—41no—
114#13063246—41no—
115#13063245—22no—
116#13063245—22no—
117#13063245—41no—
118#13063245—41no—
119#13063235—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43—21no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4×D4×C43—22no—
132C4×D4×C43C2×C414yes—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#102×C43—22no—
140#102×C43—22no—
141#97×C43—22no—
142#95×C43—21no—
143C24×C43—21no—
144C23×D43—21no—
145C23×D43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C412yes—
152C22×C4×C43—24no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—24no—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—24no—
164C2×C22⋊D43—24no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—81no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C2×C22⋊D43—81no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179#10621898—432no—
180C2×D172—24no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—24no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—42no—
193C2×D172—42no—
194C2×D172—81no—
195C2×D172—81no—
196C2×D172C22×C412yes—
197C2×D172C22×C412yes—
198C2×C4×D43—24no—
199C2×C4×D43—24no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×Dic86—22no—
205C2×Dic86—22no—
206C2×Dic86C22⋊C414yes—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43#4112yescomplemented
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43C22×C412yes—
218C4⋊C4×C43#4112yescomplemented
219C22⋊C4×C43—24no—
220C42×C43—81no—
221C42×C43C22×C412yes—
222C42×C43C2×D412yes—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43C22⋊C414yes—
230Dic43⋊C4—42no—
231Dic43⋊C4—81no—
232Dic43⋊C4C22⋊C414yes—
233Dic43⋊C4C22⋊C414yes—
234C4×Dic43—42no—
235C4×Dic43—81no—
236C4×Dic43C22×C412yes—
237C4×Dic43C22×C412yes—
238C4×Dic43C2×D412yes—
239C4×Dic43C2×D412yes—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—41no—
271D4×C43—41no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—48no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C2×C22⋊C412yes—
287C2×C4×C43C2×C22⋊C412yes—
288C2×C4×C43C23×C411yescharacteristic
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C432−1+411yescharacteristic
294C22⋊D43—48no—
295C22⋊D43—48no—
296C22⋊D43—84no—
297C22⋊D43—84no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43AGL(1,ℤ/8)12yes—
315C2×Dic43AGL(1,ℤ/8)12yes—
316D172—22no—
317D172—22no—
318D172—22no—
319D172—22no—
320D172—48no—
321D172—41no—
322D172—41no—
323D172—41no—
324D172—41no—
325D172—84no—
326C4×D43—48no—
327C4×D43—48no—
328Dic86—28no—
329C8×C43—22no—
330C8×C43—41no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333#22545—431nomaximal, Sylow
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43C22×C22⋊C411yescharacteristic
342C22×C43#54811yescharacteristic
343C22×C43#55011yescharacteristic
344C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C43#57611yescharacteristic
347C22×C43#57711yescharacteristic
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—42no—
365C4×C43—42no—
366C4×C43—81no—
367C4×C43C4×#4111yescharacteristic
368C4×C43#52011yescharacteristic
369C4×C43#54811yescharacteristic
370C4×C43#55011yescharacteristic
371Dic43—22no—
372Dic43—22no—
373Dic43—22no—
374Dic43—81no—
375Dic43—81no—
376Dic43#41814yes—
377C2×#550—431no—
378C2×#446—431no—
379#2355—431no—
380#1982—431no—
381#1982—431no—
382#1982—431no—
383#1961—431no—
384#1961—431no—
385#1957—431no—
386#1804—431no—
387#1804—431no—
388#1802—431no—
389#1762—431no—
390#1762D4311yescharacteristic, complemented
391C4×#102—431no—
392C2×C43—82no—
393C2×C43#234111yescharacteristic
394C2×C43C2×#41811yescharacteristic
395C2×C43#289711yescharacteristic
396C2×C43#336611yescharacteristic
397C2×C43#336811yescharacteristic
398C2×C43#339711yescharacteristic
399C2×C43#339911yescharacteristic
400D43—82no—
401D43—82no—
402C22×#41—861no—
403#550—438no—
404#550—864no—
405C2×#127—431no—
406C2×#127—431no—
407C2×#127—431no—
408C2×#121—861no—
409C2×#121—861no—
410C2×#121—861no—
411C2×C4×Q8—431no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4C2×D4311yescharacteristic
415#446—864no—
416C2×C4⋊C8—431no—
417C2×C4⋊C8—431no—
418C2×C4⋊C8—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102C2×D4311yescharacteristic
430C2×#102C2×D4311yescharacteristic
431C2×#97—431no—
432C2×#97C2×D4311yescharacteristic
433C2×C4×C8—431no—
434#391—861no—
435#387—861no—
436#387—861no—
437#384—431no—
438#382—431no—
439#382—431no—
440C4×C4⋊C4—431no—
441C4×C4⋊C4—431no—
442C4×C4⋊C4—861no—
443C4×C4⋊C4C2×D4311yescharacteristic
444#340—431no—
445#340—431no—
446#340C2×D4311yescharacteristic
447#340C2×D4311yescharacteristic
448C43#2254511yescharacteristic, complemented, Sylow
449C2×#41—868no—
450C2×#41—1724no—
451C2×#41—1724no—
452C22×Q8—431no—
453C22×D4—431no—
454C22×D4—431no—
455C22×D4—861no—
456C22×D4—861no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4—861no—
460C22×D4—861no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—21no—
463C23×C4—861no—
464C23×C4—861no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469#127—434no—
470#127—434no—
471#127—434no—
472#127—862no—
473#127—862no—
474#127—862no—
475#121—868no—
476#121—868no—
477#121—868no—
478C4×Q8—434no—
479C4×Q8—434no—
480C4×D4—22no—
481C4×D4—434no—
482C4×D4—434no—
483C4×D4—862no—
484C4×D4—862no—
485C4×D4C4×D4314yes—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C4⋊C4C22×D4311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C42—21no—
500C2×C42—431no—
501C2×C42—431no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42C22×D4311yescharacteristic
505C4⋊C8—862no—
506C4⋊C8—862no—
507C4⋊C8—862no—
508#102—22no—
509#102—22no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—862no—
514#102—1721no—
515#102—1721no—
516#102—1721no—
517#102—1721no—
518#102—1721no—
519#102—1721no—
520#97—22no—
521#97—862no—
522C4×C8—862no—
523#95—21no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528#95—861no—
529#95—861no—
530C24—21no—
531C24—861no—
532C24—861no—
533#41—17232no—
534C2×Q8—434no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—432no—
543C2×D4—432no—
544C2×D4—864no—
545C2×D4—864no—
546C2×D4—864no—
547C2×D4—864no—
548C2×D4—864no—
549C2×D4—864no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—3441no—
561C2×D4—3441no—
562C2×D4—3441no—
563C2×D4—3441no—
564C2×D4—3441no—
565C2×D4—3441no—
566C2×D4—1722no—
567C2×D4—1722no—
568C2×D4—1722no—
569C2×D4—1722no—
570C2×D4—1722no—
571C2×D4—1722no—
572C2×D4C2×C4×D4312yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8#1062189812yescomplemented
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—434no—
611C4⋊C4—434no—
612C4⋊C4—434no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—3441no—
618C4⋊C4—1722no—
619C4⋊C4C2×C4×D4312yes—
620C4⋊C4#1062189812yescomplemented
621C22⋊C4—24no—
622C22⋊C4—864no—
623C22⋊C4—864no—
624C42—81no—
625C42—432no—
626C42—432no—
627C42—432no—
628C42—432no—
629C42—3441no—
630C42—1722no—
631C42C2×C4×D4312yes—
632C42D4×D4312yes—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—862no—
641C23—862no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23C2×D4×D4311yescharacteristic
655Q8—868no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—862no—
661D4—862no—
662D4—862no—
663D4—862no—
664D4—3444no—
665D4—3444no—
666D4—3444no—
667D4—1728no—
668D4—1728no—
669D4—1728no—
670D4—1721no—
671D4—1721no—
672D4—1721no—
673D4—1721no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—432no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—1728no—
701C2×C4—1728no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4C22⋊C4×D4312yes—
709C2×C4C22⋊C4×D4312yes—
710C2×C4C22×C4×D4311yescharacteristic
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4C2×#1062189811yescharacteristic
713C2×C4C2×#1062189811yescharacteristic
714C2×C4#1306337111yescharacteristic
715C2×C4#1306337211yescharacteristic
716C8—22no—
717C8—41no—
718C8—1721no—
719C8—1721no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—3441no—
728C22—3441no—
729C22—3441no—
730C22—3441no—
731C22—3441no—
732C22—3441no—
733C22—3441no—
734C22—3441no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22C2×C22⋊C4×D4311yescharacteristic
742C22#1458355811yescharacteristic
743C22#1458357011yescharacteristic
744C22AGL(1,ℤ/8)×D4311yescharacteristic
745C22AGL(1,ℤ/8)×D4311yescharacteristic
746C22#1458370311yescharacteristic
747C22#1458370811yescharacteristic
748C4—22no—
749C4—22no—
750C4—42no—
751C4—42no—
752C4—81no—
753C4—434no—
754C4—862no—
755C4—862no—
756C4—862no—
757C4—3441no—
758C4—3441no—
759C4C4×#1062189811yescharacteristic
760C4#1458337911yescharacteristic
761C4#1458355811yescharacteristic
762C4#1458357011yescharacteristic
763C2—82no—
764C2—3442no—
765C2—3442no—
766C2#1913743511yescharacteristic
767C2#418×D4311yescharacteristic
768C2#1914311911yescharacteristic
769C2#1914730311yescharacteristic
770C2#1914732511yescharacteristic
771C2#1914761611yescharacteristic
772C2#1914763811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583570C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22545
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14583027C2semidirect
3. #19137553C2semidirect
4. #19135522C2semidirect
5. #19135520C2semidirect
6. #19135520C2semidirect
7. #19135419C2semidirect
8. #19135417C2semidirect
9. #19135399C2semidirect
10. #19134605C2semidirect
11. #19134604C2semidirect
12. #19134594C2semidirect
13. #19134419C2semidirect
14. #19134409C2semidirect
15. C43×#1762C2semidirect
18. #14583570C4semidirect
212. C2×C8×C43#41semidirect
218. C4⋊C4×C43#41semidirect
390. #1762D43semidirect
448. C43#22545semidirect
605. C2×C8#10621898semidirect
620. C4⋊C4#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835702
C2×#145830272
#191375532
#191355222
#191355202
#191354192
#191354172
#191353992
#191346052
#191346042
#191345942
#191344192
#191344092
C43×#17622
#2254543