Finite Group Databasebeta

← #25124770

Subgroups — #25124770

Order 11008.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583433C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135836C211yesmaximal, characteristic, complemented
6#19135798C211yesmaximal, characteristic, complemented
7#19135784C211yesmaximal, characteristic, complemented
8#19135741C211yesmaximal, characteristic, complemented
9#19135671C211yesmaximal, characteristic, complemented
10#19135598C211yesmaximal, characteristic, complemented
11#19135591C211yesmaximal, characteristic
12C4×#13063248C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic, complemented
14C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C4×#121×C43C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18#14583433—24no—
19#14583433—24no—
20C2×#13063319—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063313C2211yescharacteristic
23C2×#13063308—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×#13063282—21no—
30C4×#10621883—24no—
31C4×#10621882—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C4×C43⋊C8C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×C4×D4×C43—21no—
54C2×C4×D4×C43C2211yescharacteristic
55C22×C42×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#386—21no—
60C43×#380C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C4×C22⋊C4×C43—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882—22no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063319—28no—
78#13063317—22no—
79#13063317—22no—
80#13063313—22no—
81#13063313—22no—
82#13063308—28no—
83#13063304—22no—
84#13063304—22no—
85#13063299—22no—
86#13063299—22no—
87C4×Dic86—22no—
88C4×Dic86D414yescomplemented
89C4×D172—22no—
90C4×D172D414yescomplemented
91C4×C22⋊D43—28no—
92#13063282—28no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105#13063258—22no—
106#13063256—22no—
107#13063248—22no—
108#13063248—22no—
109#13063248—22no—
110#13063246—22no—
111#13063246—22no—
112#13063245—22no—
113#13063245—22no—
114#13063245—22no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117C4×C43⋊C8—22no—
118C4×C43⋊C8—22no—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43D411yescharacteristic
123C23×C4×C43D411yescharacteristic
124C23×C4×C43C2311yescharacteristic
125#121×C43—22no—
126#121×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C4×D4×C43—44no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—22no—
140C2×C42×C43—22no—
141C2×C42×C43—21no—
142C2×C42×C43D411yescharacteristic
143C2×C42×C43D411yescharacteristic
144C2×C42×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C23×D43—21no—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43#4112yes—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—22no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—41no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—24no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172C2×D412yes—
197C2×C4×D43—24no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86C2×D412yes—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43#4112yes—
213C22⋊C4×C43—24no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C42×C43—22no—
219C42×C43—22no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—42no—
223C42×C43C2×D412yes—
224C42×C43C2×D412yes—
225C22⋊Dic43—24no—
226#10621883—28no—
227#10621882—28no—
228(C2×D43)⋊C4—24no—
229(C2×D43)⋊C4—24no—
230(C2×D43)⋊C4—24no—
231(C2×D43)⋊C4—24no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43C2×D412yes—
235C4⋊Dic43C2×D412yes—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240C4×Dic43—24no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8#4112yes—
252C2×C43⋊C8#4112yes—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43#13512yes—
267C23×C43C22×D411yescharacteristic
268C22×D43—22no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—48no—
278D4×C43—41no—
279D4×C43—41no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—44no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—44no—
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—84no—
307C2×C4×C43#12012yes—
308C2×C4×C43#12012yes—
309C2×C4×C43#13512yes—
310C2×C4×C43AGL(1,ℤ/8)12yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C22⋊D43—48no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327D172—22no—
328D172—22no—
329D172—41no—
330D172—41no—
331C4×D43—48no—
332Dic86—22no—
333Dic86—22no—
334Dic86—41no—
335Dic86—41no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340#23569—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43C2×#12011yescharacteristic
356C22×C43#52511yescharacteristic
357C22×C43#53211yescharacteristic
358C22×C43C2×#13511yescharacteristic
359C22×C43C2×#13511yescharacteristic
360C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C43#57511yescharacteristic
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C4×C43—22no—
370C4×C43—42no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43#44914yes—
377C4×C43#52511yescharacteristic
378C4×C43#52511yescharacteristic
379C4×C43#53211yescharacteristic
380C4×C43#53211yescharacteristic
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
384C2×#529—431no—
385C2×C4×SD16—431no—
386C2×C4×D8—431no—
387C4×#121D4311yescharacteristic, complemented
388#2059—431no—
389#2042—431no—
390#2036—431no—
391#2034—431no—
392#2025—431no—
393#2012—431no—
394#2000—431no—
395#1999—431no—
396C4×#103—431no—
397C4×#102—431no—
398C4×C22⋊C8—431no—
399C2×C43—42no—
400C2×C43—82no—
401C2×C43#238811yescharacteristic
402C2×C43C2×#44911yescharacteristic
403C2×C43#300211yescharacteristic
404C2×C43#310211yescharacteristic
405C2×C43#310511yescharacteristic
406C2×C43#316811yescharacteristic
407C2×C43#317111yescharacteristic
408D43—82no—
409C22×SD16—431no—
410C22×D8—431no—
411#529—864no—
412#529—864no—
413C2×#126—861no—
414C2×#125—431no—
415C2×#124—431no—
416C2×#123—861no—
417C2×C22⋊Q8—431no—
418C2×#121—431no—
419C2×#121C2×D4311yescharacteristic
420C2×C4×Q8—431no—
421C2×C4×D4—21no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C2×C4×D4C2×D4311yescharacteristic
425C2×#117—861no—
426C22×C42C2×D4311yescharacteristic
427C4×SD16—864no—
428C4×D8—864no—
429C2×#107—431no—
430C2×#106—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C4×C8—431no—
442C2×C4×C8—431no—
443#390C2×D4311yescharacteristic
444#389C2×D4311yescharacteristic
445#388—21no—
446#386—21no—
447#380C2×D4311yescharacteristic
448C4×C4⋊C4C2×D4311yescharacteristic
449C4×C22⋊C4—21no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340—431no—
454#336—431no—
455#336—431no—
456C43#2356911yescharacteristic, complemented, Sylow
457C22×Q8—431no—
458C22×D4—21no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—21no—
463C23×C4—861no—
464C23×C4C22⋊D4311yescharacteristic
465C23×C4C22⋊D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—862no—
470C2×D8—862no—
471C2×D8—862no—
472C2×D8—862no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—431no—
477#126—868no—
478#125—862no—
479#125—862no—
480#124—862no—
481#124—862no—
482#123—868no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485#121—22no—
486#121—22no—
487#121—862no—
488#121—862no—
489C4×Q8—434no—
490C4×Q8—862no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—44no—
494C4×D4—434no—
495C4×D4—868no—
496C4×D4—862no—
497#117—868no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—21no—
521C2×C42—861no—
522C2×C42C22⋊D4311yescharacteristic
523C2×C42C22⋊D4311yescharacteristic
524C2×C42C22×D4311yescharacteristic
525C2×C42C22×D4311yescharacteristic
526#107—862no—
527#106—862no—
528#103—862no—
529#103—862no—
530#103—862no—
531#102—862no—
532#102—862no—
533#102—862no—
534#102—862no—
535#102—862no—
536C22⋊C8—862no—
537C22⋊C8—862no—
538C4×C8—862no—
539C4×C8—862no—
540#95—21no—
541#95—21no—
542#95—21no—
543C24—21no—
544C24—861no—
545C24C2×C22⋊D4311yescharacteristic
546C2×Q8—432no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—432no—
561C2×D4—864no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—1722no—
568C2×D4—1722no—
569C2×D4#1062189812yes—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—864no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600SD16—868no—
601D8—868no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—432no—
621C4⋊C4—432no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4#1062189812yes—
629C22⋊C4—24no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—22no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—42no—
644C42—864no—
645C42D4×D4312yes—
646C42D4×D4312yes—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—862no—
661C23—1721no—
662C23—1721no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23#1306334512yes—
668C23C22×C22⋊D4311yescharacteristic
669Q8—862no—
670Q8—862no—
671Q8—1721no—
672Q8—1721no—
673D4—22no—
674D4—22no—
675D4—48no—
676D4—41no—
677D4—41no—
678D4—862no—
679D4—862no—
680D4—1728no—
681D4—1721no—
682D4—1721no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—44no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1728no—
720C2×C4#1306329312yes—
721C2×C4#1306329312yes—
722C2×C4#1306334512yes—
723C2×C4#1306335112yes—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C2×D4×D4311yescharacteristic
726C2×C4#41×D4311yescharacteristic
727C2×C4#41×D4311yescharacteristic
728C2×C4C2×#1062189811yescharacteristic
729C2×C4C2×#1062189811yescharacteristic
730C8—862no—
731C8—862no—
732C8—1721no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—3441no—
749C22—3441no—
750C22—3441no—
751C22—3441no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22C2×#1306329311yescharacteristic
756C22#1458341011yescharacteristic
757C22#1458344511yescharacteristic
758C22C2×#1306334511yescharacteristic
759C22C2×#1306334511yescharacteristic
760C22C2×#1306335111yescharacteristic
761C22#1458369711yescharacteristic
762C4—22no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—1722no—
770C4—1722no—
771C4—1722no—
772C4#1458304214yes—
773C4#1458340811yescharacteristic
774C4#1458340811yescharacteristic
775C4#1458344611yescharacteristic
776C4#1458344611yescharacteristic
777C2—42no—
778C2—82no—
779C2—3442no—
780C2#1913781011yescharacteristic
781C2C2×#1458304211yescharacteristic
782C2#1914381111yescharacteristic
783C2#1914461311yescharacteristic
784C2#1914464211yescharacteristic
785C2#1914515911yescharacteristic
786C2#1914518411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#121×C43C2
socleC23×C43C22×D4
prime radical#19135591C2
hypercenterC4×#121D43
hypocenterC43#23569
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14583433C2semidirect
2. C2×C4×#10621883C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19135933C2semidirect
5. #19135836C2semidirect
6. #19135798C2semidirect
7. #19135784C2semidirect
8. #19135741C2semidirect
9. #19135671C2semidirect
10. #19135598C2semidirect
12. C4×#13063248C2semidirect
13. C4×#13063245C2semidirect
14. C4×C22⋊(C43⋊C8)C2semidirect
15. C4×#121×C43C2semidirect
88. C4×Dic86D4semidirect
90. C4×D172D4semidirect
387. C4×#121D43semidirect
456. C43#23569semidirect

Maximal subgroups

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

subgroupindex
C2×#145834332
C2×C4×#106218832
C2×C4×#106218822
#191359332
#191358362
#191357982
#191357842
#191357412
#191356712
#191355982
#191355912
C4×#130632482
C4×#130632452
C4×C22⋊(C43⋊C8)2
C4×#121×C432
#2356943