Finite Group Databasebeta

← #25130722

Subgroups — #25130722

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2C2×#14583199C211yesmaximal, characteristic, complemented
3C2×#14583009C211yesmaximal, characteristic, complemented
4#19135784C211yesmaximal, characteristic, complemented
5#19135777C211yesmaximal, characteristic, complemented
6#19135591C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135563C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic, complemented
10#19134918C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134787C211yesmaximal, characteristic, complemented
14#19134592C211yesmaximal, characteristic, complemented
15C43×#2537C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17#14583595—24no—
18#14583595—24no—
19C2×#13063320—21no—
20C2×#13063317C2211yescharacteristic
21C2×#13063307—21no—
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×C4×D172C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×#13063284C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29#14583199—24no—
30#14583009—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×#121×C43—21no—
53C2×#121×C43C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#394—21no—
58C43×#394—21no—
59C43×#384C2211yescharacteristic
60C43×#380—21no—
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063320—28no—
76#13063317—22no—
77#13063317D414yescomplemented
78#13063307—28no—
79#13063299—22no—
80#13063299—22no—
81#13063299—22no—
82#13063299—22no—
83#13063297—28no—
84C4×D172—22no—
85C4×D172D414yescomplemented
86(C22⋊D43)⋊C4—28no—
87#13063284—22no—
88#13063284—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063256—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063245—22no—
110#13063245—41no—
111#13063245—41no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C22⋊(C43⋊C8)—41no—
116#13063236—22no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43D411yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124#121×C43—22no—
125#121×C43—22no—
126#121×C43—41no—
127#121×C43—41no—
128#121×C43—44no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43C2311yescharacteristic
147#95×C43—21no—
148#95×C43—21no—
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C24×C43C2×D411yescharacteristic
152C23×D43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—41no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43#4112yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—81no—
196C2×C22⋊D43—81no—
197C22×Dic43—24no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—81no—
202C22×Dic43—81no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172C2×D412yes—
209C2×C4×D43—24no—
210C2×C4×D43—81no—
211C2×C4×D43—81no—
212C4⋊C4×C43—22no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—42no—
220C4⋊C4×C43—81no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C42×C43C2×D412yes—
229C42×C43C2×D412yes—
230C22⋊Dic43—24no—
231#10621882—28no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235C4⋊Dic43—24no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43C2×D412yes—
240C4⋊Dic43C2×D412yes—
241C4⋊Dic43C2×D412yes—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244C4×Dic43—24no—
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—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8#4112yes—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—22no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43AGL(1,ℤ/8)12yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—44no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—84no—
292D4×C43—84no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—84no—
321C2×C4×C43#12012yes—
322C2×C4×C43#12012yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×C4×C432−1+411yescharacteristic
329C22⋊D43—48no—
330C22⋊D43—84no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—84no—
341D172—22no—
342D172—22no—
343D172—41no—
344D172—41no—
345C4×D43—84no—
346C43⋊C8—22no—
347C43⋊C8—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350#24136—431nomaximal, Sylow
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—42no—
366C22×C43—41no—
367C22×C43—42no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43C2×#12011yescharacteristic
373C22×C43#54611yescharacteristic
374C22×C43#54711yescharacteristic
375C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C43#57511yescharacteristic
377C22×C43#57611yescharacteristic
378C22×C43#57711yescharacteristic
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—81no—
383C2×D43—81no—
384C2×D43—81no—
385C2×D43—81no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—81no—
391C4×C43—81no—
392C4×C43—81no—
393C4×C43#52511yescharacteristic
394C4×C43#53711yescharacteristic
395C4×C43#54811yescharacteristic
396C4×C43#55011yescharacteristic
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400C2×#553—431no—
401C2×#478—431no—
402C2×#442—431no—
403#2537D4311yescharacteristic, complemented
404#2034—431no—
405#2033—431no—
406#1999—431no—
407#1999—431no—
408#1992—431no—
409#1955—431no—
410#1875—431no—
411#1874—431no—
412#1854—431no—
413#1853—431no—
414#1802—431no—
415C2×C43—42no—
416C2×C43—81no—
417C2×C43—82no—
418C2×C43#240711yescharacteristic
419C2×C43#300611yescharacteristic
420C2×C43#301211yescharacteristic
421C2×C43#330711yescharacteristic
422C2×C43#331811yescharacteristic
423C2×C43#334511yescharacteristic
424C2×C43#334711yescharacteristic
425D43—82no—
426C22×D8—431no—
427#553—864no—
428#553—864no—
429C2×#126—861no—
430C2×#125—431no—
431C2×#123—861no—
432C2×#121—21no—
433C2×#121—431no—
434C2×#121—431no—
435C2×#121—861no—
436C2×#121C2×D4311yescharacteristic
437C2×#121C2×D4311yescharacteristic
438C2×C4×D4—431no—
439C2×C4×D4—861no—
440C2×C4×D4C2×D4311yescharacteristic
441C2×C4×D4C2×D4311yescharacteristic
442C2×#117—431no—
443C22×C4⋊C4—431no—
444#478—864no—
445#442—864no—
446C2×#107—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×C4⋊C8—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C22⋊C8—431no—
460C2×#97—431no—
461#394—21no—
462#394—21no—
463#384C2×D4311yescharacteristic
464#380—21no—
465#380C2×D4311yescharacteristic
466#380C2×D4311yescharacteristic
467#340—431no—
468#340—431no—
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473C43#2413611yescharacteristic, complemented, Sylow
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—431no—
477C22×D4—861no—
478C22×D4—861no—
479C22×D4C22⋊D4311yescharacteristic
480C22×D4C22×D4311yescharacteristic
481C23×C4—21no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4C22×D4311yescharacteristic
485C23×C4C22×D4311yescharacteristic
486C2×D8—862no—
487C2×D8—862no—
488C2×D8—862no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—431no—
492C22×C8—431no—
493#126—868no—
494#125—434no—
495#125—862no—
496#123—868no—
497#121—22no—
498#121—22no—
499#121—41no—
500#121—41no—
501#121—44no—
502#121—862no—
503#121—862no—
504#121—862no—
505#121—862no—
506#121—868no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—434no—
512C4×D4—868no—
513C4×D4—862no—
514#117—862no—
515#117—862no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—862no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22⋊D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C42—861no—
542C2×C42C22×D4311yescharacteristic
543#107—862no—
544#106—862no—
545#106—862no—
546C4⋊C8—862no—
547#102—862no—
548#102—862no—
549#102—862no—
550#102—862no—
551#102—1721no—
552#102—1721no—
553C22⋊C8—862no—
554C22⋊C8—862no—
555C22⋊C8—1721no—
556C22⋊C8—1721no—
557#97—862no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—861no—
562C24C2×C22⋊D4311yescharacteristic
563C24C2×C22⋊D4311yescharacteristic
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—432no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—3441no—
587C2×D4—3441no—
588C2×D4—1722no—
589C2×D4—1722no—
590C2×D4#1062190012yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—864no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—864no—
614C22×C4—3441no—
615C22×C4—3441no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C2×C22⋊D4311yescharacteristic
622C22×C4C23×D4311yescharacteristic
623D8—868no—
624C2×C8—432no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—42no—
644C4⋊C4—81no—
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—432no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C42—864no—
666C42D4×D4312yes—
667C42D4×D4312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—862no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23#1306335112yes—
696C23C22×C22⋊D4311yescharacteristic
697D4—22no—
698D4—22no—
699D4—44no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—862no—
705D4—862no—
706D4—3444no—
707D4—1728no—
708D4—1721no—
709D4—1721no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—3444no—
742C2×C4—3444no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4#1306329312yes—
750C2×C4#1306329312yes—
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4C2×D4×D4311yescharacteristic
753C2×C4#41×D4311yescharacteristic
754C2×C4C2×#1062190011yescharacteristic
755C2×C4#1306337011yescharacteristic
756C2×C4#1306337211yescharacteristic
757C8—862no—
758C8—1721no—
759C8—1721no—
760C8—1721no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—3441no—
783C22—3441no—
784C22—3441no—
785C22—3441no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22C2×#1306329311yescharacteristic
790C22#1458354311yescharacteristic
791C22#1458354811yescharacteristic
792C22C2×#1306335111yescharacteristic
793C22#1458369711yescharacteristic
794C22#1458370211yescharacteristic
795C22#1458370711yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—81no—
801C4—81no—
802C4—81no—
803C4—1722no—
804C4—1722no—
805C4—1722no—
806C4#1458340911yescharacteristic
807C4#1458347811yescharacteristic
808C4#1458355511yescharacteristic
809C4#1458356711yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—3442no—
814C2#1913793611yescharacteristic
815C2#1914384511yescharacteristic
816C2#1914389611yescharacteristic
817C2#1914657111yescharacteristic
818C2#1914673611yescharacteristic
819C2#1914706511yescharacteristic
820C2#1914709511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2537C2
socleC23×C43C22×D4
hypercenter#2537D43
hypocenterC43#24136
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. C2×#14583199C2semidirect
3. C2×#14583009C2semidirect
4. #19135784C2semidirect
5. #19135777C2semidirect
6. #19135591C2semidirect
7. #19135591C2semidirect
8. #19135563C2semidirect
9. #19135394C2semidirect
10. #19134918C2semidirect
11. #19134913C2semidirect
12. #19134792C2semidirect
13. #19134787C2semidirect
14. #19134592C2semidirect
15. C43×#2537C2semidirect
77. #13063317D4semidirect
85. C4×D172D4semidirect
403. #2537D43semidirect
473. C43#24136semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145831992
C2×#145830092
#191357842
#191357772
#191355912
#191355632
#191353942
#191349182
#191349132
#191347922
#191347872
#191345922
C43×#25372
#2413643