Finite Group Databasebeta

← #25117243

Subgroups — #25117243

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583031C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4#19137638C211yesmaximal, characteristic, complemented
5#19137416C211yesmaximal, characteristic, complemented
6#19135275C211yesmaximal, characteristic, complemented
7#19135212C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134853C211yesmaximal, characteristic, complemented
12#19134793C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic, complemented
15C43×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic, complemented
22C2×#13063287C2211yescharacteristic
23C2×#13063283C2211yescharacteristic
24C2×C22⋊C4×D43—21no—
25#14583031C418yescomplemented
26#14582979—24no—
27C2×#13063258C2211yescharacteristic, complemented
28#14582902—24no—
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic, complemented
34C2×#13063245C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic, complemented
37#14582802C2211yescharacteristic
38#14582799—21no—
39#14582795C2211yescharacteristic, complemented
40#14582793—21no—
41#14582776—21no—
42#14582775—21no—
43#14582775—21no—
44#14582756C2211yescharacteristic
45#14582754—21no—
46C4×C4⋊Dic43C2211yescharacteristic, complemented
47C22⋊C4×Dic43—21no—
48C4×(C2×D43)⋊C4C2211yescharacteristic
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582654C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C22×D8×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic, complemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic, complemented
59C2×#97×C43C2211yescharacteristic, complemented
60C43×#390C2211yescharacteristic
61C43×#390C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—41no—
70C2×D4×D43—41no—
71C2×D4×D43C2×C414yescomplemented
72C23×Dic43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C2×#10621882—22no—
77C2×#10621882—22no—
78C2×#10621882C2×C414yes—
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872—41no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063296—22no—
85#13063296C2×C414yescomplemented
86C4×D172—22no—
87C4×D172—41no—
88D4×Dic43—22no—
89D4×Dic43—41no—
90#13063287—22no—
91#13063287—41no—
92#13063283—22no—
93#13063283—41no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×(C2×D43)⋊C4D411yescharacteristic
108C22⋊C4×D43—44no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112#13063258—22no—
113#13063247C2×C414yescomplemented
114#13063247D414yescomplemented
115#13063246—22no—
116#13063246—41no—
117#13063246C2×C414yescomplemented
118#13063245—22no—
119(C2×D43)⋊C8C2×C414yescomplemented
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95D411yescharacteristic
125C43⋊#95D411yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C2×D8×C43—41no—
129C2×D8×C43—41no—
130C2×D8×C43C2×C414yescomplemented
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43C2311yescharacteristic
140#106×C43—41no—
141#102×C43—22no—
142#102×C43—22no—
143#97×C43—41no—
144C24×C43—21no—
145C24×C43—21no—
146C23×D43—21no—
147C23×D43—24no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—81no—
153C23×D43—81no—
154C23×D43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43C22×C412yes—
166C2×D4×C43C22×C412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C2×C22⋊D43—24no—
173C2×C22⋊D43—24no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—81no—
177C2×C22⋊D43—81no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43—81no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187D4×D43—28no—
188D4×D43—44no—
189D4×D43—44no—
190D4×D43—44no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172C22×C412yes—
195C2×D172C2×D412yes—
196C2×D172#4112yes—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—81no—
206C2×C4×D43—81no—
207C2×C4×D43C22×C412yes—
208C2×C4×D43#4112yes—
209D8×C43—44no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43C22×C412yes—
215C2×C8×C43C2×D412yes—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—81no—
223C22⋊C4×C43—81no—
224C42×C43—21no—
225C42×C43—21no—
226C22⋊Dic43—24no—
227C22⋊Dic43—42no—
228C22⋊Dic43—42no—
229C22⋊Dic43—81no—
230#10621882—28no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—41no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43C22×C412yes—
242C4⋊Dic43C2×D412yes—
243Dic43⋊C4—81no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—42no—
247C4×Dic43—81no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8C22×C412yes—
254#10621872—44no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—21no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—48no—
280C22×D43—48no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—84no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43C4×D412yes—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C22⋊D43—48no—
318C22⋊D43—84no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—22no—
324C2×Dic43—21no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—84no—
336C2×Dic43C4×D412yes—
337C2×Dic43AGL(1,ℤ/8)12yes—
338D172—22no—
339D172—22no—
340D172—22no—
341D172C4×D414yes—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—84no—
347C4×D43—84no—
348C8×C43—22no—
349C8×C43—22no—
350C43⋊C8—22no—
351C43⋊C8—41no—
352#22880—431nomaximal, Sylow
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43C2×C4×D411yescharacteristic
368C22×C43D4211yescharacteristic
369C22×C43#54611yescharacteristic
370C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C43#57511yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57611yescharacteristic
374C2×D43—24no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—41no—
381C2×D43—42no—
382C2×D43—41no—
383C2×D43—42no—
384C2×D43—41no—
385C2×D43—42no—
386C2×D43—41no—
387C2×D43—42no—
388C2×D43—816no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—81no—
392C4×C43—81no—
393C4×C43C2×C4×D411yescharacteristic
394C4×C43#51811yescharacteristic
395C4×C43#54611yescharacteristic
396C4×C43#55111yescharacteristic
397Dic43—22no—
398Dic43—22no—
399Dic43—42no—
400Dic43—42no—
401Dic43—41no—
402Dic43—81no—
403C2×#447—431no—
404C2×C4×D8—431no—
405C2×#418—431no—
406#2363—431no—
407D4×C22⋊C4—431no—
408#1972D4311yescharacteristic, complemented
409#1934—431no—
410#1925—431no—
411#1895—431no—
412#1879—431no—
413#1879—431no—
414#1864—431no—
415#1854—431no—
416#1762—431no—
417#1753—431no—
418C2×C43—82no—
419C2×C43—82no—
420C2×C43#235811yescharacteristic
421C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C43#294811yescharacteristic
423C2×C43#326411yescharacteristic
424C2×C43#326811yescharacteristic
425C2×C43#332211yescharacteristic
426C2×C43#332511yescharacteristic
427D43—42no—
428D43—44no—
429C23×D4—431no—
430C22×D8—431no—
431C22×D8C2×D4311yescharacteristic
432C22×M16—431no—
433C2×#121—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×#117—431no—
438C22×C22⋊C4—861no—
439#447—438no—
440C4×D8—864no—
441C2×#107—431no—
442C2×#106C2×D4311yescharacteristic, complemented
443#418—864no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102C2×D4311yescharacteristic
451C2×#102C2×D4311yescharacteristic, complemented
452C2×C22⋊C8—431no—
453C2×#97C2×D4311yescharacteristic, complemented
454C2×C4×C8—431no—
455#390—431no—
456#390—861no—
457#390C2×D4311yescharacteristic
458#390C2×D4311yescharacteristic, complemented
459#389—431no—
460#388—861no—
461#386—861no—
462#386—861no—
463#386—861no—
464#380—431no—
465#379—861no—
466C4×C4⋊C4—431no—
467C4×C22⋊C4—431no—
468C4×C22⋊C4—861no—
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473#336—431no—
474#336—431no—
475C43#2288011yescharacteristic, complemented, Sylow
476C25—861no—
477C22×D4—434no—
478C22×D4—431no—
479C22×D4—862no—
480C22×D4—861no—
481C22×D4—862no—
482C22×D4—862no—
483C22×D4—861no—
484C22×D4—1721no—
485C22×D4—1721no—
486C22×D4C22×D4311yescharacteristic
487C22×D4C22×D4311yescharacteristic
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C2×D8—41no—
493C2×D8—41no—
494C2×D8—434no—
495C2×D8—862no—
496C2×D8—862no—
497C2×D8C4×D4314yescomplemented
498C2×M16—862no—
499C2×M16—862no—
500C2×M16—1721no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#121—434no—
506#121—862no—
507C4×D4—862no—
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513#117—862no—
514#117—1721no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—1724no—
536C2×C42—431no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540#107—862no—
541#106—41no—
542#102—22no—
543#102—22no—
544#102—434no—
545#102—434no—
546#102—434no—
547#102—862no—
548#102—862no—
549#102—1721no—
550C22⋊C8—434no—
551#97—41no—
552C4×C8—862no—
553#95—431no—
554#95—431no—
555#95—861no—
556#95—861no—
557#95—861no—
558C24—21no—
559C24—21no—
560C24—431no—
561C24—864no—
562C24—861no—
563C24—3441no—
564C24—3441no—
565C24—1722no—
566C24—1722no—
567C24—1722no—
568C24—1722no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—432no—
580C2×D4—432no—
581C2×D4—432no—
582C2×D4—864no—
583C2×D4—868no—
584C2×D4—864no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—3441no—
589C2×D4—3441no—
590C2×D4—1724no—
591C2×D4—1724no—
592C2×D4—1724no—
593C2×D4—1722no—
594C2×D4—1722no—
595C2×D4C2×C4×D4312yes—
596C2×D4C2×C4×D4312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—431no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4—1722no—
619C22×C4—1722no—
620C22×C4D4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4C23×D4311yescharacteristic
623D8—44no—
624D8—868no—
625M16—1724no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—432no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8C2×C4×D4312yes—
637C2×C8D4×D4312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—432no—
643C4⋊C4—432no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—3441no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4—862no—
654C22⋊C4—864no—
655C22⋊C4—3441no—
656C22⋊C4—1721no—
657C22⋊C4—1722no—
658C22⋊C4—1722no—
659C22⋊C4—1722no—
660C22⋊C4—1722no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C42—21no—
664C42—21no—
665C42—861no—
666C42—861no—
667C42—3441no—
668C42—1722no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—432no—
684C23—862no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—862no—
691C23—862no—
692C23—861no—
693C23—3444no—
694C23—3444no—
695C23—3444no—
696C23—3444no—
697C23—3444no—
698C23—1728no—
699C23—1728no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—1721no—
704C23C2×D4×D4311yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—434no—
714D4—862no—
715D4—862no—
716D4—862no—
717D4—3444no—
718D4—1728no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—862no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—3444no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4C22×C4×D4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4#41×D4311yescharacteristic
759C2×C4#41×D4311yescharacteristic
760C2×C4#1306337011yescharacteristic
761C2×C4#1306337011yescharacteristic
762C8—22no—
763C8—22no—
764C8—862no—
765C8—1721no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—862no—
781C22—862no—
782C22—864no—
783C22—862no—
784C22—34416no—
785C22—1722no—
786C22—1721no—
787C22—1722no—
788C22—1722no—
789C22—1721no—
790C22—1722no—
791C22—1721no—
792C22—1721no—
793C22—1722no—
794C22—1722no—
795C22C4×D4×D4311yescharacteristic
796C22#1458353411yescharacteristic
797C22#1458353811yescharacteristic
798C22AGL(1,ℤ/8)×D4311yescharacteristic
799C22#1458369511yescharacteristic
800C22#1458370311yescharacteristic
801C22#1458370311yescharacteristic
802C4—41no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—862no—
807C4—862no—
808C4—3441no—
809C4—1722no—
810C4—1722no—
811C4—1721no—
812C4C4×D4×D4311yescharacteristic
813C4#1458337211yescharacteristic
814C4#1458353811yescharacteristic
815C4#1458357911yescharacteristic
816C2—82no—
817C2—82no—
818C2—1722no—
819C2—1724no—
820C2#1913757611yescharacteristic
821C2#1914340611yescharacteristic
822C2#1914344411yescharacteristic
823C2#1914607411yescharacteristic
824C2#1914613411yescharacteristic
825C2#1914679111yescharacteristic
826C2#1914683211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1972C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenter#1972D43
hypocenterC43#22880
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. C2×#14582979C2semidirect
3. C2×#14582902C2semidirect
4. #19137638C2semidirect
5. #19137416C2semidirect
6. #19135275C2semidirect
7. #19135212C2semidirect
8. #19135030C2semidirect
9. #19134946C2semidirect
10. #19134945C2semidirect
11. #19134853C2semidirect
12. #19134793C2semidirect
13. #19134421C2semidirect
14. #19134380C2semidirect
15. C43×#1972C2semidirect
21. C2×D4×Dic43C22semidirect
25. #14583031C4semidirect
27. C2×#13063258C22semidirect
33. C2×#13063246C22semidirect
36. C2×C8×Dic43C22semidirect
39. #14582795C22semidirect
46. C4×C4⋊Dic43C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582654C22semidirect
54. #14582653C22semidirect
56. C2×#106×C43C22semidirect
58. C2×#102×C43C22semidirect
59. C2×#97×C43C22semidirect
61. C43×#390C22semidirect
71. C2×D4×D43C2×C4semidirect
85. #13063296C2×C4semidirect
113. #13063247C2×C4semidirect
114. #13063247D4semidirect
117. #13063246C2×C4semidirect
119. (C2×D43)⋊C8C2×C4semidirect
130. C2×D8×C43C2×C4semidirect
408. #1972D43semidirect
442. C2×#106C2×D43semidirect
451. C2×#102C2×D43semidirect
453. C2×#97C2×D43semidirect
458. #390C2×D43semidirect
475. C43#22880semidirect
497. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830312
C2×#145829792
C2×#145829022
#191376382
#191374162
#191352752
#191352122
#191350302
#191349462
#191349452
#191348532
#191347932
#191344212
#191343802
C43×#19722
#2288043