Finite Group Databasebeta

← #25117247

Subgroups — #25117247

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×C4×#10621882C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4#19137629C211yesmaximal, characteristic, complemented
5#19137416C211yesmaximal, characteristic, complemented
6#19135472C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic, complemented
8#19135218C211yesmaximal, characteristic, complemented
9#19135030C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134859C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134375C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063283C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24#14583031C418yescomplemented
25C4×#10621882—24no—
26C2×#13063258C2211yescharacteristic, complemented
27C2×#13063257C2211yescharacteristic, complemented
28#14582902—24no—
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic, complemented
34C2×#13063245C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063235C2211yescharacteristic, complemented
37C2×C4×C43⋊C8C2211yescharacteristic, complemented
38#14582802C2211yescharacteristic
39#14582802C2211yescharacteristic, complemented
40#14582799—21no—
41#14582797C2211yescharacteristic, complemented
42#14582787—21no—
43#14582778—21no—
44#14582775—21no—
45#14582775—21no—
46#14582756C2211yescharacteristic
47#14582754—21no—
48C4⋊C4×Dic43C2211yescharacteristic, complemented
49C4×(C2×D43)⋊C4C2211yescharacteristic
50C4×C22⋊Dic43—21no—
51#14582662C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C22×D8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic, complemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic, complemented
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, 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
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882C2×C414yes—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063296—22no—
84#13063296C2×C414yescomplemented
85C4×D172—22no—
86C4×D172—41no—
87#13063287—22no—
88#13063287—41no—
89#13063283—22no—
90#13063283—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—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×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C22⋊C4×D43—44no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110#13063258—22no—
111#13063257—41no—
112#13063247—22no—
113#13063247C2×C414yescomplemented
114#13063246—22no—
115#13063246—22no—
116#13063246C2×C414yescomplemented
117#13063245D414yescomplemented
118(C2×D43)⋊C8C2×C414yescomplemented
119#13063235—41no—
120C4×C43⋊C8—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95D411yescharacteristic
125C43⋊#95D411yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43—21no—
129C2×D8×C43—41no—
130C2×D8×C43—41no—
131C2×D8×C43C2×C414yescomplemented
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C4×D4×C43—22no—
135C4×D4×C43—41no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C42×C43C2311yescharacteristic
142#102×C43—22no—
143#102×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×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43—81no—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—24no—
176C2×C22⋊D43—24no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—81no—
180C2×C22⋊D43—81no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
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×C43—21no—
215C2×C8×C43C22×C412yes—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—81no—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—24no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228C22⋊Dic43—81no—
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⋊Dic43—21no—
242C4⋊Dic43C22×C412yes—
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⋊C8C22×C412yes—
253C2×C43⋊C8C2×D412yes—
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—22no—
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—84no—
311C2×C4×C43AGL(1,ℤ/8)12yes—
312C2×C4×C43C23×C411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C22⋊D43—48no—
319C22⋊D43—84no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—22no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43C4×D412yes—
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—41no—
350C43⋊C8—22no—
351C43⋊C8—22no—
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—22no—
390C4×C43—42no—
391C4×C43—41no—
392C4×C43—81no—
393C4×C43C2×C4×D411yescharacteristic
394C4×C43#51811yescharacteristic
395C4×C43#54611yescharacteristic
396C4×C43#55111yescharacteristic
397Dic43—22no—
398Dic43—42no—
399Dic43—41no—
400Dic43—41no—
401Dic43—81no—
402Dic43—81no—
403C2×#447—431no—
404C2×C4×D8—431no—
405C2×#418—431no—
406#2363—431no—
407D4×C22⋊C4—431no—
408#1972—431no—
409#1934—431no—
410#1925—431no—
411#1895—431no—
412#1879—431no—
413#1879D4311yescharacteristic, complemented
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×D4C2×D4311yescharacteristic, complemented
437C2×#117—431no—
438C22×C22⋊C4—861no—
439#447—438no—
440C4×D8—864no—
441C2×#107—431no—
442C2×#106—431no—
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×#97—431no—
454C2×C4×C8—431no—
455#390—431no—
456#390—431no—
457#390—861no—
458#390C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic, complemented
473#336—431no—
474#336C2×D4311yescharacteristic, complemented
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—21no—
489C23×C4—431no—
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—22no—
508C4×D4—41no—
509C4×D4—862no—
510C4×D4—862no—
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—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—861no—
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—1721no—
542#102—22no—
543#102—41no—
544#102—434no—
545#102—434no—
546#102—434no—
547#102—862no—
548#102—862no—
549#102—862no—
550C22⋊C8—434no—
551#97—1721no—
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—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—431no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—3441no—
615C22×C4—3441no—
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—21no—
631C2×C8—432no—
632C2×C8—432no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8C2×C4×D4312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—432no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—3441no—
648C4⋊C4D4×D4312yes—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—864no—
653C22⋊C4—862no—
654C22⋊C4—3441no—
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—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—432no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—3444no—
746C2×C4—3444no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4#1306334912yes—
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—41no—
764C8—862no—
765C8—862no—
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#1458353111yescharacteristic
797C22#1458354611yescharacteristic
798C22C2×#1306334911yescharacteristic
799C22#1458369611yescharacteristic
800C22#1458370311yescharacteristic
801C22#1458370311yescharacteristic
802C4—22no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—862no—
807C4—3441no—
808C4—3441no—
809C4—1722no—
810C4—1721no—
811C4—1721no—
812C4C4×D4×D4311yescharacteristic
813C4#1458337211yescharacteristic
814C4#1458354611yescharacteristic
815C4#1458357711yescharacteristic
816C2—82no—
817C2—82no—
818C2—1722no—
819C2—1724no—
820C2#1913757811yescharacteristic
821C2C4×#1306334911yescharacteristic
822C2#1914344411yescharacteristic
823C2#1914606811yescharacteristic
824C2#1914612811yescharacteristic
825C2#1914680311yescharacteristic
826C2#1914684011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#22880
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C2×#14582902C2semidirect
4. #19137629C2semidirect
5. #19137416C2semidirect
6. #19135472C2semidirect
7. #19135281C2semidirect
8. #19135218C2semidirect
9. #19135030C2semidirect
10. #19134940C2semidirect
11. #19134859C2semidirect
12. #19134795C2semidirect
13. #19134419C2semidirect
14. #19134375C2semidirect
15. C43×#1879C2semidirect
24. #14583031C4semidirect
26. C2×#13063258C22semidirect
27. C2×#13063257C22semidirect
33. C2×#13063246C22semidirect
36. C2×#13063235C22semidirect
37. C2×C4×C43⋊C8C22semidirect
39. #14582802C22semidirect
41. #14582797C22semidirect
48. C4⋊C4×Dic43C22semidirect
51. #14582662C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582653C22semidirect
56. C2×C4×D4×C43C22semidirect
58. C2×#102×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
71. C2×D4×D43C2×C4semidirect
84. #13063296C2×C4semidirect
113. #13063247C2×C4semidirect
116. #13063246C2×C4semidirect
117. #13063245D4semidirect
118. (C2×D43)⋊C8C2×C4semidirect
131. C2×D8×C43C2×C4semidirect
413. #1879D43semidirect
436. C2×C4×D4C2×D43semidirect
451. C2×#102C2×D43semidirect
472. #340C2×D43semidirect
474. #336C2×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×C4×#106218822
C2×#145829022
#191376292
#191374162
#191354722
#191352812
#191352182
#191350302
#191349402
#191348592
#191347952
#191344192
#191343752
C43×#18792
#2288043