Finite Group Databasebeta

← #25113737

Subgroups — #25113737

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D43C211yesmaximal, characteristic
2#19137463C211yesmaximal, characteristic, complemented
3#19137416C211yesmaximal, characteristic
4#19135280C211yesmaximal, characteristic, complemented
5#19135218C211yesmaximal, characteristic, complemented
6#19135212C211yesmaximal, characteristic, complemented
7#19134843C211yesmaximal, characteristic, complemented
8#19134841C211yesmaximal, characteristic, complemented
9#19134680C211yesmaximal, characteristic, complemented
10#19134623C211yesmaximal, characteristic, complemented
11#19134524C211yesmaximal, characteristic
12C4×#13063247C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14C8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063283—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31#102×D43C418yescomplemented
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic, complemented
36#14582786—21no—
37#14582780—21no—
38#14582775—21no—
39#14582775—21no—
40#14582761—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582754—21no—
44C4⋊C4×Dic43C2211yescharacteristic, complemented
45C4×C4⋊Dic43C2211yescharacteristic, complemented
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic, complemented
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C2×D4×D43—22no—
64C2×D4×D43—22no—
65C2×D4×D43—22no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43C2×C414yes—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—41no—
76C2×C8×D43—41no—
77C2×C8×D43C2×C414yescomplemented
78C4×D172—22no—
79C4×D172—41no—
80#13063287—22no—
81#13063287—41no—
82#13063283—44no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43C2×C414yescomplemented
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4D411yescharacteristic
97C2×(C2×D43)⋊C4D411yescharacteristic
98C22⋊C4×D43—44no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063258—41no—
103#13063258—41no—
104#13063247—22no—
105#13063247C2×C414yes—
106#13063246—41no—
107#13063246C2×C414yescomplemented
108#13063245—22no—
109#13063245C2×C414yes—
110(C2×D43)⋊C8—22no—
111C8×Dic43—41no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#102×C43—41no—
130#102×C43C2×C414yescomplemented
131C4×C8×C43—41no—
132#95×C43—21no—
133C24×C43—21no—
134C23×D43—21no—
135C23×D43—24no—
136C23×D43—42no—
137C23×D43—42no—
138C23×D43—42no—
139C23×D43—42no—
140C23×D43—81no—
141C23×D43—81no—
142C23×D43C2×D411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—24no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—42no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164D4×D43—28no—
165D4×D43—44no—
166D4×D43—44no—
167D4×D43—44no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172C22×C412yes—
172C2×D172#4112yes—
173C2×D172#4112yes—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—24no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—81no—
186C2×C4×D43—81no—
187C2×C4×D43C22×C412yes—
188C2×C4×D43#4112yes—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43C22×C412yes—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—42no—
201C4⋊C4×C43C22×C412yes—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—81no—
204C42×C43—21no—
205C42×C43—21no—
206C22⋊Dic43—42no—
207C22⋊Dic43—81no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4D814yes—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—42no—
220C4⋊Dic43C22×C412yes—
221Dic43⋊C4—24no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8C22×C412yes—
232C8×D43—44no—
233C23×C43—22no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43C22×D411yescharacteristic
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—48no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—48no—
254C22×D43—84no—
255C22×D43—84no—
256C22×D43—84no—
257C22×D43—84no—
258C22×D43—84no—
259C22×D43C4×D412yes—
260C22×D43C2×D812yes—
261C22×D43#13512yes—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—41no—
265D4×C43—41no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43C2×D812yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C22⋊D43—48no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43C4×D412yes—
305C2×Dic43C2×D812yes—
306D172—22no—
307D172—22no—
308D172—22no—
309D172#11714yescomplemented
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—48no—
315C4×D43—84no—
316C4×D43—84no—
317C8×C43—22no—
318C8×C43—41no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321#22570—431nomaximal, Sylow
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43C2×C4×D411yescharacteristic
330C22×C43#54611yescharacteristic
331C22×C43#54611yescharacteristic
332C22×C43C22×D811yescharacteristic
333C22×C43C2×#13511yescharacteristic
334C22×C43#57711yescharacteristic
335C22×C43#57711yescharacteristic
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—24no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—816no—
350C2×D43C4×D814yes—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43C2×#11711yescharacteristic
357C4×C43#51811yescharacteristic
358C4×C43#55111yescharacteristic
359C4×C43#55111yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—42no—
363Dic43—41no—
364Dic43—81no—
365Dic43—81no—
366C22×#102—431no—
367#2344—431no—
368D4×C22⋊C4—431no—
369#1934—431no—
370#1934D4311yescharacteristic, complemented
371#1925—431no—
372#1925—431no—
373#1862—431no—
374#1862—431no—
375#1823—431no—
376#1808—431no—
377#1786—431no—
378C4×#102—431no—
379C4×#102—431no—
380C8×C22⋊C4—431no—
381C2×C43—82no—
382C2×C43#234211yescharacteristic
383C2×C43C2×C4×D811yescharacteristic
384C2×C43#294911yescharacteristic
385C2×C43#329411yescharacteristic
386C2×C43#329411yescharacteristic
387C2×C43#329611yescharacteristic
388C2×C43#329611yescharacteristic
389D43—24no—
390D43—44no—
391C23×D4—431no—
392C23×C8—431no—
393C2×C4×D4—431no—
394C2×C4×D4—431no—
395C2×#117—861no—
396C22×C4⋊C4—431no—
397C22×C22⋊C4—861no—
398C2×#107—431no—
399C2×#107—431no—
400C2×#102—431no—
401C2×#102—431no—
402C2×#102—431no—
403C2×#102—438no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102C2×D4311yescharacteristic
408C2×#102C2×D4311yescharacteristic
409C2×C22⋊C8—431no—
410C2×C4×C8—431no—
411C2×C4×C8C2×D4311yescharacteristic, complemented
412#390—431no—
413#390C2×D4311yescharacteristic
414#389—431no—
415#389C2×D4311yescharacteristic, complemented
416#387—861no—
417#387—861no—
418#386—861no—
419#386—861no—
420#381—861no—
421#380—431no—
422#380—431no—
423#379—861no—
424C4×C4⋊C4—431no—
425C4×C4⋊C4—431no—
426C4×C22⋊C4—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340C2×D4311yescharacteristic, complemented
432#340C2×D4311yescharacteristic, complemented
433#336—431no—
434#336—431no—
435C43#2257011yescharacteristic, complemented, Sylow
436C25—861no—
437C22×D4—434no—
438C22×D4—431no—
439C22×D4—862no—
440C22×D4—861no—
441C22×D4—862no—
442C22×D4—862no—
443C22×D4—1721no—
444C22×D4—1721no—
445C22×D4C22×D4311yescharacteristic
446C23×C4—431no—
447C23×C4—861no—
448C23×C4—861no—
449C23×C4—861no—
450C22×C8—431no—
451C22×C8—434no—
452C22×C8—431no—
453C22×C8—1721no—
454C22×C8—1721no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C4×D4—862no—
458C4×D4—862no—
459C4×D4—1721no—
460C4×D4—1721no—
461#117—1724no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—431no—
476C2×C22⋊C4—431no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—1724no—
484C2×C42—431no—
485C2×C42—861no—
486C2×C42—861no—
487C2×C42C22×D4311yescharacteristic
488#107—1721no—
489#107—1721no—
490#102—41no—
491#102—434no—
492#102—434no—
493#102—434no—
494#102—862no—
495#102—862no—
496#102—1721no—
497#102C4×D4314yescomplemented
498C22⋊C8—862no—
499C4×C8—41no—
500C4×C8—1721no—
501#95—21no—
502#95—431no—
503#95—431no—
504#95—861no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509C24—21no—
510C24—431no—
511C24—864no—
512C24—861no—
513C24—3441no—
514C24—3441no—
515C24—1722no—
516C24—1722no—
517C24—1722no—
518C24—1722no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—432no—
525C2×D4—432no—
526C2×D4—432no—
527C2×D4—864no—
528C2×D4—868no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—1724no—
533C2×D4—1724no—
534C2×D4—1724no—
535C2×D4—1722no—
536C2×D4—1722no—
537C2×D4C2×C4×D4312yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—431no—
546C22×C4—864no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—3441no—
555C22×C4—3441no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4D4×D4311yescharacteristic
563C22×C4D4×D4311yescharacteristic
564C22×C4C23×D4311yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—1724no—
577C2×C8C2×C4×D4312yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—432no—
585C4⋊C4—864no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—1722no—
592C4⋊C4C2×C4×D4312yes—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C22⋊C4—434no—
596C22⋊C4—862no—
597C22⋊C4—3441no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—21no—
604C42—21no—
605C42—861no—
606C42—861no—
607C42—1722no—
608C42—1722no—
609C23—22no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—432no—
617C23—432no—
618C23—432no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—862no—
624C23—862no—
625C23—862no—
626C23—3444no—
627C23—3444no—
628C23—3444no—
629C23—3444no—
630C23—3444no—
631C23—1728no—
632C23—1728no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23C2×D4×D4311yescharacteristic
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—434no—
643D4—862no—
644D4—862no—
645D4—862no—
646D4—1728no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—3444no—
676C2×C4—3444no—
677C2×C4—1728no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4D8×D4312yes—
687C2×C4C22×C4×D4311yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4#41×D4311yescharacteristic
690C2×C4#41×D4311yescharacteristic
691C2×C4#1306337011yescharacteristic
692C2×C4#1306337111yescharacteristic
693C8—22no—
694C8—41no—
695C8—862no—
696C8—1721no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—434no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—862no—
710C22—862no—
711C22—864no—
712C22—34416no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22C4×D4×D4311yescharacteristic
720C22#1458353811yescharacteristic
721C22#1458354211yescharacteristic
722C22C2×D8×D4311yescharacteristic
723C22#135×D4311yescharacteristic
724C22#1458370511yescharacteristic
725C22#1458370611yescharacteristic
726C4—22no—
727C4—42no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—862no—
732C4—862no—
733C4—3441no—
734C4—3441no—
735C4—1722no—
736C4—1721no—
737C4#117×D4311yescharacteristic
738C4#1458337111yescharacteristic
739C4#1458357411yescharacteristic
740C4#1458357711yescharacteristic
741C2—82no—
742C2—864no—
743C2—1724no—
744C2#1913744311yescharacteristic
745C2C4×D8×D4311yescharacteristic
746C2#1914344911yescharacteristic
747C2#1914640311yescharacteristic
748C2#1914640711yescharacteristic
749C2#1914642511yescharacteristic
750C2#1914642911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43#22570
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #19137463C2semidirect
4. #19135280C2semidirect
5. #19135218C2semidirect
6. #19135212C2semidirect
7. #19134843C2semidirect
8. #19134841C2semidirect
9. #19134680C2semidirect
10. #19134623C2semidirect
12. C4×#13063247C2semidirect
13. #19134409C2semidirect
14. C8×(C2×D43)⋊C4C2semidirect
15. C43×#1934C2semidirect
23. C2×#13063258C22semidirect
24. C2×#13063258C22semidirect
31. #102×D43C4semidirect
33. C2×C8×Dic43C22semidirect
35. #14582798C22semidirect
44. C4⋊C4×Dic43C22semidirect
45. C4×C4⋊Dic43C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582653C22semidirect
55. C2×C4×C8×C43C22semidirect
57. C43×#389C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
77. C2×C8×D43C2×C4semidirect
89. C4⋊C4×D43C2×C4semidirect
107. #13063246C2×C4semidirect
130. #102×C43C2×C4semidirect
309. D172#117semidirect
370. #1934D43semidirect
411. C2×C4×C8C2×D43semidirect
415. #389C2×D43semidirect
431. #340C2×D43semidirect
432. #340C2×D43semidirect
435. C43#22570semidirect
497. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D432
#191374632
#191374162
#191352802
#191352182
#191352122
#191348432
#191348412
#191346802
#191346232
#191345242
C4×#130632472
#191344092
C8×(C2×D43)⋊C42
C43×#19342
#2257043