Finite Group Databasebeta

← #25112905

Subgroups — #25112905

Order 11008.

1194 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×#14583614C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3#19137527C211yesmaximal, characteristic, complemented
4#19135568C211yesmaximal, characteristic, complemented
5#19135547C211yesmaximal, characteristic, complemented
6#19135030C211yesmaximal, characteristic, complemented
7#19135020C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134689C211yesmaximal, characteristic, complemented
11#19134688C211yesmaximal, characteristic, complemented
12#19134605C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583614—24no—
19#14583614C418yescomplemented
20C2×#13063325C2211yescharacteristic
21C2×#13063311—21no—
22C2×#13063311—21no—
23C2×#13063299—21no—
24C2×#13063296C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×#13063284—21no—
28C2×#13063283C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582972—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38#14582790—21no—
39#14582784—21no—
40#14582777—21no—
41#14582765C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4×(C2×D43)⋊C4—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×D172D411yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77#13063325—22no—
78#13063325C2×C414yescomplemented
79#13063311—28no—
80#13063311—28no—
81#13063299—28no—
82#13063296—22no—
83#13063296—22no—
84#13063296C2×C414yes—
85#13063296C2×C414yescomplemented
86C4×D172C2×C414yes—
87C4×D172D414yes—
88#13063284—28no—
89#13063283—22no—
90#13063283—22no—
91#13063283—22no—
92#13063283—41no—
93#13063283C2×C414yes—
94#13063283C2×C414yescomplemented
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43D411yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C4⋊C4×D43—22no—
103C4⋊C4×D43—41no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4D411yescharacteristic
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C4⋊(C43⋊C8)—22no—
117#13063246—41no—
118#13063246—41no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4×D4×C43—22no—
130C4×D4×C43C2×C414yescomplemented
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137#102×C43—22no—
138#102×C43—22no—
139#97×C43—22no—
140#95×C43—21no—
141C24×C43—21no—
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—24no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—81no—
162C2×C22⋊D43—81no—
163C2×C22⋊D43—81no—
164C2×C22⋊D43—81no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×D172—41no—
172C2×D172—41no—
173C2×D172C22⋊C414yes—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—81no—
185C2×C4×D43C22×C412yes—
186C2×C4×D43C22×C412yes—
187C2×C4×D43C2×D412yes—
188C2×C4×D43C2×D412yes—
189C2×Dic86—24no—
190C2×Dic86—81no—
191C2×Dic86—81no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43#4112yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C22×C412yes—
203C4⋊C4×C43#4112yes—
204C22⋊C4×C43—24no—
205C42×C43—81no—
206C42×C43C22×C412yes—
207C42×C43C2×D412yes—
208C22⋊Dic43—24no—
209C22⋊Dic43—24no—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—81no—
215(C2×D43)⋊C4C22⋊C414yes—
216(C2×D43)⋊C4C22⋊C414yes—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43C22⋊C414yes—
225C4⋊Dic43C22×C412yes—
226C4⋊Dic43C22×C412yes—
227Dic43⋊C4—42no—
228C4×Dic43—24no—
229C4×Dic43—24no—
230C4×Dic43—42no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237#10621872—44no—
238C8×D43—44no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43C22×D411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43C2×C22⋊C412yes—
260C22×D43C2×C22⋊C412yes—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—41no—
264D4×C43—41no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—48no—
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×C43C2×C22⋊C412yes—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C432−1+411yescharacteristic
287C22⋊D43—84no—
288C22⋊D43—84no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—41no—
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×Dic43—41no—
305C2×Dic43C2×C22⋊C412yes—
306C2×Dic43C2×C22⋊C412yes—
307D172—44no—
308C4×D43—22no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—84no—
317Dic86—84no—
318C8×C43—22no—
319C8×C43—41no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322#22492—431nomaximal, Sylow
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43C22×C22⋊C411yescharacteristic
331C22×C43#54611yescharacteristic
332C22×C43#54711yescharacteristic
333C22×C43#57511yescharacteristic
334C22×C43#57511yescharacteristic
335C22×C43#57611yescharacteristic
336C22×C43#57711yescharacteristic
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—81no—
356C4×C43C4×#4111yescharacteristic
357C4×C43#52011yescharacteristic
358C4×C43#54611yescharacteristic
359C4×C43#54711yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—42no—
363Dic43—42no—
364Dic43—81no—
365Dic43—81no—
366C2×#555—431no—
367C2×#435—431no—
368#2352—431no—
369#1993—431no—
370#1988—431no—
371#1895—431no—
372#1893—431no—
373#1875—431no—
374#1874—431no—
375#1825—431no—
376#1825—431no—
377#1804—431no—
378#1762D4311yescharacteristic, complemented
379#1736—431no—
380#1735—431no—
381C2×C43—82no—
382C2×C43#233911yescharacteristic
383C2×C43#289611yescharacteristic
384C2×C43#289711yescharacteristic
385C2×C43#331911yescharacteristic
386C2×C43#332111yescharacteristic
387C2×C43#334711yescharacteristic
388C2×C43#334811yescharacteristic
389D43—42no—
390D43—42no—
391C22×M16—431no—
392C23×C8—431no—
393#555—438no—
394#555—864no—
395C2×C4⋊Q8—431no—
396C2×#124—861no—
397C2×#124—861no—
398C2×#121—431no—
399C2×#121—431no—
400C2×#121—861no—
401C2×C4×D4—431no—
402C2×C4×D4C2×D4311yescharacteristic
403C2×#117—431no—
404C2×#117—431no—
405C2×#117—431no—
406C2×#117—861no—
407C22×C4⋊C4—431no—
408#435—864no—
409C2×C4⋊C8—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102C2×D4311yescharacteristic
413C2×#102C2×D4311yescharacteristic
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×#97C2×D4311yescharacteristic
417#388—861no—
418#387—861no—
419#386—861no—
420#382—431no—
421#380—431no—
422#380—431no—
423C4×C4⋊C4C2×D4311yescharacteristic
424C4×C22⋊C4—861no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340C2×D4311yescharacteristic
436#340C2×D4311yescharacteristic
437C43#2249211yescharacteristic, complemented, Sylow
438C22×Q8—861no—
439C22×D4—431no—
440C22×D4—861no—
441C22×D4—861no—
442C22×D4C22×D4311yescharacteristic
443C23×C4—21no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—861no—
447C2×M16—862no—
448C2×M16—862no—
449C2×M16—1721no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8—862no—
453C22×C8—862no—
454C22×C8—1721no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C4⋊Q8—434no—
458C4⋊Q8—862no—
459#124—868no—
460#124—868no—
461#121—434no—
462#121—434no—
463#121—868no—
464#121—862no—
465#121—862no—
466C4×D4—22no—
467C4×D4—434no—
468C4×D4—434no—
469C4×D4C4×D4314yescomplemented
470#117—434no—
471#117—434no—
472#117—862no—
473#117—862no—
474#117—868no—
475#117—862no—
476#117—1721no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—1721no—
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C42—21no—
500C2×C42—861no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42C22×D4311yescharacteristic
504C4⋊C8—862no—
505#102—22no—
506#102—22no—
507#102—1721no—
508#102—1721no—
509C22⋊C8—862no—
510C22⋊C8—862no—
511#97—22no—
512#95—21no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—21no—
518C24—431no—
519C24—431no—
520C2×Q8—864no—
521C2×Q8—3441no—
522C2×Q8—3441no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—434no—
529C2×D4—864no—
530C2×D4—864no—
531C2×D4—3441no—
532C2×D4—3441no—
533C2×D4—3441no—
534C2×D4—3441no—
535C2×D4—1721no—
536C2×D4—1721no—
537C2×D4C2×C4×D4312yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—3441no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4C23×D4311yescharacteristic
568M16—1724no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—1724no—
581C2×C8#1062189812yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—434no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—864no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—1722no—
597C4⋊C4C2×C4×D4312yes—
598C4⋊C4#1062189812yes—
599C22⋊C4—24no—
600C22⋊C4—434no—
601C22⋊C4—434no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—81no—
610C42—864no—
611C42—864no—
612C42—1722no—
613C42C2×C4×D4312yes—
614C42D4×D4312yes—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—432no—
623C23—432no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23C2×D4×D4311yescharacteristic
637Q8—3444no—
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—3444no—
643D4—3444no—
644D4—1724no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—48no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—3444no—
676C2×C4—1721no—
677C2×C4—1721no—
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×C4C22⋊C4×D4312yes—
687C2×C4C22⋊C4×D4312yes—
688C2×C4C22×C4×D4311yescharacteristic
689C2×C4C2×D4×D4311yescharacteristic
690C2×C4C2×#1062189811yescharacteristic
691C2×C4C2×#1062189811yescharacteristic
692C2×C4#1306337111yescharacteristic
693C2×C4#1306337211yescharacteristic
694C8—22no—
695C8—41no—
696C8—1721no—
697C8—1721no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—862no—
710C22—862no—
711C22—1721no—
712C22—1721no—
713C22—1721no—
714C22—1721no—
715C22—1721no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22C2×C22⋊C4×D4311yescharacteristic
720C22#1458354511yescharacteristic
721C22#1458355411yescharacteristic
722C22#1458369511yescharacteristic
723C22#1458369511yescharacteristic
724C22#1458370311yescharacteristic
725C22#1458370811yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—862no—
732C4—862no—
733C4—3441no—
734C4—3441no—
735C4—1722no—
736C4—1722no—
737C4C4×#1062189811yescharacteristic
738C4#1458337911yescharacteristic
739C4#1458354511yescharacteristic
740C4#1458355411yescharacteristic
741C2—82no—
742C2—1722no—
743C2—1722no—
744C2#1913742611yescharacteristic
745C2#1914310911yescharacteristic
746C2#1914311911yescharacteristic
747C2#1914675611yescharacteristic
748C2#1914678611yescharacteristic
749C2#1914710011yescharacteristic
750C2#1914711511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#14583614C2
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#22492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. #19137527C2semidirect
4. #19135568C2semidirect
5. #19135547C2semidirect
6. #19135030C2semidirect
7. #19135020C2semidirect
8. #19134914C2semidirect
9. #19134909C2semidirect
10. #19134689C2semidirect
11. #19134688C2semidirect
12. #19134605C2semidirect
13. #19134313C2semidirect
14. #19134310C2semidirect
15. C43×#1762C2semidirect
19. #14583614C4semidirect
78. #13063325C2×C4semidirect
85. #13063296C2×C4semidirect
94. #13063283C2×C4semidirect
130. C4×D4×C43C2×C4semidirect
378. #1762D43semidirect
437. C43#22492semidirect
469. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145829722
#191375272
#191355682
#191355472
#191350302
#191350202
#191349142
#191349092
#191346892
#191346882
#191346052
#191343132
#191343102
C43×#17622
#2249243