Finite Group Databasebeta

← #25112985

Subgroups — #25112985

Order 11008.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583601C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3#19137539C211yesmaximal, characteristic, complemented
4#19135562C211yesmaximal, characteristic, complemented
5#19135549C211yesmaximal, characteristic, complemented
6#19135020C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic, complemented
9#19134688C211yesmaximal, characteristic, complemented
10#19134679C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#1895C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17#14583601—24no—
18#14583601C418yescomplemented
19C2×#13063318—21no—
20C2×#13063316C2211yescharacteristic
21C2×#13063309—21no—
22C2×#13063297—21no—
23C2×#13063296C2211yescharacteristic
24C2×D4×Dic43—21no—
25C2×D4×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31#14582968—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38#14582799—21no—
39#14582793—21no—
40#14582788—21no—
41#14582768C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44#14582750—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43D411yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C4×D43C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C2×C8×D43—22no—
70C2×C8×D43—22no—
71C2×C8×D43—41no—
72#13063318—28no—
73#13063316—22no—
74#13063316C2×C414yes—
75#13063309—28no—
76#13063297—28no—
77#13063296—22no—
78#13063296C2×C414yes—
79D4×Dic43—28no—
80D4×Dic43—22no—
81D4×Dic43C2×C414yes—
82C4×C22⋊D43C2×C414yes—
83C4×C22⋊D43D414yes—
84#13063284—22no—
85#13063284—41no—
86#13063283—22no—
87#13063283—22no—
88#13063283—41no—
89#13063283C2×C414yes—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2×C414yes—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43D411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116#13063246—22no—
117#13063246—41no—
118C22⋊(C43⋊C8)—22no—
119(C2×D43)⋊C8—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43—21no—
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43—22no—
127C2×M16×C43—22no—
128C2×M16×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#121×C43—22no—
132#121×C43C2×C414yes—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138#102×C43—22no—
139#102×C43—41no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—24no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—42no—
151C2×D4×C43—42no—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—81no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43C22⋊C414yes—
170C22×Dic43—24no—
171C22×Dic43—24no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—81no—
177C22×Dic43—81no—
178C22×Dic43—81no—
179C22×Dic43—81no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43C22×C412yes—
188C2×C4×D43C2×D412yes—
189M16×C43—44no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43#4112yes—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43C22×C412yes—
202C22⋊C4×C43—24no—
203C22⋊C4×C43—81no—
204C22⋊Dic43—24no—
205C22⋊Dic43—24no—
206C22⋊Dic43—42no—
207C22⋊Dic43C22⋊C414yes—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—81no—
211(C2×D43)⋊C4C22⋊C414yes—
212C4⋊Dic43—24no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—24no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22×C412yes—
220C4⋊Dic43C22×C412yes—
221C4⋊Dic43#4112yes—
222Dic43⋊C4—24no—
223Dic43⋊C4—42no—
224Dic43⋊C4—81no—
225Dic43⋊C4C22⋊C414yes—
226C4×Dic43—24no—
227C4×Dic43—42no—
228C4×Dic43—42no—
229C4×Dic43—42no—
230C4×Dic43C22×C412yes—
231C4×Dic43C2×D412yes—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C8×D43—44no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43C2×C22⋊C412yes—
253C23×C43C22×D411yescharacteristic
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43C2×C22⋊C412yes—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—48no—
264D4×C43—41no—
265D4×C43—41no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
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×C43—41no—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C22⋊D43—44no—
289C22⋊D43—84no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—84no—
309C2×Dic43—84no—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C2×Dic43C2×C22⋊C412yes—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C8×C43—22no—
318C8×C43—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#22498—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43C22×C22⋊C411yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43#54711yescharacteristic
339C22×C43#57511yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57611yescharacteristic
342C22×C43#57711yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43C4×#4111yescharacteristic
355C4×C43#52011yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#54711yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43—81no—
365C2×#553—431no—
366C2×#435—431no—
367#2354—431no—
368#1992—431no—
369#1989—431no—
370#1895D4311yescharacteristic, complemented
371#1893—431no—
372#1875—431no—
373#1875—431no—
374#1825—431no—
375#1823—431no—
376#1802—431no—
377#1762—431no—
378#1736—431no—
379#1735—431no—
380C2×C43—42no—
381C2×C43—82no—
382C2×C43#233911yescharacteristic
383C2×C43#289611yescharacteristic
384C2×C43#289711yescharacteristic
385C2×C43#330711yescharacteristic
386C2×C43#330911yescharacteristic
387C2×C43#334711yescharacteristic
388C2×C43#335011yescharacteristic
389D43—42no—
390C22×M16C2×D4311yescharacteristic
391C23×C8—431no—
392#553—438no—
393#553—864no—
394C2×#126—861no—
395C2×#125—431no—
396C2×#123—861no—
397C2×#121—431no—
398C2×#121—861no—
399C2×#121C2×D4311yescharacteristic
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×C4×D4—861no—
403C2×#117—431no—
404C2×#117—431no—
405C2×#117—431no—
406C22×C4⋊C4—431no—
407#435—864no—
408C2×C4⋊C8—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102C2×D4311yescharacteristic
412C2×#102C2×D4311yescharacteristic
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×#97—431no—
416#390—861no—
417#388—861no—
418#388—861no—
419#384—431no—
420#380—431no—
421#380C2×D4311yescharacteristic
422C4×C4⋊C4—431no—
423C4×C4⋊C4—861no—
424#340—431no—
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#340C2×D4311yescharacteristic
435#340C2×D4311yescharacteristic
436C43#2249811yescharacteristic, complemented, Sylow
437C22×D4—21no—
438C22×D4—431no—
439C22×D4—861no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—431no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8—862no—
451C22×C8—862no—
452C22×C8—1721no—
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455#126—868no—
456#125—434no—
457#125—862no—
458#123—868no—
459#121—22no—
460#121—434no—
461#121—862no—
462#121—868no—
463#121C4×D4314yes—
464C4×D4—434no—
465C4×D4—434no—
466C4×D4—434no—
467C4×D4—862no—
468C4×D4—868no—
469#117—434no—
470#117—862no—
471#117—862no—
472#117—862no—
473#117—1721no—
474#117—1721no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—434no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C42—431no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42—861no—
505C4⋊C8—862no—
506#102—22no—
507#102—41no—
508#102—862no—
509#102—1721no—
510C22⋊C8—862no—
511C22⋊C8—862no—
512#97—862no—
513#95—21no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—431no—
518C24D4×D4311yescharacteristic
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—434no—
528C2×D4—864no—
529C2×D4—3441no—
530C2×D4—3441no—
531C2×D4—1721no—
532C2×D4—1721no—
533C2×D4C2×C4×D4312yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—864no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—864no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—3441no—
557C22×C4—3441no—
558C22×C4—3441no—
559C22×C4—3441no—
560C22×C4C2×C4×D4312yes—
561C22×C4D4×D4311yescharacteristic
562C22×C4D4×D4312yes—
563C22×C4C23×D4311yescharacteristic
564M16—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—1724no—
577C2×C8#1062190012yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—434no—
584C4⋊C4—432no—
585C4⋊C4—432no—
586C4⋊C4—432no—
587C4⋊C4—864no—
588C4⋊C4—864no—
589C4⋊C4—864no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—3441no—
596C4⋊C4—1722no—
597C4⋊C4C2×C4×D4312yes—
598C22⋊C4—24no—
599C22⋊C4—81no—
600C22⋊C4—434no—
601C22⋊C4—434no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C22⋊C4—3441no—
606C22⋊C4—1722no—
607C22⋊C4—1722no—
608C42—432no—
609C42—432no—
610C42—864no—
611C42—1722no—
612C42—1722no—
613C42—1722no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—432no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23C22⋊C4×D4312yes—
635C23C2×D4×D4311yescharacteristic
636D4—22no—
637D4—22no—
638D4—48no—
639D4—41no—
640D4—41no—
641D4—3444no—
642D4—1724no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—861no—
662C2×C4—861no—
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—862no—
673C2×C4—862no—
674C2×C4—3444no—
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×C4C22⋊C4×D4312yes—
686C2×C4C22×C4×D4311yescharacteristic
687C2×C4C2×D4×D4311yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4C2×#1062190011yescharacteristic
690C2×C4#1306337011yescharacteristic
691C2×C4#1306337211yescharacteristic
692C8—22no—
693C8—41no—
694C8—1721no—
695C8—1721no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—1721no—
714C22—1721no—
715C22—1721no—
716C22—1721no—
717C22C2×C22⋊C4×D4311yescharacteristic
718C22#1458353811yescharacteristic
719C22#1458354911yescharacteristic
720C22#1458369511yescharacteristic
721C22#1458369511yescharacteristic
722C22#1458370311yescharacteristic
723C22#1458370811yescharacteristic
724C4—22no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4—862no—
729C4—862no—
730C4—862no—
731C4—3441no—
732C4—1722no—
733C4—1722no—
734C4—1722no—
735C4C4×#1062190011yescharacteristic
736C4#1458337811yescharacteristic
737C4#1458353611yescharacteristic
738C4#1458354711yescharacteristic
739C2—42no—
740C2—82no—
741C2—1722no—
742C2#1913742111yescharacteristic
743C2#1914310911yescharacteristic
744C2#1914311911yescharacteristic
745C2#1914656611yescharacteristic
746C2#1914659611yescharacteristic
747C2#1914709011yescharacteristic
748C2#1914713511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#14583601C2
cosocleC22×C4×C43C24
hypercenter#1895D43
hypocenterC43#22498
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. #19137539C2semidirect
4. #19135562C2semidirect
5. #19135549C2semidirect
6. #19135020C2semidirect
7. #19134918C2semidirect
8. #19134914C2semidirect
9. #19134688C2semidirect
10. #19134679C2semidirect
11. #19134593C2semidirect
12. #19134422C2semidirect
13. #19134315C2semidirect
14. #19134310C2semidirect
15. C43×#1895C2semidirect
18. #14583601C4semidirect
370. #1895D43semidirect
436. C43#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#145836012
C2×#145829682
#191375392
#191355622
#191355492
#191350202
#191349182
#191349142
#191346882
#191346792
#191345932
#191344222
#191343152
#191343102
C43×#18952
#2249843