Finite Group Databasebeta

← #25112910

Subgroups — #25112910

Order 11008.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583596C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3#19137491C211yesmaximal, characteristic, complemented
4#19135562C211yesmaximal, characteristic, complemented
5#19135551C211yesmaximal, characteristic, complemented
6#19135020C211yesmaximal, characteristic, complemented
7#19134913C211yesmaximal, characteristic, complemented
8#19134909C211yesmaximal, characteristic, complemented
9#19134687C211yesmaximal, characteristic, complemented
10#19134684C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1895C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17#14583596—24no—
18#14583596C418yescomplemented
19C2×#13063318—21no—
20C2×#13063316C2211yescharacteristic
21C2×#13063306—21no—
22C2×#13063296—21no—
23C2×#13063296C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582968—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39#14582796—21no—
40#14582773—21no—
41#14582771—21no—
42#14582768C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
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×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C2×C8×D43—22no—
72C2×C8×D43—22no—
73C2×C8×D43—41no—
74#13063318—28no—
75#13063316—22no—
76#13063316C2×C414yescomplemented
77#13063306—28no—
78#13063296—28no—
79#13063296—22no—
80#13063296C2×C414yescomplemented
81D4×Dic43—22no—
82D4×Dic43C2×C414yescomplemented
83C4×C22⋊D43C2×C414yes—
84C4×C22⋊D43D414yes—
85(C22⋊D43)⋊C4—28no—
86(C22⋊D43)⋊C4—44no—
87#13063284—22no—
88#13063284C2×C414yescomplemented
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—41no—
106C4⋊C4×D43C2×C414yescomplemented
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063246—22no—
118#13063246—41no—
119C22⋊(C43⋊C8)—22no—
120(C2×D43)⋊C8—22no—
121#13063235—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—22no—
128C2×M16×C43—22no—
129C2×M16×C43—41no—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132#121×C43—22no—
133#121×C43C2×C414yescomplemented
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139#102×C43—22no—
140#102×C43—41no—
141#95×C43—21no—
142C24×C43—21no—
143C24×C43C2×D411yescharacteristic
144C23×D43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43—24no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—81no—
152C2×D4×C43—81no—
153C2×D4×C43C22×C412yes—
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×C43—21no—
161C22×C4×C43C22×C412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—24no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43C22⋊C414yes—
171C22×Dic43—24no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—81no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—24no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C4×D43—81no—
194C2×C4×D43C22×C412yes—
195C2×C4×D43C2×D412yes—
196M16×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43#4112yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43C22×C412yes—
209C22⋊C4×C43—24no—
210C22⋊C4×C43—42no—
211C22⋊Dic43—24no—
212C22⋊Dic43—24no—
213C22⋊Dic43—24no—
214C22⋊Dic43C22⋊C414yes—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4C22⋊C414yes—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—24no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—42no—
224C4⋊Dic43C22×C412yes—
225C4⋊Dic43C22×C412yes—
226C4⋊Dic43#4112yes—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231Dic43⋊C4—81no—
232Dic43⋊C4C22⋊C414yes—
233C4×Dic43—24no—
234C4×Dic43—42no—
235C4×Dic43C22×C412yes—
236C4×Dic43C2×D412yes—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C8×D43—44no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—22no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43C2×C22⋊C412yes—
258C23×C43C22×D411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43C2×C22⋊C412yes—
264C22×D43AGL(1,ℤ/8)12yes—
265C22×D43#13712yes—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C2×C22⋊C412yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C432−1+411yescharacteristic
293C22⋊D43—28no—
294C22⋊D43—48no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—84no—
314C2×Dic43—84no—
315C2×Dic43C2×C22⋊C412yes—
316C2×Dic43C2×C22⋊C412yes—
317C2×Dic43C2×C22⋊C412yes—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—84no—
323C4×D43—84no—
324C8×C43—22no—
325C8×C43—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#22493—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43C22×C22⋊C411yescharacteristic
344C22×C43#54611yescharacteristic
345C22×C43#54711yescharacteristic
346C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C43C2×#13711yescharacteristic
348C22×C43#57611yescharacteristic
349C22×C43#57711yescharacteristic
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43#41714yes—
357C4×C43—22no—
358C4×C43—42no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43C4×#4111yescharacteristic
362C4×C43#52011yescharacteristic
363C4×C43#54611yescharacteristic
364C4×C43#54711yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—22no—
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43—81no—
372C2×#553—431no—
373C2×#435—431no—
374D4×C4⋊C4—431no—
375#1992—431no—
376#1989—431no—
377#1895D4311yescharacteristic, complemented
378#1893—431no—
379#1874—431no—
380#1874—431no—
381#1825—431no—
382#1824—431no—
383#1802—431no—
384#1762—431no—
385#1736—431no—
386C2×#340—431no—
387C2×C43—42no—
388C2×C43—82no—
389C2×C43#233911yescharacteristic
390C2×C43C2×#41711yescharacteristic
391C2×C43#289711yescharacteristic
392C2×C43#331811yescharacteristic
393C2×C43#332011yescharacteristic
394C2×C43#334511yescharacteristic
395C2×C43#334611yescharacteristic
396D43—24no—
397C22×M16C2×D4311yescharacteristic
398C23×C8—431no—
399#553—438no—
400#553—864no—
401C2×#126—861no—
402C2×#125—431no—
403C2×#123—861no—
404C2×#121—431no—
405C2×#121—861no—
406C2×#121C2×D4311yescharacteristic
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C2×C4×D4—861no—
410C2×C4×D4—861no—
411C2×#117—431no—
412C22×C4⋊C4—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4—431no—
415#435—864no—
416C2×C4⋊C8—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102C2×D4311yescharacteristic
420C2×#102C2×D4311yescharacteristic
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×#97—431no—
424#389—861no—
425#385—861no—
426#385—861no—
427#384—431no—
428#380—431no—
429#380C2×D4311yescharacteristic
430C4×C4⋊C4—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340C2×D4311yescharacteristic
442#340C2×D4311yescharacteristic
443C43#2249311yescharacteristic, complemented, Sylow
444C22×D4—21no—
445C22×D4—431no—
446C22×D4—861no—
447C22×D4C22×D4311yescharacteristic
448C23×C4—431no—
449C23×C4—861no—
450C23×C4—861no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8—1721no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#126—868no—
465#125—434no—
466#125—862no—
467#123—868no—
468#121—22no—
469#121—434no—
470#121—862no—
471#121—868no—
472#121C4×D4314yescomplemented
473C4×D4—434no—
474C4×D4—434no—
475C4×D4—434no—
476C4×D4—862no—
477C4×D4—868no—
478C4×D4—1724no—
479#117—434no—
480#117—862no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—434no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—862no—
488C2×C4⋊C4—862no—
489C2×C4⋊C4—862no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—1721no—
498C2×C4⋊C4—1721no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C42—431no—
511C2×C42—861no—
512C2×C42—861no—
513C4⋊C8—862no—
514#102—22no—
515#102—41no—
516#102—862no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—862no—
520#97—862no—
521#95—21no—
522#95—861no—
523#95—861no—
524C24—21no—
525C24—431no—
526C24D4×D4311yescharacteristic
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—434no—
536C2×D4—862no—
537C2×D4—862no—
538C2×D4—864no—
539C2×D4—1722no—
540C2×D4—1722no—
541C2×D4C2×C4×D4312yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—432no—
553C22×C4—432no—
554C22×C4—864no—
555C22×C4—864no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4C2×C4×D4312yes—
575C22×C4D4×D4311yescharacteristic
576C22×C4D4×D4312yes—
577C22×C4C23×D4311yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—1724no—
591C2×C8#1062190012yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—434no—
598C4⋊C4—432no—
599C4⋊C4—432no—
600C4⋊C4—432no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—3441no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4C2×C4×D4312yes—
614C22⋊C4—24no—
615C22⋊C4—42no—
616C22⋊C4—434no—
617C22⋊C4—434no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4—1722no—
622C42—432no—
623C42—432no—
624C42—864no—
625C42—1722no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—432no—
640C23—432no—
641C23—432no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23C22⋊C4×D4312yes—
647C23C2×D4×D4311yescharacteristic
648D4—22no—
649D4—22no—
650D4—41no—
651D4—41no—
652D4—84no—
653D4—868no—
654D4—1728no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—432no—
671C2×C4—432no—
672C2×C4—432no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—3444no—
687C2×C4—3444no—
688C2×C4—3444no—
689C2×C4—3444no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4C22⋊C4×D4312yes—
700C2×C4C22×C4×D4311yescharacteristic
701C2×C4C2×D4×D4311yescharacteristic
702C2×C4#41×D4311yescharacteristic
703C2×C4C2×#1062190011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337211yescharacteristic
706C8—22no—
707C8—41no—
708C8—1721no—
709C8—1721no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—434no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22C2×C22⋊C4×D4311yescharacteristic
732C22#1458353811yescharacteristic
733C22#1458354911yescharacteristic
734C22AGL(1,ℤ/8)×D4311yescharacteristic
735C22#137×D4311yescharacteristic
736C22#1458370311yescharacteristic
737C22#1458370911yescharacteristic
738C4—22no—
739C4—42no—
740C4—81no—
741C4—81no—
742C4—862no—
743C4—862no—
744C4—862no—
745C4—3441no—
746C4—1722no—
747C4—1722no—
748C4—1722no—
749C4C4×#1062190011yescharacteristic
750C4#1458337811yescharacteristic
751C4#1458353611yescharacteristic
752C4#1458354711yescharacteristic
753C2—42no—
754C2—82no—
755C2—864no—
756C2#1913742111yescharacteristic
757C2#417×D4311yescharacteristic
758C2#1914312011yescharacteristic
759C2#1914673111yescharacteristic
760C2#1914676111yescharacteristic
761C2#1914706011yescharacteristic
762C2#1914707511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#14583596C2
cosocleC22×C4×C43C24
hypercenter#1895D43
hypocenterC43#22493
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. #19137491C2semidirect
4. #19135562C2semidirect
5. #19135551C2semidirect
6. #19135020C2semidirect
7. #19134913C2semidirect
8. #19134909C2semidirect
9. #19134687C2semidirect
10. #19134684C2semidirect
11. #19134593C2semidirect
12. #19134422C2semidirect
13. #19134315C2semidirect
14. #340×D43C2semidirect
15. C43×#1895C2semidirect
18. #14583596C4semidirect
76. #13063316C2×C4semidirect
80. #13063296C2×C4semidirect
82. D4×Dic43C2×C4semidirect
88. #13063284C2×C4semidirect
106. C4⋊C4×D43C2×C4semidirect
133. #121×C43C2×C4semidirect
377. #1895D43semidirect
443. C43#22493semidirect
472. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835962
C2×#145829682
#191374912
#191355622
#191355512
#191350202
#191349132
#191349092
#191346872
#191346842
#191345932
#191344222
#191343152
#340×D432
C43×#18952
#2249343