Finite Group Databasebeta

← #25113053

Subgroups — #25113053

Order 11008.

1246 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×#14583612C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
4#19135554C211yesmaximal, characteristic, complemented
5#19135541C211yesmaximal, characteristic, complemented
6#19135033C211yesmaximal, characteristic, complemented
7#19135032C211yesmaximal, characteristic, complemented
8#19134912C211yesmaximal, characteristic, complemented
9#19134911C211yesmaximal, characteristic, complemented
10#19134690C211yesmaximal, characteristic, complemented
11#19134689C211yesmaximal, characteristic, complemented
12#19134594C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17#14583612—24no—
18#14583612C418yescomplemented
19C2×#13063324C2211yescharacteristic
20C2×#13063313—21no—
21C2×#13063311—21no—
22C2×#13063300C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063298—21no—
25C2×#13063287C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063282—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31#14582975—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40#14582794—21no—
41#14582772—21no—
42#14582770—21no—
43#14582768C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×D172—21no—
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43D411yescharacteristic
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C2×#10621872—22no—
71C2×#10621872—22no—
72C2×#10621872—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324—22no—
76#13063324C2×C414yescomplemented
77#13063313—28no—
78#13063311—28no—
79#13063300—22no—
80#13063300C2×C414yescomplemented
81#13063299—22no—
82#13063299C2×C414yescomplemented
83#13063298—28no—
84#13063287—22no—
85#13063287C2×C414yescomplemented
86C4×C22⋊D43—44no—
87C4×C22⋊D43C2×C414yes—
88C4×C22⋊D43D414yes—
89#13063283—22no—
90#13063283C2×C414yescomplemented
91#13063282—28no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C4⋊C4×D43—22no—
101C4⋊C4×D43—41no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
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×Dic43C2311yescharacteristic
113Dic43⋊C8—22no—
114#13063247—22no—
115#13063247—41no—
116#13063245—22no—
117#13063245—41no—
118C22⋊(C43⋊C8)—22no—
119(C2×D43)⋊C8—22no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C23×C4×C43—21no—
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43—22no—
127C2×M16×C43—22no—
128C2×M16×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#117×C43—22no—
132#117×C43C2×C414yescomplemented
133C2×C4⋊C4×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—41no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C42×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43—21no—
144C23×D43C2×D411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—81no—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—81no—
164C2×C22⋊D43—81no—
165C2×C22⋊D43C22⋊C414yes—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×D172—21no—
173C2×D172—24no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—81no—
179C2×D172—81no—
180C2×D172C22×C412yes—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—24no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43C22×C412yes—
192C2×C4×D43C2×D412yes—
193C2×Dic86—24no—
194C2×Dic86—81no—
195C2×Dic86—81no—
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×C43—42no—
209C4⋊C4×C43C22×C412yes—
210C4⋊C4×C43C22×C412yes—
211C4⋊C4×C43#4112yes—
212C22⋊C4×C43—24no—
213C42×C43—24no—
214C22⋊Dic43—42no—
215C22⋊Dic43C22⋊C414yes—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—24no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4C22⋊C414yes—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43C22×C412yes—
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—
243#10621872—44no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43C2×C22⋊C412yes—
251C23×C43C22×D411yescharacteristic
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—22no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43C2×C22⋊C412yes—
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—22no—
274C2×C4×C43—22no—
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×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—84no—
285C2×C4×C43C2×C22⋊C412yes—
286C2×C4×C43C23×C411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C432−1+411yescharacteristic
292C22⋊D43—28no—
293C22⋊D43—84no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
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×Dic43C2×C22⋊C412yes—
308C2×Dic43C2×C22⋊C412yes—
309C2×Dic43C2×C22⋊C412yes—
310C2×Dic43AGL(1,ℤ/8)12yes—
311C2×Dic43#13712yes—
312D172—22no—
313D172—22no—
314D172—41no—
315D172—41no—
316D172—84no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—48no—
322C4×D43—84no—
323Dic86—84no—
324C8×C43—22no—
325C8×C43—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#22503—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C22×C22⋊C411yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43#54711yescharacteristic
339C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C43C2×#13711yescharacteristic
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—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C4×C43—22no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43—81no—
362C4×C43C4×#4111yescharacteristic
363C4×C43#52011yescharacteristic
364C4×C43#54611yescharacteristic
365C4×C43#54711yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—42no—
369Dic43—81no—
370Dic43—81no—
371Dic43#41714yes—
372C2×#555—431no—
373C2×#436—431no—
374D4×C4⋊C4—431no—
375#1990—431no—
376#1987—431no—
377#1895—431no—
378#1895—431no—
379#1874—431no—
380#1874—431no—
381#1825—431no—
382#1825—431no—
383#1802—431no—
384C4×#102—431no—
385#1736—431no—
386#1736D4311yescharacteristic, complemented
387C2×C43—42no—
388C2×C43#233911yescharacteristic
389C2×C43C2×#41711yescharacteristic
390C2×C43#289711yescharacteristic
391C2×C43#332511yescharacteristic
392C2×C43#332911yescharacteristic
393C2×C43#335411yescharacteristic
394C2×C43#335711yescharacteristic
395D43—42no—
396D43—82no—
397C22×M16—431no—
398C22×M16C2×D4311yescharacteristic
399#555—438no—
400#555—864no—
401C2×C4⋊Q8—431no—
402C2×#124—861no—
403C2×#124—861no—
404C2×#121—431no—
405C2×#121—431no—
406C2×#121—861no—
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C2×C4×D4—861no—
410C2×#117—431no—
411C2×#117—861no—
412C2×#117C2×D4311yescharacteristic
413C22×C4⋊C4—431no—
414C22×C4⋊C4C2×D4311yescharacteristic
415#436—864no—
416C2×C4⋊C8—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C4×C8—431no—
424#389—861no—
425#385—861no—
426#385—861no—
427#384—431no—
428#380—431no—
429#380—431no—
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#340C2×D4311yescharacteristic
440#340C2×D4311yescharacteristic
441#340C2×D4311yescharacteristic
442#340C2×D4311yescharacteristic
443C43#2250311yescharacteristic, complemented, Sylow
444C22×Q8—861no—
445C22×D4—431no—
446C22×D4—431no—
447C22×D4—861no—
448C22×D4—861no—
449C23×C4—21no—
450C23×C4—431no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C2×M16—862no—
458C2×M16—862no—
459C2×M16—1721no—
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C4⋊Q8—434no—
465C4⋊Q8—862no—
466#124—868no—
467#124—868no—
468#121—434no—
469#121—434no—
470#121—868no—
471#121—862no—
472#121—862no—
473C4×D4—434no—
474C4×D4—434no—
475C4×D4—434no—
476C4×D4—862no—
477C4×D4—1724no—
478#117—22no—
479#117—434no—
480#117—868no—
481#117—862no—
482#117C4×D4314yescomplemented
483C2×C4⋊C4—22no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—862no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—1721no—
496C2×C4⋊C4C22×D4311yescharacteristic
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C42—21no—
510C2×C42—431no—
511C2×C42—861no—
512C2×C42—861no—
513C4⋊C8—862no—
514#102—862no—
515#102—862no—
516#102—1721no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—862no—
520C4×C8—862no—
521#95—861no—
522#95—861no—
523#95—861no—
524C24—431no—
525C24—861no—
526C24D4×D4311yescharacteristic
527C2×Q8—864no—
528C2×Q8—3441no—
529C2×Q8—3441no—
530C2×D4—434no—
531C2×D4—432no—
532C2×D4—864no—
533C2×D4—862no—
534C2×D4—862no—
535C2×D4—864no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—3441no—
542C2×D4—3441no—
543C2×D4—3441no—
544C2×D4—3441no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—864no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
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—
579M16—1724no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8#1062189812yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—434no—
599C4⋊C4—432no—
600C4⋊C4—864no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—3441no—
607C4⋊C4—1722no—
608C4⋊C4—1722no—
609C4⋊C4C2×C4×D4312yes—
610C4⋊C4C2×C4×D4312yes—
611C4⋊C4#1062189812yes—
612C22⋊C4—24no—
613C22⋊C4—434no—
614C22⋊C4—434no—
615C22⋊C4—864no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C42—24no—
622C42—432no—
623C42—432no—
624C42—864no—
625C42—1722no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—432no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—862no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23C22⋊C4×D4312yes—
647C23C2×D4×D4311yescharacteristic
648Q8—3444no—
649D4—868no—
650D4—862no—
651D4—862no—
652D4—3444no—
653D4—3444no—
654D4—1721no—
655D4—1721no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—84no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—3444no—
690C2×C4—1728no—
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×C4C2×#1062189811yescharacteristic
703C2×C4C2×#1062189811yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337311yescharacteristic
706C8—22no—
707C8—41no—
708C8—1721no—
709C8—1721no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—3441no—
721C22—3441no—
722C22—3441no—
723C22—3441no—
724C22—1722no—
725C22—1722no—
726C22—1722no—
727C22—1721no—
728C22—1721no—
729C22—1721no—
730C22—1721no—
731C22C2×C22⋊C4×D4311yescharacteristic
732C22#1458353911yescharacteristic
733C22#1458355011yescharacteristic
734C22AGL(1,ℤ/8)×D4311yescharacteristic
735C22#137×D4311yescharacteristic
736C22#1458370311yescharacteristic
737C22#1458370811yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—81no—
743C4—434no—
744C4—862no—
745C4—862no—
746C4—3441no—
747C4—3441no—
748C4—1722no—
749C4C4×#1062189811yescharacteristic
750C4#1458338011yescharacteristic
751C4#1458353911yescharacteristic
752C4#1458355011yescharacteristic
753C2—42no—
754C2—3442no—
755C2—1722no—
756C2#1913742211yescharacteristic
757C2#417×D4311yescharacteristic
758C2#1914311911yescharacteristic
759C2#1914683311yescharacteristic
760C2#1914688511yescharacteristic
761C2#1914718611yescharacteristic
762C2#1914721711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC2×#14583612C2
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#22503
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C4⋊C4×C22⋊D43C2semidirect
4. #19135554C2semidirect
5. #19135541C2semidirect
6. #19135033C2semidirect
7. #19135032C2semidirect
8. #19134912C2semidirect
9. #19134911C2semidirect
10. #19134690C2semidirect
11. #19134689C2semidirect
12. #19134594C2semidirect
13. #19134409C2semidirect
14. #19134313C2semidirect
15. C43×#1736C2semidirect
18. #14583612C4semidirect
76. #13063324C2×C4semidirect
80. #13063300C2×C4semidirect
82. #13063299C2×C4semidirect
85. #13063287C2×C4semidirect
90. #13063283C2×C4semidirect
132. #117×C43C2×C4semidirect
386. #1736D43semidirect
443. C43#22503semidirect
482. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836122
C2×#145829752
C4⋊C4×C22⋊D432
#191355542
#191355412
#191350332
#191350322
#191349122
#191349112
#191346902
#191346892
#191345942
#191344092
#191343132
C43×#17362
#2250343