Finite Group Databasebeta

← #25096426

Subgroups — #25096426

Order 11008.

1470 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2#407×D43C211yesmaximal, characteristic
3#19136976C211yesmaximal, characteristic
4#19134695C211yesmaximal, characteristic, complemented
5#19134694C211yesmaximal, characteristic, complemented
6#19134693C214yesmaximal, complemented
7#19134692C211yesmaximal, characteristic, complemented
8#19134303C214yesmaximal, complemented
9C43×#1826C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C2×M16×D43C2212yes—
12C2×#13063284C2211yescharacteristic
13C2×#13063283C411yescharacteristic, complemented
14C2×#13063283C411yescharacteristic, complemented
15C2×#13063282—21no—
16C2×#13063282C2212yes—
17C2×#13063281—21no—
18#117×D43—21no—
19#117×D43—21no—
20#117×D43—21no—
21#117×D43—21no—
22#117×D43C412yescomplemented
23#117×D43C412yescomplemented
24#117×D43C2212yes—
25#117×D43C2212yes—
26C2×C4⋊C4×D43C411yescharacteristic, complemented
27C2×C4⋊C4×D43C411yescharacteristic, complemented
28C2×C22⋊C4×D43—21no—
29C2×C42×D43—21no—
30#14582863C2211yescharacteristic
31#14582862C2212yes—
32#14582861—21no—
33#14582861—21no—
34C22⋊C8×D43—21no—
35C22⋊C8×D43—21no—
36#14582761—21no—
37#14582758—21no—
38#14582757—21no—
39#14582754—21no—
40C4×(C2×D43)⋊C4C2212yes—
41C4×C22⋊Dic43C2211yescharacteristic
42#14582660C2214yescomplemented
43#14582659C2214yescomplemented
44#14582658C2214yescomplemented
45C2×#117×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#339C2214yescomplemented
49C24×D43D411yescharacteristic
50C23×Dic43D411yescharacteristic
51C22×C4×D43—28no—
52C22×C4×D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43C2×C411yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621877C2312yes—
67C2×#10621872—22no—
68M16×D43—28no—
69C2×C8×D43—22no—
70#13063284—21no—
71#13063284—21no—
72#13063284C2×C412yes—
73#13063284C2312yes—
74#13063283—21no—
75#13063283—21no—
76#13063283—21no—
77#13063283—21no—
78#13063283C2×C412yes—
79#13063283C2×C412yes—
80#13063283C2×C412yes—
81#13063283C2×C412yes—
82#13063282—22no—
83#13063282—22no—
84#13063282—22no—
85#13063282—22no—
86#13063282—28no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—22no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43C2×C412yes—
101C4⋊C4×D43C2×C412yes—
102C4⋊C4×D43C2×C412yes—
103C4⋊C4×D43C2×C412yes—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C22⋊C4×D43—22no—
111C22⋊C4×D43—22no—
112C22⋊C4×D43—22no—
113C22⋊C4×D43—22no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2312yes—
118C42×D43—22no—
119C42×D43—22no—
120C42×D43—22no—
121C42×D43—22no—
122C22⋊(C43⋊C8)—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126C43⋊#95—21no—
127C43⋊#95—22no—
128C23×C4×C43C2311yescharacteristic
129C2×M16×C43C2312yes—
130#117×C43—21no—
131#117×C43—21no—
132#117×C43C2×C412yes—
133#117×C43C2312yes—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C4⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43C2312yes—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#95×C43—21no—
143C24×C43C2×D411yescharacteristic
144C23×D43—24no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43C22⋊C411yescharacteristic
148C23×D43C22⋊C411yescharacteristic
149C23×D43C22⋊C411yescharacteristic
150C23×D43C22⋊C411yescharacteristic
151C23×D43C2×D411yescharacteristic
152C23×D43C2×D411yescharacteristic
153C22×C4×C43—24no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—22no—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—24no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—22no—
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C22⋊C411yescharacteristic
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C22⋊C411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C2×C4×D43—24no—
174C2×C4×D43—24no—
175C2×C4×D43—24no—
176C2×C4×D43—24no—
177C2×C4×D43—24no—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—24no—
181C2×C4×D43—24no—
182C2×C4×D43—24no—
183C2×C4×D43—22no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—24no—
188C2×C4×D43—44no—
189C2×C4×D43—44no—
190C2×C4×D43C22⋊C411yescharacteristic
191C2×C4×D43C22⋊C411yescharacteristic
192C2×C4×D43C22⋊C411yescharacteristic
193C2×C4×D43C22⋊C411yescharacteristic
194C2×C4×D43C22⋊C411yescharacteristic
195C2×C4×D43C22⋊C411yescharacteristic
196C2×C4×D43C22⋊C411yescharacteristic
197C2×C4×D43C22⋊C411yescharacteristic
198C2×C4×D43C22×C411yescharacteristic
199C2×C4×D43C22×C411yescharacteristic
200C2×C4×D43C22×C411yescharacteristic
201C2×C4×D43C22×C411yescharacteristic
202C2×C4×D43C2×D411yescharacteristic
203C2×C4×D43C2×D411yescharacteristic
204C2×C4×D43C2×D411yescharacteristic
205C2×C4×D43C2×D411yescharacteristic
206C2×C4×D43#4118yes—
207M16×C43—24no—
208C2×C8×C43—22no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43C22×C412yes—
212C4⋊C4×C43C22×C412yes—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—42no—
216C42×C43—22no—
217C42×C43—22no—
218C42×C43—24no—
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—42no—
222(C2×D43)⋊C4—22no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—44no—
227(C2×D43)⋊C4—44no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C22×C412yes—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—44no—
237C4×Dic43—22no—
238C4×Dic43—22no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C4×Dic43—24no—
244#10621877—24no—
245C2×C43⋊C8—22no—
246#10621872—44no—
247C8×D43—44no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43C2×C22⋊C411yescharacteristic
252C23×C43C2×C22⋊C411yescharacteristic
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—416no—
272C22×D43C2×C22⋊C411yescharacteristic
273C22×D43C2×C22⋊C411yescharacteristic
274C22×D43C2×C22⋊C411yescharacteristic
275C22×D43C2×C22⋊C411yescharacteristic
276C22×D43#12314yes—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43C2×C22⋊C411yescharacteristic
290C2×C4×C43C2×C22⋊C411yescharacteristic
291C2×C4×C43C23×C411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C2×#4114yes—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43C2×C22⋊C411yescharacteristic
307C2×Dic43C2×C22⋊C411yescharacteristic
308C2×Dic43C2×C22⋊C411yescharacteristic
309C2×Dic43C2×C22⋊C411yescharacteristic
310C2×Dic43#12314yes—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—44no—
324C4×D43—44no—
325C4×D43—44no—
326C4×D43—44no—
327C4×D43#11714yes—
328C4×D43#11714yes—
329C4×D43#12314yes—
330C4×D43#12314yes—
331C8×C43—42no—
332C43⋊C8—42no—
333#20705—431nomaximal, Sylow
334C22×C43—21no—
335C22×C43—21no—
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—44no—
342C22×C43#42112yes—
343C22×C43C22×C22⋊C411yescharacteristic
344C22×C43C2×#12312yes—
345C2×D43—28no—
346C2×D43—21no—
347C2×D43—21no—
348C2×D43—21no—
349C2×D43—21no—
350C2×D43—21no—
351C2×D43—21no—
352C2×D43—21no—
353C2×D43—21no—
354C2×D43—21no—
355C2×D43—44no—
356C2×D43—44no—
357C2×D43—44no—
358C2×D43—44no—
359C2×D43—44no—
360C2×D43#38112yes—
361C2×D43#38112yes—
362C2×D43#42112yes—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43—82no—
368C4×C43C2×#11712yes—
369C4×C43C2×#12312yes—
370Dic43—21no—
371Dic43—21no—
372Dic43—42no—
373Dic43—42no—
374Dic43—82no—
375Dic43#38112yes—
376Dic43#38112yes—
377C22×#117—431no—
378C2×#407—431no—
379#2280—431no—
380#1826—431no—
381#1826—431no—
382#1826—434no—
383#1826—431no—
384#1826D4311yescharacteristic, complemented
385#1733—434no—
386C2×C43—22no—
387C2×C43—22no—
388C2×C43—41no—
389C2×C43C2×#38111yescharacteristic
390C2×C43C2×#42111yescharacteristic
391C2×C43C2×#42111yescharacteristic
392D43—22no—
393D43—22no—
394D43—22no—
395D43—41no—
396C24×C4—431no—
397C22×M16—432no—
398C2×#117—432no—
399C2×#117—431no—
400C2×#117—432no—
401C2×#117—432no—
402C2×#117—432no—
403C2×#117—432no—
404C2×#117—431no—
405C2×#117—431no—
406C2×#117—861no—
407C2×#117—861no—
408C2×#117—861no—
409C2×#117—861no—
410C2×#117—861no—
411C2×#117—861no—
412C2×#117C2×D4311yescharacteristic
413C22×C4⋊C4—431no—
414C22×C4⋊C4—431no—
415C22×C22⋊C4—861no—
416C22×C42—861no—
417#407—431no—
418#407—432no—
419#407—861no—
420#407—861no—
421#407C2×D4311yescharacteristic
422C2×C22⋊C8—861no—
423C2×C22⋊C8—861no—
424#381—861no—
425#380—861no—
426#380—861no—
427#379—861no—
428C4×C22⋊C4—431no—
429C4×C22⋊C4—432no—
430C4×C22⋊C4C2×D4311yescharacteristic
431#339—434no—
432#339—434no—
433#339—434no—
434#339C2×D4314yescomplemented
435C43#2070511yescharacteristic, complemented, Sylow
436C25—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—868no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C2×M16—432no—
455C2×M16—862no—
456C2×M16—868no—
457C2×M16C22×D4312yes—
458C22×C8—862no—
459#117—21no—
460#117—21no—
461#117—432no—
462#117—432no—
463#117—432no—
464#117—432no—
465#117—432no—
466#117—432no—
467#117—862no—
468#117—862no—
469#117—862no—
470#117—862no—
471#117—868no—
472#117—862no—
473#117—862no—
474#117—862no—
475#117—862no—
476#117—861no—
477#117—861no—
478#117—861no—
479#117—861no—
480#117—861no—
481#117—861no—
482#117C4×D4312yes—
483#117C22×D4312yes—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—432no—
487C2×C4⋊C4—432no—
488C2×C4⋊C4—432no—
489C2×C4⋊C4—432no—
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—862no—
497C2×C4⋊C4C4×D4311yescharacteristic
498C2×C4⋊C4C4×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—862no—
502C2×C22⋊C4—862no—
503C2×C22⋊C4—862no—
504C2×C22⋊C4—862no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—862no—
509C2×C22⋊C4—862no—
510C2×C22⋊C4—861no—
511C2×C42—21no—
512C2×C42—432no—
513C2×C42—862no—
514C2×C42—862no—
515C2×C42—862no—
516C2×C42—862no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42C22×D4312yes—
521C22⋊C8—21no—
522C22⋊C8—21no—
523C22⋊C8—862no—
524C22⋊C8—862no—
525C22⋊C8—861no—
526C22⋊C8—861no—
527#95—21no—
528#95—862no—
529#95—861no—
530C24—431no—
531C24—431no—
532C24—431no—
533C24—431no—
534C24—431no—
535C24—431no—
536C24—864no—
537C24—1722no—
538C24—1722no—
539C24D4×D4311yescharacteristic
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—438no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—864no—
568C22×C4—864no—
569C22×C4—864no—
570C22×C4—864no—
571C22×C4—864no—
572C22×C4—864no—
573C22×C4—864no—
574C22×C4—864no—
575C22×C4—864no—
576C22×C4—864no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—862no—
586C22×C4—1724no—
587C22×C4—1724no—
588C22×C4C2×C4×D4311yescharacteristic
589C22×C4C2×C4×D4311yescharacteristic
590C22×C4D4×D4311yescharacteristic
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4311yescharacteristic
593C22×C4C23×D4311yescharacteristic
594M16—24no—
595M16—864no—
596M16—1724no—
597C2×C8—22no—
598C2×C8—862no—
599C2×C8—1724no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—432no—
603C4⋊C4—432no—
604C4⋊C4—862no—
605C4⋊C4—862no—
606C4⋊C4—862no—
607C4⋊C4—862no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—1724no—
611C4⋊C4C2×C4×D4312yes—
612C4⋊C4C2×C4×D4312yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C22⋊C4—1724no—
623C22⋊C4—1724no—
624C22⋊C4—1722no—
625C42—22no—
626C42—22no—
627C42—24no—
628C42—862no—
629C42—862no—
630C42—862no—
631C42—862no—
632C42—862no—
633C42—862no—
634C42—864no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—431no—
639C23—431no—
640C23—431no—
641C23—434no—
642C23—431no—
643C23—862no—
644C23—862no—
645C23—862no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—862no—
651C23—862no—
652C23—862no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23—1721no—
660C23—17216no—
661C23C22⋊C4×D4311yescharacteristic
662C23C22⋊C4×D4311yescharacteristic
663C23C2×D4×D4311yescharacteristic
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—431no—
677C2×C4—431no—
678C2×C4—434no—
679C2×C4—434no—
680C2×C4—434no—
681C2×C4—434no—
682C2×C4—434no—
683C2×C4—431no—
684C2×C4—431no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—1724no—
705C2×C4—1724no—
706C2×C4—1724no—
707C2×C4—1724no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4C22⋊C4×D4311yescharacteristic
714C2×C4C22⋊C4×D4311yescharacteristic
715C2×C4C22×C4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4#41×D4314yes—
718C8—42no—
719C8—1722no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—432no—
729C22—432no—
730C22—432no—
731C22—868no—
732C22—861no—
733C22—861no—
734C22—861no—
735C22—861no—
736C22—861no—
737C22—861no—
738C22—861no—
739C22—861no—
740C22—861no—
741C22—1724no—
742C22—1724no—
743C22—1724no—
744C22—1724no—
745C22—1724no—
746C22#1458291412yes—
747C22C2×C22⋊C4×D4311yescharacteristic
748C22#123×D4312yes—
749C4—21no—
750C4—21no—
751C4—42no—
752C4—42no—
753C4—82no—
754C4—432no—
755C4—432no—
756C4—861no—
757C4—861no—
758C4—3442no—
759C4—1722no—
760C4—1722no—
761C4#117×D4312yes—
762C4#123×D4312yes—
763C2—22no—
764C2—22no—
765C2—41no—
766C2—862no—
767C2—862no—
768C2—862no—
769C2—1721no—
770C2#381×D4311yescharacteristic
771C2#421×D4311yescharacteristic
772C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#20705
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #19134695C2semidirect
5. #19134694C2semidirect
6. #19134693C2semidirect
7. #19134692C2semidirect
8. #19134303C2semidirect
9. C43×#1826C2semidirect
13. C2×#13063283C4semidirect
14. C2×#13063283C4semidirect
22. #117×D43C4semidirect
23. #117×D43C4semidirect
26. C2×C4⋊C4×D43C4semidirect
27. C2×C4⋊C4×D43C4semidirect
42. #14582660C22semidirect
43. #14582659C22semidirect
44. #14582658C22semidirect
48. C43×#339C22semidirect
384. #1826D43semidirect
434. #339C2×D43semidirect
435. C43#20705semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
#407×D432
#191369762
#191346952
#191346942
#191346932
#191346922
#191343032
C43×#18262
#2070543