Finite Group Databasebeta

← D43×#2077 #25125421

Subgroups — D43×#2077 #25125421

Order 11008.

1270 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×#106×D43C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D43C211yesmaximal, characteristic
3#380×D43C211yesmaximal, characteristic
4#380×D43C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic, complemented
6#19136033C211yesmaximal, characteristic, complemented
7#19136032C211yesmaximal, characteristic, complemented
8#19136031C211yesmaximal, characteristic, complemented
9#19136030C211yesmaximal, characteristic, complemented
10#19136029C211yesmaximal, characteristic, complemented
11#19136028C211yesmaximal, characteristic, complemented
12#340×D43C211yesmaximal, characteristic, complemented
13#340×D43C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#2077C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24C2×C22⋊C4×D43—21no—
25C2×#13063257C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28#106×D43—24no—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C22⋊C8×D43—24no—
33#14582759C2211yescharacteristic
34#14582759C2211yescharacteristic
35#14582758—21no—
36#14582758—21no—
37#14582757—21no—
38#14582757—21no—
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#95×D43—21no—
44#95×D43—21no—
45#14582662C2211yescharacteristic, complemented
46#14582662C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54C2×#106×C43C2211yescharacteristic, complemented
55C2×C22⋊C8×C43C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C24×D43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43D411yescharacteristic
74C22×C4×D43D411yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—22no—
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43D414yes—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—22no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C22⋊C4×D43—44no—
108C22⋊C4×D43—44no—
109#13063257—22no—
110#13063256—22no—
111#13063256—22no—
112C22⋊(C43⋊C8)—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130#106×C43—22no—
131C22⋊C8×C43—22no—
132#95×C43—21no—
133#95×C43—21no—
134C24×C43C2×D411yescharacteristic
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—22no—
139C23×D43—22no—
140C23×D43—22no—
141C23×D43SD1614yes—
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
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—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—44no—
178C2×C4×D43—44no—
179C2×C4×D43—44no—
180C2×C4×D43—44no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43C2×D412yes—
194C2×C4×D43#4112yes—
195C2×C4×D43#4112yes—
196C2×C4×D43#4112yes—
197C2×C4×D43#4112yes—
198C2×C4×D43#4112yes—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43C2×D412yes—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C2×D412yes—
239C8×D43—28no—
240C8×D43—44no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43C2×SD1612yes—
248C23×C43C22×D411yescharacteristic
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—28no—
256C22×D43—28no—
257C22×D43—28no—
258C22×D43—44no—
259C22×D43—44no—
260C22×D43—44no—
261C22×D43—44no—
262C22×D43#12112yes—
263C22×D43#12312yes—
264C22×D43#12312yes—
265C22×D43C2×SD1612yes—
266C22×D43C2×SD1612yes—
267C22×D43#13512yes—
268C22×D43AGL(1,ℤ/8)12yes—
269C22×D43#13712yes—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
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×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—44no—
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—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43#12112yes—
312C2×Dic43#12312yes—
313C2×Dic43#12312yes—
314C4×D43—44no—
315C4×D43—41no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—44no—
320C4×D43—84no—
321C4×D43—84no—
322C4×D43—84no—
323C4×D43—84no—
324C4×D43#12314yes—
325C4×D43#12414yes—
326C4×D43#12614yes—
327C4×D43#12614yes—
328C8×C43—22no—
329C8×C43—41no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332C2×#2077—431nomaximal, Sylow
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43C2×#12111yescharacteristic
341C22×C43C2×#12311yescharacteristic
342C22×C43C2×#12311yescharacteristic
343C22×C43C22×SD1611yescharacteristic
344C22×C43C2×#13511yescharacteristic
345C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C43C2×#13711yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—41no—
354C2×D43—416no—
355C2×D43#39714yes—
356C2×D43#46514yes—
357C2×D43#46814yes—
358C2×D43#48114yes—
359C2×D43#48214yes—
360C2×D43#48314yes—
361C2×D43#48514yes—
362C4×C43—41no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43C2×#12311yescharacteristic
368C4×C43C2×#12411yescharacteristic
369C4×C43C2×#12611yescharacteristic
370C4×C43C2×#12611yescharacteristic
371Dic43—41no—
372Dic43—81no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376Dic43#39714yes—
377C22×#106—431no—
378C22×C22⋊C8—431no—
379C2×#380—431no—
380C2×#380—431no—
381#2077—431no—
382#2077—431no—
383#2077—431no—
384#2077—431no—
385#2077—431no—
386#2077—431no—
387#2077—431no—
388#2077D4311yescharacteristic, direct product factor
389C2×#340—431no—
390C2×#340—431no—
391C2×#340—431no—
392C2×C43—42no—
393C2×C43C2×#39711yescharacteristic
394C2×C43C2×#46511yescharacteristic
395C2×C43C2×#46811yescharacteristic
396C2×C43C2×#48311yescharacteristic
397C2×C43C2×#48211yescharacteristic
398C2×C43C2×#48511yescharacteristic
399C2×C43C2×#48111yescharacteristic
400D43—42no—
401D43#207718yesdirect product factor
402C24×C4—431no—
403C23×C8—431no—
404C23×C8—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4—431no—
408C22×C4⋊C4—431no—
409C22×C22⋊C4—861no—
410C22×C22⋊C4—861no—
411C2×#106—431no—
412C2×#106—431no—
413C2×#106—431no—
414C2×#106—864no—
415C2×#106C2×D4311yescharacteristic, complemented
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419C2×C22⋊C8—864no—
420C2×C22⋊C8C2×D4311yescharacteristic
421#380—431no—
422#380—431no—
423#380—431no—
424#380—431no—
425#380—431no—
426#380—431no—
427#380—861no—
428#380—861no—
429#380—861no—
430#380—861no—
431#380C2×D4311yescharacteristic
432#380C2×D4311yescharacteristic
433C2×#95—861no—
434C2×#95—861no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340C2×D4311yescharacteristic, complemented
445#340C2×D4311yescharacteristic, complemented
446#340C2×D4311yescharacteristic, complemented
447C43C2×#207711yescharacteristic, complemented, Sylow
448C25—431no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—862no—
455C23×C4—862no—
456C23×C4—862no—
457C23×C4—862no—
458C23×C4—862no—
459C23×C4—862no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C22×C8—431no—
466C22×C8—434no—
467C22×C8—431no—
468C22×C8—862no—
469C22×C8—862no—
470C22×C8—862no—
471C22×C8—862no—
472C22×C8—862no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—862no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—862no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C4⋊C4C22×D4311yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—1724no—
504C2×C22⋊C4—1724no—
505#106—22no—
506#106—862no—
507#106—862no—
508#106—862no—
509C22⋊C8—22no—
510C22⋊C8—862no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513#95—21no—
514#95—21no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521C24—431no—
522C24—434no—
523C24—431no—
524C24—862no—
525C24—862no—
526C24—862no—
527C24—862no—
528C24—862no—
529C24—862no—
530C24D4×D4311yescharacteristic
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
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—432no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—431no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—1724no—
569C22×C4—1724no—
570C22×C4—1724no—
571C22×C4—1724no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4—1722no—
584C22×C4D4×D4311yescharacteristic
585C22×C4C23×D4311yescharacteristic
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—432no—
592C2×C8—868no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—1724no—
599C2×C8D4×D4312yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—1722no—
617C4⋊C4—1722no—
618C4⋊C4—1722no—
619C4⋊C4—1722no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C22⋊C4—1722no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—432no—
638C23—432no—
639C23—432no—
640C23—432no—
641C23—432no—
642C23—868no—
643C23—868no—
644C23—868no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—1724no—
652C23—1724no—
653C23—1724no—
654C23—1724no—
655C23SD16×D4312yes—
656C23C2×D4×D4311yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
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—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—432no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—434no—
680C2×C4—434no—
681C2×C4—434no—
682C2×C4—434no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—3444no—
687C2×C4—3444no—
688C2×C4—3444no—
689C2×C4—3444no—
690C2×C4—1724no—
691C2×C4—1724no—
692C2×C4—1724no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4#41×D4311yescharacteristic
711C2×C4#41×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4#41×D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C8—22no—
716C8—41no—
717C8—862no—
718C8—1721no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—434no—
727C22—434no—
728C22—434no—
729C22—434no—
730C22—434no—
731C22—434no—
732C22—434no—
733C22—862no—
734C22—862no—
735C22—862no—
736C22—17216no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22#121×D4311yescharacteristic
742C22#123×D4311yescharacteristic
743C22#123×D4311yescharacteristic
744C22C2×SD16×D4311yescharacteristic
745C22#135×D4311yescharacteristic
746C22AGL(1,ℤ/8)×D4311yescharacteristic
747C22#137×D4311yescharacteristic
748C4—41no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—434no—
754C4—3441no—
755C4—3441no—
756C4—3441no—
757C4—3441no—
758C4—1721no—
759C4#123×D4311yescharacteristic
760C4#124×D4311yescharacteristic
761C4#126×D4311yescharacteristic
762C4#126×D4311yescharacteristic
763C2—42no—
764C2—438no—
765C2—1722no—
766C2#397×D4311yescharacteristic
767C2#465×D4311yescharacteristic
768C2#468×D4311yescharacteristic
769C2#483×D4311yescharacteristic
770C2#482×D4311yescharacteristic
771C2#485×D4311yescharacteristic
772C2#481×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2077C2
socleC23×C43C22×D4
prime radicalC24×D43D4
hypercenter#2077D43
hypocenterC43C2×#2077
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#106×D43C2semidirect
5. #19136034C2semidirect
6. #19136033C2semidirect
7. #19136032C2semidirect
8. #19136031C2semidirect
9. #19136030C2semidirect
10. #19136029C2semidirect
11. #19136028C2semidirect
12. #340×D43C2semidirect
13. #340×D43C2semidirect
14. #340×D43C2semidirect
15. C43×#2077C2semidirect
25. C2×#13063257C22semidirect
26. C2×#13063256C22semidirect
27. C2×#13063256C22semidirect
45. #14582662C22semidirect
46. #14582662C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. C2×#106×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
388. #2077D43direct (N × H)
401. D43#2077direct (N × H)
415. C2×#106C2×D43semidirect
444. #340C2×D43semidirect
445. #340C2×D43semidirect
446. #340C2×D43semidirect
447. C43C2×#2077semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D432
C2×C22⋊C8×D432
#380×D432
#191360342
#191360332
#191360322
#191360312
#191360302
#191360292
#191360282
#340×D432
C43×#20772
C2×#207743