Finite Group Databasebeta

← D43×#1936 #25099223

Subgroups — D43×#1936 #25099223

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D43C211yesmaximal, characteristic
2C2×#102×D43C211yesmaximal, characteristic
3C2×#97×D43C211yesmaximal, characteristic, complemented
4#390×D43C211yesmaximal, characteristic
5#389×D43C211yesmaximal, characteristic, complemented
6#19135295C211yesmaximal, characteristic, complemented
7#19135294C211yesmaximal, characteristic, complemented
8#19135293C211yesmaximal, characteristic, complemented
9#19135292C211yesmaximal, characteristic, complemented
10#19135291C211yesmaximal, characteristic, complemented
11#19135290C211yesmaximal, characteristic, complemented
12#19135289C211yesmaximal, characteristic, complemented
13#340×D43C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×C4⋊C4×D43—21no—
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C22⋊C4×D43—21no—
24C2×C22⋊C4×D43—21no—
25C2×C42×D43C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32#102×D43—24no—
33#102×D43C418yescomplemented
34C2×#13063236C2211yescharacteristic, complemented
35C2×#13063235C2211yescharacteristic, complemented
36C2×#13063235C2211yescharacteristic, complemented
37#97×D43—24no—
38#14582802C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582799—21no—
42#14582799—21no—
43#14582798C2211yescharacteristic, complemented
44#14582797C2211yescharacteristic, complemented
45#14582796—21no—
46#14582795C2211yescharacteristic, complemented
47#14582794—21no—
48#95×D43—21no—
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic, complemented
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C2×D4×D43—22no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43C2×C414yes—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43D411yescharacteristic
75C22×C4×D43D411yescharacteristic
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×D43C2×C414yes—
84C2×C8×D43D414yes—
85C2×C4⋊Dic43—21no—
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—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—22no—
95C4⋊C4×D43—22no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—44no—
100C4⋊C4×D43C2×C414yes—
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—
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C42×D43—22no—
113C42×D43—22no—
114#13063247—22no—
115#13063247C2×C414yescomplemented
116#13063246—22no—
117#13063246C2×C414yescomplemented
118#13063245—22no—
119#13063245C2×C414yescomplemented
120#13063236—22no—
121#13063235—22no—
122#13063235—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C22×D4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#102×C43—22no—
137#102×C43C2×C414yescomplemented
138#97×C43—22no—
139#95×C43—21no—
140C24×C43—21no—
141C23×D43—21no—
142C23×D43—24no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43—42no—
149C23×D43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43C22×C412yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—24no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171D4×D43—28no—
172D4×D43—28no—
173D4×D43—44no—
174D4×D43—44no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172C22×C412yes—
181C2×C4×D43—24no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43C22×C412yes—
197C2×C4×D43C2×D412yes—
198C2×C4×D43#4112yes—
199C2×C4×D43#4112yes—
200C2×C4×D43#4112yes—
201C2×C4×D43#4112yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C22×C412yes—
207C2×C8×C43C2×D412yes—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—42no—
214C4⋊C4×C43C22×C412yes—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C42×C43—21no—
218C42×C43—21no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8C22×C412yes—
246C2×C43⋊C8C2×D412yes—
247C8×D43—28no—
248C8×D43—28no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C22×D411yescharacteristic
257C22×D43—22no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—48no—
265C22×D43—48no—
266C22×D43—48no—
267C22×D43—84no—
268C22×D43—84no—
269C22×D43—84no—
270C22×D43—84no—
271C22×D43C4×D412yes—
272C22×D43#12112yes—
273C22×D43#12412yes—
274C22×D43AGL(1,ℤ/8)12yes—
275C22×D43AGL(1,ℤ/8)12yes—
276C22×D43AGL(1,ℤ/8)12yes—
277C22×D43#13712yes—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—41no—
281D4×C43—41no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43C23×C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C22⋊D43—48no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43C4×D412yes—
320C2×Dic43#12112yes—
321C2×Dic43#12412yes—
322D172—22no—
323D172—22no—
324D172—41no—
325D172—41no—
326C4×D43—48no—
327C4×D43—44no—
328C4×D43—44no—
329C4×D43—84no—
330C4×D43—84no—
331C4×D43#11714yes—
332C4×D43C4×D414yes—
333C4×D43#12314yes—
334C4×D43#12614yes—
335C8×C43—22no—
336C8×C43—22no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339C2×#1936—431nomaximal, Sylow
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43C2×#12111yescharacteristic
349C22×C43C2×#12411yescharacteristic
350C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C43C2×#13711yescharacteristic
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—816no—
362C2×D43#38814yes—
363C2×D43#44014yes—
364C2×D43#44214yes—
365C2×D43#46814yes—
366C2×D43#46914yes—
367C2×D43#48914yes—
368C2×D43#49014yes—
369C4×C43—42no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—81no—
373C4×C43—81no—
374C4×C43C2×#11711yescharacteristic
375C4×C43C2×C4×D411yescharacteristic
376C4×C43C2×#12311yescharacteristic
377C4×C43C2×#12611yescharacteristic
378Dic43—42no—
379Dic43—41no—
380Dic43—41no—
381Dic43—81no—
382Dic43—81no—
383Dic43#38814yes—
384C22×#102—431no—
385C22×#102—431no—
386C22×#97—431no—
387C2×#390—431no—
388C2×#389—431no—
389#1936—431no—
390#1936—431no—
391#1936—431no—
392#1936—431no—
393#1936—431no—
394#1936—431no—
395#1936—431no—
396#1936D4311yescharacteristic, direct product factor
397C2×#340—431no—
398C2×#340—431no—
399C2×C43—82no—
400C2×C43C2×#38811yescharacteristic
401C2×C43C2×#44011yescharacteristic
402C2×C43C2×#44211yescharacteristic
403C2×C43C2×#46811yescharacteristic
404C2×C43C2×#46911yescharacteristic
405C2×C43C2×#48911yescharacteristic
406C2×C43C2×#49011yescharacteristic
407D43—82no—
408D43#193618yesdirect product factor
409C23×D4—431no—
410C23×C8—431no—
411C23×C8—431no—
412C22×C4⋊C4—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—861no—
416C22×C22⋊C4—861no—
417C22×C22⋊C4—861no—
418C22×C42—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—438no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—864no—
427C2×#102C2×D4311yescharacteristic
428C2×#102C2×D4311yescharacteristic
429C2×#97—431no—
430C2×#97—431no—
431C2×#97—431no—
432C2×#97—864no—
433C2×#97C2×D4311yescharacteristic, complemented
434#390—431no—
435#390—431no—
436#390—431no—
437#390—861no—
438#390—861no—
439#390C2×D4311yescharacteristic
440#389—431no—
441#389—431no—
442#389—431no—
443#389—861no—
444#389—861no—
445#389C2×D4311yescharacteristic, complemented
446C2×#95—861no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340C2×D4311yescharacteristic, complemented
454#340C2×D4311yescharacteristic, complemented
455C43C2×#193611yescharacteristic, complemented, Sylow
456C25—861no—
457C22×D4—434no—
458C22×D4—431no—
459C22×D4—862no—
460C22×D4—862no—
461C22×D4—862no—
462C22×D4—862no—
463C22×D4—862no—
464C22×D4—861no—
465C22×D4C22×D4311yescharacteristic
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—861no—
470C23×C4—861no—
471C23×C4—861no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—434no—
475C22×C8—434no—
476C22×C8—862no—
477C22×C8—862no—
478C22×C8—862no—
479C22×C8—862no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C2×C4⋊C4—21no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—434no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—862no—
488C2×C4⋊C4—862no—
489C2×C4⋊C4—862no—
490C2×C4⋊C4—862no—
491C2×C4⋊C4—862no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—1724no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—1724no—
511C2×C22⋊C4—1724no—
512C2×C42—431no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—862no—
516C2×C42—862no—
517C2×C42C22×D4311yescharacteristic
518#102—22no—
519#102—434no—
520#102—434no—
521#102—434no—
522#102—862no—
523#102—862no—
524#102—862no—
525#102C4×D4314yescomplemented
526#97—22no—
527#97—862no—
528#97—862no—
529#97—862no—
530#95—21no—
531#95—861no—
532#95—861no—
533#95—861no—
534C24—21no—
535C24—431no—
536C24—864no—
537C24—861no—
538C24—1722no—
539C24—1722no—
540C24—1722no—
541C24—1722no—
542C24—1722no—
543C24—1722no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—432no—
550C2×D4—868no—
551C2×D4—868no—
552C2×D4—864no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—1724no—
559C2×D4—1724no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4C2×C4×D4312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—431no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—864no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4D4×D4311yescharacteristic
594C22×C4D4×D4311yescharacteristic
595C22×C4C23×D4311yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—432no—
601C2×C8—432no—
602C2×C8—868no—
603C2×C8—868no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8C2×C4×D4312yes—
609C2×C8D4×D4312yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—1722no—
624C4⋊C4—1722no—
625C4⋊C4—1722no—
626C4⋊C4—1722no—
627C4⋊C4—1722no—
628C4⋊C4C2×C4×D4312yes—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—1722no—
632C22⋊C4—1722no—
633C22⋊C4—1722no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—21no—
638C42—21no—
639C42—862no—
640C42—862no—
641C42—861no—
642C42—861no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—432no—
651C23—432no—
652C23—432no—
653C23—432no—
654C23—432no—
655C23—432no—
656C23—432no—
657C23—862no—
658C23—3444no—
659C23—3444no—
660C23—3444no—
661C23—3444no—
662C23—1728no—
663C23—1728no—
664C23—1728no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23C2×D4×D4311yescharacteristic
672D4—22no—
673D4—22no—
674D4—41no—
675D4—41no—
676D4—862no—
677D4—862no—
678D4—1728no—
679D4—1721no—
680D4—1721no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—434no—
700C2×C4—434no—
701C2×C4—434no—
702C2×C4—434no—
703C2×C4—862no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—3444no—
711C2×C4—3444no—
712C2×C4—1724no—
713C2×C4—1724no—
714C2×C4—1728no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4C22×C4×D4311yescharacteristic
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4#41×D4311yescharacteristic
726C2×C4#41×D4311yescharacteristic
727C2×C4#41×D4311yescharacteristic
728C2×C4#41×D4311yescharacteristic
729C8—22no—
730C8—22no—
731C8—862no—
732C8—862no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—434no—
741C22—434no—
742C22—434no—
743C22—434no—
744C22—434no—
745C22—434no—
746C22—434no—
747C22—34416no—
748C22—3441no—
749C22—3441no—
750C22—3441no—
751C22—3441no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22C4×D4×D4311yescharacteristic
756C22#121×D4311yescharacteristic
757C22#124×D4311yescharacteristic
758C22AGL(1,ℤ/8)×D4311yescharacteristic
759C22AGL(1,ℤ/8)×D4311yescharacteristic
760C22AGL(1,ℤ/8)×D4311yescharacteristic
761C22#137×D4311yescharacteristic
762C4—42no—
763C4—41no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4—434no—
768C4—3441no—
769C4—3441no—
770C4—1722no—
771C4—1721no—
772C4—1721no—
773C4#117×D4311yescharacteristic
774C4C4×D4×D4311yescharacteristic
775C4#123×D4311yescharacteristic
776C4#126×D4311yescharacteristic
777C2—82no—
778C2—438no—
779C2—3442no—
780C2#388×D4311yescharacteristic
781C2#440×D4311yescharacteristic
782C2#442×D4311yescharacteristic
783C2#468×D4311yescharacteristic
784C2#469×D4311yescharacteristic
785C2#489×D4311yescharacteristic
786C2#490×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43C2×#1936
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
3. C2×#97×D43C2semidirect
5. #389×D43C2semidirect
6. #19135295C2semidirect
7. #19135294C2semidirect
8. #19135293C2semidirect
9. #19135292C2semidirect
10. #19135291C2semidirect
11. #19135290C2semidirect
12. #19135289C2semidirect
13. #340×D43C2semidirect
14. #340×D43C2semidirect
15. C43×#1936C2semidirect
33. #102×D43C4semidirect
34. C2×#13063236C22semidirect
35. C2×#13063235C22semidirect
36. C2×#13063235C22semidirect
43. #14582798C22semidirect
44. #14582797C22semidirect
46. #14582795C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
57. C2×#97×C43C22semidirect
59. C43×#389C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
115. #13063247C2×C4semidirect
117. #13063246C2×C4semidirect
119. #13063245C2×C4semidirect
137. #102×C43C2×C4semidirect
396. #1936D43direct (N × H)
408. D43#1936direct (N × H)
433. C2×#97C2×D43semidirect
445. #389C2×D43semidirect
453. #340C2×D43semidirect
454. #340C2×D43semidirect
455. C43C2×#1936semidirect
525. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D432
C2×#97×D432
#390×D432
#389×D432
#191352952
#191352942
#191352932
#191352922
#191352912
#191352902
#191352892
#340×D432
C43×#19362
C2×#193643