Finite Group Databasebeta

← #25103048

Subgroups — #25103048

Order 11008.

910 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144046C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3#19143305C211yesmaximal, characteristic, complemented
4#131×Dic43C211yesmaximal, characteristic, complemented
5#19135512C211yesmaximal, characteristic, complemented
6#19135367C211yesmaximal, characteristic, complemented
7#19135246C211yesmaximal, characteristic, complemented
8#19135242C211yesmaximal, characteristic, complemented
9#19134924C211yesmaximal, characteristic, complemented
10#19134920C211yesmaximal, characteristic, complemented
11#19134613C211yesmaximal, characteristic, complemented
12#19134463C211yesmaximal, characteristic, complemented
13#19134439C211yesmaximal, characteristic, complemented
14#19134437C211yesmaximal, characteristic, complemented
15C2×C43×#444C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19#14583445C2211yescharacteristic
20#41×Dic43C2211yescharacteristic
21#14583123C411yescharacteristic, complemented
22#14583119C411yescharacteristic, complemented
23#14583116C411yescharacteristic, complemented
24#14583112C411yescharacteristic, complemented
25#14583107C411yescharacteristic, complemented
26#14583102C411yescharacteristic, complemented
27#14583097C411yescharacteristic, complemented
28#14583092C411yescharacteristic, complemented
29#14583019—24no—
30#14582975—21no—
31#14582975—21no—
32C8×C22⋊D43—21no—
33C8×C22⋊D43—21no—
34C2×#13063260C2211yescharacteristic
35#14582922C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063253C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41#14582896C2211yescharacteristic
42#14582895C2211yescharacteristic
43#14582867C2211yescharacteristic
44#14582866C2211yescharacteristic
45#14582857—21no—
46#14582857C2211yescharacteristic
47#14582854—21no—
48#14582854C2211yescharacteristic
49M16×Dic43—21no—
50M16×Dic43C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52C2×C8×Dic43—21no—
53C2×C8×Dic43C2211yescharacteristic
54C4×Dic43⋊C4C2211yescharacteristic
55#14582664C2211yescharacteristic
56#14582663C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582654C2211yescharacteristic
60#14582653C2211yescharacteristic
61C2×#135×C43C2211yescharacteristic
62C2×#131×C43C2211yescharacteristic
63C2×#131×C43C2211yescharacteristic
64C43×#444—24no—
65C2×#108×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic
68C2×#97×C43C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063345—22no—
71#13063345—22no—
72C2×#10621885C2×C411yescharacteristic
73C2×#10621883C2×C411yescharacteristic
74C2×#10621884C2×C411yescharacteristic
75C2×#10621882C2×C411yescharacteristic
76#13063332—22no—
77#13063332—22no—
78#13063331—22no—
79#13063331—22no—
80C2×#10621877—21no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C22×C43⋊C8—21no—
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C2×C8×D43—21no—
88#13063323C2×C411yescharacteristic
89#13063321C2×C411yescharacteristic
90#13063314C2×C411yescharacteristic
91#13063312C2×C411yescharacteristic
92#13063297—21no—
93#13063297—21no—
94Q8×Dic43C2×C411yescharacteristic
95Q8×Dic43C2×C411yescharacteristic
96D4×Dic43—21no—
97D4×Dic43—21no—
98D4×Dic43C2×C411yescharacteristic
99D4×Dic43C2×C411yescharacteristic
100C4×C22⋊D43—21no—
101C4×C22⋊D43—21no—
102#13063284—21no—
103#13063284C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108#13063260—22no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8C2×C411yescharacteristic
112Dic43⋊C8C2×C411yescharacteristic
113Dic43⋊C8C2×C411yescharacteristic
114Dic43⋊C8C2×C411yescharacteristic
115#13063253—22no—
116#13063252—22no—
117#13063252—22no—
118#13063251—22no—
119#13063250C2×C411yescharacteristic
120#13063250C2×C411yescharacteristic
121#13063249C2×C411yescharacteristic
122#13063249C2×C411yescharacteristic
123#13063247C2×C411yescharacteristic
124#13063247C2×C411yescharacteristic
125#13063246C2×C411yescharacteristic
126#13063246C2×C411yescharacteristic
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129(C2×D43)⋊C8—21no—
130(C2×D43)⋊C8—21no—
131#13063235—22no—
132#13063235—21no—
133#13063235—21no—
134#13063235—21no—
135C8×Dic43—21no—
136C8×Dic43—21no—
137C8×Dic43—21no—
138C8×Dic43D411yescharacteristic
139C8×Dic43D411yescharacteristic
140C8×Dic43D411yescharacteristic
141C8×Dic43D411yescharacteristic
142C43⋊#95—21no—
143C2×#41×C43C2311yescharacteristic
144C2×#41×C43C2311yescharacteristic
145#135×C43—22no—
146#135×C43—22no—
147C2×Q16×C43C2×C411yescharacteristic
148C2×SD16×C43C2×C411yescharacteristic
149C2×SD16×C43C2×C411yescharacteristic
150C2×D8×C43C2×C411yescharacteristic
151#131×C43—22no—
152#131×C43—22no—
153#131×C43—22no—
154#131×C43D414yescomplemented
155C2×M16×C43—21no—
156C2×M16×C43—21no—
157C2×M16×C43C2311yescharacteristic
158C2×M16×C43C2311yescharacteristic
159C22×C8×C43—21no—
160C22×C8×C43—21no—
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C2×C42×C43C2311yescharacteristic
164#108×C43—22no—
165#104×C43—22no—
166#104×C43—22no—
167#97×C43—22no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43C2×D412yes—
175#41×C43#4112yes—
176C2×Q8×C43C22×C411yescharacteristic
177C2×Q8×C43C22×C411yescharacteristic
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43C22×C411yescharacteristic
181C2×D4×C43C22×C411yescharacteristic
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43#4111yescharacteristic
193C22×Dic43#4111yescharacteristic
194#10621898—21no—
195#10621898—21no—
196#10621898—21no—
197#10621898—21no—
198C2×D172C22×C411yescharacteristic
199C2×C4×D43—21no—
200C2×Dic86C22×C411yescharacteristic
201Q16×C43—22no—
202SD16×C43—22no—
203SD16×C43—22no—
204D8×C43—22no—
205M16×C43—21no—
206M16×C43—24no—
207M16×C43—21no—
208M16×C43—21no—
209M16×C43—42no—
210M16×C43C2×D412yes—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—24no—
215C2×C8×C43—21no—
216C2×C8×C43—42no—
217C2×C8×C43C22×C411yescharacteristic
218C2×C8×C43C22×C411yescharacteristic
219C2×C8×C43C2×D411yescharacteristic
220C2×C8×C43C2×D411yescharacteristic
221C2×C8×C43C2×D412yes—
222C2×C8×C43#4112yes—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—21no—
226C22⋊Dic43—21no—
227C22⋊Dic43—21no—
228C22⋊Dic43—21no—
229C22⋊Dic43—21no—
230#10621885—22no—
231#10621884—22no—
232#10621883—22no—
233#10621882—22no—
234(C2×D43)⋊C4—21no—
235(C2×D43)⋊C4—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43C22×C411yescharacteristic
239C4⋊Dic43C22×C411yescharacteristic
240Dic43⋊C4—21no—
241Dic43⋊C4—21no—
242Dic43⋊C4—42no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43C22×C411yescharacteristic
249C4×Dic43C22×C411yescharacteristic
250C4×Dic43C2×D411yescharacteristic
251C4×Dic43C2×D411yescharacteristic
252#10621877—24no—
253#10621877—21no—
254#10621877—21no—
255#10621877—21no—
256#10621877#4112yes—
257C2×C43⋊C8—24no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C22×C411yescharacteristic
265C2×C43⋊C8C22×C411yescharacteristic
266C2×C43⋊C8C2×D411yescharacteristic
267C2×C43⋊C8C2×D411yescharacteristic
268#10621872—42no—
269C8×D43—42no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43C2×#4111yescharacteristic
273C22×D43—21no—
274Q8×C43—21no—
275Q8×C43—21no—
276Q8×C43—21no—
277Q8×C43C4×D412yes—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—21no—
281D4×C43—21no—
282D4×C43—21no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43C4×D412yes—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—21no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43C23×C411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C22⋊D43—42no—
302C22⋊D43—41no—
303C22⋊D43—41no—
304C22⋊D43—42no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—41no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43C4×D411yescharacteristic
316C2×Dic43C4×D411yescharacteristic
317C2×Dic43C4×D411yescharacteristic
318C2×Dic43C4×D411yescharacteristic
319D172—21no—
320D172—21no—
321C4×D43—41no—
322C4×D43—41no—
323Dic86—21no—
324Dic86—21no—
325C8×C43—21no—
326C8×C43—21no—
327C8×C43—22no—
328C8×C43—41no—
329C8×C43#12112yes—
330C8×C43#12112yes—
331C43⋊C8—21no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—22no—
335C43⋊C8—21no—
336C43⋊C8—41no—
337#21518—431nomaximal, Sylow
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—22no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43C2×C4×D411yescharacteristic
347C22×C43#52911yescharacteristic
348C22×C43#53211yescharacteristic
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C4×C43—22no—
353C4×C43—41no—
354C4×C43—81no—
355C4×C43C2×C4×D411yescharacteristic
356C4×C43C4×#4111yescharacteristic
357C4×C43C2×#12111yescharacteristic
358C4×C43#52511yescharacteristic
359Dic43—21no—
360Dic43—21no—
361Dic43—21no—
362Dic43—41no—
363Dic43—41no—
364Dic43—41no—
365Dic43—81no—
366Dic43#44412yescomplemented
367#3035—431no—
368C2×#444—431no—
369C2×#444D4311yescharacteristic, complemented
370#2931—431no—
371C4×#131—431no—
372#1980—431no—
373#1950—431no—
374#1929—431no—
375#1929—431no—
376#1876—431no—
377#1876—431no—
378#1806—431no—
379#1770—431no—
380#1765—431no—
381#1765—431no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—42no—
385C2×C43—81no—
386C2×C43C4×#12111yescharacteristic
387C2×C43C2×#44411yescharacteristic
388C2×C43#295511yescharacteristic
389D43—81no—
390C2×#135—431no—
391C2×#135C2×D4311yescharacteristic
392C2×#131—431no—
393C2×#131—431no—
394C2×#131C2×D4311yescharacteristic
395C2×#131C2×D4311yescharacteristic
396#532—431no—
397C4×#41—431no—
398#464—431no—
399#464—431no—
400#463—431no—
401#463—431no—
402#462—431no—
403#461—431no—
404#460—431no—
405#459—431no—
406#444—24no—
407#444—864no—
408#436—861no—
409#436—861no—
410C8×D4—861no—
411C8×D4—861no—
412C2×#108—431no—
413C2×#108C2×D4311yescharacteristic
414#423—431no—
415C2×C4⋊C8—431no—
416C2×#104—431no—
417C2×#104—431no—
418C2×#104—431no—
419C2×#104—431no—
420C2×#104C2×D4311yescharacteristic
421C2×#104C2×D4311yescharacteristic
422#416—431no—
423#416—431no—
424#408—431no—
425#408—431no—
426#405—431no—
427#405—431no—
428#405—861no—
429#405—861no—
430C4×M16—431no—
431C4×M16—861no—
432C2×#97—431no—
433C2×#97C2×D4311yescharacteristic
434C2×C4×C8—431no—
435C2×C4×C8—861no—
436C4×C4⋊C4—431no—
437#341—431no—
438#341—431no—
439#339—431no—
440#339—431no—
441#336—431no—
442#336—431no—
443C43#2151811yescharacteristic, complemented, Sylow
444C2×#41—431no—
445C2×#41C22×D4311yescharacteristic
446C2×#41C22×D4311yescharacteristic
447#135—22no—
448#135—22no—
449#135—862no—
450#135—862no—
451C2×Q16—431no—
452C2×Q16C4×D4311yescharacteristic
453C2×SD16—431no—
454C2×SD16—431no—
455C2×SD16C4×D4311yescharacteristic
456C2×SD16C4×D4311yescharacteristic
457C2×D8—431no—
458C2×D8C4×D4311yescharacteristic
459#131—22no—
460#131—22no—
461#131—22no—
462#131—862no—
463#131—862no—
464#131—862no—
465#131—862no—
466#131C22⋊D4314yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—431no—
470C2×M16—431no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16C22×D4311yescharacteristic
474C2×M16C22×D4311yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—861no—
480C22×C8—861no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C4⋊Q8—431no—
484#127—431no—
485#124—431no—
486#124—431no—
487#121—861no—
488#121—861no—
489C4×Q8—431no—
490C4×Q8—431no—
491C4×D4—431no—
492C4×D4—431no—
493C4×D4—861no—
494C4×D4—861no—
495C4×D4—861no—
496C4×D4—861no—
497#117—431no—
498#117—861no—
499C2×C4⋊C4—861no—
500C2×C42—431no—
501C2×C42—431no—
502C2×C42—861no—
503C2×C42C22×D4311yescharacteristic
504#108—22no—
505#108—862no—
506C4⋊C8—431no—
507C4⋊C8—431no—
508C4⋊C8—431no—
509C4⋊C8—431no—
510C4⋊C8—861no—
511C4⋊C8—861no—
512#104—22no—
513#104—22no—
514#104—862no—
515#104—862no—
516#104—862no—
517#104—862no—
518#103—431no—
519#103—431no—
520#103—431no—
521#103—431no—
522#102—431no—
523#102—431no—
524#102—431no—
525#102—431no—
526C22⋊C8—861no—
527C22⋊C8—861no—
528C22⋊C8—861no—
529C22⋊C8—861no—
530#97—22no—
531#97—861no—
532#97—861no—
533#97—861no—
534#97—862no—
535C4×C8—431no—
536C4×C8—431no—
537C4×C8—431no—
538C4×C8—431no—
539C4×C8—861no—
540C4×C8—861no—
541C4×C8—861no—
542#95—861no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—861no—
550#41—861no—
551#41—861no—
552#41—861no—
553#41#1062189812yes—
554#41C2×C22⋊D4312yes—
555C2×Q8—431no—
556C2×Q8C2×C4×D4311yescharacteristic
557C2×Q8C2×C4×D4311yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—431no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4C2×C4×D4311yescharacteristic
565C2×D4C2×C4×D4311yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4C23×D4311yescharacteristic
576Q16—22no—
577Q16—862no—
578SD16—22no—
579SD16—22no—
580SD16—862no—
581SD16—862no—
582D8—22no—
583D8—862no—
584M16—21no—
585M16—24no—
586M16—21no—
587M16—21no—
588M16—42no—
589M16—432no—
590M16—864no—
591M16—861no—
592M16—861no—
593M16—861no—
594M16—1722no—
595M16C2×C22⋊D4312yes—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—24no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—431no—
603C2×C8—431no—
604C2×C8—431no—
605C2×C8—431no—
606C2×C8—864no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—1722no—
614C2×C8C2×C4×D4311yescharacteristic
615C2×C8C2×C4×D4311yescharacteristic
616C2×C8D4×D4311yescharacteristic
617C2×C8D4×D4311yescharacteristic
618C2×C8#1062190012yes—
619C2×C8C2×C22⋊D4312yes—
620C4⋊C4—431no—
621C4⋊C4—431no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—1722no—
627C22⋊C4—861no—
628C22⋊C4—861no—
629C22⋊C4—861no—
630C22⋊C4—861no—
631C22⋊C4—861no—
632C22⋊C4—861no—
633C22⋊C4—861no—
634C42—21no—
635C42—21no—
636C42—431no—
637C42—431no—
638C42—431no—
639C42—431no—
640C42—861no—
641C42—861no—
642C42—861no—
643C42—861no—
644C42—861no—
645C23—21no—
646C23—21no—
647C23—861no—
648C23#41×D4311yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—861no—
653Q8—861no—
654Q8C4×C22⋊D4312yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—41no—
661D4—41no—
662D4—861no—
663D4—861no—
664D4—1722no—
665D4—1722no—
666D4—1721no—
667D4—1721no—
668D4C4×C22⋊D4312yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—431no—
679C2×C4—431no—
680C2×C4—431no—
681C2×C4—431no—
682C2×C4—862no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—1722no—
687C2×C4—1721no—
688C2×C4—1722no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4C22×C4×D4311yescharacteristic
695C2×C4C2×D4×D4311yescharacteristic
696C2×C4C22×C22⋊D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4C2×#1062190011yescharacteristic
699C2×C4C2×#1062189811yescharacteristic
700C8—21no—
701C8—21no—
702C8—22no—
703C8—41no—
704C8—861no—
705C8—861no—
706C8—861no—
707C8—861no—
708C8—862no—
709C8—1721no—
710C8#1306329712yes—
711C8#1306329712yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—1721no—
721C22—1721no—
722C22—1721no—
723C22C4×D4×D4311yescharacteristic
724C22#1458342911yescharacteristic
725C22#1458344511yescharacteristic
726C4—22no—
727C4—41no—
728C4—81no—
729C4—432no—
730C4—861no—
731C4—861no—
732C4—861no—
733C4—3441no—
734C4—1721no—
735C4—1721no—
736C4—1721no—
737C4C2×C4×C22⋊D4311yescharacteristic
738C4C4×#1062190011yescharacteristic
739C4C2×#1306329711yescharacteristic
740C4#1458340811yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—3441no—
746C2C4×#1306329711yescharacteristic
747C2#444×D4311yescharacteristic
748C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#444C2
socleC22×C43C2×C4×D4
prime radical#19144046C2
cosocleC22×C4×C43C24
hypercenterC2×#444D43
hypocenterC43#21518
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. #19143305C2semidirect
4. #131×Dic43C2semidirect
5. #19135512C2semidirect
6. #19135367C2semidirect
7. #19135246C2semidirect
8. #19135242C2semidirect
9. #19134924C2semidirect
10. #19134920C2semidirect
11. #19134613C2semidirect
12. #19134463C2semidirect
13. #19134439C2semidirect
14. #19134437C2semidirect
15. C2×C43×#444C2semidirect
21. #14583123C4semidirect
22. #14583119C4semidirect
23. #14583116C4semidirect
24. #14583112C4semidirect
25. #14583107C4semidirect
26. #14583102C4semidirect
27. #14583097C4semidirect
28. #14583092C4semidirect
154. #131×C43D4semidirect
366. Dic43#444semidirect
369. C2×#444D43semidirect
443. C43#21518semidirect
466. #131C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191440462
C2×#145830192
#191433052
#131×Dic432
#191355122
#191353672
#191352462
#191352422
#191349242
#191349202
#191346132
#191344632
#191344392
#191344372
C2×C43×#4442
#2151843