Finite Group Databasebeta

← #25003270

Subgroups — #25003270

Order 11008.

1430 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C22×#13063253C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582900C211yesmaximal, characteristic, complemented
5C2×#14582667C211yesmaximal, characteristic, complemented
6#19132825C211yesmaximal, characteristic, complemented
7C22×#104×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583477—22no—
11#14583477—22no—
12#14583477—22no—
13#14583477C414yescomplemented
14C2×#13063304—21no—
15C2×#13063301—21no—
16C2×#13063299—21no—
17C2×#13063297—22no—
18C2×#13063296—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C2×#13063253—22no—
22C2×#13063253—22no—
23C2×#13063253—22no—
24#14582901—22no—
25#14582901—22no—
26#14582900—22no—
27#14582900—22no—
28C2×#13063250—21no—
29C2×#13063249—21no—
30C2×#13063247—21no—
31C2×#13063246—21no—
32C2×C43⋊#95—22no—
33#14582667—22no—
34C22×#41×C43C2211yescharacteristic
35C22×M16×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C2×#104×C43—22no—
38C2×#104×C43—22no—
39C2×#104×C43—22no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898C2×C412yes—
51C2×#10621898D412yes—
52C22×Dic86D411yescharacteristic
53C22×D172D411yescharacteristic
54C22×C22⋊D43—21no—
55C22×C22⋊D43—22no—
56C23×Dic43—21no—
57C23×Dic43D412yes—
58C22×C4×D43—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877—21no—
63C2×#10621877—21no—
64C2×#10621877D412yescomplemented
65C22×C43⋊C8—21no—
66#13063304—24no—
67#13063304—24no—
68#13063301—24no—
69#13063301—24no—
70#13063299—24no—
71#13063299—24no—
72#13063297—28no—
73#13063297—28no—
74#13063296—24no—
75#13063296—24no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2×C412yes—
86C2×C4⋊Dic43D412yes—
87C2×C4⋊Dic43D412yescomplemented
88C2×Dic43⋊C4—22no—
89C2×C22⋊Dic43—22no—
90C2×(C2×D43)⋊C4—22no—
91#13063253—28no—
92#13063250—24no—
93#13063249—24no—
94#13063247—24no—
95#13063246—24no—
96C43⋊#95—44no—
97C2×#41×C43—21no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43—21no—
107C2×#41×C43C2×C412yes—
108C2×#41×C43D412yes—
109C22×Q8×C43D411yescharacteristic
110C22×D4×C43—21no—
111C22×D4×C43D411yescharacteristic
112C23×C4×C43—21no—
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43D412yescomplemented
121C22×C8×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43D412yescomplemented
128#104×C43—28no—
129C24×C43—21no—
130C24×C43C2×D411yescharacteristic
131C23×D43—21no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—22no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147#41×C43—41no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C22⋊C412yes—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43C22⋊C412yes—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—21no—
171C22×C4×C43—22no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C22×C4×C43#4111yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C2×C22⋊D43—28no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—41no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C2×C22⋊D43—82no—
202C2×C22⋊D43—82no—
203C22×Dic43—22no—
204C22×Dic43—21no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—42no—
208C22×Dic43—42no—
209C22×Dic43—42no—
210C22×Dic43—42no—
211C22×Dic43—41no—
212C22×Dic43—41no—
213C22×Dic43C22⋊C414yes—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221#10621898—22no—
222#10621898—41no—
223#10621898—41no—
224#10621898—41no—
225#10621898—41no—
226#10621898—41no—
227#10621898—41no—
228#10621898—41no—
229#10621898—41no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172C22⋊C412yes—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—41no—
239C2×C4×D43—41no—
240C2×C4×D43—41no—
241C2×C4×D43—41no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—21no—
247C2×Dic86C22⋊C412yes—
248M16×C43—22no—
249M16×C43—22no—
250M16×C43—41no—
251M16×C43—41no—
252C2×C8×C43—22no—
253C2×C8×C43—41no—
254C2×C8×C43—41no—
255C42×C43—22no—
256C42×C43—22no—
257C42×C43—41no—
258C42×C43—41no—
259C22⋊Dic43—28no—
260(C2×D43)⋊C4—28no—
261C4⋊Dic43—22no—
262C4⋊Dic43—22no—
263C4⋊Dic43—22no—
264C4⋊Dic43—22no—
265C4⋊Dic43—22no—
266C4⋊Dic43—22no—
267C4⋊Dic43—41no—
268C4⋊Dic43—41no—
269Dic43⋊C4—28no—
270#10621877—22no—
271#10621877—22no—
272#10621877—41no—
273#10621877—41no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—41no—
276C2×C43⋊C8—41no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—22no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43C2×C22⋊C411yescharacteristic
289C23×C43#12011yescharacteristic
290C23×C43#12011yescharacteristic
291C23×C43#12111yescharacteristic
292C23×C43#12111yescharacteristic
293C23×C43#12411yescharacteristic
294C23×C43#12711yescharacteristic
295C22×D43—22no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—41no—
305Q8×C43—41no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—42no—
309D4×C43—42no—
310D4×C43—42no—
311D4×C43—42no—
312D4×C43—41no—
313D4×C43—41no—
314C2×C4×C43—24no—
315C2×C4×C43—22no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43C2×C22⋊C411yescharacteristic
329C2×C4×C43C2×C22⋊C411yescharacteristic
330C2×C4×C43C4×D411yescharacteristic
331C2×C4×C43C4×D411yescharacteristic
332C2×C4×C43C4×D411yescharacteristic
333C2×C4×C43C4×D411yescharacteristic
334C2×C4×C43#12011yescharacteristic
335C2×C4×C43#12011yescharacteristic
336C2×C4×C43#12011yescharacteristic
337C2×C4×C43#12011yescharacteristic
338C2×C4×C43#12011yescharacteristic
339C2×C4×C43#12011yescharacteristic
340C2×C4×C43#12111yescharacteristic
341C2×C4×C43#12111yescharacteristic
342C2×C4×C43#12111yescharacteristic
343C2×C4×C43#12111yescharacteristic
344C2×C4×C43#12111yescharacteristic
345C2×C4×C43#12111yescharacteristic
346C2×C4×C43#12111yescharacteristic
347C2×C4×C43#12111yescharacteristic
348C2×C4×C43#12111yescharacteristic
349C2×C4×C43#12111yescharacteristic
350C2×C4×C43#12311yescharacteristic
351C2×C4×C43#12311yescharacteristic
352C2×C4×C43#12311yescharacteristic
353C2×C4×C43#12311yescharacteristic
354C2×C4×C43#12411yescharacteristic
355C2×C4×C43#12711yescharacteristic
356C22⋊D43—42no—
357C22⋊D43—42no—
358C22⋊D43—42no—
359C22⋊D43—42no—
360C22⋊D43—88no—
361C2×Dic43—22no—
362C2×Dic43—24no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43—44no—
368C2×Dic43—44no—
369C2×Dic43—42no—
370C2×Dic43—82no—
371C2×Dic43—82no—
372C2×Dic43—81no—
373C2×Dic43—81no—
374D172—22no—
375D172—22no—
376D172—41no—
377D172—41no—
378C4×D43—42no—
379C4×D43—42no—
380C4×D43—42no—
381C4×D43—42no—
382Dic86—22no—
383Dic86—22no—
384Dic86—41no—
385Dic86—41no—
386C8×C43—42no—
387C43⋊C8—42no—
388#11002—431nomaximal, Sylow
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—21no—
397C22×C43—21no—
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43#37911yescharacteristic
409C22×C43#39011yescharacteristic
410C22×C43#39011yescharacteristic
411C22×C43#39211yescharacteristic
412C22×C43#39211yescharacteristic
413C22×C43#39411yescharacteristic
414C22×C43#39411yescharacteristic
415C22×C43#45311yescharacteristic
416C22×C43#45411yescharacteristic
417C22×C43#45511yescharacteristic
418C22×C43#45611yescharacteristic
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—81no—
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C4×C43—44no—
427C4×C43—42no—
428C4×C43#38611yescharacteristic
429C4×C43#38611yescharacteristic
430C4×C43#38611yescharacteristic
431C4×C43#38611yescharacteristic
432C4×C43#39211yescharacteristic
433C4×C43#39211yescharacteristic
434C4×C43#39411yescharacteristic
435C4×C43#39411yescharacteristic
436Dic43—44no—
437Dic43—42no—
438Dic43—82no—
439C2×#537—431no—
440C22×#104—431no—
441C22×#104D4311yescharacteristic, complemented
442C2×#417—431no—
443C2×#417—431no—
444C2×#343—431no—
445C4⋊#95—431no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—82no—
451C2×C43#143811yescharacteristic
452C2×C43#179211yescharacteristic
453C2×C43#179311yescharacteristic
454C2×C43#200611yescharacteristic
455C2×C43#200711yescharacteristic
456C2×C43#203911yescharacteristic
457C2×C43#204011yescharacteristic
458D43—82no—
459C22×#41—431no—
460C22×#41C2×D4311yescharacteristic
461C22×M16—431no—
462C22×M16C2×D4311yescharacteristic
463#537—434no—
464#537—862no—
465#537—862no—
466#537—862no—
467C2×C22⋊Q8—861no—
468C2×C22⋊Q8—861no—
469C2×#121—861no—
470C2×#121—862no—
471C2×#121—861no—
472C22×C4⋊C4—431no—
473C22×C4⋊C4—431no—
474C22×C42C2×D4311yescharacteristic
475C2×#104—22no—
476C2×#104—22no—
477C2×#104—22no—
478C2×#104—862no—
479C2×#104—862no—
480C2×#104—862no—
481#417—862no—
482#417—862no—
483#417—862no—
484#417—862no—
485C2×#103—861no—
486C2×#103—861no—
487C2×#102—861no—
488C2×#102—861no—
489C2×#95—862no—
490#343—862no—
491C43#1100211yescharacteristic, complemented, Sylow
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—432no—
503C2×#41—432no—
504C2×#41—861no—
505C2×#41—861no—
506C2×#41—861no—
507C2×#41—861no—
508C2×#41—861no—
509C2×#41—861no—
510C2×#41—861no—
511C2×#41—861no—
512C2×#41—861no—
513C2×#41—861no—
514C2×#41C4×D4312yes—
515C2×#41C22⋊D4312yes—
516C22×Q8—431no—
517C22×Q8D17211yescharacteristic
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—862no—
521C22×D4—861no—
522C22×D4D17211yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—432no—
526C23×C4—861no—
527C23×C4—861no—
528C23×C4C22×D4311yescharacteristic
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—432no—
535C2×M16—861no—
536C2×M16—861no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16C22⋊D4312yescomplemented
541C22×C8—21no—
542C22×C8—861no—
543C22⋊Q8—864no—
544C22⋊Q8—864no—
545C22⋊Q8—864no—
546C22⋊Q8—864no—
547#121—864no—
548#121—864no—
549#121—868no—
550#121—864no—
551#121—868no—
552#121—864no—
553C2×C4⋊C4—432no—
554C2×C4⋊C4—432no—
555C2×C4⋊C4—432no—
556C2×C4⋊C4—862no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C22⋊C4—862no—
567C2×C22⋊C4—862no—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—21no—
573C2×C42C22⋊D4312yescomplemented
574#104—28no—
575#104—868no—
576#103—864no—
577#103—864no—
578#102—864no—
579#102—864no—
580#95—1724no—
581C24—21no—
582C24—861no—
583C24D4×D4311yescharacteristic
584#41—22no—
585#41—22no—
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—862no—
601#41—862no—
602#41—862no—
603#41—862no—
604#41—862no—
605#41—862no—
606#41—862no—
607#41—862no—
608#41—1721no—
609#41—1721no—
610#41—1721no—
611#41—1721no—
612#41—1721no—
613#41—1721no—
614#41—1721no—
615#41—1721no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—432no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8—861no—
627C2×Q8(C2×D43)⋊C412yes—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—41no—
639C2×D4—432no—
640C2×D4—868no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—3442no—
649C2×D4—3442no—
650C2×D4—1721no—
651C2×D4—1721no—
652C2×D4—1721no—
653C2×D4—1721no—
654C2×D4(C2×D43)⋊C412yes—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—434no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—861no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—1722no—
677C22×C4—1722no—
678C22×C4—1721no—
679C22×C4—1721no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1721no—
683C22×C4—1721no—
684C22×C4—1721no—
685C22×C4—1721no—
686C22×C4C2×C4×D4311yescharacteristic
687C22×C4C2×D17211yescharacteristic
688C22×C4#1062189811yescharacteristic
689C22×C4#1062189811yescharacteristic
690C22×C4D4×D4311yescharacteristic
691C22×C4D4×D4311yescharacteristic
692C22×C4D4×D4311yescharacteristic
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4311yescharacteristic
695C22×C4#1062190011yescharacteristic
696C22×C4#1062190011yescharacteristic
697C22×C4C2×C22⋊D4311yescharacteristic
698C22×C4C2×C22⋊D4311yescharacteristic
699C22×C4C2×C22⋊D4311yescharacteristic
700M16—22no—
701M16—22no—
702M16—41no—
703M16—41no—
704M16—862no—
705M16—862no—
706M16—1721no—
707M16—1721no—
708C2×C8—22no—
709C2×C8—41no—
710C2×C8—41no—
711C2×C8—862no—
712C2×C8—1721no—
713C2×C8—1721no—
714C4⋊C4—868no—
715C4⋊C4—862no—
716C4⋊C4—862no—
717C4⋊C4—862no—
718C4⋊C4—862no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—1721no—
722C4⋊C4—1721no—
723C22⋊C4—868no—
724C22⋊C4—868no—
725C42—22no—
726C42—22no—
727C42—41no—
728C42—41no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—862no—
741C23—1721no—
742C23—1721no—
743C23—1721no—
744C23—1721no—
745C23—1721no—
746C23—1721no—
747C23C22⋊C4×D4311yescharacteristic
748C23#1306329311yescharacteristic
749C23#1306329511yescharacteristic
750C23#1306329711yescharacteristic
751C23#1306329811yescharacteristic
752C23#1306331111yescharacteristic
753C23#1306332111yescharacteristic
754Q8—22no—
755Q8—22no—
756Q8—41no—
757Q8—41no—
758Q8—862no—
759Q8—862no—
760Q8—1721no—
761Q8—1721no—
762D4—22no—
763D4—22no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—41no—
769D4—41no—
770D4—862no—
771D4—862no—
772D4—3448no—
773D4—1722no—
774D4—1722no—
775D4—1722no—
776D4—1722no—
777D4—1721no—
778D4—1721no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—864no—
794C2×C4—862no—
795C2×C4—3442no—
796C2×C4—3441no—
797C2×C4—3441no—
798C2×C4—3442no—
799C2×C4—1724no—
800C2×C4—1722no—
801C2×C4—1721no—
802C2×C4—1722no—
803C2×C4—1721no—
804C2×C4—1722no—
805C2×C4—1722no—
806C2×C4—1722no—
807C2×C4—1722no—
808C2×C4—1722no—
809C2×C4—1724no—
810C2×C4C22⋊C4×D4311yescharacteristic
811C2×C4C2×(C2×D43)⋊C411yescharacteristic
812C2×C4(C22⋊D43)⋊C411yescharacteristic
813C2×C4(C22⋊D43)⋊C411yescharacteristic
814C2×C4C4×C22⋊D4311yescharacteristic
815C2×C4C4×C22⋊D4311yescharacteristic
816C2×C4#1306329311yescharacteristic
817C2×C4#1306329311yescharacteristic
818C2×C4#1306329311yescharacteristic
819C2×C4#1306329411yescharacteristic
820C2×C4#1306329511yescharacteristic
821C2×C4#1306329511yescharacteristic
822C2×C4#1306329611yescharacteristic
823C2×C4#1306329611yescharacteristic
824C2×C4#1306329711yescharacteristic
825C2×C4#1306329711yescharacteristic
826C2×C4#1306329711yescharacteristic
827C2×C4#1306329811yescharacteristic
828C2×C4#1306329811yescharacteristic
829C2×C4#1306329811yescharacteristic
830C2×C4#1306329911yescharacteristic
831C2×C4#1306329911yescharacteristic
832C2×C4#1306330711yescharacteristic
833C2×C4#1306330711yescharacteristic
834C2×C4#1306330811yescharacteristic
835C2×C4#1306330911yescharacteristic
836C2×C4#1306331111yescharacteristic
837C2×C4#1306332111yescharacteristic
838C8—42no—
839C8—1722no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—3441no—
860C22—3441no—
861C22—3441no—
862C22—3441no—
863C22—1722no—
864C22—1722no—
865C22—1722no—
866C22#1458275411yescharacteristic
867C22#1458279911yescharacteristic
868C22#1458279911yescharacteristic
869C22#1458280711yescharacteristic
870C22#1458280811yescharacteristic
871C22#1458281411yescharacteristic
872C22#1458281511yescharacteristic
873C22#1458306811yescharacteristic
874C22#1458307311yescharacteristic
875C22#1458307811yescharacteristic
876C22#1458308311yescharacteristic
877C4—44no—
878C4—42no—
879C4—3442no—
880C4—1724no—
881C4—1722no—
882C4#1458277511yescharacteristic
883C4#1458277511yescharacteristic
884C4#1458277611yescharacteristic
885C4#1458277811yescharacteristic
886C4#1458280711yescharacteristic
887C4#1458280811yescharacteristic
888C4#1458281411yescharacteristic
889C4#1458281511yescharacteristic
890C2—21no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—82no—
895C2—3442no—
896C2#1913283411yescharacteristic
897C2#1913455011yescharacteristic
898C2#1913455511yescharacteristic
899C2#1913563811yescharacteristic
900C2#1913564311yescharacteristic
901C2#1913581811yescharacteristic
902C2#1913582311yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#104×C43C2
socleC23×C43#120
prime radicalC2×#14583477C2
cosocleC23×C4×C43C23
hypercenterC22×#104D43
hypocenterC43#11002
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#13063253C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582900C2semidirect
5. C2×#14582667C2semidirect
6. #19132825C2semidirect
7. C22×#104×C43C2semidirect
13. #14583477C4semidirect
64. C2×#10621877D4semidirect
87. C2×C4⋊Dic43D4semidirect
120. C2×M16×C43D4semidirect
127. C2×C42×C43D4semidirect
441. C22×#104D43semidirect
491. C43#11002semidirect
540. C2×M16C22⋊D43semidirect
573. C2×C42C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C22×#130632532
C2×#145829012
C2×#145829002
C2×#145826672
#191328252
C22×#104×C432
#1100243