Finite Group Databasebeta

← C2×#19135640 #25123555

Subgroups — C2×#19135640 #25123555

Order 11008.

2038 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063356C211yesmaximal, characteristic, complemented
2C2×#14583477C211yesmaximal, characteristic
3C22×#13063252C211yesmaximal, characteristic, complemented
4C22×#13063251C211yesmaximal, characteristic, complemented
5C2×#14582806C211yesmaximal, characteristic, complemented
6#19135640C218yesmaximal, direct product factor
7C2×#14582667C211yesmaximal, characteristic, complemented
8C22×#137×C43C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C2×#13063356—22no—
11C2×#13063356—24no—
12C2×#13063356—24no—
13C2×#13063356C2214yescomplemented
14C22×#10621885—21no—
15C22×#10621884—21no—
16C22×#10621877C2211yescharacteristic
17#14583477—22no—
18#14583477—22no—
19#14583477—22no—
20#14583477C2214yes—
21C2×#13063304—21no—
22C2×#13063301—21no—
23C2×#13063299—21no—
24C2×#13063297—22no—
25C2×#13063296—21no—
26C22×C4⋊Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C2×#13063252—24no—
29C2×#13063252C2214yescomplemented
30C2×#13063251—24no—
31C2×#13063251C2214yescomplemented
32#14582806—22no—
33#14582806C2214yescomplemented
34C2×C43⋊#95—22no—
35#14582667C2214yescomplemented
36C22×#41×C43C2211yescharacteristic
37C23×Q8×C43C2211yescharacteristic
38C2×#137×C43—22no—
39C2×#137×C43—24no—
40C2×#137×C43—24no—
41C2×#137×C43C2214yescomplemented
42C22×Q16×C43—21no—
43C22×SD16×C43—21no—
44C22×M16×C43C2211yescharacteristic
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898D412yes—
52C2×#10621898C2312yes—
53C22×Dic86D411yescharacteristic
54C22×D172D411yescharacteristic
55C22×C22⋊D43—21no—
56C22×C22⋊D43—22no—
57C23×Dic43—21no—
58C23×Dic43D412yes—
59C22×C4×D43—21no—
60#13063356—216no—
61#13063356—28no—
62#13063356—28no—
63C2×#10621885—28no—
64C2×#10621885—24no—
65C2×#10621884—28no—
66C2×#10621884—24no—
67C2×#10621877—21no—
68C2×#10621877—22no—
69C2×#10621877D414yescomplemented
70C2×#10621877C2312yes—
71C22×C43⋊C8—21no—
72#13063304—24no—
73#13063304—24no—
74#13063301—24no—
75#13063301—24no—
76#13063299—24no—
77#13063299—24no—
78#13063297—28no—
79#13063297—28no—
80#13063296—24no—
81#13063296—24no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43D412yes—
87C2×C4⋊Dic43C2312yes—
88C2×Dic43⋊C4—22no—
89C2×C22⋊Dic43—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×C4×Dic43—22no—
92C2×C4×Dic43—22no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2312yes—
95#13063252—28no—
96#13063251—28no—
97C43⋊#95—28no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—22no—
101C2×#41×C43—22no—
102C2×#41×C43—22no—
103C2×#41×C43—22no—
104C2×#41×C43D412yes—
105C2×#41×C43C2312yes—
106C22×Q8×C43—21no—
107C22×Q8×C43—22no—
108C22×Q8×C43—21no—
109C22×Q8×C43—21no—
110C22×Q8×C43—22no—
111C22×Q8×C43—21no—
112C22×Q8×C43—21no—
113C22×Q8×C43—22no—
114C22×Q8×C43D411yescharacteristic
115C22×Q8×C43D414yescomplemented
116C22×Q8×C43C2312yes—
117C22×D4×C43—21no—
118C22×D4×C43D411yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122#137×C43—216no—
123#137×C43—28no—
124#137×C43—28no—
125C2×Q16×C43—28no—
126C2×Q16×C43—24no—
127C2×SD16×C43—28no—
128C2×SD16×C43—24no—
129C2×M16×C43—22no—
130C2×M16×C43—21no—
131C2×M16×C43D414yescomplemented
132C2×M16×C43C2312yes—
133C22×C8×C43—21no—
134C24×C43—21no—
135C24×C43C2×D411yescharacteristic
136C23×D43—21no—
137#41×C43—24no—
138#41×C43—24no—
139#41×C43—22no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—42no—
144#41×C43—42no—
145#41×C43—42no—
146#41×C43—42no—
147C2×Q8×C43—21no—
148C2×Q8×C43—24no—
149C2×Q8×C43—22no—
150C2×Q8×C43—24no—
151C2×Q8×C43—22no—
152C2×Q8×C43—24no—
153C2×Q8×C43—24no—
154C2×Q8×C43—24no—
155C2×Q8×C43—22no—
156C2×Q8×C43—22no—
157C2×Q8×C43—22no—
158C2×Q8×C43—22no—
159C2×Q8×C43—22no—
160C2×Q8×C43—41no—
161C2×Q8×C43—41no—
162C2×Q8×C43—42no—
163C2×Q8×C43—42no—
164C2×Q8×C43—42no—
165C2×Q8×C43—42no—
166C2×Q8×C43—42no—
167C2×Q8×C43C2×D412yes—
168C2×Q8×C43C2×D414yescomplemented
169C2×D4×C43—21no—
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43—42no—
175C2×D4×C43—42no—
176C2×D4×C43C2×D412yes—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—21no—
180C22×C4×C43—24no—
181C22×C4×C43—22no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43—41no—
185C22×C4×C43—41no—
186C22×C4×C43—42no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43#4112yes—
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—28no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—84no—
203C22×Dic43—24no—
204C22×Dic43—22no—
205C22×Dic43—21no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—42no—
209C22×Dic43—44no—
210C22×Dic43—42no—
211C22×Dic43C2×D414yes—
212#10621898—24no—
213#10621898—24no—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—42no—
219#10621898—42no—
220#10621898—42no—
221#10621898—42no—
222C2×D172—21no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172C2×D412yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—21no—
233C2×Dic86C2×D412yes—
234Q16×C43—216no—
235SD16×C43—216no—
236M16×C43—24no—
237M16×C43—22no—
238M16×C43C2×D414yescomplemented
239C2×C8×C43—24no—
240C2×C8×C43—22no—
241C22⋊Dic43—28no—
242#10621885—216no—
243#10621884—216no—
244(C2×D43)⋊C4—28no—
245C4⋊Dic43—22no—
246C4⋊Dic43—22no—
247C4⋊Dic43—22no—
248C4⋊Dic43—22no—
249Dic43⋊C4—28no—
250C4×Dic43—22no—
251C4×Dic43—22no—
252C4×Dic43—42no—
253#10621877—24no—
254#10621877—22no—
255#10621877C2×D414yescomplemented
256C2×C43⋊C8—24no—
257C2×C43⋊C8—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—42no—
262C23×C43—42no—
263C23×C43—42no—
264C23×C43#12011yescharacteristic
265C23×C43#12011yescharacteristic
266C23×C43#12112yes—
267C23×C43#12712yes—
268C23×C43C22×D411yescharacteristic
269C22×D43—22no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273Q8×C43—24no—
274Q8×C43—24no—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—42no—
278Q8×C43—42no—
279Q8×C43—44no—
280Q8×C43—44no—
281Q8×C43—42no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—42no—
285D4×C43—42no—
286D4×C43—44no—
287D4×C43—42no—
288C2×C4×C43—22no—
289C2×C4×C43—24no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—44no—
294C2×C4×C43—44no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—44no—
298C2×C4×C43#12012yes—
299C2×C4×C43#12012yes—
300C2×C4×C43#12011yescharacteristic
301C2×C4×C43#12011yescharacteristic
302C2×C4×C43#12012yes—
303C2×C4×C43#12012yes—
304C2×C4×C43#12112yes—
305C2×C4×C43#12112yes—
306C2×C4×C43#12112yes—
307C2×C4×C43#12112yes—
308C2×C4×C43#12112yes—
309C2×C4×C43#12712yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C22⋊D43—42no—
317C22⋊D43—42no—
318C22⋊D43—44no—
319C22⋊D43—88no—
320C2×Dic43—24no—
321C2×Dic43—22no—
322C2×Dic43—24no—
323C2×Dic43—42no—
324C2×Dic43—48no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—82no—
330D172—22no—
331D172—22no—
332D172—42no—
333C4×D43—42no—
334C4×D43—42no—
335C4×D43—44no—
336Dic86—22no—
337Dic86—22no—
338Dic86—42no—
339C8×C43—24no—
340C43⋊C8—24no—
341C2×#2007—431nomaximal, Sylow
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—24no—
347C22×C43—24no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—84no—
352C22×C43#39212yes—
353C22×C43#39212yes—
354C22×C43#45512yes—
355C22×C43#45612yes—
356C22×C43C2×#12011yescharacteristic
357C22×C43C2×#12111yescharacteristic
358C22×C43C2×#12711yescharacteristic
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—84no—
363C4×C43—42no—
364C4×C43—44no—
365C4×C43#39212yes—
366C4×C43#39212yes—
367C4×C43C2×#12011yescharacteristic
368C4×C43C2×#12011yescharacteristic
369C4×C43C2×#12111yescharacteristic
370C4×C43C2×#12111yescharacteristic
371Dic43—44no—
372Dic43—42no—
373Dic43—44no—
374C22×#137—431no—
375C22×#137D4311yescharacteristic, complemented
376C2×#537—431no—
377C22×#104—431no—
378C22×#104—431no—
379C2×#391—431no—
380#2007—438no—
381C2×#343—431no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—22no—
385C2×C43—82no—
386C2×C43#200714yescomplemented
387C2×C43C2×#39211yescharacteristic
388C2×C43C2×#45511yescharacteristic
389C2×C43C2×#45611yescharacteristic
390D43—82no—
391C22×#41—431no—
392C22×#41C2×D4311yescharacteristic
393C23×Q8C2×D4311yescharacteristic
394C2×#137—22no—
395C2×#137—24no—
396C2×#137—24no—
397C2×#137—434no—
398C2×#137—864no—
399C2×#137—862no—
400C2×#137—864no—
401C2×#137C2×D4314yescomplemented
402C22×Q16—21no—
403C22×Q16—861no—
404C22×SD16—21no—
405C22×SD16—861no—
406C22×M16—431no—
407C22×M16C2×D4311yescharacteristic
408#537—434no—
409#537—862no—
410#537—862no—
411#537—862no—
412C2×C22⋊Q8—861no—
413C2×C22⋊Q8—861no—
414C2×#121—861no—
415C2×#121—862no—
416C2×#121—861no—
417C22×C4⋊C4—431no—
418C22×C42—431no—
419C2×#104—434no—
420C2×#104—434no—
421C2×#104—864no—
422C2×#104—864no—
423#391—434no—
424#391—862no—
425C2×#95—862no—
426#343—434no—
427C43C2×#200711yescharacteristic, complemented, Sylow
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—432no—
435C2×#41—432no—
436C2×#41—861no—
437C2×#41—861no—
438C2×#41—862no—
439C2×#41—862no—
440C2×#41—862no—
441C2×#41—862no—
442C2×#41C22⋊D4312yes—
443C2×#41C22×D4312yes—
444C22×Q8—21no—
445C22×Q8—22no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—22no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—431no—
453C22×Q8C22⋊D4311yescharacteristic
454C22×Q8C22⋊D4314yescomplemented
455C22×Q8C22×D4312yes—
456C22×D4—21no—
457C22×D4—431no—
458C22×D4—862no—
459C22×D4—861no—
460C22×D4C22⋊D4311yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—432no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467#137—216no—
468#137—28no—
469#137—28no—
470#137—868no—
471#137—8616no—
472#137—868no—
473C2×Q16—28no—
474C2×Q16—24no—
475C2×Q16—864no—
476C2×Q16—868no—
477C2×SD16—28no—
478C2×SD16—24no—
479C2×SD16—864no—
480C2×SD16—868no—
481C2×M16—22no—
482C2×M16—21no—
483C2×M16—434no—
484C2×M16—432no—
485C2×M16—861no—
486C2×M16—862no—
487C2×M16C22⋊D4314yescomplemented
488C2×M16C22×D4312yes—
489C22×C8—21no—
490C22×C8—861no—
491C22⋊Q8—864no—
492C22⋊Q8—864no—
493C22⋊Q8—864no—
494C22⋊Q8—864no—
495#121—864no—
496#121—864no—
497#121—868no—
498#121—864no—
499#121—868no—
500#121—864no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C22⋊C4—862no—
509C2×C22⋊C4—862no—
510C2×C42—432no—
511C2×C42—862no—
512C2×C42—862no—
513C2×C42—861no—
514#104—868no—
515#104—868no—
516#95—868no—
517C24—21no—
518C24—861no—
519C24D4×D4311yescharacteristic
520#41—24no—
521#41—24no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—42no—
527#41—42no—
528#41—42no—
529#41—42no—
530#41—864no—
531#41—864no—
532#41—862no—
533#41—862no—
534#41—862no—
535#41—862no—
536#41—1722no—
537#41—1722no—
538#41—1722no—
539#41—1722no—
540C2×Q8—21no—
541C2×Q8—24no—
542C2×Q8—22no—
543C2×Q8—24no—
544C2×Q8—24no—
545C2×Q8—24no—
546C2×Q8—22no—
547C2×Q8—24no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—432no—
561C2×Q8—861no—
562C2×Q8—862no—
563C2×Q8—862no—
564C2×Q8C2×C22⋊D4312yes—
565C2×Q8C2×C22⋊D4314yescomplemented
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—432no—
574C2×D4—868no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—861no—
579C2×D4—862no—
580C2×D4—3444no—
581C2×D4—1722no—
582C2×D4—1722no—
583C2×D4C2×C22⋊D4312yes—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—434no—
595C22×C4—862no—
596C22×C4—864no—
597C22×C4—862no—
598C22×C4—861no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—1724no—
603C22×C4—1722no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4D4×D4312yes—
611C22×C4#1062190012yes—
612C22×C4C2×C22⋊D4312yes—
613C22×C4C2×C22⋊D4311yescharacteristic
614C22×C4C2×C22⋊D4311yescharacteristic
615C22×C4C2×C22⋊D4312yes—
616C22×C4C23×D4311yescharacteristic
617Q16—216no—
618Q16—8616no—
619SD16—216no—
620SD16—8616no—
621M16—24no—
622M16—22no—
623M16—434no—
624M16—864no—
625M16—862no—
626M16C2×C22⋊D4314yescomplemented
627C2×C8—24no—
628C2×C8—22no—
629C2×C8—864no—
630C2×C8—862no—
631C4⋊C4—868no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C4⋊C4—862no—
636C22⋊C4—868no—
637C22⋊C4—868no—
638C42—862no—
639C42—862no—
640C42—1722no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—862no—
648C23—1722no—
649C23—1722no—
650C23—1722no—
651C23#1306329311yescharacteristic
652C23#1306329311yescharacteristic
653C23#1306329712yes—
654C23#1306332112yes—
655C23C2×D4×D4311yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—22no—
659Q8—22no—
660Q8—44no—
661Q8—44no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—862no—
666Q8—862no—
667Q8—1722no—
668D4—22no—
669D4—22no—
670D4—44no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—862no—
675D4—862no—
676D4—3448no—
677D4—1724no—
678D4—1722no—
679D4—1722no—
680D4—1722no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—864no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—3442no—
695C2×C4—1728no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1724no—
699C2×C4—1722no—
700C2×C4—1724no—
701C2×C4—1722no—
702C2×C4—1722no—
703C2×C4—1724no—
704C2×C4#1306329311yescharacteristic
705C2×C4#1306329311yescharacteristic
706C2×C4#1306329312yes—
707C2×C4#1306329312yes—
708C2×C4#1306329412yes—
709C2×C4#1306329412yes—
710C2×C4#1306329612yes—
711C2×C4#1306329612yes—
712C2×C4#1306329712yes—
713C2×C4#1306329712yes—
714C2×C4#1306329712yes—
715C2×C4#1306332112yes—
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C22×C22⋊D4311yescharacteristic
719C2×C4C22×C22⋊D4311yescharacteristic
720C2×C4C22×C22⋊D4311yescharacteristic
721C2×C4C2×#1062190011yescharacteristic
722C8—24no—
723C8—864no—
724C22—24no—
725C22—24no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—3444no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22#1458280712yes—
739C22#1458280712yes—
740C22#1458307512yes—
741C22#1458308012yes—
742C22C2×#1306329311yescharacteristic
743C22C2×#1306329711yescharacteristic
744C22C2×#1306332111yescharacteristic
745C4—42no—
746C4—44no—
747C4—1724no—
748C4—1724no—
749C4—1722no—
750C4#1458280712yes—
751C4#1458280712yes—
752C4C2×#1306329311yescharacteristic
753C4C2×#1306329411yescharacteristic
754C4C2×#1306329611yescharacteristic
755C4C2×#1306329711yescharacteristic
756C2—21no—
757C2—22no—
758C2—21no—
759C2—82no—
760C2—3442no—
761C2#1913564014yesdirect product factor
762C2C2×#1458280711yescharacteristic
763C2C2×#1458307511yescharacteristic
764C2C2×#1458308011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#137×C43C2
socleC23×C43#120
prime radicalC2×#14583477C2
hypercenterC22×#137D43
hypocenterC43C2×#2007
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#13063356C2semidirect
3. C22×#13063252C2semidirect
4. C22×#13063251C2semidirect
5. C2×#14582806C2semidirect
6. #19135640C2direct (N × H)
7. C2×#14582667C2semidirect
8. C22×#137×C43C2semidirect
13. C2×#13063356C22semidirect
29. C2×#13063252C22semidirect
31. C2×#13063251C22semidirect
33. #14582806C22semidirect
35. #14582667C22semidirect
41. C2×#137×C43C22semidirect
69. C2×#10621877D4semidirect
115. C22×Q8×C43D4semidirect
131. C2×M16×C43D4semidirect
168. C2×Q8×C43C2×D4semidirect
238. M16×C43C2×D4semidirect
255. #10621877C2×D4semidirect
375. C22×#137D43semidirect
386. C2×C43#2007semidirect
401. C2×#137C2×D43semidirect
427. C43C2×#2007semidirect
454. C22×Q8C22⋊D43semidirect
487. C2×M16C22⋊D43semidirect
565. C2×Q8C2×C22⋊D43semidirect
626. M16C2×C22⋊D43semidirect
761. C2#19135640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633562
C2×#145834772
C22×#130632522
C22×#130632512
C2×#145828062
#191356402
C2×#145826672
C22×#137×C432
C2×#200743