Finite Group Databasebeta

← C2×#19145446 #25967249

Subgroups — C2×#19145446 #25967249

Order 11008.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic, complemented
3#19145446C2116yesmaximal, direct product factor
4C2×#14583218C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583210C211yesmaximal, characteristic, complemented
8C2×#14583149C211yesmaximal, characteristic, complemented
9C2×#14583148C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583048C211yesmaximal, characteristic, complemented
14C2×#14583031C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621872C2211yescharacteristic, complemented
22C22×C8×D43C2211yescharacteristic, complemented
23#14583477—24no—
24#14583477C2218yescomplemented
25#14583465—24no—
26#14583465C2218yescomplemented
27C2×#13063321—21no—
28C2×#13063311—21no—
29C2×#13063304—21no—
30C2×#13063301C2211yescharacteristic
31C2×#13063301C2211yescharacteristic, complemented
32C2×#13063300C2211yescharacteristic
33C2×#13063299—21no—
34C2×#13063299C2211yescharacteristic
35C2×#13063297—21no—
36C2×#13063297—21no—
37C2×#13063296C2211yescharacteristic
38C2×#13063296C2211yescharacteristic
39C2×#13063296C2211yescharacteristic, complemented
40C2×#13063295—21no—
41C2×#13063293—21no—
42C2×#13063283C2211yescharacteristic
43C22×C4⋊Dic43C2211yescharacteristic, complemented
44#14583238C2218yescomplemented
45#14583222C2218yescomplemented
46#14583218C2218yescomplemented
47#14583210C2218yescomplemented
48#14583149C2218yescomplemented
49#14583148C2218yescomplemented
50#14583134C2218yescomplemented
51#14583125C2218yescomplemented
52#14583048C2218yescomplemented
53#14583044C2218yescomplemented
54#14583031C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063257C2211yescharacteristic, complemented
58C2×#13063257C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic, complemented
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic, complemented
70C22×SD16×C43C2211yescharacteristic
71C22×D8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#449C2218yescomplemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898D414yes—
81C2×#10621898C2314yes—
82C22×Dic86D411yescharacteristic
83C22×D172—21no—
84C22×D172D411yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43D411yescharacteristic
92C22×C22⋊D43D411yescharacteristic
93C2×D4×D43—22no—
94C2×D4×D43—42no—
95C2×D4×D43—42no—
96C2×D4×D43C2314yes—
97C23×Dic43—21no—
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2311yescharacteristic
100C2×#10621884—42no—
101C2×#10621884C2314yes—
102C2×#10621882—42no—
103C2×#10621882C2314yes—
104C2×#10621872—42no—
105C2×#10621872C2314yescomplemented
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108C2×C8×D43—42no—
109C2×C8×D43C2314yescomplemented
110#13063321—28no—
111#13063311—28no—
112#13063304—28no—
113#13063301—22no—
114#13063301—22no—
115#13063301C2314yes—
116#13063301C2314yescomplemented
117#13063300—22no—
118#13063300C2314yes—
119#13063299—22no—
120#13063299—28no—
121#13063299C2314yes—
122#13063297—28no—
123#13063297—28no—
124#13063296—22no—
125#13063296—22no—
126#13063296—22no—
127#13063296C2314yes—
128#13063296C2314yes—
129#13063296C2314yescomplemented
130#13063295—28no—
131#13063293—28no—
132#13063283—22no—
133#13063283C2314yes—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43—22no—
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×C4⋊Dic43C2311yescharacteristic
139C2×C4⋊Dic43C2314yescomplemented
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×C4×Dic43—21no—
151#13063258C2314yescomplemented
152#13063258C2314yescomplemented
153#13063257C2314yescomplemented
154#13063257C2314yescomplemented
155#13063249C2314yescomplemented
156#13063247C2314yes—
157#13063247C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160#13063246C2314yescomplemented
161C22⋊(C43⋊C8)C2314yescomplemented
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yescomplemented
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43—21no—
170C22×D4×C43—21no—
171C22×D4×C43C2311yescharacteristic
172C22×D4×C43C2311yescharacteristic
173C23×C4×C43—21no—
174C23×C4×C43C2311yescharacteristic
175C2×SD16×C43—42no—
176C2×SD16×C43C2314yes—
177C2×D8×C43—42no—
178C2×D8×C43C2314yes—
179C22×C8×C43C2311yescharacteristic
180C22×C8×C43C2311yescharacteristic
181#121×C43—22no—
182#121×C43C2314yes—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yescomplemented
186#102×C43C2314yescomplemented
187C22⋊C8×C43C2314yescomplemented
188C24×C43—21no—
189C24×C43—21no—
190C24×C43C2×D411yescharacteristic
191C23×D43—21no—
192C23×D43—24no—
193C23×D43—44no—
194C23×D43—82no—
195C23×D43—82no—
196C23×D43C2×D411yescharacteristic
197C23×D43C2×D411yescharacteristic
198#41×C43—44no—
199#41×C43—44no—
200#41×C43—48no—
201C2×Q8×C43—21no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43C2412yes—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—24no—
208C2×D4×C43—24no—
209C2×D4×C43—22no—
210C2×D4×C43—22no—
211C2×D4×C43—22no—
212C2×D4×C43—22no—
213C2×D4×C43—44no—
214C2×D4×C43—82no—
215C2×D4×C43C2412yes—
216C2×D4×C43C2412yes—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—24no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—44no—
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2412yes—
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—24no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—24no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—42no—
233C2×C22⋊D43—42no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—82no—
236C2×C22⋊D43—82no—
237C2×C22⋊D43—82no—
238C2×C22⋊D43—82no—
239C2×C22⋊D43C2×D414yes—
240C2×C22⋊D43C2×D414yes—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—24no—
245C22×Dic43—82no—
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248D4×D43—44no—
249D4×D43—44no—
250D4×D43—48no—
251#10621898—48no—
252#10621898—44no—
253#10621898—44no—
254C2×D172—21no—
255C2×D172—24no—
256C2×D172—22no—
257C2×D172—22no—
258C2×D172—42no—
259C2×D172—82no—
260C2×D172C2×D414yes—
261C2×D172C2412yes—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×C4×D43—22no—
265C2×C4×D43—22no—
266C2×C4×D43C2×D412yes—
267C2×C4×D43C2×D412yes—
268C2×C4×D43C2412yes—
269C2×C4×D43C2412yes—
270C2×Dic86—42no—
271C2×Dic86C2×D414yes—
272SD16×C43—44no—
273D8×C43—44no—
274C2×C8×C43—22no—
275C2×C8×C43—22no—
276C2×C8×C43C2412yes—
277C2×C8×C43C2412yes—
278C4⋊C4×C43—21no—
279C4⋊C4×C43C2412yes—
280C22⋊C4×C43—24no—
281C22⋊Dic43—24no—
282C22⋊Dic43—24no—
283C22⋊Dic43—24no—
284#10621884—44no—
285#10621882—44no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43—24no—
294C4⋊Dic43—21no—
295C4⋊Dic43C2412yes—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2412yes—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300C4×Dic43—24no—
301C2×C43⋊C8—22no—
302C2×C43⋊C8—22no—
303C2×C43⋊C8C2412yes—
304C2×C43⋊C8C2412yes—
305#10621872—44no—
306C8×D43—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43C22×D412yes—
319C23×C43C22×D411yescharacteristic
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—48no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—84no—
332C22×D43—84no—
333C22×D43—816no—
334C22×D43C22×D412yes—
335C22×D43C22×D412yes—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—42no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—48no—
344D4×C43—42no—
345D4×C43—42no—
346D4×C43—84no—
347C2×C4×C43—22no—
348C2×C4×C43—24no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—48no—
354C2×C4×C43—42no—
355C2×C4×C43—42no—
356C2×C4×C43C22×D412yes—
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43H(5,𝔽2)12yes—
359C2×C4×C43H(5,𝔽2)12yes—
360C2×C4×C43C2511yescharacteristic
361C22⋊D43—44no—
362C22⋊D43—44no—
363C22⋊D43—48no—
364C22⋊D43—84no—
365C22⋊D43—84no—
366C22⋊D43—84no—
367C22⋊D43—84no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—84no—
377C2×Dic43C22×D412yes—
378C2×Dic43C22×D412yes—
379D172—22no—
380D172—22no—
381D172—44no—
382D172—42no—
383D172—84no—
384C4×D43—24no—
385C4×D43—24no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—22no—
389C4×D43—22no—
390Dic86—44no—
391C8×C43—22no—
392C8×C43—22no—
393C43⋊C8—22no—
394C43⋊C8—22no—
395C2×#3198—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—44no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—84no—
407C22×C43—84no—
408C22×C43#53412yes—
409C22×C43#57612yes—
410C22×C43#57712yes—
411C22×C43C23×D411yescharacteristic
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—44no—
419C2×D43—44no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—816no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43#53412yes—
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431Dic43—22no—
432Dic43—22no—
433Dic43—42no—
434Dic43—42no—
435Dic43—42no—
436C2×#537—431no—
437C2×#535—431no—
438#3198—4316no—
439C2×#481—431no—
440C2×#485—431no—
441C2×#482—431no—
442C2×#480—431no—
443C2×#469—431no—
444C2×#468—431no—
445C2×#466—431no—
446C2×#465—431no—
447C2×#449—431no—
448C2×#449D4311yescharacteristic, complemented
449C2×#450—431no—
450C2×#447—431no—
451C2×#408—431no—
452C2×C43—42no—
453C2×C43—82no—
454C2×C43—82no—
455C2×C43#319814yescomplemented
456C2×C43C2×#53411yescharacteristic
457C2×C43C2×#57611yescharacteristic
458C2×C43C2×#57711yescharacteristic
459D43—42no—
460D43—42no—
461D43—82no—
462C22×#41—431no—
463C22×#41C2×D4311yescharacteristic, complemented
464C23×D4—431no—
465C22×SD16—431no—
466C22×SD16C2×D4311yescharacteristic
467C22×D8—431no—
468C22×D8C2×D4311yescharacteristic
469C22×M16—431no—
470C23×C8—431no—
471#537—438no—
472#537—864no—
473#535—438no—
474#535—864no—
475C2×#127—861no—
476C2×#124—861no—
477C2×C22⋊Q8—431no—
478C2×C22⋊Q8—431no—
479C2×C22⋊Q8—861no—
480C2×#121—431no—
481C2×#121—431no—
482C2×#121—431no—
483C2×#121—431no—
484C2×#121—431no—
485C2×#121—861no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121C2×D4311yescharacteristic
489C2×#120—861no—
490C2×#120—861no—
491C2×#117—431no—
492C22×C4⋊C4—431no—
493#485—438no—
494#482—438no—
495#481—438no—
496#480—438no—
497#469—438no—
498#468—438no—
499#466—438no—
500#465—438no—
501#450—438no—
502#449—438no—
503#449C2×D4318yescomplemented
504#447—438no—
505C2×#107—431no—
506C2×#107—431no—
507C2×#106—431no—
508C2×#106—431no—
509C2×#103—431no—
510C2×#103C2×D4311yescharacteristic, complemented
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102—431no—
516C2×#102C2×D4311yescharacteristic, complemented
517#408—438no—
518C2×C22⋊C8—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C22⋊C8C2×D4311yescharacteristic, complemented
522C43C2×#319811yescharacteristic, complemented, Sylow
523C25—861no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—434no—
528C2×#41—434no—
529C2×#41—1722no—
530C2×#41—1722no—
531C2×#41C22×D4314yescomplemented
532C22×Q8—431no—
533C22×Q8C22×D4311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—431no—
537C22×D4—431no—
538C22×D4—434no—
539C22×D4—431no—
540C22×D4—431no—
541C22×D4—861no—
542C22×D4—862no—
543C22×D4—861no—
544C22×D4—861no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—1722no—
549C22×D4—1722no—
550C22×D4C22×D4311yescharacteristic
551C22×D4C22×D4311yescharacteristic
552C23×C4—21no—
553C23×C4—431no—
554C23×C4—431no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×SD16—42no—
558C2×SD16—434no—
559C2×SD16—1722no—
560C2×SD16C22×D4314yes—
561C2×D8—42no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8C22×D4314yes—
565C2×M16—434no—
566C2×M16—1722no—
567C22×C8—431no—
568C22×C8—431no—
569C22×C8—434no—
570C22×C8—1722no—
571C22×C8C22×D4311yescharacteristic
572C22×C8C22×D4311yescharacteristic
573#127—868no—
574#124—868no—
575C22⋊Q8—434no—
576C22⋊Q8—434no—
577C22⋊Q8—868no—
578C22⋊Q8—862no—
579C22⋊Q8—862no—
580#121—22no—
581#121—434no—
582#121—434no—
583#121—434no—
584#121—434no—
585#121—434no—
586#121—862no—
587#121—868no—
588#121—862no—
589#121—862no—
590#121—862no—
591#121—868no—
592#121—868no—
593#121—862no—
594#121C22×D4314yes—
595#120—868no—
596#120—868no—
597#117—434no—
598#117—862no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—434no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—861no—
618#107—434no—
619#107—434no—
620#106—434no—
621#106—434no—
622#103—434no—
623#103C22×D4314yescomplemented
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102—434no—
629#102C22×D4314yescomplemented
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8C22×D4314yescomplemented
634C24—21no—
635C24—21no—
636C24—431no—
637C24—431no—
638C24—864no—
639C24—861no—
640C24—3442no—
641C24—3442no—
642C24—1724no—
643C24D4×D4311yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—1728no—
648#41—1724no—
649#41—1724no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—434no—
654C2×Q8—1722no—
655C2×Q8C23×D4312yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—44no—
665C2×D4—82no—
666C2×D4—434no—
667C2×D4—434no—
668C2×D4—434no—
669C2×D4—432no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—864no—
676C2×D4—861no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—1722no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1728no—
688C2×D4—1722no—
689C2×D4—1722no—
690C2×D4—1724no—
691C2×D4C23×D4312yes—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—44no—
699C22×C4—431no—
700C22×C4—431no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—864no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—3442no—
714C22×C4D4×D4312yes—
715C22×C4D4×D4311yescharacteristic
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—44no—
719SD16—1724no—
720D8—44no—
721D8—1724no—
722M16—1724no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—862no—
728C2×C8—862no—
729C2×C8—1724no—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—21no—
733C4⋊C4—432no—
734C4⋊C4—432no—
735C4⋊C4—432no—
736C4⋊C4—864no—
737C4⋊C4—864no—
738C4⋊C4—864no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—864no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C42—864no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—432no—
765C23—432no—
766C23—862no—
767C23—862no—
768C23—862no—
769C23—862no—
770C23—862no—
771C23—862no—
772C23—862no—
773C23—3444no—
774C23—3444no—
775C23—34416no—
776C23—1728no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C2×D4×D4312yes—
781C23C2×D4×D4311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—1724no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—84no—
794D4—862no—
795D4—862no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—3444no—
801D4—1724no—
802D4—1724no—
803D4—1724no—
804D4—1728no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—432no—
816C2×C4—432no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—864no—
820C2×C4—864no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—3444no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4C2×D4×D4312yes—
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#1306337012yes—
835C2×C4#1306337012yes—
836C2×C4C24×D4311yescharacteristic
837C8—22no—
838C8—22no—
839C8—862no—
840C8—862no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—34416no—
860C22—3444no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1724no—
865C22—1724no—
866C22#1458345912yes—
867C22#1458370312yes—
868C22#1458370612yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—862no—
874C4—862no—
875C4—1722no—
876C4—1722no—
877C4—1722no—
878C4#1458345912yes—
879C4C2×#1306337011yescharacteristic
880C4C2×#1306337011yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914544614yesdirect product factor
888C2C2×#1458345911yescharacteristic
889C2C2×#1458370311yescharacteristic
890C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583477C2semidirect
2. C2×#14583465C2semidirect
3. #19145446C2direct (N × H)
4. C2×#14583218C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583210C2semidirect
8. C2×#14583149C2semidirect
9. C2×#14583148C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583048C2semidirect
14. C2×#14583031C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#449C2semidirect
21. C22×#10621872C22semidirect
22. C22×C8×D43C22semidirect
24. #14583477C22semidirect
26. #14583465C22semidirect
31. C2×#13063301C22semidirect
39. C2×#13063296C22semidirect
43. C22×C4⋊Dic43C22semidirect
44. #14583238C22semidirect
45. #14583222C22semidirect
46. #14583218C22semidirect
47. #14583210C22semidirect
48. #14583149C22semidirect
49. #14583148C22semidirect
50. #14583134C22semidirect
51. #14583125C22semidirect
52. #14583048C22semidirect
53. #14583044C22semidirect
54. #14583031C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063257C22semidirect
58. C2×#13063257C22semidirect
59. C2×#13063249C22semidirect
64. C2×#13063246C22semidirect
65. #14582864C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
69. C22×#41×C43C22semidirect
73. C43×#449C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
105. C2×#10621872C23semidirect
109. C2×C8×D43C23semidirect
116. #13063301C23semidirect
129. #13063296C23semidirect
139. C2×C4⋊Dic43C23semidirect
151. #13063258C23semidirect
152. #13063258C23semidirect
153. #13063257C23semidirect
154. #13063257C23semidirect
155. #13063249C23semidirect
160. #13063246C23semidirect
161. C22⋊(C43⋊C8)C23semidirect
167. C2×#41×C43C23semidirect
185. #103×C43C23semidirect
186. #102×C43C23semidirect
187. C22⋊C8×C43C23semidirect
448. C2×#449D43semidirect
455. C2×C43#3198semidirect
463. C22×#41C2×D43semidirect
503. #449C2×D43semidirect
510. C2×#103C2×D43semidirect
516. C2×#102C2×D43semidirect
521. C2×C22⋊C8C2×D43semidirect
522. C43C2×#3198semidirect
531. C2×#41C22×D43semidirect
623. #103C22×D43semidirect
629. #102C22×D43semidirect
633. C22⋊C8C22×D43semidirect
887. C2#19145446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145834652
#191454462
C2×#145832182
C2×#145832382
C2×#145832222
C2×#145832102
C2×#145831492
C2×#145831482
C2×#145831342
C2×#145831252
C2×#145830442
C2×#145830482
C2×#145830312
C2×#145828642
C2×C43×#4492
C2×#319843