Finite Group Databasebeta

← C2×#19145643 #25967926

Subgroups — C2×#19145643 #25967926

Order 11008.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583502C211yesmaximal, characteristic, complemented
2C2×#14583463C211yesmaximal, characteristic, complemented
3#19145643C2116yesmaximal, direct product factor
4C2×#14583285C211yesmaximal, characteristic, complemented
5C2×#14583274C211yesmaximal, characteristic, complemented
6C2×#14583262C211yesmaximal, characteristic, complemented
7C2×#14583255C211yesmaximal, characteristic, complemented
8C2×#14583117C211yesmaximal, characteristic, complemented
9C2×#14583116C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583092C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583035C211yesmaximal, characteristic, complemented
14C2×#14583032C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C22×#10621884C2211yescharacteristic, complemented
19C22×D344C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic, complemented
24#14583502—24no—
25#14583502C2218yescomplemented
26#14583463—24no—
27#14583463C2218yescomplemented
28C2×#13063321C2211yescharacteristic
29C2×#13063321C2211yescharacteristic
30C2×#13063321C2211yescharacteristic, complemented
31C2×#13063316C2211yescharacteristic, complemented
32C2×#13063314C2211yescharacteristic
33C2×#13063314C2211yescharacteristic
34C2×#13063309—21no—
35C2×#13063307—21no—
36C2×#13063299—21no—
37C2×#13063299—21no—
38C2×#13063299C2211yescharacteristic
39C2×#13063297—21no—
40C2×#13063296—21no—
41C2×#13063293—21no—
42C2×#13063293—21no—
43C2×D4×Dic43C2211yescharacteristic, complemented
44C2×#13063287C2211yescharacteristic, complemented
45C2×#13063284C2211yescharacteristic
46#14583285C2218yescomplemented
47#14583274C2218yescomplemented
48#14583262C2218yescomplemented
49#14583255C2218yescomplemented
50#14583117C2218yescomplemented
51#14583116C2218yescomplemented
52#14583093C2218yescomplemented
53#14583092C2218yescomplemented
54#14583044C2218yescomplemented
55#14583035C2218yescomplemented
56#14583032C2218yescomplemented
57#14582957C2218yescomplemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59C2×Dic43⋊C8C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic, complemented
71C22×D8×C43C2211yescharacteristic, complemented
72C2×#121×C43C2211yescharacteristic
73C43×#449C2218yescomplemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43—21no—
78C22×D172—21no—
79C22×D172—22no—
80C22×D172—42no—
81C22×D172—42no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2314yes—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C2×#10621884—42no—
96C2×#10621884C2314yescomplemented
97C2×D344—42no—
98C2×D344—42no—
99C2×D344C2314yes—
100C2×D344C2314yes—
101C2×#10621882—42no—
102C2×#10621882—42no—
103C2×#10621882—42no—
104C2×#10621882C2314yes—
105C2×#10621882C2314yes—
106C2×#10621882C2314yescomplemented
107C22×C43⋊C8C2311yescharacteristic
108C22×C43⋊C8C2311yescharacteristic
109#13063321—22no—
110#13063321—22no—
111#13063321—22no—
112#13063321C2314yes—
113#13063321C2314yes—
114#13063321C2314yescomplemented
115#13063316—22no—
116#13063316C2314yescomplemented
117#13063314—22no—
118#13063314—22no—
119#13063314C2314yes—
120#13063314C2314yes—
121#13063309—28no—
122#13063307—28no—
123#13063299—22no—
124#13063299—28no—
125#13063299—28no—
126#13063299C2314yes—
127#13063297—28no—
128#13063296—28no—
129#13063293—28no—
130#13063293—28no—
131D4×Dic43—22no—
132D4×Dic43C2314yescomplemented
133#13063287—22no—
134#13063287C2314yescomplemented
135#13063284D414yes—
136#13063284C2314yes—
137C2×C4⋊Dic43—21no—
138C2×C4⋊Dic43D411yescharacteristic
139C2×C4⋊Dic43D411yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43D411yescharacteristic
144C2×C22⋊Dic43D411yescharacteristic
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×(C2×D43)⋊C4—21no—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153Dic43⋊C8C2314yescomplemented
154Dic43⋊C8C2314yescomplemented
155#13063249C2314yescomplemented
156#13063247C2314yes—
157#13063247C2314yes—
158#13063246C2314yescomplemented
159#13063245C2314yes—
160#13063245C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162#13063235C2314yescomplemented
163C8×Dic43C2314yescomplemented
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yes—
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×C43C2314yescomplemented
177C2×D8×C43—42no—
178C2×D8×C43C2314yescomplemented
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×C43C2314yes—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43C2×D411yescharacteristic
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—24no—
195C23×D43—44no—
196C23×D43—82no—
197C23×D43—82no—
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—24no—
233C2×C22⋊D43—24no—
234C2×C22⋊D43—82no—
235C2×C22⋊D43—82no—
236C2×C22⋊D43—82no—
237C2×C22⋊D43—82no—
238C2×C22⋊D43—82no—
239C2×C22⋊D43—82no—
240C2×C22⋊D43—82no—
241C22×Dic43—24no—
242C22×Dic43—21no—
243C22×Dic43—82no—
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248C2×D172—21no—
249C2×D172—24no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172—22no—
258C2×D172—44no—
259C2×D172—44no—
260C2×D172—48no—
261C2×D172—44no—
262C2×D172C2412yes—
263C2×D172C2412yes—
264C2×D172C2412yes—
265C2×C4×D43—24no—
266C2×C4×D43—82no—
267SD16×C43—44no—
268D8×C43—44no—
269C2×C8×C43—22no—
270C2×C8×C43—22no—
271C2×C8×C43C2412yes—
272C2×C8×C43C2412yes—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2412yes—
275C22⋊C4×C43—24no—
276C22⋊Dic43—24no—
277C22⋊Dic43C2×D414yes—
278C22⋊Dic43C2×D414yes—
279#10621884—44no—
280#10621882—44no—
281#10621882—44no—
282#10621882—44no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289C4⋊Dic43—21no—
290C4⋊Dic43—24no—
291C4⋊Dic43C2×D414yes—
292C4⋊Dic43C2×D414yes—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—24no—
295C4×Dic43C2×D412yes—
296C4×Dic43C2×D412yes—
297C4×Dic43C2412yes—
298C4×Dic43C2412yes—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303D344—44no—
304D344—44no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43C22×D412yes—
317C23×C43C22×D411yescharacteristic
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—48no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—84no—
332C22×D43—84no—
333C22×D43—816no—
334Q8×C43—22no—
335Q8×C43—22no—
336Q8×C43—42no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—48no—
342D4×C43—42no—
343D4×C43—42no—
344D4×C43—84no—
345C2×C4×C43—22no—
346C2×C4×C43—24no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—48no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43H(5,𝔽2)12yes—
357C2×C4×C43H(5,𝔽2)12yes—
358C2×C4×C43C2511yescharacteristic
359C22⋊D43—84no—
360C22⋊D43—84no—
361C22⋊D43—84no—
362C22⋊D43—84no—
363C22⋊D43—84no—
364C22⋊D43—84no—
365C22⋊D43—84no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—42no—
372C2×Dic43—84no—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376C2×Dic43C22×D412yes—
377D172—22no—
378D172—22no—
379D172—22no—
380D172—22no—
381D172—22no—
382D172—22no—
383D172—48no—
384D172—42no—
385D172—42no—
386D172—42no—
387C4×D43—84no—
388C8×C43—22no—
389C8×C43—22no—
390C43⋊C8—22no—
391C43⋊C8—22no—
392C2×#3220—431nomaximal, Sylow
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—44no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—84no—
404C22×C43—84no—
405C22×C43#53512yes—
406C22×C43#57612yes—
407C22×C43#57612yes—
408C22×C43C23×D411yescharacteristic
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—816no—
419C2×D43—84no—
420C2×D43—84no—
421C2×D43—84no—
422C4×C43—22no—
423C4×C43—42no—
424C4×C43—42no—
425C4×C43#53512yes—
426C4×C43C2×H(5,𝔽2)11yescharacteristic
427C4×C43C2×H(5,𝔽2)11yescharacteristic
428Dic43—22no—
429Dic43—22no—
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433C2×#540—431no—
434C2×#535—431no—
435#3220—4316no—
436C2×#496—431no—
437C2×#493—431no—
438C2×#490—431no—
439C2×#488—431no—
440C2×#463—431no—
441C2×#463—431no—
442C2×#459—431no—
443C2×#459—431no—
444C2×#449—431no—
445C2×#449D4311yescharacteristic, complemented
446C2×#447—431no—
447C2×#447—431no—
448C2×#433—431no—
449C2×C43—42no—
450C2×C43—82no—
451C2×C43—82no—
452C2×C43#322014yescomplemented
453C2×C43C2×#53511yescharacteristic
454C2×C43C2×#57611yescharacteristic
455C2×C43C2×#57611yescharacteristic
456D43—82no—
457D43—82no—
458D43—82no—
459C22×#41C2×D4311yescharacteristic
460C23×D4—431no—
461C22×SD16—431no—
462C22×SD16C2×D4311yescharacteristic, complemented
463C22×D8—431no—
464C22×D8—431no—
465C22×D8—431no—
466C22×D8—431no—
467C22×D8—431no—
468C22×D8C2×D4311yescharacteristic, complemented
469#540—438no—
470#540—864no—
471#535—438no—
472#535—864no—
473C2×#127—431no—
474C2×#127—431no—
475C2×#127—431no—
476C2×#125—431no—
477C2×#124—431no—
478C2×#124—431no—
479C2×#123—861no—
480C2×#123—861no—
481C2×#121—431no—
482C2×#121—861no—
483C2×#121—861no—
484C2×#121—861no—
485C2×#121—861no—
486C2×#121C2×D4311yescharacteristic
487C2×#120—861no—
488C2×#120—861no—
489C2×C4×D4—431no—
490C2×C4×D4—431no—
491C2×#117—431no—
492#496—438no—
493#493—438no—
494#490—438no—
495#488—438no—
496#463—438no—
497#463—438no—
498#459—438no—
499#459—438no—
500#449—438no—
501#449C2×D4318yescomplemented
502#447—438no—
503#447—438no—
504#433—438no—
505C2×C4⋊C8—431no—
506C2×C4⋊C8—431no—
507C2×#103—431no—
508C2×#103C2×D4311yescharacteristic, complemented
509C2×#102—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102C2×D4311yescharacteristic, complemented
515C2×C22⋊C8—431no—
516C2×C22⋊C8C2×D4311yescharacteristic
517C2×#97—431no—
518C2×C4×C8—431no—
519C43C2×#322011yescharacteristic, complemented, Sylow
520C25—861no—
521C2×#41—22no—
522C2×#41—42no—
523C2×#41—42no—
524C2×#41C22×D4314yes—
525C22×Q8C22×D4311yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—431no—
531C22×D4—434no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4—861no—
536C22×D4—861no—
537C22×D4—861no—
538C22×D4—861no—
539C22×D4—861no—
540C22×D4—862no—
541C22×D4—1722no—
542C22×D4—1722no—
543C22×D4C22×D4311yescharacteristic
544C22×D4C22×D4311yescharacteristic
545C23×C4—21no—
546C23×C4—861no—
547C23×C4—861no—
548C23×C4C22×D4311yescharacteristic
549C2×SD16—42no—
550C2×SD16—434no—
551C2×SD16—1722no—
552C2×SD16C22×D4314yescomplemented
553C2×D8—42no—
554C2×D8—434no—
555C2×D8—434no—
556C2×D8—434no—
557C2×D8—434no—
558C2×D8—434no—
559C2×D8—1722no—
560C2×D8—1722no—
561C2×D8—1722no—
562C2×D8—1722no—
563C2×D8—1722no—
564C2×D8C22×D4314yescomplemented
565C22×C8—431no—
566C22×C8—431no—
567C22×C8C22×D4311yescharacteristic
568C22×C8C22×D4311yescharacteristic
569#127—434no—
570#127—434no—
571#127—434no—
572#127—862no—
573#127—862no—
574#127—862no—
575#125—434no—
576#125—862no—
577#124—434no—
578#124—434no—
579#124—862no—
580#124—862no—
581#123—868no—
582#123—868no—
583#121—22no—
584#121—434no—
585#121—868no—
586#121—868no—
587#121—868no—
588#121—868no—
589#121—862no—
590#121C22×D4314yes—
591#120—868no—
592#120—868no—
593C4×D4—434no—
594C4×D4—434no—
595C4×D4—862no—
596C4×D4—862no—
597#117—434no—
598#117—434no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—431no—
607C2×C22⋊C4—431no—
608C2×C22⋊C4—861no—
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×C42—431no—
616C2×C42—431no—
617C4⋊C8—434no—
618C4⋊C8—434no—
619#103—434no—
620#103C22×D4314yescomplemented
621#102—434no—
622#102—434no—
623#102—434no—
624#102—434no—
625#102—434no—
626#102C22×D4314yescomplemented
627C22⋊C8—434no—
628C22⋊C8C22×D4314yes—
629#97—434no—
630C4×C8—434no—
631C24—21no—
632C24—21no—
633C24—864no—
634C24—861no—
635C24—861no—
636C24—861no—
637C24—3442no—
638C24—3442no—
639C24—1724no—
640C24D4×D4311yescharacteristic
641#41—44no—
642#41—44no—
643#41—48no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8C23×D4312yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—44no—
657C2×D4—82no—
658C2×D4—432no—
659C2×D4—432no—
660C2×D4—432no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—864no—
668C2×D4—861no—
669C2×D4—864no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—862no—
673C2×D4—862no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—3442no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—3442no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1724no—
688C2×D4—1728no—
689C2×D4C23×D4312yes—
690C2×D4C23×D4312yes—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—24no—
696C22×C4—44no—
697C22×C4—431no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—431no—
701C22×C4—864no—
702C22×C4—864no—
703C22×C4—861no—
704C22×C4—3442no—
705C22×C4—3442no—
706C22×C4D4×D4312yes—
707C22×C4D4×D4311yescharacteristic
708C22×C4C23×D4312yes—
709C22×C4C23×D4311yescharacteristic
710SD16—44no—
711SD16—1724no—
712D8—44no—
713D8—1724no—
714D8—1724no—
715D8—1724no—
716D8—1724no—
717D8—1724no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—432no—
721C2×C8—432no—
722C2×C8—862no—
723C2×C8—862no—
724C2×C8C23×D4312yes—
725C2×C8C23×D4312yes—
726C4⋊C4—21no—
727C4⋊C4—434no—
728C4⋊C4—434no—
729C4⋊C4—432no—
730C4⋊C4—864no—
731C4⋊C4—864no—
732C4⋊C4—861no—
733C4⋊C4C23×D4312yes—
734C22⋊C4—24no—
735C22⋊C4—434no—
736C22⋊C4—434no—
737C22⋊C4—864no—
738C22⋊C4—864no—
739C22⋊C4—864no—
740C22⋊C4—864no—
741C22⋊C4—864no—
742C22⋊C4—864no—
743C22⋊C4—864no—
744C42—432no—
745C42—432no—
746C42—432no—
747C42—432no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—3444no—
763C23—3444no—
764C23—34416no—
765C23—1728no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23—1722no—
771C23—1722no—
772C23—1722no—
773C23—1722no—
774C23—1722no—
775C23C2×D4×D4312yes—
776C23C2×D4×D4311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—42no—
786D4—42no—
787D4—84no—
788D4—862no—
789D4—862no—
790D4—862no—
791D4—862no—
792D4—862no—
793D4—862no—
794D4—3444no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—3444no—
801D4—1728no—
802D4—1722no—
803D4—1722no—
804D4—1722no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—48no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—432no—
815C2×C4—432no—
816C2×C4—432no—
817C2×C4—432no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—3444no—
824C2×C4—3444no—
825C2×C4—1722no—
826C2×C4C2×D4×D4312yes—
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4#1306337012yes—
829C2×C4#1306337012yes—
830C2×C4C24×D4311yescharacteristic
831C8—22no—
832C8—22no—
833C8—862no—
834C8—862no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—84no—
846C22—84no—
847C22—34416no—
848C22—3444no—
849C22—3444no—
850C22—3444no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22#1458346412yes—
861C22#1458370112yes—
862C22#1458370312yes—
863C22C22×D4×D4311yescharacteristic
864C4—22no—
865C4—42no—
866C4—42no—
867C4—862no—
868C4—862no—
869C4—862no—
870C4—862no—
871C4—1722no—
872C4#1458346412yes—
873C4C2×#1306337011yescharacteristic
874C4C2×#1306337011yescharacteristic
875C2—42no—
876C2—82no—
877C2—82no—
878C2—3442no—
879C2—3442no—
880C2—3442no—
881C2#1914564314yesdirect product factor
882C2C2×#1458346411yescharacteristic
883C2C2×#1458370111yescharacteristic
884C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3220
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×#14583502C2semidirect
2. C2×#14583463C2semidirect
3. #19145643C2direct (N × H)
4. C2×#14583285C2semidirect
5. C2×#14583274C2semidirect
6. C2×#14583262C2semidirect
7. C2×#14583255C2semidirect
8. C2×#14583117C2semidirect
9. C2×#14583116C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583092C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583035C2semidirect
14. C2×#14583032C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#449C2semidirect
18. C22×#10621884C22semidirect
23. C22×#10621882C22semidirect
25. #14583502C22semidirect
27. #14583463C22semidirect
30. C2×#13063321C22semidirect
31. C2×#13063316C22semidirect
43. C2×D4×Dic43C22semidirect
44. C2×#13063287C22semidirect
46. #14583285C22semidirect
47. #14583274C22semidirect
48. #14583262C22semidirect
49. #14583255C22semidirect
50. #14583117C22semidirect
51. #14583116C22semidirect
52. #14583093C22semidirect
53. #14583092C22semidirect
54. #14583044C22semidirect
55. #14583035C22semidirect
56. #14583032C22semidirect
57. #14582957C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. C2×Dic43⋊C8C22semidirect
60. C2×#13063249C22semidirect
63. C2×#13063246C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
70. C22×SD16×C43C22semidirect
71. C22×D8×C43C22semidirect
73. C43×#449C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#102×C43C22semidirect
96. C2×#10621884C23semidirect
106. C2×#10621882C23semidirect
114. #13063321C23semidirect
116. #13063316C23semidirect
132. D4×Dic43C23semidirect
134. #13063287C23semidirect
153. Dic43⋊C8C23semidirect
154. Dic43⋊C8C23semidirect
155. #13063249C23semidirect
158. #13063246C23semidirect
162. #13063235C23semidirect
163. C8×Dic43C23semidirect
176. C2×SD16×C43C23semidirect
178. C2×D8×C43C23semidirect
185. #103×C43C23semidirect
186. #102×C43C23semidirect
445. C2×#449D43semidirect
452. C2×C43#3220semidirect
462. C22×SD16C2×D43semidirect
468. C22×D8C2×D43semidirect
501. #449C2×D43semidirect
508. C2×#103C2×D43semidirect
514. C2×#102C2×D43semidirect
519. C43C2×#3220semidirect
552. C2×SD16C22×D43semidirect
564. C2×D8C22×D43semidirect
620. #103C22×D43semidirect
626. #102C22×D43semidirect
881. C2#19145643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835022
C2×#145834632
#191456432
C2×#145832852
C2×#145832742
C2×#145832622
C2×#145832552
C2×#145831172
C2×#145831162
C2×#145830932
C2×#145830922
C2×#145830442
C2×#145830352
C2×#145830322
C2×#145829572
C2×C43×#4492
C2×#322043