Finite Group Databasebeta

← C2×#19143876 #25963016

Subgroups — C2×#19143876 #25963016

Order 11008.

4910 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic, complemented
2C22×#13063352C211yesmaximal, characteristic, complemented
3C22×SD16×D43C211yesmaximal, characteristic, complemented
4C2×#14583465C211yesmaximal, characteristic, complemented
5#19143876C2116yesmaximal, direct product factor
6C2×#14583047C211yesmaximal, characteristic, complemented
7C2×#14583046C211yesmaximal, characteristic, complemented
8C2×#14583043C211yesmaximal, characteristic, complemented
9C2×#14583042C211yesmaximal, characteristic, complemented
10C2×#14583039C211yesmaximal, characteristic, complemented
11C2×#14583038C211yesmaximal, characteristic, complemented
12C2×#14583036C211yesmaximal, characteristic, complemented
13C2×#14582906C211yesmaximal, characteristic, complemented
14C2×#14582894C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#448C211yesmaximal, characteristic, complemented
17C2×#13063373—28no—
18C2×#13063373—24no—
19C2×#13063373—28no—
20C2×#13063373C2218yescomplemented
21C22×#10621902—21no—
22C22×#10621902C2211yescharacteristic
23C22×#10621902C2211yescharacteristic, complemented
24C22×#10621898—21no—
25C22×#10621898—21no—
26C22×#10621898C2211yescharacteristic
27C22×#10621898C2211yescharacteristic, complemented
28C22×Q8×D43—21no—
29C22×Q8×D43C2211yescharacteristic
30C22×Q8×D43C2211yescharacteristic, complemented
31C22×D4×D43C2211yescharacteristic
32C2×#13063352—28no—
33C2×#13063352C2218yescomplemented
34C22×#10621873C2211yescharacteristic
35C22×#10621883C2211yescharacteristic
36C22×#10621884C2211yescharacteristic
37C22×#10621884C2211yescharacteristic
38C2×SD16×D43—28no—
39C2×SD16×D43C2218yescomplemented
40C22×D344C2211yescharacteristic
41C22×#10621882C2211yescharacteristic
42C22×#10621872C2211yescharacteristic
43C22×C8×D43C2211yescharacteristic
44#14583465—24no—
45#14583465C2218yescomplemented
46C2×#13063321—21no—
47C2×#13063311—21no—
48C2×#13063300C2211yescharacteristic
49C2×#13063299C2211yescharacteristic
50C2×#13063296C2211yescharacteristic
51C2×#13063295—21no—
52C2×#13063293—21no—
53C2×#13063283C2211yescharacteristic
54#14583047C2218yescomplemented
55#14583046C2218yescomplemented
56#14583043C2218yescomplemented
57#14583042C2218yescomplemented
58#14583039C2218yescomplemented
59#14583038C2218yescomplemented
60#14583036C2218yescomplemented
61#14582906C2218yescomplemented
62#14582894C2218yescomplemented
63C2×#13063250C2211yescharacteristic, complemented
64C2×#13063249C2211yescharacteristic, complemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063248C2211yescharacteristic, complemented
67C2×#13063247C2211yescharacteristic, complemented
68C2×#13063245C2211yescharacteristic, complemented
69#14582864C2218yescomplemented
70C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
71C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
72C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
73C23×Q8×C43C2211yescharacteristic, complemented
74C22×SD16×C43C2211yescharacteristic
75C22×SD16×C43C2211yescharacteristic
76C2×#121×C43C2211yescharacteristic
77C43×#448C2218yescomplemented
78C2×#103×C43C2211yescharacteristic, complemented
79C2×#103×C43C2211yescharacteristic, complemented
80C2×C22⋊C8×C43C2211yescharacteristic, complemented
81C24×D43—21no—
82#13063373—264no—
83#13063373—232no—
84#13063373—232no—
85C2×#10621902—216no—
86C2×#10621902—24no—
87C2×#10621902—28no—
88C2×#10621902—24no—
89C2×#10621902—24no—
90C2×#10621902—22no—
91C2×#10621902—22no—
92C2×#10621902D418yescomplemented
93C2×#10621902C2314yes—
94C2×#10621902C2314yescomplemented
95C2×#10621898—216no—
96C2×#10621898—216no—
97C2×#10621898—22no—
98C2×#10621898—28no—
99C2×#10621898—28no—
100C2×#10621898—24no—
101C2×#10621898—24no—
102C2×#10621898—24no—
103C2×#10621898—24no—
104C2×#10621898D414yes—
105C2×#10621898C2314yes—
106C2×#10621898C2314yescomplemented
107C22×Dic86—21no—
108C22×Dic86—21no—
109C22×Dic86D411yescharacteristic
110C22×Dic86C2311yescharacteristic
111C2×Q8×D43—216no—
112C2×Q8×D43—24no—
113C2×Q8×D43—24no—
114C2×Q8×D43—22no—
115C2×Q8×D43—22no—
116C2×Q8×D43—28no—
117C2×Q8×D43—24no—
118C2×Q8×D43D418yescomplemented
119C2×Q8×D43C2314yes—
120C2×Q8×D43C2314yescomplemented
121C22×D172—21no—
122C22×D172—21no—
123C22×D172—21no—
124C22×D172D411yescharacteristic
125C22×D172C2311yescharacteristic
126C22×D172C2311yescharacteristic
127C22×C22⋊D43—21no—
128C22×C22⋊D43—21no—
129C22×C22⋊D43—21no—
130C22×C22⋊D43—21no—
131C22×C22⋊D43D411yescharacteristic
132C22×C22⋊D43D411yescharacteristic
133C2×D4×D43—24no—
134C2×D4×D43—24no—
135C2×D4×D43—22no—
136C2×D4×D43C2314yes—
137C22×C4×D43—21no—
138C22×C4×D43—21no—
139C22×C4×D43—21no—
140C22×C4×D43—21no—
141C22×C4×D43—21no—
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144#13063352—232no—
145C2×#10621873—24no—
146C2×#10621873C2314yes—
147C2×#10621883—24no—
148C2×#10621883C2314yes—
149C2×#10621884—24no—
150C2×#10621884—24no—
151C2×#10621884C2314yes—
152C2×#10621884C2314yes—
153SD16×D43—232no—
154C2×D344—24no—
155C2×D344C2314yes—
156C2×#10621882—24no—
157C2×#10621882C2314yes—
158C2×#10621872—24no—
159C2×#10621872C2314yes—
160C22×C43⋊C8C2311yescharacteristic
161C22×C43⋊C8C2311yescharacteristic
162C2×C8×D43—24no—
163C2×C8×D43C2314yes—
164#13063321—28no—
165#13063311—28no—
166#13063300—22no—
167#13063300C2314yes—
168#13063299—22no—
169#13063299C2314yes—
170#13063296—22no—
171#13063296C2314yes—
172#13063295—28no—
173#13063293—28no—
174#13063283—22no—
175#13063283C2314yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C22⋊Dic43—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×C4×Dic43—21no—
182#13063250C2314yescomplemented
183#13063249C2314yescomplemented
184#13063249C2314yescomplemented
185#13063248C2314yescomplemented
186#13063247C2314yescomplemented
187#13063245C2314yescomplemented
188C22⋊(C43⋊C8)C2314yescomplemented
189(C2×D43)⋊C8C2314yescomplemented
190(C2×D43)⋊C8C2314yescomplemented
191C22×Q8×C43—24no—
192C22×Q8×C43—24no—
193C22×Q8×C43—21no—
194C22×Q8×C43—22no—
195C22×Q8×C43C2311yescharacteristic
196C22×Q8×C43C2311yescharacteristic
197C22×Q8×C43C2314yescomplemented
198C22×D4×C43—21no—
199C22×D4×C43C2311yescharacteristic
200C23×C4×C43—21no—
201C23×C4×C43C2311yescharacteristic
202C2×SD16×C43—24no—
203C2×SD16×C43—24no—
204C2×SD16×C43C2314yes—
205C2×SD16×C43C2314yes—
206C22×C8×C43C2311yescharacteristic
207C22×C8×C43C2311yescharacteristic
208#121×C43—22no—
209#121×C43C2314yes—
210C2×C4⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43—21no—
212#103×C43C2314yescomplemented
213#103×C43C2314yescomplemented
214C22⋊C8×C43C2314yescomplemented
215C24×C43—21no—
216C24×C43C2×D411yescharacteristic
217C23×D43—21no—
218C23×D43—21no—
219C23×D43—24no—
220C23×D43—44no—
221C23×D43—82no—
222C23×D43—82no—
223C23×D43C2×D411yescharacteristic
224C23×D43C2×D411yescharacteristic
225C2×Q8×C43—28no—
226C2×Q8×C43—216no—
227C2×Q8×C43—28no—
228C2×Q8×C43—28no—
229C2×Q8×C43—22no—
230C2×Q8×C43—22no—
231C2×Q8×C43—21no—
232C2×Q8×C43—21no—
233C2×Q8×C43—24no—
234C2×Q8×C43C2×D414yes—
235C2×Q8×C43C2×D414yes—
236C2×Q8×C43C2412yes—
237C2×Q8×C43C2412yes—
238C2×D4×C43—21no—
239C2×D4×C43—24no—
240C2×D4×C43—22no—
241C2×D4×C43—22no—
242C2×D4×C43—82no—
243C2×D4×C43C2412yes—
244C22×C4×C43—28no—
245C22×C4×C43—22no—
246C22×C4×C43—22no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—24no—
250C22×C4×C43—21no—
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D412yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2411yescharacteristic
255C2×C22⋊D43—28no—
256C2×C22⋊D43—24no—
257C2×C22⋊D43—24no—
258C2×C22⋊D43—24no—
259C2×C22⋊D43—24no—
260C2×C22⋊D43—24no—
261C2×C22⋊D43—24no—
262C2×C22⋊D43—44no—
263C2×C22⋊D43—82no—
264C2×C22⋊D43—82no—
265C2×C22⋊D43C2×D414yes—
266C2×C22⋊D43C2×D414yes—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43C2×D411yescharacteristic
270C22×Dic43C2×D411yescharacteristic
271#10621902—264no—
272#10621902—216no—
273#10621902—28no—
274#10621902—28no—
275#10621902—216no—
276#10621902—28no—
277#10621902C2×D4116yescomplemented
278Q8×D43—216no—
279Q8×D43—264no—
280Q8×D43—28no—
281Q8×D43—216no—
282Q8×D43—28no—
283Q8×D43—28no—
284Q8×D43C2×D4116yescomplemented
285D4×D43—28no—
286D4×D43—28no—
287D4×D43—48no—
288#10621898—264no—
289#10621898—216no—
290#10621898—264no—
291#10621898—28no—
292#10621898—216no—
293#10621898—28no—
294#10621898—28no—
295#10621898—28no—
296C2×D172—28no—
297C2×D172—22no—
298C2×D172—21no—
299C2×D172—21no—
300C2×D172—28no—
301C2×D172—24no—
302C2×D172—24no—
303C2×D172—24no—
304C2×D172—24no—
305C2×D172—22no—
306C2×D172—22no—
307C2×D172—82no—
308C2×D172C2×D414yes—
309C2×D172C2×D414yes—
310C2×D172C2412yes—
311C2×D172C2412yes—
312C2×C4×D43—28no—
313C2×C4×D43—28no—
314C2×C4×D43—28no—
315C2×C4×D43—24no—
316C2×C4×D43—22no—
317C2×C4×D43—22no—
318C2×C4×D43—28no—
319C2×C4×D43—24no—
320C2×C4×D43—24no—
321C2×C4×D43—28no—
322C2×C4×D43—24no—
323C2×C4×D43—24no—
324C2×C4×D43C2×D414yes—
325C2×C4×D43C2×D414yes—
326C2×C4×D43C2×D412yes—
327C2×C4×D43C2×D412yes—
328C2×C4×D43C2412yes—
329C2×C4×D43C2412yes—
330C2×Dic86—28no—
331C2×Dic86—21no—
332C2×Dic86—22no—
333C2×Dic86—24no—
334C2×Dic86—28no—
335C2×Dic86—24no—
336C2×Dic86—24no—
337C2×Dic86C2×D414yes—
338C2×Dic86C2×D414yes—
339C2×Dic86C2412yes—
340SD16×C43—28no—
341SD16×C43—28no—
342C2×C8×C43—22no—
343C2×C8×C43—22no—
344C2×C8×C43C2412yes—
345C2×C8×C43C2412yes—
346C4⋊C4×C43—21no—
347C4⋊C4×C43C2412yes—
348C22⋊C4×C43—24no—
349C22⋊Dic43—24no—
350#10621884—28no—
351#10621884—28no—
352#10621883—28no—
353#10621882—28no—
354(C2×D43)⋊C4—24no—
355(C2×D43)⋊C4—24no—
356(C2×D43)⋊C4—24no—
357C4⋊Dic43—21no—
358C4⋊Dic43C2412yes—
359C4×Dic43—24no—
360C2×C43⋊C8—22no—
361C2×C43⋊C8—22no—
362C2×C43⋊C8C2412yes—
363C2×C43⋊C8C2412yes—
364D344—28no—
365#10621873—28no—
366#10621872—28no—
367C8×D43—28no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—42no—
373C23×C43—42no—
374C23×C43—42no—
375C23×C43C22×D412yes—
376C23×C43C22×D411yescharacteristic
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—24no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—42no—
386C22×D43—42no—
387C22×D43—42no—
388C22×D43—42no—
389C22×D43—42no—
390C22×D43—48no—
391C22×D43—84no—
392C22×D43—84no—
393C22×D43—816no—
394C22×D43#12014yes—
395C22×D43C22×D412yes—
396C22×D43C22×D412yes—
397Q8×C43—216no—
398Q8×C43—24no—
399Q8×C43—24no—
400Q8×C43—22no—
401Q8×C43—22no—
402Q8×C43C22×D414yes—
403Q8×C43C22×D414yes—
404D4×C43—22no—
405D4×C43—22no—
406D4×C43—42no—
407D4×C43—84no—
408C2×C4×C43—216no—
409C2×C4×C43—24no—
410C2×C4×C43—24no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—24no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—42no—
419C2×C4×C43C22×D412yes—
420C2×C4×C43C22×D411yescharacteristic
421C2×C4×C43C22×D412yes—
422C2×C4×C43C22×D412yes—
423C2×C4×C43C2511yescharacteristic
424C22⋊D43—216no—
425C22⋊D43—28no—
426C22⋊D43—28no—
427C22⋊D43—48no—
428C22⋊D43—84no—
429C22⋊D43—84no—
430C2×Dic43—22no—
431C2×Dic43—24no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—42no—
435C2×Dic43#12014yes—
436C2×Dic43C22×D412yes—
437C2×Dic43C22×D412yes—
438D172—216no—
439D172—216no—
440D172—28no—
441D172—24no—
442D172—22no—
443D172—22no—
444D172—22no—
445D172—42no—
446D172—84no—
447D172C22×D414yes—
448C4×D43—216no—
449C4×D43—216no—
450C4×D43—216no—
451C4×D43—216no—
452C4×D43—24no—
453C4×D43—22no—
454C4×D43—22no—
455C4×D43—216no—
456C4×D43#12018yes—
457C4×D43C22×D414yes—
458C4×D43C22×D414yes—
459Dic86—216no—
460Dic86—24no—
461Dic86—22no—
462Dic86—216no—
463Dic86—28no—
464Dic86C22×D414yes—
465C8×C43—22no—
466C8×C43—22no—
467C43⋊C8—22no—
468C43⋊C8—22no—
469C2×#3010—431nomaximal, Sylow
470C22×C43—22no—
471C22×C43—22no—
472C22×C43—22no—
473C22×C43—44no—
474C22×C43—42no—
475C22×C43—42no—
476C22×C43—42no—
477C22×C43—84no—
478C22×C43C2×#12012yes—
479C22×C43#57712yes—
480C22×C43#57712yes—
481C22×C43C23×D411yescharacteristic
482C2×D43—28no—
483C2×D43—22no—
484C2×D43—22no—
485C2×D43—24no—
486C2×D43—22no—
487C2×D43—22no—
488C2×D43—22no—
489C2×D43—44no—
490C2×D43—48no—
491C2×D43—42no—
492C2×D43—42no—
493C2×D43—42no—
494C2×D43—42no—
495C2×D43—42no—
496C2×D43—816no—
497C2×D43—84no—
498C2×D43C2×#12014yes—
499C4×C43—24no—
500C4×C43—24no—
501C4×C43—22no—
502C4×C43—42no—
503C4×C43C2×#12012yes—
504C4×C43C23×D411yescharacteristic
505C4×C43C23×D411yescharacteristic
506Dic43—22no—
507Dic43—24no—
508Dic43—42no—
509Dic43C2×#12014yes—
510C22×2−1+4—431no—
511C22×AGL(1,ℤ/8)—431no—
512C23×SD16—431no—
513C2×#535—431no—
514#3010—4316no—
515C2×#449—431no—
516C2×#449—431no—
517C2×#449—431no—
518C2×#449—431no—
519C2×#448—431no—
520C2×#448—431no—
521C2×#448—431no—
522C2×#448D4311yescharacteristic, complemented
523C2×#419—431no—
524C2×#416—431no—
525C2×#408—431no—
526C2×C43—42no—
527C2×C43—82no—
528C2×C43#301014yescomplemented
529C2×C43C22×#12011yescharacteristic
530C2×C43C2×#57711yescharacteristic
531C2×C43C2×#57711yescharacteristic
532D43—24no—
533D43—42no—
534D43—44no—
535D43—82no—
536C2×2−1+4—438no—
537C2×2−1+4—868no—
538C2×2−1+4—868no—
539C2×2−1+4—864no—
540C22×#41—431no—
541C22×#41—431no—
542C22×#41—431no—
543C22×#41—431no—
544C22×#41—861no—
545C22×#41—861no—
546C22×#41—861no—
547C23×Q8—431no—
548C23×Q8—431no—
549C23×Q8—861no—
550C23×Q8C2×D4311yescharacteristic, complemented
551C23×D4—431no—
552C2×AGL(1,ℤ/8)—438no—
553C2×AGL(1,ℤ/8)—868no—
554C22×SD16—431no—
555C22×SD16—431no—
556C22×SD16—431no—
557C22×SD16—438no—
558C22×SD16—431no—
559C22×SD16—868no—
560C22×SD16C2×D4311yescharacteristic
561C22×SD16C2×D4311yescharacteristic
562C22×D8—431no—
563C22×D8—431no—
564C22×M16—431no—
565C23×C8—431no—
566#535—438no—
567#535—864no—
568C2×#127—861no—
569C2×#124—861no—
570C2×#121—431no—
571C2×#121—431no—
572C2×#121—431no—
573C2×#121C2×D4311yescharacteristic
574C2×#120—861no—
575C2×#120—861no—
576C2×#117—431no—
577#449—438no—
578#449—438no—
579#449—438no—
580#449—438no—
581#448—438no—
582#448—438no—
583#448—438no—
584#448C2×D4318yescomplemented
585#419—438no—
586#416—438no—
587C2×#103—431no—
588C2×#103—431no—
589C2×#103—431no—
590C2×#103—431no—
591C2×#103C2×D4311yescharacteristic, complemented
592C2×#103C2×D4311yescharacteristic, complemented
593C2×#102—431no—
594C2×#102—431no—
595#408—438no—
596C2×C22⋊C8—431no—
597C2×C22⋊C8—431no—
598C2×C22⋊C8—431no—
599C2×C22⋊C8C2×D4311yescharacteristic, complemented
600C43C2×#301011yescharacteristic, complemented, Sylow
601C25—861no—
6022−1+4—8632no—
6032−1+4—8632no—
6042−1+4—8664no—
605C2×#41—434no—
606C2×#41—434no—
607C2×#41—438no—
608C2×#41—434no—
609C2×#41—434no—
610C2×#41—434no—
611C2×#41—864no—
612C2×#41—864no—
613C2×#41—864no—
614C2×#41—868no—
615C2×#41—868no—
616C2×#41—864no—
617C2×#41—8616no—
618C2×#41—8616no—
619C2×#41—862no—
620C2×#41—864no—
621C2×#41—862no—
622C2×#41—864no—
623C2×#41—868no—
624C2×#41—8616no—
625C2×#41—864no—
626C2×#41—862no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—21no—
630C22×Q8—22no—
631C22×Q8—431no—
632C22×Q8—438no—
633C22×Q8—434no—
634C22×Q8—434no—
635C22×Q8—431no—
636C22×Q8—861no—
637C22×Q8—861no—
638C22×Q8—862no—
639C22×Q8—864no—
640C22×Q8—862no—
641C22×Q8—864no—
642C22×Q8—868no—
643C22×Q8—8616no—
644C22×Q8—864no—
645C22×Q8C22×D4311yescharacteristic
646C22×Q8C22×D4311yescharacteristic
647C22×Q8C22×D4314yescomplemented
648C22×D4—21no—
649C22×D4—431no—
650C22×D4—431no—
651C22×D4—434no—
652C22×D4—431no—
653C22×D4—431no—
654C22×D4—431no—
655C22×D4—861no—
656C22×D4—861no—
657C22×D4—861no—
658C22×D4—864no—
659C22×D4—864no—
660C22×D4—862no—
661C22×D4—861no—
662C22×D4—861no—
663C22×D4—861no—
664C22×D4—861no—
665C22×D4C22×D4311yescharacteristic
666C23×C4—21no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—861no—
670C23×C4—861no—
671C23×C4—861no—
672C23×C4—861no—
673C23×C4—861no—
674C23×C4C22×D4311yescharacteristic
675AGL(1,ℤ/8)—8632no—
676C2×SD16—24no—
677C2×SD16—24no—
678C2×SD16—434no—
679C2×SD16—434no—
680C2×SD16—434no—
681C2×SD16—434no—
682C2×SD16—864no—
683C2×SD16—8632no—
684C2×SD16—864no—
685C2×SD16—864no—
686C2×SD16—864no—
687C2×SD16C22×D4314yes—
688C2×SD16C22×D4314yes—
689C2×D8—434no—
690C2×D8—434no—
691C2×D8—864no—
692C2×D8—864no—
693C2×M16—434no—
694C2×M16—864no—
695C22×C8—431no—
696C22×C8—431no—
697C22×C8—434no—
698C22×C8—864no—
699C22×C8C22×D4311yescharacteristic
700C22×C8C22×D4311yescharacteristic
701#127—868no—
702#124—868no—
703#121—22no—
704#121—434no—
705#121—434no—
706#121—434no—
707#121—862no—
708#121—862no—
709#121—862no—
710#121C22×D4314yes—
711#120—868no—
712#120—868no—
713#117—434no—
714#117—862no—
715C2×C4⋊C4—431no—
716C2×C4⋊C4C22×D4311yescharacteristic
717C2×C22⋊C4—21no—
718C2×C22⋊C4—861no—
719C2×C22⋊C4—861no—
720C2×C22⋊C4—861no—
721C2×C22⋊C4—861no—
722C2×C42—861no—
723#103—434no—
724#103—434no—
725#103—434no—
726#103—434no—
727#103C22×D4314yescomplemented
728#103C22×D4314yescomplemented
729#102—434no—
730#102—434no—
731C22⋊C8—434no—
732C22⋊C8—434no—
733C22⋊C8—434no—
734C22⋊C8C22×D4314yescomplemented
735C24—21no—
736C24—431no—
737C24—431no—
738C24—864no—
739C24—861no—
740C24—861no—
741C24—3442no—
742C24—3442no—
743C24—1724no—
744C24D4×D4311yescharacteristic
745#41—4316no—
746#41—8616no—
747#41—868no—
748#41—868no—
749#41—868no—
750#41—868no—
751#41—8664no—
752#41—8664no—
753#41—8616no—
754#41—8616no—
755#41—868no—
756#41—868no—
757#41—8664no—
758#41—8616no—
759#41—868no—
760C2×Q8—28no—
761C2×Q8—216no—
762C2×Q8—28no—
763C2×Q8—28no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—24no—
769C2×Q8—434no—
770C2×Q8—4316no—
771C2×Q8—434no—
772C2×Q8—432no—
773C2×Q8—868no—
774C2×Q8—864no—
775C2×Q8—864no—
776C2×Q8—864no—
777C2×Q8—868no—
778C2×Q8—8616no—
779C2×Q8—868no—
780C2×Q8—868no—
781C2×Q8—8664no—
782C2×Q8—8616no—
783C2×Q8—868no—
784C2×Q8—862no—
785C2×Q8—861no—
786C2×Q8D4×D4314yes—
787C2×Q8D4×D4314yes—
788C2×Q8C23×D4312yes—
789C2×Q8C23×D4312yes—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—82no—
795C2×D4—434no—
796C2×D4—434no—
797C2×D4—434no—
798C2×D4—434no—
799C2×D4—432no—
800C2×D4—432no—
801C2×D4—864no—
802C2×D4—868no—
803C2×D4—864no—
804C2×D4—864no—
805C2×D4—868no—
806C2×D4—864no—
807C2×D4—868no—
808C2×D4—868no—
809C2×D4—864no—
810C2×D4—864no—
811C2×D4—864no—
812C2×D4—868no—
813C2×D4—864no—
814C2×D4—864no—
815C2×D4—864no—
816C2×D4—861no—
817C2×D4—862no—
818C2×D4—862no—
819C2×D4—862no—
820C2×D4—861no—
821C2×D4—3442no—
822C2×D4—3442no—
823C2×D4—3442no—
824C2×D4—1728no—
825C2×D4—1724no—
826C2×D4C23×D4312yes—
827C22×C4—28no—
828C22×C4—24no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—431no—
835C22×C4—432no—
836C22×C4—434no—
837C22×C4—434no—
838C22×C4—432no—
839C22×C4—431no—
840C22×C4—432no—
841C22×C4—432no—
842C22×C4—868no—
843C22×C4—864no—
844C22×C4—864no—
845C22×C4—868no—
846C22×C4—864no—
847C22×C4—864no—
848C22×C4—868no—
849C22×C4—868no—
850C22×C4—868no—
851C22×C4—861no—
852C22×C4—862no—
853C22×C4—862no—
854C22×C4—864no—
855C22×C4—861no—
856C22×C4D4×D4312yes—
857C22×C4D4×D4311yescharacteristic
858C22×C4C23×D4312yes—
859C22×C4C23×D4311yescharacteristic
860SD16—28no—
861SD16—28no—
862SD16—868no—
863SD16—868no—
864SD16—868no—
865SD16—868no—
866D8—868no—
867D8—868no—
868M16—868no—
869C2×C8—22no—
870C2×C8—22no—
871C2×C8—432no—
872C2×C8—432no—
873C2×C8—868no—
874C2×C8—862no—
875C2×C8—862no—
876C2×C8C23×D4312yes—
877C2×C8C23×D4312yes—
878C4⋊C4—21no—
879C4⋊C4—432no—
880C4⋊C4—861no—
881C4⋊C4C23×D4312yes—
882C22⋊C4—24no—
883C22⋊C4—864no—
884C22⋊C4—864no—
885C22⋊C4—864no—
886C22⋊C4—864no—
887C42—864no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—434no—
896C23—432no—
897C23—432no—
898C23—862no—
899C23—862no—
900C23—864no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—3444no—
907C23—3444no—
908C23—34416no—
909C23—1728no—
910C23—1722no—
911C23—1722no—
912C23—1722no—
913C23—1722no—
914C23—1722no—
915C23C2×D4×D4312yes—
916C23C2×D4×D4311yescharacteristic
917Q8—216no—
918Q8—24no—
919Q8—24no—
920Q8—22no—
921Q8—22no—
922Q8—434no—
923Q8—8616no—
924Q8—868no—
925Q8—8616no—
926Q8—864no—
927Q8—862no—
928Q8C2×D4×D4314yes—
929Q8C2×D4×D4314yes—
930D4—22no—
931D4—22no—
932D4—42no—
933D4—84no—
934D4—434no—
935D4—868no—
936D4—8616no—
937D4—8616no—
938D4—868no—
939D4—868no—
940D4—8616no—
941D4—864no—
942D4—862no—
943D4—862no—
944D4—862no—
945D4—3444no—
946D4—3444no—
947D4—3444no—
948D4—1728no—
949D4—1722no—
950C2×C4—216no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—42no—
961C2×C4—434no—
962C2×C4—432no—
963C2×C4—438no—
964C2×C4—434no—
965C2×C4—434no—
966C2×C4—432no—
967C2×C4—8616no—
968C2×C4—8616no—
969C2×C4—8616no—
970C2×C4—8616no—
971C2×C4—8616no—
972C2×C4—862no—
973C2×C4—864no—
974C2×C4—862no—
975C2×C4—864no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—862no—
979C2×C4—1722no—
980C2×C4C2×D4×D4312yes—
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4C2×D4×D4312yes—
983C2×C4C2×D4×D4312yes—
984C2×C4C24×D4311yescharacteristic
985C8—22no—
986C8—22no—
987C8—862no—
988C8—862no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—44no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—84no—
997C22—434no—
998C22—862no—
999C22—862no—
1000C22—868no—
1001C22—864no—
1002C22—862no—
1003C22—862no—
1004C22—862no—
1005C22—34416no—
1006C22—3444no—
1007C22—1722no—
1008C22—1722no—
1009C22—1722no—
1010C22—1722no—
1011C22—1722no—
1012C22—1724no—
1013C22—1728no—
1014C22#120×D4312yes—
1015C22#1458370512yes—
1016C22#1458370812yes—
1017C22C22×D4×D4311yescharacteristic
1018C4—24no—
1019C4—24no—
1020C4—22no—
1021C4—42no—
1022C4—434no—
1023C4—862no—
1024C4—864no—
1025C4—1722no—
1026C4#120×D4312yes—
1027C4C22×D4×D4311yescharacteristic
1028C4C22×D4×D4311yescharacteristic
1029C2—42no—
1030C2—82no—
1031C2—864no—
1032C2—3442no—
1033C2—1722no—
1034C2—1724no—
1035C2#1914387614yesdirect product factor
1036C2C2×#120×D4311yescharacteristic
1037C2C2×#1458370511yescharacteristic
1038C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
hypercenterC2×#448D43
hypocenterC43C2×#3010
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#13063373C2semidirect
2. C22×#13063352C2semidirect
3. C22×SD16×D43C2semidirect
4. C2×#14583465C2semidirect
5. #19143876C2direct (N × H)
6. C2×#14583047C2semidirect
7. C2×#14583046C2semidirect
8. C2×#14583043C2semidirect
9. C2×#14583042C2semidirect
10. C2×#14583039C2semidirect
11. C2×#14583038C2semidirect
12. C2×#14583036C2semidirect
13. C2×#14582906C2semidirect
14. C2×#14582894C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#448C2semidirect
20. C2×#13063373C22semidirect
23. C22×#10621902C22semidirect
27. C22×#10621898C22semidirect
30. C22×Q8×D43C22semidirect
33. C2×#13063352C22semidirect
39. C2×SD16×D43C22semidirect
45. #14583465C22semidirect
54. #14583047C22semidirect
55. #14583046C22semidirect
56. #14583043C22semidirect
57. #14583042C22semidirect
58. #14583039C22semidirect
59. #14583038C22semidirect
60. #14583036C22semidirect
61. #14582906C22semidirect
62. #14582894C22semidirect
63. C2×#13063250C22semidirect
64. C2×#13063249C22semidirect
65. C2×#13063249C22semidirect
66. C2×#13063248C22semidirect
67. C2×#13063247C22semidirect
68. C2×#13063245C22semidirect
69. #14582864C22semidirect
70. C2×C22⋊(C43⋊C8)C22semidirect
71. C2×(C2×D43)⋊C8C22semidirect
72. C2×(C2×D43)⋊C8C22semidirect
73. C23×Q8×C43C22semidirect
77. C43×#448C22semidirect
78. C2×#103×C43C22semidirect
79. C2×#103×C43C22semidirect
80. C2×C22⋊C8×C43C22semidirect
92. C2×#10621902D4semidirect
94. C2×#10621902C23semidirect
106. C2×#10621898C23semidirect
118. C2×Q8×D43D4semidirect
120. C2×Q8×D43C23semidirect
182. #13063250C23semidirect
183. #13063249C23semidirect
184. #13063249C23semidirect
185. #13063248C23semidirect
186. #13063247C23semidirect
187. #13063245C23semidirect
188. C22⋊(C43⋊C8)C23semidirect
189. (C2×D43)⋊C8C23semidirect
190. (C2×D43)⋊C8C23semidirect
197. C22×Q8×C43C23semidirect
212. #103×C43C23semidirect
213. #103×C43C23semidirect
214. C22⋊C8×C43C23semidirect
277. #10621902C2×D4semidirect
284. Q8×D43C2×D4semidirect
522. C2×#448D43semidirect
528. C2×C43#3010semidirect
550. C23×Q8C2×D43semidirect
584. #448C2×D43semidirect
591. C2×#103C2×D43semidirect
592. C2×#103C2×D43semidirect
599. C2×C22⋊C8C2×D43semidirect
600. C43C2×#3010semidirect
647. C22×Q8C22×D43semidirect
727. #103C22×D43semidirect
728. #103C22×D43semidirect
734. C22⋊C8C22×D43semidirect
1035. C2#19143876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633732
C22×#130633522
C22×SD16×D432
C2×#145834652
#191438762
C2×#145830472
C2×#145830462
C2×#145830432
C2×#145830422
C2×#145830392
C2×#145830382
C2×#145830362
C2×#145829062
C2×#145828942
C2×#145828642
C2×C43×#4482
C2×#301043