Finite Group Databasebeta

← C2×#19144086 #25963458

Subgroups — C2×#19144086 #25963458

Order 11008.

2918 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063352C211yesmaximal, characteristic
3C2×#124×D43C211yesmaximal, characteristic, complemented
4C2×C4×#10621902C211yesmaximal, characteristic, complemented
5#19144086C2116yesmaximal, direct product factor
6C2×#14583123C211yesmaximal, characteristic, complemented
7C2×#14583121C211yesmaximal, characteristic, complemented
8C2×#14583119C211yesmaximal, characteristic, complemented
9C2×#14583117C211yesmaximal, characteristic, complemented
10C2×#14583115C211yesmaximal, characteristic, complemented
11C2×#14583113C211yesmaximal, characteristic, complemented
12C2×#14583111C211yesmaximal, characteristic, complemented
13C2×#14582921C211yesmaximal, characteristic, complemented
14C2×#14582906C211yesmaximal, characteristic, complemented
15C2×#14582902C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C2×#13063352—28no—
23C2×#13063352C2218yes—
24C22×#10621885C2211yescharacteristic, complemented
25C22×#10621873C2211yescharacteristic, complemented
26C22×#10621884C2211yescharacteristic
27C22×#10621884C2211yescharacteristic, complemented
28C22×D344C2211yescharacteristic
29C22×#10621882C2211yescharacteristic
30C22×#10621872C2211yescharacteristic
31C22×#10621872C2211yescharacteristic
32C2×#13063314C2211yescharacteristic
33C2×#13063313C2211yescharacteristic
34C2×#13063312C2211yescharacteristic
35C2×#13063311—21no—
36C2×#13063311—21no—
37#124×D43—24no—
38#124×D43C2218yescomplemented
39C4×#10621902—24no—
40C4×#10621902C2218yescomplemented
41C2×Q8×Dic43C2211yescharacteristic, complemented
42C2×C4×D172—21no—
43C2×C4×D172C2211yescharacteristic, complemented
44C2×#13063287—21no—
45C2×#13063287C2211yescharacteristic, complemented
46C2×#13063283—21no—
47C2×#13063283C2211yescharacteristic
48C2×C22⋊C4×D43—21no—
49C2×C22⋊C4×D43—21no—
50C2×C42×D43—21no—
51C2×C42×D43C2211yescharacteristic
52#14583123C2218yescomplemented
53#14583121C2218yescomplemented
54#14583119C2218yescomplemented
55#14583117C2218yescomplemented
56#14583115C2218yescomplemented
57#14583113C2218yescomplemented
58#14583111C2218yescomplemented
59#14582921C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
61C2×Dic43⋊C8C2211yescharacteristic, complemented
62C2×Dic43⋊C8C2211yescharacteristic, complemented
63#14582906C2218yescomplemented
64#14582902C2218yescomplemented
65C2×#13063250C2211yescharacteristic, complemented
66C2×#13063249C2211yescharacteristic, complemented
67C2×#13063248C2211yescharacteristic, complemented
68C2×#13063247C2211yescharacteristic
69C2×#13063246C2211yescharacteristic
70C2×#13063245C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic, complemented
72C22×SD16×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic, complemented
75C43×#464C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×#102×C43C2211yescharacteristic
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902D418yes—
83C2×#10621902C2314yes—
84C22×Dic86—21no—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—22no—
87C2×Q8×D43—24no—
88C2×Q8×D43—24no—
89C2×Q8×D43C2314yes—
90C22×D172—21no—
91C22×D172C2311yescharacteristic
92C22×D172C2311yescharacteristic
93C22×C22⋊D43—21no—
94C2×D4×D43—24no—
95C2×D4×D43—22no—
96C2×D4×D43—24no—
97C2×D4×D43C2314yes—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43D411yescharacteristic
103C22×C4×D43D411yescharacteristic
104C22×C4×D43C2311yescharacteristic
105#13063357—232no—
106#13063352—232no—
107C2×#10621885—24no—
108C2×#10621885C2314yescomplemented
109C2×#10621873—24no—
110C2×#10621873C2314yescomplemented
111C2×#10621884—24no—
112C2×#10621884—24no—
113C2×#10621884C2314yes—
114C2×#10621884C2314yescomplemented
115C2×D344—24no—
116C2×D344C2314yes—
117C2×#10621882—24no—
118C2×#10621882C2314yes—
119C2×#10621872—24no—
120C2×#10621872—24no—
121C2×#10621872C2314yes—
122C2×#10621872C2314yes—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2311yescharacteristic
125#13063314—22no—
126#13063314C2314yes—
127#13063313—22no—
128#13063313C2314yes—
129#13063312—22no—
130#13063312C2314yes—
131#13063311—28no—
132#13063311—28no—
133Q8×Dic43—22no—
134Q8×Dic43C2314yescomplemented
135C4×D172—28no—
136C4×D172—22no—
137C4×D172C2314yescomplemented
138#13063287—28no—
139#13063287—22no—
140#13063287C2314yescomplemented
141#13063283—22no—
142#13063283—28no—
143#13063283C2314yes—
144C2×C4⋊Dic43—21no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×C22⋊Dic43—21no—
147C2×C22⋊Dic43—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C22⋊C4×D43—28no—
156C22⋊C4×D43—28no—
157C2×C4×Dic43—21no—
158C2×C4×Dic43—21no—
159C2×C4×Dic43D411yescharacteristic
160C2×C4×Dic43D411yescharacteristic
161C2×C4×Dic43C2311yescharacteristic
162C42×D43—28no—
163C42×D43D414yes—
164C42×D43C2314yes—
165C4⋊(C43⋊C8)C2314yescomplemented
166Dic43⋊C8C2314yescomplemented
167Dic43⋊C8C2314yescomplemented
168#13063250C2314yescomplemented
169#13063249C2314yescomplemented
170#13063248C2314yescomplemented
171#13063247C2314yes—
172#13063246C2314yes—
173#13063245C2314yes—
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C22×D4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yescomplemented
179C2×SD16×C43—24no—
180C2×SD16×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183#124×C43—22no—
184#124×C43C2314yes—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yescomplemented
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C22⋊C4×C43—21no—
190C2×C22⋊C4×C43—21no—
191C2×C42×C43—21no—
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43C2314yescomplemented
194#103×C43C2314yescomplemented
195#102×C43C2314yes—
196C24×C43—21no—
197C23×D43—21no—
198C23×D43—21no—
199C23×D43—24no—
200C23×D43—44no—
201C23×D43—44no—
202C23×D43—44no—
203C23×D43C2×D411yescharacteristic
204C2×Q8×C43—21no—
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43—22no—
209C2×Q8×C43C2×D414yes—
210C2×Q8×C43C2412yes—
211C2×Q8×C43C2412yes—
212C2×D4×C43—21no—
213C2×D4×C43—22no—
214C2×D4×C43—22no—
215C2×D4×C43C2412yes—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—24no—
223C2×C22⋊D43—44no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—216no—
230#10621902—28no—
231#10621902C2×D4116yes—
232Q8×D43—28no—
233Q8×D43—28no—
234Q8×D43—48no—
235D4×D43—28no—
236D4×D43—28no—
237D4×D43—48no—
238C2×D172—21no—
239C2×D172—22no—
240C2×D172—21no—
241C2×D172—28no—
242C2×D172—24no—
243C2×D172—22no—
244C2×D172—22no—
245C2×D172C2×D414yes—
246C2×D172C2412yes—
247C2×D172C2412yes—
248C2×C4×D43—28no—
249C2×C4×D43—24no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—24no—
253C2×C4×D43—42no—
254C2×C4×D43—42no—
255C2×C4×D43—44no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43C2×D414yes—
259C2×C4×D43C2×D414yes—
260C2×C4×D43C2×D414yes—
261C2×C4×D43C2×D412yes—
262C2×C4×D43#4114yes—
263C2×C4×D43C2412yes—
264C2×Dic86—22no—
265C2×Dic86—22no—
266C2×Dic86—21no—
267C2×Dic86—24no—
268C2×Dic86—44no—
269C2×Dic86C2412yes—
270Q16×C43—28no—
271SD16×C43—28no—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—24no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43C2412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C42×C43—24no—
282C42×C43C2×D412yes—
283C42×C43C2412yes—
284C22⋊Dic43—24no—
285C22⋊Dic43—24no—
286#10621885—28no—
287#10621884—28no—
288#10621884—28no—
289#10621882—28no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294(C2×D43)⋊C4—24no—
295(C2×D43)⋊C4—24no—
296(C2×D43)⋊C4—24no—
297C4⋊Dic43—21no—
298C4⋊Dic43—24no—
299C4⋊Dic43C2412yes—
300C4×Dic43—24no—
301C4×Dic43—24no—
302C4×Dic43C2×D414yes—
303C4×Dic43C2×D412yes—
304C4×Dic43C2×D414yes—
305C4×Dic43C2412yes—
306C2×C43⋊C8—22no—
307C2×C43⋊C8—22no—
308C2×C43⋊C8C2412yes—
309C2×C43⋊C8C2412yes—
310D344—28no—
311#10621873—28no—
312#10621872—28no—
313#10621872—28no—
314C23×C43—22no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43C22×D411yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—24no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—48no—
325C22×D43—48no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—48no—
332C22×D43—816no—
333C22×D43#12114yes—
334C22×D43C22×D412yes—
335Q8×C43—24no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—42no—
340Q8×C43C22×D414yes—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—42no—
344C2×C4×C43—24no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D412yes—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D412yes—
356C2×C4×C43C2×#4112yes—
357C2×C4×C43C2511yescharacteristic
358C22⋊D43—48no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—42no—
364C2×Dic43—42no—
365C2×Dic43#12114yes—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368C2×Dic43C22×D412yes—
369D172—216no—
370D172—24no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—42no—
375D172C22×D414yes—
376C4×D43—216no—
377C4×D43—44no—
378C4×D43—44no—
379C4×D43—48no—
380C4×D43—48no—
381C4×D43—48no—
382C4×D43#12118yes—
383C4×D43C22×D414yes—
384C4×D43C2×#4114yes—
385Dic86—22no—
386Dic86—22no—
387Dic86—42no—
388Dic86—48no—
389C8×C43—22no—
390C8×C43—22no—
391C43⋊C8—22no—
392C43⋊C8—22no—
393C2×#3040—431nomaximal, Sylow
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—84no—
398C22×C43C2×#12112yes—
399C22×C43#57512yes—
400C22×C43#57512yes—
401C22×C43C23×D411yescharacteristic
402C2×D43—28no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—24no—
406C2×D43—48no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—816no—
413C2×D43—84no—
414C2×D43C2×#12114yes—
415C4×C43—24no—
416C4×C43—22no—
417C4×C43—22no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43C2×#12112yes—
421C4×C43C23×D411yescharacteristic
422C4×C43C22×#4111yescharacteristic
423Dic43—22no—
424Dic43—22no—
425Dic43—42no—
426Dic43—42no—
427Dic43C2×#12114yes—
428C22×#137—431no—
429C22×AGL(1,ℤ/8)—431no—
430C22×#124—431no—
431C2×C4×#41—431no—
432#3040—4316no—
433C2×#464—431no—
434C2×#464—431no—
435C2×#464—431no—
436C2×#464D4311yescharacteristic, complemented
437C2×#463—431no—
438C2×#463—431no—
439C2×#463—431no—
440C2×#463—431no—
441C2×#423—431no—
442C2×#419—431no—
443C2×#418—431no—
444C2×C43—82no—
445C2×C43#304014yescomplemented
446C2×C43C22×#12111yescharacteristic
447C2×C43C2×#57511yescharacteristic
448C2×C43C2×#57511yescharacteristic
449D43—24no—
450D43—44no—
451D43—82no—
452C22×#41—431no—
453C23×Q8—431no—
454C23×D4—431no—
455C2×#137—438no—
456C2×#137—868no—
457C2×AGL(1,ℤ/8)—438no—
458C2×AGL(1,ℤ/8)—868no—
459C22×Q16—431no—
460C22×Q16C2×D4311yescharacteristic, complemented
461C22×SD16—431no—
462C22×SD16—431no—
463C22×SD16—431no—
464C22×SD16C2×D4311yescharacteristic
465C22×D8—431no—
466C22×D8—431no—
467C22×M16—431no—
468C22×M16—431no—
469C2×#124—431no—
470C2×#124—431no—
471C2×#124—438no—
472C2×#124—431no—
473C2×#124—861no—
474C2×#124—861no—
475C2×#124—864no—
476C2×#124C2×D4311yescharacteristic
477C4×#41—438no—
478C4×#41—864no—
479C2×C4×Q8—431no—
480C2×C4×Q8C2×D4311yescharacteristic, complemented
481C2×C4×D4—431no—
482C2×C4×D4—431no—
483C2×C4×D4—861no—
484C2×C4×D4—861no—
485C2×#117—431no—
486C2×#117—861no—
487C22×C22⋊C4—861no—
488C22×C22⋊C4—861no—
489C22×C42—431no—
490C22×C42—861no—
491#464—438no—
492#464—438no—
493#464—438no—
494#464C2×D4318yescomplemented
495#463—438no—
496#463—438no—
497#463—438no—
498#463—438no—
499#423—438no—
500C2×C4⋊C8—431no—
501C2×C4⋊C8—431no—
502C2×C4⋊C8—431no—
503C2×C4⋊C8C2×D4311yescharacteristic, complemented
504#419—438no—
505#418—438no—
506C2×#103—431no—
507C2×#103—431no—
508C2×#103—431no—
509C2×#103C2×D4311yescharacteristic, complemented
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102C2×D4311yescharacteristic
514C43C2×#304011yescharacteristic, complemented, Sylow
515C25—861no—
516C2×#41—438no—
517C2×#41—434no—
518C2×#41—862no—
519C2×#41—864no—
520C22×Q8—434no—
521C22×Q8—431no—
522C22×Q8—861no—
523C22×Q8—862no—
524C22×Q8—864no—
525C22×Q8—864no—
526C22×Q8C22×D4311yescharacteristic
527C22×Q8C22×D4311yescharacteristic
528C22×D4—434no—
529C22×D4—431no—
530C22×D4—431no—
531C22×D4—861no—
532C22×D4—864no—
533C22×D4—864no—
534C22×D4—862no—
535C22×D4—861no—
536C22×D4C22×D4311yescharacteristic
537C23×C4—431no—
538C23×C4—431no—
539C23×C4—431no—
540C23×C4—861no—
541C23×C4—861no—
542C23×C4—861no—
543C23×C4—861no—
544#137—8632no—
545AGL(1,ℤ/8)—8632no—
546C2×Q16—24no—
547C2×Q16—434no—
548C2×Q16—864no—
549C2×Q16C22×D4314yescomplemented
550C2×SD16—24no—
551C2×SD16—434no—
552C2×SD16—434no—
553C2×SD16—434no—
554C2×SD16—864no—
555C2×SD16—864no—
556C2×SD16—864no—
557C2×SD16C22×D4314yes—
558C2×D8—434no—
559C2×D8—434no—
560C2×D8—864no—
561C2×D8—864no—
562C2×M16—434no—
563C2×M16—434no—
564C2×M16—864no—
565C2×M16—864no—
566C22×C8—431no—
567C22×C8—431no—
568C22×C8C22×D4311yescharacteristic
569C22×C8C22×D4311yescharacteristic
570#124—22no—
571#124—434no—
572#124—434no—
573#124—434no—
574#124—868no—
575#124—868no—
576#124—862no—
577#124—862no—
578#124—862no—
579#124C22×D4314yes—
580C4×Q8—22no—
581C4×Q8—434no—
582C4×Q8—862no—
583C4×Q8C22×D4314yescomplemented
584C4×D4—434no—
585C4×D4—434no—
586C4×D4—868no—
587C4×D4—862no—
588C4×D4—868no—
589C4×D4—862no—
590#117—434no—
591#117—868no—
592#117—862no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—868no—
600C2×C22⋊C4—868no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C42—21no—
611C2×C42—431no—
612C2×C42—431no—
613C2×C42—431no—
614C2×C42—434no—
615C2×C42—434no—
616C2×C42—868no—
617C2×C42—861no—
618C2×C42—861no—
619C2×C42C22×D4311yescharacteristic
620C4⋊C8—434no—
621C4⋊C8—434no—
622C4⋊C8—434no—
623C4⋊C8C22×D4314yescomplemented
624#103—434no—
625#103—434no—
626#103—434no—
627#103C22×D4314yescomplemented
628#102—434no—
629#102—434no—
630#102—434no—
631#102C22×D4314yes—
632C24—21no—
633C24—431no—
634C24—864no—
635C24—861no—
636C24—861no—
637C24—1724no—
638C24—1724no—
639C24—1724no—
640#41—4316no—
641#41—8616no—
642#41—868no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—432no—
649C2×Q8—864no—
650C2×Q8—868no—
651C2×Q8—868no—
652C2×Q8—861no—
653C2×Q8—862no—
654C2×Q8—862no—
655C2×Q8—1724no—
656C2×Q8—1728no—
657C2×Q8D4×D4314yes—
658C2×Q8C23×D4312yes—
659C2×Q8C23×D4312yes—
660C2×D4—22no—
661C2×D4—21no—
662C2×D4—22no—
663C2×D4—434no—
664C2×D4—432no—
665C2×D4—432no—
666C2×D4—864no—
667C2×D4—868no—
668C2×D4—868no—
669C2×D4—868no—
670C2×D4—864no—
671C2×D4—861no—
672C2×D4—862no—
673C2×D4—861no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—1728no—
677C2×D4—1724no—
678C2×D4C23×D4312yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—431no—
683C22×C4—432no—
684C22×C4—434no—
685C22×C4—434no—
686C22×C4—432no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—434no—
690C22×C4—434no—
691C22×C4—864no—
692C22×C4—868no—
693C22×C4—864no—
694C22×C4—864no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—864no—
698C22×C4—1722no—
699C22×C4—1722no—
700C22×C4—1724no—
701C22×C4—1724no—
702C22×C4—1724no—
703C22×C4D4×D4311yescharacteristic
704C22×C4D4×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706Q16—28no—
707Q16—868no—
708SD16—28no—
709SD16—868no—
710SD16—868no—
711SD16—868no—
712D8—868no—
713D8—868no—
714M16—868no—
715M16—868no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—432no—
719C2×C8—432no—
720C2×C8—862no—
721C2×C8—862no—
722C2×C8C23×D4312yes—
723C2×C8C23×D4312yes—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—432no—
727C4⋊C4—864no—
728C4⋊C4—861no—
729C4⋊C4C23×D4312yes—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
738C22⋊C4—864no—
739C22⋊C4—864no—
740C22⋊C4—864no—
741C42—24no—
742C42—434no—
743C42—434no—
744C42—432no—
745C42—432no—
746C42—864no—
747C42—864no—
748C42D4×D4312yes—
749C42C23×D4312yes—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—434no—
755C23—432no—
756C23—862no—
757C23—862no—
758C23—864no—
759C23—862no—
760C23—862no—
761C23—34416no—
762C23—1728no—
763C23—1728no—
764C23—1728no—
765C23—1722no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23C2×D4×D4311yescharacteristic
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—862no—
777Q8—862no—
778Q8—1728no—
779Q8—1722no—
780Q8C2×D4×D4314yes—
781D4—22no—
782D4—22no—
783D4—42no—
784D4—434no—
785D4—8616no—
786D4—864no—
787D4—862no—
788D4—862no—
789D4—862no—
790D4—1728no—
791D4—1722no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—434no—
801C2×C4—432no—
802C2×C4—438no—
803C2×C4—434no—
804C2×C4—434no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—8616no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—1724no—
813C2×C4—1724no—
814C2×C4—1728no—
815C2×C4—1728no—
816C2×C4—1728no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4312yes—
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4312yes—
823C2×C4#41×D4312yes—
824C2×C4C24×D4311yescharacteristic
825C8—22no—
826C8—22no—
827C8—862no—
828C8—862no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—84no—
833C22—434no—
834C22—862no—
835C22—862no—
836C22—868no—
837C22—864no—
838C22—34416no—
839C22—3444no—
840C22—1722no—
841C22—1722no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22—1728no—
846C22#121×D4312yes—
847C22#1458369612yes—
848C22#1458369812yes—
849C22C22×D4×D4311yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—434no—
856C4—862no—
857C4—862no—
858C4—1722no—
859C4—1722no—
860C4#121×D4312yes—
861C4C22×D4×D4311yescharacteristic
862C4C2×#41×D4311yescharacteristic
863C2—82no—
864C2—864no—
865C2—3442no—
866C2—1724no—
867C2#1914408614yesdirect product factor
868C2C2×#121×D4311yescharacteristic
869C2C2×#1458369611yescharacteristic
870C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×#13063352C2
hypercenterC2×#464D43
hypocenterC43C2×#3040
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
3. C2×#124×D43C2semidirect
4. C2×C4×#10621902C2semidirect
5. #19144086C2direct (N × H)
6. C2×#14583123C2semidirect
7. C2×#14583121C2semidirect
8. C2×#14583119C2semidirect
9. C2×#14583117C2semidirect
10. C2×#14583115C2semidirect
11. C2×#14583113C2semidirect
12. C2×#14583111C2semidirect
13. C2×#14582921C2semidirect
14. C2×#14582906C2semidirect
15. C2×#14582902C2semidirect
16. C2×C43×#464C2semidirect
21. C2×#13063357C22semidirect
24. C22×#10621885C22semidirect
25. C22×#10621873C22semidirect
27. C22×#10621884C22semidirect
38. #124×D43C22semidirect
40. C4×#10621902C22semidirect
41. C2×Q8×Dic43C22semidirect
43. C2×C4×D172C22semidirect
45. C2×#13063287C22semidirect
52. #14583123C22semidirect
53. #14583121C22semidirect
54. #14583119C22semidirect
55. #14583117C22semidirect
56. #14583115C22semidirect
57. #14583113C22semidirect
58. #14583111C22semidirect
59. #14582921C22semidirect
60. C2×C4⋊(C43⋊C8)C22semidirect
61. C2×Dic43⋊C8C22semidirect
62. C2×Dic43⋊C8C22semidirect
63. #14582906C22semidirect
64. #14582902C22semidirect
65. C2×#13063250C22semidirect
66. C2×#13063249C22semidirect
67. C2×#13063248C22semidirect
71. C22×Q16×C43C22semidirect
74. C2×C4×Q8×C43C22semidirect
75. C43×#464C22semidirect
76. C2×C4⋊C8×C43C22semidirect
77. C2×#103×C43C22semidirect
108. C2×#10621885C23semidirect
110. C2×#10621873C23semidirect
114. C2×#10621884C23semidirect
134. Q8×Dic43C23semidirect
137. C4×D172C23semidirect
140. #13063287C23semidirect
165. C4⋊(C43⋊C8)C23semidirect
166. Dic43⋊C8C23semidirect
167. Dic43⋊C8C23semidirect
168. #13063250C23semidirect
169. #13063249C23semidirect
170. #13063248C23semidirect
178. C2×Q16×C43C23semidirect
186. C4×Q8×C43C23semidirect
193. C4⋊C8×C43C23semidirect
194. #103×C43C23semidirect
436. C2×#464D43semidirect
445. C2×C43#3040semidirect
460. C22×Q16C2×D43semidirect
480. C2×C4×Q8C2×D43semidirect
494. #464C2×D43semidirect
503. C2×C4⋊C8C2×D43semidirect
509. C2×#103C2×D43semidirect
514. C43C2×#3040semidirect
549. C2×Q16C22×D43semidirect
583. C4×Q8C22×D43semidirect
623. C4⋊C8C22×D43semidirect
627. #103C22×D43semidirect
867. C2#19144086direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C22×#130633522
C2×#124×D432
C2×C4×#106219022
#191440862
C2×#145831232
C2×#145831212
C2×#145831192
C2×#145831172
C2×#145831152
C2×#145831132
C2×#145831112
C2×#145829212
C2×#145829062
C2×#145829022
C2×C43×#4642
C2×#304043