Finite Group Databasebeta

← C2×#19146247 #25971750

Subgroups — C2×#19146247 #25971750

Order 11008.

2762 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063354C211yesmaximal, characteristic, complemented
3C2×#14583561C211yesmaximal, characteristic, complemented
4C2×#14583557C211yesmaximal, characteristic, complemented
5#19146247C2116yesmaximal, direct product factor
6C2×#14583281C211yesmaximal, characteristic, complemented
7C2×#14583148C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583122C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583043C211yesmaximal, characteristic, complemented
12C2×#14583056C211yesmaximal, characteristic, complemented
13C2×#14583053C211yesmaximal, characteristic, complemented
14C2×C4×#10621885C211yesmaximal, characteristic, complemented
15C2×#14582976C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C22×Q8×D43C2211yescharacteristic
21C2×#13063357—28no—
22C2×#13063357C2218yescomplemented
23C2×#13063354—28no—
24C2×#13063354C2218yescomplemented
25C22×Dic172C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621885C2211yescharacteristic
28C22×#10621873C2211yescharacteristic
29C22×#10621883C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C22×#10621882C2211yescharacteristic
32C22×#10621872C2211yescharacteristic
33C22×#10621872C2211yescharacteristic
34#14583561—24no—
35#14583561C2218yescomplemented
36#14583557—24no—
37#14583557C2218yescomplemented
38C2×#13063313—21no—
39C2×#13063313C2211yescharacteristic
40C2×#13063311—21no—
41C2×#13063305—21no—
42C2×#13063305C2211yescharacteristic
43C2×#13063302—21no—
44C2×#13063301C2211yescharacteristic
45C2×#13063300—21no—
46C2×#13063300C2211yescharacteristic
47C2×#13063298—21no—
48C2×#13063296C2211yescharacteristic
49C2×C4×Dic86C2211yescharacteristic
50C2×C4×D172—21no—
51C2×C4×D172C2211yescharacteristic
52C2×(C22⋊D43)⋊C4—21no—
53#14583281C2218yescomplemented
54#14583148C2218yescomplemented
55#14583144C2218yescomplemented
56#14583122C2218yescomplemented
57#14583056C2218yescomplemented
58#14583053C2218yescomplemented
59#14583045C2218yescomplemented
60#14583043C2218yescomplemented
61C4×#10621885C2218yescomplemented
62#14582976C2218yescomplemented
63C2×#13063258C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×C4×C43⋊C8C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C43×#464C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#102×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902—42no—
82C2×#10621902C2314yes—
83C2×#10621900—22no—
84C2×#10621900—24no—
85C2×#10621900—42no—
86C2×#10621900C2314yes—
87C22×Dic86—21no—
88C22×Dic86—21no—
89C22×Dic86C2311yescharacteristic
90C22×Dic86C2311yescharacteristic
91C2×Q8×D43—22no—
92C2×Q8×D43—22no—
93C2×Q8×D43—24no—
94C2×Q8×D43—24no—
95C2×Q8×D43—42no—
96C2×Q8×D43—42no—
97C2×Q8×D43C2314yes—
98C2×Q8×D43C2314yes—
99C22×D172—21no—
100C22×D172—21no—
101C22×D172D411yescharacteristic
102C22×D172C2311yescharacteristic
103C22×C22⋊D43—21no—
104C22×C22⋊D43—21no—
105C23×Dic43—21no—
106C22×C4×D43—21no—
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43C2311yescharacteristic
110C22×C4×D43C2311yescharacteristic
111#13063357—232no—
112#13063354—232no—
113C2×Dic172—24no—
114C2×Dic172C2314yes—
115C2×#10621885—42no—
116C2×#10621885D418yescomplemented
117C2×#10621885C2314yes—
118C2×#10621885C2314yes—
119C2×#10621873—24no—
120C2×#10621873C2314yes—
121C2×#10621883—24no—
122C2×#10621883C2314yes—
123C2×#10621884—24no—
124C2×#10621884C2314yes—
125C2×#10621882—42no—
126C2×#10621882C2314yes—
127C2×#10621872—24no—
128C2×#10621872—24no—
129C2×#10621872C2314yes—
130C2×#10621872C2314yes—
131C22×C43⋊C8C2311yescharacteristic
132C22×C43⋊C8C2311yescharacteristic
133#13063313—22no—
134#13063313—28no—
135#13063313C2314yes—
136#13063311—28no—
137#13063305—22no—
138#13063305—28no—
139#13063305C2314yes—
140#13063302—28no—
141#13063301—22no—
142#13063301C2314yes—
143#13063300—28no—
144#13063300—22no—
145#13063300C2314yes—
146#13063298—28no—
147#13063296—22no—
148#13063296C2314yes—
149C4×Dic86—22no—
150C4×Dic86C2314yes—
151C4×D172—28no—
152C4×D172D414yes—
153C4×D172C2314yes—
154(C22⋊D43)⋊C4—28no—
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43D411yescharacteristic
157C2×C4⋊Dic43C2311yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×C22⋊Dic43—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4D411yescharacteristic
167C2×(C2×D43)⋊C4D411yescharacteristic
168C2×C4×Dic43—21no—
169#13063258C2314yes—
170#13063250C2314yes—
171#13063249C2314yes—
172#13063248C2314yes—
173#13063247C2314yes—
174(C2×D43)⋊C8C2314yes—
175(C2×D43)⋊C8C2314yes—
176C4×C43⋊C8C2314yes—
177C22×Q8×C43C2311yescharacteristic
178C22×Q8×C43C2311yescharacteristic
179C22×D4×C43C2311yescharacteristic
180C2×Q16×C43—24no—
181C2×Q16×C43C2314yes—
182C2×SD16×C43—24no—
183C2×SD16×C43C2314yes—
184C22×C8×C43C2311yescharacteristic
185C22×C8×C43C2311yescharacteristic
186#124×C43—22no—
187#124×C43C2314yes—
188C4×Q8×C43—22no—
189C4×Q8×C43C2314yes—
190C2×C4⋊C4×C43—21no—
191C2×C4⋊C4×C43C2311yescharacteristic
192C2×C22⋊C4×C43—21no—
193C2×C22⋊C4×C43—21no—
194C2×C42×C43—21no—
195C2×C42×C43C2311yescharacteristic
196C4⋊C8×C43C2314yes—
197#103×C43C2314yes—
198#102×C43C2314yes—
199C24×C43—21no—
200C23×D43—21no—
201C23×D43C2×D411yescharacteristic
202C23×D43C2×D411yescharacteristic
203C2×Q8×C43—21no—
204C2×Q8×C43—21no—
205C2×Q8×C43—22no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43C2×D414yes—
209C2×Q8×C43C2412yes—
210C2×Q8×C43C2412yes—
211C2×D4×C43—21no—
212C2×D4×C43—22no—
213C2×D4×C43—22no—
214C2×D4×C43C2412yes—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2411yescharacteristic
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C22×Dic43—24no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—44no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232#10621902—28no—
233#10621902—44no—
234#10621902—48no—
235Q8×D43—28no—
236Q8×D43—28no—
237Q8×D43—44no—
238Q8×D43—44no—
239Q8×D43—48no—
240Q8×D43—48no—
241#10621900—28no—
242#10621900—44no—
243#10621900—48no—
244C2×D172—21no—
245C2×D172—24no—
246C2×D172—24no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—42no—
250C2×D172—44no—
251C2×D172—44no—
252C2×D172C2×D414yes—
253C2×D172C2412yes—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—24no—
261C2×C4×D43—44no—
262C2×C4×D43—44no—
263C2×C4×D43—44no—
264C2×C4×D43C2×D412yes—
265C2×C4×D43C2×D412yes—
266C2×C4×D43C2412yes—
267C2×C4×D43C2412yes—
268C2×Dic86—21no—
269C2×Dic86—22no—
270C2×Dic86—22no—
271C2×Dic86—22no—
272C2×Dic86—21no—
273C2×Dic86—24no—
274C2×Dic86—24no—
275C2×Dic86—44no—
276C2×Dic86—44no—
277C2×Dic86C2×D414yes—
278C2×Dic86C2412yes—
279C2×Dic86C2412yes—
280Q16×C43—28no—
281SD16×C43—28no—
282C2×C8×C43—22no—
283C2×C8×C43—22no—
284C2×C8×C43C2412yes—
285C2×C8×C43C2412yes—
286C4⋊C4×C43—24no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43C2412yes—
289C22⋊C4×C43—24no—
290C22⋊C4×C43—24no—
291C42×C43—24no—
292C42×C43C2×D412yes—
293C42×C43C2412yes—
294C22⋊Dic43—24no—
295#10621885—44no—
296#10621885C2×D4116yescomplemented
297#10621884—28no—
298#10621883—28no—
299#10621882—44no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4C2×D414yes—
306(C2×D43)⋊C4C2×D414yes—
307C4⋊Dic43—21no—
308C4⋊Dic43—24no—
309C4⋊Dic43C2×D414yes—
310C4⋊Dic43C2412yes—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313C4×Dic43—24no—
314C2×C43⋊C8—22no—
315C2×C43⋊C8C2×D414yes—
316C2×C43⋊C8C2412yes—
317C2×C43⋊C8C2412yes—
318Dic172—28no—
319#10621873—28no—
320#10621872—28no—
321#10621872—28no—
322C23×C43—22no—
323C23×C43—42no—
324C23×C43—42no—
325C23×C43—42no—
326C23×C43C22×D411yescharacteristic
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43C22×D412yes—
338C22×D43C22×D412yes—
339Q8×C43—24no—
340Q8×C43—22no—
341Q8×C43—22no—
342Q8×C43—22no—
343Q8×C43—42no—
344Q8×C43C22×D414yes—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—42no—
348C2×C4×C43—24no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—42no—
355C2×C4×C43—42no—
356C2×C4×C43C22×D412yes—
357C2×C4×C43C22×D412yes—
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D412yes—
360C2×C4×C43H(5,𝔽2)12yes—
361C2×C4×C43C2511yescharacteristic
362C22⋊D43—48no—
363C22⋊D43—48no—
364C2×Dic43—24no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—48no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375D172—22no—
376D172—22no—
377D172—44no—
378D172—48no—
379D172—48no—
380D172—42no—
381C4×D43—24no—
382C4×D43—24no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—22no—
387C4×D43—48no—
388C4×D43—48no—
389C4×D43—48no—
390Dic86—24no—
391Dic86—22no—
392Dic86—22no—
393Dic86—22no—
394Dic86—48no—
395Dic86—48no—
396Dic86—42no—
397Dic86C22×D414yes—
398C8×C43—22no—
399C8×C43—22no—
400C43⋊C8—22no—
401C43⋊C8C22×D414yes—
402C2×#3277—431nomaximal, Sylow
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—84no—
407C22×C43D4212yes—
408C22×C43#57512yes—
409C22×C43#57812yes—
410C22×C43C23×D411yescharacteristic
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—44no—
418C2×D43—44no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—84no—
423C4×C43—24no—
424C4×C43—22no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43D4212yes—
429C4×C43C23×D411yescharacteristic
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431Dic43—24no—
432Dic43—22no—
433Dic43—22no—
434Dic43—42no—
435Dic43—42no—
436C22×#137—431no—
437C22×#137—431no—
438C2×#548—431no—
439C2×#548—431no—
440#3277—4316no—
441C2×#495—431no—
442C2×#468—431no—
443C2×#468—431no—
444C2×#464—431no—
445C2×#464D4311yescharacteristic, complemented
446C2×#449—431no—
447C2×#449—431no—
448C2×#451—431no—
449C2×#451—431no—
450C2×C4×Q16—431no—
451C2×#436—431no—
452C2×C43—82no—
453C2×C43#327714yescomplemented
454C2×C43C2×D4211yescharacteristic
455C2×C43C2×#57511yescharacteristic
456C2×C43C2×#57811yescharacteristic
457D43—42no—
458D43—42no—
459D43—82no—
460C22×#41—431no—
461C22×#41—431no—
462C23×Q8—431no—
463C23×Q8—431no—
464C2×#137—438no—
465C2×#137—438no—
466C2×#137—868no—
467C2×#137—868no—
468C22×Q16—431no—
469C22×Q16—431no—
470C22×Q16—431no—
471C22×Q16C2×D4311yescharacteristic
472C22×SD16—431no—
473C22×SD16—431no—
474C22×SD16—431no—
475C22×SD16C2×D4311yescharacteristic
476C22×D8—431no—
477C22×M16—431no—
478C22×M16—431no—
479#548—438no—
480#548—438no—
481#548—864no—
482#548—864no—
483C2×#124—431no—
484C2×#124—861no—
485C2×#124—861no—
486C2×#124C2×D4311yescharacteristic
487C2×C22⋊Q8—431no—
488C2×C22⋊Q8—431no—
489C2×C22⋊Q8—861no—
490C2×C22⋊Q8—861no—
491C2×#121—431no—
492C2×#121—431no—
493C2×#121—861no—
494C2×#121—861no—
495C2×C4×Q8—431no—
496C2×C4×Q8C2×D4311yescharacteristic
497C2×C4×D4—431no—
498C2×C4×D4—861no—
499C2×C4×D4—861no—
500#495—438no—
501#468—438no—
502#468—438no—
503#464—438no—
504#464C2×D4318yescomplemented
505#451—438no—
506#451—438no—
507#449—438no—
508#449—438no—
509C4×Q16—438no—
510#436—438no—
511C2×#107—431no—
512C2×C4⋊C8C2×D4311yescharacteristic
513C2×#103—431no—
514C2×#103—431no—
515C2×#103—431no—
516C2×#103C2×D4311yescharacteristic
517C2×#102—431no—
518C2×#102C2×D4311yescharacteristic
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C4×C8—431no—
522C43C2×#327711yescharacteristic, complemented, Sylow
523C2×#41—434no—
524C2×#41—434no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—864no—
528C2×#41—864no—
529C2×#41—1722no—
530C2×#41—1722no—
531C22×Q8—434no—
532C22×Q8—434no—
533C22×Q8—431no—
534C22×Q8—431no—
535C22×Q8—861no—
536C22×Q8—861no—
537C22×Q8—862no—
538C22×Q8—862no—
539C22×Q8—864no—
540C22×Q8—864no—
541C22×Q8—1722no—
542C22×Q8—1722no—
543C22×Q8C22×D4311yescharacteristic
544C22×Q8C22×D4311yescharacteristic
545C22×D4—431no—
546C22×D4—431no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4—861no—
550C22×D4—861no—
551C22×D4C22×D4311yescharacteristic
552C23×C4—431no—
553C23×C4—431no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4—861no—
557C23×C4—861no—
558#137—8632no—
559#137—8632no—
560C2×Q16—24no—
561C2×Q16—438no—
562C2×Q16—434no—
563C2×Q16—434no—
564C2×Q16—434no—
565C2×Q16—864no—
566C2×Q16—1722no—
567C2×Q16C22×D4314yes—
568C2×SD16—24no—
569C2×SD16—434no—
570C2×SD16—434no—
571C2×SD16—434no—
572C2×SD16—864no—
573C2×SD16—864no—
574C2×SD16—864no—
575C2×SD16C22×D4314yes—
576C2×D8—434no—
577C2×D8—1722no—
578C2×M16—434no—
579C2×M16—434no—
580C2×M16—864no—
581C2×M16—864no—
582C22×C8—431no—
583C22×C8—431no—
584C22×C8C22×D4311yescharacteristic
585C22×C8C22×D4311yescharacteristic
586#124—22no—
587#124—434no—
588#124—868no—
589#124—868no—
590#124—862no—
591#124C22×D4314yes—
592C22⋊Q8—434no—
593C22⋊Q8—434no—
594C22⋊Q8—868no—
595C22⋊Q8—868no—
596C22⋊Q8—862no—
597C22⋊Q8—862no—
598#121—434no—
599#121—434no—
600#121—868no—
601#121—862no—
602#121—868no—
603#121—862no—
604C4×Q8—22no—
605C4×Q8—434no—
606C4×Q8—862no—
607C4×Q8C22×D4314yes—
608C4×D4—434no—
609C4×D4—434no—
610C4×D4—868no—
611C4×D4—868no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—431no—
614C2×C4⋊C4—431no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—431no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C42—21no—
630C2×C42—861no—
631C2×C42C22×D4311yescharacteristic
632#107—434no—
633C4⋊C8C22×D4314yes—
634#103—434no—
635#103—434no—
636#103—434no—
637#103C22×D4314yes—
638#102—434no—
639#102C22×D4314yes—
640C22⋊C8—434no—
641C22⋊C8—434no—
642C4×C8—434no—
643C24—21no—
644C24—431no—
645C24—431no—
646C24—861no—
647#41—868no—
648#41—868no—
649#41—1724no—
650#41—1728no—
651#41—1724no—
652#41—1728no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—22no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—434no—
659C2×Q8—432no—
660C2×Q8—432no—
661C2×Q8—864no—
662C2×Q8—864no—
663C2×Q8—861no—
664C2×Q8—861no—
665C2×Q8—862no—
666C2×Q8—868no—
667C2×Q8—868no—
668C2×Q8—862no—
669C2×Q8—862no—
670C2×Q8—1724no—
671C2×Q8—1724no—
672C2×Q8—1724no—
673C2×Q8—1724no—
674C2×Q8—1728no—
675C2×Q8—1728no—
676C2×Q8D4×D4314yes—
677C2×Q8C23×D4312yes—
678C2×Q8C23×D4312yes—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—434no—
683C2×D4—432no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—864no—
688C2×D4—862no—
689C2×D4—861no—
690C2×D4—862no—
691C2×D4—1722no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4—1724no—
695C2×D4—1724no—
696C2×D4C23×D4312yes—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—431no—
701C22×C4—431no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—864no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—864no—
710C22×C4—861no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—862no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—1724no—
718C22×C4—1724no—
719C22×C4—1724no—
720C22×C4—1724no—
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724Q16—28no—
725Q16—4316no—
726Q16—868no—
727Q16—1724no—
728SD16—28no—
729SD16—868no—
730SD16—868no—
731SD16—868no—
732D8—1724no—
733M16—868no—
734M16—868no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—434no—
738C2×C8—432no—
739C2×C8—432no—
740C2×C8—862no—
741C2×C8C23×D4312yes—
742C2×C8C23×D4312yes—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—434no—
746C4⋊C4—432no—
747C4⋊C4—864no—
748C4⋊C4—864no—
749C4⋊C4—861no—
750C4⋊C4—864no—
751C4⋊C4C23×D4312yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—434no—
755C22⋊C4—434no—
756C22⋊C4—864no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C22⋊C4—864no—
760C22⋊C4—864no—
761C22⋊C4—864no—
762C42—24no—
763C42—864no—
764C42D4×D4312yes—
765C42C23×D4312yes—
766C23—22no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—432no—
771C23—432no—
772C23—862no—
773C23—862no—
774C23—862no—
775C23—862no—
776C23—862no—
777C23—862no—
778C23—862no—
779C23—1722no—
780C23—1722no—
781C23—1722no—
782C23C2×D4×D4311yescharacteristic
783Q8—22no—
784Q8—24no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—434no—
789Q8—862no—
790Q8—864no—
791Q8—862no—
792Q8—862no—
793Q8—1728no—
794Q8—1728no—
795Q8—1722no—
796Q8C2×D4×D4314yes—
797D4—22no—
798D4—22no—
799D4—42no—
800D4—862no—
801D4—862no—
802D4—1724no—
803D4—1728no—
804D4—1728no—
805D4—1728no—
806D4—1728no—
807D4—1722no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—432no—
817C2×C4—432no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—864no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—864no—
827C2×C4—864no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—1728no—
831C2×C4—1728no—
832C2×C4—1728no—
833C2×C4—1728no—
834C2×C4—1722no—
835C2×C4—1722no—
836C2×C4C2×D4×D4312yes—
837C2×C4C2×D4×D4312yes—
838C2×C4C2×D4×D4312yes—
839C2×C4C2×D4×D4311yescharacteristic
840C2×C4#1306337112yes—
841C2×C4C24×D4311yescharacteristic
842C8—22no—
843C8—22no—
844C8—434no—
845C8—862no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—84no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—3444no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22—1724no—
861C22—1724no—
862C22#1458353312yes—
863C22#1458369612yes—
864C22#1458371512yes—
865C22C22×D4×D4311yescharacteristic
866C4—24no—
867C4—22no—
868C4—22no—
869C4—42no—
870C4—42no—
871C4—862no—
872C4—862no—
873C4—864no—
874C4—1722no—
875C4—1722no—
876C4#1458353312yes—
877C4C22×D4×D4311yescharacteristic
878C4C2×#1306337111yescharacteristic
879C2—82no—
880C2—3442no—
881C2—1722no—
882C2—1722no—
883C2#1914624714yesdirect product factor
884C2C2×#1458353311yescharacteristic
885C2C2×#1458369611yescharacteristic
886C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
hypercenterC2×#464D43
hypocenterC43C2×#3277
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
2. C22×#13063354C2semidirect
3. C2×#14583561C2semidirect
4. C2×#14583557C2semidirect
5. #19146247C2direct (N × H)
6. C2×#14583281C2semidirect
7. C2×#14583148C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583122C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583043C2semidirect
12. C2×#14583056C2semidirect
13. C2×#14583053C2semidirect
14. C2×C4×#10621885C2semidirect
15. C2×#14582976C2semidirect
16. C2×C43×#464C2semidirect
22. C2×#13063357C22semidirect
24. C2×#13063354C22semidirect
35. #14583561C22semidirect
37. #14583557C22semidirect
53. #14583281C22semidirect
54. #14583148C22semidirect
55. #14583144C22semidirect
56. #14583122C22semidirect
57. #14583056C22semidirect
58. #14583053C22semidirect
59. #14583045C22semidirect
60. #14583043C22semidirect
61. C4×#10621885C22semidirect
62. #14582976C22semidirect
75. C43×#464C22semidirect
116. C2×#10621885D4semidirect
296. #10621885C2×D4semidirect
445. C2×#464D43semidirect
453. C2×C43#3277semidirect
504. #464C2×D43semidirect
522. C43C2×#3277semidirect
883. C2#19146247direct (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×#130633542
C2×#145835612
C2×#145835572
#191462472
C2×#145832812
C2×#145831482
C2×#145831442
C2×#145831222
C2×#145830452
C2×#145830432
C2×#145830562
C2×#145830532
C2×C4×#106218852
C2×#145829762
C2×C43×#4642
C2×#327743