Finite Group Databasebeta

← C2×#19145683 #25967946

Subgroups — C2×#19145683 #25967946

Order 11008.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583468C211yesmaximal, characteristic, complemented
2#19145683C2116yesmaximal, direct product factor
3C2×#14583289C211yesmaximal, characteristic, complemented
4C2×#14583281C211yesmaximal, characteristic, complemented
5C2×#14583261C211yesmaximal, characteristic, complemented
6C2×#14583247C211yesmaximal, characteristic, complemented
7C2×#14583121C211yesmaximal, characteristic, complemented
8C2×#14583099C211yesmaximal, characteristic, complemented
9C2×#14583114C211yesmaximal, characteristic, complemented
10C2×#14583094C211yesmaximal, characteristic, complemented
11C2×#14583059C211yesmaximal, characteristic, complemented
12C2×#14583042C211yesmaximal, characteristic, complemented
13C2×#14583049C211yesmaximal, characteristic, complemented
14C2×#14583032C211yesmaximal, characteristic, complemented
15C2×#14582960C211yesmaximal, characteristic, complemented
16C2×C43×#542C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic, complemented
20C22×#10621883C2211yescharacteristic, complemented
21C22×#10621884C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×#10621884C2211yescharacteristic, complemented
24C22×#10621882C2211yescharacteristic
25C22×#10621882C2211yescharacteristic
26C22×#10621882C2211yescharacteristic, complemented
27#14583468—24no—
28#14583468C2218yescomplemented
29C2×#13063322C2211yescharacteristic
30C2×#13063322C2211yescharacteristic
31C2×#13063313C2211yescharacteristic
32C2×#13063313C2211yescharacteristic
33C2×#13063300—21no—
34C2×#13063300—21no—
35C2×#13063295—21no—
36C2×#13063295—21no—
37#14583289C2218yescomplemented
38#14583281C2218yescomplemented
39#14583261C2218yescomplemented
40#14583247C2218yescomplemented
41#14583121C2218yescomplemented
42#14583114C2218yescomplemented
43#14583099C2218yescomplemented
44#14583094C2218yescomplemented
45#14583059C2218yescomplemented
46#14583049C2218yescomplemented
47#14583042C2218yescomplemented
48#14583032C2218yescomplemented
49#14582960C2218yescomplemented
50C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
52C2×#13063248C2211yescharacteristic, complemented
53C2×#13063248C2211yescharacteristic, complemented
54C2×#13063245C2211yescharacteristic
55C2×#13063245C2211yescharacteristic
56C2×#13063245C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic, complemented
59C2×#13063245C2211yescharacteristic, complemented
60C2×C22⋊(C43⋊C8)C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×#13063236C2211yescharacteristic, complemented
63C2×C4×C43⋊C8C2211yescharacteristic, complemented
64C43×#542—24no—
65C43×#542C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic, complemented
67C2×#126×C43—21no—
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic, complemented
70C2×#123×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C22⋊Q8×C43C2211yescharacteristic
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic, complemented
75C2×C4×D4×C43C2211yescharacteristic, complemented
76C2×#117×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621898—22no—
79C2×#10621898—42no—
80C2×#10621898—42no—
81C2×#10621898C2314yes—
82C22×Dic86C2311yescharacteristic
83C22×D172—21no—
84C22×D172—22no—
85C22×D172—21no—
86C22×D172—21no—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172—42no—
90C22×D172—42no—
91C22×D172C2311yescharacteristic
92C22×D172C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×D172C2314yes—
95C22×C22⋊D43—21no—
96C22×C4×D43—21no—
97C2×#10621885—42no—
98C2×#10621885C2314yescomplemented
99C2×#10621883—42no—
100C2×#10621883C2314yescomplemented
101C2×#10621884—42no—
102C2×#10621884—42no—
103C2×#10621884—42no—
104C2×#10621884C2314yes—
105C2×#10621884C2314yes—
106C2×#10621884C2314yescomplemented
107C2×#10621882—42no—
108C2×#10621882—42no—
109C2×#10621882—42no—
110C2×#10621882C2314yes—
111C2×#10621882C2314yes—
112C2×#10621882C2314yescomplemented
113C22×C43⋊C8C2311yescharacteristic
114C22×C43⋊C8C2311yescharacteristic
115C22×C43⋊C8C2311yescharacteristic
116C22×C43⋊C8C2311yescharacteristic
117#13063322—22no—
118#13063322—22no—
119#13063322C2314yes—
120#13063322C2314yes—
121#13063313—22no—
122#13063313—22no—
123#13063313C2314yes—
124#13063313C2314yes—
125#13063300—28no—
126#13063300—28no—
127#13063295—28no—
128#13063295—28no—
129C2×(C2×D43)⋊C4—21no—
130C2×(C2×D43)⋊C4—21no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C4⋊(C43⋊C8)C2314yescomplemented
134C4⋊(C43⋊C8)C2314yescomplemented
135#13063248C2314yescomplemented
136#13063248C2314yescomplemented
137#13063245C2314yes—
138#13063245C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141#13063245C2314yescomplemented
142#13063245C2314yescomplemented
143C22⋊(C43⋊C8)C2314yes—
144C22⋊(C43⋊C8)C2314yes—
145#13063236C2314yescomplemented
146C4×C43⋊C8C2314yescomplemented
147C22×Q8×C43—21no—
148C22×Q8×C43C2311yescharacteristic
149C22×D4×C43—21no—
150C22×D4×C43C2311yescharacteristic
151C23×C4×C43—21no—
152C23×C4×C43C2311yescharacteristic
153C4⋊Q8×C43—22no—
154C4⋊Q8×C43C2314yescomplemented
155#126×C43—28no—
156#124×C43—28no—
157#124×C43—22no—
158#124×C43C2314yescomplemented
159#123×C43—28no—
160C22⋊Q8×C43—22no—
161C22⋊Q8×C43—28no—
162C22⋊Q8×C43C2314yes—
163#121×C43—22no—
164#121×C43C2314yes—
165C4×Q8×C43—22no—
166C4×Q8×C43C2314yescomplemented
167C4×D4×C43—22no—
168C4×D4×C43C2314yescomplemented
169#117×C43D414yes—
170#117×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43D411yescharacteristic
175C2×C4⋊C4×C43D411yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C22⋊C4×C43D411yescharacteristic
184C2×C22⋊C4×C43D411yescharacteristic
185C2×C42×C43—21no—
186C2×C42×C43C2311yescharacteristic
187C2×C42×C43C2311yescharacteristic
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—24no—
194C23×D43—44no—
195C23×D43—82no—
196C23×D43—82no—
197C2×Q8×C43—21no—
198C2×Q8×C43—24no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43—82no—
202C2×Q8×C43C2412yes—
203C2×D4×C43—21no—
204C2×D4×C43—24no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—82no—
208C2×D4×C43C2412yes—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—24no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—82no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—24no—
225C2×C22⋊D43—44no—
226C22×Dic43—21no—
227#10621898—44no—
228#10621898—44no—
229#10621898—48no—
230C2×D172—24no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—24no—
235C2×D172—24no—
236C2×D172—24no—
237C2×D172—24no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—44no—
245C2×D172—44no—
246C2×D172—48no—
247C2×D172—44no—
248C2×D172—82no—
249C2×D172—82no—
250C2×D172—82no—
251C2×D172—82no—
252C2×D172C2412yes—
253C2×D172C2412yes—
254C2×D172C2412yes—
255C2×C4×D43—24no—
256C2×C4×D43—44no—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86—21no—
260C2×Dic86C2412yes—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—24no—
263C4⋊C4×C43—24no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C2×D414yes—
267C4⋊C4×C43C2×D414yes—
268C4⋊C4×C43C2412yes—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—24no—
271C22⋊C4×C43—24no—
272C22⋊C4×C43—24no—
273C22⋊C4×C43—24no—
274C22⋊C4×C43—24no—
275C22⋊C4×C43C2×D414yes—
276C22⋊C4×C43C2×D414yes—
277C42×C43—24no—
278C42×C43C2×D412yes—
279C42×C43C2×D412yes—
280C42×C43C2412yes—
281C42×C43C2412yes—
282#10621885—44no—
283#10621884—44no—
284#10621884—44no—
285#10621884—44no—
286#10621883—44no—
287#10621882—44no—
288#10621882—44no—
289#10621882—44no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—22no—
296C2×C43⋊C8—22no—
297C2×C43⋊C8—22no—
298C2×C43⋊C8C2412yes—
299C2×C43⋊C8C2412yes—
300C2×C43⋊C8C2412yes—
301C2×C43⋊C8C2412yes—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43C22×D412yes—
310C23×C43C22×D411yescharacteristic
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—48no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—42no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—42no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—84no—
325C22×D43—84no—
326C22×D43—816no—
327Q8×C43—22no—
328Q8×C43—22no—
329Q8×C43—42no—
330Q8×C43—84no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—42no—
334D4×C43—84no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—24no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—42no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—84no—
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D412yes—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D412yes—
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—48no—
360C2×Dic43—22no—
361C2×Dic43—42no—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—48no—
369D172—42no—
370D172—42no—
371D172—42no—
372D172—84no—
373D172—84no—
374D172—84no—
375D172—84no—
376C4×D43—48no—
377Dic86—22no—
378Dic86—22no—
379Dic86—42no—
380C43⋊C8—22no—
381C43⋊C8—22no—
382C43⋊C8—22no—
383C43⋊C8—22no—
384C2×#3224—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—44no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—84no—
393C22×C43#53512yes—
394C22×C43#57612yes—
395C22×C43#57712yes—
396C22×C43C23×D411yescharacteristic
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—816no—
407C2×D43—84no—
408C2×D43—84no—
409C2×D43—84no—
410C4×C43—22no—
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—22no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43—42no—
418C4×C43#53512yes—
419C4×C43C2×H(5,𝔽2)11yescharacteristic
420C4×C43C2×H(5,𝔽2)11yescharacteristic
421Dic43—42no—
422C2×#542D4311yescharacteristic, complemented
423C2×#535—431no—
424#3224—4316no—
425C2×#496—431no—
426C2×#495—431no—
427C2×#489—431no—
428C2×#486—431no—
429C2×#464—431no—
430C2×#460—431no—
431C2×#463—431no—
432C2×#459—431no—
433C2×#452—431no—
434C2×#449—431no—
435C2×#450—431no—
436C2×#447—431no—
437C2×#433—431no—
438C2×C43—42no—
439C2×C43—82no—
440C2×C43#322414yescomplemented
441C2×C43C2×#53511yescharacteristic
442C2×C43C2×#57611yescharacteristic
443C2×C43C2×#57711yescharacteristic
444D43—82no—
445D43—82no—
446D43—82no—
447C22×#41—431no—
448C23×D4—431no—
449C22×Q16—431no—
450C22×SD16—431no—
451C22×SD16—431no—
452C22×SD16—431no—
453C22×SD16—431no—
454C22×D8—431no—
455C22×D8—431no—
456C22×D8—431no—
457#542—24no—
458#542C2×D4318yescomplemented
459#535—438no—
460#535—864no—
461C2×C4⋊Q8C2×D4311yescharacteristic, complemented
462C2×#127—431no—
463C2×#127—431no—
464C2×#126—21no—
465C2×#124—21no—
466C2×#124—431no—
467C2×#124—431no—
468C2×#124C2×D4311yescharacteristic, complemented
469C2×#123—21no—
470C2×C22⋊Q8—21no—
471C2×C22⋊Q8C2×D4311yescharacteristic
472C2×#121—861no—
473C2×#121—861no—
474C2×#121C2×D4311yescharacteristic
475C2×#120—861no—
476C2×#120—861no—
477C2×C4×Q8C2×D4311yescharacteristic, complemented
478C2×C4×D4C2×D4311yescharacteristic, complemented
479C2×#117C2×D4311yescharacteristic
480#496—438no—
481#495—438no—
482#489—438no—
483#486—438no—
484#464—438no—
485#463—438no—
486#460—438no—
487#459—438no—
488#452—438no—
489#450—438no—
490#449—438no—
491#447—438no—
492#433—438no—
493C2×C4⋊C8—431no—
494C2×C4⋊C8—431no—
495C2×#103—431no—
496C2×#103—431no—
497C2×#102—431no—
498C2×#102—431no—
499C2×#102—431no—
500C2×#102—431no—
501C2×#102—431no—
502C2×#102—431no—
503C2×C22⋊C8—431no—
504C2×C22⋊C8—431no—
505C2×#97—431no—
506C2×C4×C8—431no—
507C43C2×#322411yescharacteristic, complemented, Sylow
508C25—861no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—1722no—
512C2×#41—1722no—
513C22×Q8—21no—
514C22×Q8—431no—
515C22×Q8C22×D4311yescharacteristic
516C22×D4—21no—
517C22×D4—431no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—434no—
521C22×D4—861no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4—862no—
528C22×D4—1722no—
529C22×D4—1722no—
530C22×D4C22×D4311yescharacteristic
531C23×C4—21no—
532C23×C4—861no—
533C23×C4C22×D4311yescharacteristic
534C2×Q16—434no—
535C2×Q16—1722no—
536C2×SD16—434no—
537C2×SD16—434no—
538C2×SD16—434no—
539C2×SD16—434no—
540C2×SD16—1722no—
541C2×SD16—1722no—
542C2×SD16—1722no—
543C2×SD16—1722no—
544C2×D8—434no—
545C2×D8—434no—
546C2×D8—434no—
547C2×D8—1722no—
548C2×D8—1722no—
549C2×D8—1722no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—431no—
553C22×C8—431no—
554C4⋊Q8—22no—
555C4⋊Q8C22×D4314yescomplemented
556#127—434no—
557#127—434no—
558#127—862no—
559#127—862no—
560#126—28no—
561#124—28no—
562#124—22no—
563#124—434no—
564#124—434no—
565#124—862no—
566#124—862no—
567#124C22×D4314yescomplemented
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—28no—
571C22⋊Q8C22×D4314yes—
572#121—22no—
573#121—868no—
574#121—868no—
575#121C22×D4314yes—
576#120—868no—
577#120—868no—
578C4×Q8—22no—
579C4×Q8C22×D4314yescomplemented
580C4×D4—22no—
581C4×D4C22×D4314yescomplemented
582#117C22⋊D4314yes—
583#117C22×D4314yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4C22⋊D4311yescharacteristic
588C2×C4⋊C4C22⋊D4311yescharacteristic
589C2×C4⋊C4C22×D4311yescharacteristic
590C2×C4⋊C4C22×D4311yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—861no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4C22⋊D4311yescharacteristic
601C2×C22⋊C4C22⋊D4311yescharacteristic
602C2×C42—21no—
603C2×C42C22×D4311yescharacteristic
604C2×C42C22×D4311yescharacteristic
605C4⋊C8—434no—
606C4⋊C8—434no—
607#103—434no—
608#103—434no—
609#102—434no—
610#102—434no—
611#102—434no—
612#102—434no—
613#102—434no—
614#102—434no—
615C22⋊C8—434no—
616C22⋊C8—434no—
617#97—434no—
618C4×C8—434no—
619C24—21no—
620C24—864no—
621C24—861no—
622C24—861no—
623C24—861no—
624C24—3442no—
625C24—3442no—
626C24—1724no—
627C24C2×C22⋊D4311yescharacteristic
628#41—1724no—
629#41—1724no—
630#41—1728no—
631C2×Q8—21no—
632C2×Q8—24no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—432no—
637C2×Q8—861no—
638C2×Q8—862no—
639C2×Q8—862no—
640C2×Q8C23×D4312yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—82no—
646C2×D4—432no—
647C2×D4—432no—
648C2×D4—432no—
649C2×D4—864no—
650C2×D4—864no—
651C2×D4—864no—
652C2×D4—864no—
653C2×D4—864no—
654C2×D4—864no—
655C2×D4—861no—
656C2×D4—861no—
657C2×D4—861no—
658C2×D4—862no—
659C2×D4—862no—
660C2×D4—862no—
661C2×D4—862no—
662C2×D4—862no—
663C2×D4—862no—
664C2×D4—3442no—
665C2×D4—3442no—
666C2×D4—3442no—
667C2×D4—3442no—
668C2×D4—1724no—
669C2×D4—1724no—
670C2×D4—1724no—
671C2×D4—1728no—
672C2×D4—1724no—
673C2×D4C23×D4312yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—82no—
681C22×C4—861no—
682C22×C4—864no—
683C22×C4—1724no—
684C22×C4C2×C22⋊D4312yes—
685C22×C4C2×C22⋊D4311yescharacteristic
686C22×C4C2×C22⋊D4311yescharacteristic
687C22×C4C2×C22⋊D4311yescharacteristic
688C22×C4C2×C22⋊D4311yescharacteristic
689C22×C4C2×C22⋊D4311yescharacteristic
690C22×C4C23×D4312yes—
691C22×C4C23×D4311yescharacteristic
692Q16—1724no—
693SD16—1724no—
694SD16—1724no—
695SD16—1724no—
696SD16—1724no—
697D8—1724no—
698D8—1724no—
699D8—1724no—
700C2×C8—432no—
701C2×C8—432no—
702C2×C8—432no—
703C2×C8—432no—
704C2×C8—862no—
705C2×C8—862no—
706C2×C8—862no—
707C2×C8—862no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4C2×C22⋊D4314yes—
714C4⋊C4C2×C22⋊D4314yes—
715C4⋊C4C23×D4312yes—
716C4⋊C4C23×D4312yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—864no—
723C22⋊C4—864no—
724C22⋊C4—864no—
725C22⋊C4—864no—
726C22⋊C4C2×C22⋊D4314yes—
727C22⋊C4C2×C22⋊D4314yes—
728C42—24no—
729C42C2×C22⋊D4312yes—
730C42C2×C22⋊D4312yes—
731C42C23×D4312yes—
732C42C23×D4312yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—3444no—
744C23—3444no—
745C23—34416no—
746C23—1728no—
747C23—1722no—
748C23—1722no—
749C23—1722no—
750C23—1722no—
751C23—1722no—
752C23—1722no—
753C23—1722no—
754C23—1722no—
755C23—1722no—
756C23C22×C22⋊D4312yes—
757C23C22×C22⋊D4311yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—862no—
763Q8—862no—
764Q8—1722no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—84no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—862no—
774D4—862no—
775D4—3444no—
776D4—3444no—
777D4—3444no—
778D4—3444no—
779D4—1728no—
780D4—1728no—
781D4—1722no—
782D4—1722no—
783D4—1722no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—862no—
800C2×C4—1728no—
801C2×C4—1722no—
802C2×C4C22×C22⋊D4312yes—
803C2×C4C22×C22⋊D4312yes—
804C2×C4C22×C22⋊D4312yes—
805C2×C4C22×C22⋊D4312yes—
806C2×C4C22×C22⋊D4312yes—
807C2×C4C22×C22⋊D4311yescharacteristic
808C2×C4#1306337112yes—
809C2×C4#1306337112yes—
810C2×C4C24×D4311yescharacteristic
811C8—862no—
812C8—862no—
813C8—862no—
814C8—862no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—34416no—
824C22—3444no—
825C22—3444no—
826C22—3444no—
827C22—1722no—
828C22—1722no—
829C22—1722no—
830C22—1722no—
831C22—1722no—
832C22—1722no—
833C22—1722no—
834C22—1722no—
835C22—1722no—
836C22#1458346312yes—
837C22#1458370212yes—
838C22#1458370712yes—
839C22C23×C22⋊D4311yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—1722no—
849C4#1458346312yes—
850C4C2×#1306337111yescharacteristic
851C4C2×#1306337111yescharacteristic
852C2—42no—
853C2—82no—
854C2—3442no—
855C2—3442no—
856C2—3442no—
857C2#1914568314yesdirect product factor
858C2C2×#1458346311yescharacteristic
859C2C2×#1458370211yescharacteristic
860C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
hypercenterC2×#542D43
hypocenterC43C2×#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583468C2semidirect
2. #19145683C2direct (N × H)
3. C2×#14583289C2semidirect
4. C2×#14583281C2semidirect
5. C2×#14583261C2semidirect
6. C2×#14583247C2semidirect
7. C2×#14583121C2semidirect
8. C2×#14583099C2semidirect
9. C2×#14583114C2semidirect
10. C2×#14583094C2semidirect
11. C2×#14583059C2semidirect
12. C2×#14583042C2semidirect
13. C2×#14583049C2semidirect
14. C2×#14583032C2semidirect
15. C2×#14582960C2semidirect
16. C2×C43×#542C2semidirect
19. C22×#10621885C22semidirect
20. C22×#10621883C22semidirect
23. C22×#10621884C22semidirect
26. C22×#10621882C22semidirect
28. #14583468C22semidirect
37. #14583289C22semidirect
38. #14583281C22semidirect
39. #14583261C22semidirect
40. #14583247C22semidirect
41. #14583121C22semidirect
42. #14583114C22semidirect
43. #14583099C22semidirect
44. #14583094C22semidirect
45. #14583059C22semidirect
46. #14583049C22semidirect
47. #14583042C22semidirect
48. #14583032C22semidirect
49. #14582960C22semidirect
50. C2×C4⋊(C43⋊C8)C22semidirect
51. C2×C4⋊(C43⋊C8)C22semidirect
52. C2×#13063248C22semidirect
53. C2×#13063248C22semidirect
58. C2×#13063245C22semidirect
59. C2×#13063245C22semidirect
62. C2×#13063236C22semidirect
63. C2×C4×C43⋊C8C22semidirect
65. C43×#542C22semidirect
66. C2×C4⋊Q8×C43C22semidirect
69. C2×#124×C43C22semidirect
74. C2×C4×Q8×C43C22semidirect
75. C2×C4×D4×C43C22semidirect
98. C2×#10621885C23semidirect
100. C2×#10621883C23semidirect
106. C2×#10621884C23semidirect
112. C2×#10621882C23semidirect
133. C4⋊(C43⋊C8)C23semidirect
134. C4⋊(C43⋊C8)C23semidirect
135. #13063248C23semidirect
136. #13063248C23semidirect
141. #13063245C23semidirect
142. #13063245C23semidirect
145. #13063236C23semidirect
146. C4×C43⋊C8C23semidirect
154. C4⋊Q8×C43C23semidirect
158. #124×C43C23semidirect
166. C4×Q8×C43C23semidirect
168. C4×D4×C43C23semidirect
422. C2×#542D43semidirect
440. C2×C43#3224semidirect
458. #542C2×D43semidirect
461. C2×C4⋊Q8C2×D43semidirect
468. C2×#124C2×D43semidirect
477. C2×C4×Q8C2×D43semidirect
478. C2×C4×D4C2×D43semidirect
507. C43C2×#3224semidirect
555. C4⋊Q8C22×D43semidirect
567. #124C22×D43semidirect
579. C4×Q8C22×D43semidirect
581. C4×D4C22×D43semidirect
857. C2#19145683direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834682
#191456832
C2×#145832892
C2×#145832812
C2×#145832612
C2×#145832472
C2×#145831212
C2×#145830992
C2×#145831142
C2×#145830942
C2×#145830592
C2×#145830422
C2×#145830492
C2×#145830322
C2×#145829602
C2×C43×#5422
C2×#322443