Finite Group Databasebeta

← C2×#19145459 #25967263

Subgroups — C2×#19145459 #25967263

Order 11008.

2506 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583468C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic, complemented
3#19145459C2116yesmaximal, direct product factor
4C2×#14583226C211yesmaximal, characteristic, complemented
5C2×#14583225C211yesmaximal, characteristic, complemented
6C2×#14583223C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583136C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583035C211yesmaximal, characteristic, complemented
12C2×#14583034C211yesmaximal, characteristic, complemented
13C2×#14583034C211yesmaximal, characteristic, complemented
14C2×#14583032C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×D172C2211yescharacteristic, complemented
19C22×D4×D43C2211yescharacteristic, complemented
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic, complemented
25C22×C8×D43C2211yescharacteristic, complemented
26#14583468—24no—
27#14583468C2218yescomplemented
28#14583465—24no—
29#14583465C2218yescomplemented
30C2×#13063322—21no—
31C2×#13063321—21no—
32C2×#13063313—21no—
33C2×#13063311—21no—
34C2×#13063300C2211yescharacteristic
35C2×#13063300C2211yescharacteristic
36C2×#13063300C2211yescharacteristic, complemented
37C2×#13063300C2211yescharacteristic, complemented
38C2×#13063300C2211yescharacteristic, complemented
39C2×#13063299C2211yescharacteristic
40C2×#13063296C2211yescharacteristic, complemented
41C2×#13063295—21no—
42C2×#13063295—21no—
43C2×#13063295—21no—
44C2×#13063293—21no—
45C2×#13063283C2211yescharacteristic, complemented
46#14583226C2218yescomplemented
47#14583225C2218yescomplemented
48#14583223C2218yescomplemented
49#14583153C2218yescomplemented
50#14583151C2218yescomplemented
51#14583136C2218yescomplemented
52#14583134C2218yescomplemented
53#14583035C2218yescomplemented
54#14583034C2218yescomplemented
55#14583034C2218yescomplemented
56#14583032C2218yescomplemented
57C2×#13063258C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063247C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic, complemented
61C2×#13063245C2211yescharacteristic, complemented
62C2×#13063245C2211yescharacteristic, complemented
63C2×#13063245C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic, complemented
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C24×D43—21no—
79C2×#10621898—42no—
80C2×#10621898—42no—
81C2×#10621898D414yes—
82C2×#10621898C2314yes—
83C22×Dic86D411yescharacteristic
84C22×D172—21no—
85C22×D172—22no—
86C22×D172—21no—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172—21no—
90C22×D172—21no—
91C22×D172—42no—
92C22×D172—42no—
93C22×D172D411yescharacteristic
94C22×D172C2311yescharacteristic
95C22×D172C2311yescharacteristic
96C22×D172C2311yescharacteristic
97C22×D172C2314yescomplemented
98C22×C22⋊D43—21no—
99C22×C22⋊D43—21no—
100C22×C22⋊D43—21no—
101C22×C22⋊D43D411yescharacteristic
102C22×C22⋊D43D411yescharacteristic
103C2×D4×D43—22no—
104C2×D4×D43—42no—
105C2×D4×D43—42no—
106C2×D4×D43C2314yescomplemented
107C22×C4×D43C2311yescharacteristic
108C22×C4×D43C2311yescharacteristic
109C2×D344—42no—
110C2×D344—42no—
111C2×D344C2314yes—
112C2×D344C2314yes—
113C2×#10621882—42no—
114C2×#10621882—42no—
115C2×#10621882C2314yes—
116C2×#10621882C2314yes—
117C2×#10621872—42no—
118C2×#10621872C2314yescomplemented
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C2×C8×D43—42no—
122C2×C8×D43C2314yescomplemented
123#13063322—28no—
124#13063321—28no—
125#13063313—28no—
126#13063311—28no—
127#13063300—22no—
128#13063300—22no—
129#13063300—22no—
130#13063300—22no—
131#13063300—22no—
132#13063300C2314yes—
133#13063300C2314yes—
134#13063300C2314yescomplemented
135#13063300C2314yescomplemented
136#13063300C2314yescomplemented
137#13063299—22no—
138#13063299C2314yes—
139#13063296—22no—
140#13063296C2314yescomplemented
141#13063295—28no—
142#13063295—28no—
143#13063295—28no—
144#13063293—28no—
145#13063283—22no—
146#13063283C2314yescomplemented
147C2×C4⋊Dic43C2311yescharacteristic
148C2×C22⋊Dic43—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—
155C2×(C2×D43)⋊C4—21no—
156C2×C4×Dic43—21no—
157#13063258C2314yescomplemented
158#13063256C2314yescomplemented
159#13063247C2314yescomplemented
160#13063247C2314yescomplemented
161#13063245C2314yescomplemented
162#13063245C2314yescomplemented
163#13063245C2314yescomplemented
164#13063245C2314yescomplemented
165C22⋊(C43⋊C8)C2314yescomplemented
166(C2×D43)⋊C8C2314yescomplemented
167(C2×D43)⋊C8C2314yescomplemented
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173#121×C43—22no—
174#121×C43C2314yes—
175#117×C43—22no—
176#117×C43C2314yescomplemented
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183#107×C43C2314yescomplemented
184#106×C43C2314yescomplemented
185#102×C43C2314yescomplemented
186#102×C43C2314yescomplemented
187C22⋊C8×C43C2314yescomplemented
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—24no—
194C23×D43—24no—
195C23×D43—44no—
196C23×D43—44no—
197C23×D43—82no—
198C23×D43—82no—
199C23×D43—82no—
200C23×D43—82no—
201C23×D43C2×D411yescharacteristic
202C23×D43C2×D411yescharacteristic
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—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—42no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43C2×D414yes—
227C2×C22⋊D43C2×D414yes—
228C22×Dic43—21no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231D4×D43—44no—
232D4×D43—44no—
233D4×D43—48no—
234#10621898—48no—
235#10621898—44no—
236#10621898—44no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—24no—
241C2×D172—24no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—24no—
245C2×D172—24no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—22no—
252C2×D172—42no—
253C2×D172—44no—
254C2×D172—44no—
255C2×D172—48no—
256C2×D172—44no—
257C2×D172—82no—
258C2×D172—82no—
259C2×D172—82no—
260C2×D172—82no—
261C2×D172—82no—
262C2×D172C2×D414yes—
263C2×D172C2412yes—
264C2×D172C2412yes—
265C2×D172C2412yes—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—22no—
269C2×C4×D43—22no—
270C2×C4×D43C2×D412yes—
271C2×C4×D43C2×D412yes—
272C2×C4×D43C2412yes—
273C2×C4×D43C2412yes—
274C2×Dic86—42no—
275C2×Dic86C2×D414yes—
276C2×C8×C43—22no—
277C2×C8×C43—22no—
278C2×C8×C43C2412yes—
279C2×C8×C43C2412yes—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43C2412yes—
284C4⋊C4×C43C2412yes—
285C4⋊C4×C43C2412yes—
286C22⋊C4×C43—24no—
287C22⋊C4×C43—24no—
288C42×C43—24no—
289C22⋊Dic43—24no—
290#10621882—44no—
291#10621882—44no—
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—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—24no—
299C4⋊Dic43—21no—
300C4⋊Dic43C2412yes—
301C4×Dic43—24no—
302C2×C43⋊C8—22no—
303C2×C43⋊C8—22no—
304C2×C43⋊C8C2412yes—
305C2×C43⋊C8C2412yes—
306D344—44no—
307D344—44no—
308#10621872—44no—
309C8×D43—44no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43C22×D412yes—
318C23×C43C22×D411yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—48no—
329C22×D43—48no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—42no—
334C22×D43—42no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43—84no—
342C22×D43—84no—
343C22×D43—816no—
344C22×D43—816no—
345C22×D43C22×D412yes—
346C22×D43C22×D412yes—
347D4×C43—22no—
348D4×C43—22no—
349D4×C43—42no—
350D4×C43—84no—
351C2×C4×C43—22no—
352C2×C4×C43—24no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—42no—
359C2×C4×C43—42no—
360C2×C4×C43—42no—
361C2×C4×C43C22×D412yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43H(5,𝔽2)12yes—
364C2×C4×C43H(5,𝔽2)12yes—
365C2×C4×C43C2511yescharacteristic
366C22⋊D43—44no—
367C22⋊D43—44no—
368C22⋊D43—48no—
369C22⋊D43—84no—
370C22⋊D43—84no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—42no—
375C2×Dic43C22×D412yes—
376C2×Dic43C22×D412yes—
377D172—22no—
378D172—22no—
379D172—22no—
380D172—22no—
381D172—22no—
382D172—22no—
383D172—44no—
384D172—48no—
385D172—42no—
386D172—42no—
387D172—42no—
388D172—84no—
389D172—84no—
390D172—84no—
391D172—84no—
392D172—84no—
393C4×D43—24no—
394C4×D43—24no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—22no—
398C4×D43—22no—
399Dic86—44no—
400C8×C43—22no—
401C8×C43—22no—
402C43⋊C8—22no—
403C43⋊C8—22no—
404C2×#3199—431nomaximal, Sylow
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—44no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—84no—
413C22×C43#53412yes—
414C22×C43#57612yes—
415C22×C43#57612yes—
416C22×C43C23×D411yescharacteristic
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—22no—
421C2×D43—22no—
422C2×D43—22no—
423C2×D43—44no—
424C2×D43—44no—
425C2×D43—42no—
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—816no—
435C2×D43—816no—
436C2×D43—84no—
437C2×D43—84no—
438C2×D43—84no—
439C4×C43—22no—
440C4×C43—42no—
441C4×C43—42no—
442C4×C43—42no—
443C4×C43#53412yes—
444C4×C43C2×H(5,𝔽2)11yescharacteristic
445C4×C43C2×H(5,𝔽2)11yescharacteristic
446Dic43—22no—
447Dic43—22no—
448Dic43—42no—
449C2×#535—431no—
450C2×#535—431no—
451#3199—4316no—
452C2×#482—431no—
453C2×#482—431no—
454C2×#482—431no—
455C2×#482D4311yescharacteristic, complemented
456C2×#469—431no—
457C2×#469—431no—
458C2×#466—431no—
459C2×#466—431no—
460C2×#447—431no—
461C2×#447—431no—
462C2×#447—431no—
463C2×#447—431no—
464C2×#408—431no—
465C2×C43—42no—
466C2×C43—82no—
467C2×C43#319914yescomplemented
468C2×C43C2×#53411yescharacteristic
469C2×C43C2×#57611yescharacteristic
470C2×C43C2×#57611yescharacteristic
471D43—42no—
472D43—42no—
473D43—82no—
474D43—82no—
475D43—82no—
476C22×#41—431no—
477C23×D4—431no—
478C23×D4—431no—
479C22×D8—431no—
480C22×D8—431no—
481C22×D8—431no—
482C22×D8—431no—
483C22×M16—431no—
484C23×C8—431no—
485#535—438no—
486#535—438no—
487#535—864no—
488#535—864no—
489C2×#127—861no—
490C2×#127—861no—
491C2×#124—861no—
492C2×#124—861no—
493C2×#121—431no—
494C2×#121—431no—
495C2×#121—431no—
496C2×#121—431no—
497C2×#121—431no—
498C2×#121—431no—
499C2×#121—431no—
500C2×#121C2×D4311yescharacteristic
501C2×#120—861no—
502C2×#120—861no—
503C2×#120—861no—
504C2×#120—861no—
505C2×#117—431no—
506C2×#117C2×D4311yescharacteristic, complemented
507#482—438no—
508#482—438no—
509#482—438no—
510#482C2×D4318yescomplemented
511#469—438no—
512#469—438no—
513#466—438no—
514#466—438no—
515#447—438no—
516#447—438no—
517#447—438no—
518#447—438no—
519C2×#107—431no—
520C2×#107C2×D4311yescharacteristic, complemented
521C2×#106—431no—
522C2×#106C2×D4311yescharacteristic, complemented
523C2×#102—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102C2×D4311yescharacteristic, complemented
530C2×#102C2×D4311yescharacteristic, complemented
531#408—438no—
532C2×C22⋊C8—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×C22⋊C8C2×D4311yescharacteristic, complemented
536C43C2×#319911yescharacteristic, complemented, Sylow
537C25—861no—
538C25—861no—
539C2×#41—434no—
540C2×#41—434no—
541C2×#41—1722no—
542C2×#41—1722no—
543C22×Q8—431no—
544C22×D4—21no—
545C22×D4—431no—
546C22×D4—431no—
547C22×D4—434no—
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—431no—
551C22×D4—431no—
552C22×D4—434no—
553C22×D4—861no—
554C22×D4—861no—
555C22×D4—861no—
556C22×D4—861no—
557C22×D4—861no—
558C22×D4—862no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—862no—
564C22×D4—1722no—
565C22×D4—1722no—
566C22×D4—1722no—
567C22×D4—1722no—
568C22×D4C22×D4311yescharacteristic
569C23×C4—431no—
570C23×C4—431no—
571C23×C4C22×D4311yescharacteristic
572C2×D8—434no—
573C2×D8—434no—
574C2×D8—434no—
575C2×D8—434no—
576C2×D8—1722no—
577C2×D8—1722no—
578C2×D8—1722no—
579C2×D8—1722no—
580C2×M16—434no—
581C2×M16—1722no—
582C22×C8—431no—
583C22×C8—431no—
584C22×C8—434no—
585C22×C8—1722no—
586C22×C8C22×D4311yescharacteristic
587C22×C8C22×D4311yescharacteristic
588#127—868no—
589#127—868no—
590#124—868no—
591#124—868no—
592#121—22no—
593#121—434no—
594#121—434no—
595#121—434no—
596#121—434no—
597#121—434no—
598#121—434no—
599#121—434no—
600#121—862no—
601#121—862no—
602#121—862no—
603#121—862no—
604#121—862no—
605#121—862no—
606#121—862no—
607#121C22×D4314yes—
608#120—868no—
609#120—868no—
610#120—868no—
611#120—868no—
612#117—22no—
613#117—434no—
614#117—862no—
615#117C22×D4314yescomplemented
616C2×C4⋊C4—431no—
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C4⋊C4C22×D4311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—861no—
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×C22⋊C4—861no—
630C2×C42—21no—
631C2×C42—861no—
632#107—434no—
633#107C22×D4314yescomplemented
634#106—434no—
635#106C22×D4314yescomplemented
636#102—434no—
637#102—434no—
638#102—434no—
639#102—434no—
640#102—434no—
641#102—434no—
642#102C22×D4314yescomplemented
643#102C22×D4314yescomplemented
644C22⋊C8—434no—
645C22⋊C8—434no—
646C22⋊C8—434no—
647C22⋊C8C22×D4314yescomplemented
648C24—21no—
649C24—431no—
650C24—431no—
651C24—864no—
652C24—864no—
653C24—861no—
654C24—861no—
655C24—861no—
656C24—3442no—
657C24—3442no—
658C24—3442no—
659C24—3442no—
660C24—1724no—
661C24—1724no—
662C24D4×D4311yescharacteristic
663#41—1728no—
664#41—1724no—
665#41—1724no—
666C2×Q8—434no—
667C2×Q8—1722no—
668C2×D4—24no—
669C2×D4—21no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—82no—
673C2×D4—434no—
674C2×D4—434no—
675C2×D4—434no—
676C2×D4—432no—
677C2×D4—432no—
678C2×D4—432no—
679C2×D4—864no—
680C2×D4—864no—
681C2×D4—864no—
682C2×D4—864no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4—864no—
691C2×D4—862no—
692C2×D4—862no—
693C2×D4—862no—
694C2×D4—862no—
695C2×D4—862no—
696C2×D4—862no—
697C2×D4—3442no—
698C2×D4—3442no—
699C2×D4—3442no—
700C2×D4—3442no—
701C2×D4—3442no—
702C2×D4—3442no—
703C2×D4—3442no—
704C2×D4—1724no—
705C2×D4—1724no—
706C2×D4—1722no—
707C2×D4—1724no—
708C2×D4—1728no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4—1728no—
712C2×D4—1722no—
713C2×D4—1722no—
714C2×D4—1724no—
715C2×D4C23×D4312yes—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—861no—
732C22×C4D4×D4312yes—
733C22×C4D4×D4311yescharacteristic
734C22×C4C23×D4312yes—
735C22×C4C23×D4311yescharacteristic
736D8—1724no—
737D8—1724no—
738D8—1724no—
739D8—1724no—
740M16—1724no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—432no—
744C2×C8—432no—
745C2×C8—862no—
746C2×C8—862no—
747C2×C8—1724no—
748C2×C8C23×D4312yes—
749C2×C8C23×D4312yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—432no—
754C4⋊C4—861no—
755C4⋊C4C23×D4312yes—
756C4⋊C4C23×D4312yes—
757C4⋊C4C23×D4312yes—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—864no—
761C22⋊C4—864no—
762C22⋊C4—864no—
763C22⋊C4—864no—
764C22⋊C4—864no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C42—24no—
769C42—864no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—432no—
778C23—432no—
779C23—862no—
780C23—862no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—3444no—
789C23—3444no—
790C23—3444no—
791C23—3444no—
792C23—34416no—
793C23—34416no—
794C23—1728no—
795C23—1728no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23—1722no—
800C23—1722no—
801C23—1722no—
802C23—1722no—
803C23—1722no—
804C23—1722no—
805C23C2×D4×D4312yes—
806C23C2×D4×D4311yescharacteristic
807Q8—1724no—
808D4—22no—
809D4—22no—
810D4—42no—
811D4—84no—
812D4—862no—
813D4—862no—
814D4—862no—
815D4—862no—
816D4—862no—
817D4—862no—
818D4—3444no—
819D4—3444no—
820D4—3444no—
821D4—3444no—
822D4—3444no—
823D4—3444no—
824D4—3444no—
825D4—1724no—
826D4—1728no—
827D4—1724no—
828D4—1724no—
829D4—1728no—
830D4—1722no—
831D4—1722no—
832D4—1722no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—432no—
844C2×C4—432no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—864no—
848C2×C4—864no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—862no—
854C2×C4—1722no—
855C2×C4C2×D4×D4312yes—
856C2×C4C2×D4×D4311yescharacteristic
857C2×C4#1306337112yes—
858C2×C4#1306337112yes—
859C2×C4C24×D4311yescharacteristic
860C8—22no—
861C8—22no—
862C8—862no—
863C8—862no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—44no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—84no—
872C22—862no—
873C22—862no—
874C22—862no—
875C22—862no—
876C22—862no—
877C22—862no—
878C22—34416no—
879C22—34416no—
880C22—3444no—
881C22—3444no—
882C22—3444no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22—1722no—
887C22—1722no—
888C22—1722no—
889C22—1722no—
890C22—1722no—
891C22—1722no—
892C22—1724no—
893C22—1724no—
894C22#1458346012yes—
895C22#1458370112yes—
896C22#1458370312yes—
897C22C22×D4×D4311yescharacteristic
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—862no—
903C4—862no—
904C4—1722no—
905C4#1458346012yes—
906C4C2×#1306337111yescharacteristic
907C4C2×#1306337111yescharacteristic
908C2—42no—
909C2—82no—
910C2—3442no—
911C2—3442no—
912C2—3442no—
913C2—1722no—
914C2—1722no—
915C2#1914545914yesdirect product factor
916C2C2×#1458346011yescharacteristic
917C2C2×#1458370111yescharacteristic
918C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
hypercenterC2×#482D43
hypocenterC43C2×#3199
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#14583468C2semidirect
2. C2×#14583465C2semidirect
3. #19145459C2direct (N × H)
4. C2×#14583226C2semidirect
5. C2×#14583225C2semidirect
6. C2×#14583223C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583136C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583035C2semidirect
12. C2×#14583034C2semidirect
13. C2×#14583034C2semidirect
14. C2×#14583032C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#482C2semidirect
18. C23×D172C22semidirect
19. C22×D4×D43C22semidirect
24. C22×#10621872C22semidirect
25. C22×C8×D43C22semidirect
27. #14583468C22semidirect
29. #14583465C22semidirect
36. C2×#13063300C22semidirect
37. C2×#13063300C22semidirect
38. C2×#13063300C22semidirect
40. C2×#13063296C22semidirect
45. C2×#13063283C22semidirect
46. #14583226C22semidirect
47. #14583225C22semidirect
48. #14583223C22semidirect
49. #14583153C22semidirect
50. #14583151C22semidirect
51. #14583136C22semidirect
52. #14583134C22semidirect
53. #14583035C22semidirect
54. #14583034C22semidirect
55. #14583034C22semidirect
56. #14583032C22semidirect
57. C2×#13063258C22semidirect
58. C2×#13063256C22semidirect
59. C2×#13063247C22semidirect
60. C2×#13063247C22semidirect
61. C2×#13063245C22semidirect
62. C2×#13063245C22semidirect
63. C2×#13063245C22semidirect
64. C2×#13063245C22semidirect
65. #14582864C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C2×#117×C43C22semidirect
71. C43×#482C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#102×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
97. C22×D172C23semidirect
106. C2×D4×D43C23semidirect
118. C2×#10621872C23semidirect
122. C2×C8×D43C23semidirect
134. #13063300C23semidirect
135. #13063300C23semidirect
136. #13063300C23semidirect
140. #13063296C23semidirect
146. #13063283C23semidirect
157. #13063258C23semidirect
158. #13063256C23semidirect
159. #13063247C23semidirect
160. #13063247C23semidirect
161. #13063245C23semidirect
162. #13063245C23semidirect
163. #13063245C23semidirect
164. #13063245C23semidirect
165. C22⋊(C43⋊C8)C23semidirect
166. (C2×D43)⋊C8C23semidirect
167. (C2×D43)⋊C8C23semidirect
176. #117×C43C23semidirect
183. #107×C43C23semidirect
184. #106×C43C23semidirect
185. #102×C43C23semidirect
186. #102×C43C23semidirect
187. C22⋊C8×C43C23semidirect
455. C2×#482D43semidirect
467. C2×C43#3199semidirect
506. C2×#117C2×D43semidirect
510. #482C2×D43semidirect
520. C2×#107C2×D43semidirect
522. C2×#106C2×D43semidirect
529. C2×#102C2×D43semidirect
530. C2×#102C2×D43semidirect
535. C2×C22⋊C8C2×D43semidirect
536. C43C2×#3199semidirect
615. #117C22×D43semidirect
633. #107C22×D43semidirect
635. #106C22×D43semidirect
642. #102C22×D43semidirect
643. #102C22×D43semidirect
647. C22⋊C8C22×D43semidirect
915. C2#19145459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834682
C2×#145834652
#191454592
C2×#145832262
C2×#145832252
C2×#145832232
C2×#145831532
C2×#145831512
C2×#145831362
C2×#145831342
C2×#145830352
C2×#145830342
C2×#145830322
C2×#145828642
C2×C43×#4822
C2×#319943