Finite Group Databasebeta

← C2×#19144840 #25964893

Subgroups — C2×#19144840 #25964893

Order 11008.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583505C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic, complemented
3#19144840C2116yesmaximal, direct product factor
4C2×#14583226C211yesmaximal, characteristic, complemented
5C2×#14583225C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583095C211yesmaximal, characteristic, complemented
8C2×#14583094C211yesmaximal, characteristic, complemented
9C2×#14583034C211yesmaximal, characteristic, complemented
10C2×#14583034C211yesmaximal, characteristic, complemented
11C2×#14583010C211yesmaximal, characteristic, complemented
12C2×#14583008C211yesmaximal, characteristic, complemented
13C2×#14582981C211yesmaximal, characteristic, complemented
14C2×#14582979C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×D344C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22#14583505—24no—
23#14583505C2218yescomplemented
24C2×#13063322C2211yescharacteristic, complemented
25C2×#13063310—21no—
26C2×#13063310—21no—
27C2×#13063300—21no—
28C2×#13063300—21no—
29C2×#13063300C2211yescharacteristic
30C2×#13063300C2211yescharacteristic
31#14583371—24no—
32#14583371C2218yescomplemented
33C2×C4×D172C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic
35C2×#13063287C2211yescharacteristic
36C2×#13063287C2211yescharacteristic, complemented
37C2×#13063287C2211yescharacteristic, complemented
38C2×C4×C22⋊D43—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42C22×(C2×D43)⋊C4—21no—
43C2×C22⋊C4×D43—21no—
44#14583226C2218yescomplemented
45#14583225C2218yescomplemented
46#14583196C2218yescomplemented
47#14583095C2218yescomplemented
48#14583094C2218yescomplemented
49#14583034C2218yescomplemented
50#14583034C2218yescomplemented
51#14583010C2218yescomplemented
52#14583008C2218yescomplemented
53#14582981C2218yescomplemented
54#14582979C2218yescomplemented
55#14582959C2218yescomplemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59C2×#13063247C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic, complemented
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C2×#125×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C22×D172—21no—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C2×D4×D43—24no—
87C2×D4×D43—24no—
88C2×D4×D43—22no—
89C2×D4×D43C2314yes—
90C23×Dic43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96C2×D344—24no—
97C2×D344—24no—
98C2×D344C2314yes—
99C2×D344C2314yes—
100C2×#10621882—24no—
101C2×#10621882—24no—
102C2×#10621882C2314yes—
103C2×#10621882C2314yes—
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106#13063322—22no—
107#13063322C2314yescomplemented
108#13063310—28no—
109#13063310—28no—
110#13063300—22no—
111#13063300—22no—
112#13063300—28no—
113#13063300—28no—
114#13063300C2314yes—
115#13063300C2314yes—
116C4×D172—22no—
117C4×D172C2314yes—
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120#13063287—22no—
121#13063287—22no—
122#13063287—22no—
123#13063287C2314yes—
124#13063287C2314yescomplemented
125#13063287C2314yescomplemented
126C4×C22⋊D43—28no—
127(C22⋊D43)⋊C4—28no—
128#13063283—22no—
129#13063283C2314yes—
130#13063282D414yes—
131#13063282C2314yes—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4D411yescharacteristic
134C2×Dic43⋊C4D411yescharacteristic
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—28no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×(C2×D43)⋊C4D411yescharacteristic
146C22⋊C4×D43—28no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yescomplemented
150#13063256C2314yescomplemented
151C4⋊(C43⋊C8)C2314yescomplemented
152#13063247C2314yescomplemented
153#13063247C2314yescomplemented
154#13063245C2314yes—
155#13063245C2314yes—
156#13063245C2314yescomplemented
157#13063245C2314yescomplemented
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yescomplemented
161C8×Dic43C2314yescomplemented
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166#125×C43—22no—
167#125×C43C2314yescomplemented
168C4×D4×C43—22no—
169C4×D4×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43C2314yescomplemented
178#106×C43C2314yescomplemented
179C4⋊C8×C43C2314yescomplemented
180#102×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43—28no—
185C23×D43—24no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—82no—
189C23×D43—82no—
190C23×D43C2×D411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43—22no—
193C2×D4×C43#4114yes—
194C2×D4×C43C2412yes—
195C22×C4×C43—24no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—82no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—28no—
204C2×C22⋊D43—24no—
205C22×Dic43—24no—
206C22×Dic43—21no—
207C22×Dic43—82no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211D4×D43—216no—
212D4×D43—28no—
213D4×D43—28no—
214C2×D172—21no—
215C2×D172—22no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—24no—
219C2×D172—24no—
220C2×D172—24no—
221C2×D172—24no—
222C2×D172—22no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172—82no—
227C2×D172—82no—
228C2×D172—82no—
229C2×D172—82no—
230C2×D172#4114yes—
231C2×D172C2412yes—
232C2×D172C2412yes—
233C2×D172C2412yes—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—82no—
241C2×C4×D43—82no—
242C2×C4×D43—82no—
243C2×C4×D43—82no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2412yes—
246C2×C8×C43—22no—
247C2×C8×C43—22no—
248C2×C8×C43C2412yes—
249C2×C8×C43C2412yes—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C22⋊C4×C43—24no—
259C42×C43C2×D412yes—
260C42×C43C2412yes—
261C22⋊Dic43—24no—
262#10621882—28no—
263#10621882—28no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4C2×D414yes—
272(C2×D43)⋊C4C2×D414yes—
273C4⋊Dic43—21no—
274C4⋊Dic43C2412yes—
275Dic43⋊C4C2×D414yes—
276Dic43⋊C4C2×D414yes—
277C4×Dic43—24no—
278C4×Dic43C2×D412yes—
279C4×Dic43C2412yes—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8C2412yes—
283C2×C43⋊C8C2412yes—
284D344—28no—
285D344—28no—
286C23×C43—24no—
287C23×C43—22no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43C22×D411yescharacteristic
291C22×D43—22no—
292C22×D43—24no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—216no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—84no—
308C22×D43—84no—
309C22×D43—816no—
310C22×D43C22×D412yes—
311D4×C43—24no—
312D4×C43—22no—
313D4×C43C2×#4114yes—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—84no—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4112yes—
327C2×C4×C43C2×#4112yes—
328C2×C4×C43C2511yescharacteristic
329C22⋊D43—216no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—42no—
335C2×Dic43—84no—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338C2×Dic43C22×D412yes—
339D172—24no—
340D172—22no—
341D172—22no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—42no—
346D172—42no—
347D172—84no—
348D172—84no—
349D172—84no—
350D172—84no—
351D172C2×#4114yes—
352C4×D43—24no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—84no—
356C4×D43—84no—
357C4×D43—84no—
358C4×D43—84no—
359C8×C43—22no—
360C8×C43—22no—
361C43⋊C8—22no—
362C43⋊C8—22no—
363C2×#3122—431nomaximal, Sylow
364C22×C43—24no—
365C22×C43—48no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43#52512yes—
369C22×C43#57612yes—
370C22×C43#57612yes—
371C22×C43C23×D411yescharacteristic
372C2×D43—22no—
373C2×D43—24no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—44no—
377C2×D43—48no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—816no—
387C2×D43—84no—
388C2×D43—84no—
389C4×C43—22no—
390C4×C43—22no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43#52512yes—
395C4×C43C22×#4111yescharacteristic
396C4×C43C22×#4111yescharacteristic
397Dic43—22no—
398Dic43—22no—
399Dic43—22no—
400Dic43—42no—
401C2×#540—431no—
402C2×#518—431no—
403#3122—4316no—
404C2×#482—431no—
405C2×#482—431no—
406C2×#478—431no—
407C2×#478D4311yescharacteristic, complemented
408C2×#459—431no—
409C2×#459—431no—
410C2×#447—431no—
411C2×#447—431no—
412C2×#442—431no—
413C2×#442—431no—
414C2×C4×D8—431no—
415C2×C4×D8—431no—
416C2×#433—431no—
417C2×C43—44no—
418C2×C43#312214yescomplemented
419C2×C43C2×#52511yescharacteristic
420C2×C43C2×#57611yescharacteristic
421C2×C43C2×#57611yescharacteristic
422D43—42no—
423D43—44no—
424D43—82no—
425D43—82no—
426C23×D4—431no—
427C22×D8—431no—
428C22×D8—431no—
429C22×D8—431no—
430C22×D8—431no—
431#540—438no—
432#540—864no—
433C2×#127—431no—
434C2×#125C2×D4311yescharacteristic, complemented
435C2×#123—861no—
436C2×#123—861no—
437C2×#121—431no—
438C2×#121—431no—
439C2×#121—861no—
440C2×#121—861no—
441#518—438no—
442#518—864no—
443C2×C4×D4—431no—
444C2×C4×D4—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4—861no—
449C2×C4×D4—861no—
450C2×C4×D4C2×D4311yescharacteristic
451C2×#117—431no—
452C2×#117—431no—
453C22×C22⋊C4—861no—
454C22×C22⋊C4—861no—
455#482—438no—
456#482—438no—
457#478—438no—
458#478C2×D4318yescomplemented
459#459—438no—
460#459—438no—
461#447—438no—
462#447—438no—
463#442—438no—
464#442—438no—
465C4×D8—438no—
466C4×D8—438no—
467#433—438no—
468C2×#107—431no—
469C2×#107C2×D4311yescharacteristic, complemented
470C2×#106—431no—
471C2×#106C2×D4311yescharacteristic, complemented
472C2×C4⋊C8—431no—
473C2×C4⋊C8C2×D4311yescharacteristic, complemented
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102C2×D4311yescharacteristic
481C2×#102C2×D4311yescharacteristic
482C2×C22⋊C8—431no—
483C2×C22⋊C8—431no—
484C2×#97—431no—
485C2×C4×C8—431no—
486C43C2×#312211yescharacteristic, complemented, Sylow
487C25—861no—
488C22×D4—434no—
489C22×D4—431no—
490C22×D4—431no—
491C22×D4—431no—
492C22×D4—861no—
493C22×D4—861no—
494C22×D4—862no—
495C22×D4—861no—
496C22×D4—864no—
497C22×D4—864no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4C22×D4311yescharacteristic
501C23×C4—21no—
502C23×C4—431no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—861no—
508C2×D8—434no—
509C2×D8—434no—
510C2×D8—434no—
511C2×D8—434no—
512C2×D8—864no—
513C2×D8—864no—
514C2×D8—864no—
515C2×D8—864no—
516C22×C8—431no—
517C22×C8—431no—
518C22×C8C22×D4311yescharacteristic
519C22×C8C22×D4311yescharacteristic
520#127—434no—
521#127—862no—
522#125—22no—
523#125C22×D4314yescomplemented
524#123—868no—
525#123—868no—
526#121—434no—
527#121—434no—
528#121—868no—
529#121—868no—
530#121—862no—
531#121—862no—
532C4×D4—22no—
533C4×D4—434no—
534C4×D4—434no—
535C4×D4—434no—
536C4×D4—434no—
537C4×D4—434no—
538C4×D4—862no—
539C4×D4—862no—
540C4×D4—862no—
541C4×D4—862no—
542C4×D4—868no—
543C4×D4—868no—
544C4×D4—862no—
545C4×D4C22×D4314yes—
546#117—434no—
547#117—434no—
548#117—434no—
549#117—862no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—431no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—868no—
562C2×C22⋊C4—868no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—431no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575#107C22×D4314yescomplemented
576#106—434no—
577#106C22×D4314yescomplemented
578C4⋊C8—434no—
579C4⋊C8C22×D4314yescomplemented
580#102—434no—
581#102—434no—
582#102—434no—
583#102—434no—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yes—
588C22⋊C8—434no—
589C22⋊C8—434no—
590#97—434no—
591C4×C8—434no—
592C24—21no—
593C24—431no—
594C24—864no—
595C24—868no—
596C24—861no—
597C24—861no—
598C24—861no—
599C24—3442no—
600C24—3442no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—434no—
604C2×D4—432no—
605C2×D4—432no—
606C2×D4—432no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—868no—
611C2×D4—8616no—
612C2×D4—868no—
613C2×D4—868no—
614C2×D4—861no—
615C2×D4—864no—
616C2×D4—864no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—3442no—
627C2×D4—3442no—
628C2×D4#1062190214yes—
629C2×D4C23×D4312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—861no—
647C22×C4—864no—
648C22×C4—3442no—
649C22×C4—3442no—
650C22×C4—3442no—
651C22×C4—3442no—
652C22×C4—3442no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656D8—868no—
657D8—868no—
658D8—868no—
659D8—868no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8C23×D4312yes—
667C2×C8C23×D4312yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—434no—
674C4⋊C4—434no—
675C4⋊C4—432no—
676C4⋊C4—861no—
677C4⋊C4C23×D4312yes—
678C4⋊C4C23×D4312yes—
679C4⋊C4C23×D4312yes—
680C22⋊C4—24no—
681C22⋊C4—434no—
682C22⋊C4—434no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C42—432no—
692C42—432no—
693C42—864no—
694C42D4×D4312yes—
695C42C23×D4312yes—
696C23—24no—
697C23—22no—
698C23—42no—
699C23—42no—
700C23—432no—
701C23—8616no—
702C23—862no—
703C23—864no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—3444no—
710C23—3444no—
711C23—34416no—
712C23—1722no—
713C23—1722no—
714C23—1722no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23—1722no—
719C23—1722no—
720C23C2×D4×D4311yescharacteristic
721D4—24no—
722D4—22no—
723D4—434no—
724D4—8616no—
725D4—864no—
726D4—862no—
727D4—862no—
728D4—862no—
729D4—862no—
730D4—862no—
731D4—3444no—
732D4—3444no—
733D4—3444no—
734D4—3444no—
735D4—1722no—
736D4—1722no—
737D4C2×#1062190214yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—84no—
747C2×C4—432no—
748C2×C4—432no—
749C2×C4—432no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—3444no—
758C2×C4—3444no—
759C2×C4—3444no—
760C2×C4—3444no—
761C2×C4—3444no—
762C2×C4—1722no—
763C2×C4C2×D4×D4312yes—
764C2×C4C2×D4×D4312yes—
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4312yes—
767C2×C4C2×#1062190212yes—
768C2×C4C24×D4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—862no—
772C8—862no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—862no—
778C22—862no—
779C22—862no—
780C22—864no—
781C22—34416no—
782C22—3444no—
783C22—3444no—
784C22—1722no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22—1724no—
793C22—1728no—
794C22#1458341212yes—
795C22#1458370112yes—
796C22#1458370312yes—
797C22C22×D4×D4311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—862no—
804C4—862no—
805C4—862no—
806C4—1722no—
807C4#1458341212yes—
808C4C2×#41×D4311yescharacteristic
809C4C22×#1062190211yescharacteristic
810C2—44no—
811C2—3442no—
812C2—3442no—
813C2—1722no—
814C2—1724no—
815C2#1914484014yesdirect product factor
816C2C2×#1458341211yescharacteristic
817C2C2×#1458370111yescharacteristic
818C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
hypercenterC2×#478D43
hypocenterC43C2×#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583505C2semidirect
2. C2×#14583371C2semidirect
3. #19144840C2direct (N × H)
4. C2×#14583226C2semidirect
5. C2×#14583225C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583095C2semidirect
8. C2×#14583094C2semidirect
9. C2×#14583034C2semidirect
10. C2×#14583034C2semidirect
11. C2×#14583010C2semidirect
12. C2×#14583008C2semidirect
13. C2×#14582981C2semidirect
14. C2×#14582979C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#478C2semidirect
23. #14583505C22semidirect
24. C2×#13063322C22semidirect
32. #14583371C22semidirect
36. C2×#13063287C22semidirect
37. C2×#13063287C22semidirect
44. #14583226C22semidirect
45. #14583225C22semidirect
46. #14583196C22semidirect
47. #14583095C22semidirect
48. #14583094C22semidirect
49. #14583034C22semidirect
50. #14583034C22semidirect
51. #14583010C22semidirect
52. #14583008C22semidirect
53. #14582981C22semidirect
54. #14582979C22semidirect
55. #14582959C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063256C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. C2×#13063247C22semidirect
60. C2×#13063247C22semidirect
63. C2×#13063245C22semidirect
64. C2×#13063245C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
69. C2×#125×C43C22semidirect
71. C43×#478C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×C4⋊C8×C43C22semidirect
107. #13063322C23semidirect
124. #13063287C23semidirect
125. #13063287C23semidirect
149. #13063258C23semidirect
150. #13063256C23semidirect
151. C4⋊(C43⋊C8)C23semidirect
152. #13063247C23semidirect
153. #13063247C23semidirect
156. #13063245C23semidirect
157. #13063245C23semidirect
160. #13063235C23semidirect
161. C8×Dic43C23semidirect
167. #125×C43C23semidirect
177. #107×C43C23semidirect
178. #106×C43C23semidirect
179. C4⋊C8×C43C23semidirect
407. C2×#478D43semidirect
418. C2×C43#3122semidirect
434. C2×#125C2×D43semidirect
458. #478C2×D43semidirect
469. C2×#107C2×D43semidirect
471. C2×#106C2×D43semidirect
473. C2×C4⋊C8C2×D43semidirect
486. C43C2×#3122semidirect
523. #125C22×D43semidirect
575. #107C22×D43semidirect
577. #106C22×D43semidirect
579. C4⋊C8C22×D43semidirect
815. C2#19144840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835052
C2×#145833712
#191448402
C2×#145832262
C2×#145832252
C2×#145831962
C2×#145830952
C2×#145830942
C2×#145830342
C2×#145830102
C2×#145830082
C2×#145829812
C2×#145829792
C2×#145829592
C2×C43×#4782
C2×#312243