Finite Group Databasebeta

← C2×#19144776 #25964825

Subgroups — C2×#19144776 #25964825

Order 11008.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583518C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic, complemented
3#19144776C2116yesmaximal, direct product factor
4C2×#14583239C211yesmaximal, characteristic, complemented
5C2×#14583221C211yesmaximal, characteristic, complemented
6C2×#14583189C211yesmaximal, characteristic, complemented
7C2×#14583180C211yesmaximal, characteristic, complemented
8C2×#14583111C211yesmaximal, characteristic, complemented
9C2×#14583048C211yesmaximal, characteristic, complemented
10C2×#14583031C211yesmaximal, characteristic
11C2×#14583008C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×#14582984C211yesmaximal, characteristic, complemented
14C2×D8×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#463C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20#14583518—24no—
21#14583518C2218yescomplemented
22C2×#13063325C2211yescharacteristic, complemented
23C2×#13063318—21no—
24C2×#13063311—21no—
25C2×#13063309—21no—
26C2×#13063302—21no—
27C2×#13063301C2211yescharacteristic
28C2×#13063296C2211yescharacteristic
29#14583371—24no—
30#14583371C2218yescomplemented
31C2×Q8×Dic43C2211yescharacteristic, complemented
32C2×C4×D172C2211yescharacteristic
33C2×D4×Dic43C2211yescharacteristic
34C2×D4×Dic43C2211yescharacteristic, complemented
35C2×#13063287C2211yescharacteristic
36C2×C4×C22⋊D43—21no—
37C2×(C22⋊D43)⋊C4—21no—
38C2×#13063283C2211yescharacteristic
39C2×#13063282C2211yescharacteristic
40C22×(C2×D43)⋊C4—21no—
41C2×C22⋊C4×D43—21no—
42#14583239C2218yescomplemented
43#14583221C2218yescomplemented
44#14583189C2218yescomplemented
45#14583180C2218yescomplemented
46#14583111C2218yescomplemented
47#14583048C2218yescomplemented
48#14583031C2218yes—
49#14583008C2218yescomplemented
50#14583000C2218yescomplemented
51#14582984C2218yescomplemented
52D8×Dic43C2218yescomplemented
53#14582959C2218yescomplemented
54C2×#13063259C2211yescharacteristic, complemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063256C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic, complemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic, complemented
72C2×C4×D4×C43C2211yescharacteristic
73C43×#463C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×Dic86—21no—
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C2×D4×D43—24no—
83C2×D4×D43—24no—
84C2×D4×D43—22no—
85C2×D4×D43C2314yes—
86C23×Dic43—21no—
87C23×Dic43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C2×#10621884—24no—
92C2×#10621884C2314yes—
93C2×#10621882—24no—
94C2×#10621882C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063325—22no—
98#13063325C2314yescomplemented
99#13063318—28no—
100#13063311—28no—
101#13063309—28no—
102#13063302—28no—
103#13063301—22no—
104#13063301C2314yes—
105#13063296—22no—
106#13063296C2314yes—
107Q8×Dic43—22no—
108Q8×Dic43C2314yescomplemented
109C4×D172—22no—
110C4×D172C2314yes—
111D4×Dic43—22no—
112D4×Dic43—22no—
113D4×Dic43C2314yes—
114D4×Dic43C2314yescomplemented
115#13063287—22no—
116#13063287C2314yes—
117C4×C22⋊D43—28no—
118(C22⋊D43)⋊C4—28no—
119#13063283—22no—
120#13063283C2314yes—
121#13063282D414yes—
122#13063282C2314yes—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4D411yescharacteristic
130C2×Dic43⋊C4D411yescharacteristic
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—28no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×(C2×D43)⋊C4D411yescharacteristic
141C22⋊C4×D43—28no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063259C2314yescomplemented
146#13063259C2314yescomplemented
147#13063256C2314yescomplemented
148#13063256C2314yescomplemented
149C4⋊(C43⋊C8)C2314yescomplemented
150#13063249C2314yescomplemented
151#13063247C2314yes—
152#13063247C2314yes—
153#13063246C2314yes—
154#13063246C2314yes—
155#13063246C2314yescomplemented
156(C2×D43)⋊C8C2314yes—
157(C2×D43)⋊C8C2314yes—
158#13063235C2314yescomplemented
159C8×Dic43C2314yescomplemented
160C22×Q8×C43C2311yescharacteristic
161C22×D4×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C2×SD16×C43—24no—
165C2×SD16×C43C2314yes—
166C2×D8×C43—24no—
167C2×D8×C43C2314yes—
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170#124×C43—22no—
171#124×C43C2314yescomplemented
172C4×D4×C43—22no—
173C4×D4×C43C2314yes—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yescomplemented
180#103×C43C2314yescomplemented
181#102×C43C2314yescomplemented
182C24×C43—21no—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43—28no—
186C23×D43—24no—
187C23×D43—82no—
188C23×D43—82no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43C2412yes—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43#4114yes—
200C2×D4×C43C2412yes—
201C2×D4×C43C2412yes—
202C22×C4×C43—24no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—82no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—28no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—82no—
213C22×Dic43—24no—
214C22×Dic43—24no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—82no—
219C22×Dic43—82no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223D4×D43—216no—
224D4×D43—28no—
225D4×D43—28no—
226C2×D172—21no—
227C2×D172—22no—
228C2×D172#4114yes—
229C2×D172C2412yes—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—82no—
235C2×C4×D43—82no—
236C2×C4×D43C2×D412yes—
237C2×C4×D43C2412yes—
238C2×Dic86—24no—
239C2×Dic86—82no—
240SD16×C43—28no—
241D8×C43—28no—
242C2×C8×C43—22no—
243C2×C8×C43—22no—
244C2×C8×C43C2412yes—
245C2×C8×C43C2412yes—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C2412yes—
248C22⋊C4×C43—24no—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C42×C43C2×D412yes—
252C42×C43C2412yes—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256#10621884—28no—
257#10621882—28no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4C2×D414yes—
263(C2×D43)⋊C4C2×D414yes—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4C2×D414yes—
274Dic43⋊C4C2×D414yes—
275C4×Dic43—24no—
276C4×Dic43—24no—
277C4×Dic43C2×D412yes—
278C4×Dic43C2412yes—
279C2×C43⋊C8—22no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8C2412yes—
282C2×C43⋊C8C2412yes—
283C23×C43—24no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43C22×D411yescharacteristic
292C22×D43—22no—
293C22×D43—24no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—216no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—816no—
303C22×D43C22×D412yes—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—42no—
307D4×C43—24no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—42no—
312D4×C43C2×#4114yes—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—84no—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C2×#4112yes—
324C2×C4×C43C2×#4112yes—
325C2×C4×C43C2511yescharacteristic
326C22⋊D43—216no—
327C22⋊D43—84no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—84no—
338C2×Dic43—84no—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342D172—24no—
343D172—22no—
344D172C2×#4114yes—
345C4×D43—24no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—84no—
349C4×D43—84no—
350Dic86—84no—
351C8×C43—22no—
352C8×C43—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C2×#3118—431nomaximal, Sylow
356C22×C43—24no—
357C22×C43—48no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—84no—
364C22×C43#52512yes—
365C22×C43#57612yes—
366C22×C43#57712yes—
367C22×C43C23×D411yescharacteristic
368C2×D43—22no—
369C2×D43—24no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—44no—
373C2×D43—48no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—816no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43#52512yes—
382C4×C43C22×#4111yescharacteristic
383C4×C43C22×#4111yescharacteristic
384Dic43—22no—
385Dic43—22no—
386Dic43—22no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C2×#542—431no—
391C2×#518—431no—
392#3118—4316no—
393C2×#485—431no—
394C2×#482—431no—
395C2×#476—431no—
396C2×#474—431no—
397C2×#463—431no—
398C2×#463D4311yescharacteristic, complemented
399C2×#450—431no—
400C2×#447—431no—
401C2×#442—431no—
402C2×#440—431no—
403C2×C4×SD16—431no—
404C2×C4×D8—431no—
405C2×#433—431no—
406C2×C43—44no—
407C2×C43—82no—
408C2×C43#311814yescomplemented
409C2×C43C2×#52511yescharacteristic
410C2×C43C2×#57611yescharacteristic
411C2×C43C2×#57711yescharacteristic
412D43—42no—
413D43—44no—
414C23×D4—431no—
415C22×SD16—431no—
416C22×SD16C2×D4311yescharacteristic
417C22×D8—431no—
418C22×D8C2×D4311yescharacteristic
419#542—438no—
420#542—864no—
421C2×C4⋊Q8—431no—
422C2×#126—861no—
423C2×#124—861no—
424C2×#124C2×D4311yescharacteristic, complemented
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429#518—438no—
430#518—864no—
431C2×C4×Q8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×C4×D4C2×D4311yescharacteristic
439C2×#117—431no—
440C2×#117—431no—
441C22×C22⋊C4—861no—
442C22×C22⋊C4—861no—
443#485—438no—
444#482—438no—
445#476—438no—
446#474—438no—
447#463—438no—
448#463C2×D4318yescomplemented
449#450—438no—
450#447—438no—
451#442—438no—
452#440—438no—
453C4×SD16—438no—
454C4×D8—438no—
455#433—438no—
456C2×#107—431no—
457C2×#107—431no—
458C2×#106—431no—
459C2×#106—431no—
460C2×C4⋊C8—431no—
461C2×C4⋊C8C2×D4311yescharacteristic, complemented
462C2×#103—431no—
463C2×#103C2×D4311yescharacteristic, complemented
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102C2×D4311yescharacteristic, complemented
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×#97—431no—
473C2×C4×C8—431no—
474C43C2×#311811yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8—861no—
477C22×Q8C22×D4311yescharacteristic
478C22×D4—434no—
479C22×D4—431no—
480C22×D4—862no—
481C22×D4—861no—
482C22×D4—864no—
483C22×D4—864no—
484C22×D4—861no—
485C22×D4C22×D4311yescharacteristic
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4—861no—
493C2×SD16—24no—
494C2×SD16—434no—
495C2×SD16—864no—
496C2×SD16C22×D4314yes—
497C2×D8—24no—
498C2×D8—434no—
499C2×D8—864no—
500C2×D8C22×D4314yes—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505C4⋊Q8—434no—
506C4⋊Q8—862no—
507#126—868no—
508#124—22no—
509#124—868no—
510#124C22×D4314yescomplemented
511#123—868no—
512C22⋊Q8—434no—
513C22⋊Q8—868no—
514C22⋊Q8—862no—
515#121—434no—
516#121—862no—
517C4×Q8—434no—
518C4×Q8—862no—
519C4×D4—22no—
520C4×D4—434no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—862no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—868no—
528C4×D4—868no—
529C4×D4—862no—
530C4×D4C22×D4314yes—
531#117—434no—
532#117—434no—
533#117—434no—
534#117—862no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—431no—
548C2×C22⋊C4—431no—
549C2×C22⋊C4—868no—
550C2×C22⋊C4—868no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C42—431no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
564#106—434no—
565#106—434no—
566C4⋊C8—434no—
567C4⋊C8C22×D4314yescomplemented
568#103—434no—
569#103C22×D4314yescomplemented
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574#102—434no—
575#102C22×D4314yescomplemented
576C22⋊C8—434no—
577C22⋊C8—434no—
578#97—434no—
579C4×C8—434no—
580C24—21no—
581C24—21no—
582C24—431no—
583C24—864no—
584C24—868no—
585C24—861no—
586C24—3442no—
587C24—3442no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—864no—
592C2×Q8—3442no—
593C2×Q8C23×D4312yes—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—434no—
600C2×D4—432no—
601C2×D4—864no—
602C2×D4—868no—
603C2×D4—8616no—
604C2×D4—868no—
605C2×D4—868no—
606C2×D4—864no—
607C2×D4—861no—
608C2×D4—862no—
609C2×D4—3442no—
610C2×D4#1062190014yes—
611C2×D4C23×D4312yes—
612C2×D4C23×D4312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—82no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—864no—
631C22×C4—3442no—
632C22×C4—3442no—
633C22×C4—3442no—
634C22×C4—3442no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638SD16—28no—
639SD16—868no—
640D8—28no—
641D8—868no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8C23×D4312yes—
649C2×C8C23×D4312yes—
650C4⋊C4—21no—
651C4⋊C4—434no—
652C4⋊C4—434no—
653C4⋊C4—432no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—864no—
662C4⋊C4C23×D4312yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—434no—
667C22⋊C4—434no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C42—432no—
676C42—432no—
677C42—864no—
678C42—864no—
679C42D4×D4312yes—
680C42C23×D4312yes—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—432no—
690C23—8616no—
691C23—862no—
692C23—864no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—3444no—
697C23—3444no—
698C23—34416no—
699C23—1722no—
700C23—1722no—
701C23C2×D4×D4311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—3444no—
706D4—24no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—434no—
712D4—8616no—
713D4—864no—
714D4—862no—
715D4—3444no—
716D4C2×#1062190014yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—432no—
725C2×C4—432no—
726C2×C4—432no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—864no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—3444no—
739C2×C4—3444no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4C2×D4×D4312yes—
744C2×C4C2×D4×D4312yes—
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4#41×D4312yes—
747C2×C4C2×#1062190012yes—
748C2×C4C24×D4311yescharacteristic
749C8—22no—
750C8—22no—
751C8—862no—
752C8—862no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—862no—
762C22—862no—
763C22—862no—
764C22—864no—
765C22—34416no—
766C22—1722no—
767C22—1722no—
768C22—1724no—
769C22—1728no—
770C22#1458340912yes—
771C22#1458370112yes—
772C22#1458370912yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—862no—
779C4—862no—
780C4—862no—
781C4—1722no—
782C4—1722no—
783C4—1722no—
784C4#1458340912yes—
785C4C2×#41×D4311yescharacteristic
786C4C22×#1062190011yescharacteristic
787C2—44no—
788C2—82no—
789C2—1722no—
790C2—1724no—
791C2#1914477614yesdirect product factor
792C2C2×#1458340911yescharacteristic
793C2C2×#1458370111yescharacteristic
794C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
hypercenterC2×#463D43
hypocenterC43C2×#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583518C2semidirect
2. C2×#14583371C2semidirect
3. #19144776C2direct (N × H)
4. C2×#14583239C2semidirect
5. C2×#14583221C2semidirect
6. C2×#14583189C2semidirect
7. C2×#14583180C2semidirect
8. C2×#14583111C2semidirect
9. C2×#14583048C2semidirect
11. C2×#14583008C2semidirect
12. C2×#14583000C2semidirect
13. C2×#14582984C2semidirect
14. C2×D8×Dic43C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#463C2semidirect
21. #14583518C22semidirect
22. C2×#13063325C22semidirect
30. #14583371C22semidirect
31. C2×Q8×Dic43C22semidirect
34. C2×D4×Dic43C22semidirect
42. #14583239C22semidirect
43. #14583221C22semidirect
44. #14583189C22semidirect
45. #14583180C22semidirect
46. #14583111C22semidirect
47. #14583048C22semidirect
49. #14583008C22semidirect
50. #14583000C22semidirect
51. #14582984C22semidirect
52. D8×Dic43C22semidirect
53. #14582959C22semidirect
54. C2×#13063259C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063256C22semidirect
57. C2×#13063256C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. C2×#13063249C22semidirect
64. C2×#13063246C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
71. C2×#124×C43C22semidirect
73. C43×#463C22semidirect
74. C2×C4⋊C8×C43C22semidirect
75. C2×#103×C43C22semidirect
76. C2×#102×C43C22semidirect
98. #13063325C23semidirect
108. Q8×Dic43C23semidirect
114. D4×Dic43C23semidirect
145. #13063259C23semidirect
146. #13063259C23semidirect
147. #13063256C23semidirect
148. #13063256C23semidirect
149. C4⋊(C43⋊C8)C23semidirect
150. #13063249C23semidirect
155. #13063246C23semidirect
158. #13063235C23semidirect
159. C8×Dic43C23semidirect
171. #124×C43C23semidirect
179. C4⋊C8×C43C23semidirect
180. #103×C43C23semidirect
181. #102×C43C23semidirect
398. C2×#463D43semidirect
408. C2×C43#3118semidirect
424. C2×#124C2×D43semidirect
448. #463C2×D43semidirect
461. C2×C4⋊C8C2×D43semidirect
463. C2×#103C2×D43semidirect
469. C2×#102C2×D43semidirect
474. C43C2×#3118semidirect
510. #124C22×D43semidirect
567. C4⋊C8C22×D43semidirect
569. #103C22×D43semidirect
575. #102C22×D43semidirect
791. C2#19144776direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835182
C2×#145833712
#191447762
C2×#145832392
C2×#145832212
C2×#145831892
C2×#145831802
C2×#145831112
C2×#145830482
C2×#145830312
C2×#145830082
C2×#145830002
C2×#145829842
C2×D8×Dic432
C2×#145829592
C2×C43×#4632
C2×#311843