Finite Group Databasebeta

← C2×#19146926 #25973535

Subgroups — C2×#19146926 #25973535

Order 11008.

2210 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×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic
3#19146926C2116yesmaximal, direct product factor
4C2×#14583244C211yesmaximal, characteristic, complemented
5C2×#14583213C211yesmaximal, characteristic, complemented
6C2×#14583211C211yesmaximal, characteristic, complemented
7C2×#14583192C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583142C211yesmaximal, characteristic, complemented
10C2×#14583097C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×Q16×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582974C211yesmaximal, characteristic, complemented
14C2×#14582900C211yesmaximal, characteristic, complemented
15C2×#14582899C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583607—24no—
22#14583607C2218yescomplemented
23#14583568—24no—
24#14583568C2218yes—
25C2×#13063324C2211yescharacteristic
26C2×#13063321—21no—
27C2×#13063321C2211yescharacteristic
28C2×#13063315—21no—
29C2×#13063305—21no—
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063299—21no—
33C2×#13063299C2211yescharacteristic
34C2×#13063296—21no—
35C2×#13063296C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C22×C4⋊Dic43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583244C2218yescomplemented
44#14583213C2218yescomplemented
45#14583211C2218yescomplemented
46#14583192C2218yescomplemented
47#14583147C2218yescomplemented
48#14583142C2218yescomplemented
49#14583097C2218yescomplemented
50#14583060C2218yescomplemented
51Q16×Dic43C2218yescomplemented
52#14582974C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582900C2218yescomplemented
58#14582899C2218yescomplemented
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#452C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C23×Dic43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93C2×#10621884—42no—
94C2×#10621884C2314yes—
95C2×#10621877—42no—
96C2×#10621877C2314yes—
97C2×#10621872—42no—
98C2×#10621872C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063324—22no—
102#13063324C2314yes—
103#13063321—28no—
104#13063321—22no—
105#13063321C2314yes—
106#13063315—28no—
107#13063305—28no—
108#13063302—28no—
109#13063301—22no—
110#13063301C2314yes—
111#13063299—22no—
112#13063299—28no—
113#13063299C2314yes—
114#13063296—22no—
115#13063296—28no—
116#13063296C2314yes—
117Q8×Dic43—22no—
118Q8×Dic43—22no—
119Q8×Dic43C2314yes—
120Q8×Dic43C2314yes—
121C4×C22⋊D43—28no—
122C4×C22⋊D43D414yes—
123C4×C22⋊D43C2314yes—
124(C22⋊D43)⋊C4—28no—
125C2×C4⋊Dic43—22no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2314yes—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C4⋊C4×D43—22no—
138C4⋊C4×D43C2314yes—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43D411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063259C2314yes—
149#13063258C2314yes—
150Dic43⋊C8C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160C8×Dic43C2314yes—
161C2×#41×C43—22no—
162C2×#41×C43—24no—
163C2×#41×C43—42no—
164C2×#41×C43C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43C2311yescharacteristic
171C2×Q16×C43—24no—
172C2×Q16×C43C2314yes—
173C2×SD16×C43—42no—
174C2×SD16×C43C2314yes—
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2311yescharacteristic
177C22⋊Q8×C43—22no—
178C22⋊Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182#103×C43C2314yes—
183#102×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189#41×C43—28no—
190#41×C43—44no—
191#41×C43—48no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43#4114yes—
198C2×Q8×C43C2412yes—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—24no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—44no—
205C2×D4×C43C2412yes—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—44no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—82no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43C2×D414yes—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—24no—
231C22×Dic43—82no—
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234C22×Dic43C2×D411yescharacteristic
235#10621902—28no—
236#10621902—44no—
237#10621902—48no—
238C2×D172—21no—
239C2×D172—24no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—44no—
243C2×D172C2412yes—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—44no—
249C2×C4×D43—82no—
250C2×C4×D43C2×D412yes—
251C2×C4×D43C2412yes—
252C2×Dic86—24no—
253C2×Dic86—82no—
254Q16×C43—28no—
255SD16×C43—44no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C2412yes—
263C22⋊C4×C43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43C2×D414yes—
266#10621884—44no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4C2×D414yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—24no—
273C4⋊Dic43—21no—
274C4⋊Dic43—24no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2412yes—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4C2×D414yes—
283C4×Dic43—24no—
284C4×Dic43—24no—
285C4×Dic43C2×D412yes—
286C4×Dic43C2412yes—
287#10621877—44no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8C2412yes—
291C2×C43⋊C8C2412yes—
292#10621872—44no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D412yes—
301C23×C43C22×D411yescharacteristic
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43C22×D412yes—
310Q8×C43—24no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—42no—
315Q8×C43C2×#4114yes—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—48no—
319D4×C43—42no—
320C2×C4×C43—24no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—24no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—48no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4112yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—28no—
337C22⋊D43—48no—
338C22⋊D43—84no—
339C22⋊D43—84no—
340C22⋊D43—84no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—84no—
350C2×Dic43#13714yes—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354D172—22no—
355D172—22no—
356D172—48no—
357D172—42no—
358C4×D43—24no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—48no—
362C4×D43—84no—
363Dic86—84no—
364C8×C43—22no—
365C8×C43—22no—
366C43⋊C8—22no—
367C43⋊C8—22no—
368C2×#3333—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—44no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—84no—
377C22×C43#54612yes—
378C22×C43C2×#13712yes—
379C22×C43#57612yes—
380C22×C43C23×D411yescharacteristic
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—44no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—84no—
389C4×C43—24no—
390C4×C43—22no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#54612yes—
394C4×C43C22×#4111yescharacteristic
395C4×C43C2×H(5,𝔽2)11yescharacteristic
396Dic43—22no—
397Dic43—22no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43C2×#13714yes—
402C2×#554—431no—
403C2×#550—431no—
404#3333—4316no—
405C2×#486—431no—
406C2×#480—431no—
407C2×#480—431no—
408C2×#477—431no—
409C2×#468—431no—
410C2×#468—431no—
411C2×#460—431no—
412C2×#452—431no—
413C2×#452D4311yescharacteristic, complemented
414C2×C4×Q16—431no—
415C2×#436—431no—
416C2×#417—431no—
417C2×#417—431no—
418C2×C43—42no—
419C2×C43—82no—
420C2×C43#333314yescomplemented
421C2×C43C2×#54611yescharacteristic
422C2×C43C22×#13711yescharacteristic
423C2×C43C2×#57611yescharacteristic
424D43—42no—
425D43—82no—
426C22×#41—431no—
427C22×#41C2×D4311yescharacteristic
428C22×Q16C2×D4311yescharacteristic
429C22×SD16—431no—
430C22×SD16C2×D4311yescharacteristic
431C22×M16—431no—
432C22×M16—431no—
433#554—438no—
434#554—864no—
435#550—438no—
436#550—864no—
437C2×C4⋊Q8—431no—
438C2×#127—431no—
439C2×#127—861no—
440C2×#125—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8—861no—
443C2×C22⋊Q8—861no—
444C2×C22⋊Q8C2×D4311yescharacteristic
445C2×#121—431no—
446C2×#121—431no—
447C2×#121—861no—
448C2×#121—861no—
449C2×C4×Q8—431no—
450C2×C4×Q8—431no—
451C2×C4×D4—431no—
452C2×C4×D4—861no—
453C2×C4×D4—861no—
454C22×C4⋊C4—431no—
455C22×C4⋊C4—431no—
456#486—438no—
457#480—438no—
458#480—438no—
459#477—438no—
460#468—438no—
461#468—438no—
462#460—438no—
463#452—438no—
464#452C2×D4318yescomplemented
465C4×Q16—438no—
466#436—438no—
467C2×#107—431no—
468C2×#107—431no—
469C2×#107—431no—
470C2×C4⋊C8—431no—
471#417—438no—
472#417—438no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103C2×D4311yescharacteristic
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic
483C2×C22⋊C8—431no—
484C2×C22⋊C8C2×D4311yescharacteristic
485C2×C4×C8—431no—
486C43C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—22no—
488C2×#41—24no—
489C2×#41—42no—
490C2×#41—434no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—1722no—
494C2×#41C22×D4314yes—
495C22×Q8—861no—
496C22×Q8C22×D4311yescharacteristic
497C22×Q8C22×D4311yescharacteristic
498C22×D4—21no—
499C22×D4—431no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4—861no—
505C22×D4—861no—
506C22×D4C22×D4311yescharacteristic
507C23×C4—21no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513C2×Q16—24no—
514C2×Q16C22×D4314yes—
515C2×SD16—42no—
516C2×SD16—434no—
517C2×SD16—1722no—
518C2×SD16C22×D4314yes—
519C2×M16—434no—
520C2×M16—434no—
521C2×M16—1722no—
522C2×M16—1722no—
523C22×C8—431no—
524C22×C8—431no—
525C22×C8C22×D4311yescharacteristic
526C22×C8C22×D4311yescharacteristic
527C4⋊Q8—434no—
528C4⋊Q8—862no—
529#127—434no—
530#127—862no—
531#127—868no—
532#125—868no—
533C22⋊Q8—22no—
534C22⋊Q8—434no—
535C22⋊Q8—868no—
536C22⋊Q8—868no—
537C22⋊Q8—862no—
538C22⋊Q8C22×D4314yes—
539#121—434no—
540#121—434no—
541#121—868no—
542#121—868no—
543#121—862no—
544#121—862no—
545C4×Q8—434no—
546C4×Q8—434no—
547C4×Q8—862no—
548C4×Q8—862no—
549C4×D4—434no—
550C4×D4—434no—
551C4×D4—868no—
552C4×D4—868no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—434no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—434no—
560C2×C4⋊C4—862no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—862no—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—861no—
577C2×C42—861no—
578#107—434no—
579#107—434no—
580#107—434no—
581C4⋊C8—434no—
582#103—434no—
583#103—434no—
584#103—434no—
585#103C22×D4314yes—
586#102—434no—
587#102—434no—
588#102—434no—
589#102—434no—
590#102—434no—
591#102C22×D4314yes—
592C22⋊C8—434no—
593C22⋊C8C22×D4314yes—
594C4×C8—434no—
595C24—21no—
596C24—431no—
597C24—861no—
598C24D4×D4311yescharacteristic
599#41—28no—
600#41—44no—
601#41—48no—
602#41—868no—
603#41—1724no—
604#41—1728no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—864no—
611C2×Q8—3442no—
612C2×Q8#1062190014yes—
613C2×Q8C23×D4312yes—
614C2×Q8C23×D4312yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—434no—
621C2×D4—432no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—861no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—3442no—
633C2×D4—3442no—
634C2×D4—1724no—
635C2×D4—1724no—
636C2×D4C23×D4312yes—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—864no—
650C22×C4—864no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—864no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—3442no—
658C22×C4—3442no—
659C22×C4—1724no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664Q16—28no—
665SD16—44no—
666SD16—1724no—
667M16—1724no—
668M16—1724no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—432no—
672C2×C8—432no—
673C2×C8—862no—
674C2×C8—862no—
675C2×C8C23×D4312yes—
676C2×C8C23×D4312yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—434no—
680C4⋊C4—432no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—864no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—434no—
695C22⋊C4—434no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C42—432no—
700C42—432no—
701C42—864no—
702C42—864no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—432no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23C2×D4×D4312yes—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—24no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—3444no—
726Q8C2×#1062190014yes—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—42no—
731D4—868no—
732D4—862no—
733D4—862no—
734D4—3444no—
735D4—3444no—
736D4—3444no—
737D4—1728no—
738D4—1728no—
739D4—1722no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—434no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—432no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—864no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—3444no—
764C2×C4—3444no—
765C2×C4—1728no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C2×D4×D4312yes—
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4C2×#1062190012yes—
772C2×C4#1306337012yes—
773C2×C4C24×D4311yescharacteristic
774C8—22no—
775C8—22no—
776C8—862no—
777C8—862no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—862no—
787C22—862no—
788C22—862no—
789C22—3444no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1724no—
794C22#1458353612yes—
795C22#137×D4312yes—
796C22#1458370112yes—
797C22C22×D4×D4311yescharacteristic
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—434no—
803C4—862no—
804C4—862no—
805C4—1722no—
806C4—1722no—
807C4—1722no—
808C4#1458353612yes—
809C4C22×#1062190011yescharacteristic
810C4C2×#1306337011yescharacteristic
811C2—42no—
812C2—82no—
813C2—3442no—
814C2—1722no—
815C2#1914692614yesdirect product factor
816C2C2×#1458353611yescharacteristic
817C2C2×#137×D4311yescharacteristic
818C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
hypercenterC2×#452D43
hypocenterC43C2×#3333
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583607C2semidirect
3. #19146926C2direct (N × H)
4. C2×#14583244C2semidirect
5. C2×#14583213C2semidirect
6. C2×#14583211C2semidirect
7. C2×#14583192C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583142C2semidirect
10. C2×#14583097C2semidirect
11. C2×#14583060C2semidirect
12. C2×Q16×Dic43C2semidirect
13. C2×#14582974C2semidirect
14. C2×#14582900C2semidirect
15. C2×#14582899C2semidirect
16. C2×C43×#452C2semidirect
22. #14583607C22semidirect
43. #14583244C22semidirect
44. #14583213C22semidirect
45. #14583211C22semidirect
46. #14583192C22semidirect
47. #14583147C22semidirect
48. #14583142C22semidirect
49. #14583097C22semidirect
50. #14583060C22semidirect
51. Q16×Dic43C22semidirect
52. #14582974C22semidirect
57. #14582900C22semidirect
58. #14582899C22semidirect
73. C43×#452C22semidirect
413. C2×#452D43semidirect
420. C2×C43#3333semidirect
464. #452C2×D43semidirect
486. C43C2×#3333semidirect
815. C2#19146926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835682
#191469262
C2×#145832442
C2×#145832132
C2×#145832112
C2×#145831922
C2×#145831472
C2×#145831422
C2×#145830972
C2×#145830602
C2×Q16×Dic432
C2×#145829742
C2×#145829002
C2×#145828992
C2×C43×#4522
C2×#333343