Finite Group Databasebeta

← C2×#19146590 #25973175

Subgroups — C2×#19146590 #25973175

Order 11008.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583560C211yesmaximal, characteristic, complemented
2C2×#14583549C211yesmaximal, characteristic, complemented
3#19146590C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583213C211yesmaximal, characteristic, complemented
7C2×#14583192C211yesmaximal, characteristic, complemented
8C2×#14583142C211yesmaximal, characteristic, complemented
9C2×#14583133C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic, complemented
11C2×#14583043C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×#14582967C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C22×#13063249C211yesmaximal, characteristic, complemented
16C2×C43×#448C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900—21no—
19C22×#10621882C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21C23×C43⋊C8C2211yescharacteristic
22#14583560—24no—
23#14583560C2218yescomplemented
24#14583549—24no—
25#14583549C2218yescomplemented
26C2×#13063324C2211yescharacteristic
27C2×#13063314—21no—
28C2×#13063314C2211yescharacteristic
29C2×#13063307—21no—
30C2×#13063306—21no—
31C2×#13063302—21no—
32C2×#13063301—21no—
33C2×#13063301C2211yescharacteristic
34C2×#13063299—21no—
35C2×#13063299C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×C4×C22⋊D43—21no—
40C2×C4×C22⋊D43C2211yescharacteristic
41C22×C4⋊Dic43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583260C2218yescomplemented
44#14583233C2218yescomplemented
45#14583213C2218yescomplemented
46#14583192C2218yescomplemented
47#14583142C2218yescomplemented
48#14583133C2218yescomplemented
49#14583116C2218yescomplemented
50#14583043C2218yescomplemented
51#14583000C2218yescomplemented
52#14582967C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582899C2218yescomplemented
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2218yescomplemented
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#448C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621900—28no—
82C2×#10621900—48no—
83C22×Dic86—21no—
84C22×D172—21no—
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C23×Dic43—21no—
90C23×Dic43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621882—42no—
95C2×#10621882C2314yes—
96C2×#10621872—42no—
97C2×#10621872C2314yes—
98C22×C43⋊C8—42no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2314yes—
102#13063324—22no—
103#13063324C2314yes—
104#13063314—28no—
105#13063314—22no—
106#13063314C2314yes—
107#13063307—28no—
108#13063306—28no—
109#13063302—28no—
110#13063301—22no—
111#13063301—28no—
112#13063301C2314yes—
113#13063299—22no—
114#13063299—28no—
115#13063299C2314yes—
116#13063296—22no—
117#13063296C2314yes—
118Q8×Dic43—22no—
119Q8×Dic43C2314yes—
120D4×Dic43—22no—
121D4×Dic43C2314yes—
122C4×C22⋊D43—28no—
123C4×C22⋊D43D414yes—
124C4×C22⋊D43C2314yes—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—22no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2314yes—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C4⋊C4×D43—22no—
137C4⋊C4×D43C2314yes—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43D411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×C4×Dic43—21no—
147C2×C4×Dic43C2311yescharacteristic
148#13063259C2314yes—
149#13063259C2314yes—
150#13063258C2314yes—
151Dic43⋊C8C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063246C2314yes—
159#13063245C2314yes—
160(C2×D43)⋊C8C2314yes—
161#13063235C2314yes—
162C22×Q8×C43—22no—
163C22×Q8×C43—21no—
164C22×Q8×C43—24no—
165C22×Q8×C43—42no—
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43—21no—
170C22×D4×C43C2311yescharacteristic
171C23×C4×C43—21no—
172C23×C4×C43C2311yescharacteristic
173C2×SD16×C43—24no—
174C2×SD16×C43—42no—
175C2×SD16×C43C2314yes—
176C2×SD16×C43C2314yes—
177C22×C8×C43C2311yescharacteristic
178C22×C8×C43C2311yescharacteristic
179#121×C43—22no—
180#121×C43C2314yes—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43—21no—
183#103×C43C2314yes—
184#103×C43C2314yes—
185C22⋊C8×C43C2314yes—
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—24no—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—28no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—44no—
198C2×Q8×C43—44no—
199C2×Q8×C43—48no—
200C2×Q8×C43#4114yescomplemented
201C2×Q8×C43C2412yes—
202C2×Q8×C43C2412yes—
203C2×D4×C43—21no—
204C2×D4×C43—24no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—44no—
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×C43—24no—
215C22×C4×C43—44no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D412yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2411yescharacteristic
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43C2×D414yes—
226C22×Dic43—24no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—24no—
231C22×Dic43—44no—
232C22×Dic43—44no—
233C22×Dic43C2×D411yescharacteristic
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236#10621902—28no—
237#10621902—44no—
238#10621902—48no—
239#10621900—432no—
240C2×D172—21no—
241C2×D172—24no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—44no—
245C2×D172C2412yes—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—24no—
249C2×C4×D43—24no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2412yes—
254C2×Dic86—24no—
255C2×Dic86—44no—
256SD16×C43—28no—
257SD16×C43—44no—
258C2×C8×C43—22no—
259C2×C8×C43—22no—
260C2×C8×C43C2412yes—
261C2×C8×C43C2412yes—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C22⋊C4×C43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43C2×D414yes—
268#10621882—44no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4C2×D414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—24no—
277C4⋊Dic43—21no—
278C4⋊Dic43—24no—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4C2×D414yes—
286C4×Dic43—24no—
287C4×Dic43C2×D412yes—
288C4×Dic43C2412yes—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—44no—
292C2×C43⋊C8C2412yes—
293C2×C43⋊C8C2412yes—
294#10621872—44no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43AGL(1,ℤ/8)14yes—
302C23×C43C22×D412yes—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43C22×D412yes—
312Q8×C43—24no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—48no—
317Q8×C43—42no—
318Q8×C43C2×#4114yescomplemented
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—48no—
322D4×C43—42no—
323C2×C4×C43—24no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—24no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—48no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4112yes—
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43C2511yescharacteristic
339C22⋊D43—28no—
340C22⋊D43—48no—
341C22⋊D43—48no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—48no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—48no—
352C2×Dic43—42no—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D412yes—
356D172—22no—
357D172—22no—
358D172—48no—
359D172—42no—
360C4×D43—24no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—48no—
364C4×D43—48no—
365Dic86—48no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3308—431nomaximal, Sylow
371C22×C43—22no—
372C22×C43—28no—
373C22×C43—22no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—84no—
378C22×C43#54612yes—
379C22×C43C2×AGL(1,ℤ/8)14yes—
380C22×C43C2×AGL(1,ℤ/8)12yes—
381C22×C43#57812yes—
382C22×C43C23×D411yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—44no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—84no—
391C4×C43—24no—
392C4×C43—22no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43#54612yes—
396C4×C43C22×#4111yescharacteristic
397C4×C43C2×H(5,𝔽2)11yescharacteristic
398Dic43—22no—
399Dic43—22no—
400Dic43—22no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#548—431no—
405C2×#547—431no—
406#3308—4316no—
407C2×#489—431no—
408C2×#484—431no—
409C2×#480—431no—
410C2×#477—431no—
411C2×#468—431no—
412C2×#466—431no—
413C2×#463—431no—
414C2×#449—431no—
415C2×#448D4311yescharacteristic, complemented
416C2×#440—431no—
417C2×#435—431no—
418C2×#417—431no—
419C22×#103—431no—
420C2×C43—24no—
421C2×C43—82no—
422C2×C43#330814yescomplemented
423C2×C43C2×#54611yescharacteristic
424C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C43C2×#57811yescharacteristic
426D43—42no—
427D43—82no—
428C22×#41—431no—
429C22×#41—861no—
430C23×Q8C2×D4311yescharacteristic
431C22×SD16C2×D4311yescharacteristic
432C22×SD16C2×D4311yescharacteristic
433C22×D8—431no—
434C22×M16—431no—
435C23×C8—431no—
436#548—438no—
437#548—864no—
438#547—438no—
439#547—864no—
440C2×C4⋊Q8—431no—
441C2×#124—431no—
442C2×#124—861no—
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
448C2×#121—431no—
449C2×#121—431no—
450C2×#121—861no—
451C2×#121C2×D4311yescharacteristic
452C2×C4×Q8—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—861no—
456C22×C4⋊C4—431no—
457C22×C4⋊C4—431no—
458#489—438no—
459#484—438no—
460#480—438no—
461#477—438no—
462#468—438no—
463#466—438no—
464#463—438no—
465#449—438no—
466#448C2×D4318yescomplemented
467#440—438no—
468#435—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107—431no—
472C2×C4⋊C8—431no—
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—438no—
479C2×#103C2×D4311yescharacteristic
480C2×#103C2×D4311yescharacteristic
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×C22⋊C8—431no—
486C2×C22⋊C8C2×D4311yescharacteristic
487C2×#97—431no—
488C43C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—434no—
490C2×#41—862no—
491C2×#41—868no—
492C2×#41—864no—
493C2×#41—1722no—
494C2×#41—1728no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—861no—
500C22×Q8C22×D4311yescharacteristic
501C22×Q8C22×D4314yes—
502C22×Q8C22×D4311yescharacteristic
503C22×D4—21no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4C22×D4311yescharacteristic
510C23×C4—21no—
511C23×C4—431no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C23×C4C22×D4311yescharacteristic
517C2×SD16—24no—
518C2×SD16—42no—
519C2×SD16C22×D4314yes—
520C2×SD16C22×D4314yes—
521C2×D8—434no—
522C2×D8—1722no—
523C2×M16—434no—
524C2×M16—1722no—
525C22×C8—431no—
526C22×C8—431no—
527C22×C8—434no—
528C22×C8—1722no—
529C22×C8C22×D4311yescharacteristic
530C22×C8C22×D4311yescharacteristic
531C4⋊Q8—434no—
532C4⋊Q8—862no—
533#124—434no—
534#124—862no—
535#124—868no—
536#123—868no—
537#123—868no—
538C22⋊Q8—434no—
539C22⋊Q8—868no—
540C22⋊Q8—868no—
541C22⋊Q8—862no—
542#121—22no—
543#121—434no—
544#121—434no—
545#121—868no—
546#121—862no—
547#121—862no—
548#121C22×D4314yes—
549C4×Q8—434no—
550C4×Q8—862no—
551C4×D4—434no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—862no—
555C4×D4—868no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—434no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—862no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—862no—
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C42—431no—
580C2×C42—861no—
581#107—434no—
582#107—434no—
583#107—434no—
584C4⋊C8—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#103—434no—
589#103C22×D4314yes—
590#103C22×D4314yes—
591#102—434no—
592#102—434no—
593#102—434no—
594#102—434no—
595C22⋊C8—434no—
596C22⋊C8C22×D4314yes—
597#97—434no—
598C24—21no—
599C24—431no—
600C24—861no—
601C24D4×D4311yescharacteristic
602#41—868no—
603#41—1724no—
604#41—1728no—
605#41—17232no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—864no—
617C2×Q8—1724no—
618C2×Q8#1062190014yescomplemented
619C2×Q8C23×D4312yes—
620C2×Q8C23×D4312yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—434no—
627C2×D4—432no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—861no—
633C2×D4—862no—
634C2×D4—862no—
635C2×D4—1724no—
636C2×D4—1724no—
637C2×D4—1724no—
638C2×D4C23×D4312yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—44no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—431no—
649C22×C4—432no—
650C22×C4—432no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—864no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—864no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—1724no—
661C22×C4—1724no—
662C22×C4—1724no—
663C22×C4—1724no—
664C22×C4D4×D4312yes—
665C22×C4D4×D4311yescharacteristic
666C22×C4C23×D4312yes—
667C22×C4C23×D4311yescharacteristic
668SD16—28no—
669SD16—44no—
670D8—1724no—
671M16—1724no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—432no—
675C2×C8—432no—
676C2×C8—862no—
677C2×C8—862no—
678C2×C8—1724no—
679C2×C8C23×D4312yes—
680C2×C8C23×D4312yes—
681C4⋊C4—21no—
682C4⋊C4—434no—
683C4⋊C4—432no—
684C4⋊C4—432no—
685C4⋊C4—432no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—864no—
693C4⋊C4—861no—
694C4⋊C4C23×D4312yes—
695C22⋊C4—24no—
696C22⋊C4—434no—
697C22⋊C4—434no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C42—432no—
705C42—432no—
706C42—864no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—432no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—1722no—
719C23—1722no—
720C23—1722no—
721C23#1306335214yes—
722C23C2×D4×D4312yes—
723C23C2×D4×D4311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—1728no—
731Q8C2×#1062190014yescomplemented
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—868no—
737D4—862no—
738D4—862no—
739D4—1728no—
740D4—1728no—
741D4—1728no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—432no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—864no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1728no—
772C2×C4—1722no—
773C2×C4C2×D4×D4312yes—
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×#1062190012yes—
776C2×C4#1306337012yes—
777C2×C4C24×D4311yescharacteristic
778C8—22no—
779C8—22no—
780C8—862no—
781C8—862no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22—862no—
790C22—862no—
791C22—862no—
792C22—3444no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1724no—
797C22#1458353612yes—
798C22C2×#1306335214yes—
799C22C2×#1306335212yes—
800C22#1458371512yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—862no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458353612yes—
813C4C22×#1062190011yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—24no—
816C2—82no—
817C2—3442no—
818C2—1722no—
819C2#1914659014yesdirect product factor
820C2C2×#1458353611yescharacteristic
821C2C22×#1306335211yescharacteristic
822C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
hypercenterC2×#448D43
hypocenterC43C2×#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#14583560C2semidirect
2. C2×#14583549C2semidirect
3. #19146590C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583213C2semidirect
7. C2×#14583192C2semidirect
8. C2×#14583142C2semidirect
9. C2×#14583133C2semidirect
10. C2×#14583116C2semidirect
11. C2×#14583043C2semidirect
12. C2×#14583000C2semidirect
13. C2×#14582967C2semidirect
14. C2×#14582899C2semidirect
15. C22×#13063249C2semidirect
16. C2×C43×#448C2semidirect
23. #14583560C22semidirect
25. #14583549C22semidirect
43. #14583260C22semidirect
44. #14583233C22semidirect
45. #14583213C22semidirect
46. #14583192C22semidirect
47. #14583142C22semidirect
48. #14583133C22semidirect
49. #14583116C22semidirect
50. #14583043C22semidirect
51. #14583000C22semidirect
52. #14582967C22semidirect
57. #14582899C22semidirect
62. C2×#13063249C22semidirect
73. C43×#448C22semidirect
200. C2×Q8×C43#41semidirect
318. Q8×C43C2×#41semidirect
415. C2×#448D43semidirect
422. C2×C43#3308semidirect
466. #448C2×D43semidirect
488. C43C2×#3308semidirect
618. C2×Q8#10621900semidirect
731. Q8C2×#10621900semidirect
819. C2#19146590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835602
C2×#145835492
#191465902
C2×#145832602
C2×#145832332
C2×#145832132
C2×#145831922
C2×#145831422
C2×#145831332
C2×#145831162
C2×#145830432
C2×#145830002
C2×#145829672
C2×#145828992
C22×#130632492
C2×C43×#4482
C2×#330843