Finite Group Databasebeta

← C2×#19146591 #25973176

Subgroups — C2×#19146591 #25973176

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×#14583561C211yesmaximal, characteristic, complemented
2C2×#14583554C211yesmaximal, characteristic, complemented
3#19146591C2116yesmaximal, direct product factor
4C2×#14583259C211yesmaximal, characteristic, complemented
5C2×#14583236C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583194C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583134C211yesmaximal, characteristic, complemented
10C2×#14583114C211yesmaximal, characteristic, complemented
11C2×#14583043C211yesmaximal, characteristic, complemented
12C2×#14583036C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898—21no—
19C22×Q8×D43C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583561—24no—
25#14583561C2218yescomplemented
26#14583554—24no—
27#14583554C2218yescomplemented
28C2×#13063325C2211yescharacteristic
29C2×#13063313—21no—
30C2×#13063313C2211yescharacteristic
31C2×#13063307—21no—
32C2×#13063307—21no—
33C2×#13063305—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063304—21no—
36C2×#13063300—21no—
37C2×#13063300C2211yescharacteristic
38C2×#13063296C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×C4×D172—21no—
41C2×C4×D172C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583259C2218yescomplemented
45#14583236C2218yescomplemented
46#14583214C2218yescomplemented
47#14583194C2218yescomplemented
48#14583144C2218yescomplemented
49#14583134C2218yescomplemented
50#14583114C2218yescomplemented
51#14583043C2218yescomplemented
52#14583036C2218yescomplemented
53#14582972C2218yescomplemented
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57#14582899C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63#103×D43C2218yescomplemented
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#440C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C2×#10621898—28no—
82C2×#10621898—48no—
83C22×Dic86—21no—
84C22×Dic86—21no—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—22no—
87C2×Q8×D43—24no—
88C2×Q8×D43—42no—
89C2×Q8×D43C2314yes—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172D411yescharacteristic
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43C2311yescharacteristic
101C22×C4×D43C2311yescharacteristic
102C2×#10621883—42no—
103C2×#10621883C2314yes—
104C2×#10621882—42no—
105C2×#10621882C2314yes—
106C2×#10621872—42no—
107C2×#10621872C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C2×C8×D43—42no—
111C2×C8×D43C2314yes—
112#13063325—22no—
113#13063325C2314yes—
114#13063313—22no—
115#13063313—28no—
116#13063313C2314yes—
117#13063307—28no—
118#13063307—28no—
119#13063305—22no—
120#13063305—28no—
121#13063305C2314yes—
122#13063304—28no—
123#13063300—28no—
124#13063300—22no—
125#13063300C2314yes—
126#13063296—22no—
127#13063296—22no—
128#13063296C2314yes—
129#13063296C2314yes—
130C4×D172—28no—
131C4×D172D414yes—
132C4×D172C2314yes—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43D411yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C4⋊C4×D43C2314yes—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4D411yescharacteristic
151C2×(C2×D43)⋊C4D411yescharacteristic
152#13063258C2314yes—
153#13063258C2314yes—
154C4⋊(C43⋊C8)C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063249C2314yes—
159#13063248C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C2×SD16×C43—24no—
169C2×SD16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C4×Q8×C43—22no—
173C4×Q8×C43C2314yes—
174C4×D4×C43—22no—
175C4×D4×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181C2×C42×C43C2311yescharacteristic
182#107×C43C2314yes—
183#103×C43C2314yes—
184#102×C43C2314yes—
185#97×C43C2314yes—
186C24×C43—21no—
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—22no—
192C2×Q8×C43#4114yescomplemented
193C2×Q8×C43C2412yes—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43C2412yes—
198C22×C4×C43—24no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—44no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—44no—
209C2×C22⋊D43—44no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215#10621902—28no—
216#10621902—44no—
217#10621902—48no—
218Q8×D43—28no—
219Q8×D43—44no—
220Q8×D43—48no—
221#10621898—432no—
222C2×D172—21no—
223C2×D172—24no—
224C2×D172—24no—
225C2×D172—24no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—44no—
229C2×D172—44no—
230C2×D172C2×D414yes—
231C2×D172C2412yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
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—44no—
241C2×C4×D43—44no—
242C2×C4×D43—44no—
243C2×C4×D43—44no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2×D412yes—
246C2×C4×D43C2412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—22no—
249C2×Dic86—22no—
250C2×Dic86—24no—
251C2×Dic86—21no—
252C2×Dic86—24no—
253C2×Dic86—44no—
254C2×Dic86—44no—
255C2×Dic86C2412yes—
256SD16×C43—28no—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C22⋊C4×C43—24no—
267C42×C43—24no—
268C42×C43C2×D412yes—
269C42×C43C2412yes—
270C22⋊Dic43—24no—
271C22⋊Dic43—24no—
272#10621883—44no—
273#10621882—44no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4C2×D414yes—
279(C2×D43)⋊C4C2×D414yes—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—24no—
283C4⋊Dic43—24no—
284C4⋊Dic43C2×D414yes—
285C4⋊Dic43C2412yes—
286C4⋊Dic43C2412yes—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293#10621872—44no—
294C8×D43—44no—
295C23×C43—22no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43AGL(1,ℤ/8)14yes—
310C22×D43C22×D412yes—
311C22×D43C22×D412yes—
312Q8×C43—24no—
313Q8×C43—22no—
314Q8×C43C2×#4114yescomplemented
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—42no—
318C2×C4×C43—24no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—48no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4112yes—
331C2×C4×C43H(5,𝔽2)12yes—
332C2×C4×C43C2511yescharacteristic
333C22⋊D43—48no—
334C22⋊D43—48no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—28no—
346D172—22no—
347D172—22no—
348D172—48no—
349D172—48no—
350D172—42no—
351C4×D43—24no—
352C4×D43—24no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—48no—
358C4×D43—48no—
359C4×D43—48no—
360C4×D43—48no—
361Dic86—22no—
362Dic86—22no—
363Dic86—48no—
364Dic86—48no—
365Dic86—42no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3308—431nomaximal, Sylow
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—84no—
375C22×C43#54612yes—
376C22×C43C2×AGL(1,ℤ/8)12yes—
377C22×C43#57812yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—22no—
380C2×D43—28no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—44no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—84no—
390C2×D43C2×AGL(1,ℤ/8)14yes—
391C4×C43—24no—
392C4×C43—22no—
393C4×C43—22no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43#54612yes—
397C4×C43C22×#4111yescharacteristic
398C4×C43C2×H(5,𝔽2)11yescharacteristic
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×#448—431no—
416C2×#440D4311yescharacteristic, complemented
417C2×#435—431no—
418C2×#417—431no—
419C22×#103—431no—
420C2×C43—82no—
421C2×C43#330814yescomplemented
422C2×C43C2×#54611yescharacteristic
423C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C43C2×#57811yescharacteristic
425D43—24no—
426D43—42no—
427D43—82no—
428C22×#41—431no—
429C22×#41—861no—
430C23×Q8—431no—
431C22×SD16—431no—
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—431no—
451C2×#121—861no—
452C2×C4×Q8C2×D4311yescharacteristic
453C2×C4×D4—431no—
454C2×C4×D4—861no—
455C2×C4×D4C2×D4311yescharacteristic
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#448—438no—
467#440C2×D4318yescomplemented
468#435—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107C2×D4311yescharacteristic
472C2×C4⋊C8—431no—
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—438no—
480C2×#103C2×D4311yescharacteristic
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102C2×D4311yescharacteristic
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×#97C2×D4311yescharacteristic
488C43C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—434no—
490C2×#41—868no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—1728no—
494C2×#41—1722no—
495C22×Q8—434no—
496C22×Q8—431no—
497C22×Q8—861no—
498C22×Q8—862no—
499C22×Q8—861no—
500C22×Q8—864no—
501C22×Q8—1722no—
502C22×Q8C22×D4311yescharacteristic
503C22×D4—431no—
504C22×D4—431no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4C22×D4311yescharacteristic
510C23×C4—21no—
511C23×C4—431no—
512C23×C4—431no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C23×C4—861no—
517C2×SD16—24no—
518C2×SD16—434no—
519C2×SD16—1722no—
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—868no—
535#124—862no—
536#123—868no—
537#123—868no—
538C22⋊Q8—434no—
539C22⋊Q8—868no—
540C22⋊Q8—862no—
541C22⋊Q8—868no—
542#121—434no—
543#121—434no—
544#121—434no—
545#121—862no—
546#121—868no—
547#121—862no—
548#121—862no—
549C4×Q8—22no—
550C4×Q8C22×D4314yes—
551C4×D4—22no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—868no—
555C4×D4C22×D4314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—434no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—862no—
563C2×C4⋊C4—862no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
580C2×C42C22×D4311yescharacteristic
581#107—434no—
582#107—434no—
583#107C22×D4314yes—
584C4⋊C8—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#103—434no—
589#103—434no—
590#103C22×D4314yes—
591#102—434no—
592#102—434no—
593#102—434no—
594#102C22×D4314yes—
595C22⋊C8—434no—
596C22⋊C8—434no—
597#97C22×D4314yes—
598C24—21no—
599C24—431no—
600C24—431no—
601C24—861no—
602#41—868no—
603#41—17232no—
604#41—1724no—
605#41—1728no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—432no—
609C2×Q8—864no—
610C2×Q8—861no—
611C2×Q8—864no—
612C2×Q8—868no—
613C2×Q8—862no—
614C2×Q8—862no—
615C2×Q8—1724no—
616C2×Q8—1724no—
617C2×Q8—1724no—
618C2×Q8—1728no—
619C2×Q8#1062189814yescomplemented
620C2×Q8C23×D4312yes—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—434no—
625C2×D4—432no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—861no—
632C2×D4—862no—
633C2×D4—862no—
634C2×D4—1724no—
635C2×D4—1724no—
636C2×D4—1724no—
637C2×D4—1724no—
638C2×D4C23×D4312yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—864no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—864no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—1724no—
662C22×C4—1724no—
663C22×C4—1724no—
664C22×C4—1724no—
665C22×C4D4×D4311yescharacteristic
666C22×C4D4×D4311yescharacteristic
667C22×C4C23×D4311yescharacteristic
668SD16—28no—
669SD16—1724no—
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—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—434no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—864no—
693C4⋊C4C23×D4312yes—
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—24no—
705C42D4×D4312yes—
706C42C23×D4312yes—
707C23—22no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—434no—
712C23—432no—
713C23—432no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—862no—
720C23—1722no—
721C23—1722no—
722C23—1722no—
723C23C2×D4×D4311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—862no—
727Q8—862no—
728Q8—1728no—
729Q8—1728no—
730Q8—1722no—
731Q8C2×#1062189814yescomplemented
732D4—22no—
733D4—22no—
734D4—42no—
735D4—868no—
736D4—862no—
737D4—862no—
738D4—1728no—
739D4—1728no—
740D4—1728no—
741D4—1728no—
742D4—1722no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—864no—
761C2×C4—864no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—1728no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4C2×D4×D4312yes—
773C2×C4C2×D4×D4312yes—
774C2×C4C2×D4×D4311yescharacteristic
775C2×C4C2×#1062189812yes—
776C2×C4#1306337112yes—
777C2×C4C24×D4311yescharacteristic
778C8—22no—
779C8—22no—
780C8—862no—
781C8—862no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—434no—
787C22—862no—
788C22—862no—
789C22—868no—
790C22—862no—
791C22—862no—
792C22—862no—
793C22—3444no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1724no—
798C22#1458354512yes—
799C22AGL(1,ℤ/8)×D4312yes—
800C22#1458371512yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—24no—
804C4—22no—
805C4—42no—
806C4—42no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458354512yes—
813C4C22×#1062189811yescharacteristic
814C4C2×#1306337111yescharacteristic
815C2—82no—
816C2—864no—
817C2—3442no—
818C2—1722no—
819C2#1914659114yesdirect product factor
820C2C2×#1458354511yescharacteristic
821C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
822C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
hypercenterC2×#440D43
hypocenterC43C2×#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#14583561C2semidirect
2. C2×#14583554C2semidirect
3. #19146591C2direct (N × H)
4. C2×#14583259C2semidirect
5. C2×#14583236C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583194C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583134C2semidirect
10. C2×#14583114C2semidirect
11. C2×#14583043C2semidirect
12. C2×#14583036C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582899C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#440C2semidirect
25. #14583561C22semidirect
27. #14583554C22semidirect
44. #14583259C22semidirect
45. #14583236C22semidirect
46. #14583214C22semidirect
47. #14583194C22semidirect
48. #14583144C22semidirect
49. #14583134C22semidirect
50. #14583114C22semidirect
51. #14583043C22semidirect
52. #14583036C22semidirect
53. #14582972C22semidirect
57. #14582899C22semidirect
63. #103×D43C22semidirect
72. C43×#440C22semidirect
192. C2×Q8×C43#41semidirect
314. Q8×C43C2×#41semidirect
416. C2×#440D43semidirect
421. C2×C43#3308semidirect
467. #440C2×D43semidirect
488. C43C2×#3308semidirect
619. C2×Q8#10621898semidirect
731. Q8C2×#10621898semidirect
819. C2#19146591direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835612
C2×#145835542
#191465912
C2×#145832592
C2×#145832362
C2×#145832142
C2×#145831942
C2×#145831442
C2×#145831342
C2×#145831142
C2×#145830432
C2×#145830362
C2×#145829722
C2×#145828992
C2×#103×D432
C2×C43×#4402
C2×#330843