Finite Group Databasebeta

← C2×#19147390 #25976287

Subgroups — C2×#19147390 #25976287

Order 11008.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583632C211yesmaximal, characteristic, complemented
2C2×#14583564C211yesmaximal, characteristic, complemented
3#19147390C2116yesmaximal, direct product factor
4C2×#14583261C211yesmaximal, characteristic, complemented
5C2×#14583257C211yesmaximal, characteristic, complemented
6C2×#14583244C211yesmaximal, characteristic, complemented
7C2×#14583183C211yesmaximal, characteristic, complemented
8C2×#14583188C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583113C211yesmaximal, characteristic, complemented
11C2×#14583093C211yesmaximal, characteristic
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14583010C211yesmaximal, characteristic, complemented
14C2×#14583009C211yesmaximal, characteristic, complemented
15C2×#14582986C211yesmaximal, characteristic, complemented
16C2×C43×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D43—21no—
18C22×#10621873C2211yescharacteristic
19C22×D344C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21#14583632—24no—
22#14583632C2218yescomplemented
23#14583564—24no—
24#14583564C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063324C2211yescharacteristic
27C2×#13063321C2211yescharacteristic
28C2×#13063313C2211yescharacteristic
29C2×#13063312C2211yescharacteristic
30C2×#13063311—21no—
31C2×#13063308—21no—
32C2×#13063307—21no—
33C2×#13063303—21no—
34C2×#13063303—21no—
35C2×#13063301—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×#13063290C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063287C2211yescharacteristic
42C2×C4×C22⋊D43—21no—
43#14583261C2218yescomplemented
44#14583257C2218yescomplemented
45#14583244C2218yescomplemented
46#14583188C2218yescomplemented
47#14583183C2218yescomplemented
48#14583115C2218yescomplemented
49#14583113C2218yescomplemented
50#14583093C2218yes—
51#14583028C2218yescomplemented
52#14583010C2218yescomplemented
53#14583009C2218yescomplemented
54#14582986C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#476C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86D411yescharacteristic
80C22×Dic86C2311yescharacteristic
81C2×Q8×D43—28no—
82C2×Q8×D43—48no—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C2×#10621873—24no—
92C2×#10621873C2314yes—
93C2×D344—24no—
94C2×D344C2314yes—
95C2×#10621882—24no—
96C2×#10621882C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99#13063324—22no—
100#13063324—22no—
101#13063324C2314yes—
102#13063324C2314yes—
103#13063321—22no—
104#13063321C2314yes—
105#13063313—22no—
106#13063313C2314yes—
107#13063312—22no—
108#13063312C2314yes—
109#13063311—28no—
110#13063308—28no—
111#13063307—28no—
112#13063303—28no—
113#13063303—28no—
114#13063301—28no—
115C4×Dic86D414yes—
116C4×Dic86C2314yes—
117#13063290—22no—
118#13063290C2314yes—
119C4×D172—22no—
120C4×D172C2314yes—
121#13063287—22no—
122#13063287—22no—
123#13063287—22no—
124#13063287C2314yes—
125#13063287C2314yes—
126#13063287C2314yes—
127C4×C22⋊D43—28no—
128C2×C4⋊Dic43D411yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4D411yescharacteristic
134C2×Dic43⋊C4D411yescharacteristic
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—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×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145C2×C4×Dic43C2311yescharacteristic
146#13063256C2314yes—
147Dic43⋊C8C2314yes—
148Dic43⋊C8C2314yes—
149#13063250C2314yes—
150#13063248C2314yes—
151#13063248C2314yes—
152#13063247C2314yes—
153#13063246C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157#13063236C2314yes—
158#13063235C2314yes—
159C8×Dic43C2314yes—
160C22×Q8×C43—21no—
161C22×D4×C43C2311yescharacteristic
162C23×C4×C43—21no—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C4⋊Q8×C43—22no—
166C4⋊Q8×C43C2314yes—
167C4×D4×C43—22no—
168C4×D4×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C22⋊C4×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#106×C43C2314yes—
176#106×C43C2314yes—
177C4⋊C8×C43C2314yes—
178#102×C43C2314yes—
179#102×C43C2314yes—
180C24×C43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C2×Q8×C43—24no—
184C2×Q8×C43—44no—
185C2×D4×C43—21no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43C2412yes—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—82no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—44no—
200C2×C22⋊D43—82no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207Q8×D43—432no—
208C2×D172—21no—
209C2×D172—22no—
210C2×D172—21no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172#4114yes—
214C2×D172C2412yes—
215C2×D172C2412yes—
216C2×C4×D43—24no—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43—44no—
223C2×C4×D43—82no—
224C2×Dic86—24no—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—21no—
228C2×Dic86—24no—
229C2×Dic86—24no—
230C2×Dic86—44no—
231C2×Dic86—44no—
232C2×Dic86C2×D414yes—
233C2×Dic86C2412yes—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C4⋊C4×C43C2412yes—
244C4⋊C4×C43C2412yes—
245C22⋊C4×C43—24no—
246C42×C43C2×D412yes—
247C42×C43C2412yes—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250#10621882—28no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43C2×D414yes—
259C4⋊Dic43C2412yes—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4C2×D414yes—
264Dic43⋊C4C2×D414yes—
265C4×Dic43—24no—
266C4×Dic43C2×D412yes—
267C4×Dic43C2×D412yes—
268C4×Dic43C2412yes—
269C4×Dic43C2412yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274D344—28no—
275#10621873—28no—
276C23×C43—22no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43C22×D411yescharacteristic
281C22×D43—24no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289Q8×C43—48no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—42no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—84no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4112yes—
306C2×C4×C432−1+412yes—
307C2×C4×C43C2511yescharacteristic
308C22⋊D43—48no—
309C22⋊D43—84no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43AGL(1,ℤ/8)14yes—
318C2×Dic43C22×D412yes—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321C2×Dic43C22×D412yes—
322D172—24no—
323D172—22no—
324D172—22no—
325D172—22no—
326D172—42no—
327D172C2×#4114yes—
328C4×D43—48no—
329C4×D43—48no—
330C4×D43—48no—
331C4×D43—84no—
332Dic86—28no—
333Dic86—22no—
334Dic86—22no—
335Dic86—48no—
336Dic86—42no—
337Dic86—48no—
338C8×C43—22no—
339C8×C43—22no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C2×#3373—431nomaximal, Sylow
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—84no—
347C22×C43#54812yes—
348C22×C43C2×AGL(1,ℤ/8)12yes—
349C22×C43#57712yes—
350C22×C43C23×D411yescharacteristic
351C2×D43—24no—
352C2×D43—48no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—84no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43#54812yes—
365C4×C43C22×#4111yescharacteristic
366C4×C43C2×2−1+411yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—22no—
370Dic43—42no—
371Dic43—42no—
372Dic43C2×AGL(1,ℤ/8)14yes—
373C2×#559—431no—
374C2×D4×Q8—431no—
375#3373—4316no—
376C2×#489—431no—
377C2×#489—431no—
378C2×#486—431no—
379C2×#475—431no—
380C2×#476—431no—
381C2×#476D4311yescharacteristic, complemented
382C2×#463—431no—
383C2×#463—431no—
384C2×#459—431no—
385C2×#446—431no—
386C2×#442—431no—
387C2×#442—431no—
388C2×C4×SD16—431no—
389C2×C43—82no—
390C2×C43#337314yescomplemented
391C2×C43C2×#54811yescharacteristic
392C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C43C2×#57711yescharacteristic
394D43—44no—
395D43—82no—
396C23×Q8—861no—
397C22×SD16—431no—
398C22×D8—431no—
399C22×D8—431no—
400#559—438no—
401#559—864no—
402D4×Q8—438no—
403D4×Q8—864no—
404C2×C4⋊Q8—431no—
405C2×C4⋊Q8—431no—
406C2×C4⋊Q8C2×D4311yescharacteristic
407C2×#127—431no—
408C2×#124—431no—
409C2×#124—431no—
410C2×#124—861no—
411C2×#123—861no—
412C2×#123—861no—
413C2×C22⋊Q8—861no—
414C2×C22⋊Q8—861no—
415C2×C22⋊Q8—861no—
416C2×C4×Q8—431no—
417C2×C4×Q8—431no—
418C2×C4×D4—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×C4×D4—431no—
422C2×C4×D4—861no—
423C2×C4×D4C2×D4311yescharacteristic
424#489—438no—
425#489—438no—
426#486—438no—
427#476—438no—
428#476C2×D4318yescomplemented
429#475—438no—
430#463—438no—
431#463—438no—
432#459—438no—
433#446—438no—
434#442—438no—
435#442—438no—
436C4×SD16—438no—
437C2×#106—431no—
438C2×#106C2×D4311yescharacteristic
439C2×#106C2×D4311yescharacteristic
440C2×C4⋊C8—431no—
441C2×C4⋊C8—431no—
442C2×C4⋊C8C2×D4311yescharacteristic
443C2×#103—431no—
444C2×#103—431no—
445C2×#103—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102C2×D4311yescharacteristic
452C2×#102C2×D4311yescharacteristic
453C2×#97—431no—
454C2×#97—431no—
455C2×C4×C8—431no—
456C43C2×#337311yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×Q8—431no—
459C22×Q8—431no—
460C22×Q8—861no—
461C22×Q8—861no—
462C22×Q8—868no—
463C22×Q8—1728no—
464C22×D4—431no—
465C22×D4—431no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4C22×D4311yescharacteristic
469C23×C4—21no—
470C23×C4—861no—
471C23×C4—861no—
472C23×C4—861no—
473C23×C4—861no—
474C2×SD16—434no—
475C2×SD16—864no—
476C2×D8—434no—
477C2×D8—434no—
478C2×D8—864no—
479C2×D8—864no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C4⋊Q8—22no—
485C4⋊Q8—434no—
486C4⋊Q8—434no—
487C4⋊Q8—862no—
488C4⋊Q8—862no—
489C4⋊Q8C22×D4314yes—
490#127—434no—
491#127—862no—
492#124—434no—
493#124—434no—
494#124—862no—
495#124—868no—
496#124—862no—
497#123—868no—
498#123—868no—
499C22⋊Q8—868no—
500C22⋊Q8—868no—
501C22⋊Q8—868no—
502C4×Q8—434no—
503C4×Q8—434no—
504C4×Q8—434no—
505C4×Q8—862no—
506C4×D4—22no—
507C4×D4—434no—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—434no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—868no—
515C4×D4—862no—
516C4×D4C22×D4314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—861no—
540C2×C42C22×D4311yescharacteristic
541#106—434no—
542#106C22×D4314yes—
543#106C22×D4314yes—
544C4⋊C8—434no—
545C4⋊C8—434no—
546C4⋊C8C22×D4314yes—
547#103—434no—
548#103—434no—
549#103—434no—
550#102—434no—
551#102—434no—
552#102—434no—
553#102—434no—
554#102—434no—
555#102C22×D4314yes—
556#102C22×D4314yes—
557#97—434no—
558#97—434no—
559C4×C8—434no—
560C24—21no—
561C24—861no—
562C24—861no—
563C2×Q8—24no—
564C2×Q8—44no—
565C2×Q8—434no—
566C2×Q8—432no—
567C2×Q8—864no—
568C2×Q8—864no—
569C2×Q8—864no—
570C2×Q8—861no—
571C2×Q8—862no—
572C2×Q8—862no—
573C2×Q8—1724no—
574C2×Q8—1724no—
575C2×Q8—17232no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—434no—
580C2×D4—432no—
581C2×D4—432no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—3442no—
590C2×D4—1724no—
591C2×D4C23×D4312yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—82no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—864no—
602C22×C4—864no—
603C22×C4—864no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—864no—
607C22×C4—3442no—
608C22×C4—1724no—
609C22×C4—1724no—
610C22×C4—1724no—
611C22×C4D4×D4311yescharacteristic
612C22×C4D4×D4311yescharacteristic
613C22×C4C23×D4311yescharacteristic
614SD16—868no—
615D8—868no—
616D8—868no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—432no—
620C2×C8—432no—
621C2×C8—862no—
622C2×C8—862no—
623C2×C8C23×D4312yes—
624C2×C8C23×D4312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—434no—
630C4⋊C4—434no—
631C4⋊C4—434no—
632C4⋊C4—432no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—861no—
637C4⋊C4C23×D4312yes—
638C4⋊C4C23×D4312yes—
639C4⋊C4C23×D4312yes—
640C22⋊C4—24no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C42—432no—
650C42—432no—
651C42—432no—
652C42—432no—
653C42—864no—
654C42D4×D4312yes—
655C42C23×D4312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—864no—
661C23—862no—
662C23—862no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23—1722no—
667C23—1722no—
668C23C2×D4×D4311yescharacteristic
669Q8—48no—
670Q8—868no—
671Q8—862no—
672Q8—862no—
673Q8—1728no—
674Q8—1728no—
675Q8—1722no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—434no—
680D4—864no—
681D4—862no—
682D4—862no—
683D4—862no—
684D4—3444no—
685D4—1728no—
686D4—1722no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—434no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—432no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—3444no—
707C2×C4—1728no—
708C2×C4—1728no—
709C2×C4—1728no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4C2×D4×D4312yes—
713C2×C4C2×D4×D4312yes—
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4#41×D4312yes—
716C2×C4#1306337312yes—
717C2×C4C24×D4311yescharacteristic
718C8—22no—
719C8—22no—
720C8—862no—
721C8—862no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—864no—
727C22—3444no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1728no—
734C22#1458355912yes—
735C22AGL(1,ℤ/8)×D4312yes—
736C22#1458370512yes—
737C22C22×D4×D4311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—434no—
744C4—862no—
745C4—862no—
746C4—862no—
747C4—1722no—
748C4—1722no—
749C4#1458355912yes—
750C4C2×#41×D4311yescharacteristic
751C4C2×#1306337311yescharacteristic
752C2—82no—
753C2—3442no—
754C2—1724no—
755C2#1914739014yesdirect product factor
756C2C2×#1458355911yescharacteristic
757C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
758C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#476C2
socleC23×C43C22×D4
prime radicalC2×#14583093C2
hypercenterC2×#476D43
hypocenterC43C2×#3373
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#14583632C2semidirect
2. C2×#14583564C2semidirect
3. #19147390C2direct (N × H)
4. C2×#14583261C2semidirect
5. C2×#14583257C2semidirect
6. C2×#14583244C2semidirect
7. C2×#14583183C2semidirect
8. C2×#14583188C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583113C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14583010C2semidirect
14. C2×#14583009C2semidirect
15. C2×#14582986C2semidirect
16. C2×C43×#476C2semidirect
22. #14583632C22semidirect
24. #14583564C22semidirect
43. #14583261C22semidirect
44. #14583257C22semidirect
45. #14583244C22semidirect
46. #14583188C22semidirect
47. #14583183C22semidirect
48. #14583115C22semidirect
49. #14583113C22semidirect
51. #14583028C22semidirect
52. #14583010C22semidirect
53. #14583009C22semidirect
54. #14582986C22semidirect
71. C43×#476C22semidirect
381. C2×#476D43semidirect
390. C2×C43#3373semidirect
428. #476C2×D43semidirect
456. C43C2×#3373semidirect
755. C2#19147390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836322
C2×#145835642
#191473902
C2×#145832612
C2×#145832572
C2×#145832442
C2×#145831832
C2×#145831882
C2×#145831152
C2×#145831132
C2×#145830932
C2×#145830282
C2×#145830102
C2×#145830092
C2×#145829862
C2×C43×#4762
C2×#337343