Finite Group Databasebeta

← C2×#19147305 #25976251

Subgroups — C2×#19147305 #25976251

Order 11008.

2198 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583605C211yesmaximal, characteristic, complemented
2C2×#14583570C211yesmaximal, characteristic, complemented
3#19147305C2116yesmaximal, direct product factor
4C2×#14583265C211yesmaximal, characteristic, complemented
5C2×#14583262C211yesmaximal, characteristic, complemented
6C2×#14583244C211yesmaximal, characteristic, complemented
7C2×#14583202C211yesmaximal, characteristic, complemented
8C2×#14583188C211yesmaximal, characteristic, complemented
9C2×#14583095C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583093C211yesmaximal, characteristic, complemented
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14583010C211yesmaximal, characteristic, complemented
14C2×#14583009C211yesmaximal, characteristic, complemented
15C2×#14582981C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×D344C2211yescharacteristic
19C22×D344C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21#14583605—24no—
22#14583605C2218yescomplemented
23#14583570—24no—
24#14583570C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063322C2211yescharacteristic
27C2×#13063321C2211yescharacteristic
28C2×#13063321C2211yescharacteristic
29C2×#13063316C2211yescharacteristic
30C2×#13063305—21no—
31C2×#13063303—21no—
32C2×#13063303—21no—
33C2×#13063299—21no—
34C2×#13063298—21no—
35C2×#13063298—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063287C2211yescharacteristic
42C2×C4⋊C4×D43—21no—
43#14583265C2218yescomplemented
44#14583262C2218yescomplemented
45#14583244C2218yescomplemented
46#14583202C2218yescomplemented
47#14583188C2218yescomplemented
48#14583095C2218yescomplemented
49#14583093C2218yescomplemented
50#14583093C2218yescomplemented
51#14583028C2218yescomplemented
52#14583010C2218yescomplemented
53#14583009C2218yescomplemented
54#14582981C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063247C2211yescharacteristic
59C2×#13063247C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×Dic86D411yescharacteristic
81C22×D172—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C2×D344—24no—
96C2×D344—24no—
97C2×D344C2314yes—
98C2×D344C2314yes—
99C2×#10621882—24no—
100C2×#10621882C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103#13063324—22no—
104#13063324C2314yes—
105#13063322—22no—
106#13063322C2314yes—
107#13063321—22no—
108#13063321—22no—
109#13063321C2314yes—
110#13063321C2314yes—
111#13063316—22no—
112#13063316C2314yes—
113#13063305—28no—
114#13063303—28no—
115#13063303—28no—
116#13063299—28no—
117#13063298—28no—
118#13063298—28no—
119C4×Dic86D414yes—
120C4×Dic86C2314yes—
121C4×D172—22no—
122C4×D172C2314yes—
123#13063287—22no—
124#13063287—22no—
125#13063287—22no—
126#13063287—22no—
127#13063287C2314yes—
128#13063287C2314yes—
129#13063287C2314yes—
130#13063287C2314yes—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43D411yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C2×Dic43⋊C4D411yescharacteristic
138C4⋊C4×D43—28no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×C4×Dic43C2311yescharacteristic
145C2×C4×Dic43C2311yescharacteristic
146#13063256C2314yes—
147Dic43⋊C8C2314yes—
148Dic43⋊C8C2314yes—
149#13063247C2314yes—
150#13063247C2314yes—
151#13063246C2314yes—
152#13063245C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157#13063236C2314yes—
158#13063235C2314yes—
159C8×Dic43C2314yes—
160C22×D4×C43C2311yescharacteristic
161C23×C4×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164#125×C43—22no—
165#125×C43C2314yes—
166C4×D4×C43—22no—
167C4×D4×C43C2314yes—
168C2×C4⋊C4×C43—21no—
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#107×C43C2314yes—
176#106×C43C2314yes—
177C4⋊C8×C43C2314yes—
178#102×C43C2314yes—
179#102×C43C2314yes—
180C24×C43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43C2412yes—
188C22×C4×C43—24no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—44no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—44no—
201C2×C22⋊D43—44no—
202C2×C22⋊D43—82no—
203C2×C22⋊D43—82no—
204C22×Dic43—21no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209#10621898—432no—
210C2×D172—21no—
211C2×D172—22no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—24no—
215C2×D172—24no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—44no—
221C2×D172—82no—
222C2×D172#4114yescomplemented
223C2×D172C2412yes—
224C2×D172C2412yes—
225C2×D172C2412yes—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—82no—
235C2×C4×D43—82no—
236C2×Dic86—24no—
237C2×Dic86—24no—
238C2×Dic86—82no—
239C2×Dic86C2×D414yes—
240C2×C8×C43—22no—
241C2×C8×C43—22no—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2412yes—
250C4⋊C4×C43C2412yes—
251C4⋊C4×C43C2412yes—
252C22⋊C4×C43—24no—
253C42×C43C2×D412yes—
254C42×C43C2412yes—
255#10621882—28no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261C4⋊Dic43—21no—
262C4⋊Dic43—24no—
263C4⋊Dic43C2×D414yes—
264C4⋊Dic43C2412yes—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4C2×D414yes—
268Dic43⋊C4C2×D414yes—
269C4×Dic43C2×D412yes—
270C4×Dic43C2×D412yes—
271C4×Dic43C2412yes—
272C4×Dic43C2412yes—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8C2412yes—
276C2×C43⋊C8C2412yes—
277D344—28no—
278D344—28no—
279C23×C43—22no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43C22×D411yescharacteristic
284C22×D43—24no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—42no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—48no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4112yes—
312C2×C4×C432−1+412yes—
313C2×C4×C43C2511yescharacteristic
314C22⋊D43—48no—
315C22⋊D43—48no—
316C22⋊D43—84no—
317C22⋊D43—84no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—42no—
323C2×Dic43AGL(1,ℤ/8)14yes—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328D172—24no—
329D172—22no—
330D172—22no—
331D172—22no—
332D172—22no—
333D172—22no—
334D172—48no—
335D172—42no—
336D172—42no—
337D172—84no—
338D172C2×#4114yescomplemented
339C4×D43—48no—
340C4×D43—48no—
341C4×D43—48no—
342C4×D43—84no—
343C4×D43—84no—
344Dic86—28no—
345Dic86—84no—
346C8×C43—22no—
347C8×C43—22no—
348C43⋊C8—22no—
349C43⋊C8—22no—
350C2×#3366—431nomaximal, Sylow
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—84no—
355C22×C43#54812yes—
356C22×C43C2×AGL(1,ℤ/8)12yes—
357C22×C43#57612yes—
358C22×C43C23×D411yescharacteristic
359C2×D43—24no—
360C2×D43—48no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—84no—
370C2×D43—84no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43#54812yes—
377C4×C43C22×#4111yescharacteristic
378C4×C43C2×2−1+411yescharacteristic
379Dic43—22no—
380Dic43—22no—
381Dic43—22no—
382Dic43—42no—
383Dic43C2×AGL(1,ℤ/8)14yes—
384C2×#554—431no—
385C2×#550—431no—
386#3366—4316no—
387C2×#490—431no—
388C2×#490—431no—
389C2×#486—431no—
390C2×#478—431no—
391C2×#478D4311yescharacteristic, complemented
392C2×#476—431no—
393C2×#459—431no—
394C2×#459—431no—
395C2×#459—431no—
396C2×#446—431no—
397C2×#442—431no—
398C2×#442—431no—
399C2×C4×D8—431no—
400C2×C43—82no—
401C2×C43#336614yescomplemented
402C2×C43C2×#54811yescharacteristic
403C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
404C2×C43C2×#57611yescharacteristic
405D43—44no—
406D43—82no—
407D43—82no—
408C22×#41—861no—
409C22×D8—431no—
410C22×D8—431no—
411C22×D8—431no—
412#554—438no—
413#554—864no—
414#550—438no—
415#550—864no—
416C2×C4⋊Q8—431no—
417C2×#127—431no—
418C2×#127—431no—
419C2×#127—431no—
420C2×#125—431no—
421C2×#125C2×D4311yescharacteristic
422C2×C22⋊Q8—861no—
423C2×C22⋊Q8—861no—
424C2×C22⋊Q8—861no—
425C2×#121—861no—
426C2×#121—861no—
427C2×#121—861no—
428C2×C4×Q8—431no—
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×C4×D4—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4C2×D4311yescharacteristic
435C22×C4⋊C4—861no—
436#490—438no—
437#490—438no—
438#486—438no—
439#478—438no—
440#478C2×D4318yescomplemented
441#476—438no—
442#459—438no—
443#459—438no—
444#459—438no—
445#446—438no—
446#442—438no—
447#442—438no—
448C4×D8—438no—
449C2×#107C2×D4311yescharacteristic
450C2×#106—431no—
451C2×#106C2×D4311yescharacteristic
452C2×C4⋊C8—431no—
453C2×C4⋊C8—431no—
454C2×C4⋊C8C2×D4311yescharacteristic
455C2×#102—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×#102—431no—
460C2×#102—431no—
461C2×#102—431no—
462C2×#102—431no—
463C2×#102C2×D4311yescharacteristic
464C2×#102C2×D4311yescharacteristic
465C2×#97—431no—
466C2×#97—431no—
467C2×C4×C8—431no—
468C43C2×#336611yescharacteristic, complemented, Sylow
469C2×#41—868no—
470C2×#41—1728no—
471C22×Q8—431no—
472C22×Q8—861no—
473C22×D4—431no—
474C22×D4—431no—
475C22×D4—431no—
476C22×D4—861no—
477C22×D4—861no—
478C22×D4—861no—
479C22×D4—861no—
480C22×D4—861no—
481C22×D4—861no—
482C22×D4C22×D4311yescharacteristic
483C23×C4—21no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C2×D8—434no—
490C2×D8—434no—
491C2×D8—434no—
492C2×D8—864no—
493C2×D8—864no—
494C2×D8—864no—
495C22×C8—431no—
496C22×C8—431no—
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4311yescharacteristic
499C4⋊Q8—434no—
500C4⋊Q8—862no—
501#127—434no—
502#127—434no—
503#127—434no—
504#127—862no—
505#127—862no—
506#127—862no—
507#125—22no—
508#125—434no—
509#125—862no—
510#125C22×D4314yes—
511C22⋊Q8—868no—
512C22⋊Q8—868no—
513C22⋊Q8—868no—
514#121—868no—
515#121—868no—
516#121—868no—
517C4×Q8—434no—
518C4×Q8—434no—
519C4×D4—22no—
520C4×D4—434no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—434no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4C22×D4314yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—868no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42C22×D4311yescharacteristic
553#107C22×D4314yes—
554#106—434no—
555#106C22×D4314yes—
556C4⋊C8—434no—
557C4⋊C8—434no—
558C4⋊C8C22×D4314yes—
559#102—434no—
560#102—434no—
561#102—434no—
562#102—434no—
563#102—434no—
564#102—434no—
565#102—434no—
566#102—434no—
567#102C22×D4314yes—
568#102C22×D4314yes—
569#97—434no—
570#97—434no—
571C4×C8—434no—
572C24—21no—
573C24—861no—
574C24—861no—
575C24—861no—
576#41—17232no—
577C2×Q8—434no—
578C2×Q8—864no—
579C2×Q8—864no—
580C2×Q8—3442no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—434no—
585C2×D4—432no—
586C2×D4—432no—
587C2×D4—432no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—864no—
591C2×D4—864no—
592C2×D4—861no—
593C2×D4—864no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—864no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—3442no—
603C2×D4—3442no—
604C2×D4—3442no—
605C2×D4—1724no—
606C2×D4—1724no—
607C2×D4—1724no—
608C2×D4C23×D4312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—864no—
619C22×C4—864no—
620C22×C4—864no—
621C22×C4—864no—
622C22×C4—861no—
623C22×C4—864no—
624C22×C4—3442no—
625C22×C4—3442no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4—1724no—
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4C23×D4311yescharacteristic
632D8—868no—
633D8—868no—
634D8—868no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—432no—
638C2×C8—432no—
639C2×C8—862no—
640C2×C8—862no—
641C2×C8C23×D4312yes—
642C2×C8C23×D4312yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—434no—
649C4⋊C4—434no—
650C4⋊C4—434no—
651C4⋊C4—432no—
652C4⋊C4—864no—
653C4⋊C4—864no—
654C4⋊C4—864no—
655C4⋊C4—861no—
656C4⋊C4C23×D4312yes—
657C4⋊C4C23×D4312yes—
658C4⋊C4C23×D4312yes—
659C22⋊C4—24no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C42—432no—
666C42—432no—
667C42—432no—
668C42—432no—
669C42D4×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—864no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—868no—
689Q8—3444no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—434no—
694D4—864no—
695D4—862no—
696D4—862no—
697D4—862no—
698D4—862no—
699D4—862no—
700D4—3444no—
701D4—3444no—
702D4—3444no—
703D4—1728no—
704D4—1728no—
705D4—1728no—
706D4—1722no—
707D4—1722no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—434no—
718C2×C4—432no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—3444no—
727C2×C4—3444no—
728C2×C4—1728no—
729C2×C4—1728no—
730C2×C4—1728no—
731C2×C4—1722no—
732C2×C4C2×D4×D4312yes—
733C2×C4C2×D4×D4312yes—
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4#41×D4312yes—
736C2×C4#1306337312yes—
737C2×C4C24×D4311yescharacteristic
738C8—22no—
739C8—22no—
740C8—862no—
741C8—862no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—864no—
747C22—3444no—
748C22—3444no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1722no—
756C22—1722no—
757C22—1728no—
758C22#1458355912yes—
759C22AGL(1,ℤ/8)×D4312yes—
760C22#1458370112yes—
761C22C22×D4×D4311yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—434no—
768C4—862no—
769C4—862no—
770C4—862no—
771C4—1722no—
772C4#1458355912yes—
773C4C2×#41×D4311yescharacteristic
774C4C2×#1306337311yescharacteristic
775C2—82no—
776C2—3442no—
777C2—3442no—
778C2—1724no—
779C2#1914730514yesdirect product factor
780C2C2×#1458355911yescharacteristic
781C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
782C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
hypercenterC2×#478D43
hypocenterC43C2×#3366
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583605C2semidirect
2. C2×#14583570C2semidirect
3. #19147305C2direct (N × H)
4. C2×#14583265C2semidirect
5. C2×#14583262C2semidirect
6. C2×#14583244C2semidirect
7. C2×#14583202C2semidirect
8. C2×#14583188C2semidirect
9. C2×#14583095C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583093C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14583010C2semidirect
14. C2×#14583009C2semidirect
15. C2×#14582981C2semidirect
16. C2×C43×#478C2semidirect
22. #14583605C22semidirect
24. #14583570C22semidirect
43. #14583265C22semidirect
44. #14583262C22semidirect
45. #14583244C22semidirect
46. #14583202C22semidirect
47. #14583188C22semidirect
48. #14583095C22semidirect
49. #14583093C22semidirect
50. #14583093C22semidirect
51. #14583028C22semidirect
52. #14583010C22semidirect
53. #14583009C22semidirect
54. #14582981C22semidirect
71. C43×#478C22semidirect
222. C2×D172#41semidirect
338. D172C2×#41semidirect
391. C2×#478D43semidirect
401. C2×C43#3366semidirect
440. #478C2×D43semidirect
468. C43C2×#3366semidirect
779. C2#19147305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836052
C2×#145835702
#191473052
C2×#145832652
C2×#145832622
C2×#145832442
C2×#145832022
C2×#145831882
C2×#145830952
C2×#145830932
C2×#145830282
C2×#145830102
C2×#145830092
C2×#145829812
C2×C43×#4782
C2×#336643