Finite Group Databasebeta

← C2×#19147183 #25975306

Subgroups — C2×#19147183 #25975306

Order 11008.

2146 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic, complemented
2C2×#14583550C211yesmaximal, characteristic, complemented
3#19147183C2116yesmaximal, direct product factor
4C2×#14583296C211yesmaximal, characteristic, complemented
5C2×#14583216C211yesmaximal, characteristic, complemented
6C2×#14583225C211yesmaximal, characteristic, complemented
7C2×#14583224C211yesmaximal, characteristic, complemented
8C2×#14583188C211yesmaximal, characteristic, complemented
9C2×#14583177C211yesmaximal, characteristic, complemented
10C2×#14583151C211yesmaximal, characteristic, complemented
11C2×#14583150C211yesmaximal, characteristic, complemented
12C2×#14582979C211yesmaximal, characteristic, complemented
13C2×#14582974C211yesmaximal, characteristic, complemented
14C2×#14582939C211yesmaximal, characteristic, complemented
15C2×#14582938C211yesmaximal, characteristic, complemented
16C2×C43×#481C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621882C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583613—24no—
22#14583613C2218yescomplemented
23#14583550—24no—
24#14583550C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063324C2211yescharacteristic
27C2×#13063312—21no—
28C2×#13063311—21no—
29C2×#13063310—21no—
30C2×#13063308—21no—
31C2×#13063303—21no—
32C2×#13063300C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063297—21no—
35C2×#13063296C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×#13063284C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×#13063281—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583296C2218yescomplemented
44#14583225C2218yescomplemented
45#14583224C2218yescomplemented
46#14583216C2218yescomplemented
47#14583188C2218yescomplemented
48#14583177C2218yescomplemented
49#14583151C2218yescomplemented
50#14583150C2218yescomplemented
51#14582979C2218yescomplemented
52#14582974C2218yescomplemented
53#14582939C2218yescomplemented
54#14582938C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×#13063256C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#481C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C22⋊D43D411yescharacteristic
86C23×Dic43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621882—24no—
91C2×#10621882C2314yes—
92C2×#10621877—24no—
93C2×#10621877C2314yes—
94C2×#10621872—24no—
95C2×#10621872C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063324—22no—
99#13063324—22no—
100#13063324C2314yes—
101#13063324C2314yes—
102#13063312—28no—
103#13063311—28no—
104#13063310—28no—
105#13063308—28no—
106#13063303—28no—
107#13063300—22no—
108#13063300C2314yes—
109#13063299—22no—
110#13063299C2314yes—
111#13063297—28no—
112#13063296—22no—
113#13063296C2314yes—
114D4×Dic43—22no—
115D4×Dic43C2314yes—
116#13063287—22no—
117#13063287C2314yes—
118C4×C22⋊D43D414yes—
119C4×C22⋊D43C2314yes—
120#13063284—22no—
121#13063284C2314yes—
122#13063283—22no—
123#13063283C2314yes—
124#13063281—28no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4D411yescharacteristic
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43D411yescharacteristic
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43C2311yescharacteristic
146#13063259C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152#13063256C2314yes—
153Dic43⋊C8C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158(C2×D43)⋊C8C2314yes—
159C8×Dic43C2314yes—
160C22×D4×C43—21no—
161C22×D4×C43C2311yescharacteristic
162C23×C4×C43—21no—
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166#121×C43—22no—
167#121×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—22no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2314yes—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175#106×C43C2314yes—
176#106×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179C22⋊C8×C43C2314yes—
180C24×C43—21no—
181C24×C43C2×D411yescharacteristic
182C23×D43—21no—
183C23×D43C2×D411yescharacteristic
184C2×D4×C43—21no—
185C2×D4×C43—24no—
186C2×D4×C43—22no—
187C2×D4×C43—22no—
188C2×D4×C43—82no—
189C2×D4×C43C2412yes—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—24no—
196C22×C4×C43—44no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—44no—
205C2×C22⋊D43—82no—
206C2×C22⋊D43C2×D414yes—
207C22×Dic43—24no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—44no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215#10621898—432no—
216C2×D172—21no—
217C2×D172—24no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—44no—
221C2×D172C2412yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×C4×D43C2×D412yes—
229C2×C4×D43C2412yes—
230C2×Dic86—24no—
231C2×Dic86—24no—
232C2×Dic86—44no—
233C2×Dic86—82no—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43C2412yes—
237C2×C8×C43C2412yes—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C4⋊C4×C43C2412yes—
244C4⋊C4×C43C2412yes—
245C22⋊C4×C43—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43C2×D414yes—
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)⋊C4C2×D414yes—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4C2×D414yes—
266C4×Dic43—24no—
267C4×Dic43—24no—
268C4×Dic43C2×D412yes—
269C4×Dic43C2412yes—
270#10621877—28no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8#4114yescomplemented
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275#10621872—28no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43C22×D412yes—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—42no—
296D4×C43—84no—
297C2×C4×C43—22no—
298C2×C4×C43—24no—
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×D411yescharacteristic
310C2×C4×C43C2×#4112yes—
311C2×C4×C432−1+412yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—28no—
314C22⋊D43—48no—
315C22⋊D43—84no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—48no—
325C2×Dic43AGL(1,ℤ/8)14yes—
326C2×Dic43C22×D412yes—
327C2×Dic43C22×D412yes—
328C2×Dic43C22×D412yes—
329D172—22no—
330D172—22no—
331D172—48no—
332D172—42no—
333C4×D43—24no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—48no—
337C4×D43—48no—
338Dic86—48no—
339Dic86—84no—
340C8×C43—22no—
341C8×C43—22no—
342C43⋊C8—22no—
343C43⋊C8C2×#4114yescomplemented
344C2×#3354—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—44no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—84no—
353C22×C43#54712yes—
354C22×C43C2×AGL(1,ℤ/8)12yes—
355C22×C43#57712yes—
356C22×C43C23×D411yescharacteristic
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—44no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—84no—
365C4×C43—22no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43#54712yes—
370C4×C43C22×#4111yescharacteristic
371C4×C43C2×2−1+411yescharacteristic
372Dic43—22no—
373Dic43—22no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43C2×AGL(1,ℤ/8)14yes—
378C2×#555—431no—
379C2×#547—431no—
380#3354—4316no—
381C2×#498—431no—
382C2×#481—431no—
383C2×#481D4311yescharacteristic, complemented
384C2×#482—431no—
385C2×#482—431no—
386C2×#476—431no—
387C2×#474—431no—
388C2×#469—431no—
389C2×#469—431no—
390C2×C4×D8—431no—
391C2×#436—431no—
392C2×#428—431no—
393C2×#428—431no—
394C2×C43—42no—
395C2×C43—82no—
396C2×C43#335414yescomplemented
397C2×C43C2×#54711yescharacteristic
398C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C43C2×#57711yescharacteristic
400D43—42no—
401D43—82no—
402C22×#41—861no—
403C22×D8—431no—
404C22×M16—431no—
405C22×M16—431no—
406#555—438no—
407#555—864no—
408#547—438no—
409#547—864no—
410C2×C4⋊Q8—431no—
411C2×C4⋊Q8—431no—
412C2×#124—861no—
413C2×#124—861no—
414C2×#123—861no—
415C2×#123—861no—
416C2×C22⋊Q8—861no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—431no—
420C2×#121—861no—
421C2×#121C2×D4311yescharacteristic
422C2×C4×D4—431no—
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×#117—431no—
426C2×#117—431no—
427C2×#117—861no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4C2×D4311yescharacteristic
430#498—438no—
431#482—438no—
432#482—438no—
433#481—438no—
434#481C2×D4318yescomplemented
435#476—438no—
436#474—438no—
437#469—438no—
438#469—438no—
439C4×D8—438no—
440#436—438no—
441#428—438no—
442#428—438no—
443C2×#107—431no—
444C2×#107—431no—
445C2×#107—431no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×#106—431no—
450C2×#106C2×D4311yescharacteristic
451C2×#106C2×D4311yescharacteristic
452C2×C4⋊C8—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×#102C2×D4311yescharacteristic
458C2×#102C2×D4311yescharacteristic
459C2×C22⋊C8—431no—
460C2×C22⋊C8C2×D4311yescharacteristic
461C2×C4×C8—431no—
462C43C2×#335411yescharacteristic, complemented, Sylow
463C2×#41—868no—
464C2×#41—1728no—
465C22×Q8—861no—
466C22×Q8—861no—
467C22×D4—21no—
468C22×D4—431no—
469C22×D4—431no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4C22×D4311yescharacteristic
474C23×C4—21no—
475C23×C4—431no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4—861no—
479C23×C4C22×D4311yescharacteristic
480C2×D8—434no—
481C2×D8—864no—
482C2×M16—434no—
483C2×M16—434no—
484C2×M16—864no—
485C2×M16—864no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—434no—
491C4⋊Q8—434no—
492C4⋊Q8—862no—
493C4⋊Q8—862no—
494#124—868no—
495#124—868no—
496#123—868no—
497#123—868no—
498C22⋊Q8—868no—
499#121—22no—
500#121—434no—
501#121—434no—
502#121—434no—
503#121—862no—
504#121—862no—
505#121—868no—
506#121—862no—
507#121C22×D4314yes—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—434no—
511C4×D4—434no—
512C4×D4—862no—
513C4×D4—862no—
514#117—434no—
515#117—434no—
516#117—868no—
517#117—862no—
518#117—862no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4C22×D4311yescharacteristic
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C4⋊C4C22×D4314yes—
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C42—431no—
545C2×C42—861no—
546C2×C42—861no—
547#107—434no—
548#107—434no—
549#107—434no—
550#106—434no—
551#106—434no—
552#106—434no—
553#106—434no—
554#106C22×D4314yes—
555#106C22×D4314yes—
556C4⋊C8—434no—
557#102—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102C22×D4314yes—
562#102C22×D4314yes—
563C22⋊C8—434no—
564C22⋊C8C22×D4314yes—
565C4×C8—434no—
566C24—21no—
567C24—431no—
568C24—861no—
569C24D4×D4311yescharacteristic
570#41—17232no—
571C2×Q8—864no—
572C2×Q8—864no—
573C2×Q8—3442no—
574C2×Q8—1724no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4—434no—
581C2×D4—432no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—864no—
585C2×D4—864no—
586C2×D4—861no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—3442no—
590C2×D4—1724no—
591C2×D4—1724no—
592C2×D4C23×D4312yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—44no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—1724no—
614C22×C4—1724no—
615C22×C4—1724no—
616C22×C4D4×D4312yes—
617C22×C4D4×D4311yescharacteristic
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620D8—868no—
621M16—868no—
622M16—868no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—434no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—862no—
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—434no—
636C4⋊C4—432no—
637C4⋊C4—432no—
638C4⋊C4—432no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4C23×D4312yes—
646C4⋊C4C23×D4312yes—
647C4⋊C4C23×D4312yes—
648C22⋊C4—24no—
649C22⋊C4—434no—
650C22⋊C4—434no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C42—432no—
659C42—432no—
660C42—864no—
661C42—864no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—432no—
670C23—862no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—1722no—
675C23—1722no—
676C23—1722no—
677C23C2×D4×D4312yes—
678C23C2×D4×D4311yescharacteristic
679Q8—3444no—
680Q8—1728no—
681D4—22no—
682D4—22no—
683D4—42no—
684D4—84no—
685D4—868no—
686D4—862no—
687D4—862no—
688D4—3444no—
689D4—1728no—
690D4—1728no—
691D4—1722no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—434no—
704C2×C4—432no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—864no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—1728no—
716C2×C4—1728no—
717C2×C4—1728no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4#1306337212yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—434no—
729C8—862no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22—3444no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22—1724no—
746C22#1458354712yes—
747C22AGL(1,ℤ/8)×D4312yes—
748C22#1458370512yes—
749C22C22×D4×D4311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—434no—
755C4—862no—
756C4—862no—
757C4—1722no—
758C4—1722no—
759C4—1722no—
760C4#1458354712yes—
761C4C2×#41×D4311yescharacteristic
762C4C2×#1306337211yescharacteristic
763C2—42no—
764C2—82no—
765C2—3442no—
766C2—1722no—
767C2#1914718314yesdirect product factor
768C2C2×#1458354711yescharacteristic
769C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
770C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#481C2
socleC23×C43C22×D4
hypercenterC2×#481D43
hypocenterC43C2×#3354
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#14583613C2semidirect
2. C2×#14583550C2semidirect
3. #19147183C2direct (N × H)
4. C2×#14583296C2semidirect
5. C2×#14583216C2semidirect
6. C2×#14583225C2semidirect
7. C2×#14583224C2semidirect
8. C2×#14583188C2semidirect
9. C2×#14583177C2semidirect
10. C2×#14583151C2semidirect
11. C2×#14583150C2semidirect
12. C2×#14582979C2semidirect
13. C2×#14582974C2semidirect
14. C2×#14582939C2semidirect
15. C2×#14582938C2semidirect
16. C2×C43×#481C2semidirect
22. #14583613C22semidirect
24. #14583550C22semidirect
43. #14583296C22semidirect
44. #14583225C22semidirect
45. #14583224C22semidirect
46. #14583216C22semidirect
47. #14583188C22semidirect
48. #14583177C22semidirect
49. #14583151C22semidirect
50. #14583150C22semidirect
51. #14582979C22semidirect
52. #14582974C22semidirect
53. #14582939C22semidirect
54. #14582938C22semidirect
71. C43×#481C22semidirect
272. C2×C43⋊C8#41semidirect
343. C43⋊C8C2×#41semidirect
383. C2×#481D43semidirect
396. C2×C43#3354semidirect
434. #481C2×D43semidirect
462. C43C2×#3354semidirect
767. C2#19147183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145835502
#191471832
C2×#145832962
C2×#145832162
C2×#145832252
C2×#145832242
C2×#145831882
C2×#145831772
C2×#145831512
C2×#145831502
C2×#145829792
C2×#145829742
C2×#145829392
C2×#145829382
C2×C43×#4812
C2×#335443