Finite Group Databasebeta

← C2×#19147066 #25975161

Subgroups — C2×#19147066 #25975161

Order 11008.

2158 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×#14583593C211yesmaximal, characteristic, complemented
2C2×#14583550C211yesmaximal, characteristic, complemented
3#19147066C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583217C211yesmaximal, characteristic, complemented
7C2×#14583223C211yesmaximal, characteristic, complemented
8C2×#14583214C211yesmaximal, characteristic, complemented
9C2×#14583202C211yesmaximal, characteristic, complemented
10C2×#14583188C211yesmaximal, characteristic, complemented
11C2×#14583152C211yesmaximal, characteristic, complemented
12C2×#14583136C211yesmaximal, characteristic, complemented
13C2×#14583010C211yesmaximal, characteristic, complemented
14C2×#14582968C211yesmaximal, characteristic, complemented
15C2×#106×D43C211yesmaximal, characteristic, complemented
16C2×C43×#428C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×D344C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583593—24no—
21#14583593C2218yescomplemented
22#14583550—24no—
23#14583550C2218yescomplemented
24C2×#13063324C2211yescharacteristic
25C2×#13063319—21no—
26C2×#13063316C2211yescharacteristic
27C2×#13063310—21no—
28C2×#13063308—21no—
29C2×#13063307—21no—
30C2×#13063303—21no—
31C2×#13063300C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35C2×#13063298—21no—
36C2×C4×D172—21no—
37C2×#13063287C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583307C2218yescomplemented
43#14583223C2218yescomplemented
44#14583219C2218yescomplemented
45#14583217C2218yescomplemented
46#14583214C2218yescomplemented
47#14583202C2218yescomplemented
48#14583188C2218yescomplemented
49#14583152C2218yescomplemented
50#14583136C2218yescomplemented
51#14583010C2218yescomplemented
52#14582968C2218yescomplemented
53C2×#13063258C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58#106×D43C2218yescomplemented
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#428C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#107×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#106×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43D411yescharacteristic
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C2×D344—24no—
93C2×D344C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—24no—
97C2×C8×D43C2314yes—
98#13063324—22no—
99#13063324C2314yes—
100#13063319—28no—
101#13063316—22no—
102#13063316C2314yes—
103#13063310—28no—
104#13063308—28no—
105#13063307—28no—
106#13063303—28no—
107#13063300—22no—
108#13063300—22no—
109#13063300C2314yes—
110#13063300C2314yes—
111#13063299—22no—
112#13063299—22no—
113#13063299C2314yes—
114#13063299C2314yes—
115#13063298—28no—
116C4×D172—28no—
117#13063287—22no—
118#13063287—22no—
119#13063287C2314yes—
120#13063287C2314yes—
121C4×C22⋊D43D414yes—
122C4×C22⋊D43C2314yes—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C4⋊C4×D43—22no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C2×C22⋊Dic43D411yescharacteristic
136C2×(C2×D43)⋊C4—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)⋊C4D411yescharacteristic
143C2×C4×Dic43C2311yescharacteristic
144#13063258C2314yes—
145#13063257C2314yes—
146#13063256C2314yes—
147#13063256C2314yes—
148#13063256C2314yes—
149Dic43⋊C8C2314yes—
150#13063247C2314yes—
151#13063247C2314yes—
152#13063245C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156C22⋊(C43⋊C8)C2314yes—
157(C2×D43)⋊C8C2314yes—
158#13063235C2314yes—
159C23×C4×C43—21no—
160C23×C4×C43C2311yescharacteristic
161C2×M16×C43—24no—
162C2×M16×C43C2314yes—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#117×C43—22no—
166#117×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—22no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2314yes—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C42×C43—21no—
176#107×C43C2314yes—
177#107×C43C2314yes—
178#106×C43C2314yes—
179#106×C43C2314yes—
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C23×D43—21no—
183C23×D43C2×D411yescharacteristic
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—24no—
191C22×C4×C43—44no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—44no—
200C2×C22⋊D43—82no—
201C2×C22⋊D43C2×D414yes—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207#10621898—432no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—24no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—22no—
216C2×D172—44no—
217C2×D172—44no—
218C2×D172C2412yes—
219C2×D172C2412yes—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×C4×D43—82no—
229C2×C4×D43—82no—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2412yes—
232C2×Dic86—24no—
233C2×Dic86—44no—
234M16×C43—28no—
235C2×C8×C43—22no—
236C2×C8×C43#4114yescomplemented
237C2×C8×C43C2412yes—
238C2×C8×C43C2412yes—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43C2412yes—
245C4⋊C4×C43C2412yes—
246C4⋊C4×C43C2412yes—
247C4⋊C4×C43C2412yes—
248C22⋊C4×C43—24no—
249C42×C43—24no—
250C22⋊Dic43C2×D414yes—
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—
257(C2×D43)⋊C4C2×D414yes—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—24no—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4C2×D414yes—
268C4×Dic43C2×D412yes—
269C4×Dic43C2412yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274D344—28no—
275C8×D43—28no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43C22×D412yes—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43AGL(1,ℤ/8)14yes—
292C22×D43C22×D412yes—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—48no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4112yes—
309C2×C4×C432−1+412yes—
310C2×C4×C43C2511yescharacteristic
311C22⋊D43—28no—
312C22⋊D43—48no—
313C22⋊D43—84no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324D172—22no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—48no—
329D172—48no—
330D172—42no—
331D172—42no—
332C4×D43—24no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—48no—
336C4×D43—48no—
337C4×D43—84no—
338C4×D43—84no—
339Dic86—48no—
340C8×C43—22no—
341C8×C43C2×#4114yescomplemented
342C43⋊C8—22no—
343C43⋊C8—22no—
344C2×#3345—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—44no—
349C22×C43#54712yes—
350C22×C43C2×AGL(1,ℤ/8)12yes—
351C22×C43#57712yes—
352C22×C43C23×D411yescharacteristic
353C2×D43—28no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—84no—
363C2×D43—84no—
364C2×D43C2×AGL(1,ℤ/8)14yes—
365C4×C43—22no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43#54712yes—
371C4×C43C22×#4111yescharacteristic
372C4×C43C2×2−1+411yescharacteristic
373Dic43—22no—
374Dic43—22no—
375Dic43—22no—
376Dic43—42no—
377Dic43—42no—
378C2×#553—431no—
379C2×#547—431no—
380#3345—4316no—
381C2×#501—431no—
382C2×#481—431no—
383C2×#481—431no—
384C2×#482—431no—
385C2×#480—431no—
386C2×#478—431no—
387C2×#476—431no—
388C2×#469—431no—
389C2×#466—431no—
390C2×#442—431no—
391C2×#435—431no—
392C2×#428D4311yescharacteristic, complemented
393C22×#106—431no—
394C2×C43—42no—
395C2×C43#334514yescomplemented
396C2×C43C2×#54711yescharacteristic
397C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C43C2×#57711yescharacteristic
399D43—24no—
400D43—82no—
401D43—82no—
402C22×#41—861no—
403C22×D8—431no—
404C22×M16C2×D4311yescharacteristic
405C23×C8—431no—
406#553—438no—
407#553—864no—
408#547—438no—
409#547—864no—
410C2×C4⋊Q8—431no—
411C2×#126—861no—
412C2×#125—431no—
413C2×#123—861no—
414C2×#123—861no—
415C2×#123—861no—
416C2×C22⋊Q8—861no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—861no—
422C2×C4×D4—431no—
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×C4×D4—861no—
426C2×#117C2×D4311yescharacteristic
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4C2×D4311yescharacteristic
430#501—438no—
431#482—438no—
432#481—438no—
433#481—438no—
434#480—438no—
435#478—438no—
436#476—438no—
437#469—438no—
438#466—438no—
439#442—438no—
440#435—438no—
441#428C2×D4318yescomplemented
442C2×#107—431no—
443C2×#107C2×D4311yescharacteristic
444C2×#107C2×D4311yescharacteristic
445C2×#106—431no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×#106—438no—
450C2×#106C2×D4311yescharacteristic
451C2×#106C2×D4311yescharacteristic
452C2×C4⋊C8—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×#97—431no—
462C43C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—868no—
464C2×#41—1728no—
465C22×Q8—861no—
466C22×D4—431no—
467C22×D4—431no—
468C22×D4—431no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C23×C4—21no—
474C23×C4—431no—
475C23×C4—861no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4—861no—
479C23×C4C22×D4311yescharacteristic
480C2×D8—434no—
481C2×D8—864no—
482C2×M16—24no—
483C2×M16C22×D4314yes—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—434no—
487C22×C8—864no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—434no—
491C4⋊Q8—862no—
492#126—868no—
493#125—434no—
494#125—862no—
495#123—868no—
496#123—868no—
497#123—868no—
498C22⋊Q8—868no—
499#121—434no—
500#121—434no—
501#121—434no—
502#121—434no—
503#121—868no—
504#121—862no—
505#121—862no—
506#121—862no—
507#121—862no—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—434no—
511C4×D4—434no—
512C4×D4—868no—
513C4×D4—862no—
514C4×D4—862no—
515#117—22no—
516#117C22×D4314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—862no—
525C2×C4⋊C4—862no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C4⋊C4C22×D4314yes—
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—21no—
546C2×C42—431no—
547#107—434no—
548#107C22×D4314yes—
549#107C22×D4314yes—
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#102—434no—
562#102—434no—
563C22⋊C8—434no—
564C22⋊C8—434no—
565#97—434no—
566C24—431no—
567C24—861no—
568C24—861no—
569C24D4×D4311yescharacteristic
570#41—17232no—
571C2×Q8—864no—
572C2×Q8—1724no—
573C2×D4—434no—
574C2×D4—432no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—3442no—
588C2×D4—1724no—
589C2×D4—1724no—
590C2×D4—1724no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—432no—
603C22×C4—432no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—864no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—3442no—
613C22×C4—3442no—
614C22×C4—1724no—
615C22×C4—1724no—
616C22×C4D4×D4312yes—
617C22×C4D4×D4311yescharacteristic
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620D8—868no—
621M16—28no—
622C2×C8—22no—
623C2×C8—432no—
624C2×C8—432no—
625C2×C8—862no—
626C2×C8—862no—
627C2×C8—868no—
628C2×C8#1062189814yescomplemented
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—434no—
637C4⋊C4—432no—
638C4⋊C4—432no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4C23×D4312yes—
647C4⋊C4C23×D4312yes—
648C4⋊C4C23×D4312yes—
649C4⋊C4C23×D4312yes—
650C22⋊C4—24no—
651C22⋊C4—434no—
652C22⋊C4—434no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C42—24no—
660C42—432no—
661C42—432no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—434no—
666C23—432no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—862no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23—1722no—
676C23—1722no—
677C23C2×D4×D4312yes—
678C23C2×D4×D4311yescharacteristic
679Q8—1728no—
680D4—868no—
681D4—862no—
682D4—862no—
683D4—862no—
684D4—862no—
685D4—3444no—
686D4—1728no—
687D4—1728no—
688D4—1728no—
689D4—1722no—
690D4—1722no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—432no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—864no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—3444no—
716C2×C4—3444no—
717C2×C4—1728no—
718C2×C4—1728no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4C2×D4×D4312yes—
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C2×#1062189812yes—
724C2×C4#1306337312yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—862no—
728C8—862no—
729C8C2×#1062189814yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—434no—
735C22—862no—
736C22—862no—
737C22—868no—
738C22—3444no—
739C22—3444no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22—1722no—
746C22#1458355012yes—
747C22AGL(1,ℤ/8)×D4312yes—
748C22#1458370812yes—
749C22C22×D4×D4311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—862no—
756C4—862no—
757C4—862no—
758C4—1722no—
759C4—1722no—
760C4#1458355012yes—
761C4C22×#1062189811yescharacteristic
762C4C2×#1306337311yescharacteristic
763C2—42no—
764C2—864no—
765C2—3442no—
766C2—3442no—
767C2#1914706614yesdirect product factor
768C2C2×#1458355011yescharacteristic
769C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
770C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
hypercenterC2×#428D43
hypocenterC43C2×#3345
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#14583593C2semidirect
2. C2×#14583550C2semidirect
3. #19147066C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583217C2semidirect
7. C2×#14583223C2semidirect
8. C2×#14583214C2semidirect
9. C2×#14583202C2semidirect
10. C2×#14583188C2semidirect
11. C2×#14583152C2semidirect
12. C2×#14583136C2semidirect
13. C2×#14583010C2semidirect
14. C2×#14582968C2semidirect
15. C2×#106×D43C2semidirect
16. C2×C43×#428C2semidirect
21. #14583593C22semidirect
23. #14583550C22semidirect
42. #14583307C22semidirect
43. #14583223C22semidirect
44. #14583219C22semidirect
45. #14583217C22semidirect
46. #14583214C22semidirect
47. #14583202C22semidirect
48. #14583188C22semidirect
49. #14583152C22semidirect
50. #14583136C22semidirect
51. #14583010C22semidirect
52. #14582968C22semidirect
58. #106×D43C22semidirect
72. C43×#428C22semidirect
236. C2×C8×C43#41semidirect
341. C8×C43C2×#41semidirect
392. C2×#428D43semidirect
395. C2×C43#3345semidirect
441. #428C2×D43semidirect
462. C43C2×#3345semidirect
628. C2×C8#10621898semidirect
729. C8C2×#10621898semidirect
767. C2#19147066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835932
C2×#145835502
#191470662
C2×#145833072
C2×#145832192
C2×#145832172
C2×#145832232
C2×#145832142
C2×#145832022
C2×#145831882
C2×#145831522
C2×#145831362
C2×#145830102
C2×#145829682
C2×#106×D432
C2×C43×#4282
C2×#334543