Finite Group Databasebeta

← C2×#19146937 #25975004

Subgroups — C2×#19146937 #25975004

Order 11008.

2374 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×#14583550C211yesmaximal, characteristic, complemented
2C2×#14583549C211yesmaximal, characteristic, complemented
3#19146937C2116yesmaximal, direct product factor
4C2×#14583303C211yesmaximal, characteristic, complemented
5C2×#14583214C211yesmaximal, characteristic, complemented
6C2×#14583213C211yesmaximal, characteristic, complemented
7C2×#14583211C211yesmaximal, characteristic, complemented
8C2×#14583178C211yesmaximal, characteristic, complemented
9C2×#14583177C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583133C211yesmaximal, characteristic, complemented
12C2×#14582979C211yesmaximal, characteristic, complemented
13C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
14C22×#13063258C211yesmaximal, characteristic, complemented
15C2×#107×D43C211yesmaximal, characteristic, complemented
16C2×C43×#480C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621900—21no—
19C22×#10621882C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583550—24no—
23#14583550C2218yescomplemented
24#14583549—24no—
25#14583549C2218yescomplemented
26C2×#13063324C2211yescharacteristic
27C2×#13063324C2211yescharacteristic
28C2×#13063310—21no—
29C2×#13063308—21no—
30C2×#13063307—21no—
31C2×#13063306—21no—
32C2×#13063303—21no—
33C2×#13063302—21no—
34C2×#13063300C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43C2211yescharacteristic
40C22×C4⋊Dic43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583303C2218yescomplemented
44#14583214C2218yescomplemented
45#14583213C2218yescomplemented
46#14583211C2218yescomplemented
47#14583178C2218yescomplemented
48#14583177C2218yescomplemented
49#14583134C2218yescomplemented
50#14583133C2218yescomplemented
51#14582979C2218yescomplemented
52(C22⋊D43)⋊C8C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063258C2211yescharacteristic
60C2×#13063258C2218yescomplemented
61#107×D43C2218yescomplemented
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×#480C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C2×#10621900—28no—
80C2×#10621900—48no—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×D172—21no—
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43D411yescharacteristic
88C23×Dic43—21no—
89C23×Dic43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621882—24no—
95C2×#10621882C2314yes—
96C22×C43⋊C8—24no—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C2×C8×D43—24no—
101C2×C8×D43C2314yes—
102#13063324—22no—
103#13063324—22no—
104#13063324C2314yes—
105#13063324C2314yes—
106#13063310—28no—
107#13063308—28no—
108#13063307—28no—
109#13063306—28no—
110#13063303—28no—
111#13063302—28no—
112#13063300—22no—
113#13063300C2314yes—
114#13063299—22no—
115#13063299C2314yes—
116#13063296—22no—
117#13063296C2314yes—
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120#13063287—22no—
121#13063287C2314yes—
122C4×C22⋊D43D414yes—
123C4×C22⋊D43C2314yes—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—22no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2314yes—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C4⋊C4×D43—22no—
136C4⋊C4×D43—22no—
137C4⋊C4×D43C2314yes—
138C4⋊C4×D43C2314yes—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43D411yescharacteristic
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063259C2314yes—
149#13063258C2314yes—
150#13063258C2314yes—
151#13063258C2314yes—
152#13063258C2314yes—
153#13063258C2314yes—
154Dic43⋊C8C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160C8×Dic43C2314yes—
161C22×D4×C43—21no—
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C23×C4×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167#121×C43—22no—
168#121×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—22no—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2314yes—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176#107×C43C2314yes—
177#107×C43C2314yes—
178#102×C43C2314yes—
179#102×C43C2314yes—
180C22⋊C8×C43C2314yes—
181C24×C43—21no—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C23×D43C2×D411yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43—24no—
187C2×D4×C43—22no—
188C2×D4×C43—22no—
189C2×D4×C43—44no—
190C2×D4×C43C2412yes—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—24no—
197C22×C4×C43—44no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—44no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43D818yescomplemented
207C2×C22⋊D43C2×D414yes—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—24no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621900—432no—
219#10621898—432no—
220C2×D172—21no—
221C2×D172—24no—
222C2×D172—22no—
223C2×D172—22no—
224C2×D172—44no—
225C2×D172C2412yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
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×D43C2×D412yes—
235C2×C4×D43C2412yes—
236C2×Dic86—24no—
237C2×Dic86—24no—
238C2×Dic86—44no—
239C2×Dic86—44no—
240C2×C8×C43—22no—
241C2×C8×C43—22no—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C2412yes—
249C4⋊C4×C43C2412yes—
250C4⋊C4×C43C2412yes—
251C22⋊C4×C43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43C2×D414yes—
255#10621882—28no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4C2×D414yes—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—24no—
264C4⋊Dic43C2412yes—
265C4⋊Dic43C2412yes—
266C4⋊Dic43C2412yes—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4C2×D414yes—
272C4×Dic43C2×D412yes—
273C4×Dic43C2412yes—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—28no—
276C2×C43⋊C8#4114yescomplemented
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279C8×D43—28no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43C2×D814yes—
287C23×C43C22×D412yes—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43C2×D814yes—
296C22×D43C22×D412yes—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—48no—
300D4×C43—42no—
301C2×C4×C43—22no—
302C2×C4×C43—24no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—48no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4112yes—
315C2×C4×C432−1+412yes—
316C2×C4×C43C2511yescharacteristic
317C22⋊D43—48no—
318C22⋊D43—48no—
319C22⋊D43C2×D8116yescomplemented
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—48no—
329C2×Dic43—48no—
330C2×Dic43C2×D814yes—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334D172—22no—
335D172—22no—
336D172—48no—
337D172—42no—
338C4×D43—24no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—48no—
342C4×D43—48no—
343C4×D43—48no—
344Dic86—48no—
345Dic86—48no—
346C8×C43—22no—
347C8×C43—22no—
348C43⋊C8—22no—
349C43⋊C8C2×#4114yescomplemented
350C2×#3334—431nomaximal, Sylow
351C22×C43—28no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—84no—
358C22×C43#54712yes—
359C22×C43C22×D814yes—
360C22×C43C22×D812yes—
361C22×C43#57812yes—
362C22×C43C23×D411yescharacteristic
363C2×D43—28no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—84no—
370C2×D43C22×D814yes—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43#54712yes—
376C4×C43C22×#4111yescharacteristic
377C4×C43C2×2−1+411yescharacteristic
378Dic43—22no—
379Dic43—22no—
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383Dic43C22×D814yes—
384C2×#547—431no—
385C2×#547—431no—
386#3334—4316no—
387C2×#500—431no—
388C2×#480—431no—
389C2×#480—431no—
390C2×#480—431no—
391C2×#480D4311yescharacteristic, complemented
392C2×#474—431no—
393C2×#474—431no—
394C2×#466—431no—
395C2×#466—431no—
396C2×C4×D8—431no—
397C2×C8×D4—431no—
398C22×#107—431no—
399C22×#107—431no—
400C2×C43—24no—
401C2×C43—82no—
402C2×C43#333414yescomplemented
403C2×C43C2×#54711yescharacteristic
404C2×C43C23×D811yescharacteristic
405C2×C43C2×#57811yescharacteristic
406D43—24no—
407D43—82no—
408C22×#41—861no—
409C22×#41—861no—
410C22×D8—431no—
411C23×C8—431no—
412C23×C8—431no—
413#547—438no—
414#547—438no—
415#547—864no—
416#547—864no—
417C2×C4⋊Q8—431no—
418C2×C4⋊Q8—431no—
419C2×#123—861no—
420C2×#123—861no—
421C2×#123—861no—
422C2×#123—861no—
423C2×C22⋊Q8—861no—
424C2×C22⋊Q8—861no—
425C2×#121—431no—
426C2×#121—431no—
427C2×#121—431no—
428C2×#121C2×D4311yescharacteristic
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×C4×D4—431no—
432C22×C4⋊C4—431no—
433C22×C4⋊C4—431no—
434C22×C4⋊C4—431no—
435C22×C4⋊C4C2×D4311yescharacteristic
436#500—438no—
437#480—438no—
438#480—438no—
439#480—438no—
440#480C2×D4318yescomplemented
441#474—438no—
442#474—438no—
443#466—438no—
444#466—438no—
445C4×D8—438no—
446C8×D4—438no—
447C2×#107—431no—
448C2×#107—431no—
449C2×#107—438no—
450C2×#107—431no—
451C2×#107—431no—
452C2×#107—431no—
453C2×#107—431no—
454C2×#107—431no—
455C2×#107—438no—
456C2×#107C2×D4311yescharacteristic
457C2×#107C2×D4311yescharacteristic
458C2×C4⋊C8—431no—
459C2×#102—431no—
460C2×#102—431no—
461C2×#102—431no—
462C2×#102—431no—
463C2×#102C2×D4311yescharacteristic
464C2×#102C2×D4311yescharacteristic
465C2×C22⋊C8—431no—
466C2×C22⋊C8C2×D4311yescharacteristic
467C2×C4×C8—431no—
468C43C2×#333411yescharacteristic, complemented, Sylow
469C2×#41—868no—
470C2×#41—868no—
471C2×#41—1728no—
472C2×#41—1728no—
473C22×Q8—861no—
474C22×Q8—861no—
475C22×D4—21no—
476C22×D4—431no—
477C22×D4—431no—
478C22×D4—861no—
479C22×D4—861no—
480C22×D4—861no—
481C22×D4C22×D4311yescharacteristic
482C23×C4—21no—
483C23×C4—431no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4C22×D4311yescharacteristic
490C2×D8—434no—
491C2×D8—864no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—434no—
495C22×C8—434no—
496C22×C8—864no—
497C22×C8—864no—
498C22×C8C22×D4311yescharacteristic
499C22×C8C22×D4311yescharacteristic
500C4⋊Q8—434no—
501C4⋊Q8—434no—
502C4⋊Q8—862no—
503C4⋊Q8—862no—
504#123—868no—
505#123—868no—
506#123—868no—
507#123—868no—
508C22⋊Q8—868no—
509C22⋊Q8—868no—
510#121—22no—
511#121—434no—
512#121—434no—
513#121—434no—
514#121—862no—
515#121—862no—
516#121—862no—
517#121C22×D4314yes—
518C4×D4—434no—
519C4×D4—434no—
520C4×D4—434no—
521C4×D4—434no—
522C4×D4—862no—
523C4×D4—862no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—431no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—434no—
531C2×C4⋊C4—434no—
532C2×C4⋊C4—434no—
533C2×C4⋊C4—862no—
534C2×C4⋊C4—862no—
535C2×C4⋊C4—861no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4314yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—431no—
547C2×C22⋊C4—431no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C42—431no—
554#107—434no—
555#107—434no—
556#107—434no—
557#107—434no—
558#107—434no—
559#107—434no—
560#107—434no—
561#107C22×D4314yes—
562#107C22×D4314yes—
563C4⋊C8—434no—
564#102—434no—
565#102—434no—
566#102—434no—
567#102—434no—
568#102C22×D4314yes—
569#102C22×D4314yes—
570C22⋊C8—434no—
571C22⋊C8C22×D4314yes—
572C4×C8—434no—
573C24—21no—
574C24—431no—
575C24—861no—
576C24D4×D4311yescharacteristic
577#41—17232no—
578#41—17232no—
579C2×Q8—864no—
580C2×Q8—864no—
581C2×Q8—1724no—
582C2×Q8—1724no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—44no—
588C2×D4—438no—
589C2×D4—434no—
590C2×D4—432no—
591C2×D4—864no—
592C2×D4—864no—
593C2×D4—864no—
594C2×D4—861no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—1724no—
598C2×D4—1724no—
599C2×D4—1724no—
600C2×D4C23×D4312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—864no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—864no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4D4×D4312yes—
629C22×C4D4×D4311yescharacteristic
630C22×C4C23×D4312yes—
631C22×C4C23×D4311yescharacteristic
632D8—868no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—434no—
636C2×C8—432no—
637C2×C8—432no—
638C2×C8—868no—
639C2×C8—868no—
640C2×C8—862no—
641C2×C8C23×D4312yes—
642C2×C8C23×D4312yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—434no—
648C4⋊C4—432no—
649C4⋊C4—432no—
650C4⋊C4—432no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4—864no—
654C4⋊C4—864no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—864no—
659C4⋊C4C23×D4312yes—
660C4⋊C4C23×D4312yes—
661C4⋊C4C23×D4312yes—
662C22⋊C4—24no—
663C22⋊C4—434no—
664C22⋊C4—434no—
665C22⋊C4—864no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C42—432no—
671C42—432no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—434no—
679C23—432no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23D8×D4314yes—
687C23C2×D4×D4312yes—
688C23C2×D4×D4311yescharacteristic
689Q8—1728no—
690Q8—1728no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—4316no—
696D4—862no—
697D4—862no—
698D4—1728no—
699D4—1728no—
700D4—1728no—
701D4—1722no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—434no—
714C2×C4—432no—
715C2×C4—432no—
716C2×C4—432no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—864no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—1728no—
726C2×C4—1728no—
727C2×C4—1728no—
728C2×C4—1728no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1728no—
733C2×C4C2×D4×D4312yes—
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4#41×D4312yes—
736C2×C4#1306337212yes—
737C2×C4C24×D4311yescharacteristic
738C8—22no—
739C8—22no—
740C8—434no—
741C8—862no—
742C22—22no—
743C22—22no—
744C22—28no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—434no—
750C22—862no—
751C22—862no—
752C22—868no—
753C22—3444no—
754C22—1722no—
755C22—1722no—
756C22—1722no—
757C22#1458354712yes—
758C22C2×D8×D4314yes—
759C22C2×D8×D4312yes—
760C22#1458371512yes—
761C22C22×D4×D4311yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—434no—
767C4—862no—
768C4—862no—
769C4—1722no—
770C4—1722no—
771C4—1722no—
772C4#1458354712yes—
773C4C2×#41×D4311yescharacteristic
774C4C2×#1306337211yescharacteristic
775C2—24no—
776C2—82no—
777C2—864no—
778C2—3442no—
779C2#1914693714yesdirect product factor
780C2C2×#1458354711yescharacteristic
781C2C22×D8×D4311yescharacteristic
782C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
hypercenterC2×#480D43
hypocenterC43C2×#3334
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#14583550C2semidirect
2. C2×#14583549C2semidirect
3. #19146937C2direct (N × H)
4. C2×#14583303C2semidirect
5. C2×#14583214C2semidirect
6. C2×#14583213C2semidirect
7. C2×#14583211C2semidirect
8. C2×#14583178C2semidirect
9. C2×#14583177C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583133C2semidirect
12. C2×#14582979C2semidirect
13. C2×(C22⋊D43)⋊C8C2semidirect
14. C22×#13063258C2semidirect
15. C2×#107×D43C2semidirect
16. C2×C43×#480C2semidirect
23. #14583550C22semidirect
25. #14583549C22semidirect
43. #14583303C22semidirect
44. #14583214C22semidirect
45. #14583213C22semidirect
46. #14583211C22semidirect
47. #14583178C22semidirect
48. #14583177C22semidirect
49. #14583134C22semidirect
50. #14583133C22semidirect
51. #14582979C22semidirect
52. (C22⋊D43)⋊C8C22semidirect
60. C2×#13063258C22semidirect
61. #107×D43C22semidirect
71. C43×#480C22semidirect
206. C2×C22⋊D43D8semidirect
276. C2×C43⋊C8#41semidirect
319. C22⋊D43C2×D8semidirect
349. C43⋊C8C2×#41semidirect
391. C2×#480D43semidirect
402. C2×C43#3334semidirect
440. #480C2×D43semidirect
468. C43C2×#3334semidirect
779. C2#19146937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835502
C2×#145835492
#191469372
C2×#145833032
C2×#145832142
C2×#145832132
C2×#145832112
C2×#145831782
C2×#145831772
C2×#145831342
C2×#145831332
C2×#145829792
C2×(C22⋊D43)⋊C82
C22×#130632582
C2×#107×D432
C2×C43×#4802
C2×#333443