Finite Group Databasebeta

← C2×#19146553 #25973104

Subgroups — C2×#19146553 #25973104

Order 11008.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583552C211yesmaximal, characteristic, complemented
2C2×#14583544C211yesmaximal, characteristic, complemented
3#19146553C2116yesmaximal, direct product factor
4C2×#14583261C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583231C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583034C211yesmaximal, characteristic, complemented
12C2×#14583009C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#476C211yesmaximal, characteristic, complemented
17C22×#10621902—21no—
18C22×#10621900C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C22×#10621873C2211yescharacteristic, complemented
21C22×D344C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621872C2211yescharacteristic, complemented
24C22×C8×D43C2211yescharacteristic
25#14583552—24no—
26#14583552C2218yescomplemented
27#14583544—24no—
28#14583544C2218yescomplemented
29C2×#13063313C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063310—21no—
32C2×#13063309—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063301—21no—
35C2×#13063300C2211yescharacteristic
36C2×#13063300C2211yescharacteristic
37C2×#13063300C2211yescharacteristic, complemented
38C2×#13063299—21no—
39C2×#13063295—21no—
40C2×C4×D172C2211yescharacteristic
41C2×C4×D172C2211yescharacteristic, complemented
42C2×C4⋊C4×D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic, complemented
44C22×(C2×D43)⋊C4—21no—
45#14583261C2218yescomplemented
46#14583231C2218yescomplemented
47#14583219C2218yescomplemented
48#14583153C2218yescomplemented
49#14583129C2218yescomplemented
50#14583115C2218yescomplemented
51#14583045C2218yescomplemented
52#14583034C2218yescomplemented
53#14583009C2218yescomplemented
54#14582969C2218yescomplemented
55C2×#13063256C2211yescharacteristic, complemented
56#14582897C2218yescomplemented
57C2×#13063250C2211yescharacteristic, complemented
58C2×#13063248C2211yescharacteristic, complemented
59C2×#13063248C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65#102×D43C2218yescomplemented
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×#13063236C2211yescharacteristic, complemented
69C2×C4⋊Q8×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C43×#476C2218yescomplemented
72C2×#106×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621902—28no—
79C2×#10621902—48no—
80C2×#10621900—24no—
81C2×#10621900—22no—
82C2×#10621900—42no—
83C2×#10621900C2314yes—
84C22×Dic86C2311yescharacteristic
85C22×D172—21no—
86C22×D172—21no—
87C22×D172—21no—
88C22×D172D411yescharacteristic
89C22×D172C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C2×D4×D43—24no—
94C2×D4×D43—22no—
95C2×D4×D43—42no—
96C2×D4×D43C2314yes—
97C23×Dic43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2311yescharacteristic
103C2×#10621873—42no—
104C2×#10621873C2314yescomplemented
105C2×D344—42no—
106C2×D344C2314yes—
107C2×#10621882—24no—
108C2×#10621882C2314yes—
109C2×#10621872—42no—
110C2×#10621872C2314yescomplemented
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113C2×C8×D43—42no—
114C2×C8×D43C2314yes—
115#13063313—22no—
116#13063313C2314yes—
117#13063310—28no—
118#13063310—28no—
119#13063309—28no—
120#13063305—22no—
121#13063305C2314yes—
122#13063301—28no—
123#13063300—22no—
124#13063300—22no—
125#13063300—22no—
126#13063300C2314yes—
127#13063300C2314yes—
128#13063300C2314yescomplemented
129#13063299—28no—
130#13063295—28no—
131C4×D172—22no—
132C4×D172D414yes—
133C4×D172C2314yes—
134C4×D172C2314yescomplemented
135C2×C4⋊Dic43—21no—
136C2×C4⋊Dic43D411yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C4⋊C4×D43C2314yescomplemented
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—28no—
152C2×(C2×D43)⋊C4D411yescharacteristic
153C2×(C2×D43)⋊C4D411yescharacteristic
154#13063256C2314yescomplemented
155#13063250C2314yescomplemented
156#13063248C2314yescomplemented
157#13063248C2314yescomplemented
158#13063247C2314yes—
159#13063246C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162#13063245C2314yescomplemented
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yescomplemented
165#13063236C2314yescomplemented
166C22×Q8×C43—21no—
167C22×D4×C43C2311yescharacteristic
168C23×C4×C43—21no—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C4⋊Q8×C43—22no—
172C4⋊Q8×C43C2314yescomplemented
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#106×C43C2314yescomplemented
182#106×C43C2314yescomplemented
183C4⋊C8×C43C2314yescomplemented
184#102×C43C2314yes—
185#102×C43C2314yes—
186C24×C43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—24no—
190C23×D43—44no—
191C23×D43—44no—
192C23×D43—82no—
193C23×D43C2×D411yescharacteristic
194C23×D43C2×D411yescharacteristic
195C2×Q8×C43—24no—
196C2×Q8×C43—44no—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43#4114yescomplemented
200C2×D4×C43C2412yes—
201C22×C4×C43—24no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—82no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—44no—
212C2×C22⋊D43—44no—
213C22×Dic43—24no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—44no—
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219#10621902—432no—
220#10621900—28no—
221#10621900—44no—
222#10621900—48no—
223D4×D43—28no—
224D4×D43—44no—
225D4×D43—48no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—24no—
229C2×D172—24no—
230C2×D172—24no—
231C2×D172—24no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—44no—
237C2×D172—44no—
238C2×D172—82no—
239C2×D172C2×D414yes—
240C2×D172C2412yes—
241C2×D172C2412yes—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—24no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2×D412yes—
254C2×C4×D43C2412yes—
255C2×C4×D43C2412yes—
256C2×Dic86—22no—
257C2×Dic86—22no—
258C2×Dic86—21no—
259C2×Dic86C2412yes—
260C2×C8×C43—22no—
261C2×C8×C43—22no—
262C2×C8×C43C2412yes—
263C2×C8×C43C2412yes—
264C4⋊C4×C43—24no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43C2412yes—
269C4⋊C4×C43C2412yes—
270C4⋊C4×C43C2412yes—
271C22⋊C4×C43—24no—
272C42×C43C2×D412yes—
273C42×C43C2412yes—
274#10621882—28no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4C2×D414yes—
283(C2×D43)⋊C4C2×D414yes—
284C4⋊Dic43—21no—
285C4⋊Dic43—24no—
286C4⋊Dic43C2×D414yes—
287C4⋊Dic43C2412yes—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8C2412yes—
293C2×C43⋊C8C2412yes—
294D344—44no—
295#10621873—44no—
296#10621872—44no—
297C8×D43—44no—
298C23×C43—24no—
299C23×C43—22no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—48no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—48no—
318C22×D43—84no—
319C22×D43—816no—
320C22×D43AGL(1,ℤ/8)14yes—
321C22×D43C22×D412yes—
322C22×D43C22×D412yes—
323Q8×C43—48no—
324D4×C43—24no—
325D4×C43—22no—
326D4×C43C2×#4114yescomplemented
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43—42no—
335C2×C4×C43—84no—
336C2×C4×C43C22×D412yes—
337C2×C4×C43C22×D412yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4112yes—
340C2×C4×C43H(5,𝔽2)12yes—
341C2×C4×C43C2511yescharacteristic
342C22⋊D43—48no—
343C22⋊D43—48no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—48no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353D172—28no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—48no—
359D172—48no—
360D172—42no—
361D172—42no—
362D172—84no—
363C4×D43—24no—
364C4×D43—24no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—48no—
370C4×D43—48no—
371C4×D43—48no—
372Dic86—22no—
373Dic86—22no—
374Dic86—42no—
375C8×C43—22no—
376C8×C43—22no—
377C43⋊C8—22no—
378C43⋊C8—22no—
379C2×#3306—431nomaximal, Sylow
380C22×C43—24no—
381C22×C43—48no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43#54612yes—
385C22×C43C2×AGL(1,ℤ/8)12yes—
386C22×C43#57712yes—
387C22×C43C23×D411yescharacteristic
388C2×D43—22no—
389C2×D43—28no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—44no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—816no—
402C2×D43—84no—
403C2×D43—84no—
404C2×D43C2×AGL(1,ℤ/8)14yes—
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—42no—
408C4×C43—42no—
409C4×C43—42no—
410C4×C43#54612yes—
411C4×C43C22×#4111yescharacteristic
412C4×C43C2×H(5,𝔽2)11yescharacteristic
413Dic43—22no—
414Dic43—22no—
415Dic43—42no—
416Dic43—42no—
417C2×#547—431no—
418C2×#546—431no—
419#3306—4316no—
420C2×#489—431no—
421C2×#481—431no—
422C2×#483—431no—
423C2×#476D4311yescharacteristic, complemented
424C2×#469—431no—
425C2×#465—431no—
426C2×#463—431no—
427C2×#449—431no—
428C2×#447—431no—
429C2×#442—431no—
430C2×#435—431no—
431C2×#417—431no—
432C22×#102—431no—
433C2×C43—44no—
434C2×C43#330614yescomplemented
435C2×C43C2×#54611yescharacteristic
436C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
437C2×C43C2×#57711yescharacteristic
438D43—24no—
439D43—42no—
440D43—82no—
441D43—82no—
442C22×#41—431no—
443C22×#41—861no—
444C23×D4—431no—
445C22×SD16—431no—
446C22×D8—431no—
447C22×D8—431no—
448C22×M16—431no—
449C23×C8—431no—
450#547—438no—
451#547—864no—
452#546—438no—
453#546—864no—
454C2×C4⋊Q8C2×D4311yescharacteristic, complemented
455C2×#124—431no—
456C2×#123—861no—
457C2×#123—861no—
458C2×#123—861no—
459C2×C22⋊Q8—431no—
460C2×C22⋊Q8—861no—
461C2×#121—431no—
462C2×#121—431no—
463C2×#121—431no—
464C2×#121—861no—
465C2×#120—861no—
466C2×C4×D4—431no—
467C2×C4×D4—431no—
468C2×C4×D4C2×D4311yescharacteristic
469C22×C4⋊C4—431no—
470C22×C4⋊C4—431no—
471C22×C22⋊C4—861no—
472#489—438no—
473#483—438no—
474#481—438no—
475#476C2×D4318yescomplemented
476#469—438no—
477#465—438no—
478#463—438no—
479#449—438no—
480#447—438no—
481#442—438no—
482#435—438no—
483C2×#106—431no—
484C2×#106C2×D4311yescharacteristic, complemented
485C2×#106C2×D4311yescharacteristic, complemented
486C2×C4⋊C8C2×D4311yescharacteristic, complemented
487#417—438no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—438no—
497C2×#102C2×D4311yescharacteristic
498C2×#102C2×D4311yescharacteristic
499C2×C22⋊C8—431no—
500C2×C22⋊C8—431no—
501C2×#97—431no—
502C43C2×#330611yescharacteristic, complemented, Sylow
503C25—861no—
504C2×#41—434no—
505C2×#41—862no—
506C2×#41—868no—
507C2×#41—864no—
508C2×#41—1722no—
509C2×#41—1728no—
510C22×Q8—21no—
511C22×Q8—431no—
512C22×D4—434no—
513C22×D4—431no—
514C22×D4—431no—
515C22×D4—431no—
516C22×D4—861no—
517C22×D4—861no—
518C22×D4—861no—
519C22×D4—862no—
520C22×D4—861no—
521C22×D4—864no—
522C22×D4—861no—
523C22×D4—1722no—
524C22×D4C22×D4311yescharacteristic
525C23×C4—21no—
526C23×C4—431no—
527C23×C4—431no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4—861no—
532C2×SD16—434no—
533C2×SD16—1722no—
534C2×D8—434no—
535C2×D8—434no—
536C2×D8—864no—
537C2×D8—1722no—
538C2×M16—434no—
539C2×M16—1722no—
540C22×C8—431no—
541C22×C8—431no—
542C22×C8—434no—
543C22×C8—1722no—
544C22×C8C22×D4311yescharacteristic
545C22×C8C22×D4311yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8C22×D4314yescomplemented
548#124—434no—
549#124—862no—
550#123—868no—
551#123—868no—
552#123—868no—
553C22⋊Q8—434no—
554C22⋊Q8—862no—
555C22⋊Q8—868no—
556#121—434no—
557#121—434no—
558#121—434no—
559#121—868no—
560#121—862no—
561#121—862no—
562#121—862no—
563#120—868no—
564C4×D4—22no—
565C4×D4—434no—
566C4×D4—434no—
567C4×D4—434no—
568C4×D4—862no—
569C4×D4C22×D4314yes—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—434no—
574C2×C4⋊C4—434no—
575C2×C4⋊C4—862no—
576C2×C4⋊C4—862no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C4⋊C4C22×D4311yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—431no—
585C2×C22⋊C4—431no—
586C2×C22⋊C4—868no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C42C22×D4311yescharacteristic
595#106—434no—
596#106C22×D4314yescomplemented
597#106C22×D4314yescomplemented
598C4⋊C8C22×D4314yescomplemented
599#103—434no—
600#103—434no—
601#103—434no—
602#102—434no—
603#102—434no—
604#102—434no—
605#102—434no—
606#102—434no—
607#102C22×D4314yes—
608#102C22×D4314yes—
609C22⋊C8—434no—
610C22⋊C8—434no—
611#97—434no—
612C24—21no—
613C24—431no—
614C24—431no—
615C24—864no—
616C24—861no—
617C24—861no—
618C24—3442no—
619C24—1724no—
620C24—1724no—
621#41—868no—
622#41—1724no—
623#41—1728no—
624#41—17232no—
625C2×Q8—24no—
626C2×Q8—44no—
627C2×Q8—432no—
628C2×Q8—861no—
629C2×Q8—862no—
630C2×Q8—862no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—434no—
634C2×D4—432no—
635C2×D4—432no—
636C2×D4—864no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—864no—
640C2×D4—864no—
641C2×D4—868no—
642C2×D4—864no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—862no—
646C2×D4—862no—
647C2×D4—862no—
648C2×D4—862no—
649C2×D4—3442no—
650C2×D4—1724no—
651C2×D4—1724no—
652C2×D4—1724no—
653C2×D4—1728no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4#1062190214yescomplemented
657C2×D4C23×D4312yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—82no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—432no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—864no—
670C22×C4—864no—
671C22×C4—864no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—864no—
679C22×C4—1724no—
680C22×C4—1724no—
681C22×C4—1724no—
682C22×C4—1724no—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686SD16—1724no—
687D8—868no—
688D8—1724no—
689M16—1724no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—432no—
693C2×C8—432no—
694C2×C8—862no—
695C2×C8—862no—
696C2×C8—1724no—
697C2×C8C23×D4312yes—
698C2×C8C23×D4312yes—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—434no—
704C4⋊C4—432no—
705C4⋊C4—864no—
706C4⋊C4—864no—
707C4⋊C4—864no—
708C4⋊C4—861no—
709C4⋊C4C23×D4312yes—
710C4⋊C4C23×D4312yes—
711C4⋊C4C23×D4312yes—
712C22⋊C4—24no—
713C22⋊C4—434no—
714C22⋊C4—434no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—864no—
722C42D4×D4312yes—
723C42C23×D4312yes—
724C23—22no—
725C23—24no—
726C23—42no—
727C23—42no—
728C23—434no—
729C23—432no—
730C23—432no—
731C23—862no—
732C23—862no—
733C23—862no—
734C23—862no—
735C23—862no—
736C23—862no—
737C23—862no—
738C23—34416no—
739C23—3444no—
740C23—1728no—
741C23—1728no—
742C23—1722no—
743C23—1722no—
744C23—1722no—
745C23—1722no—
746C23—1722no—
747C23—1722no—
748C23C2×D4×D4311yescharacteristic
749Q8—48no—
750Q8—862no—
751Q8—862no—
752Q8—1722no—
753D4—22no—
754D4—24no—
755D4—868no—
756D4—862no—
757D4—862no—
758D4—862no—
759D4—862no—
760D4—3444no—
761D4—1728no—
762D4—1728no—
763D4—1728no—
764D4—1728no—
765D4—1722no—
766D4—1722no—
767D4C2×#1062190214yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—84no—
777C2×C4—432no—
778C2×C4—432no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—864no—
786C2×C4—864no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—1728no—
790C2×C4—1728no—
791C2×C4—1728no—
792C2×C4—1728no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4C2×D4×D4312yes—
796C2×C4C2×D4×D4312yes—
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4C2×#1062190212yes—
799C2×C4#1306337112yes—
800C2×C4C24×D4311yescharacteristic
801C8—22no—
802C8—22no—
803C8—862no—
804C8—862no—
805C22—24no—
806C22—42no—
807C22—42no—
808C22—48no—
809C22—434no—
810C22—862no—
811C22—862no—
812C22—868no—
813C22—862no—
814C22—862no—
815C22—862no—
816C22—34416no—
817C22—3444no—
818C22—3444no—
819C22—1722no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1724no—
826C22#1458354012yes—
827C22AGL(1,ℤ/8)×D4312yes—
828C22#1458370512yes—
829C22C22×D4×D4311yescharacteristic
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—862no—
836C4—862no—
837C4—1722no—
838C4—1722no—
839C4#1458354012yes—
840C4C22×#1062190211yescharacteristic
841C4C2×#1306337111yescharacteristic
842C2—44no—
843C2—864no—
844C2—3442no—
845C2—3442no—
846C2—1722no—
847C2#1914655314yesdirect product factor
848C2C2×#1458354011yescharacteristic
849C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
850C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#476C2
socleC23×C43C22×D4
hypercenterC2×#476D43
hypocenterC43C2×#3306
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×#14583552C2semidirect
2. C2×#14583544C2semidirect
3. #19146553C2direct (N × H)
4. C2×#14583261C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583231C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583034C2semidirect
12. C2×#14583009C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582897C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#476C2semidirect
20. C22×#10621873C22semidirect
23. C22×#10621872C22semidirect
26. #14583552C22semidirect
28. #14583544C22semidirect
37. C2×#13063300C22semidirect
41. C2×C4×D172C22semidirect
43. C2×C4⋊C4×D43C22semidirect
45. #14583261C22semidirect
46. #14583231C22semidirect
47. #14583219C22semidirect
48. #14583153C22semidirect
49. #14583129C22semidirect
50. #14583115C22semidirect
51. #14583045C22semidirect
52. #14583034C22semidirect
53. #14583009C22semidirect
54. #14582969C22semidirect
55. C2×#13063256C22semidirect
56. #14582897C22semidirect
57. C2×#13063250C22semidirect
58. C2×#13063248C22semidirect
59. C2×#13063248C22semidirect
64. C2×#13063245C22semidirect
65. #102×D43C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×#13063236C22semidirect
69. C2×C4⋊Q8×C43C22semidirect
71. C43×#476C22semidirect
72. C2×#106×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×C4⋊C8×C43C22semidirect
104. C2×#10621873C23semidirect
110. C2×#10621872C23semidirect
128. #13063300C23semidirect
134. C4×D172C23semidirect
143. C4⋊C4×D43C23semidirect
154. #13063256C23semidirect
155. #13063250C23semidirect
156. #13063248C23semidirect
157. #13063248C23semidirect
162. #13063245C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. #13063236C23semidirect
172. C4⋊Q8×C43C23semidirect
181. #106×C43C23semidirect
182. #106×C43C23semidirect
183. C4⋊C8×C43C23semidirect
199. C2×D4×C43#41semidirect
326. D4×C43C2×#41semidirect
423. C2×#476D43semidirect
434. C2×C43#3306semidirect
454. C2×C4⋊Q8C2×D43semidirect
475. #476C2×D43semidirect
484. C2×#106C2×D43semidirect
485. C2×#106C2×D43semidirect
486. C2×C4⋊C8C2×D43semidirect
502. C43C2×#3306semidirect
547. C4⋊Q8C22×D43semidirect
596. #106C22×D43semidirect
597. #106C22×D43semidirect
598. C4⋊C8C22×D43semidirect
656. C2×D4#10621902semidirect
767. D4C2×#10621902semidirect
847. C2#19146553direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835522
C2×#145835442
#191465532
C2×#145832612
C2×#145832192
C2×#145832312
C2×#145831532
C2×#145831292
C2×#145831152
C2×#145830452
C2×#145830342
C2×#145830092
C2×#145829692
C2×#145828972
C2×#102×D432
C2×C43×#4762
C2×#330643