Finite Group Databasebeta

← C2×#19146739 #25973158

Subgroups — C2×#19146739 #25973158

Order 11008.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583593C211yesmaximal, characteristic, complemented
2C2×#14583533C211yesmaximal, characteristic, complemented
3#19146739C2116yesmaximal, direct product factor
4C2×#14583262C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583202C211yesmaximal, characteristic, complemented
7C2×#14583150C211yesmaximal, characteristic, complemented
8C2×#14583136C211yesmaximal, characteristic, complemented
9C2×#14583093C211yesmaximal, characteristic, complemented
10C2×#14583035C211yesmaximal, characteristic, complemented
11C2×#14583034C211yesmaximal, characteristic, complemented
12C2×#14583010C211yesmaximal, characteristic, complemented
13C2×#14582973C211yesmaximal, characteristic, complemented
14C2×#14582903C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C22×D4×D43—21no—
19C22×D4×D43C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic, complemented
22C22×#10621882C2211yescharacteristic, complemented
23C22×#10621877C2211yescharacteristic, complemented
24C22×C8×D43C2211yescharacteristic, complemented
25#14583593—24no—
26#14583593C2218yescomplemented
27#14583533—24no—
28#14583533C2218yescomplemented
29C2×#13063321C2211yescharacteristic
30C2×#13063319—21no—
31C2×#13063316C2211yescharacteristic, complemented
32C2×#13063307—21no—
33C2×#13063300C2211yescharacteristic
34C2×#13063300C2211yescharacteristic, complemented
35C2×#13063299C2211yescharacteristic, complemented
36C2×#13063298—21no—
37C2×#13063298—21no—
38C2×#13063295—21no—
39C2×#13063293—21no—
40C2×C4×D172—21no—
41C2×#13063287C2211yescharacteristic
42C2×#13063287C2211yescharacteristic, complemented
43C2×C4×C22⋊D43C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic, complemented
45#14583262C2218yescomplemented
46#14583219C2218yescomplemented
47#14583202C2218yescomplemented
48#14583150C2218yescomplemented
49#14583136C2218yescomplemented
50#14583093C2218yescomplemented
51#14583035C2218yescomplemented
52#14583034C2218yescomplemented
53#14583010C2218yescomplemented
54#14582973C2218yescomplemented
55C2×#13063256C2211yescharacteristic, complemented
56C2×Dic43⋊C8C2211yescharacteristic, complemented
57#14582903C2218yescomplemented
58C2×#13063247C2211yescharacteristic
59C2×#13063247C2211yescharacteristic, complemented
60C2×#13063246C2211yescharacteristic, complemented
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65C2×#13063245C2211yescharacteristic, complemented
66#102×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×#13063235C2211yescharacteristic, complemented
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic, complemented
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C24×D43—21no—
79C22×D172—24no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172—22no—
84C22×D172—42no—
85C22×D172C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×D172C2314yes—
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C2×D4×D43—28no—
95C2×D4×D43—24no—
96C2×D4×D43—22no—
97C2×D4×D43—42no—
98C2×D4×D43—48no—
99C2×D4×D43C2314yes—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104C2×D344—24no—
105C2×D344—42no—
106C2×D344C2314yes—
107C2×D344C2314yescomplemented
108C2×#10621882—42no—
109C2×#10621882C2314yescomplemented
110C2×#10621877—42no—
111C2×#10621877C2314yescomplemented
112C22×C43⋊C8C2311yescharacteristic
113C22×C43⋊C8C2311yescharacteristic
114C2×C8×D43—42no—
115C2×C8×D43C2314yescomplemented
116#13063321—22no—
117#13063321C2314yes—
118#13063319—28no—
119#13063316—22no—
120#13063316C2314yescomplemented
121#13063307—28no—
122#13063300—22no—
123#13063300—22no—
124#13063300C2314yes—
125#13063300C2314yescomplemented
126#13063299—22no—
127#13063299C2314yescomplemented
128#13063298—28no—
129#13063298—28no—
130#13063295—28no—
131#13063293—28no—
132C4×D172—28no—
133#13063287—22no—
134#13063287—22no—
135#13063287C2314yes—
136#13063287C2314yescomplemented
137C4×C22⋊D43D414yes—
138C4×C22⋊D43C2314yes—
139C2×C4⋊Dic43—21no—
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4D411yescharacteristic
144C4⋊C4×D43—22no—
145C4⋊C4×D43C2314yescomplemented
146C2×C22⋊Dic43D411yescharacteristic
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4D411yescharacteristic
153C2×C4×Dic43C2311yescharacteristic
154#13063256C2314yescomplemented
155Dic43⋊C8C2314yescomplemented
156#13063247C2314yes—
157#13063247C2314yescomplemented
158#13063246C2314yescomplemented
159#13063245C2314yes—
160#13063245C2314yes—
161#13063245C2314yescomplemented
162#13063245C2314yescomplemented
163#13063245C2314yescomplemented
164(C2×D43)⋊C8C2314yescomplemented
165#13063235C2314yescomplemented
166C22×D4×C43—21no—
167C22×D4×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171#121×C43—22no—
172#121×C43C2314yes—
173#117×C43—22no—
174#117×C43C2314yescomplemented
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181#107×C43C2314yescomplemented
182#106×C43C2314yescomplemented
183#102×C43C2314yescomplemented
184#102×C43C2314yescomplemented
185C22⋊C8×C43C2314yescomplemented
186C24×C43—21no—
187C24×C43C2×D411yescharacteristic
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—24no—
192C23×D43—24no—
193C23×D43—44no—
194C23×D43—44no—
195C23×D43—44no—
196C23×D43—44no—
197C23×D43—82no—
198C23×D43—82no—
199C23×D43C2×D411yescharacteristic
200C2×D4×C43—21no—
201C2×D4×C43—24no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—44no—
205C2×D4×C43C2412yes—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2412yes—
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—82no—
223C2×C22⋊D43—82no—
224C2×C22⋊D43C2×D414yes—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229D4×D43—28no—
230D4×D43—44no—
231D4×D43—48no—
232D4×D43—432no—
233C2×D172—21no—
234C2×D172—22no—
235C2×D172—21no—
236C2×D172—24no—
237C2×D172—21no—
238C2×D172—24no—
239C2×D172—24no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—28no—
245C2×D172—44no—
246C2×D172—44no—
247C2×D172—48no—
248C2×D172—44no—
249C2×D172—44no—
250C2×D172#4114yes—
251C2×D172C2412yes—
252C2×D172C2412yes—
253C2×D172C2412yes—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—24no—
257C2×C4×D43—24no—
258C2×C4×D43—24no—
259C2×C4×D43—44no—
260C2×C4×D43—82no—
261C2×C4×D43—82no—
262C2×C4×D43C2×D412yes—
263C2×C4×D43C2412yes—
264C2×C8×C43—22no—
265C2×C8×C43—22no—
266C2×C8×C43C2412yes—
267C2×C8×C43C2412yes—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43C2412yes—
272C4⋊C4×C43C2412yes—
273C4⋊C4×C43C2412yes—
274C22⋊C4×C43—24no—
275C22⋊C4×C43—24no—
276C42×C43—24no—
277C22⋊Dic43C2×D414yes—
278#10621882—44no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4C2×D414yes—
285C4⋊Dic43—21no—
286C4⋊Dic43—24no—
287C4⋊Dic43C2412yes—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290Dic43⋊C4C2×D414yes—
291C4×Dic43C2×D412yes—
292C4×Dic43C2412yes—
293#10621877—44no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—22no—
296C2×C43⋊C8C2412yes—
297C2×C43⋊C8C2412yes—
298D344—28no—
299D344—44no—
300C8×D43—44no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43C22×D412yes—
309C23×C43C22×D411yescharacteristic
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—24no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—48no—
317C22×D43—48no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—48no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—48no—
328C22×D43—84no—
329C22×D43—816no—
330C22×D43—84no—
331C22×D43—816no—
332C22×D43AGL(1,ℤ/8)14yes—
333C22×D43C22×D412yes—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—48no—
337D4×C43—42no—
338C2×C4×C43—22no—
339C2×C4×C43—24no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—42no—
346C2×C4×C43—42no—
347C2×C4×C43—42no—
348C2×C4×C43C22×D412yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C2×#4112yes—
351C2×C4×C43H(5,𝔽2)12yes—
352C2×C4×C43C2511yescharacteristic
353C22⋊D43—28no—
354C22⋊D43—48no—
355C22⋊D43—48no—
356C22⋊D43—84no—
357C22⋊D43—84no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—42no—
363C2×Dic43C22×D412yes—
364C2×Dic43C22×D412yes—
365C2×Dic43C22×D412yes—
366D172—24no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—22no—
371D172—22no—
372D172—48no—
373D172—48no—
374D172—48no—
375D172—42no—
376D172—42no—
377D172C2×#4114yes—
378C4×D43—24no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—48no—
382C4×D43—84no—
383C4×D43—84no—
384C8×C43—22no—
385C8×C43—22no—
386C43⋊C8—22no—
387C43⋊C8—22no—
388C2×#3318—431nomaximal, Sylow
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—44no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—84no—
397C22×C43#54612yes—
398C22×C43C2×AGL(1,ℤ/8)12yes—
399C22×C43#57612yes—
400C22×C43C23×D411yescharacteristic
401C2×D43—22no—
402C2×D43—28no—
403C2×D43—22no—
404C2×D43—24no—
405C2×D43—48no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—816no—
415C2×D43—816no—
416C2×D43—84no—
417C2×D43—84no—
418C2×D43C2×AGL(1,ℤ/8)14yes—
419C4×C43—22no—
420C4×C43—42no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43#54612yes—
424C4×C43C22×#4111yescharacteristic
425C4×C43C2×H(5,𝔽2)11yescharacteristic
426Dic43—22no—
427Dic43—22no—
428Dic43—22no—
429Dic43—42no—
430C2×#553—431no—
431C2×D42—431no—
432#3318—4316no—
433C2×#490—431no—
434C2×#481—431no—
435C2×#482D4311yescharacteristic, complemented
436C2×#478—431no—
437C2×#469—431no—
438C2×#466—431no—
439C2×#459—431no—
440C2×#447—431no—
441C2×#447—431no—
442C2×#442—431no—
443C2×#435—431no—
444C2×#418—431no—
445C22×#102—431no—
446C2×C43—42no—
447C2×C43—82no—
448C2×C43#331814yescomplemented
449C2×C43C2×#54611yescharacteristic
450C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
451C2×C43C2×#57611yescharacteristic
452D43—24no—
453D43—44no—
454D43—82no—
455D43—82no—
456C23×D4—431no—
457C23×D4—431no—
458C23×D4—861no—
459C22×D8—431no—
460C22×D8—431no—
461C22×D8—431no—
462C22×M16—431no—
463C23×C8—431no—
464#553—438no—
465#553—864no—
466D42—438no—
467D42—864no—
468C2×#127—431no—
469C2×#126—861no—
470C2×#125—431no—
471C2×#123—861no—
472C2×#121—431no—
473C2×#121—431no—
474C2×#121—431no—
475C2×#121—861no—
476C2×#121—861no—
477C2×#121C2×D4311yescharacteristic
478C2×#120—861no—
479C2×#120—861no—
480C2×C4×D4—431no—
481C2×C4×D4—431no—
482C2×C4×D4—431no—
483C2×C4×D4—861no—
484C2×#117C2×D4311yescharacteristic, complemented
485C22×C4⋊C4—431no—
486#490—438no—
487#482C2×D4318yescomplemented
488#481—438no—
489#478—438no—
490#469—438no—
491#466—438no—
492#459—438no—
493#447—438no—
494#447—438no—
495#442—438no—
496#435—438no—
497C2×#107C2×D4311yescharacteristic, complemented
498C2×#106—431no—
499C2×#106C2×D4311yescharacteristic, complemented
500C2×C4⋊C8—431no—
501#418—438no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—438no—
511C2×#102C2×D4311yescharacteristic, complemented
512C2×#102C2×D4311yescharacteristic, complemented
513C2×C22⋊C8—431no—
514C2×C22⋊C8C2×D4311yescharacteristic, complemented
515C2×#97—431no—
516C43C2×#331811yescharacteristic, complemented, Sylow
517C25—861no—
518C25—861no—
519C22×D4—21no—
520C22×D4—431no—
521C22×D4—434no—
522C22×D4—431no—
523C22×D4—431no—
524C22×D4—431no—
525C22×D4—434no—
526C22×D4—864no—
527C22×D4—861no—
528C22×D4—861no—
529C22×D4—862no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—864no—
534C22×D4—868no—
535C22×D4—861no—
536C22×D4—861no—
537C22×D4—862no—
538C22×D4—1722no—
539C22×D4—1722no—
540C22×D4—1728no—
541C22×D4C22×D4311yescharacteristic
542C23×C4—431no—
543C23×C4—861no—
544C23×C4—861no—
545C23×C4—861no—
546C23×C4C22×D4311yescharacteristic
547C2×D8—434no—
548C2×D8—434no—
549C2×D8—434no—
550C2×D8—864no—
551C2×D8—1722no—
552C2×D8—1722no—
553C2×M16—434no—
554C2×M16—1722no—
555C22×C8—431no—
556C22×C8—431no—
557C22×C8—434no—
558C22×C8—1722no—
559C22×C8C22×D4311yescharacteristic
560C22×C8C22×D4311yescharacteristic
561#127—434no—
562#127—862no—
563#126—868no—
564#125—434no—
565#125—862no—
566#123—868no—
567#121—22no—
568#121—434no—
569#121—434no—
570#121—434no—
571#121—868no—
572#121—868no—
573#121—862no—
574#121—862no—
575#121—862no—
576#121C22×D4314yes—
577#120—868no—
578#120—868no—
579C4×D4—434no—
580C4×D4—434no—
581C4×D4—434no—
582C4×D4—434no—
583C4×D4—868no—
584C4×D4—862no—
585C4×D4—862no—
586#117—22no—
587#117C22×D4314yescomplemented
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—434no—
591C2×C4⋊C4—862no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C4⋊C4C22×D4311yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—431no—
601C2×C22⋊C4—431no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C42—21no—
608C2×C42—431no—
609#107C22×D4314yescomplemented
610#106—434no—
611#106C22×D4314yescomplemented
612C4⋊C8—434no—
613#102—434no—
614#102—434no—
615#102—434no—
616#102—434no—
617#102—434no—
618#102—434no—
619#102—434no—
620#102—434no—
621#102C22×D4314yescomplemented
622#102C22×D4314yescomplemented
623C22⋊C8—434no—
624C22⋊C8C22×D4314yescomplemented
625#97—434no—
626C24—21no—
627C24—431no—
628C24—864no—
629C24—861no—
630C24—864no—
631C24—861no—
632C24—861no—
633C24—3442no—
634C24—3442no—
635C24—1724no—
636C24—1724no—
637C24—1724no—
638C24—1724no—
639C24D4×D4311yescharacteristic
640C2×D4—24no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—44no—
645C2×D4—434no—
646C2×D4—434no—
647C2×D4—432no—
648C2×D4—432no—
649C2×D4—432no—
650C2×D4—868no—
651C2×D4—864no—
652C2×D4—864no—
653C2×D4—864no—
654C2×D4—864no—
655C2×D4—864no—
656C2×D4—868no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—861no—
660C2×D4—861no—
661C2×D4—864no—
662C2×D4—861no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—862no—
666C2×D4—862no—
667C2×D4—862no—
668C2×D4—3442no—
669C2×D4—3442no—
670C2×D4—1724no—
671C2×D4—1728no—
672C2×D4—1724no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1724no—
676C2×D4—1728no—
677C2×D4—1724no—
678C2×D4—1724no—
679C2×D4—17232no—
680C2×D4C23×D4312yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—864no—
692C22×C4—864no—
693C22×C4—864no—
694C22×C4—862no—
695C22×C4—862no—
696C22×C4—861no—
697C22×C4—3442no—
698C22×C4—3442no—
699C22×C4—1724no—
700C22×C4D4×D4312yes—
701C22×C4D4×D4311yescharacteristic
702C22×C4C23×D4312yes—
703C22×C4C23×D4311yescharacteristic
704D8—868no—
705D8—1724no—
706D8—1724no—
707M16—1724no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—432no—
711C2×C8—432no—
712C2×C8—862no—
713C2×C8—862no—
714C2×C8—1724no—
715C2×C8C23×D4312yes—
716C2×C8C23×D4312yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—434no—
721C4⋊C4—432no—
722C4⋊C4—864no—
723C4⋊C4—864no—
724C4⋊C4—864no—
725C4⋊C4—861no—
726C4⋊C4C23×D4312yes—
727C4⋊C4C23×D4312yes—
728C4⋊C4C23×D4312yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—434no—
732C22⋊C4—434no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
738C42—24no—
739C42—432no—
740C42—432no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—434no—
749C23—432no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—864no—
754C23—862no—
755C23—862no—
756C23—3444no—
757C23—3444no—
758C23—34416no—
759C23—34416no—
760C23—1728no—
761C23—1728no—
762C23—1728no—
763C23—1728no—
764C23—1722no—
765C23—1722no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23—1722no—
771C23—1722no—
772C23C2×D4×D4312yes—
773C23C2×D4×D4311yescharacteristic
774D4—22no—
775D4—22no—
776D4—48no—
777D4—42no—
778D4—434no—
779D4—868no—
780D4—862no—
781D4—862no—
782D4—862no—
783D4—862no—
784D4—862no—
785D4—864no—
786D4—3444no—
787D4—3444no—
788D4—1728no—
789D4—1728no—
790D4—1728no—
791D4—1728no—
792D4—1728no—
793D4—1722no—
794D4—1722no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—864no—
814C2×C4—862no—
815C2×C4—3444no—
816C2×C4—3444no—
817C2×C4—1728no—
818C2×C4—1722no—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4#41×D4312yes—
822C2×C4#1306337112yes—
823C2×C4C24×D4311yescharacteristic
824C8—22no—
825C8—22no—
826C8—862no—
827C8—862no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—84no—
836C22—434no—
837C22—862no—
838C22—862no—
839C22—868no—
840C22—864no—
841C22—34416no—
842C22—34416no—
843C22—3444no—
844C22—3444no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1728no—
854C22#1458354112yes—
855C22AGL(1,ℤ/8)×D4312yes—
856C22#1458370112yes—
857C22C22×D4×D4311yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—862no—
863C4—862no—
864C4—862no—
865C4—1722no—
866C4#1458354112yes—
867C4C2×#41×D4311yescharacteristic
868C4C2×#1306337111yescharacteristic
869C2—42no—
870C2—82no—
871C2—864no—
872C2—3442no—
873C2—3442no—
874C2—1724no—
875C2#1914673914yesdirect product factor
876C2C2×#1458354111yescharacteristic
877C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
878C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
hypercenterC2×#482D43
hypocenterC43C2×#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#14583593C2semidirect
2. C2×#14583533C2semidirect
3. #19146739C2direct (N × H)
4. C2×#14583262C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583202C2semidirect
7. C2×#14583150C2semidirect
8. C2×#14583136C2semidirect
9. C2×#14583093C2semidirect
10. C2×#14583035C2semidirect
11. C2×#14583034C2semidirect
12. C2×#14583010C2semidirect
13. C2×#14582973C2semidirect
14. C2×#14582903C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#482C2semidirect
21. C22×D344C22semidirect
22. C22×#10621882C22semidirect
23. C22×#10621877C22semidirect
24. C22×C8×D43C22semidirect
26. #14583593C22semidirect
28. #14583533C22semidirect
31. C2×#13063316C22semidirect
34. C2×#13063300C22semidirect
35. C2×#13063299C22semidirect
42. C2×#13063287C22semidirect
44. C2×C4⋊C4×D43C22semidirect
45. #14583262C22semidirect
46. #14583219C22semidirect
47. #14583202C22semidirect
48. #14583150C22semidirect
49. #14583136C22semidirect
50. #14583093C22semidirect
51. #14583035C22semidirect
52. #14583034C22semidirect
53. #14583010C22semidirect
54. #14582973C22semidirect
55. C2×#13063256C22semidirect
56. C2×Dic43⋊C8C22semidirect
57. #14582903C22semidirect
59. C2×#13063247C22semidirect
60. C2×#13063246C22semidirect
63. C2×#13063245C22semidirect
64. C2×#13063245C22semidirect
65. C2×#13063245C22semidirect
66. #102×D43C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×#13063235C22semidirect
70. C2×#117×C43C22semidirect
71. C43×#482C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#102×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
107. C2×D344C23semidirect
109. C2×#10621882C23semidirect
111. C2×#10621877C23semidirect
115. C2×C8×D43C23semidirect
120. #13063316C23semidirect
125. #13063300C23semidirect
127. #13063299C23semidirect
136. #13063287C23semidirect
145. C4⋊C4×D43C23semidirect
154. #13063256C23semidirect
155. Dic43⋊C8C23semidirect
157. #13063247C23semidirect
158. #13063246C23semidirect
161. #13063245C23semidirect
162. #13063245C23semidirect
163. #13063245C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. #13063235C23semidirect
174. #117×C43C23semidirect
181. #107×C43C23semidirect
182. #106×C43C23semidirect
183. #102×C43C23semidirect
184. #102×C43C23semidirect
185. C22⋊C8×C43C23semidirect
435. C2×#482D43semidirect
448. C2×C43#3318semidirect
484. C2×#117C2×D43semidirect
487. #482C2×D43semidirect
497. C2×#107C2×D43semidirect
499. C2×#106C2×D43semidirect
511. C2×#102C2×D43semidirect
512. C2×#102C2×D43semidirect
514. C2×C22⋊C8C2×D43semidirect
516. C43C2×#3318semidirect
587. #117C22×D43semidirect
609. #107C22×D43semidirect
611. #106C22×D43semidirect
621. #102C22×D43semidirect
622. #102C22×D43semidirect
624. C22⋊C8C22×D43semidirect
875. C2#19146739direct (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×#145835332
#191467392
C2×#145832622
C2×#145832192
C2×#145832022
C2×#145831502
C2×#145831362
C2×#145830932
C2×#145830352
C2×#145830342
C2×#145830102
C2×#145829732
C2×#145829032
C2×#102×D432
C2×C43×#4822
C2×#331843