Finite Group Databasebeta

← C2×#19146833 #25973434

Subgroups — C2×#19146833 #25973434

Order 11008.

2630 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×#14583612C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D43C211yesmaximal, characteristic, complemented
3#19146833C2116yesmaximal, direct product factor
4C2×#14583244C211yesmaximal, characteristic, complemented
5C2×#14583223C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583152C211yesmaximal, characteristic, complemented
9C2×#14583151C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583034C211yesmaximal, characteristic, complemented
12C2×#14583033C211yesmaximal, characteristic, complemented
13C2×#14582979C211yesmaximal, characteristic, complemented
14C2×#14582975C211yesmaximal, characteristic, complemented
15C2×#14582902C211yesmaximal, characteristic, complemented
16C2×C43×#418C211yesmaximal, characteristic, complemented
17C23×C22⋊D43—21no—
18C22×D4×D43C2211yescharacteristic
19C22×D344C2211yescharacteristic, complemented
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic, complemented
22C22×#10621872C2211yescharacteristic, complemented
23#14583612—24no—
24#14583612C2218yescomplemented
25D4×C22⋊D43—24no—
26D4×C22⋊D43C2218yescomplemented
27C2×#13063324C2211yescharacteristic, complemented
28C2×#13063321C2211yescharacteristic
29C2×#13063313—21no—
30C2×#13063311—21no—
31C2×#13063300C2211yescharacteristic, complemented
32C2×#13063299C2211yescharacteristic
33C2×#13063299C2211yescharacteristic, complemented
34C2×#13063298—21no—
35C2×#13063297—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063294—21no—
38C2×#13063293—21no—
39C2×D4×Dic43C2211yescharacteristic
40C2×#13063287C2211yescharacteristic, complemented
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×#13063283C2211yescharacteristic, complemented
43C2×#13063282—21no—
44#14583244C2218yescomplemented
45#14583223C2218yescomplemented
46#14583222C2218yescomplemented
47#14583187C2218yescomplemented
48#14583152C2218yescomplemented
49#14583151C2218yescomplemented
50#14583093C2218yescomplemented
51#14583034C2218yescomplemented
52#14583033C2218yescomplemented
53#14582979C2218yescomplemented
54#14582975C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59#14582902C2218yescomplemented
60C2×#13063247C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65C2×#13063245C2211yescharacteristic, complemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C23×D4×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic, complemented
71C2×#117×C43C2211yescharacteristic, complemented
72C43×#418C2218yescomplemented
73C2×#102×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×Dic86—21no—
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C22⋊D43—28no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—48no—
90C22×C22⋊D43D411yescharacteristic
91C2×D4×D43—24no—
92C2×D4×D43—22no—
93C2×D4×D43—42no—
94C2×D4×D43C2314yes—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×D344—42no—
99C2×D344C2314yescomplemented
100C2×#10621882—24no—
101C2×#10621882—42no—
102C2×#10621882C2314yes—
103C2×#10621882C2314yescomplemented
104C2×#10621872—42no—
105C2×#10621872C2314yescomplemented
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108#13063324—22no—
109#13063324C2314yescomplemented
110#13063321—22no—
111#13063321C2314yes—
112#13063313—28no—
113#13063311—28no—
114#13063300—22no—
115#13063300C2314yescomplemented
116#13063299—22no—
117#13063299—22no—
118#13063299C2314yes—
119#13063299C2314yescomplemented
120#13063298—28no—
121#13063297—28no—
122#13063296—22no—
123#13063296C2314yes—
124#13063294—28no—
125#13063293—28no—
126D4×Dic43—22no—
127D4×Dic43C2314yes—
128#13063287—22no—
129#13063287C2314yescomplemented
130C4×C22⋊D43D414yes—
131C4×C22⋊D43C2314yes—
132#13063283—22no—
133#13063283C2314yescomplemented
134#13063282—28no—
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4D411yescharacteristic
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)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×C4×Dic43—21no—
149C2×C4×Dic43C2311yescharacteristic
150#13063258C2314yescomplemented
151#13063257C2314yescomplemented
152#13063256C2314yescomplemented
153Dic43⋊C8C2314yescomplemented
154#13063247C2314yescomplemented
155#13063247C2314yescomplemented
156#13063246C2314yes—
157#13063246C2314yescomplemented
158#13063245C2314yescomplemented
159#13063245C2314yescomplemented
160C22⋊(C43⋊C8)C2314yescomplemented
161(C2×D43)⋊C8C2314yescomplemented
162C8×Dic43C2314yescomplemented
163C25×C43—21no—
164C22×D4×C43—24no—
165C22×D4×C43—21no—
166C22×D4×C43—22no—
167C22×D4×C43—42no—
168C22×D4×C43C2311yescharacteristic
169C22×D4×C43C2314yes—
170C22×D4×C43C2311yescharacteristic
171C23×C4×C43C2311yescharacteristic
172C2×M16×C43—42no—
173C2×M16×C43C2314yescomplemented
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176#117×C43—22no—
177#117×C43C2314yescomplemented
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C42×C43—21no—
182#102×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yescomplemented
185#102×C43C2314yescomplemented
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—24no—
189C24×C43—44no—
190C24×C43—44no—
191C24×C43—82no—
192C24×C43C2×D411yescharacteristic
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—24no—
196C23×D43—44no—
197C23×D43—44no—
198C23×D43—82no—
199C23×D43C2×D411yescharacteristic
200C2×D4×C43—21no—
201C2×D4×C43—24no—
202C2×D4×C43—21no—
203C2×D4×C43—22no—
204C2×D4×C43—28no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—44no—
208C2×D4×C43—44no—
209C2×D4×C43—48no—
210C2×D4×C43#4114yes—
211C2×D4×C43C2412yes—
212C2×D4×C43C2412yes—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D412yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2411yescharacteristic
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—432no—
232C2×C22⋊D43—44no—
233C2×C22⋊D43—82no—
234C2×C22⋊D43—82no—
235C2×C22⋊D43C2×D414yes—
236C22×Dic43—24no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—44no—
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243D4×D43—28no—
244D4×D43—44no—
245D4×D43—48no—
246C2×D172—21no—
247C2×D172—21no—
248C2×D172—24no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—22no—
252C2×D172—22no—
253C2×D172—82no—
254C2×D172C2412yes—
255C2×D172C2412yes—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—44no—
260C2×C4×D43C2×D412yes—
261C2×C4×D43C2412yes—
262C2×Dic86—24no—
263C2×Dic86—82no—
264M16×C43—44no—
265C2×C8×C43—22no—
266C2×C8×C43—22no—
267C2×C8×C43C2412yes—
268C2×C8×C43C2412yes—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43C2412yes—
272C4⋊C4×C43C2412yes—
273C22⋊C4×C43—24no—
274C42×C43—24no—
275C22⋊Dic43—24no—
276C22⋊Dic43—24no—
277C22⋊Dic43C2×D414yes—
278#10621882—28no—
279#10621882—44no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4C2×D414yes—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43C2412yes—
289C4⋊Dic43C2412yes—
290Dic43⋊C4—24no—
291Dic43⋊C4C2×D414yes—
292C4×Dic43—24no—
293C4×Dic43C2×D412yes—
294C4×Dic43C2412yes—
295C2×C43⋊C8—22no—
296C2×C43⋊C8—22no—
297C2×C43⋊C8C2412yes—
298C2×C43⋊C8C2412yes—
299D344—44no—
300#10621872—44no—
301C23×C43—24no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—48no—
308C23×C43—48no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—84no—
315C23×C43—816no—
316C23×C43C22×D412yes—
317C23×C43C22×D411yescharacteristic
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—48no—
324C22×D43—48no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—84no—
332C22×D43—816no—
333C22×D43C22×D412yes—
334D4×C43—24no—
335D4×C43—22no—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—48no—
339D4×C43—42no—
340D4×C43C2×#4114yes—
341C2×C4×C43—22no—
342C2×C4×C43—24no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43C22×D412yes—
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4112yes—
352C2×C4×C43H(5,𝔽2)12yes—
353C2×C4×C43C2511yescharacteristic
354C22⋊D43—28no—
355C22⋊D43—48no—
356C22⋊D43—48no—
357C22⋊D43—48no—
358C22⋊D43—48no—
359C22⋊D43—84no—
360C22⋊D43—84no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43—48no—
368C2×Dic43AGL(1,ℤ/8)14yes—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—42no—
377D172—42no—
378D172—84no—
379C4×D43—24no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—48no—
383Dic86—84no—
384C8×C43—22no—
385C8×C43—22no—
386C43⋊C8—22no—
387C43⋊C8—22no—
388C2×#3325—431nomaximal, Sylow
389C22×C43—24no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—42no—
394C22×C43—48no—
395C22×C43—44no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—816no—
401C22×C43—84no—
402C22×C43#54612yes—
403C22×C43C2×AGL(1,ℤ/8)12yes—
404C22×C43#57612yes—
405C22×C43C23×D411yescharacteristic
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—44no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—816no—
417C2×D43—84no—
418C2×D43—84no—
419C4×C43—22no—
420C4×C43—42no—
421C4×C43—42no—
422C4×C43#54612yes—
423C4×C43C22×#4111yescharacteristic
424C4×C43C2×H(5,𝔽2)11yescharacteristic
425Dic43—22no—
426Dic43—22no—
427Dic43—42no—
428Dic43—42no—
429Dic43C2×AGL(1,ℤ/8)14yes—
430C2×#555—431no—
431C2×D42—431no—
432#3325—4316no—
433C2×#486—431no—
434C2×#482—431no—
435C2×#482—431no—
436C2×#476—431no—
437C2×#469—431no—
438C2×#469—431no—
439C2×#459—431no—
440C2×#447—431no—
441C2×#447—431no—
442C2×C4×D8—431no—
443C2×#436—431no—
444C2×#418—431no—
445C2×#418D4311yescharacteristic, complemented
446C2×C43—44no—
447C2×C43—42no—
448C2×C43—82no—
449C2×C43#332514yescomplemented
450C2×C43C2×#54611yescharacteristic
451C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C43C2×#57611yescharacteristic
453D43—42no—
454D43—82no—
455D43—82no—
456C23×D4—431no—
457C23×D4—861no—
458C23×D4C2×D4311yescharacteristic
459C22×D8—431no—
460C22×D8—431no—
461C22×D8—431no—
462C22×M16—431no—
463C22×M16C2×D4311yescharacteristic, complemented
464#555—438no—
465#555—864no—
466D42—438no—
467D42—864no—
468C2×C4⋊Q8—431no—
469C2×#127—431no—
470C2×#124—861no—
471C2×#124—861no—
472C2×#121—431no—
473C2×#121—431no—
474C2×#121—431no—
475C2×#121—431no—
476C2×#121—861no—
477C2×#121—861no—
478C2×#120—861no—
479C2×#120—861no—
480C2×C4×D4—431no—
481C2×C4×D4—431no—
482C2×C4×D4—431no—
483C2×#117—431no—
484C2×#117—861no—
485C2×#117C2×D4311yescharacteristic, complemented
486#486—438no—
487#482—438no—
488#482—438no—
489#476—438no—
490#469—438no—
491#469—438no—
492#459—438no—
493#447—438no—
494#447—438no—
495C4×D8—438no—
496#436—438no—
497C2×#107—431no—
498C2×#106—431no—
499C2×#106—431no—
500C2×C4⋊C8—431no—
501#418—438no—
502#418C2×D4318yescomplemented
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102C2×D4311yescharacteristic
510C2×#102C2×D4311yescharacteristic
511C2×#102C2×D4311yescharacteristic, complemented
512C2×#102C2×D4311yescharacteristic, complemented
513C2×C22⋊C8—431no—
514C2×C22⋊C8—431no—
515C2×C4×C8—431no—
516C43C2×#332511yescharacteristic, complemented, Sylow
517C25—21no—
518C25—861no—
519C22×Q8—861no—
520C22×D4—24no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—42no—
524C22×D4—431no—
525C22×D4—434no—
526C22×D4—431no—
527C22×D4—431no—
528C22×D4—861no—
529C22×D4—862no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—868no—
534C22×D4—864no—
535C22×D4—861no—
536C22×D4—861no—
537C22×D4—861no—
538C22×D4—1722no—
539C22×D4—1728no—
540C22×D4C22×D4311yescharacteristic
541C22×D4C22×D4314yes—
542C22×D4C22×D4311yescharacteristic
543C23×C4—431no—
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—42no—
554C2×M16—434no—
555C2×M16—1722no—
556C2×M16C22×D4314yescomplemented
557C22×C8—431no—
558C22×C8—431no—
559C22×C8C22×D4311yescharacteristic
560C22×C8C22×D4311yescharacteristic
561C4⋊Q8—434no—
562C4⋊Q8—862no—
563#127—434no—
564#127—862no—
565#124—868no—
566#124—868no—
567#121—434no—
568#121—434no—
569#121—434no—
570#121—434no—
571#121—868no—
572#121—862no—
573#121—868no—
574#121—862no—
575#121—862no—
576#121—862no—
577#120—868no—
578#120—868no—
579C4×D4—434no—
580C4×D4—434no—
581C4×D4—434no—
582C4×D4—434no—
583C4×D4—862no—
584C4×D4—862no—
585#117—22no—
586#117—434no—
587#117—868no—
588#117—862no—
589#117C22×D4314yescomplemented
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4C22×D4311yescharacteristic
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—431no—
598C2×C22⋊C4—431no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C42—21no—
607C2×C42—431no—
608C2×C42—861no—
609#107—434no—
610#106—434no—
611#106—434no—
612C4⋊C8—434no—
613#102—434no—
614#102—434no—
615#102—434no—
616#102—434no—
617#102—434no—
618#102—434no—
619#102C22×D4314yes—
620#102C22×D4314yes—
621#102C22×D4314yescomplemented
622#102C22×D4314yescomplemented
623C22⋊C8—434no—
624C22⋊C8—434no—
625C4×C8—434no—
626C24—21no—
627C24—21no—
628C24—24no—
629C24—44no—
630C24—44no—
631C24—82no—
632C24—431no—
633C24—864no—
634C24—861no—
635C24—861no—
636C24—3442no—
637C24—1724no—
638C24—1724no—
639C24D4×D4311yescharacteristic
640C2×Q8—864no—
641C2×Q8—3442no—
642C2×D4—28no—
643C2×D4—21no—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—48no—
651C2×D4—44no—
652C2×D4—434no—
653C2×D4—432no—
654C2×D4—432no—
655C2×D4—864no—
656C2×D4—864no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—868no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—862no—
667C2×D4—862no—
668C2×D4—862no—
669C2×D4—862no—
670C2×D4—3442no—
671C2×D4—3442no—
672C2×D4—3442no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1728no—
676C2×D4—1724no—
677C2×D4—17232no—
678C2×D4—1724no—
679C2×D4—1724no—
680C2×D4#1062189814yes—
681C2×D4C23×D4312yes—
682C2×D4C23×D4312yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—431no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—864no—
693C22×C4—864no—
694C22×C4—862no—
695C22×C4—862no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—1724no—
699C22×C4—1724no—
700C22×C4D4×D4312yes—
701C22×C4D4×D4311yescharacteristic
702C22×C4C23×D4312yes—
703C22×C4C23×D4311yescharacteristic
704D8—868no—
705D8—1724no—
706D8—1724no—
707M16—44no—
708M16—1724no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—432no—
712C2×C8—432no—
713C2×C8—862no—
714C2×C8—862no—
715C2×C8C23×D4312yes—
716C2×C8C23×D4312yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—434no—
720C4⋊C4—432no—
721C4⋊C4—432no—
722C4⋊C4—864no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4C23×D4312yes—
726C4⋊C4C23×D4312yes—
727C22⋊C4—24no—
728C22⋊C4—434no—
729C22⋊C4—434no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C42—24no—
738C42—432no—
739C42—432no—
740C42—864no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—22no—
747C23—48no—
748C23—48no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—84no—
755C23—816no—
756C23—432no—
757C23—862no—
758C23—862no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—3444no—
763C23—34416no—
764C23—1728no—
765C23—1728no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23—1722no—
771C23—1722no—
772C23C2×D4×D4312yes—
773C23C2×D4×D4311yescharacteristic
774Q8—3444no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—24no—
779D4—48no—
780D4—42no—
781D4—868no—
782D4—862no—
783D4—862no—
784D4—862no—
785D4—862no—
786D4—3444no—
787D4—3444no—
788D4—3444no—
789D4—1728no—
790D4—1728no—
791D4—1728no—
792D4—1728no—
793D4—1722no—
794D4—1722no—
795D4C2×#1062189814yes—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—434no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—1728no—
816C2×C4—1728no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4C2×#1062189812yes—
822C2×C4#1306337012yes—
823C2×C4C24×D4311yescharacteristic
824C8—22no—
825C8—22no—
826C8—862no—
827C8—862no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—48no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—84no—
841C22—862no—
842C22—862no—
843C22—862no—
844C22—34416no—
845C22—3444no—
846C22—3444no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1724no—
854C22#1458353912yes—
855C22AGL(1,ℤ/8)×D4312yes—
856C22#1458370312yes—
857C22C22×D4×D4311yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—434no—
862C4—862no—
863C4—862no—
864C4—1722no—
865C4—1722no—
866C4#1458353912yes—
867C4C22×#1062189811yescharacteristic
868C4C2×#1306337011yescharacteristic
869C2—42no—
870C2—44no—
871C2—82no—
872C2—3442no—
873C2—3442no—
874C2—1722no—
875C2#1914683314yesdirect product factor
876C2C2×#1458353911yescharacteristic
877C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
878C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
hypercenterC2×#418D43
hypocenterC43C2×#3325
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#14583612C2semidirect
2. C2×D4×C22⋊D43C2semidirect
3. #19146833C2direct (N × H)
4. C2×#14583244C2semidirect
5. C2×#14583223C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583152C2semidirect
9. C2×#14583151C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583034C2semidirect
12. C2×#14583033C2semidirect
13. C2×#14582979C2semidirect
14. C2×#14582975C2semidirect
15. C2×#14582902C2semidirect
16. C2×C43×#418C2semidirect
19. C22×D344C22semidirect
21. C22×#10621882C22semidirect
22. C22×#10621872C22semidirect
24. #14583612C22semidirect
26. D4×C22⋊D43C22semidirect
27. C2×#13063324C22semidirect
31. C2×#13063300C22semidirect
33. C2×#13063299C22semidirect
40. C2×#13063287C22semidirect
42. C2×#13063283C22semidirect
44. #14583244C22semidirect
45. #14583223C22semidirect
46. #14583222C22semidirect
47. #14583187C22semidirect
48. #14583152C22semidirect
49. #14583151C22semidirect
50. #14583093C22semidirect
51. #14583034C22semidirect
52. #14583033C22semidirect
53. #14582979C22semidirect
54. #14582975C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063257C22semidirect
57. C2×#13063256C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. #14582902C22semidirect
60. C2×#13063247C22semidirect
61. C2×#13063247C22semidirect
63. C2×#13063246C22semidirect
64. C2×#13063245C22semidirect
65. C2×#13063245C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×C8×Dic43C22semidirect
70. C22×M16×C43C22semidirect
71. C2×#117×C43C22semidirect
72. C43×#418C22semidirect
75. C2×#102×C43C22semidirect
76. C2×#102×C43C22semidirect
99. C2×D344C23semidirect
103. C2×#10621882C23semidirect
105. C2×#10621872C23semidirect
109. #13063324C23semidirect
115. #13063300C23semidirect
119. #13063299C23semidirect
129. #13063287C23semidirect
133. #13063283C23semidirect
150. #13063258C23semidirect
151. #13063257C23semidirect
152. #13063256C23semidirect
153. Dic43⋊C8C23semidirect
154. #13063247C23semidirect
155. #13063247C23semidirect
157. #13063246C23semidirect
158. #13063245C23semidirect
159. #13063245C23semidirect
160. C22⋊(C43⋊C8)C23semidirect
161. (C2×D43)⋊C8C23semidirect
162. C8×Dic43C23semidirect
173. C2×M16×C43C23semidirect
177. #117×C43C23semidirect
184. #102×C43C23semidirect
185. #102×C43C23semidirect
445. C2×#418D43semidirect
449. C2×C43#3325semidirect
463. C22×M16C2×D43semidirect
485. C2×#117C2×D43semidirect
502. #418C2×D43semidirect
511. C2×#102C2×D43semidirect
512. C2×#102C2×D43semidirect
516. C43C2×#3325semidirect
556. C2×M16C22×D43semidirect
589. #117C22×D43semidirect
621. #102C22×D43semidirect
622. #102C22×D43semidirect
875. C2#19146833direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836122
C2×D4×C22⋊D432
#191468332
C2×#145832442
C2×#145832232
C2×#145832222
C2×#145831872
C2×#145831522
C2×#145831512
C2×#145830932
C2×#145830342
C2×#145830332
C2×#145829792
C2×#145829752
C2×#145829022
C2×C43×#4182
C2×#332543