Finite Group Databasebeta

← #25116910

Subgroups — #25116910

Order 11008.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C22×#13063246C211yesmaximal, characteristic, complemented
4#19137609C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135295C211yesmaximal, characteristic, complemented
7#19135219C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134787C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic, complemented
21C2×(C22⋊D43)⋊C4—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23#14583033C418yescomplemented
24#14583009—24no—
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063246—24no—
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic, complemented
35C2×#13063245C2211yescharacteristic, complemented
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063236C2211yescharacteristic, complemented
38C2×#13063236C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic, complemented
40#14582797C2211yescharacteristic, complemented
41#14582791—21no—
42#14582776—21no—
43#14582773—21no—
44C4×C4⋊Dic43C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51C23×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C22×C22⋊C4×C43—21no—
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#386—21no—
58C43×#386—21no—
59C43×#380C2211yescharacteristic
60C43×#379—21no—
61C4×C22⋊C4×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—41no—
69C2×#10621882—41no—
70C2×#10621882C2×C414yescomplemented
71C2×#10621882C2×C414yescomplemented
72C22×C43⋊C8—22no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063299—22no—
80#13063299C2×C414yescomplemented
81C4×D172—22no—
82C4×D172—41no—
83(C22⋊D43)⋊C4—44no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96#13063256—22no—
97#13063256—41no—
98#13063246—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246C2×C414yescomplemented
102#13063246C2×C414yescomplemented
103#13063246D414yescomplemented
104#13063245—22no—
105#13063245—41no—
106C22⋊(C43⋊C8)C2×C414yescomplemented
107#13063236—22no—
108#13063236—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C25×C43—21no—
112C22×D4×C43—22no—
113C22×D4×C43—22no—
114C22×D4×C43—21no—
115C22×D4×C43—22no—
116C22×D4×C43—41no—
117C22×D4×C43—41no—
118C22×D4×C43C2×C414yescomplemented
119C22×D4×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43—21no—
123C23×C4×C43C2311yescharacteristic
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C4×D4×C43—41no—
127C4×D4×C43—41no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—44no—
138C2×C22⋊C4×C43D411yescharacteristic
139C2×C22⋊C4×C43D411yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142#95×C43—21no—
143#95×C43D411yescharacteristic
144#95×C43D411yescharacteristic
145C24×C43—21no—
146C24×C43—21no—
147C24×C43—24no—
148C24×C43—42no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—42no—
152C24×C43—81no—
153C24×C43—81no—
154C24×C43C2×D411yescharacteristic
155C23×D43—21no—
156C2×D4×C43—24no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—28no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43—44no—
171C2×D4×C43C22×C412yes—
172C2×D4×C43C22×C412yes—
173C2×D4×C43C2×D412yes—
174C2×D4×C43#4112yes—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43C22×C412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43#4112yes—
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—24no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—81no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172C22×C412yes—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×C4×D43—81no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—81no—
225C22⋊C4×C43—81no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230#10621882—28no—
231#10621882—44no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—42no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—81no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—42no—
241C4⋊Dic43C22×C412yes—
242C4⋊Dic43C2×D412yes—
243Dic43⋊C4—42no—
244C4×Dic43—42no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—44no—
255C2×C43⋊C8C22×C412yes—
256C2×C43⋊C8C22×C412yes—
257C2×C43⋊C8C2×D412yes—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—48no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—48no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43—84no—
282C23×C43—84no—
283C23×C43C4×D412yes—
284C23×C43AGL(1,ℤ/8)12yes—
285C23×C43AGL(1,ℤ/8)12yes—
286C23×C43C22×D411yescharacteristic
287C22×D43—22no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—48no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43C4×D414yescomplemented
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—84no—
328C2×C4×C43—84no—
329C2×C4×C43C4×D412yes—
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C22⋊D43—48no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—84no—
347D172—22no—
348D172—22no—
349D172—41no—
350D172—41no—
351C4×D43—84no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#22858—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—24no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—816no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43#44214yescomplemented
379C22×C43C2×C4×D411yescharacteristic
380C22×C43D4211yescharacteristic
381C22×C43#54611yescharacteristic
382C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C43#57611yescharacteristic
385C22×C43#57711yescharacteristic
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C2×D43—81no—
393C4×C43—22no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43—41no—
398C4×C43—81no—
399C4×C43—81no—
400C4×C43C2×C4×D411yescharacteristic
401C4×C43#51811yescharacteristic
402C4×C43#54611yescharacteristic
403C4×C43#55111yescharacteristic
404Dic43—42no—
405Dic43—42no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
409C22×#102—431no—
410#2361—431no—
411D4×C22⋊C4D4311yescharacteristic, complemented
412#1972—431no—
413#1936—431no—
414#1926—431no—
415#1893—431no—
416#1879—431no—
417#1879—431no—
418#1864—431no—
419#1853—431no—
420#1762—431no—
421#1752—431no—
422C2×C43—24no—
423C2×C43—44no—
424C2×C43—82no—
425C2×C43#235811yescharacteristic
426C2×C43C2×#44211yescharacteristic
427C2×C43#294611yescharacteristic
428C2×C43#326411yescharacteristic
429C2×C43#326511yescharacteristic
430C2×C43#330611yescharacteristic
431C2×C43#331811yescharacteristic
432D43—82no—
433C23×D4C2×D4311yescharacteristic
434C22×D8—431no—
435C22×D8—431no—
436C23×C8—431no—
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—861no—
440C2×C4×D4C2×D4311yescharacteristic
441C2×C4×D4C2×D4311yescharacteristic
442C22×C4⋊C4—431no—
443C22×C22⋊C4—21no—
444#447—438no—
445#442—864no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—864no—
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97—431no—
460#390—431no—
461#390C2×D4311yescharacteristic
462#390C2×D4311yescharacteristic
463#389—431no—
464#388—861no—
465#386—21no—
466#386—21no—
467#386—861no—
468#385—861no—
469#380C2×D4311yescharacteristic
470#379—21no—
471C4×C4⋊C4—431no—
472C4×C22⋊C4C2×D4311yescharacteristic
473#340—431no—
474#340—431no—
475#340—431no—
476#340—431no—
477#336—431no—
478#336—431no—
479C43#2285811yescharacteristic, complemented, Sylow
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—431no—
488C22×D4—861no—
489C22×D4C4×D4314yescomplemented
490C22×D4C22×D4311yescharacteristic
491C22×D4C22×D4311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—862no—
500C2×D8—862no—
501C2×D8—1721no—
502C2×D8—1721no—
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8—862no—
508C22×C8—862no—
509C22×C8—1721no—
510#121—434no—
511#121—862no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—862no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—862no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—1721no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—44no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C22⋊C4C22⋊D4311yescharacteristic
542C2×C42—861no—
543C2×C42C22×D4311yescharacteristic
544C2×C42C22×D4311yescharacteristic
545#106—862no—
546#106—1721no—
547#102—434no—
548#102—434no—
549#102—434no—
550#102—862no—
551#102—862no—
552#102—862no—
553#102—862no—
554#102—1721no—
555C22⋊C8—434no—
556#97—862no—
557#97—1721no—
558#95—21no—
559#95—861no—
560#95—861no—
561#95C22⋊D4311yescharacteristic
562#95C22⋊D4311yescharacteristic
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—861no—
573C24C2×C22⋊D4311yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—432no—
590C2×D4—864no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—1722no—
597C2×D4—1722no—
598C2×D4C2×C4×D4312yes—
599C2×D4C2×C4×D4312yes—
600C2×D4D4×D4312yes—
601C2×D4#1062190012yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—3441no—
618C22×C4—3441no—
619C22×C4—1722no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4C2×C4×D4312yes—
624C22×C4#1062189812yes—
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C2×C22⋊D4311yescharacteristic
629C22×C4C2×C22⋊D4311yescharacteristic
630C22×C4C23×D4311yescharacteristic
631D8—868no—
632D8—1724no—
633C2×C8—432no—
634C2×C8—432no—
635C2×C8—432no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—1724no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—432no—
651C4⋊C4—432no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—1722no—
657C4⋊C4—1722no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—864no—
668C22⋊C4—3441no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—1722no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—48no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—862no—
702C23—1721no—
703C23—1721no—
704C23—1721no—
705C23—1721no—
706C23—1721no—
707C23—1721no—
708C23C4×C22⋊D4312yes—
709C23#1306335012yes—
710C23#1306335112yes—
711C23C22×C22⋊D4311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—862no—
721D4—862no—
722D4—1728no—
723D4—1721no—
724D4—1721no—
725D4(C22⋊D43)⋊C414yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—3444no—
755C2×C4—3444no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4C4×C22⋊D4312yes—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4C2×#1062190011yescharacteristic
767C2×C4C2×#1062189811yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337011yescharacteristic
770C8—862no—
771C8—862no—
772C8—862no—
773C8—1721no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—3441no—
796C22—3441no—
797C22—3441no—
798C22—3441no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22#1458300914yescomplemented
803C22C2×C4×C22⋊D4311yescharacteristic
804C22D4×C22⋊D4311yescharacteristic
805C22#1458354311yescharacteristic
806C22C2×#1306335011yescharacteristic
807C22C2×#1306335111yescharacteristic
808C22#1458370211yescharacteristic
809C22#1458371011yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—3441no—
818C4—1722no—
819C4—1722no—
820C4C2×(C22⋊D43)⋊C411yescharacteristic
821C4#1458337211yescharacteristic
822C4#1458353911yescharacteristic
823C4#1458357511yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—3442no—
828C2#1913757411yescharacteristic
829C2C2×#1458300911yescharacteristic
830C2#1914342711yescharacteristic
831C2#1914607611yescharacteristic
832C2#1914608611yescharacteristic
833C2#1914655611yescharacteristic
834C2#1914673611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenterD4×C22⋊C4D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C22×#13063246C2semidirect
4. #19137609C2semidirect
5. #19135470C2semidirect
6. #19135295C2semidirect
7. #19135219C2semidirect
8. #19135021C2semidirect
9. #19134946C2semidirect
10. #19134943C2semidirect
11. #19134856C2semidirect
12. #19134787C2semidirect
13. #19134420C2semidirect
14. #19134373C2semidirect
15. D4×C22⋊C4×C43C2semidirect
20. C2×C4×D172C22semidirect
23. #14583033C4semidirect
25. C2×#13063256C22semidirect
26. C2×#13063256C22semidirect
34. C2×#13063245C22semidirect
35. C2×#13063245C22semidirect
37. C2×#13063236C22semidirect
38. C2×#13063236C22semidirect
39. #14582801C22semidirect
40. #14582797C22semidirect
44. C4×C4⋊Dic43C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582654C22semidirect
50. #14582654C22semidirect
70. C2×#10621882C2×C4semidirect
71. C2×#10621882C2×C4semidirect
80. #13063299C2×C4semidirect
101. #13063246C2×C4semidirect
102. #13063246C2×C4semidirect
103. #13063246D4semidirect
106. C22⋊(C43⋊C8)C2×C4semidirect
118. C22×D4×C43C2×C4semidirect
302. D4×C43C4×D4semidirect
378. C22×C43#442semidirect
411. D4×C22⋊C4D43semidirect
479. C43#22858semidirect
489. C22×D4C4×D43semidirect
725. D4(C22⋊D43)⋊C4semidirect
802. C22#14583009semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
C2×#145830092
C22×#130632462
#191376092
#191354702
#191352952
#191352192
#191350212
#191349462
#191349432
#191348562
#191347872
#191344202
#191343732
D4×C22⋊C4×C432
#2285843