Finite Group Databasebeta

← #25116915

Subgroups — #25116915

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×#14583032C211yesmaximal, characteristic
2C2×#14583009C211yesmaximal, characteristic, complemented
3C22×#13063245C211yesmaximal, characteristic, complemented
4C22⋊C4×D172C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135291C211yesmaximal, characteristic, complemented
7#19135222C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134855C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15C43×#2361C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23#14583032C418yescomplemented
24#14583009—24no—
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063246C2211yescharacteristic, complemented
28C2×#13063246C2211yescharacteristic, complemented
29C2×#13063245—24no—
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063236C2211yescharacteristic, complemented
38C2×#13063236C2211yescharacteristic, complemented
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582777—21no—
42#14582777—21no—
43#14582759C2211yescharacteristic
44#14582754—21no—
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43—21no—
53C2×C4×D4×C43C2211yescharacteristic, complemented
54C22×C4⋊C4×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic, complemented
56C43×#389C2211yescharacteristic, complemented
57C43×#388—21no—
58C43×#386—21no—
59C43×#385—21no—
60C4×C4⋊C4×C43C2211yescharacteristic, complemented
61C4×C22⋊C4×C43C2211yescharacteristic
62C24×D43—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2×C414yescomplemented
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—41no—
77C2×#10621882—41no—
78C2×#10621882C2×C414yescomplemented
79C2×#10621882C2×C414yescomplemented
80C22×C43⋊C8—22no—
81C22×C43⋊C8—22no—
82C22×C43⋊C8—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—41no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C22⋊C4×D43—44no—
101#13063256—22no—
102#13063256—41no—
103#13063246—22no—
104#13063246—41no—
105#13063245—22no—
106#13063245—22no—
107#13063245—22no—
108#13063245C2×C414yescomplemented
109#13063245C2×C414yescomplemented
110#13063245D414yescomplemented
111C22⋊(C43⋊C8)C2×C414yescomplemented
112#13063236—22no—
113#13063236—41no—
114C43⋊#95—21no—
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43—21no—
119C23×C4×C43C2311yescharacteristic
120#121×C43—22no—
121#121×C43C2×C414yescomplemented
122C4×D4×C43—22no—
123C4×D4×C43—41no—
124C4×D4×C43—44no—
125C2×C4⋊C4×C43—22no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—41no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141#95×C43—21no—
142#95×C43—21no—
143#95×C43D411yescharacteristic
144#95×C43D411yescharacteristic
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—24no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43—42no—
154C23×D43—81no—
155C23×D43—81no—
156C2×D4×C43—21no—
157C2×D4×C43—24no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43C22×C412yes—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—81no—
177C22×C4×C43—81no—
178C22×C4×C43C22×C412yes—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43#4112yes—
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C22×Dic43—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—24no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—28no—
198C2×D172—42no—
199C2×D172—42no—
200C2×D172—44no—
201C2×D172—44no—
202C2×D172—44no—
203C2×D172C22×C412yes—
204C2×D172C22×C412yes—
205C2×D172C2×D412yes—
206C2×D172#4112yes—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43—81no—
212C2×C4×D43—81no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—42no—
218C4⋊C4×C43—42no—
219C4⋊C4×C43C22×C412yes—
220C4⋊C4×C43C2×D412yes—
221C22⋊C4×C43—24no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—81no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—42no—
232C22⋊Dic43—42no—
233#10621882—28no—
234#10621882—44no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—81no—
240(C2×D43)⋊C4—81no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
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—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43C4×D412yes—
270C23×C43AGL(1,ℤ/8)12yes—
271C23×C43AGL(1,ℤ/8)12yes—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—48no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—48no—
289C22×D43—84no—
290C22×D43—84no—
291C22×D43—84no—
292C22×D43—84no—
293C22×D43—84no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—48no—
297D4×C43—41no—
298D4×C43—41no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
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—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—84no—
327C2×C4×C43—84no—
328C2×C4×C43C4×D412yes—
329C2×C4×C43C23×C411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341D172—22no—
342D172—22no—
343D172—22no—
344D172—22no—
345D172—22no—
346D172—48no—
347D172—41no—
348D172—41no—
349D172C4×D414yescomplemented
350C4×D43—84no—
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—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43#44214yescomplemented
371C22×C43C2×C4×D411yescharacteristic
372C22×C43D4211yescharacteristic
373C22×C43#54611yescharacteristic
374C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C43#57611yescharacteristic
377C22×C43#57711yescharacteristic
378C2×D43—24no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—816no—
389C2×D43—81no—
390C2×D43—81no—
391C2×D43—81no—
392C2×D43—81no—
393C4×C43—22no—
394C4×C43—42no—
395C4×C43—41no—
396C4×C43—42no—
397C4×C43—41no—
398C4×C43—41no—
399C4×C43—41no—
400C4×C43—81no—
401C4×C43C2×C4×D411yescharacteristic
402C4×C43#51811yescharacteristic
403C4×C43#54611yescharacteristic
404C4×C43#55111yescharacteristic
405Dic43—81no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
409C22×#102—431no—
410#2361D4311yescharacteristic, complemented
411D4×C22⋊C4—431no—
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—82no—
424C2×C43#235811yescharacteristic
425C2×C43C2×#44211yescharacteristic
426C2×C43#294611yescharacteristic
427C2×C43#326411yescharacteristic
428C2×C43#326511yescharacteristic
429C2×C43#330611yescharacteristic
430C2×C43#331811yescharacteristic
431D43—44no—
432D43—82no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8—431no—
436C23×C8—431no—
437C2×#121C2×D4311yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4C2×D4311yescharacteristic, complemented
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4—861no—
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#390—431no—
462#390C2×D4311yescharacteristic, complemented
463#389C2×D4311yescharacteristic, complemented
464#388—21no—
465#386—21no—
466#386—861no—
467#386—861no—
468#385—21no—
469#380—431no—
470#379—861no—
471C4×C4⋊C4C2×D4311yescharacteristic, complemented
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—861no—
481C22×D4—21no—
482C22×D4—434no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—862no—
486C22×D4—862no—
487C22×D4—862no—
488C22×D4—861no—
489C22×D4—1721no—
490C22×D4—1721no—
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—22no—
511#121C4×D4314yescomplemented
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—44no—
515C4×D4—862no—
516C4×D4—862no—
517C4×D4—1721no—
518C4×D4—1721no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4C22×D4311yescharacteristic
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—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—1724no—
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C22⋊C4C22⋊D4311yescharacteristic
542C2×C42—21no—
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—21no—
560#95—861no—
561#95C22⋊D4311yescharacteristic
562#95C22⋊D4311yescharacteristic
563C24—21no—
564C24—861no—
565C24—864no—
566C24—861no—
567C24—3441no—
568C24—3441no—
569C24—1722no—
570C24—1722no—
571C24—1722no—
572C24—1722no—
573C24C2×C22⋊D4311yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—432no—
583C2×D4—432no—
584C2×D4—432no—
585C2×D4—432no—
586C2×D4—868no—
587C2×D4—864no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—1724no—
597C2×D4—1724no—
598C2×D4—1724no—
599C2×D4—1722no—
600C2×D4—1722no—
601C2×D4C2×C4×D4312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
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—42no—
651C4⋊C4—42no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4C2×C4×D4312yes—
657C4⋊C4D4×D4312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—3441no—
665C22⋊C4—3441no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—862no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—3444no—
692C23—3444no—
693C23—3444no—
694C23—3444no—
695C23—3444no—
696C23—1728no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1728no—
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—48no—
715D4—41no—
716D4—41no—
717D4—434no—
718D4—862no—
719D4—862no—
720D4—862no—
721D4—862no—
722D4—862no—
723D4—1728no—
724D4—1721no—
725D4—1721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4—3444no—
756C2×C4—3444no—
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×C4#41×D4311yescharacteristic
767C2×C4C2×#1062189811yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337111yescharacteristic
770C8—862no—
771C8—862no—
772C8—862no—
773C8—1721no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—864no—
788C22—34416no—
789C22—3441no—
790C22—3441no—
791C22—3441no—
792C22—3441no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22#1458300914yescomplemented
803C22C2×C4×C22⋊D4311yescharacteristic
804C22D4×C22⋊D4311yescharacteristic
805C22#1458353711yescharacteristic
806C22C2×#1306335011yescharacteristic
807C22C2×#1306335111yescharacteristic
808C22#1458370211yescharacteristic
809C22#1458370711yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—41no—
815C4—42no—
816C4—41no—
817C4—81no—
818C4—3441no—
819C4—3441no—
820C4C4×D4×D4311yescharacteristic
821C4#1458337111yescharacteristic
822C4#1458354511yescharacteristic
823C4#1458357811yescharacteristic
824C2—24no—
825C2—82no—
826C2—3442no—
827C2—1724no—
828C2#1913757211yescharacteristic
829C2C2×#1458300911yescharacteristic
830C2#1914342311yescharacteristic
831C2#1914607111yescharacteristic
832C2#1914609111yescharacteristic
833C2#1914655011yescharacteristic
834C2#1914673011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2361C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#2361D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#14583009C2semidirect
3. C22×#13063245C2semidirect
4. C22⋊C4×D172C2semidirect
5. #19135470C2semidirect
6. #19135291C2semidirect
7. #19135222C2semidirect
8. #19135024C2semidirect
9. #19134946C2semidirect
10. #19134943C2semidirect
11. #19134855C2semidirect
12. #19134788C2semidirect
13. #19134423C2semidirect
14. #19134373C2semidirect
15. C43×#2361C2semidirect
23. #14583032C4semidirect
25. C2×#13063256C22semidirect
26. C2×#13063256C22semidirect
27. C2×#13063246C22semidirect
28. C2×#13063246C22semidirect
37. C2×#13063236C22semidirect
38. C2×#13063236C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582654C22semidirect
50. #14582654C22semidirect
53. C2×C4×D4×C43C22semidirect
55. C43×#390C22semidirect
56. C43×#389C22semidirect
60. C4×C4⋊C4×C43C22semidirect
69. C22×D172C2×C4semidirect
78. C2×#10621882C2×C4semidirect
79. C2×#10621882C2×C4semidirect
108. #13063245C2×C4semidirect
109. #13063245C2×C4semidirect
110. #13063245D4semidirect
111. C22⋊(C43⋊C8)C2×C4semidirect
121. #121×C43C2×C4semidirect
349. D172C4×D4semidirect
370. C22×C43#442semidirect
410. #2361D43semidirect
441. C2×C4×D4C2×D43semidirect
462. #390C2×D43semidirect
463. #389C2×D43semidirect
471. C4×C4⋊C4C2×D43semidirect
479. C43#22858semidirect
511. #121C4×D43semidirect
802. C22#14583009semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
C2×#145830092
C22×#130632452
C22⋊C4×D1722
#191354702
#191352912
#191352222
#191350242
#191349462
#191349432
#191348552
#191347882
#191344232
#191343732
C43×#23612
#2285843