Finite Group Databasebeta

← #25116914

Subgroups — #25116914

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×#14583008C211yesmaximal, characteristic, complemented
3#19137611C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19135468C211yesmaximal, characteristic, complemented
6#19135289C211yesmaximal, characteristic, complemented
7#19135225C211yesmaximal, characteristic, complemented
8#19135023C211yesmaximal, characteristic, complemented
9#19134941C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134854C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic, complemented
14#19134371C211yesmaximal, characteristic, complemented
15C22×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic, complemented
22C2×C4×C22⋊D43—21no—
23C22×C22⋊Dic43—21no—
24#14583033C418yescomplemented
25#14583008—24no—
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28C2×#13063247C2211yescharacteristic, complemented
29C2×#13063247C2211yescharacteristic, complemented
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063235C2211yescharacteristic, complemented
34C2×#13063235C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582800C2211yescharacteristic, complemented
38#14582795C2211yescharacteristic, complemented
39#14582789—21no—
40#14582779—21no—
41#14582779—21no—
42#14582778—21no—
43#14582770—21no—
44#14582759C2211yescharacteristic
45#14582755—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C2×#102×C43—24no—
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—41no—
70C2×#10621882—41no—
71C2×#10621882C2×C414yescomplemented
72C2×#10621882C2×C414yescomplemented
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063299—22no—
76#13063299C2×C414yescomplemented
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—41no—
80D4×Dic43—41no—
81#13063287—22no—
82#13063287—41no—
83C4×C22⋊D43—44no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—44no—
96C2×C22⋊Dic43D411yescharacteristic
97C2×C22⋊Dic43D411yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063256—22no—
106#13063256—41no—
107#13063247—22no—
108#13063247—41no—
109#13063246C2×C414yescomplemented
110#13063246C2×C414yescomplemented
111C22⋊(C43⋊C8)C2×C414yescomplemented
112#13063235—22no—
113#13063235—41no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C25×C43—21no—
120C22×D4×C43—22no—
121C22×D4×C43—22no—
122C22×D4×C43—21no—
123C22×D4×C43—22no—
124C22×D4×C43—41no—
125C22×D4×C43—41no—
126C22×D4×C43C2×C414yescomplemented
127C22×D4×C43C2311yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C23×C4×C43—21no—
130C23×C4×C43C2311yescharacteristic
131C22×C8×C43—22no—
132C22×C8×C43—22no—
133C22×C8×C43—41no—
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—41no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43D414yescomplemented
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—81no—
184C22×C4×C43C22×C412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43#4112yes—
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—24no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—81no—
199C22×Dic43—81no—
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
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—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—44no—
219C2×C8×C43C2×D412yes—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43C2×D412yes—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—42no—
228C22⋊Dic43—42no—
229C22⋊Dic43—42no—
230C22⋊Dic43—42no—
231C22⋊Dic43—42no—
232C22⋊Dic43—81no—
233C22⋊Dic43—81no—
234#10621882—28no—
235#10621882—44no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—81no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43C22×C412yes—
246Dic43⋊C4—42no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—42no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C22×C412yes—
257C2×C43⋊C8C22×C412yes—
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—22no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—84no—
316C2×C4×C43C4×D412yes—
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—48no—
324C2×Dic43—22no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—84no—
346C2×Dic43—84no—
347D172—22no—
348D172—22no—
349D172—41no—
350D172—41no—
351C4×D43—84no—
352C8×C43—22no—
353C8×C43—41no—
354C43⋊C8—22no—
355C43⋊C8—22no—
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—42no—
395C4×C43—81no—
396C4×C43C2×C4×D411yescharacteristic
397C4×C43#51811yescharacteristic
398C4×C43#54611yescharacteristic
399C4×C43#55111yescharacteristic
400Dic43—42no—
401Dic43—41no—
402Dic43—41no—
403Dic43—41no—
404Dic43—41no—
405Dic43—81no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
409C22×#102D4311yescharacteristic, complemented
410#2361—431no—
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—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×C8C2×D4311yescharacteristic
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4—861no—
444#447—438no—
445#442—864no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#102—24no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102C2×D4311yescharacteristic
454C2×#102C2×D4311yescharacteristic
455C2×#102C2×D4311yescharacteristic
456C2×#102C2×D4311yescharacteristic
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97—431no—
460#390—431no—
461#390—431no—
462#390—431no—
463#389—431no—
464#388—861no—
465#386—861no—
466#386—861no—
467#386—861no—
468#385—861no—
469#380—431no—
470#379—861no—
471C4×C4⋊C4—431no—
472C4×C22⋊C4—431no—
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—21no—
484C22×D4—22no—
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—861no—
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—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510#121—434no—
511#121—862no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515C4×D4—1721no—
516C4×D4—1721no—
517C4×D4—1721no—
518C4×D4—1724no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
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—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—1724no—
542C2×C42—431no—
543C2×C42—431no—
544C2×C42—861no—
545#106—862no—
546#106—1721no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—434no—
551#102—434no—
552#102—862no—
553#102—1721no—
554#102C22⋊D4314yescomplemented
555C22⋊C8—434no—
556#97—862no—
557#97—1721no—
558#95—431no—
559#95—431no—
560#95—861no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—861no—
573C24D4×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×D4#1062189812yes—
601C2×D4C2×C22⋊D4312yes—
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—81no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—3441no—
619C22×C4—3441no—
620C22×C4—3441no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4C2×C4×D4312yes—
628C22×C4D4×D4311yescharacteristic
629C22×C4#1062190012yes—
630C22×C4C23×D4311yescharacteristic
631D8—868no—
632D8—1724no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—44no—
639C2×C8—432no—
640C2×C8—432no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8C2×C22⋊D4312yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—432no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—1722no—
657C4⋊C4C2×C22⋊D4312yes—
658C22⋊C4—862no—
659C22⋊C4—862no—
660C22⋊C4—864no—
661C22⋊C4—3441no—
662C22⋊C4—3441no—
663C22⋊C4—3441no—
664C22⋊C4—1722no—
665C22⋊C4—1722no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—861no—
672C42—861no—
673C42—861no—
674C42—861no—
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—
708C23(C22⋊D43)⋊C412yes—
709C23#1306334912yes—
710C23#1306335212yes—
711C23C2×D4×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—
725D4C4×C22⋊D4314yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—862no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—3444no—
753C2×C4—3444no—
754C2×C4—3444no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1721no—
760C2×C4—1721no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4(C22⋊D43)⋊C412yes—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C22×C22⋊D4311yescharacteristic
766C2×C4C2×#1062190011yescharacteristic
767C2×C4C2×#1062189811yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337011yescharacteristic
770C8—22no—
771C8—41no—
772C8—862no—
773C8—862no—
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#1458300814yescomplemented
803C22C2×(C22⋊D43)⋊C411yescharacteristic
804C22D4×C22⋊D4311yescharacteristic
805C22#1458353911yescharacteristic
806C22C2×#1306334911yescharacteristic
807C22C2×#1306335211yescharacteristic
808C22#1458370011yescharacteristic
809C22#1458370511yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—3441no—
814C4—3441no—
815C4—1721no—
816C4—1721no—
817C4—1721no—
818C4—1722no—
819C4—1721no—
820C4C2×C4×C22⋊D4311yescharacteristic
821C4#1458337211yescharacteristic
822C4#1458354311yescharacteristic
823C4#1458357511yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—3442no—
828C2#1913757411yescharacteristic
829C2C2×#1458300811yescharacteristic
830C2#1914342111yescharacteristic
831C2#1914607511yescharacteristic
832C2#1914609011yescharacteristic
833C2#1914655211yescharacteristic
834C2#1914673211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenterC22×#102D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. #19137611C2semidirect
4. D4×C22⋊Dic43C2semidirect
5. #19135468C2semidirect
6. #19135289C2semidirect
7. #19135225C2semidirect
8. #19135023C2semidirect
9. #19134941C2semidirect
10. #19134940C2semidirect
11. #19134854C2semidirect
12. #19134788C2semidirect
13. #19134422C2semidirect
14. #19134371C2semidirect
15. C22×#102×C43C2semidirect
21. C2×#13063287C22semidirect
24. #14583033C4semidirect
26. C2×#13063256C22semidirect
27. C2×#13063256C22semidirect
28. C2×#13063247C22semidirect
29. C2×#13063247C22semidirect
33. C2×#13063235C22semidirect
34. C2×#13063235C22semidirect
37. #14582800C22semidirect
38. #14582795C22semidirect
46. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
71. C2×#10621882C2×C4semidirect
72. C2×#10621882C2×C4semidirect
76. #13063299C2×C4semidirect
109. #13063246C2×C4semidirect
110. #13063246C2×C4semidirect
111. C22⋊(C43⋊C8)C2×C4semidirect
126. C22×D4×C43C2×C4semidirect
144. #102×C43D4semidirect
302. D4×C43C4×D4semidirect
378. C22×C43#442semidirect
409. C22×#102D43semidirect
479. C43#22858semidirect
489. C22×D4C4×D43semidirect
554. #102C22⋊D43semidirect
725. D4C4×C22⋊D43semidirect
802. C22#14583008semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
C2×#145830082
#191376112
D4×C22⋊Dic432
#191354682
#191352892
#191352252
#191350232
#191349412
#191349402
#191348542
#191347882
#191344222
#191343712
C22×#102×C432
#2285843