Finite Group Databasebeta

← #25116913

Subgroups — #25116913

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×#14583031C211yesmaximal, characteristic
2C2×#14583008C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic, complemented
4#19137616C211yesmaximal, characteristic, complemented
5#19137416C211yesmaximal, characteristic, complemented
6#19135289C211yesmaximal, characteristic, complemented
7#19135219C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134853C211yesmaximal, characteristic, complemented
12#19134786C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C43×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic, complemented
22C2×#13063287C2211yescharacteristic
23C2×(C22⋊D43)⋊C4—21no—
24C2×C4⋊C4×D43C2211yescharacteristic
25C2×C22⋊C4×D43—21no—
26#14583031C418yescomplemented
27#14583008—24no—
28C2×#13063256C2211yescharacteristic, complemented
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic, complemented
34C2×#13063245C2211yescharacteristic
35#102×D43—24no—
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×#13063235C2211yescharacteristic, complemented
38#14582802C2211yescharacteristic
39#14582795C2211yescharacteristic, complemented
40#14582787—21no—
41#14582775—21no—
42#14582775—21no—
43#14582775—21no—
44#14582771—21no—
45#14582756C2211yescharacteristic
46#14582754—21no—
47C4×C4⋊Dic43C2211yescharacteristic, complemented
48C4×(C2×D43)⋊C4C2211yescharacteristic
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582654C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C22×D8×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic, complemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic, complemented
59C2×#97×C43C2211yescharacteristic, complemented
60C43×#390C2211yescharacteristic
61C43×#390C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—41no—
70C2×D4×D43—41no—
71C2×D4×D43C2×C414yescomplemented
72C23×Dic43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621882—22no—
78C2×#10621882—22no—
79C2×#10621882C2×C414yescomplemented
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43—41no—
85#13063296—22no—
86#13063296C2×C414yescomplemented
87C4×D172—22no—
88C4×D172—41no—
89D4×Dic43—22no—
90D4×Dic43—41no—
91#13063287—22no—
92#13063287—41no—
93(C22⋊D43)⋊C4—44no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43—41no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×(C2×D43)⋊C4D411yescharacteristic
110C22⋊C4×D43—44no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063256—22no—
114#13063247C2×C414yescomplemented
115#13063247D414yescomplemented
116#13063246—22no—
117#13063246—41no—
118#13063246C2×C414yescomplemented
119#13063245—22no—
120(C2×D43)⋊C8C2×C414yescomplemented
121#13063235—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95D411yescharacteristic
126C43⋊#95D411yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C2×D8×C43—41no—
130C2×D8×C43—41no—
131C2×D8×C43C2×C414yescomplemented
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43C2311yescharacteristic
141#106×C43—41no—
142#102×C43—22no—
143#102×C43—22no—
144#97×C43—41no—
145C24×C43—21no—
146C24×C43—21no—
147C23×D43—21no—
148C23×D43—24no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—42no—
152C23×D43—42no—
153C23×D43—81no—
154C23×D43—81no—
155C23×D43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43C22×C412yes—
167C2×D4×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—24no—
174C2×C22⋊D43—24no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43—81no—
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188D4×D43—28no—
189D4×D43—44no—
190D4×D43—44no—
191D4×D43—44no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172C22×C412yes—
196C2×D172C2×D412yes—
197C2×D172#4112yes—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—81no—
209C2×C4×D43—81no—
210C2×C4×D43—81no—
211C2×C4×D43C22×C412yes—
212C2×C4×D43#4112yes—
213D8×C43—44no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43C22×C412yes—
219C2×C8×C43C2×D412yes—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43—81no—
228C42×C43—21no—
229C42×C43—21no—
230C22⋊Dic43—24no—
231C22⋊Dic43—42no—
232C22⋊Dic43—42no—
233C22⋊Dic43—81no—
234#10621882—28no—
235(C2×D43)⋊C4—22no—
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—42no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43C22×C412yes—
245C4⋊Dic43C2×D412yes—
246Dic43⋊C4—42no—
247Dic43⋊C4—42no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—42no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C22×C412yes—
257C8×D43—44no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43C22×D411yescharacteristic
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—48no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—48no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43—84no—
289C22×D43—84no—
290C22×D43—84no—
291C22×D43C4×D412yes—
292C22×D43AGL(1,ℤ/8)12yes—
293C22×D43AGL(1,ℤ/8)12yes—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—41no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C22⋊D43—48no—
321C22⋊D43—48no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—22no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—22no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—84no—
340C2×Dic43C4×D412yes—
341D172—22no—
342D172—22no—
343D172—22no—
344D172C4×D414yescomplemented
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—84no—
350C4×D43—84no—
351C4×D43—84no—
352C8×C43—22no—
353C8×C43—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356#22858—431nomaximal, Sylow
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
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—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—24no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—816no—
392C2×D43#44214yescomplemented
393C4×C43—41no—
394C4×C43—41no—
395C4×C43—81no—
396C4×C43—81no—
397C4×C43C2×C4×D411yescharacteristic
398C4×C43#51811yescharacteristic
399C4×C43#54611yescharacteristic
400C4×C43#55111yescharacteristic
401Dic43—22no—
402Dic43—42no—
403Dic43—42no—
404Dic43—41no—
405Dic43—41no—
406Dic43—81no—
407C2×#447—431no—
408C2×#442—431no—
409C22×#102—431no—
410#2361—431no—
411D4×C22⋊C4—431no—
412#1972D4311yescharacteristic, complemented
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—82no—
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—24no—
432D43—44no—
433C23×D4—431no—
434C22×D8—431no—
435C22×D8C2×D4311yescharacteristic
436C23×C8—431no—
437C2×#121—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C22⋊C4—861no—
444#447—438no—
445#442—864no—
446C2×#106—431no—
447C2×#106C2×D4311yescharacteristic, complemented
448C2×#102—431no—
449C2×#102—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—864no—
455C2×#102C2×D4311yescharacteristic
456C2×#102C2×D4311yescharacteristic, complemented
457C2×C22⋊C8—431no—
458C2×#97—431no—
459C2×#97C2×D4311yescharacteristic, complemented
460#390—431no—
461#390C2×D4311yescharacteristic
462#390C2×D4311yescharacteristic, complemented
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—861no—
481C22×D4—434no—
482C22×D4—431no—
483C22×D4—862no—
484C22×D4—861no—
485C22×D4—862no—
486C22×D4—862no—
487C22×D4—861no—
488C22×D4—1721no—
489C22×D4—1721no—
490C22×D4C22×D4311yescharacteristic
491C22×D4C22×D4311yescharacteristic
492C23×C4—431no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C2×D8—41no—
498C2×D8—41no—
499C2×D8—434no—
500C2×D8—862no—
501C2×D8—862no—
502C2×D8C4×D4314yescomplemented
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—862no—
506C22×C8—862no—
507C22×C8—1721no—
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—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—431no—
533C2×C22⋊C4—431no—
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—861no—
544C2×C42C22×D4311yescharacteristic
545#106—41no—
546#106—862no—
547#102—22no—
548#102—22no—
549#102—434no—
550#102—434no—
551#102—434no—
552#102—862no—
553#102—862no—
554#102—1721no—
555C22⋊C8—434no—
556#97—41no—
557#97—862no—
558#95—431no—
559#95—431no—
560#95—861no—
561#95—861no—
562#95—861no—
563C24—21no—
564C24—21no—
565C24—431no—
566C24—864no—
567C24—861no—
568C24—3441no—
569C24—3441no—
570C24—1722no—
571C24—1722no—
572C24—1722no—
573C24—1722no—
574C2×D4—21no—
575C2×D4—21no—
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—432no—
585C2×D4—432no—
586C2×D4—432no—
587C2×D4—864no—
588C2×D4—868no—
589C2×D4—864no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—1724no—
594C2×D4—1724no—
595C2×D4—1724no—
596C2×D4—1722no—
597C2×D4—1722no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4C2×C4×D4312yes—
601C2×D4C2×C4×D4312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—431no—
605C22×C4—432no—
606C22×C4—432no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—3441no—
617C22×C4—3441no—
618C22×C4—3441no—
619C22×C4—3441no—
620C22×C4—1722no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4D4×D4311yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4C23×D4311yescharacteristic
631D8—44no—
632D8—868no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—432no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—1724no—
644C2×C8C2×C4×D4312yes—
645C2×C8D4×D4312yes—
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—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—862no—
663C22⋊C4—862no—
664C22⋊C4—864no—
665C22⋊C4—3441no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4—1722no—
669C22⋊C4—1722no—
670C22⋊C4—1722no—
671C42—21no—
672C42—21no—
673C42—861no—
674C42—861no—
675C42—1722no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—432no—
691C23—432no—
692C23—432no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—862no—
698C23—862no—
699C23—862no—
700C23—3444no—
701C23—3444no—
702C23—3444no—
703C23—3444no—
704C23—3444no—
705C23—1728no—
706C23—1728no—
707C23—1721no—
708C23—1721no—
709C23—1721no—
710C23—1721no—
711C23C2×D4×D4311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—434no—
721D4—862no—
722D4—862no—
723D4—862no—
724D4—1728no—
725D4—1728no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—432no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—862no—
753C2×C4—3444no—
754C2×C4—3444no—
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×C4—1721no—
764C2×C4C22×C4×D4311yescharacteristic
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4#41×D4311yescharacteristic
767C2×C4#41×D4311yescharacteristic
768C2×C4#1306337011yescharacteristic
769C2×C4#1306337011yescharacteristic
770C8—22no—
771C8—22no—
772C8—862no—
773C8—1721no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—434no—
789C22—862no—
790C22—862no—
791C22—862no—
792C22—862no—
793C22—862no—
794C22—862no—
795C22—864no—
796C22—34416no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22—1722no—
803C22C4×D4×D4311yescharacteristic
804C22#1458353411yescharacteristic
805C22#1458353811yescharacteristic
806C22AGL(1,ℤ/8)×D4311yescharacteristic
807C22AGL(1,ℤ/8)×D4311yescharacteristic
808C22#1458370311yescharacteristic
809C22#1458370911yescharacteristic
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C4—862no—
815C4—3441no—
816C4—1721no—
817C4—1722no—
818C4—1721no—
819C4—1722no—
820C4C4×D4×D4311yescharacteristic
821C4#1458337211yescharacteristic
822C4#1458353811yescharacteristic
823C4#1458357911yescharacteristic
824C2—82no—
825C2—82no—
826C2—864no—
827C2—1724no—
828C2#1913757611yescharacteristic
829C2#442×D4311yescharacteristic
830C2#1914342411yescharacteristic
831C2#1914607411yescharacteristic
832C2#1914608911yescharacteristic
833C2#1914655111yescharacteristic
834C2#1914673111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1972C2
socleC23×C43C22×D4
prime radicalC2×#14583031C2
cosocleC22×C4×C43C24
hypercenter#1972D43
hypocenterC43#22858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. C2×#102×D43C2semidirect
4. #19137616C2semidirect
5. #19137416C2semidirect
6. #19135289C2semidirect
7. #19135219C2semidirect
8. #19135020C2semidirect
9. #19134946C2semidirect
10. #19134945C2semidirect
11. #19134853C2semidirect
12. #19134786C2semidirect
13. #19134421C2semidirect
14. #19134372C2semidirect
15. C43×#1972C2semidirect
21. C2×D4×Dic43C22semidirect
26. #14583031C4semidirect
28. C2×#13063256C22semidirect
33. C2×#13063246C22semidirect
37. C2×#13063235C22semidirect
39. #14582795C22semidirect
47. C4×C4⋊Dic43C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582654C22semidirect
54. #14582653C22semidirect
56. C2×#106×C43C22semidirect
58. C2×#102×C43C22semidirect
59. C2×#97×C43C22semidirect
61. C43×#390C22semidirect
71. C2×D4×D43C2×C4semidirect
79. C2×#10621882C2×C4semidirect
86. #13063296C2×C4semidirect
114. #13063247C2×C4semidirect
115. #13063247D4semidirect
118. #13063246C2×C4semidirect
120. (C2×D43)⋊C8C2×C4semidirect
131. C2×D8×C43C2×C4semidirect
344. D172C4×D4semidirect
392. C2×D43#442semidirect
412. #1972D43semidirect
447. C2×#106C2×D43semidirect
456. C2×#102C2×D43semidirect
459. C2×#97C2×D43semidirect
462. #390C2×D43semidirect
479. C43#22858semidirect
502. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830312
C2×#145830082
C2×#102×D432
#191376162
#191374162
#191352892
#191352192
#191350202
#191349462
#191349452
#191348532
#191347862
#191344212
#191343722
C43×#19722
#2285843