Finite Group Databasebeta

← #25063084

Subgroups — #25063084

Order 11008.

1138 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063373C211yesmaximal, characteristic
2#19143714C211yesmaximal, characteristic, complemented
3#19143557C211yesmaximal, characteristic, complemented
4#19133040C211yesmaximal, characteristic, complemented
5#19133035C211yesmaximal, characteristic, complemented
6#19133033C211yesmaximal, characteristic, complemented
7#19133028C211yesmaximal, characteristic, complemented
8#19133027C211yesmaximal, characteristic, complemented
9#19133024C211yesmaximal, characteristic, complemented
10#19133022C211yesmaximal, characteristic, complemented
11#19132988C211yesmaximal, characteristic, complemented
12#19132981C211yesmaximal, characteristic, complemented
13#19132976C211yesmaximal, characteristic, complemented
14Q8⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1491C211yesmaximal, characteristic, complemented
16C2×#13063373C411yescharacteristic
17#14583381—21no—
18#14583381C411yescharacteristic
19#14583381C411yescharacteristic
20#14583380—21no—
21#14583380—21no—
22#14583380C411yescharacteristic
23#14583380C411yescharacteristic
24#14583377C411yescharacteristic
25#14583375—21no—
26#14583375C411yescharacteristic
27#14583375C411yescharacteristic
28C4×#10621902—21no—
29C4×#10621902C2211yescharacteristic
30C4×#10621902C2211yescharacteristic
31C4×#10621898—21no—
32C4×#10621898—21no—
33C4×#10621898C2211yescharacteristic
34C4×#10621898C2211yescharacteristic
35C4×Q8×D43—21no—
36C4×Q8×D43C2211yescharacteristic
37C4×Q8×D43C2211yescharacteristic
38#14583027—21no—
39#14583027—21no—
40#14582975—21no—
41#14582974—21no—
42#14582973—21no—
43#14582972—21no—
44#14582972—21no—
45#14582968—21no—
46#14582955C2211yescharacteristic
47#14582952C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582950C2211yescharacteristic
50#14582950C2211yescharacteristic
51#14582923C2211yescharacteristic
52#14582921C2211yescharacteristic
53C4⋊C8×D43C2211yescharacteristic
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58Q8⋊(C43⋊C8)C2211yescharacteristic
59Q8⋊(C43⋊C8)C2211yescharacteristic
60Q8⋊(C43⋊C8)C2211yescharacteristic
61Q8⋊(C43⋊C8)C2211yescharacteristic
62#14582629C2211yescharacteristic
63#14582629C2211yescharacteristic
64#14582628C2211yescharacteristic
65#14582628C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C2×C4×Q8×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C4×M16×C43C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×Q8⋊C8C2211yescharacteristic
74C43×Q8⋊C8C2211yescharacteristic
75#13063373—24no—
76#13063373—24no—
77C2×#10621902—21no—
78C2×#10621902C2×C411yescharacteristic
79C2×#10621902C2×C411yescharacteristic
80C2×#10621898—21no—
81C2×#10621898—21no—
82C2×#10621898C2×C411yescharacteristic
83C2×#10621898C2×C411yescharacteristic
84C2×Q8×D43—21no—
85C2×Q8×D43C2×C411yescharacteristic
86C2×Q8×D43C2×C411yescharacteristic
87C2×#10621877—21no—
88C2×#10621872—21no—
89C2×#10621872—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92Q8×Dic43—21no—
93Q8×Dic43—21no—
94Q8×Dic43C2×C411yescharacteristic
95Q8×Dic43C2×C411yescharacteristic
96Q8×Dic43C2×C411yescharacteristic
97Q8×Dic43C2×C411yescharacteristic
98C4×Dic86—21no—
99C4×Dic86—21no—
100C4×Dic86—21no—
101C4×Dic86—21no—
102C4×Dic86C2×C411yescharacteristic
103C4×Dic86D411yescharacteristic
104C4×Dic86D411yescharacteristic
105C4×Dic86C2311yescharacteristic
106#13063290—21no—
107#13063290—21no—
108#13063290—21no—
109#13063290—21no—
110#13063290—21no—
111#13063290C2×C411yescharacteristic
112#13063290C2×C411yescharacteristic
113C4×D172—21no—
114C4×D172—21no—
115C4×D172—21no—
116C4×D172—21no—
117C4×D172C2×C411yescharacteristic
118C4×D172D411yescharacteristic
119C4×D172D411yescharacteristic
120C4×D172C2311yescharacteristic
121#13063287—21no—
122#13063287—21no—
123#13063287—21no—
124#13063287—21no—
125#13063287—21no—
126#13063287C2×C411yescharacteristic
127#13063287C2×C411yescharacteristic
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43—21no—
133C4×C22⋊D43—21no—
134C4×C22⋊D43D411yescharacteristic
135C4×C22⋊D43D411yescharacteristic
136C4×C22⋊D43D411yescharacteristic
137C4×C22⋊D43D411yescharacteristic
138#13063284—21no—
139#13063284—21no—
140#13063284C2×C411yescharacteristic
141#13063284C2×C411yescharacteristic
142#13063283—21no—
143#13063283—21no—
144#13063283—21no—
145#13063283—21no—
146#13063283—21no—
147#13063283C2×C411yescharacteristic
148#13063283C2×C411yescharacteristic
149#13063282—21no—
150#13063282—21no—
151#13063282—21no—
152#13063282—21no—
153#13063282—21no—
154#13063282C2×C411yescharacteristic
155#13063282C2×C411yescharacteristic
156C4⋊C4×D43—21no—
157C4⋊C4×D43—21no—
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43C2×C411yescharacteristic
162C4⋊C4×D43C2×C411yescharacteristic
163C42×D43—21no—
164C42×D43—21no—
165C42×D43—21no—
166C42×D43—21no—
167C42×D43—21no—
168C42×D43C2311yescharacteristic
169C42×D43C2311yescharacteristic
170C4⋊(C43⋊C8)—21no—
171C4⋊(C43⋊C8)—21no—
172C4⋊(C43⋊C8)C2311yescharacteristic
173C4⋊(C43⋊C8)C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177Dic43⋊C8—21no—
178C22⋊(C43⋊C8)—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183#13063235—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C8×Dic43—21no—
189C22×Q8×C43C2×C411yescharacteristic
190C2×M16×C43—21no—
191C4×Q8×C43—21no—
192C4×Q8×C43—21no—
193C4×Q8×C43C2×C411yescharacteristic
194C4×Q8×C43C2×C411yescharacteristic
195C4×Q8×C43C2311yescharacteristic
196C4×Q8×C43C2311yescharacteristic
197C2×C4⋊C4×C43—21no—
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C42×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204#97×C43—21no—
205#97×C43—21no—
206C4×C8×C43C2311yescharacteristic
207C4×C8×C43C2311yescharacteristic
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43—21no—
211C2×Q8×C43C22×C411yescharacteristic
212C2×Q8×C43C22×C411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C2×C22⋊D43—21no—
219C2×C22⋊D43C22⋊C411yescharacteristic
220C2×C22⋊D43C22⋊C411yescharacteristic
221#10621902—28no—
222#10621902—22no—
223#10621902—22no—
224#10621902—22no—
225#10621902M1614yescomplemented
226Q8×D43—28no—
227Q8×D43—22no—
228Q8×D43—22no—
229Q8×D43—22no—
230Q8×D43M1614yescomplemented
231#10621898—28no—
232#10621898—28no—
233#10621898—22no—
234#10621898—22no—
235#10621898—22no—
236#10621898—22no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172C22⋊C411yescharacteristic
240C2×D172C22×C411yescharacteristic
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43C22×C411yescharacteristic
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86—21no—
260C2×Dic86C22⋊C411yescharacteristic
261C2×Dic86C22×C411yescharacteristic
262M16×C43—42no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43C22×C411yescharacteristic
273C4⋊C4×C43C22×C411yescharacteristic
274C42×C43—21no—
275C42×C43—21no—
276C42×C43—21no—
277C42×C43—21no—
278C42×C43C22×C411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2411yescharacteristic
282C22⋊Dic43—21no—
283C22⋊Dic43C22⋊C411yescharacteristic
284C22⋊Dic43C22⋊C411yescharacteristic
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4C22⋊C411yescharacteristic
292(C2×D43)⋊C4C22⋊C411yescharacteristic
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43C22⋊C411yescharacteristic
300C4⋊Dic43C22⋊C411yescharacteristic
301C4⋊Dic43C22×C411yescharacteristic
302C4⋊Dic43C22×C411yescharacteristic
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43C22×C411yescharacteristic
325C4×Dic43C22×C411yescharacteristic
326C4×Dic43C2×D411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329C4×Dic43C2×D411yescharacteristic
330#10621877—81no—
331C2×C43⋊C8—21no—
332C2×C43⋊C8—21no—
333C2×C43⋊C8—21no—
334C2×C43⋊C8—21no—
335#10621872—42no—
336#10621872—81no—
337C8×D43—42no—
338C8×D43—81no—
339C23×C43C2×C22⋊C411yescharacteristic
340C22×D43—21no—
341C22×D43C2×C22⋊C411yescharacteristic
342C22×D43C2×C22⋊C411yescharacteristic
343Q8×C43—24no—
344Q8×C43—21no—
345Q8×C43—21no—
346Q8×C43C2×M1612yes—
347Q8×C43C2×M1612yes—
348C2×C4×C43—24no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—41no—
358C2×C4×C43—81no—
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C2×C22⋊C411yescharacteristic
362C2×C4×C43C23×C411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C22⋊D43—24no—
366C22⋊D43—22no—
367C22⋊D43—22no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377D172—24no—
378D172—24no—
379D172—22no—
380D172—21no—
381D172C2×M1612yes—
382C4×D43—24no—
383C4×D43—24no—
384C4×D43—24no—
385C4×D43—24no—
386C4×D43—21no—
387C4×D43—21no—
388C4×D43—21no—
389C4×D43—21no—
390C4×D43—21no—
391C4×D43—21no—
392C4×D43—24no—
393C4×D43—41no—
394C4×D43—41no—
395C4×D43—41no—
396C4×D43—41no—
397C4×D43—81no—
398C4×D43—81no—
399C4×D43—81no—
400C4×D43—81no—
401C4×D43—81no—
402C4×D43C2×M1612yes—
403C4×D43C2×M1612yes—
404Dic86—24no—
405Dic86—21no—
406Dic86—24no—
407Dic86—22no—
408Dic86C2×M1612yes—
409C8×C43—22no—
410C8×C43—41no—
411C8×C43—41no—
412C8×C43—41no—
413C43⋊C8—41no—
414C43⋊C8—41no—
415C43⋊C8—41no—
416C43⋊C8—41no—
417#17454—431nomaximal, Sylow
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43C22×C22⋊C411yescharacteristic
422C2×D43—21no—
423C2×D43—21no—
424C2×D43—22no—
425C2×D43—21no—
426C2×D43—21no—
427C2×D43—21no—
428C2×D43—41no—
429C2×D43—41no—
430C2×D43#40712yes—
431C4×C43—22no—
432C4×C43—22no—
433C4×C43—21no—
434C4×C43—21no—
435C4×C43—21no—
436C4×C43—21no—
437C4×C43—41no—
438C4×C43—41no—
439C4×C43C22×M1611yescharacteristic
440C4×C43C22×M1611yescharacteristic
441C4×C43#57711yescharacteristic
442C4×C43#57811yescharacteristic
443Dic43—21no—
444Dic43—22no—
445Dic43—21no—
446Dic43—21no—
447Dic43—21no—
448Dic43—21no—
449Dic43—41no—
450Dic43—41no—
451Dic43#40712yes—
452C4×2−1+4—431no—
453#2989—431no—
454#2965—431no—
455#1491—431no—
456#1491D4311yescharacteristic, complemented
457#1489—431no—
458#1489—431no—
459#1488—431no—
460#1488—431no—
461#1487—431no—
462#1487—431no—
463#1479—431no—
464#1477—431no—
465#1476—431no—
466C2×Q8⋊C8—431no—
467C2×C43—41no—
468C2×C43C2×#40711yescharacteristic
469C2×C43#289811yescharacteristic
470C2×C43#290111yescharacteristic
471D43—22no—
472D43—41no—
473D43—42no—
474C2×2−1+4—431no—
475#520—431no—
476#520—431no—
477#520—431no—
478#520—431no—
479#520—861no—
480#520—861no—
481#520—861no—
482#519—431no—
483#519—431no—
484#519—431no—
485#519—861no—
486C4×#41—431no—
487C4×#41—431no—
488C4×#41—431no—
489C4×#41—431no—
490C4×#41—861no—
491C4×#41—861no—
492C4×#41—861no—
493C2×C4×Q8—431no—
494C2×C4×Q8—431no—
495C2×C4×Q8—861no—
496C2×C4×Q8C2×D4311yescharacteristic
497#446—861no—
498#446—861no—
499#436—861no—
500#436—861no—
501#435—861no—
502#435—861no—
503#435—861no—
504#435—861no—
505#432—431no—
506#432C2×D4311yescharacteristic
507#431—431no—
508#431—431no—
509#431—431no—
510#431—431no—
511#423—431no—
512#423—431no—
513C2×C4⋊C8—431no—
514C4×M16—431no—
515C4×M16C2×D4311yescharacteristic
516C2×C4×C8—431no—
517Q8⋊C8—431no—
518Q8⋊C8—431no—
519Q8⋊C8—431no—
520Q8⋊C8—431no—
521Q8⋊C8—431no—
522Q8⋊C8—431no—
523Q8⋊C8—431no—
524Q8⋊C8—431no—
525Q8⋊C8C2×D4311yescharacteristic
526Q8⋊C8C2×D4311yescharacteristic
527Q8⋊C8C2×D4311yescharacteristic
528Q8⋊C8C2×D4311yescharacteristic
529D4⋊C8—431no—
530D4⋊C8—431no—
531D4⋊C8—431no—
532D4⋊C8—431no—
533C43#1745411yescharacteristic, complemented, Sylow
5342−1+4—864no—
5352−1+4—864no—
536C2×#41—431no—
537C2×#41—431no—
538C2×#41—431no—
539C2×#41—431no—
540C2×#41—861no—
541C2×#41—861no—
542C2×#41—861no—
543C22×Q8—431no—
544C22×Q8—431no—
545C22×Q8—861no—
546C22×Q8C4×D4311yescharacteristic
547C2×M16—21no—
548C2×M16—861no—
549C2×M16—861no—
550C2×M16—861no—
551C22×C8—861no—
552C22×C8—861no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8—431no—
556C4×Q8—431no—
557C4×Q8—431no—
558C4×Q8—431no—
559C4×Q8—431no—
560C4×Q8—431no—
561C4×Q8—431no—
562C4×Q8—431no—
563C4×Q8—431no—
564C4×Q8—431no—
565C4×Q8—861no—
566C4×Q8—861no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8—861no—
570C4×Q8—861no—
571C4×Q8—861no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8C4×D4311yescharacteristic
577C4×Q8C4×D4311yescharacteristic
578C4×Q8C22×D4311yescharacteristic
579C4×Q8C22×D4311yescharacteristic
580C4×D4—431no—
581C4×D4—431no—
582C4×D4—431no—
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—431no—
587C4×D4—431no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4—861no—
601C4×D4—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605#117—431no—
606#117—431no—
607#117—431no—
608#117—431no—
609#117—431no—
610#117—431no—
611#117—861no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117—861no—
616#117—861no—
617#117—861no—
618#117—861no—
619#117—861no—
620#117—861no—
621#117—861no—
622#117—861no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—431no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—861no—
627C2×C4⋊C4—861no—
628C2×C4⋊C4—861no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4C4×D4311yescharacteristic
632C2×C42—21no—
633C2×C42—431no—
634C2×C42—431no—
635C2×C42—861no—
636C2×C42—861no—
637C2×C42—861no—
638C2×C42—861no—
639C2×C42—861no—
640C2×C42C22×D4311yescharacteristic
641C4⋊C8—431no—
642C4⋊C8—431no—
643C4⋊C8—861no—
644C4⋊C8—861no—
645C4⋊C8—861no—
646C4⋊C8—861no—
647C4⋊C8—861no—
648C4⋊C8—861no—
649C4⋊C8C22×D4311yescharacteristic
650C4⋊C8C22×D4311yescharacteristic
651C22⋊C8—21no—
652C22⋊C8—861no—
653C22⋊C8—861no—
654C22⋊C8—861no—
655C22⋊C8—861no—
656C22⋊C8—861no—
657#97—21no—
658#97—21no—
659#97—861no—
660#97—861no—
661C4×C8—431no—
662C4×C8—431no—
663C4×C8—861no—
664C4×C8—861no—
665C4×C8C22×D4311yescharacteristic
666C4×C8C22×D4311yescharacteristic
667#41—434no—
668#41—862no—
669#41—862no—
670#41—862no—
671#41—862no—
672#41—868no—
673#41—868no—
674#41—862no—
675#41—862no—
676#41—868no—
677#41—862no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—21no—
681C2×Q8—431no—
682C2×Q8—434no—
683C2×Q8—431no—
684C2×Q8—861no—
685C2×Q8—861no—
686C2×Q8—862no—
687C2×Q8—862no—
688C2×Q8—868no—
689C2×Q8—862no—
690C2×Q8C2×C4×D4311yescharacteristic
691C2×Q8C2×C4×D4311yescharacteristic
692C2×D4—431no—
693C2×D4—431no—
694C2×D4—431no—
695C2×D4—431no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—861no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—431no—
702C22×C4—431no—
703C22×C4—431no—
704C22×C4—431no—
705C22×C4—431no—
706C22×C4—431no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4C2×C4×D4311yescharacteristic
719C22×C4D4×D4311yescharacteristic
720C22×C4D4×D4311yescharacteristic
721M16—42no—
722M16—3441no—
723M16—3441no—
724M16—1722no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—861no—
730C2×C8—861no—
731C2×C8—861no—
732C2×C8—861no—
733C2×C8—3441no—
734C2×C8—1722no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—431no—
741C4⋊C4—431no—
742C4⋊C4—431no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4C2×C4×D4311yescharacteristic
759C4⋊C4C2×C4×D4311yescharacteristic
760C22⋊C4—431no—
761C22⋊C4—431no—
762C22⋊C4—431no—
763C22⋊C4—431no—
764C22⋊C4—431no—
765C22⋊C4—431no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—431no—
778C42—431no—
779C42—431no—
780C42—431no—
781C42—431no—
782C42—431no—
783C42—861no—
784C42—861no—
785C42—861no—
786C42—861no—
787C42—861no—
788C42—861no—
789C42—861no—
790C42—861no—
791C42—861no—
792C42—861no—
793C42—861no—
794C42C2×C4×D4311yescharacteristic
795C42D4×D4311yescharacteristic
796C42D4×D4311yescharacteristic
797C42C23×D4311yescharacteristic
798C23—431no—
799C23—431no—
800C23—861no—
801C23C22⋊C4×D4311yescharacteristic
802Q8—24no—
803Q8—21no—
804Q8—21no—
805Q8—432no—
806Q8—864no—
807Q8—862no—
808Q8—864no—
809Q8—861no—
810Q8M16×D4312yes—
811Q8M16×D4312yes—
812D4—432no—
813D4—862no—
814D4—864no—
815D4—864no—
816D4—862no—
817D4—862no—
818D4—864no—
819D4—861no—
820C2×C4—24no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—41no—
830C2×C4—81no—
831C2×C4—431no—
832C2×C4—432no—
833C2×C4—432no—
834C2×C4—431no—
835C2×C4—431no—
836C2×C4—431no—
837C2×C4—431no—
838C2×C4—431no—
839C2×C4—864no—
840C2×C4—864no—
841C2×C4—864no—
842C2×C4—864no—
843C2×C4—864no—
844C2×C4—861no—
845C2×C4—861no—
846C2×C4—861no—
847C2×C4—861no—
848C2×C4—861no—
849C2×C4—861no—
850C2×C4—861no—
851C2×C4—861no—
852C2×C4—861no—
853C2×C4—3441no—
854C2×C4—3441no—
855C2×C4—3441no—
856C2×C4—3441no—
857C2×C4—3441no—
858C2×C4—1721no—
859C2×C4—1721no—
860C2×C4—1721no—
861C2×C4—1721no—
862C2×C4C22⋊C4×D4311yescharacteristic
863C2×C4C22⋊C4×D4311yescharacteristic
864C2×C4C22⋊C4×D4311yescharacteristic
865C2×C4C22×C4×D4311yescharacteristic
866C2×C4C2×D4×D4311yescharacteristic
867C2×C4C2×D4×D4311yescharacteristic
868C8—22no—
869C8—41no—
870C8—41no—
871C8—41no—
872C8—1721no—
873C8—1721no—
874C8—1721no—
875C8—1721no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—432no—
880C22—861no—
881C22—861no—
882C22—862no—
883C22—861no—
884C22—861no—
885C22—861no—
886C22—1721no—
887C22—1721no—
888C22C2×C22⋊C4×D4311yescharacteristic
889C4—22no—
890C4—22no—
891C4—21no—
892C4—21no—
893C4—21no—
894C4—21no—
895C4—41no—
896C4—41no—
897C4—432no—
898C4—861no—
899C4—862no—
900C4—861no—
901C4—861no—
902C4—861no—
903C4—861no—
904C4—1721no—
905C4—1721no—
906C4C2×M16×D4311yescharacteristic
907C4C2×M16×D4311yescharacteristic
908C4#1458370811yescharacteristic
909C4#1458371511yescharacteristic
910C2—41no—
911C2—862no—
912C2—1721no—
913C2—1722no—
914C2#407×D4311yescharacteristic
915C2#1914312711yescharacteristic
916C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1491C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063373C4
cosocleC42×C43C24
hypercenter#1491D43
hypocenterC43#17454
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. #19143714C2semidirect
3. #19143557C2semidirect
4. #19133040C2semidirect
5. #19133035C2semidirect
6. #19133033C2semidirect
7. #19133028C2semidirect
8. #19133027C2semidirect
9. #19133024C2semidirect
10. #19133022C2semidirect
11. #19132988C2semidirect
12. #19132981C2semidirect
13. #19132976C2semidirect
14. Q8⋊C8×D43C2semidirect
15. C43×#1491C2semidirect
225. #10621902M16semidirect
230. Q8×D43M16semidirect
456. #1491D43semidirect
533. C43#17454semidirect

Maximal subgroups

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

subgroupindex
C4×#130633732
#191437142
#191435572
#191330402
#191330352
#191330332
#191330282
#191330272
#191330242
#191330222
#191329882
#191329812
#191329762
Q8⋊C8×D432
C43×#14912
#1745443