Finite Group Databasebeta

← #25063082

Subgroups — #25063082

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×#13063372C211yesmaximal, characteristic
2#19143709C211yesmaximal, characteristic, complemented
3#19143557C211yesmaximal, characteristic, complemented
4#19133043C211yesmaximal, characteristic, complemented
5#19133040C211yesmaximal, characteristic, complemented
6#19133031C211yesmaximal, characteristic, complemented
7#19133029C211yesmaximal, characteristic, complemented
8#19133026C211yesmaximal, characteristic, complemented
9#19133023C211yesmaximal, characteristic, complemented
10#19133022C211yesmaximal, characteristic, complemented
11#19132988C211yesmaximal, characteristic, complemented
12#19132979C211yesmaximal, characteristic, complemented
13#19132974C211yesmaximal, characteristic, complemented
14Q8⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1489C211yesmaximal, characteristic, complemented
16C2×#13063372C411yescharacteristic
17#14583382C411yescharacteristic
18#14583379—21no—
19#14583379C411yescharacteristic
20#14583378—21no—
21#14583378—21no—
22#14583378C411yescharacteristic
23#14583378C411yescharacteristic
24#14583376—21no—
25#14583376C411yescharacteristic
26#14583375C411yescharacteristic
27#14583375C411yescharacteristic
28C4×#10621898—21no—
29C4×#10621898C2211yescharacteristic
30C4×#10621900—21no—
31C4×#10621900—21no—
32C4×#10621900C2211yescharacteristic
33C4×#10621900C2211yescharacteristic
34C2×C4×Dic86—21no—
35C2×C4×Dic86C2211yescharacteristic
36C4×Q8×D43C2211yescharacteristic
37C4×Q8×D43C2211yescharacteristic
38#14583028—21no—
39#14583027—21no—
40#14582975—21no—
41#14582975—21no—
42#14582972—21no—
43#14582969—21no—
44#14582968—21no—
45#14582968—21no—
46#14582956C2211yescharacteristic
47#14582955C2211yescharacteristic
48#14582952C2211yescharacteristic
49#14582951C2211yescharacteristic
50#14582950C2211yescharacteristic
51#14582950C2211yescharacteristic
52#14582921C2211yescharacteristic
53C4⋊C8×D43C2211yescharacteristic
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60Q8⋊(C43⋊C8)C2211yescharacteristic
61Q8⋊(C43⋊C8)C2211yescharacteristic
62#14582629C2211yescharacteristic
63#14582629C2211yescharacteristic
64#14582629C2211yescharacteristic
65#14582629C2211yescharacteristic
66D4⋊(C43⋊C8)C2211yescharacteristic
67D4⋊(C43⋊C8)C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C43×#423C2211yescharacteristic
70C4×M16×C43C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75#13063372—24no—
76#13063372—24no—
77C2×#10621898—21no—
78C2×#10621898C2×C411yescharacteristic
79C2×#10621900—21no—
80C2×#10621900—21no—
81C2×#10621900C2×C411yescharacteristic
82C2×#10621900C2×C411yescharacteristic
83C22×Dic86—21no—
84C22×Dic86C2×C411yescharacteristic
85C2×Q8×D43C2×C411yescharacteristic
86C2×Q8×D43C2×C411yescharacteristic
87C2×#10621872—21no—
88C2×#10621872—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91Q8×Dic43C2×C411yescharacteristic
92Q8×Dic43C2×C411yescharacteristic
93C4×Dic86—21no—
94C4×Dic86—21no—
95C4×Dic86—21no—
96C4×Dic86—21no—
97C4×Dic86—21no—
98C4×Dic86—21no—
99C4×Dic86—21no—
100C4×Dic86—21no—
101C4×Dic86—21no—
102C4×Dic86C2×C411yescharacteristic
103C4×Dic86C2×C411yescharacteristic
104C4×Dic86D411yescharacteristic
105C4×Dic86D411yescharacteristic
106C4×Dic86C2311yescharacteristic
107C4×Dic86C2311yescharacteristic
108#13063290—21no—
109#13063290—21no—
110#13063290—21no—
111#13063290—21no—
112#13063290C2×C411yescharacteristic
113#13063290C2×C411yescharacteristic
114#13063290C2×C411yescharacteristic
115#13063290C2×C411yescharacteristic
116C4×D172—21no—
117C4×D172D411yescharacteristic
118C4×D172D411yescharacteristic
119D4×Dic43—21no—
120D4×Dic43—21no—
121D4×Dic43C2×C411yescharacteristic
122D4×Dic43C2×C411yescharacteristic
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43D411yescharacteristic
128C4×C22⋊D43D411yescharacteristic
129C4×C22⋊D43D411yescharacteristic
130C4×C22⋊D43D411yescharacteristic
131(C22⋊D43)⋊C4—21no—
132(C22⋊D43)⋊C4—21no—
133(C22⋊D43)⋊C4—21no—
134(C22⋊D43)⋊C4—21no—
135(C22⋊D43)⋊C4—21no—
136(C22⋊D43)⋊C4—21no—
137#13063284—21no—
138#13063284C2×C411yescharacteristic
139#13063283—21no—
140#13063283—21no—
141#13063283C2×C411yescharacteristic
142#13063283C2×C411yescharacteristic
143#13063282—21no—
144#13063282—21no—
145#13063282C2×C411yescharacteristic
146#13063282C2×C411yescharacteristic
147#13063281—21no—
148#13063281—21no—
149#13063281—21no—
150#13063281—21no—
151#13063281—21no—
152#13063281—21no—
153C2×C4⋊Dic43—21no—
154C2×C4⋊Dic43C2×C411yescharacteristic
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43C2×C411yescharacteristic
161C4⋊C4×D43C2×C411yescharacteristic
162C2×C4×Dic43—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165C42×D43—21no—
166C42×D43—21no—
167C42×D43C2311yescharacteristic
168C42×D43C2311yescharacteristic
169C4⋊(C43⋊C8)—21no—
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063236—21no—
183#13063235—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C8×Dic43—21no—
189C2×#41×C43C2×C411yescharacteristic
190C2×M16×C43—21no—
191C2×M16×C43—21no—
192C4×Q8×C43C2×C411yescharacteristic
193C4×Q8×C43C2311yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43—21no—
196C4×D4×C43C2×C411yescharacteristic
197C4×D4×C43C2311yescharacteristic
198#117×C43—21no—
199#117×C43C2×C411yescharacteristic
200C2×C42×C43—21no—
201C2×C42×C43C2311yescharacteristic
202C4⋊C8×C43—21no—
203C4⋊C8×C43C2311yescharacteristic
204C4⋊C8×C43C2311yescharacteristic
205#97×C43—21no—
206C4×C8×C43C2311yescharacteristic
207C4×C8×C43C2311yescharacteristic
208#41×C43—22no—
209#41×C43—22no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43C22×C411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43C22⋊C411yescharacteristic
222C2×C22⋊D43C22⋊C411yescharacteristic
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229Q8×D43—22no—
230Q8×D43—22no—
231Q8×D43—22no—
232Q8×D43M1614yescomplemented
233#10621900—28no—
234#10621900—28no—
235#10621900—22no—
236#10621900—22no—
237#10621900—22no—
238#10621900M1614yescomplemented
239#10621898—28no—
240#10621898—22no—
241#10621898—22no—
242C2×D172C22⋊C411yescharacteristic
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43C22×C411yescharacteristic
248C2×C4×D43C22×C411yescharacteristic
249C2×C4×D43C2×D411yescharacteristic
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×C4×D43C2×D411yescharacteristic
253C2×Dic86—28no—
254C2×Dic86—21no—
255C2×Dic86—21no—
256C2×Dic86—21no—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86C22⋊C411yescharacteristic
260C2×Dic86C22×C411yescharacteristic
261C2×Dic86C22×C411yescharacteristic
262M16×C43—42no—
263M16×C43—81no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C22×C411yescharacteristic
271C4⋊C4×C43C22×C411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×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⋊Dic43—21no—
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4C22⋊C411yescharacteristic
289(C2×D43)⋊C4C22⋊C411yescharacteristic
290(C2×D43)⋊C4C22⋊C411yescharacteristic
291(C2×D43)⋊C4C22⋊C411yescharacteristic
292C4⋊Dic43—21no—
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43C22⋊C411yescharacteristic
296C4⋊Dic43C22⋊C411yescharacteristic
297C4⋊Dic43C22×C411yescharacteristic
298C4⋊Dic43C22×C411yescharacteristic
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
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×Dic43—21no—
325C4×Dic43C22×C411yescharacteristic
326C4×Dic43C22×C411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329C4×Dic43C2×D411yescharacteristic
330C4×Dic43C2×D411yescharacteristic
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×C43—21no—
340C23×C43C2×C22⋊C411yescharacteristic
341C22×D43C2×C22⋊C411yescharacteristic
342C22×D43C2×C22⋊C411yescharacteristic
343Q8×C43—21no—
344Q8×C43C2×M1612yes—
345D4×C43—24no—
346D4×C43—21no—
347D4×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—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—81no—
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C2×C22⋊C411yescharacteristic
362C2×C4×C43C2×C22⋊C411yescharacteristic
363C2×C4×C43C23×C411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C22⋊D43—24no—
367C22⋊D43—22no—
368C22⋊D43—24no—
369C22⋊D43—22no—
370C2×Dic43—24no—
371C2×Dic43—24no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—24no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—81no—
378C2×Dic43—81no—
379C2×Dic43—81no—
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C2×Dic43C2×C22⋊C411yescharacteristic
383C2×Dic43C2×C22⋊C411yescharacteristic
384C2×Dic43C2×C22⋊C411yescharacteristic
385C2×Dic43C2×C22⋊C411yescharacteristic
386D172—22no—
387C4×D43—24no—
388C4×D43—24no—
389C4×D43—21no—
390C4×D43—21no—
391C4×D43—21no—
392C4×D43—21no—
393C4×D43—21no—
394C4×D43—21no—
395C4×D43—41no—
396C4×D43—41no—
397C4×D43—81no—
398C4×D43—81no—
399C4×D43C2×M1612yes—
400C4×D43C2×M1612yes—
401Dic86—24no—
402Dic86—24no—
403Dic86—21no—
404Dic86—21no—
405Dic86—22no—
406Dic86—24no—
407Dic86C2×M1612yes—
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—22no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43C22×C22⋊C411yescharacteristic
425C2×D43—21no—
426C2×D43—21no—
427C2×D43—21no—
428C2×D43—21no—
429C2×D43—21no—
430C2×D43#40712yes—
431C4×C43—21no—
432C4×C43—22no—
433C4×C43—21no—
434C4×C43—21no—
435C4×C43—21no—
436C4×C43—41no—
437C4×C43—41no—
438C4×C43C22×M1611yescharacteristic
439C4×C43C22×M1611yescharacteristic
440C4×C43#57711yescharacteristic
441C4×C43#57811yescharacteristic
442Dic43—21no—
443Dic43—22no—
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#1491—431no—
457#1489—431no—
458#1489D4311yescharacteristic, complemented
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×C43—42no—
469C2×C43C2×#40711yescharacteristic
470C2×C43#289811yescharacteristic
471C2×C43#290111yescharacteristic
472D43—22no—
473D43—41no—
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—861no—
490C4×#41—861no—
491C4×#41—861no—
492C4×#41C2×D4311yescharacteristic
493C2×C4×Q8—431no—
494C2×C4×Q8—431no—
495C2×C4×Q8—431no—
496C2×C4×Q8—861no—
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#432—431no—
507#431—431no—
508#431—431no—
509#431—431no—
510#431—431no—
511#423—431no—
512#423C2×D4311yescharacteristic
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⋊C8—431no—
526Q8⋊C8—431no—
527Q8⋊C8C2×D4311yescharacteristic
528Q8⋊C8C2×D4311yescharacteristic
529D4⋊C8—431no—
530D4⋊C8—431no—
531D4⋊C8C2×D4311yescharacteristic
532D4⋊C8C2×D4311yescharacteristic
533C43#1745411yescharacteristic, complemented, Sylow
5342−1+4—864no—
5352−1+4—864no—
536C2×#41—431no—
537C2×#41—431no—
538C2×#41—431no—
539C2×#41—861no—
540C2×#41—861no—
541C2×#41—861no—
542C2×#41C4×D4311yescharacteristic
543C22×Q8—431no—
544C22×Q8—431no—
545C22×Q8—431no—
546C22×Q8—861no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—861no—
550C2×M16—861no—
551C22×C8—861no—
552C22×C8—861no—
553C4×Q8—431no—
554C4×Q8—431no—
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×Q8—861no—
577C4×Q8—861no—
578C4×Q8C4×D4311yescharacteristic
579C4×Q8C22×D4311yescharacteristic
580C4×D4—21no—
581C4×D4—21no—
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×D4C4×D4311yescharacteristic
604C4×D4C22×D4311yescharacteristic
605#117—21no—
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#117C4×D4311yescharacteristic
623C2×C4⋊C4—431no—
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⋊C4—861no—
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—21no—
642C4⋊C8—431no—
643C4⋊C8—431no—
644C4⋊C8—861no—
645C4⋊C8—861no—
646C4⋊C8—861no—
647C4⋊C8—861no—
648C4⋊C8—861no—
649C4⋊C8C22×D4311yescharacteristic
650C4⋊C8C22×D4311yescharacteristic
651C22⋊C8—861no—
652C22⋊C8—861no—
653C22⋊C8—861no—
654C22⋊C8—861no—
655C22⋊C8—861no—
656C22⋊C8—861no—
657#97—21no—
658#97—861no—
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—22no—
668#41—22no—
669#41—434no—
670#41—862no—
671#41—862no—
672#41—868no—
673#41—862no—
674#41—862no—
675#41—868no—
676#41—868no—
677#41—862no—
678C2×Q8—431no—
679C2×Q8—434no—
680C2×Q8—431no—
681C2×Q8—431no—
682C2×Q8—861no—
683C2×Q8—861no—
684C2×Q8—862no—
685C2×Q8—862no—
686C2×Q8—868no—
687C2×Q8—862no—
688C2×Q8—862no—
689C2×Q8—862no—
690C2×Q8—861no—
691C2×Q8C2×C4×D4311yescharacteristic
692C2×D4—21no—
693C2×D4—431no—
694C2×D4—431no—
695C2×D4—431no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4C2×C4×D4311yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—431no—
703C22×C4—431no—
704C22×C4—431no—
705C22×C4—431no—
706C22×C4—431no—
707C22×C4—431no—
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—81no—
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—431no—
738C4⋊C4—431no—
739C4⋊C4—431no—
740C4⋊C4—431no—
741C4⋊C4—431no—
742C4⋊C4—431no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—861no—
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—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—431no—
764C22⋊C4—431no—
765C22⋊C4—431no—
766C22⋊C4—431no—
767C22⋊C4—431no—
768C22⋊C4—431no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—431no—
777C42—431no—
778C42—431no—
779C42—431no—
780C42—431no—
781C42—431no—
782C42—861no—
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—21no—
799C23—431no—
800C23—431no—
801C23C22⋊C4×D4311yescharacteristic
802Q8—21no—
803Q8—432no—
804Q8—432no—
805Q8—862no—
806Q8—864no—
807Q8—864no—
808Q8—864no—
809Q8—861no—
810Q8—861no—
811Q8M16×D4312yes—
812D4—24no—
813D4—21no—
814D4—862no—
815D4—862no—
816D4—862no—
817D4—864no—
818D4—864no—
819D4M16×D4312yes—
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—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—81no—
832C2×C4—431no—
833C2×C4—432no—
834C2×C4—432no—
835C2×C4—431no—
836C2×C4—431no—
837C2×C4—431no—
838C2×C4—431no—
839C2×C4—431no—
840C2×C4—864no—
841C2×C4—864no—
842C2×C4—864no—
843C2×C4—864no—
844C2×C4—864no—
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—861no—
854C2×C4—861no—
855C2×C4—3441no—
856C2×C4—3441no—
857C2×C4—3441no—
858C2×C4—3441no—
859C2×C4—3441no—
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—22no—
878C22—21no—
879C22—21no—
880C22—41no—
881C22—41no—
882C22—432no—
883C22—861no—
884C22—861no—
885C22—861no—
886C22—861no—
887C22—861no—
888C22C2×C22⋊C4×D4311yescharacteristic
889C4—21no—
890C4—22no—
891C4—21no—
892C4—21no—
893C4—21no—
894C4—41no—
895C4—41no—
896C4—432no—
897C4—861no—
898C4—862no—
899C4—862no—
900C4—861no—
901C4—861no—
902C4—861no—
903C4—861no—
904C4—1721no—
905C4—1721no—
906C4C2×M16×D4311yescharacteristic
907C4C2×M16×D4311yescharacteristic
908C4#1458370911yescharacteristic
909C4#1458371511yescharacteristic
910C2—41no—
911C2—42no—
912C2—862no—
913C2—1721no—
914C2#407×D4311yescharacteristic
915C2#1914312611yescharacteristic
916C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1489C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063372C4
cosocleC42×C43C24
hypercenter#1489D43
hypocenterC43#17454
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #19143709C2semidirect
3. #19143557C2semidirect
4. #19133043C2semidirect
5. #19133040C2semidirect
6. #19133031C2semidirect
7. #19133029C2semidirect
8. #19133026C2semidirect
9. #19133023C2semidirect
10. #19133022C2semidirect
11. #19132988C2semidirect
12. #19132979C2semidirect
13. #19132974C2semidirect
14. Q8⋊C8×D43C2semidirect
15. C43×#1489C2semidirect
232. Q8×D43M16semidirect
238. #10621900M16semidirect
458. #1489D43semidirect
533. C43#17454semidirect

Maximal subgroups

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

subgroupindex
C4×#130633722
#191437092
#191435572
#191330432
#191330402
#191330312
#191330292
#191330262
#191330232
#191330222
#191329882
#191329792
#191329742
Q8⋊C8×D432
C43×#14892
#1745443